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## Material Information- Title:
- Human capital, convergence, and income inequality a latent variable approach
- Creator:
- Deepak, Sri Devi
- Publication Date:
- 1995
- Language:
- English
- Physical Description:
- xiii, 133 leaves : ill. ; 29 cm.
## Subjects- Subjects / Keywords:
- Capital investments ( jstor )
Countries ( jstor ) Financial investments ( jstor ) Government expenditures ( jstor ) Human capital ( jstor ) Income estimates ( jstor ) Income inequality ( jstor ) Investment income ( jstor ) Mathematical variables ( jstor ) Public investments ( jstor ) Dissertations, Academic -- Food and Resource Economics -- UF Food and Resource Economics thesis, Ph. D City of Gainesville ( local ) - Genre:
- bibliography ( marcgt )
non-fiction ( marcgt )
## Notes- Thesis:
- Thesis (Ph. D.)--University of Florida, 1995.
- Bibliography:
- Includes bibliographical references (leaves 126-132).
- General Note:
- Typescript.
- General Note:
- Vita.
- Statement of Responsibility:
- by Sri Devi Deepak.
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HUMAN CAPITAL, CONVERGENCE, AND INCOME INEQUALITY: A LATENT VARIABLE APPROACH By SRI DEVI DEEPAK A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1995 I dedicate this dissertation to my parents, Mahalakshmi and Krishna Murthy Duvvuri. Without their encouragement, blessings, and high expectations I could not have attained this level of education. ACKNOWLEDGMENTS I would like to thank my supervisory committee for their tremendous help and guidance. I also thank Dr. Henri Theil for providing me with the opportunity to assist him in his research which culminated in this dissertation. In particular, I would like to thank Dr. James L. Seale, Jr., and Dr. Charles B. Moss for their individual attention, time, and patience which helped me a great deal in completing this dissertation. I thank Dr. Max R. Langham, Dr. Gary F. Fairchild, and Dr. Douglas G. Waldo for their insightful suggestions in writing this dissertation. I especially thank my husband, Dr. M. S. Deepak, for his support and encouragement during the course of my research. I appreciate the wonderful support from the staff of the FRE Systems Support Center for their indispensable, patient, and highly efficient assistance during the arduous months of writing this dissertation. I thank Dr. John R. Gordon for all his support during the course of my program. I thank Ms. Rosemarie T. Wolfendale, Ms. Shirley A. Johnson, and Ms. Shirley T. Harris for their help and kindness throughout my program. I also thank the staff of the Documentation Division and Reference Section of the University of Florida Library (West) for their expert guidance and support for the collection of some parts of the data for my dissertation. iio1 The financial support from the Food and Resource Economics Department and Dr. James L. Seale, Jr., is greatly appreciated. iv TABLE OF CONTENTS DEDICATION ............................................... ii ACKNOWLEDGMENTS ....................................iii LIST OF TABLES ...................................... viii LIST OF FIGURES ....................................... x ABSTRACT ...........................................xii CHAPTERS 1. INTRODUCTION ............................... 1 2. EVIDENCE OF CONVERGENCE .................... 6 2.1 Studies Using Inequality Measures ................ 7 2.2 Studies Using Regression Analysis ................ 12 2.3 Studies Using Models of Economic Growth ..........................16 2.4 Studies Using Time-Series Analysis ................ 20 3. DATA ...................................... 24 3.1 Penn World Tables ..........................25 3.1.1 International Comparison Project ..............................26 3.1.2 Purchasing Power Parities ................. 28 3.1.3 Country-Product-Dummy Method ............................29 3.1.4 Elteto-Koves-Szulec Method ................. 29 3.1.5 The Geary-Khamis Method ................. 31 v 3.2 Extrapolations with ICP Data .................... 33 3.3 Mark 5 Data Set .......................... 35 3.4 Data for Estimation .......................... 38 4. INCOME AND HUMAN CAPITAL IN THE OECD COUNTRIES ....................... 42 4.1 General Latent Variable Model .................. 44 4.1.1 Structural Equations of the M odel ........................... 44 4.1.2 Implied Covariance Matrix ................. 46 4.1.3 Identification ......................... 48 4.2 Estimation ................................ 51 4.3 Empirical Model ...........................52 4.4 Parameter Estimates of the Latent Variable Model ........................56 4.5 Income and Human Capital in OECD Countries ............................ 59 4.6 Summary ............................... 103 5. INEQUALITY IN THE OECD COUNTRIES ............. 105 5.1 Graphical Inequality ........................105 5.2 Inequality via Measures of Dispersion ............. 106 5.3 Inequality Indices ..........................106 5.4 Properties of Inequality Index .................. 107 5.5 Theil's Inequality Index ...................... 108 5.6 Inequality in OECD Countries .................. 109 5.7 Summary ................................114 6. SUMMARY AND CONCLUSIONS .................. 115 APPENDICES A SEVEN REGIONS OF THE WORLD ................. 119 B EUROPE, AFRICA, AND SOUTHERN CONE .......... 120 vi C WESTERN EUROPE ............................ 121 D WESTERN PACIFIC REGION ..................... 122 E FOUR REGIONS REVISITED ...................... 123 F CHANGE IN INEQUALITY ........................ 124 REFERENCES .................................................. 126 BIOGRAPHICAL SKETCH ................................. 133 vii LIST OF TABLES Table page 3.1 Countries Represented in the International Comparison Project ...................................27 3.2 Description of Variables in PWT 5.5 File ..................... 39 4.1 Parameter Estimates of the Latent Variable Model for 22 OECD Countries, 1955-1990. ................... 58 4.2 Parameter Estimates of the Measurement Model for 22 OECD Countries, 1955-1990. .........................59 4.3 Estimated Levels of Human Capital (Hi, i= 1 to 22) in the 22 OECD Countries, 1955-1990 ..................... 61-62 4.4 Average Per Capita Levels of Human Capital (HIo, ), International Openness (OE), Investment Expenditure (IOD), and Government Expenditure (GoEcD) in the 22 OECD Countries, 1955-1990. ...........................63 4.5 Levels of Observed Income (Yi, i= 1 to 22) in the 22 OECD Countries, 1955-1990 ...................... 74-75 4.6 Levels of Estimated Income i(i, i= 1 to 22) in the 22 OECD Countries, 1955-1990 ......................76-77 4.7 Average Levels of Observed and Estimated Income Per Capita (YoED, YoBD) in the 22 OECD Countries, 1955-1990..............................................78 4.8 Summary of Cross-Country Analyses for the 22 OECD Countries, 1955-1990 ............................. 104 viii 5.1 Average Inequality in Observed Income (Jr), Estimated Income (J), Human Capital (Ja), International Openness (Jo), Investment Expenditure (J1), and Government Expenditure (J) in the 22 OECD Countries, 1955-1990. .................. 110 ix LIST OF FIGURES Hjant page 4.1 Average Level of Human Capital (HI n) in the 22 OECD Countries, 1955-1990 ...........................65 4.2 Average Level of Human Capital (fioEC), International Openness (OoED), Investment (IoaC) and Government (GoeD) Expenditures in the 22 OECD Countries, 1955-1990. ...................... 66 4.3 Comparing Countrywise Levels of Human Capital (Hi, i = 1 to 22) and Average Level of Human Capital (Ioe) in the 22 OECD Countries, 1955-1990 ............... 68-73 4.4 Average Levels of Observed and Estimated Income, Y0oE and YoE, in the 22 OECD Countries, 1955-1990. ..................................79 4.5 Comparing Countrywise Levels of Observed Income (Yi, i= 1 to 22) and Estimated Income (Yi, i= 1 to 22) in the 22 OECD Countries, 1955-1990 ...................................... 82-87 4.6 Comparing Countrywise Levels of Estimated Income (Y, i= 1 to 22) and Average Level of Estimated Income (Yo--E) in the 22 OECD Countries, 1955-1990 ...............................89-94 4.7 Relationship Between Average Levels of Observed Income (YoEC) and Human Capital (iHom) in the 22 OECD Countries, 1955-1990 .............................95 x 4.8 Countrywise Relationship Between Levels of Observed Income (Y, i= 1 to 22) and Human Capital (II, i= 1 to 22) in the 22 OECD Countries, 1955-1990 .......................................... 97-102 5.1 Observed and Estimated Income Inequality (Jy, Jr) in the 22 OECD Countries, 1955-1990. ................... .. 111 5.2 Inequality in Estimated Income (J,), Human Capital (J ), International Openness (Jo),Investment (J) and Government (Jo) Expenditures in the 22 OECD Countries, 1955-1990. ............................ 113 xi Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy HUMAN CAPITAL, CONVERGENCE, AND INCOME INEQUALITY: A LATENT VARIABLE APPROACH By Sri Devi Deepak August 1995 Chairman: James L. Seale, Jr., Major Department: Food and Resource Economics Convergence in income and its determinants, for 22 OECD countries during 19551990, was analyzed using a latent variable approach and via Theil's inequality index. Income was specified as a function of human capital, international openness, government expenditure, and investment expenditure drawing on the theoretical underpinnings from standard macroeconomic theory and from recent developments in economic growth theory. Human capital, which cannot be observed directly, was treated as a latent variable. Theil's inequality index was computed for income and its determinants. The latent variable model was estimated using maximum likelihood. The results of this estimation showed that the effects on income levels, of human capital, international openness, investment expenditure, and government expenditure were statistically significant and positive. Human capital had the greatest positive effect xii indicating that it was a key determinant of income levels for the OECD countries. Further, all the determinants were increasing over time at an average per capita level. Estimated income per capita and Theil's income inequality index were computed using the estimated human capital, the other three determinants and the parameters of estimation. The results of these computations indicated that the estimated income fitted the observed income closely and that both the observed and estimated incomes were increasing during 1955-1990. Theil's inequality index was then used to measure observed and estimated inequalities in income, human capital, international openness, investment expenditure, and government expenditure. The evidence from the income inequality analysis is in favor of the convergence component of Kuznets' hypothesis. Further, the analyses of the inequalities in income, human capital, openness, investment and government expenditures revealed that the OECD countries, as a group, were moving closer in terms of income, openness and government expenditure. However, these countries are diverging in terms of human capital and investment expenditure. xiii CHAPTER 1 INTRODUCTION Since the time of Adam Smith (1937) varying rates of economic growth have puzzled economists; thus, for the past several decades this issue has been the focus of research for economists. Three salient and apparent features of studies on economic growth are (a) long-run growth of per capita income has been sustained at a positive rate for many countries; (b) rates of growth vary across countries; and (c) methodologies vary for measuring and explaining economic growth and disparity. The principal question asked was whether countries varied greatly in their growth rates and whether these differences were the outcome of random processes. Further, the phenomenon of accelerated growth of poorer economies causing them to "converge" in per capita income level with that of the richer economies and the factors affecting this growth have become the focus of developmental and international economists. By convergence we refer to the process of the faster growth of relatively poor countries to enable them to "converge" with the growth of relatively rich countries. The divergence-convergence hypothesis originated in neoclassical economics with Kuznets' inverted-U theory (1955) which states that, in the process of economic development, inequality within a country initially increases in the early stages, stabilizes at some peak level, then declines as the latter stages of development occur (divergence followed by 1 2 convergence). Though Kuznets studies income inequality within an economy, the implications of his theory have led to many studies testing Kuznets' hypothesis across countries. From the survey of recent literature on convergence and income inequality, four types of studies have emerged: those that measure income inequality directly (Wright, 1978; Bornschier, 1983; Branco and Williamson, 1988; Theil, 1989; Berry et al., 1991; Oshima,1992; Ram, 1992; Theil and Deepak, 1993a, 1993b, 1993c, 1994; Moss et al., 1993; Seale et al., 1994; Theil and Seale, 1994), those employing regression analysis (Ram, 1988, 1989a, 1989b; Barro, 1991; Barro and Sala-i-Martin, 1992; Mankiw et al., 1992), those based on growth models (Lucas, 1988, 1993; Rebelo, 1990; Tamura, 1991; Glomm and Ravikumar, 1992; Romer, 1994), and those using time-series techniques (Weatherspoon, 1993; Weatherspoon et al., 1994). This survey shows that there is evidence that, in terms of income inequality, rich countries are converging, poor countries are diverging, and the level of affluence increases with increasing distance from the equator (Theil, 1989; Seale et al., 1994; Theil and Deepak, 1994; Theil and Seale, 1994; Moss et al., 1993). However, till recently, though researchers have failed to reject the Kuznets' hypothesis to a large extent, they failed to define, with any certainty, the determinants of convergence (or divergence). Of those that have analyzed or explored the determinants of convergence, Barro (1991), Barro and Sala-i-Martin (1992), and Mankiw et al. (1992) found, empirically, that human capital tended to be an important factor in determining convergence. Lucas 3 (1988, 1993) also concluded that, with the inclusion of human capital in the production function, an economy with a human capital stock lower than the world average would grow faster than an above average economy. Tallman and Wang (1992), reviewing studies using theories of neoclassical and endogenous growth, concluded that accumulation of human capital yielded positive dividends in terms of income and thus standards of living. This study expands on the above mentioned research and attempts to explain the process of convergence (or divergence) via factors that influence economic growth. While Weatherspoon (1993) used cointegration analysis to test for a long-term relationship in inequality among income, investment and government expenditures, and industrial employment, this study uses the latent variable model approach to analyze convergence in income levels and via directly measuring income inequality using Theil's (1989) inequality index. Specifically, per capita incomes (determined by per capita levels of human capital, international openness, investment and government expenditures) for 22 member countries of the Organization of Economic Cooperation and Development (OECD) ( USA, Canada, Japan, Austria, Belgium, Denmark, Finland, France, West Germany, Greece, Ireland, Italy, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, Turkey, UK, Australia, New Zealand) were estimated via a latent variable model (Bollen, 1989) with human capital as the latent variable. An inequality index as derived by Theil (1989) was then used to measure the inequality in per capita income and its 4 determinants. The results from the above computations were used to analyze the effect(s) of determinants of growth on patterns, if any, of convergence (or divergence). The next chapter gives a brief overview of existing evidence on convergence (or divergence). The literature is divided into four groups: studies using inequality measures, studies using regression analysis, studies using models of economic growth, and studies using time-series analysis. By and large, the studies using inequality measures and time-series analysis failed to reject Kuznets' hypothesis, while the studies using growth theories either rejected or were inconclusive in testing the inverted-U hypothesis. The regression studies show some evidence in support of convergencedivergence hypothesis. Chapter 3 deals with the data used for the analysis of this study and includes a description of the compilation of purchasing power parity data by Summers and Heston (1993) in forming the Penn World Table (Mark 5). This chapter also details the other two sources of data: Statistical Yearbook, UNESCO (1963-1993), and Basic Facts and Figures, UNESCO (1951-1962) for compiling information for the indicators of human capital in the 22 OECD countries (two countries from Asia [Japan and Turkey], two from the Western Pacific Rim [Australia, New Zealand], 16 from Europe [Austria, Belgium, Denmark, Finland, France, Greece, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, and UK], and two countries from North America [USA and Canada]). Chapter 4 presents the generalized latent variable model (Bollen, 1989), and tabulates the results of estimation of per capita income. The chapter concludes with a brief study of the patterns in observed and estimated per capita incomes and the 5 explanatory variables for the 22 OECD countries. These trends are then compared and contrasted with evidence from literature. Chapter 5 describes Theil's inequality index and presents the computations of inequalities using income, human capital, international openness, investment and government expenditures. The patterns of convergence (if any) are studied and analyzed. These results are also compared and contrasted with evidence from past studies. Chapter 6 summarizes and concludes the study. CHAPTER 2 EVIDENCE OF CONVERGENCE The interest in studying convergence has been derived from the basic relationship between development and income distribution. To achieve convergence the poorer countries need to increase their productivity at a rate greater than that in richer countries (Barro and Sala-i-Martin, 1992). The importance of the pattern of income distribution during various stages of development and the lack of adequate time-series data for most developing countries culminated in many studies which attempt to test Kuznets' hypothesis with varying methodologies. The predominant methodologies used include inequality measures (Theil, 1989; Berry et al., 1991; Oshima, 1992; Ram, 1992; Moss et al., 1993; Theil and Deepak, 1993a, 1993b, 1993c, 1994; Theil and Seale, 1994; and Seale et al., 1994), regression analysis (Wright, 1978; Bornschier, 1983; Branco and Williamson, 1988; Ram, 1988, 1989a, 1989b; Barro, 1991; Barro and Sala-i-Martin, 1992; Mankiw et al., 1992), theories of growth (Lucas, 1988, 1993; Rebelo, 1990; Tamura, 1991; Glomm and Ravikumar, 1992; Romer, 1994), and time-series analysis (Weatherspoon, 1993; Weatherspoon et al., 1994). Since the recent developments in endogenous economic growth research (Romer, 1989), growth in income is no longer treated as a random process but as something that is systematically related to other factors in the economy (Grossman and Helpman, 1991). 6 7 Summers and Heston (1988) plot the growth rates of 114 countries between 1960 and 1985 against the level of per capita income in 1960. This plot did not depict any strong correlation between initial levels of income and growth during the period, but revealed the variation in growth rates between countries. In the past, growth patterns in the world could not be studied effectively due to data constraints. But the Penn World Table (PWT) time-series data for various economic indicators compiled by Summers and Heston (1991) have changed the scenario to a large extent. 2.1 Studies Using Inequality Measures The simplest inequality measures are estimates of statistical dispersion like variance, standard deviation, and the coefficient of variation. A commonly used inequality measure is the gini coefficient which is based on the Lorenz curve (Anand and Kanbur, 1993). This statistic measures the ratio of the area between the diagonal and the Lorenz curve to the total area below the diagonal. Another measure is the Theil entropy index (also known as Theil's inequality index) which measures inequality by taking the logarithm of the ratio of the arithmetic mean income to the geometric mean income. The appropriateness of the inequality index to be used depends on the objective of the study as well as the properties of the index (Chapter 5, Section 5.4). For example, Theil (1989) used a decomposable inequality index to better assess its behavior internationally as well as regionally. Theil (1989) used the Summers and Heston (1988) data set spanning 1950-1985 to assess the economic development in five regions of the noncommunist world: the 8 North consisting of 25 countries (U.S. and Canada from the American continent, Japan and Korea on the Western Pacific Rim, and 21 countries in Western and Southern Europe), the South with 9 countries (Argentina, Chile, and Uruguay from the Southern Cone of the American continent, Australia and New Zealand on the Western Pacific Rim, and South Africa, Botswana, Lesotho, and Swaziland from the Southern tip of Africa. He measured income inequality as the natural logarithm of the ratio of arithmetic mean income to geometric mean income which was additively decomposable. He concluded that international inequality increased substantially from 1960 to 1980, and that regional inequality dominated the average within-region inequality. In 1960 the inequality in the North exceeded that in any other region, but Northern inequality declined very rapidly so that it was second lowest in 1985. In contrast to the North, Tropical Africa and Asia showed substantial increases in inequality. Berry et al. (1991) conducted an extensive analysis on world income inequality. They analyzed over 100 countries during 1950-1977. They used data from World Bank Tables (1976, 1980a), World Bank Atlas (1988), World Development Report (1980b, 1987, 1988), and the Summers and Heston (1988) data set. They computed Theil's entropy index, Atkinson's inequality, and the Gini coefficient. The major difference in their study was that they computed inequalities for gross national product (GNP) and consumption measured as a percentage of GNP to study changes in welfare. The underlying logic being that the distribution of consumption was less unequal across countries and the savings rate was below average for the poorer countries. Berry et al. (1991) contended that marginal propensities to consume decrease with decreasing income 9 and, therefore, lower savings rates in poorer countries contributed to greater inequality worldwide. They also conducted similar analyses with and without the nonmarket economies which showed that inequality in the world began increasing in the mid-sixties and continued increasing until 1986. In addition, they divided the world's inequality into deciles and showed that the income shares of the bottom half remained unchanged while the top decile gained at the expense of the sixth, seventh, and eighth deciles. Oshima (1992) tested the Kuznets hypothesis for the Asian countries. He found that though there is an upward and then a downward trend in income inequality in most Asian countries, the peak in the trend appears much earlier in the stage of development in Asia than in the West. In Asia, the peak is reached when the economy is still predominantly agricultural with per capita incomes much lower than in the West where the peak was reached when the economy was predominantly industrial. Hence, the forces and mechanics underlying Asian trends are different from the West, although those underlying Japan's trends are similar to those of the West. He concluded the reason for this difference is that Asia (with the exception of Japan) never went through the first industrial revolution of the 19th century. Ram (1992) used an inequality index, prescribed by Bourguignon (1979), to measure the regional and interstate income inequalities in the United States. The data mainly consisted of the U.S. Bureau of Economic Analysis (1989a, 1989b, 1990) estimates of state personal income per capita and total personal income. The data were available from 1950 through 1989 and covered 50 states (including Alaska and Hawaii and 48 others) and District of Columbia. He found that interstate income inequality, 10 though small in magnitude, traced along with the U-shaped profile propounded by Kuznets. Further, a simple quadratic form in terms of time fitted the data extremely well. Inequality indices for 1977 and 1988 were computed after adjusting for interstate price-level changes. These revealed large reductions in the indices and a virtual disappearance of the increase in inequality after 1978. A decomposition of the index showed that income changes accounted for most of the inequality change in each decade. Lastly, the six most influential states in terms of their impact on interstate inequality were tabulated for 1950, 1959, 1969, 1979, and 1989. Three of these states had below average income and three had above-average income. New York and California from the above-average group and Alabama and Mississippi from the below-average group contributed the largest components to interstate inequality. Moss et al. (1993) used the Summers and Heston (1993) data to analyze income changes in the G-7 countries (USA, Canada, Japan, UK, West Germany, France and Italy), for the period 1950 to 1988, using Theil's measure of income inequality. They found that for the G-7 as a whole, per capita GDP increased almost threefold in that period, while the inequality among the seven countries declined dramatically. They concluded that Japan's increasing affluence toward European levels was the reason for this dramatic decline in inequality. The income inequality among the G-7 countries declined almost uninterruptedly. Since the G-7 can be viewed as affluent, this evidence is in favor of convergence. Theil and Deepak (1993a, 1993b, 1993c, 1994) used Theil's inequality index to measure income inequality across countries and regions during the period 1950-1990. Firstly, they categorized 113 countries into seven regions--North, South, Tropical Africa, Tropical America, South-East Asia, South-Central Asia, South-West Asia (see Appendix A for countries within each region)--for the period 1950-1990. They found that the North was converging, South-East Asia was diverging, South-Central Asia presented no evidence of convergence or divergence, and the inequality values of sub-Saharan Africa tended to increase from the mid-1960s until the late 1970s and to decline thereafter--a pattern in favor of the Kuznets hypothesis. Secondly, they compared the inequality in Western Europe, Mediterranean Europe and Mediterranean Africa; South Africa and its neighbors; USA, Mexico, and Central America; the Southern Cone of South America and its neighbors (Appendix B). The results indicate a strong tendency toward more poverty when moving from temperate zones toward the Equator. Thirdly, they considered three regions in Western Europe consisting of 18 countries--non-EU, EU Center, and EU Periphery (see Appendix C for countries within each region)--and found that the income inequalities in the regions of EU and EU Center declined by more than 90%. This result was also in favor of convergence. In the case of the EU Periphery, the first 20 years provide evidence of transition from divergence to convergence. Lastly, they considered 15 noncommunist countries (Appendix D) in the Western Pacific and found that there was a strong tendency to greater poverty in movement toward the Equator from the temperate zones in the North or South. Theil and Seale (1994) used the purchasing power parity (PPP) based data for gross domestic products to assess the affluence of more than 100 non-communist countries in 1950-1990. A seven-region classification, based on the distinction between 12 temperate and tropical zones, is used to summarize the data on individual countries. The seven regions account for nearly 90 percent of the inequality among these countries in each year. Another classification, based on the position of countries with respect to the European Union, is applied to 18 countries in Western Europe. Five journeys around the world were described; the main result was that affluence tended to decline when the traveler moved from temperate zones (in either the Northern or the Southern Hemisphere) toward the Equator. Another topic considered was that of the G-7 countries, the populations of which are all concentrated in the temperate zones of the Northern Hemisphere. Also, attention was paid to Kuznets' hypothesis of divergence-convergence in a cross-country context. Seale et al. (1994) relate regional growth and the inequality across countries for four regions of the noncommunist world: the North, Sub-Saharan Africa, South-Central Asia, and South-East Asia (Appendix E). Their results indicate strong convergence in the North and strong divergence in South-East Asia, whereas the case of South-Central Asia is unclear. In the case of Sub-Saharan Africa, there is growth with divergence, in agreement with Kuznets hypothesis, but thereafter negative growth with convergence, which is a digression from the hypothesis. 2.2 Studies Using Regression Analysis Wright (1978) examined the validity of Kuznets' hypothesis versus the institutionalist hypothesis. The institutionalist hypothesis states that institutional structures and government policies are the chief determinants of income inequality. 13 Wright used a gini coefficient inequality measure to calculate the inequality in GDP per capita among 56 countries. He concluded that the cross-sectional data demonstrated that (1) inequality varies among countries at all levels; (2) variation in and level of inequality are higher among LDCs; and (3) an institutionalist variable in regressions explains far more income variation among countries than income levels. Further, the divergenceconvergence hypothesis lends itself to the conservative argument that redistribution is growth reducing, while growth itself will take a country to the declining side of the "parabola of skewness" more quickly. In the institutionalist view, reduction in inequality depends on modifications in the institutions and policies which generate it. Bornschier (1983) outlined explanations of international differences in personal income distribution that were formulated within the "world economy" and the "level of development" paradigm. He constructed the Gini index of personal income inequality for 72 countries using Ballmer-Cao and Schiedegger (1979) data. He concluded that income inequality does not vary directly with development, but with surplus, power and the structural position within the world economy. Thus less developed countries do not automatically decrease their inequality in the process of development. Ram (1988) studied the validity of Kuznets' hypothesis by extending his study to cover several countries. His hypothesis stated that intercountry inequality across nations would first increase with secular economic growth, then start to decline at some point. His sample consisted of 32 countries (24 less developed countries (LDCs) and 8 developed countries (DCs)) which were market economies from the Summers and Heston (1984) data. Average per capita world GDP was used as a proxy for the level of 14 development and Theil's income inequality measure was used to study income inequality. In addition, Ram used a Kuznets type quadratic regression to determine the relationship between the level of income and development, which represents development and inequality. The equation is J, bo + bY + b2Y + u, where J is the measure of world inequality and Y is the natural logarithm of the average real GDP per capita. The last term is the disturbance term assumed to have the standard properties for best linear unbiased estimates. Ram found that the hypothesis was well supported when both LDCs and DCs were included in the sample and there is very little support when only LDCs were considered. Branco and Williamson (1988) also tested Kuznets' hypothesis by analyzing development and income distribution. This study was unique in that it developed an absolute per capita income measure for the poorest 40% of the population in 68 countries. Their measure was the percent of income of the poorest 40% of a nation's population in 1970 divided by 40% of the 1970 population, then multiplied by the real per capita GDP of that nation in 1970 (Summers and Heston, 1984). Their findings suggested that the poorest 40% of the population lose income both relatively and absolutely in the early stages of economic development; thereafter, there are gains in income although with diminishing marginal returns at the highest levels of development. Ram (1989a) also extended his 1988 study to the world economy inclusive of 115 market economies drawn from the Summers and Heston (1984) data for the years 19601980. Using the same structure of the model as before, found that though world income 15 inequality increased since 1960, there was a noticeable deceleration in the rate of increase of inequality. Ram (1989b) attempted to study the effect of education on income inequality in LDCs. Firstly, upon reviewing the literature in this area he found contradicting evidence of the influence of education on inequality. Chiswick (1971, 1974), Chiswick and Mincer (1972), Chenery and Syrquim (1975), and Ahluwalia (1976) contended that education did influence income inequality, while Fields (1980), Psacharopoulos and Woodhall (1985), and Morrisson (1987) concluded that there was no clear evidence that education had an effect on income inequality. These contradictory results prompted Ram to conduct his study using two sets of data that yielded contradictory results. His study concluded that the effect of education on income inequality was ambiguous. He concluded that the nature of the data could be a major factor for the contradictory and inconclusive nature of the results. Barro (1991) used the neoclassical growth models developed by Solow (1956), Cass (1965), and Koopmans (1965), and the recent theories of economic growth as proposed by Lucas (1988), Rebelo (1990), Romer (1989), and Becker, Murphy, and Tamura (1990) as a guide to test convergence in real per capita GDP for 98 countries during the period 1960 to 1985. His results suggested that poor countries tend to catch up with rich countries if the poor countries have high per capita human capital in relation to their level of per capita GDP, but not otherwise. He observed that countries with high human capital have low fertility rates and high ratios of physical investment to GDP. 16 Barro and Sala-i-Martin (1992) used the neoclassical growth models developed by Ramsey (1928), Solow (1956), Cass (1965), and Koopmans (1965) to test for convergence across the 48 contiguous U.S. states using personal income since 1840 and gross state product since 1963. Their results indicated that the 48 states provided clear evidence of convergence, but the results could be reconciled quantitatively with the neoclassical model only if diminishing returns to capital set in slowly. The results for per capita GDP from a broad sample of countries were similar if a set of variables that proxy for differences in steady-state characteristics were held constant. Mankiw et al. (1992) examined whether the Solow growth model was consistent with the international variation in the standard of living. They showed that an augmented Solow model that included accumulation of human capital provided an excellent description of the cross-country data. While testing the convergence-divergence hypothesis, they concluded that holding population growth and capital accumulation constant, countries converge at a rate the augmented Solow model would predict. 2.3 Studies Using Models of Economic Growth The research on economic growth predominantly focuses on long-run economic progress, and the dominant sources are the neoclassical growth models developed by, to name a few, Solow (1956), Swan (1956), Ramsey (1928), Cass (1965), and Koopmans (1965). In general, the unexplained portions of growth were attributed to the area of technical progress which was treated as exogenous by the neoclassicalists. These models assumed that output can be produced using combinations of physical capital and labor in 17 variable proportions, and the production function was subjected to a technological factor. Thus, two exogenous processes, population growth and technological progress, determined the economy's growth rate. In recent times with the development of endogenous growth models, the premises of neoclassical growth theory have come under serious scrutiny, thus creating the need for new techniques of measurement and analysis of the growth process. Endogenous growth models indicate that endogenizing technical progress via human capital accumulation allows an economy to grow endogenously and thus results in better measurement (Lucas 1988, 1993) and understanding of determinants of economic growth and the disparities in growth rates. The neoclassical growth model predicts a zero growth rate of output per unit of input in the long run, since the output growth rate is entirely determined by exogenous factors like the population growth rate and the rate of technical progress. However, in the endogenous growth models, the growth rate of output per capita is a positive constant because human capital accumulation results in endogenous technical progress. The underlying fact is that neoclassical models fix the rate of growth and allow the marginal product of capital to vary, whereas the endogenous models fix the marginal product of capital but allow the rate of economic growth to be endogenous. Lucas (1988) considered the prospects for constructing a neoclassical theory of growth and trade that was consistent with some of the main features of economic development. He studied three models to account for the disparities in growth rates across economies: a model emphasizing physical capital accumulation and technological 18 change, a model emphasizing human capital accumulation through schooling, and a model emphasizing specialized human capital accumulation through learning by doing. He concluded that, with the inclusion of human capital in the production function, economies that are initially poor will remain relatively poor, though their long-run rate of income growth will be as that of initially wealthier economies. If traded goods are included in the model, the long-run relationship between the two kinds of capital implies the same marginal productivity of physical capital, no matter what the level of capital that has been accumulated. If labor is mobile, it will flow in general from poor countries to wealthy ones. Rebelo (1990) described a class of endogenous growth models that have constant returns to scale technologies. He hypothesized that this class of models rationalizes the existence of permanent cross-country differences in growth rates as being, at least partly, a result of differences in government policies. His analysis revealed that small differences in policy regimes could easily mean the difference between growth and stagnation. Tamura (1991) developed an endogenous growth model that produced convergence in per capita income and growth rates of output. His analysis was based on the premises that agents have identical preferences and access to identical technologies of production and investment, but differing levels of human capital. He concluded that a spillover effect of human capital in the investment technology provides below-average human capital agents with a higher rate of return on investment than above-average human capital agents; thus, below-average human capital agents grow faster than above- 19 average human capital agents. Convergence arises because below-average human capital agents gain most from learning. Glomm and Ravikumar (1992) studied the effect of endogenous growth on income inequality by using an overlapping generations model with heterogenous agents in which human capital investment through formal schooling was the engine of growth. They used simple functional forms for preferences (logarithmic), production technologies (linear), learning technology (Cobb-Douglas), and income distribution (lognormal) to highlight the distinction between the economies with public education and those with private education. They found that income inequality (measured by the standard deviation of the lognormally distributed incomes) declined more rapidly under public education. On the other hand, private education yielded greater per capita incomes unless the initial income inequality was sufficiently high. They also concluded that societies would choose public education if a majority of agents have incomes below average. Lucas (1993) made a case study of the economic growth of Philippines and South Korea as a key to emphasize the effect of on-the-job human capital accumulation on growth. With this modification to the neoclassical model, an economy with a human capital stock lower than the world average would grow faster than an above average economy. His theory indicated that, relative to the world's income and human capital, a country's human capital converged to 1 which implied that relative incomes converge to 1 at the same rate. He also observed that convergence is more likely over subsets of countries or regions of countries, where factor and final goods mobility is high. He concluded that the main engine of economic growth was the accumulation of human 20 capital and the main source of differences in living standards among nations was differences in human capital. Romer (1994) studied the origins of endogenous growth models and traced them back to the question of whether per capita income in different countries was converging. He observed that the most important policy questions about growth pertain to institutional arrangements for gaining access to knowledge and the production and use of new knowledge. 2.4 Studies Using Time-Series Analysis Weatherspoon (1993), and Weatherspoon et al. (1994) tested the convergence of the G-7 countries using Theil's inequality (entropy) index on income and three other potential factors of influence on economic growth: government expenditure, investment expenditure, and industrial employment. Pairwise convergence was supported for all four variables for the time period of 1950 to 1988. It was determined that the inequality in all four variables for the G-7 countries has declined from 1950-1988. This suggests that the G-7 countries are becoming more equal in terms of the above-mentioned variables. The inequality-transformed variables were then tested for multiple cointegration using an 1(2) procedure due to Johansen (1992). Multiple cointegration was supported for three out of four relationships suggesting that there exists a long-run equilibrium relationship among the inequalities in income, investment expenditure, and industrial employment. 21 Thus, the evidence from the inequality studies (Theil, 1989; Theil and Deepak, 1993a, 1993b, 1993c, 1994; Theil and Seale, 1994; Seale et al., 1994; Weatherspoon, 1993; Weatherspoon et al., 1994) seems to suggest that poor economies are diverging, rich economies are converging, and there is inconclusive evidence in certain cases. Neoclassical growth models (Barro, 1991; Barro and Sala-i-Martin, 1992; Mankiw et al., 1992) favor convergence and endogenous growth models (Lucas, 1988 & 1993; Romer, 1994; and Tamura, 1991) lean toward ambiguity. The OECD countries were chosen for two main reasons: the evidence from the literature supports convergence (or divergence) for these countries and the availability of reliable data. In summary, the research by Theil and Deepak (1993a, 1993b, 1993c, 1994), Moss et al. (1993), Seale et al. (1994), and Theil and Seale (1994) determined that during the period 1950-1990 the income of the G-7, non-EU, and EU Center countries increased while the inequality declined almost uninterruptedly favoring the convergence component of Kuznets' hypothesis; the income for EU Periphery countries increased but inequality fluctuated during 1950-1970 without a clear trend and then decreased showing evidence of transition from divergence to convergence components of Kuznets' hypothesis; the North, consisting of 22 countries, also showed evidence of convergence and in the case of the countries in South, the results were inconclusive. In the process of analyzing convergence across 98 countries, Barro (1991) concluded that the evidence from 20 OECD countries was stronger because these countries had higher per capita incomes and had similar basic economic and political institutions. Further, Weatherspoon (1993) and Weatherspoon et al. (1994) found that, in the long run, the G-7 22 and 14 OECD countries were becoming more equal in terms of income, investment expenditure, government expenditure, and industrial employment. The survey of the above literature on income convergence suggested that testing for convergence (or divergence) with a combination of the theories on income inequality and economic growth would prove to be an exercise that could expand the horizons of contemporary research on the subject. The evidence also suggests that though researchers have failed to reject the Kuznets' hypothesis to a large extent, they, however, failed to define, with any certainty, the determinants of convergence (or divergence) until recently. This study expanded on the above mentioned studies (Barro, 1991; Mankiw et al., 1992; Weatherspoon, 1993) and incorporated the aspects of the theory of endogenous growth to explain the process of convergence (or divergence). Barro (1991) analyzed convergence in 98 countries during 1960-1985 by studying the relationship between growth rates in per capita income, levels of per capita income, and initial level of human capital (proxied by school enrollment ratios in 1960). He found that, holding levels of human capital constant, the growth rate in per capita income was inversely related to the level of per capita income. Further, holding the initial level od per capita income constant, Barro found that there was a positive relationship between the growth rate of income and level of human capital. Therefore, in his study, convergence was evident only in countries with high levels of initial human capital and per capita income. This study carried Barro's research a step forward by analyzing the effects of levels of human capital, openness, investment and government expenditures on the levels 23 of per capita income. A multiple-variable indicator was used to estimate the level of human capital via a latent variable approach. The per capita income, estimated as a function of human capital (as a latent variable), was then analyzed for convergence with help of Theil's inequality index. This study also analyzed the convergence behavior in the determinants of income. CHAPTER 3 DATA The three sources of data for this dissertation were the Supplement to Mark 5 or the Penn World Tables (PWT 5.5) compiled by Summers and Heston (1993), Basic Facts and Figures compiled by UNESCO (1951-1962), and The Statistical Yearbook compiled by UNSECO (1963-1993). The data on income, population, international openness, government expenditure, and investment expenditure were extracted from the Summers and Heston data. The data on the four indicators for human capital--public expenditure on education as a percentage of income, per capita consumption of newsprint, levels of education at the secondary school and university levels--were compiled from the two UNESCO series. The data span 36 years, 1955 to 1990. Though there are 24 countries in the OECD group, the data for Iceland and Luxembourg were insufficient to include them in this study. Due to the nature and complexity of the PWT data, their compilation procedure is discussed in this chapter. For greater details of construction of these data, please refer to Weatherspoon (1993) who discussed this subject at great length. 24 25 3.1 Penn World Tables The PWT data efforts date back to 1978 with the formation of the International Comparison Project (ICP) (Kravis et al., 1978a). This project attempted to compile Real Gross Domestic Product Per Capita (RGDP) for more than 100 countries where RGDP is the gross domestic product per capita adjusted for differences in the purchasing power of currencies. The objective of the ICP was to approximately fill the gap in the world statistical system arising from the absence of comparative data on "real" GDP per capita. The motivation for this project came from the widely accepted fact that the exchange-rate conversions of the GDPs of different countries to a common currency such as the United States dollar did not yield a reliable basis for international comparisons. The compilations in the ICP were based on the "nominal" values of the gross product obtained from a country's national accounts. Therefore, the comparisons based on nominal values gave systematically incorrect estimates as exchange rates deviated from the conversion factors in systematic ways. The PWT data were constructed from intertemporal and interspatial extrapolations on ICP and non-ICP data and were compiled in a manner consistent with the national income identity. Thus, the nature of compilation of the PWT data makes them very valuable for empirical research. However, to comprehend the nature of the PWT data and appreciate the benefits from using PWT data over the ICP data, one needs to understand the construction and development of the ICP data. Sections 3.1.1 to 3.1.5 discuss the ICP data briefly. 26 3.1.1 International Comparison Proiect Phase I of the international comparison project (ICP) began with a pilot study in 1967, initiated by Kravis et al. (1975), at the University of Pennsylvania, which resulted in data collection for 10 countries for 1970 (Table 3.1). Two successive volumes, Phase II and Phase III, were published in 1978 and 1982. Phase II compiled data for an additional six countries and corrected the data from Phase I. Phase III compiled data, for 1975, for an additional 18 countries taking the count to 34 countries. Phase IV of this project, with 60 countries in 1980, was completed in two stages by the Statistical Office of the United Nations Secretariat (1985 and 1987). However, seven countries from Phase III withdrew from the study during this period. Therefore, there were 10, 16, 34, and 60 countries, in Phases I, II, III, and IV, respectively. In the first stage of the ICP, a classification system for gross domestic product (GDP) was developed which divided each country's GDP into numerous detailed categories. GDP data were then collected for each category. Further, prices and quantities for each item within a category were also gathered. The classification system follows the scheme proposed by the system of national accounts (SNA). This classification system was improved upon to facilitate international comparability of the data (Kravis et al., 1975). In Phases I and II, there were a total of 153 detailed categories: 110 for consumption, 38 for capital formation, and five for government. Phases II and IV have 151 detailed categories: 108 for consumption, 38 for capital formation, and five for government. Table 3.1 Countries Represented in the International Comparison Project 27 Africa America Asia Furone Countries represented in Phase I Kenya Columbia India France United States Japan W. Germany Hungary Italy United Kingdom Countries added in Phase II Iran Belgium S. Korea Netherlands Malaysia Philippines Countries added i Phase III Malawi Brazil Pakistan Austria Zambia Jamaica Sri Lanka Denmark Mexico Syria Ireland Uruguay Thailand Luxembourg Poland Romania Spain Yugoslavia Countries added in Phase IV Botswana Argentina Hong Kong Finland Cameroon Bolivia Indonesia Greece Ethiopia Canada Israel Norway Ivory Cost Chile Portugal Madagascar Costa Rica Mali Dominican Rep. Morocco Ecuador Nigeria El Salvador Senegal Gautsmala Tanzania Honduras Tunisia Panama Zimbabwe Paraguay Peru Venezuela Countries deleted in Phase IV Jamaica Iran Romania Mexico Malaysia Syria Source: Theil et al. 1989, p. 2. 28 The three categories of data used for classification were GDP or expenditure data, price data for each item for which a price could be identified, and quantity data for the items for which prices could not be identified. The expenditure data were obtained from the U. N. national accounts data. Once the base data were collected, there were steps and alternatives to calculating purchasing power parities (PPPs) for each country. 3.1.2 Purchasing Power Parities Purchasing power parity (PPP) is the number of currency units required to buy goods equivalent to what can be bought with a unit of currency of the base country (Kravis et al., 1982). From the several methods that can be used to calculate PPPs, the most frequently used by the ICP were the country-product-dummy (CPD) and EltetoKoves-Szulc (EKS) methods. These two methods are identical if all the prices for every item in each country are available. In that event, the PPPs obtained from both methods are geometric means of all the prices in the detailed category at for country c (Kravis et al., 1975). The geometric mean in country c is obtained as (3.1) GM = (H P 1,...m i(3.1) where P,, is the price of the item i in country c and m is the number of items. 29 3.1.3 Country-Product-Dummy Method The CPD is based on the assumption that the natural logarithm of the price of the item i in country c includes an item effect and a country effect; PPPs are estimated by least squares; and the relationship is stochastic. The CPD equation is 1i/ (In(P,) = A,Be + (3.2) where P,, is the price of the item i in country c, m is the number of items, e,, is normally distributed with mean zero and variance o2, Ai is the item effect on the price i in country c, and B, is the country effect on the price. In most cases this method is normalized with U. S. as the base country. 3.1.4 Elteto-Koves-Szulc Method The EKS method consists of four steps: calculate "Laspeyres" and "Paasche" type price indices; calculate "Fisher" binary price indices; fill in the Fisher matrix if needed; and finally, build an EKS matrix of transitive parities. All calculations in the EKS method are based on the prices of the "characteristic" items. A characteristic item of a country is one that is considered to be purchased frequently within that country. Each country nominates at least one such product within each detailed category. The characteristic item chosen must also be priced in at least one other country. The price indices calculated in the first step of the EKS method are not true Laspeyres and Paasche indices and thus, they are called mini-Laspeyres and mini-Paasche price indices due to their similarity to the Laspeyres and Paasche indices in time-series 30 measurement. The difference is that the ratios in the EKS method are unweighted, unlike in time-series measurement. The general representation of the mini-Laspeyres index is aP (3.3) where c and d are two different countries and m is the number of characteristic items in category a. Similarly, the mini-Paasche index is obtained as SPt (3.4) This method does not pick one base country, and thus, a matrix of mini-Laspeyres indices is created between countries with a diagonal of ones. The same is true for the mini-Paasche indices. Once the mini-Laspeyres and mini-Paasche indices are computed, the mini-Fisher price indices are constructed. The latter indices are the unweighted geometric means of the former two indices PF = (L4 P r(3.5) The matrix of mini-Fisher indices is not transitive, and the EKS method is applied to make them so. The equation for the EKS method is 31 K = wF where e cAd. (3.6) This is the PP for the detailed category a between countries c and d. The last step of the EKS method is to choose one country as a base country so that it can be compared with the CPD results. A base country can be chosen by observing the values in any of the country columns of the EKS matrix. If all the prices of items are available and are characteristic items, then the EKS method is the same as equation (3.1) if P=,, is replaced with a price index. Without the basic prices, the CPD method does not equal a geometric mean and neither does the EKS method. This is due to the fact that the respective price indices in these methods cannot be computed with missing prices. An illustration to demonstrate the computations of PPPs is given in Kravis et al. (1975). 3.1.5 The Geary-Khamis Method After estimating the PPPs, the second stage of the ICP was initiated. The GearyKhamis method provides multilateral base-invariant price and volume comparisons at the various levels of aggregation for all countries, where the volumes are expressed in "international dollars". These volumes are additive across expenditure categories, while prices are obtained by dividing expenditures in national currency by those in international dollars. Geary suggested a system of homogeneous linear equations to calculate the international prices and PPPs simultaneously. Khamis proved that this system yielded 32 non-negative international prices and PPPs. The CPD or EKS method can be used to produce the detailed category PPPs for the Geary-Khamis method. These PPPs are transitive and are relative to the U.S. dollar. Detailed categories are indicated by the subscript a = 1,..., A. The volume of detailed category a in country c is V =- EaJPPP (3.7) where E8., is the per capita expenditure (in national currency) on detailed category a in country c. This volume is expressed in U.S. dollars. However, these volumes are not additive over the detailed categories. This method introduces the international price P. of each detailed category and the overall purchasing power parity of each country c. P. is written as N P, v., e*1 which is equivalently written as N N P.v, = (E., j) where V. = V, (3.8) while T, is defined as A C A 1hich is also which is also 33 A GDP(1i) = E PV,c (3.9) where GDP, (the gross domestic product of country c in national currency) is equal to A GDPc = Eg. It can be readily verified that (3.8) and (3.9) constitute a linear system of equations with (A + N 1) unknowns in P, and 1/, ('r, = 1 for c= U.S.) (Theil et al., 1989). The product PV is interpreted as real expenditure per capita in international dollars on category a in country c, and this product is additive over all categories. Let S be any grouping of such categories, then the sum over the categories within this group S of the real expenditure gives the real gross domestic product (RGDP) per capita in international dollars on S in country c. If S consists of all detailed categories, this sum is GDP per capita in c. Further discussions of intricacies in construction can be found in Weatherspoon (1993). 3.2 Extrapolations with ICP Data There are five publications of the extrapolations on the different phases of the ICP, the first by Kravis et al. (1978b), and the rest by Summers and Heston also known as the Mark 1 (1980), Mark 3 (1984), Mark 4 (1988), and Mark 5 (1991) (MARK 2 was not published, but used by Kravis et al. 1982). This study used data from a supplement to the MARK 5 data compiled by Summers and Heston in 1993. Therefore, only the 34 MARK 5 data is discussed at length. For detailed discussions of the other data sets, please see Weatherspoon (1993). The purpose of the first paper by Kravis et al. (1978b) was to fill the gap in the world statistical system for comparative data on "real" GDP per capita for a large number of countries. The contribution of the second paper by Summers and Heston (1980) was that they extrapolated the data for the ICP and non-ICP countries forward and backward through time. The third publication by Kravis et al. (1982) had two benchmark years, 1970 and 1975, unlike the previous papers which had only 1970. The fourth publication also by Summers and Heston (1988) was basically an update of the MARK 3 data set. The regression equation used to summarize the 1970 and 1975 cross-section relationship in Mark 3 (Summers and Heston, 1984) study was 1nr = z(Ins) + a,(Inn + a(In(OP) + a (4.1) where rj (DAi/PPPDA) / DAus and nj = (DA/XR, )/DAus. PPPD"i is the purchasing power parity over domestic absorption, and XR is the exchange rate. They are both expressed in national currency units of the jth country per U.S. dollars. OPj is the measure of relative openness of the jth economy defined as ( (Exports. + Imports)/GDP ) / ( (Exportsus + Importsus)/GDPus ), an average of the ratio for five years before the cross-section year. The a's have the same expected signs as in Kravis et al. (1978b). 35 In Summers and Heston (1980), RGDPj, was based on constant prices while in Mark 3, international trade was incorporated into RGDP. The extrapolations in this data set were also treated differently and were computed at a greater disaggregated level. Data on consumption, gross domestic investment, government expenditure, and the net foreign balance, culled out from the U.N. constant-price series, were used to get real individual components expressed in 1975 international dollars for each of the years between 1950 and 1980. Mark 4 (Summers and Heston, 1988) updated the Mark 3 set. The major effort behind this project was to make the data more consistent, that is, the estimates need to adhere to the national income identity which states that total product equals total income generated by the production of the product. The implementation of consistency was done via an error-in-variables model. The objective was to adjust both the benchmark and national accounts data to make them consistent. The maximum likelihood procedure used to solve this model corrected the data sources so that they were consistent. However, a weakness of this procedure was that the asymptotic properties of maximum likelihood were not applicable. Mark 4 did not incorporate the openness variable since the exchange rates were greatly volatile during the 1970s. 3.3 Mark 5 Data Set MARK 5 covered 139 countries and RGDP per capita was obtained by extrapolating cross-section comparisons interspatially to non-benchmark countries and intertemporally to other years. This data set was based on ICP data from four 36 benchmark years: 1970, 1975, 1980, and 1985. Eighty-one countries participated in these benchmark studies and 47 participated in more than one study. Therefore, the need for relying on non-benchmark estimating methods was reduced. The national accounts data have also improved by using the World Bank's archive data. The methodology for obtaining RGDP per capita for a large number of countries has improved. All these factors make the MARK 5 the most accurate data published in recent times. The four ICP benchmark studies, Phases II to V, used in this study were all compiled in different ways and have different countries participating in different years. This is why the data needed to be made intertemporal and interspatial. Since the Phase V data were not published at that time, the authors had to calculate the RGDPs on their own using raw data from the U.N. and The World Bank. The countries that participated in the 1985 benchmark comparisons form five groups: 22 OECD countries, 11 Asian countries including Japan, 22 African countries, five European Group II countries including Finland and Austria, and a group of Caribbean countries. The Caribbean countries' comparisons were not complete at that time. The Geary-Khamis method was implemented for the OECD and Asian countries. The African countries, Hungary, Poland, and Yugoslavia all had data that allowed them to be linked to the OECD and Asian countries. The total number of countries from Phase V used in this study was 57. A different method was used for those countries which did not participate in the 1985 benchmark study, but which had participated in a previous benchmark study. The procedure was to value their 1975 or 1980 estimates of consumption (C), investment (I), 37 and government (G) expenditures at 1985 international prices. The growth rates for their components from the national accounts data and their change in international prices of the components between 1975 and 1985 or 1980 and 1985 were used. The changes in international prices were estimated from the benchmark estimates and the deflator for the numeraire country, the U.S. The 1975 and 1970 data were also re-analyzed. The May 1990 national accounts data were used for these revisions. The Geary-Khamis method was then used to aggregate the data. After the aggregation and re-estimations of the benchmark data, the nonbenchmark countries RGDP per capitas were estimated. A post-allowance PPP was computed by dividing the national currency by the PPP implicit in the post adjustment index. A structural relationship was found in the benchmark countries between PPP and its post-allowance PPP. This relationship was used to estimate non-benchmark countries' missing PPPs from their post-allowance PPPs. There were 81 benchmark countries and 57 non-benchmark countries that had to be estimated. The authors performed 12 different regressions for the benchmark studies and then these were used to obtain the non-benchmark estimates. Geary-Khamis method was used to aggregate the data resulting in consistent national absorption for all countries. It was still apparent that RGDP for poor and African countries were less accurate than estimates for rich countries. 38 3.4 Data for Estimation A supplement to the PWT5 data set, PWT 5.5, was compiled by Summers and Heston in 1993. This data set, in 1985 international prices, spans the years 1950-1990 for most countries. The information necessary for this study were extracted from this data set. A description of the variables tabulated in this document are listed in Table 3.2. Data on population (POP) and GDP per capita (RGDPCH) for the 22 OECD countries during 1955-1990 were used in estimation as tabulated. Shares of real investment and real government expenditures (i and g,) for country j (j = 1 to 22) were used to compute per capita levels of real investment and government expenditures, ;- and Gj, respectively. ; = ij RGDPCH-Ij Gj = gj RGDPCIA International openness, O, which represents the per capita level of exports and imports was compiled using OPEN variable as follows Oj = OPEN RGDPCHI where OPENj = {EXPORTS, + IMPORTS} / CGDP and CGDPj is the per capita nominal income in country j. Both the UNESCO series, Basic Facts and Figures (1951-1961) and the Statistical Yearbook (1963-1993), income and population figures from the Summers and Heston (1993) data were used to compile information on the four indicators of human capital for Table 3.2 Description of Variables in PWT 5.5 File 39 Variable Description POP Population in 000's RGDPCH Real GDP per capita in constant dollars (Chain Index) (expressed in international prices, base 1985.) c Real Consumption share of GDP [%] (1985 intl.prices) i Real Investment share of GDP [%] (1985 intl. prices) g Real Government share of GDP [%] (1985 intl. prices) RGDPL Real GDP per capita (Laspeyres index) (1985 intl. prices) RGDPTT Real GDP per capita in constant dollars adjusted for changes in terms of trade (1985 international prices for domestic absorption and current prices for exports and imports.) Y CGDP relative to U.S. [%] (U.S.= 100, current intl. prices) CGDP Real GDP per capita (current intl. prices) cc Real Consumption share of GDP [%] (current intl. prices) ci Real Investment share of GDP [%] (current intl. prices) cg Real Government share of GDP [%] (current intl. prices) P Price level GDP [%] (PPP GDP/ U.S. dollar exchange rate) PC Price level Consumption [%] ([PPP of C]/XR) PI Price level Investment [%] ([PPP of I]/XR) PG Price level Government [%] ([PPP of G]/XR) XR Exchange Rate with U.S. dollar RGDPEA Real GDP per Equivalent Adult (1985 intl. prices) RGDPW Real GDP per Worker (1985 intl. prices) OPEN Openness (Exports + Imports) / Nominal GDP Summers and Heston, 1993. 40 the 22 OECD countries during 1955-1990. Per capita public expenditure on education (PE) for country i (i= 1 to 22) was compiled as PE = pes RGDPCHi where pe was the public expenditure on education as a percentage of income. Per capita consumption of newsprint (CN for country i, expressed in metric tons, was compiled directly as tabulated in the UNESCO series'. Education at the secondary school level (ES) and university (or equivalent) level (ET) in country i were compiled as ESi = es, / POPi ET = eti / POPi where es, was the total number of people with secondary school education, ets was the total number of people with university (or equivalent) education, and POP, was the population in country i. Thus, the variables represent the shares of the population with education at the secondary and university levels, respectively. In total, the data set used in the estimation of the research model had 36 observations per country i (i= 1 to 22)for each of the 22 OECD countries (36 x 22 = 792 total observations) for each of the eight variables: income (Y), per capita public expenditure on education (PE), per capita consumption of news print (CN), education at secondary school level (ES), education at university (or equivalent) level (ET.), per The data for CN in 1986, for all the countries, was not available and was substituted by the average value of 1985 and 1987. 41 capita international openness (0O), per capita investment expenditure (I)., and per capita government expenditure (G). CHAPTER 4 INCOME AND HUMAN CAPITAL IN THE OECD COUNTRIES In this chapter, levels of per capita income in 22 OECD countries are estimated (as a function of human capital, international openness, investment and government expenditures) and analyzed. Several studies analyzing the relationship between growth with human capital and income convergence have used multiple regression techniques (Barro, 1991; Barro and Sala-i-Martin, 1992; Mankiw et al., 1992) and mathematical optimization techniques (Lucas, 1988, 1993). Tallman and Wang (1992) reviewed neoclassical and endogenous growth models to argue that improvements in formulating human capital measures in growth models could help establish a stronger link between human capital and growth. Weatherspoon (1993) used Theil's inequality index to measure inequality in income, industrial employment, investment expenditure, and government expenditure for the G-7 and 14 OECD countries during 1950-1985. He then used cointegration analysis to test for a long-run relationship among these inequalities. The basic premises of the model for estimation were derived from the national income identity for an open economy and the development of endogenous growth models. The national income identity states that national income is a function of consumption, 42 43 investment and government expenditures, and volume of exports and imports. International trade is one of the key determinants of economic interaction among countries and countries gain from trading goods and services by taking advantage of the differences between their endowments and by achieving economies of scale in production. These gains from trade are reflected in the growth (or decline) of national income. Further, the national income accounts provide information essential for studying the disparities in income among rich and poor countries (Krugman and Obstfeld, 1991). Growth theorists (Barro, 1991; Mankiw et al., 1992; Lucas, 1988, 1993; Romer, 1989, 1994; Tallman and Wang, 1992) have shown that accumulation of human capital is beneficial to the economy as a whole and the individual within the economy. Therefore, income was specified as a function of human capital, international openness, government expenditure, and investment expenditure. The model is discussed further in Section 4.2 of this chapter. The objective of this study was to analyze the nature of the influence (if any) of factors of economic growth (especially human capital) on income for the 22 OECD countries (in Chapter 1) during 1955-1990. The classical econometric treatment assumes that the observed variables, endogenous and exogenous, are measured without error. Latent variable models, on the other hand, incorporate measurement error in the observed variables into the estimation process. These errors can be correlated, and multiple indicators can measure the unobservable variable. Therefore, as the level of human capital is not directly observable, this study estimated income using a latent variable model (Bollen, 1989) with human capital as the latent variable. 44 The layout of this chapter is as follows: Section 4.1 introduces a general latent variable model, Section 4.2 gives the estimation procedures, section 4.3 describes the empirical research model, Section 4.4 gives the results of estimation, Section 4.5 tabulates the results from estimation of per capita income and analyzes the effects of human capital, openness, investment and government expenditures on income, and Section 4.6 concludes this chapter. 4.1 General Latent Variable Model The full latent variable model consists of a system of structural equations. These equations contain random variables, structural parameters, and sometimes nonrandom variables. The three types of random variables are latent, observed, and disturbance/error variables. The nonrandom variables are explanatory variables whose values remain the same in repeated random sampling (fixed or nonstochastic variables). The links between the variables are summarized in the structural parameters. The structural parameters are invariant constants that provide the "causal" relation between variables. The system of structural equations has two major subsystems: the latent variable model and the measurement model. 4.1.1 Structural Equations of the Model The first component of the structural equations is the latent variable model which encompasses the structural equations that summarize the relationships between latent variables: 45 q -Bq + I'( + ( (4.1) where n is an m x 1 vector of latent endogenous random variables; t is an n x 1 vector of latent exogenous random variables; B is the m x m coefficient matrix showing the influence of the latent endogenous variables on each other; P is the m x n coefficient matrix for the effects of t on q, and contains no zero elements. The matrix (I B) is nonsingular. The diagonal of B is always zero. r is the disturbance vector that is assumed to have an expected value of zero [ E({) = 0 ], homoscedastic, nonautocorrelated, and which is uncorrelated with t. The second component of the structural system is the measurement model: y Aq + a (4.2) x = A.9 + 8 (4.3) where y (p x 1) and x (q x 1) vectors are observed variables. AY (p x m) and A. (q x n) are the coefficient matrices that show the relation of y to 4t and x to t, respectively. e (p x 1) and 6 (q x 1) are the errors of measurement for y and x, respectively. The errors of measurement are assumed to be uncorrelated with t and r and with each other. The expected value of E and 6 are zero. To simplify matters q, E, y, and x are written as deviations from their means. Further, t cannot influence any y directly; if the x and y vectors contain measurement errors, these errors cannot influence one another directly. 46 4.1.2 Implied Covariance Matrix Covariance is a central concept for the above models: the covariance algebra helps in deriving properties of the latent and measurement models; and determine factors that influence sample covariances which in turn can affect parameter estimates. Two covariance matrices are part of the latent variable model: 4 (n x n), a symmetric matrix, is the covariance matrix of the latent exogenous variables(ts); I (m x m) is the covariance matrix of the errors in the latent variable model. Thus, the covariance matrix for is a function of B, r, t, and k. For the measurement model, 08 (q x q) and 0, (p x p) are the covariance matrices of the errors of measurement 6 and e, respectively. Specifically, k = E(('), I = E('f), O, = E(bb'), and 0, = E(ee'). The sample covariance matrix is crucial to the estimates of structural equation models since factors that affect this matrix have the potential to affect the parameter estimates. The n X (p + q) sample covariance matrix is computed as S= _i (4.4) T where z is [y x]. The population covariance matrix is denoted by E. EC is the covariance matrix of y, is the covariance matrix of x, and are the covariance matrices of y with x and x with y, respectively. Let 0 denote the vector of unknown parameters. Then, IE (0) is 2s,(e) E(yy Ae ,e ) + e (4.5) Substituting the reduced form of equation (4.1) 47 q = (+--'(A + in E(rqn') and simplifying we get Z,() A, (--' (re r' + ) [(-)-]' + 0. (4.6) which shows that the covariance of y is a complex function of six of the eight model parameter matrices or vectors. Similarly, (0) E(yx) A, (I-B)-' IAt (4.7) and -WO) .(O); Azr' [(I-B)-'' A; (4.8) Further, M (0) = E(xx) = E(I) A; + 0, (4.9) Substituting for E(Et') we have S=(0) AxOA + 0& (4.10) Therefore, the covariance matrix E (0) for the observed y and x variables as a function of the model parameters is (0) c e ) a e) l (4.11) which can also be written as 48 I"- -)1(' ~ Y[ -'l]'t e A- + (4.12) 4.1.3 Identification Investigations of identification (Bollen, 1989) begin with one or more equations relating known and unknown parameters. Known parameters are those that are known to be identified such as variances and covariances for which consistent sample estimators are readily available. The unknown parameters are those whose identification status is not known and the researcher must establish whether unique values exist for these. The unknown parameters are from the structural equation model. Identification is demonstrated by showing that the unknown parameters are functions only of the identified parameters and that these functions lead to unique solutions. If this can be done, the unknown parameters are identified; otherwise one or more parameters are unidentified. Therefore, the objective is to solve for the unknown parameters in terms of the identifiable parameters. The parameters in 0 are globally identified if no vectors 01 and 02 exist such that E (01) = E (02) unless 01 = 02. t-Rule Let p+q be the number of observed variables, and t be the number of free and unconstrained elements in 0. The t-rule for identification (Bollen, 1989) is that the number of nonredundant elements in the covariance matrix of the observed variables must 49 be greater than or equal to the number of unknown parameters in 0. In other words, the necessary but not sufficient condition of identification is: t I (p + q) (p + q + (4.13) 2 The nonredundant elements of E = E(O) imply (p + q)(p + q + 1)/2 equations. If the number of unknowns in 0 exceeds the number of equations, identification is not possible. Two-Step Rule Under this rule (Bollen, 1989), the first step is to treat the model as a confirmatory factor analysis. This implies that the original y and x are treated as x variables, and the original -9 and t are treated as t variables. The only relationships between latent variables that are of concern are their variances and covariances (f). In short, B, r, and elements of equation (4.1) are ignored. This model is identified if a unique solution exists for the structural parameters A., 4, and 0, such that no vectors and y2 exist that make E(0,) = E(02) unless 01 = 02. If the model is identified at this juncture then we move to the next step. The second step examines the latent variable equation of the original model given by (4.1) and is treated as a structural equations model with observable variables having no measurement error. Next it is determined whether B, ', and I are identified ignoring the measurement parameters considered in the first step (A, 4, and GO). This is achieved by verifying the identification of equation (4.1) using the order and rank conditions prescribed for systems of equations (Bollen, 1989). The order condition is 50 a necessary condition which requires that the number of variables excluded from the equation to be identified are at least p-1. The rank condition is necessary and sufficient for identification and requires that the ith equation, of a system of equations, is identified if the rank of Ci is equal to p-l, where c = [(I-B) I -I]. If the first step shows that the measurement parameters are identified and the second step shows that the latent variable model parameters are also identified, then this is sufficient to identify the model. This is so since the first step establishes that all parameters in the measurement model are identified, including the covariance matrix of the latent variables. The second step establishes whether B, I', 4, and *' are functions of the identified covariance matrix of the latent variables. Since this is a sufficient condition for identification, a model could fail to meet it and still be identified. However, this rule exemplifies the possibility that constraints on the latent variable relations can assist the identification of measurement parameters such that even if a model failed the two-step rule, it could still be possible to find unique solutions for the unknown parameters. MIMIC Rule The models referred to as MIMIC (Bollen, 1989) contain observed variables that are Multiple Indicators and Multiple Causes of a single latent variable. However, the MIMIC rule applies only to models in a certain form (as below) making its applicability narrow in range. The equations in this model are: 51 y + e (4.14) where x is a perfect measure of E and only one latent variable, ih, is present. Then il is directly affected by one or more x variables, and it is indicated by one or more y variables. Identification of the MIMIC models that conform to (4.14) follows if p (the number of ys) is two or greater and q (the number of xs) is one or more, provided Th is assigned a scale. Therefore, the MIMIC rule for the model in (4.14) above with p > 2 and q > 1 is a sufficient condition for identification but not a necessary one. 4.2 Estimation The hypothesis for the generalized latent variable model is E = E(O). Given the sample covariance matrix of the observed variables, S, 0 has to be chosen such that E(O) is close to S. Theoretically, this means that we need to minimize E(0) to get consistent estimators of 0. Three such minimizing fitting functions are: the maximum likelihood (ML) function; the unweighted least squares (ULS) function; and the generalized least squares (GLS) function 52 F, logjX(0)i + tr( SE-I(0) loglSj (p+q) F, (1/2) tr ([I Z(e)S- ) (4.15) FUW L (12) tr 4[S M(e1]2) Each of these functions is minimized with respect to 0. Further, the estimated values of the four explanatory variables are obtained by minimizing the weighted squared errors as proposed by Bartlett (1938): S (A'4,A)-1A~x. (4.16) The estimated or predicted per capita income is computed as: 9 = (4.17) 4.3 Empirical Model The research model in question had one endogenous variable (per capita income (Y)), one exogenous latent variable (human capital (H)), and three exogenous variables (investment expenditure (I), government expenditure (G), and international openness (0)). Income was the real gross domestic product per capita, international openness was measured as the real per capita level of exports and imports, and government and investment expenditures were measured at real per capita levels (Chapter 3, Section 3.4). Income, international openness, investment and government expenditures were assumed to be observed without error for the purposes of estimation. 53 The indicators for human capital were levels of per capita public expenditure on education (PE), per capita consumption of newsprint (CN), shares of population with high school education (ES), and shares of population with university or equivalent education (ET). In a review of growth models, Tallman and Wang (1992) concluded that there were potential gains from greater emphasis on higher education, which improved learning efficiency on the job and yielded significant positive external effects. This improvement in on-the-job learning was also important for promoting perpetual economic growth, adding significantly to individual human capital stock as well as to the stock of society's knowledge that may improve the quality of life (Lucas, 1993). Therefore, since PE gave an indication of the level of investment in human capital, CN indicated a level of reading, and ES and ET denoted the shares of educated population, they were feasible choices for indicators of human capital accumulation. Further, the availability of data was yet another reason for the choice of indicators. Therefore, there were 36 observations for each of the eight variables (Y, PE, CN, ES, ET, O, I, and G) and for each of the 22 OECD countries. Since the intention was to study the convergence behavior of these countries as a group, the data were pooled making the total number of observations in each vector to be 792. Therefore, using equations (4.1), the latent variable model for estimation was 54 HI = [Y I Y Y3 4] + (4.18) where income was assumed to be observed without error (T= y). The measurement model for estimation, similar to equation (4.3), was 'A000 6 C_ 2 000 62 E_ 3 000 63 ET 14000 + 64 (4.19) O 000 G 6s I 0 16 0 66 0G 00 1 6 where the matrix on the left-hand side consisting of PE, CN, ES, ET, O, I, G vectors corresponded to x. A was the first matrix on the right side with factor loadings wherein which X5, X6, and X7 were normalized to a value of one for purposes of estimation. t corresponded with the matrix of exogenous latent variables wherein which E, was H and E2, E3, and E4 were assumed to be directly observable as O, I, and G, respectively. Therefore, 6, = 56 = 57 = 0 for estimation. r was the vector of errors in n(=y). From equations (4.6) to (4.8) and equation (4.10), we could derive the implied covariance matrix for the observed y and x variables as a function of the model parameters: 55 e 'r'7 1 (4.20) where t was the variance-covariance matrix of (, I' is the variance in q, and 0e is the variance-covariance matrix of x. For the purposes of estimation, the data were treated as deviations from their means. In this model, the variance parameter of H, 4,, was normalized to one to facilitate estimation. This implied that H N(0,1) which eased the statistical inference of the human capital variable. The variance parameters of O, I, and G were treated as fixed as in regular regression analysis. Additionally, 21 = 4 )2 441 441 043 10441 where 41*4*3 444 was the matrix of variance-covariance between the observed O, I, and G. Therefore 2 = S2 from the sample variance matrix (Section 4.2). Further, the restriction that ,12 = 413 = 4o,4 = 0 was imposed on the 4 matrix for the purposes of estimation.2 Thus, the 4 matrix looked like 2The model was estimated with and without the restriction that 012 = 1s = 414 = 0. The likelihood ratio test failed to reject the restriction at a=0.05 level of significance. 56 10 0 0 0 #n 2 (4.21) From equations (4.15) to (4.17) above, the empirical system of equations consisted of eight coefficients yi (i=l 1 to 4), and Xj (j= 1 to 4)) and five variances (E(r'"), and E(5 Aj') (j= 1 to 4) that were to be estimated. Therefore, the number of unrestricted unknowns in the 0 vector of the empirical model were 13 and the t-rule value computed using equation (4.13) was 36. The empirical model, described by equations 4.15 and 4.16, was in the MIMIC form with p= 1l and q=7 y = + y7. q (4.22) Therefore the necessary and sufficient conditions for identification were met for this model. 4.4 Parameter Estimates of the Latent Variable Model The maximum likelihood function Fl as given in the previous section was used to estimate the parameters of this model. Table 4.1 gives the estimated parameters for the latent variable model (from equation 4.18) and their asymptotic standard errors of estimation. These results clearly indicate that human capital (as measured by a latent 57 variable), international openness, investment and government expenditures had positive and statistically significant effects on income for the 22 OECD countries. These results complied with the theoretical underpinnings from basic macroeconomic and growth theories which indicate that growth in income was positively correlated with accumulation of capital and growth in international trade. The greatest positive effect on income was imposed by the level of human capital implying that human capital was a key determinant of income in the 22 OECD countries. This result tallied with the results put forth by Barro (1991), Mankiw et al. (1992), Tallman and Wang (1992), and Lucas (1988, 1993). The positive effect of international openness was as predicted by Romer (1990) who proposed that growth in international trade yielded positive dividends for economic growth. Mankiw et al. (1992) found that, in an augmented Solow model, a higher savings rate led to higher income and higher level of human capital. Barro (1991) found that growth in income was positively related to investment expenditures. Thus, the positive effects of investment and government expenditures were not surprising. Further, the elasticities in average income (Column 5) with respect to average levels of human capital, openness, investment and government expenditures are all positive. This also lends support to the above analysis that income is positively influenced by all the four factors and especially human capital followed by investment expenditure, government expenditure, and openness in that order. 58 Table 4.1 Parameter Estimates of the Latent Variable Model for 22 OECD Countries, 1955-1990. Variables Estimates Standard Elasticities Errors 1 2 3 4 5 H 71 11.79 0.75 0.65 0 'Y2 0.08 0.01 0.03 I 73 1.58 0.04 0.46 0 ;4 1.46 0.10 0.43 E(Q') 56.04 0.26 Table 4.2 gives the estimated parameters for the measurement model (from equation 4.19) and their standard errors of estimation. The factor loadings were all positive and statistically different from zero (a= .05). This result was as expected since the indicators contributed to the accumulation of human capital (Barro, 1991; Mankiw et al., 1991; Tallman and Wang, 1992; and Lucas, 1988, 1993). Increased public expenditure on education positively influences human capital accumulation since this investment results in improvement of level of schooling, improvement in skills, and level of technology; increased consumption of newsprint denotes an increasing level of reading which in turn could indicate increases in the level of educated population; increasing shares of educated population at the secondary school and university levels indicates growth in an educated and skilled population. An increase in all four variables does indicate a better level of living standard. 59 Table 4.2 Parameter Estimates of the Measurement Model for 22 OECD Countries, 1955-1990. Variables Estimates Standard Paameters Errors 1 2 3 4 PE X, 2.65 0.08 CN k 1.04 0.04 ES k 1.43 0.08 ET X4 0.97 0.03 E(161') o8 1.51 0.06 E(0262') 0 0.54 0.02 E(33') 033 3.55 0.05 E(644') 04, 0.28 0.02 4.5 Income and Human Capital in OECD Countries Using Bartlett's method (equation 4.16) and the estimated parameters (Table 4.2), we can compute the per capita value for human capital, HI: .-1 2.7 1.5 2.7" 2.7' 1.5 P 1.0 0 05 1.0 1.0 0 0.5 CN (4.23) 1.4 0 0 3.6 1.4 1.4 0 0 3.6 ES 10 0 0.3 1 0 0 0 0.3 ET Using equation (4.17) and the parameters of estimation from Table 4.1, per capita incomes of the 22 OECD countries are computed: t = 11.79 A + 0.08 O + 1.58 1 + 1.46 G (4.24) These computations yield 792 values for human capital and per capita income for the 22 countries. Therefore, the estimation of the model yielded 36 values for each variable for each country. The values of estimated per capita income and human capital for each 60 country were weighted by their respective populations to yield an average per capita income and average per capita level of human capital for the 22 OECD countries as a group, where Y'OC was the per capita income of the group of 22 OECD countries, ni (i= 1 to 22) was the population of country i, 'i (i = 1 to 22) was the per capita income of country i, IOBC was the per capita level of human capital for the 22 OECD countries as a group, I (j= 1 to 22) was the per capita level of human capital of country j, and N was the total population in the 22 countries. Similarly, average per capita levels of observed income (YOBCD), openness (OOCD), investment (loc,) and government (Go-c) expenditures were computed for the group of 22 countries. Table 4.3 tabulates estimated levels of human capital for the 22 OECD countries individually. For the purposes of estimation, this variable was specified to be distributed as N(0,1) to ease interpretation of results. However, while reporting the results for this variable, it was rescaled to bring it to a form comparable with that of the other variables in the model. Therefore, it has to be noted that when the values in Table 4.3 are expressed as deviations from their mean, they are still distributed as N(0,1). Table 4.4 summarizes the computations of average levels of per capita human capital, openness, investment and government expenditures for the 22 OECD countries. Column 2 of this table gives the values of average level of human capital. Therefore, the value of human 61 Table 4.3 Estimated Levels of Human Capital i, i=1 to 22) in the 22 OECD Countries, 1955-1990 Year USA Canada Japan Austria Belgium Denmark Finland France Germany Greece Ireland 1 2 3 4 5 6 7 8 9 10 11 12 1955 450.18 373.93 335.50 350.76 333.01 368.62 376.09 339.33 363.01 304.13 332.65 1956 450.04 378.99 341.50 348.17 341.72 376.54 400.37 362.12 366.43 304.87 331.72 1957 459.95 402.90 344.42 343.18 354.48 379.60 408.97 356.55 369.38 306.26 331.27 1958 455.57 417.21 348.60 345.01 396.00 380.44 398.57 357.38 373.51 306.70 331.04 1959 470.54 432.82 352.79 362.30 406.66 387.97 411.26 358.91 381.03 309.38 333.44 1960 537.94 454.01 352.96 366.80 414.59 393.88 428.20 367.16 382.18 310.34 339.02 1961 491.22 467.99 362.01 366.12 431.15 412.96 448.71 396.54 395.88 311.16 343.84 1962 522.35 513.72 370.20 377.72 437.30 470.06 459.36 399.26 398.99 311.29 337.93 1963 544.43 509.49 378.75 385.14 415.85 473.04 468.49 395.62 403.32 314.98 352.12 1964 554.28 525.79 390.27 396.65 473.62 499.85 473.26 420.87 415.60 324.14 364.58 1965 576.34 573.77 395.25 406.40 429.11 529.92 479.00 431.08 430.32 321.20 371.79 1966 584.25 625.58 402.99 426.43 450.93 556.03 488.89 440.45 434.88 322.19 370.34 1967 551.46 578.06 382.49 409.69 423.12 496.46 465.22 405.97 403.21 318.36 361.21 1968 569.28 581.66 388.50 416.64 436.17 512.54 459.64 435.61 406.50 321.38 368.51 1969 598.91 608.68 397.84 425.03 456.79 530.09 479.01 448.39 417.86 327.02 378.91 1970 606.59 624.61 410.59 428.66 428.48 550.00 493.68 421.61 438.75 323.35 384.86 1971 624.13 636.52 419.49 437.67 432.18 577.22 493.20 425.25 459.12 323.56 385.54 1972 628.82 632.31 427.99 452.08 438.21 567.77 498.46 432.78 445.75 324.07 393.21 1973 654.12 654.18 440.13 462.83 480.79 571.16 518.54 506.64 455.91 328.17 406.46 1974 640.86 647.12 458.16 475.44 519.14 589.24 520.06 485.71 469.24 332.11 410.72 1975 609.82 662.52 472.41 487.67 523.56 594.19 534.03 515.66 493.19 333.82 435.72 1976 613.42 676.93 471.93 497.17 536.38 631.60 549.25 534.00 465.41 335.45 428.17 1977 648.37 694.28 481.83 498.94 550.21 572.90 544.50 537.35 491.30 336.18 440.59 1978 675.54 712.86 499.88 505.40 536.59 583.06 528.81 521.76 497.44 342.62 452.09 1979 666.53 706.72 512.95 511.74 546.60 566.09 517.28 449.16 502.43 343.52 469.16 1980 693.18 707.88 519.73 518.18 551.50 586.94 530.76 517.07 507.54 347.97 473.74 1981 693.78 726.47 534.51 531.20 555.15 584.92 535.52 542.92 504.86 347.81 494.22 1982 680.37 721.36 527.83 528.42 554.31 599.40 546.92 556.66 497.68 348.35 487.97 1983 680.30 722.33 527.81 537.65 552.00 603.00 543.49 564.34 498.07 348.02 468.34 1984 696.71 714.56 519.28 537.54 550.17 601.11 540.23 570.93 508.65 353.10 470.95 1985 713.03 720.79 525.50 543.20 550.83 600.72 559.90 561.15 507.49 362.26 476.93 1986 727.63 751.56 525.42 554.71 534.21 674.40 567.92 558.69 507.55 357.97 485.91 1987 739.10 756.00 529.36 555.06 528.16 692.75 578.20 559.12 510.44 357.73 487.79 1988 647.14 766.91 538.55 551.88 526.22 683.02 589.89 563.87 509.15 362.25 484.68 1989 661.49 768.33 543.57 556.02 551.44 678.68 608.96 572.87 510.12 369.55 488.01 1990 710.95 780.63 557.59 561.32 556.17 679.75 627.09 583.62 518.80 370.19 500.09 62 Table 4.3 (Contd) Year Italy Netherlands Norway Portugal Spain Sweden Switzerland Turkey UK Australia New Zealand 13 14 15 16 17 18 19 20 21 22 23 24 1955 331.69 387.65 369.76 302.72 304.64 356.34 379.20 305.88 366.63 377.34 384.82 1956 332.99 358.23 375.19 303.03 304.25 357.78 383.72 305.73 367.25 375.56 383.52 1957 338.74 403.36 385.55 303.43 305.68 361.66 388.59 307.68 386.70 375.39 389.24 1958 340.30 400.95 396.23 303.47 306.10 375.89 393.28 309.11 386.51 356.72 390.79 1959 346.20 411.51 408.68 307.95 310.10 382.47 400.10 308.38 394.62 397.66 392.38 1960 362.77 430.81 412.09 310.79 312.65 385.01 418.17 307.88 398.33 401.59 408.11 1961 394.38 443.53 419.48 310.45 309.40 454.59 427.01 312.21 428.33 407.55 412.65 1962 412.17 457.44 435.86 310.24 312.28 469.33 502.07 312.63 441.10 410.54 416.94 1963 420.84 469.24 459.55 310.32 315.20 515.63 499.15 314.19 448.74 416.22 420.43 1964 424.72 497.04 469.63 309.02 326.20 532.84 489.88 314.24 459.24 430.10 431.38 1965 435.90 507.57 477.49 310.06 322.89 550.21 510.01 318.24 472.68 439.84 443.82 1966 402.44 482.81 498.20 310.47 324.68 573.75 473.64 321.32 486.48 448.65 455.63 1967 422.03 499.82 465.19 308.62 327.69 609.66 476.95 320.98 456.49 437.98 435.13 1968 418.82 514.62 472.63 310.08 331.45 589.34 481.09 321.37 441.23 441.38 433.72 1969 412.48 536.25 485.50 310.52 343.25 612.96 489.60 320.43 463.59 453.87 445.53 1970 418.96 566.04 475.48 344.71 349.06 607.67 504.84 318.42 465.84 467.55 467.46 1971 433.78 577.41 498.15 320.11 350.46 611.03 516.44 329.93 479.56 486.13 491.89 1972 447.85 580.25 537.61 323.25 362.35 616.59 525.98 343.37 510.94 503.22 493.82 1973 465.31 595.38 547.16 330.08 342.92 619.65 547.24 343.63 518.19 514.77 503.62 1974 466.93 616.54 547.84 337.18 342.41 621.22 556.23 347.47 508.71 572.59 517.70 1975 452.12 632.23 560.07 350.53 350.36 624.59 549.00 351.19 512.18 579.36 511.79 1976 465.95 638.83 602.11 361.16 354.27 639.36 550.67 354.51 515.58 576.52 498.16 1977 469.70 641.12 606.20 358.85 351.87 659.77 557.14 357.76 507.12 533.92 497.65 1978 457.17 651.91 639.41 368.42 365.75 693.12 552.77 335.58 507.69 461.35 496.76 1979 485.58 657.63 646.36 365.01 367.76 704.35 555.29 334.37 510.46 573.66 488.09 1980 495.49 631.94 627.18 378.35 368.12 716.36 570.91 323.64 513.97 575.46 507.46 1981 494.27 625.45 614.41 384.84 369.16 716.65 566.32 325.69 504.40 580.05 513.52 1982 493.64 610.86 618.17 388.61 372.25 711.18 567.00 325.73 504.66 579.13 504.23 1983 482.30 585.12 631.95 375.45 375.32 689.90 573.76 331.59 505.21 585.15 502.49 1984 499.41 584.82 637.16 378.64 386.77 691.67 572.21 323.98 501.98 626.88 503.87 1985 500.03 591.31 643.34 381.79 388.56 681.16 569.92 321.14 500.43 629.52 486.85 1986 505.76 599.99 674.67 381.72 389.01 683.17 583.93 320.59 512.98 595.49 523.13 1987 512.33 618.00 694.03 389.90 395.06 683.35 583.05 316.55 519.16 567.55 533.16 1988 521.26 602.00 700.72 403.04 427.52 654.16 596.18 317.65 525.44 565.52 541.48 1989 527.79 594.71 725.45 410.67 442.02 694.70 598.70 317.49 525.93 581.28 579.73 1990 446.14 600.33 738.22 420.10 447.71 715.51 615.29 337.99 536.10 585.93 607.98 63 Table 4.4 Average Per Capita Levels of Human Capital (iocD), International Openness (Ooac), Investment Expenditure (IOEC), and Government Expenditure (GOBcD) in the 22 OECD Countries, 1955-1990 Year Human Capital International Openness Investment Government Expenditure Expenditure IOCD OoBCD IOBD GoCD 1 2 3 4 5 1955 372.83 1283.14 1430.91 804.33 1956 375.89 1365.37 1457.26 808.44 1957 383.16 1422.75 1450.56 823.91 1958 384.16 1315.70 1404.01 828.75 1959 393.24 1393.18 1541.13 840.97 1960 416.43 1542.55 1639.43 852.70 1961 415.14 1568.23 1720.29 889.76 1962 431.45 1602.20 1815.93 927.39 1963 441.45 1675.17 1898.90 948.58 1964 453.25 1790.54 2066.63 964.09 1965 466.20 1865.29 2183.51 986.99 1966 471.55 1959.88 2287.96 1041.05 1967 450.93 2002.95 2316.70 1098.33 1968 458.80 2179.37 2476.89 1122.68 1969 474.78 2364.32 2646.05 1132.43 1970 481.22 2542.15 2703.16 1150.82 1971 493.73 2608.37 2757.89 1166.60 1972 501.24 2717.41 2882.64 1175.46 1973 519.74 3088.94 3149.99 1194.64 1974 519.92 3715.18 3017.30 1220.03 1975 518.27 3341.05 2633.05 1248.78 1976 521.36 3638.81 2870.10 1271.79 1977 534.82 3722.07 2973.74 1285.45 1978 543.37 3717.13 3074.45 1318.60 1979 542.60 4094.06 3176.32 1342.82 1980 557.36 4368.00 3060.20 1360.88 1981 561.50 4435.24 3016.31 1375.90 1982 556.70 4269.67 2789.60 1392.52 1983 556.29 4254.21 2844.59 1419.41 1984 562.79 4665.34 3187.09 1450.12 1985 568.16 4733.06 3254.57 1489.07 1986 574.88 4402.15 3329.83 1530.81 1987 580.36 4519.56 3487.03 1560.68 1988 557.26 4795.09 3733.70 1583.16 1989 565.66 5158.82 3949.07 1585.50 1990 581.93 5276.98 4003.32 1610.41 64 capital was increasing over time implying that the level of human capital has been increasing over time for the 22 OECD countries. From columns 3 to 5 of this table, it can be seen that average per capita levels of openness, investment and government expenditures, respectively, were also increasing over time though at different rates. Figures 4.1 and 4.2 depict these patterns clearly. These results indicate that the per capita income could be expected to increase over time as evidence from literature had suggested (Barro, 1991; Mankiw et al., 1992). Further, comparing the estimated levels of human capital in the individual countries to the average level (from Table 4.3, Table 4.4, and Figure 4.3) revealed that six countries (USA, Canada, Denmark, Netherlands, Norway, and Sweden) had above average levels, nine countries (Japan, Austria, West Germany, Greece, Ireland, Italy, Portugal, Spain, and Turkey) had below-average levels, and seven countries (Belgium, Finland, France, Switzerland, UKD, Australia, and New Zealand) tracked the average closely. Tables 4.5 and 4.6 give the values of observed and estimated income for the 22 countries separately. Columns 2 and 3 of Table 4.7 give the average levels of per capita observed and estimated incomes (YB and 'OBCD) for the 22 countries. At a glance, this table reveals that (i) income (observed and estimated) was increasing over time, and (ii) the estimated income values fit the observed income values quite closely. Further, from this table and Figure 4.4, the estimated income is initially lower than the observed income. Towards the end of the period the estimated income is lower than the observed 65 H 800 700 600 500 400 300 I I I I I I 1955 1960 1965 1970 1975 1980 1985 1990 Year Figure 4.1 Average Level of Human Capital (Ilo-) in the 22 OECD Countries, 1955-1990 66 H, 0, I, G 5, 000 4,000 3, 000 2, 000 1, 000 I I I I I I I I 1955 1960 1965 1970 1975 1980 1985 1990 Year Figure 4.2 Average Level of Human Capital (IaoW), International Openness (Oon), Investment (Iom) and Government (Gowm) Expenditures in the 22 OECD Countries, 1955-1990 Figure 4.3 Comparing Countrywise Levels of Human Capital (Hi, i= 1 to 22) and Average Level of Human Capital (Ho) in the 22 OECD Countries, 1955-1990 00 0 I I I I 0 C L 0 4J0 o I I I I _________________ I _________________ I (I I I I ~ I I I I I U U U N U U N U N I I I I I ~ I I I I I I ________________________________ I ________________________________ I 69 H Belgium Finland 7a I " ma gQgl i l4I I fi f 0 is n1 !se Ie Iew i Is Ins i sn 1ee 1aw I7 Is !S s Y~ Yw FDirurrk H (Contd 7- w ISM I I I I I II N I I m IN -I I -II SI -1 -I -1 -i I -i cr-1 -I (%88 I II I IL I I-8 I I a\ I Ci II IP II I I I I I I I C 1 -1 1 -1 -5 -1 I I I I I I I I O .s3 a3 3 I (za 3 8 8 1 I I I I * 0 U I I I I I I I I I I I I I I I I I I I I I I I 0 I I ____________ I ____________ I I I I I U hI ~I I I I I I bO 72 Sweden Turkey a an -W I a S-o0 mi I Ii ow Swltzerland aK 7m0 S-ago 4W a SI I s s s Is I Ie n e i Cot Figure 4.3 (Contd) 73 A Austra I la New Zealand 70 o 4 . I mI I I I I I II I I I I Im I Figure 4.3 (Contd) 74 Table 4.5 Levels of Observed Income (Yi, i= 1 to 22) in the 22 OECD Countries, 1955-1990 Year USA Canada Japan Austria Belgium Denmark Finland France Germany Greece Ireland 1 2 3 4 5 6 7 8 9 10 11 12 1955 9593 7012 2125 3921 5094 5453 4598 4944 5185 1688 2969 1956 9584 7459 2260 4061 5208 5572 4675 5267 5444 1819 2896 1957 9530 7363 2401 4296 5294 5780 4666 5477 5667 1936 2861 1958 9278 7225 2511 4458 5172 5837 4595 5550 5814 2007 2843 1959 9718 7330 2706 4605 5307 6349 4910 5685 6196 2064 3030 1960 9776 7288 3033 5176 5583 6751 5367 6013 6637 2088 3184 1961 9835 7298 3436 5420 5841 7134 5755 6287 6888 2312 3348 1962 10234 7645 3643 5512 6104 7505 5825 6608 7099 2330 3482 1963 10514 7914 3983 5718 6305 7394 5911 6869 7209 2574 3632 1964 10928 8284 4449 6015 6687 8124 6233 7279 7641 2798 3787 1965 11492 8709 4600 6178 6860 8433 6607 7540 7999 3066 3862 1966 11999 9142 5041 6475 7027 8559 6690 7893 8088 3181 3862 1967 12160 9279 5547 6636 7252 8775 6752 8203 8001 3316 4014 1968 12555 9635 6223 6887 7509 9030 6837 8498 8479 3550 4355 1969 12806 10034 6842 7207 7965 9607 7522 9062 9080 3907 4657 1970 12725 10175 7500 7565 8453 9675 8247 9621 9557 4234 4884 1971 13041 10665 7700 7905 8686 9861 8358 9897 9695 4516 4822 1972 13632 11192 8224 8351 9067 10348 8861 10177 10020 4883 5028 1973 14226 11917 8769 8746 9681 10628 9425 10608 10433 5235 5596 1974 13909 12298 8503 9047 10092 10417 9799 10781 10291 4971 5701 1975 13479 12348 8572 8981 9793 10185 9767 10467 10127 5198 5756 1976 14087 12996 8871 9423 10341 10898 9510 10945 10784 5414 5805 1977 14655 13246 9193 9851 10428 11014 9466 11098 11097 5511 6243 1978 15303 13691 9549 9806 10695 11085 9554 11365 11444 5786 6628 1979 15408 14191 9982 10281 10955 11426 10358 11708 11980 5894 6806 1980 15097 14231 10292 10586 11354 11234 10985 11798 12013 5895 6785 1981 15339 14681 10602 10456 10967 10997 11013 11758 11862 5877 6964 1982 14612 13799 10849 10508 11108 11383 11339 11981 11706 5936 7023 1983 15039 14176 11042 10741 11009 11682 11577 11921 11988 5899 6875 1984 16154 15047 11456 10918 11295 12314 11841 12012 12337 5963 7084 1985 16559 15695 12004 11172 11324 12884 12128 12186 12543 6184 7215 1986 16885 16155 12240 11306 11552 13428 12283 12505 12832 6221 7144 1987 17332 16759 12703 11510 11910 13364 12745 12753 13006 6197 7423 1988 17975 17393 13475 11968 12534 13376 13499 13222 13544 6404 7753 1989 18354 17690 14045 12378 13097 13579 14371 13664 13937 6622 8406 1990 18399 17415 14836 12858 13600 13801 14219 13934 14498 6679 9080 75 Table 4.5 (Contd) Year Italy Netherlands Norway Portugal Spain Sweden Switzerland Turkey UK Australia New Zealand 13 14 15 16 17 18 19 20 21 22 23 24 1955 3645 5365 5112 1543 2669 6549 8310 1429 5968 7312 6834 1956 3773 5626 5214 1602 2850 6702 8754 1410 6020 7155 6736 1957 3904 5682 5361 1678 2943 6840 8903 1655 6105 7140 6970 1958 4042 5424 5391 1685 3056 6954 8443 1752 6092 7485 6893 1959 4277 5637 5501 1774 2940 7282 9026 1664 6314 7807 7007 1960 4636 6122 5665 1869 3196 7492 9639 1604 6548 7879 7920 1961 4993 6269 5914 2004 3573 7857 10328 1613 6690 7678 8025 1962 5285 6445 6141 2077 3912 8129 10581 1651 6697 8089 8109 1963 5580 6616 6433 2197 4207 8495 10849 1794 6927 8485 8340 1964 5657 7158 6727 2253 4413 9025 11258 1798 7276 8981 8634 1965 5765 7431 7029 2415 4692 9285 11425 1793 7378 8955 8991 1966 6085 7562 7296 2479 4988 9370 11580 1970 7482 9282 9084 1967 6499 7887 7667 2659 5163 9603 11794 2000 7665 9503 8664 1968 6863 8335 7739 2934 5429 9893 12062 2089 7934 10240 8577 1969 7270 8778 8035 3017 5864 10295 12612 2142 8001 10556 9094 1970 7669 9228 8129 3323 6017 10643 13274 2179 7695 10917 9352 1971 7689 9493 8433 3759 6173 10621 13681 2343 8312 11039 9686 1972 7815 9711 8827 3998 6653 10808 13945 2441 8963 11288 9966 1973 8383 10096 9174 4479 7116 11194 14254 2454 9410 11675 10656 1974 8788 10411 9593 4704 7454 11548 14454 2646 9156 11517 11159 1975 8354 10291 9915 4363 7389 11825 13228 2832 9014 11616 10468 1976 8909 10739 10590 4526 7531 11873 13058 2998 9300 11865 10580 1977 9104 10939 10872 4733 7589 11528 13388 3102 9550 11750 9968 1978 9371 11147 11288 4775 7544 11613 13423 3019 9912 12279 9924 1979 9930 11325 11807 4914 7458 12073 13825 2930 10220 12332 10259 1980 10445 11323 12249 5048 7495 12290 14653 2853 10028 12622 10260 1981 10382 11105 12290 5092 7319 12165 14704 2843 9933 12828 10747 1982 10349 10891 12257 5194 7351 12274 14446 2847 10126 12168 10686 1983 10369 11005 12779 5105 7378 12479 14514 2885 10536 12840 10805 1984 10649 11317 13557 4952 7403 12999 14722 2996 10781 13349 11322 1985 10895 11570 14227 5026 7547 13313 15209 3059 11137 13662 11324 1986 11199 11736 14821 5250 7820 13558 15657 3281 11580 13755 11430 1987 11547 11747 14918 5615 8321 13931 15934 3423 12151 14190 11498 1988 12021 11987 14752 5990 8809 14231 16320 3395 12751 14659 11481 1989 12367 12434 14647 6281 9305 14534 16799 3370 13050 14904 11811 1990 12557 12868 14891 6525 9664 14495 17007 3711 13068 14304 11540 76 Table 4.6 Levels of Estimated Income ( 1, i=1 to 22) in the 22 OECD Countries, 1955-1990 Year USA Canada Japan Austria Belgium Denmark Finland France Germany Greece Ireland 1 2 3 4 5 6 7 8 9 10 11 12 1955 8797.69 7116.97 4038.78 5327.55 5671.12 6032.36 6374.98 5683.44 6628.47 3531.65 4623.24 1956 8637.34 7824.74 4148.52 5207.65 5946.81 6263.32 6490.69 6121.38 6694.42 3639.48 4398.68 1957 8436.04 7544.98 4307.19 5421.78 5934.50 6506.80 6454.31 6249.57 6799.50 3713.47 4248.08 1958 8218.77 7153.03 4255.03 5519.17 5648.53 6292.25 6357.49 6315.97 6894.39 3790.09 4227.04 1959 8628.63 7239.31 4429.87 5600.65 5936.59 7144.40 6721.90 6402.74 7326.36 3856.12 4575.81 1960 8483.06 7050.75 4755.62 6234.38 6190.28 7613.40 7347.89 6742.16 7772.61 3947.30 4557.86 1961 8521.46 7050.09 5273.65 6370.57 6522.87 7796.35 7725.27 6932.05 7955.89 4147.62 4723.25 1962 8935.43 7316.07 5271.99 6320.02 6693.47 8272.63 7637.64 7174.07 8138.33 4148.63 4905.94 1963 9133.11 7418.17 5581.54 6418.88 6812.69 7867.55 7438.75 7335.22 8148.59 4354.87 5074.60 1964 9332.10 7721.68 5944.32 6831.17 7371.19 8922.02 7872.45 7782.97 8631.33 4638.66 5288.94 1965 9856.74 8231.13 5957.18 6908.21 7410.78 9235.22 8457.64 7917.41 8968.40 4899.57 5504.39 1966 10299.42 8642.58 6295.01 7264.04 7709.33 9219.50 8445.61 8252.59 8854.63 4802.35 5334.12 1967 10331.44 8437.64 6862.08 7269.07 7789.29 9410.94 8286.44 8457.28 8467.51 4856.57 5357.39 1968 10532.81 8618.33 7531.19 7443.00 7893.71 9647.26 8272.43 8750.92 8977.94 5035.37 5780.74 1969 10636.95 8995.37 8094.23 7690.30 8364.08 10436.75 8887.99 9331.40 9571.26 5470.91 6275.80 1970 10203.61 8879.80 8851.45 8195.68 8744.25 10588.66 10112.14 9611.99 10022.87 5707.66 6296.25 1971 10547.50 9205.15 8838.86 8342.88 8725.22 10695.33 10128.13 9811.41 10035.28 5870.57 6383.02 1972 10819.83 9474.53 9262.94 8763.83 8817.44 11167.47 9979.98 10070.31 10222.53 6170.95 6739.54 1973 11236.85 10063.55 9930.74 9174.50 9457.27 11697.15 10612.11 10644.95 10495.48 6933.55 7227.47 1974 10873.34 10643.88 9536.70 9358.21 10062.62 11292.97 11927.11 10790.15 9898.08 6254.53 7311.30 1975 9925.54 10595.93 9161.95 8856.20 9359.77 10365.30 11790.14 9810.48 9569.17 6301.13 6675.96 1976 10536.42 10883.38 9357.72 9467.20 9835.78 11502.90 10532.63 10483.50 10311.68 6358.53 7080.00 1977 11149.81 10963.09 9512.81 9796.58 9897.80 11375.29 10394.50 10533.35 10328.23 6391.36 7556.63 1978 11651.37 11043.70 9836.68 9553.50 10094.09 11341.32 9957.54 10500.77 10603.72 6584.79 7946.65 1979 11524.01 11791.15 10292.94 9990.30 10267.71 11673.53 11196.24 10934.63 11394.51 6857.86 8509.57 1980 10894.44 11922.47 10258.34 10442.76 10605.87 11036.71 12143.36 11053.39 11350.51 6713.87 7962.20 1981 11217.49 12640.43 10409.11 9974.28 9685.97 10338.71 11730.88 10656.76 10760.96 6370.28 8208.75 1982 10297.43 11176.82 10368.57 9584.59 9735.14 10872.61 12005.92 10852.26 10453.89 6224.60 8339.24 1983 10716.03 11505.48 10207.74 9565.95 9426.59 10877.70 12084.13 10472.86 10825.97 6230.87 7930.94 1984 12233.18 12068.64 10547.37 10109.63 9865.05 11701.00 12097.55 10438.05 11078.58 6155.06 7981.83 1985 12341.98 12587.89 10923.03 10279.05 9596.10 12315.43 12218.77 10596.14 11095.94 6381.61 7739.18 1986 12431.93 12995.84 11149.17 10333.99 9737.85 13001.85 12098.57 10993.89 11303.91 6152.73 7609.92 1987 12713.03 13706.89 11673.59 10465.21 10165.98 12496.88 12614.49 11340.79 11405.95 5922.22 7403.36 1988 12901.95 14384.36 12683.65 10963.91 10864.08 12157.62 13618.65 11851.40 11920.22 6357.50 7361.64 1989 13126.17 14823.41 13458.70 11311.00 11700.46 12447.88 15031.49 12241.81 12404.95 6414.57 8116.47 1990 12992.92 14176.48 14379.56 11864.18 12125.36 12111.65 14497.35 12442.52 12945.13 6372.22 877.88 77 Table 4.6 (Contd) Year Italy Netherlands Norway Portugal Spain Sweden Switzerland Turkey UK Australia New Zealand 13 14 15 16 17 18 19 20 21 22 23 24 1955 5514.50 6761.07 6879.14 3496.76 4154.43 7108.71 7561.72 3414.31 6425.34 7567.93 7558.55 1956 5616.18 7047.60 6901.59 3541.06 4273.60 7187.11 8070.87 3393.72 6428.86 7098.84 7356.73 1957 5759.19 7145.70 7023.27 3662.69 4347.88 7400.04 8292.34 3452.85 6470.64 7138.92 7548.77 1958 5839.59 6508.60 7118.70 3647.72 4437.20 7423.03 7270.51 3573.08 6356.64 7580.42 7386.45 1959 6055.31 6758.36 7029.04 3677.37 4195.03 7713.27 8003.70 3521.09 6535.10 7766.33 7406.19 1960 6442.15 7370.55 7091.86 3842.95 4428.09 8142.62 8941.58 3497.43 6859.13 8093.10 7724.47 1961 6776.73 7479.49 7335.40 3936.88 4744.29 8275.88 9879.31 3535.21 6944.07 7427.64 7948.30 1962 7045.08 7496.60 7518.77 4044.50 5037.56 8484.43 10049.39 3559.44 6867.64 8044.59 7727.73 1963 7280.21 7540.08 7818.13 4051.94 5183.93 8776.99 10202.12 3619.89 6977.25 8298.72 8039.51 1964 7073.67 8286.94 8047.35 4192.83 5369.73 9359.02 10650.08 3615.21 7505.48 9141.70 8480.51 1965 6862.33 8298.91 8490.24 4344.59 5695.40 9694.52 10383.50 3607.71 7540.31 9047.85 9035.77 1966 7026.56 8446.75 8763.60 4371.80 5956.59 9707.09 10352.28 3783.92 7569.48 9237.11 9373.24 1967 7415.75 8679.98 9267.23 4551.64 5981.79 9820.19 10538.43 3792.00 7842.00 9359.99 8423.46 1968 7725.67 9076.96 8927.22 4663.85 6154.58 10005.72 10613.29 3857.47 8048.96 10072.69 7855.90 1969 8080.35 9322.70 8773.81 4697.28 6550.74 10495.52 11000.04 3871.74 8022.79 10094.58 8451.74 1970 8285.84 9858.17 9703.44 5133.54 6564.79 11195.16 11968.42 3971.13 8112.43 10313.45 8635.92 1971 8099.61 9854.17 10290.76 5353.00 6488.51 10799.98 12288.69 4022.07 8151.34 10055.65 8873.53 1972 8188.95 9620.69 9792.39 5674.61 6926.45 10739.39 12281.15 4018.74 8206.72 9960.23 9102.80 1973 8749.94 9961.44 10575.86 6050.50 7326.57 10806.09 12471.45 4111.00 8898.46 10710.92 10378.71 1974 9094.63 10031.39 11434.80 6023.27 7704.65 11538.59 12733.36 4330.91 8739.38 10375.24 11628.59 1975 8082.09 9388.14 11898.73 5348.78 7520.06 11968.17 10492.99 4575.98 8402.93 10265.50 9477.74 1976 8719.65 9692.64 12698.49 5499.49 7522.21 12012.85 10345.06 4635.13 8808.67 10668.22 9654.53 1977 8582.75 9953.71 12620.92 5937.58 7377.18 11193.17 10510.39 4753.86 8833.51 10157.11 9173.52 1978 8659.04 10099.50 11452.81 6080.71 7181.22 10659.18 10886.45 4401.60 8935.18 10924.31 8669.24 1979 9040.00 10094.41 11836.86 6338.60 7117.27 11524.19 11772.88 4373.65 9105.01 10836.91 9161.81 1980 9614.07 10059.33 12499.27 6646.20 7231.59 12007.89 12898.39 4493.28 8561.56 11264.17 8887.32 1981 9186.62 9236.36 12431.43 6720.56 6932.34 11323.30 12464.35 4550.63 8275.17 11672.49 9615.32 1982 9102.17 9197.88 12551.77 6866.36 7012.02 11349.49 12082.08 4472.75 8559.19 10360.03 9792.81 1983 8966.55 9399.59 12512.59 6361.93 6939.45 11364.74 12315.54 4446.91 8916.61 11041.76 10009.04 1984 9382.49 9711.55 13562.74 6030.39 6860.76 11867.01 12676.62 4447.12 9217.27 11559.96 10643.78 1985 9516.06 10044.66 13426.96 6034.15 6991.38 12532.75 13094.06 4573.56 9326.63 11868.55 10347.82 1986 9561.95 9839.58 14580.95 6246.56 7358.05 12415.50 14069.76 4711.67 9413.30 11481.07 10231.82 1987 9830.04 9478.05 14141.08 6313.00 7943.62 12770.99 14695.97 4782.81 9799.56 11820.12 10206.83 1988 10188.1 9696.20 13655.62 6407.80 8555.98 13139.43 15114.09 4678.83 10445.90 12812.30 10172.23 1989 10385.1 10488.43 13175.96 6635.07 9218.02 13906.96 15871.16 4583.14 10691.44 12842.90 11339.54 1990 10422.5 10779.49 12649.94 6878.67 9597.00 13863.07 16119.85 4793.40 10450.70 11730.73 11109.94 78 Table 4.7 Average Levels of Observed and Estimated Income Per Capita (YOC, ) in the 22 OECD Countries, 1955-1990 Year Observed Estimated Income Income 1 2 3 1955 5603.64 6335.28 1956 5723.63 6389.51 1957 5813.63 6406.68 1958 5798.50 6332.68 1959 6061.19 6573.94 1960 6287.77 6759.70 1961 6497.31 6945.81 1962 6763.09 7155.94 1963 7021.29 7324.48 1964 7380.76 7622.04 1965 7682.17 7846.86 1966 8013.23 8098.39 1967 8232.08 8229.28 1968 8624.72 8532.40 1969 8994.56 8829.64 1970 9216.68 8961.31 1971 9480.43 9076.73 1972 9914.48 9296.54 1973 10402.89 9778.07 1974 10335.40 9653.87 1975 10127.53 9060.21 1976 10562.65 9491.47 1977 10867.58 9682.47 1978 11232.67 9889.26 1979 11497.94 10113.69 1980 11512.11 9979.04 1981 11599.01 9937.19 1982 11398.71 9590.19 1983 11633.87 9715.47 1984 12163.43 10333.14 1985 12495.18 10502.00 1986 12786.72 10656.12 1987 13162.41 10957.08 1988 13699.01 11398.60 1989 14076.57 11770.50 1990 14317.18 11902.49 79 Y, Y 15,000 10,000 5,000 I I I I I I I I 1955 1960 1965 1970 1975 1980 1985 1990 Year Figure 4.4 Average Levels of Observed and Estimated Income, Yo, and Yo~, in the 22 OECD Countries, 1955-1990 80 income and the gap is widening. This gap could be due to the pooling of data which makes the estimation process insensitive to country specific effects. The values from Tables 4.5 and 4.6 and Figure 4.5 depict the relationship between observed and estimated income for the 22 countries individually. These comparisons indicated that the model underestimates the income of three countries (USA, Canada, Switzerland), overestimates the income for five countries (Greece, Ireland, Norway, Portugal, Turkey), and fits well for the remaining 14 (Japan, Austria, Belgium, Denmark, Finland, France, Germany, Italy, Netherlands, Spain, Sweden, UKD, Australia, New Zealand). Comparing Figures 4.1, 4.2, and 4.4, it was seen that international openness, investment and government expenditures, in their average levels, had increasing trends. This result also implied that the OECD countries were increasing their trading activities and investments over time. Yet again, comparing values from Tables 4.6 and 4.7 (Column 3), and Figure 4.6 revealed that the estimated incomes of nine countries (USA, Denmark, Finland, France, Germany, Norway, Sweden, Switzerland, Australia) were above-average, six countries (Greece, Ireland, Italy, Portugal, Spain, Turkey) were below-average, and seven countries (Canada, Japan, Austria, Belgium, Netherlands, UKD, New Zealand) moved closely with the average of the group of 22 countries. Figure 4.7 depicts the relationship between YOEC and (Table 4.7, column 3 and Table 4.4, column 2, respectively) as a positive and increasing one implying that human capital did have a significant and positive effect on per capita income for the 22 OECD countries. Similarly, using the values in Tables 4.3 and 4.6, Figure 4.8 depict Figure 4.5 Comparing Countrywise Levels of Observed Income (Yi, i=--1 to 22) and Estimated Income (Yi, i=l to 22) in the 22 OECD Countries, 1955-1990 Yi 82 USA ,Japan ",op Ism I I I I I I I I I I 1955 1960 1965 1970 1975 1980 1985 1990 1955 1960 1965 1970 1975 1980 1995 1990 Canada Austr I a S I I I I I O I 19s55 1980 1965 1970 1915 190 1985 1990 1955 1950 1985 1970 1975 1980 195 1990 Yr"rnr 83 Belgium n Fnland "ooM iosao 8m e- 1 oo I55 1960 1565 1570 1975 195 1950 1955 1560 1565 1970 1975 1 ia 1985 is50 SDenmark v France 15.on Ism Ss. 15 1 .5 15 197 1975 1880 195 190 5 1555 0 1965 1s70 s19'75 198 1m 1 Figure 4.5 (Contd) 84 Germany Ire I and eo -NO is,oa S.oa S.oo I I I I I I II I I I I I I 1W5 19560 19I 1970 1975 Igo 1985 1990 1955 1560 1555 15970 175 1500 1985 19I Year 1 Greece Ita ly 15,o 15o. S.m I -M I I i I I I I1 I 1 1 1 I 1935 150 1555 1970 1975 19 0 1995 1550 1955 196550 155 1970 1575J 190 19 1930 Figure 4.5 (Contd) 85 Nether lands Portugal 11n1 1 8000 I I I I I I I I I 155 1560 19565 1970 1975 1580 195 19590 1955 1960 1965 1570 1975 1980 1985 1990 YeYewr Y Norway Spa in s11a1 a s, Ou I I I I I I I I I I I I I 1855 1960 1965 1970 1975 150 1985 15 1955 1960 1955 1970 1575 1980 1985 1990 Figure 4.5 (Contd) 86 v Sweden v Turkey o I I I I I I 1 rS 15 0 1965 1570 1975 190 1985 1590 1955 1960 1555 1970 1575 1580 1985 19s SSwi tzer land y as.nO 1s.00 I I I I I I I I I I I I I I I I 1955 960 1965 170 1975 1990 1985 1990 1955 1950 19 1970 1975 1960 1985 1IW Figure 4.5 (Contd) 87 Australia New Zealand S- .o som %= to, ag S I I I I I I I !0I 1955 19d 4985 4970 41975 9890 1995 1990 1955 1960 1995 1970 1975 1990 1905 1990 igu Y4.5 (Contd) Figure 4.5 (Contd) |

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Figure 4.5 Comparing Country wise Levels of Observed Income (YÂ¡, i=l to 22) and
Estimated Income (YÂ¡, i=l to 22) in the 22 OECD Countries, 1955-1990 o o o Yj A o- YÂ¡ 33 GDPÂ£I* Â£>K (3'9) -1 where GDPC (the gross domestic product of country c in national currency) is equal to GDF< IX, -1 It can be readily verified that (3.8) and (3.9) constitute a linear system of equations with (A + N 1) unknowns in P and l/xc (xc = 1 for c= U.S.) (Theil et al., 1989). The product P0Va>c is interpreted as real expenditure per capita in international dollars on category a in country c, and this product is additive over all categories. Let S be any grouping of such categories, then the sum over the categories within this group S of the real expenditure gives the real gross domestic product (RGDP) per capita in international dollars on S in country c. If S consists of all detailed categories, this sum is GDP per capita in c. Further discussions of intricacies in construction can be found in Weatherspoon (1993). 3.2 Extrapolations with ICP Data There are five publications of the extrapolations on the different phases of the ICP, the first by Kravis et al. (1978b), and the rest by Summers and Heston also known as the Mark 1 (1980), Mark 3 (1984), Mark 4 (1988), and Mark 5 (1991) (MARK 2 was not published, but used by Kravis et al. 1982). This study used data from a supplement to the MARK 5 data compiled by Summers and Heston in 1993. Therefore, only the REFERENCES Ahluwalia, M.S. (1976). "Income Distribution and Development: Stylized Facts." American Economic Review, 66, pp. 128-135. Anand, S. and S.M.R. Kanbur (1993). "The Kuznets Process and the Inequality Development Relationship." Journal of Development Economics, 40, pp. 25-52. Ballmer-Cao, Thanh-Huyen, and J. Scheidegger (1979). "Compendium of Data for World System Analysis." Special Issue edited by V. Bomschier and P. Heintz, Bulletin of the Sociological Institute of the University of Zurich. Barro, RJ. (1991). "Economic Growth in a Cross Section of Countries." Quarterly Journal of Economics, pp. 407-443. Barro, R.J. and X. Sala-i-Martin (1992). "Convergence." Journal of Political Economy, 100(2), pp. 223-251. Bartlett, M.S. (1938). "Methods of Estimating Mental Factors." Nature, 141, pp. 609- 710. Becker, G.S., K. M. Murphy, and R. Tamura (1990). "Human Capital, Fertility, and Economic Growth." Journal of Political Economy, 98, S12-37. Berry, A., F. Bourguignon, and C. Morrison (1991). "Global Economic Inequality and its Trends Since 1950." In L. Osberg (ed.), Economic Inequality and Poverty: International Perspectives. Armonk, New York: M. E. Sharpe, Inc., 1991. Bollen, K.A. (1989). Structural Equations with Latent Variables. New York: John Wiley & Sons. Bomschier, V. (1983). "World Economy, Level Development and Income Distribution: An Integration of Different Approaches to the Explanation of Income Inequality." World Development, 11(1), pp. 11-20. Branco, K.J., and J.B. Williamson (1988). "Economic Development and Income Distribution: A Cross-national Analysis." American Journal of Economics and Sociology, 47(3), pp. 277-297. 126 Figure 4.3 Comparing Country wise Levels of Human Capital (HÂ¡, i = l to 22) and Average Level of Human Capital (HOECD) in the 22 OECD Countries, 1955-1990 H; *- Ho, BCD The financial support from the Food and Resource Economics Department and Dr. James L. Seale, Jr., is greatly appreciated. IV 132 World Bank (1976). World Tables. Washington, DC: Johns Hopkins University Press. World Bank (1980a). World Tables. Washington, DC: Johns Hopkins University Press. World Bank (1980b). World Development Report 1980. Washington, DC: Johns Hopkins University Press. World Bank (1987). World Development Report 1987. Washington, DC: Johns Hopkins University Press. World Bank (1988). World Development Report 1988. Washington, DC: Johns Hopkins University Press. World Bank (1988). World Bank Atlas. Washington, DC: Johns Hopkins University Press. Wright, C.L. (1978). "Income Inequality and Economic Growth: Examining the Evidence." The Journal of Developing Areas, 13, pp. 49-66. 11 Firstly, they categorized 113 countries into seven regions-North, South, Tropical Africa, Tropical America, South-East Asia, South-Central Asia, South-West Asia (see Appendix A for countries within each region)for the period 1950-1990. They found that the North was converging, South-East Asia was diverging, South-Central Asia presented no evidence of convergence or divergence, and the inequality values of sub-Saharan Africa tended to increase from the mid-1960s until the late 1970s and to decline thereaftera pattern in favor of the Kuznets hypothesis. Secondly, they compared the inequality in Western Europe, Mediterranean Europe and Mediterranean Africa; South Africa and its neighbors; USA, Mexico, and Central America; the Southern Cone of South America and its neighbors (Appendix B). The results indicate a strong tendency toward more poverty when moving from temperate zones toward the Equator. Thirdly, they considered three regions in Western Europe consisting of 18 countriesnon-EU, EU Center, and EU Periphery (see Appendix C for countries within each region)-and found that the income inequalities in the regions of EU and EU Center declined by more than 90%. This result was also in favor of convergence. In the case of the EU Periphery, the first 20 years provide evidence of transition from divergence to convergence. Lastly, they considered 15 noncommunist countries (Appendix D) in the Western Pacific and found that there was a strong tendency to greater poverty in movement toward the Equator from the temperate zones in the North or South. Theil and Seale (1994) used the purchasing power parity (PPP) based data for gross domestic products to assess the affluence of more than 100 non-communist countries in 1950-1990. A seven-region classification, based on the distinction between 48 Ay(/-2*r1(Tr/ + et ai-m-'rvK (412) A^crlc/-^)^ + e6 4.1.3 Identification Investigations of identification (Bollen, 1989) begin with one or more equations relating known and unknown parameters. Known parameters are those that are known to be identified such as variances and covariances for which consistent sample estimators are readily available. The unknown parameters are those whose identification status is not known and the researcher must establish whether unique values exist for these. The unknown parameters are from the structural equation model. Identification is demonstrated by showing that the unknown parameters are functions only of the identified parameters and that these functions lead to unique solutions. If this can be done, the unknown parameters are identified; otherwise one or more parameters are unidentified. Therefore, the objective is to solve for the unknown parameters in terms of the identifiable parameters. The parameters in 0 are globally identified if no vectors 0j and 02 exist such that E (0t) = E (02) unless 0! = 02. t-Rule Let p+q be the number of observed variables, and t be the number of free and unconstrained elements in 0. The t-rule for identification (Bollen, 1989) is that the number of nonredundant elements in the covariance matrix of the observed variables must 29 3.1.3 Countrv-Product-Dummv Method The CPD is based on the assumption that the natural logarithm of the price of the item i in country c includes an item effect and a country effect; PPPs are estimated by least squares; and the relationship is stochastic. The CPD equation is (3.2) 1/m (lnC/y) = A, Be * where Pic is the price of the item i in country c, m is the number of items, eÂ¡c is normally distributed with mean zero and variance o2, AÂ¡ is the item effect on the price i in country c, and Bc is the country effect on the price. In most cases this method is normalized with U. S. as the base country. 3.1.4 Elteto-Koves-Szulc Method The EKS method consists of four steps: calculate "Laspeyres" and "Paasche" type price indices; calculate "Fisher" binary price indices; fill in the Fisher matrix if needed; and finally, build an EKS matrix of transitive parities. All calculations in the EKS method are based on the prices of the "characteristic" items. A characteristic item of a country is one that is considered to be purchased frequently within that country. Each country nominates at least one such product within each detailed category. The characteristic item chosen must also be priced in at least one other country. The price indices calculated in the first step of the EKS method are not true Laspeyres and Paasche indices and thus, they are called mini-Laspeyres and mini-Paasche price indices due to their similarity to the Laspeyres and Paasche indices in time-series 108 The Pigou-Dalton condition requires income inequality to increase whenever an income transfer is made from a poor country to a richer country. 5.5 Theils Inequality Index TheiTs index satisfies the four properties of any inequality measure: symmetry, mean independence, population homogeneity, and the Pigou-Dalton condition. Further, this index yields a statistic and is additively decomposable. Theils income inequality measures inequality by taking the logarithm of the ratio of the arithmetic mean income to the geometric mean income. When this measure is applied to per capita incomes of n countries, it can be written as J = ^ pÂ¡Lo%(p/y) where pÂ¡ is the world population share of country i, and yÂ¡ is its world income share. An advantage of J is its additive decomposition, that is, if R,,...,R<3 are regions such that each country is in exactly one region, Pg and Yg are the population and income shares of region Rg: Pg = sum, pÂ¡ and Yg = sumÂ¡ yÂ¡, where the summations are over i E Rg, then j. Â£ r, if w (5 2) which measures the inequality among regions, while J, (p/^piogJO/iy/Cy/i-,)] <5-3> measures the inequality among the countries of region Rg. The additive decomposition is then Sweden 1933 1060 HW3 1070 ir75 1060 T003 1000 Yar 10 1000 1903 1970 1073 1900 1905 1990 900 700 800 300 400 300 A H 800 700 600 500 400 300 Figure 4.3 (Contd) CHAPTER 3 DATA The three sources of data for this dissertation were the Supplement to Mark 5 or the Penn World Tables (PWT 5.5) compiled by Summers and Heston (1993), Basic Facts and Figures compiled by UNESCO (1951-1962), and The Statistical Yearbook compiled by UNSECO (1963-1993). The data on income, population, international openness, government expenditure, and investment expenditure were extracted from the Summers and Heston data. The data on the four indicators for human capital-public expenditure on education as a percentage of income, per capita consumption of newsprint, levels of education at the secondary school and university levels-were compiled from the two UNESCO series. The data span 36 years, 1955 to 1990. Though there are 24 countries in the OECD group, the data for Iceland and Luxembourg were insufficient to include them in this study. Due to the nature and complexity of the PWT data, their compilation procedure is discussed in this chapter. For greater details of construction of these data, please refer to Weatherspoon (1993) who discussed this subject at great length. 24 Table 3.2 Description of Variables in PWT 5.5 File Description 39 Variable POP Population in 000 s RGDPCH Real GDP per capita in constant dollars (Chain Index) (expressed in international prices, base 1985.) c Real Consumption share of GDP [%] (1985 intl.prices) i Real Investment share of GDP [%] (1985 inti, prices) g RGDPL Real Government share of GDP [%] (1985 inti, prices) Real GDP per capita (Laspeyres index) (1985 inti, prices) RGDPTT Real GDP per capita in constant dollars adjusted for changes in terms of trade (1985 international prices for domestic absorption and current prices for exports and imports.) Y CGDP relative to U.S. [%] (U.S. = 100, current inti, prices) CGDP Real GDP per capita (current inti, prices) cc Real Consumption share of GDP [%] (current inti, prices) ci Real Investment share of GDP [%] (current inti, prices) eg Real Government share of GDP [%] (current inti, prices) p Price level GDP [%] (PPP GDP/ U.S. dollar exchange rate) PC Price level Consumption [%] ([PPP of C]/XR) PI Price level Investment [%] ([PPP of I]/XR) PG Price level Government [%] ([PPP of G]/XR) XR Exchange Rate with U.S. dollar RGDPEA Real GDP per Equivalent Adult (1985 inti, prices) RGDPW Real GDP per Worker (1985 inti, prices) OPEN Openness (Exports + Imports) / Nominal GDP Summers and Heston, 1993. 61 Table 4.3 Estimated Levels of Human Capital (HÂ¡, i=l to 22) in the 22 OECD Countries, 1955-1990 Year USA Canada Japan Austria Belgium Denmark Finland France Germany Greece Ireland 1 2 3 4 5 6 7 8 9 10 11 12 1955 450.18 373.93 335.50 350.76 333.01 368.62 376.09 339.33 363.01 304.13 332.65 1956 450.04 378.99 341.50 348.17 341.72 376.54 400.37 362.12 366.43 304.87 331.72 1957 459.95 402.90 344.42 343.18 354.48 379.60 408.97 356.55 369.38 306.26 331.27 1958 455.57 417.21 348.60 345.01 396.00 380.44 398.57 357.38 373.51 306.70 331.04 1959 470.54 432.82 352.79 362.30 406.66 387.97 411.26 358.91 381.03 309.38 333.44 1960 537.94 454.01 352.96 366.80 414.59 393.88 428.20 367.16 382.18 310.34 339.02 1961 491.22 467.99 362.01 366.12 431.15 412.96 448.71 396.54 395.88 311.16 343.84 1962 522.35 513.72 370.20 377.72 437.30 470.06 459.36 399.26 398.99 311.29 337.93 1963 544.43 509.49 378.75 385.14 415.85 473.04 468.49 395.62 403.32 314.98 352.12 1964 554.28 525.79 390.27 396.65 473.62 499.85 473.26 420.87 415.60 324.14 364.58 1965 576.34 573.77 395.25 406.40 429.11 529.92 479.00 431.08 430.32 321.20 371.79 1966 584.25 625.58 402.99 426.43 450.93 556.03 488.89 440.45 434.88 322.19 370.34 1967 551.46 578.06 382.49 409.69 423.12 496.46 465.22 405.97 403.21 318.36 361.21 1968 569.28 581.66 388.50 416.64 436.17 512.54 459.64 435.61 406.50 321.38 368.51 1969 598.91 608.68 397.84 425.03 456.79 530.09 479.01 448.39 417.86 327.02 378.91 1970 606.59 624.61 410.59 428.66 428.48 550.00 493.68 421.61 438.75 323.35 384.86 1971 624.13 636.52 419.49 437.67 432.18 577.22 493.20 425.25 459.12 323.56 385.54 1972 628.82 632.31 427.99 452.08 438.21 567.77 498.46 432.78 445.75 324.07 393.21 1973 654.12 654.18 440.13 462.83 480.79 571.16 518.54 506.64 455.91 328.17 406.46 1974 640.86 647.12 458.16 475.44 519.14 589.24 520.06 485.71 469.24 332.11 410.72 1975 609.82 662.52 472.41 487.67 523.56 594.19 534.03 515.66 493.19 333.82 435.72 1976 613.42 676.93 471.93 497.17 536.38 631.60 549.25 534.00 465.41 335.45 428.17 1977 648.37 694.28 481.83 498.94 550.21 572.90 544.50 537.35 491.30 336.18 440.59 1978 675.54 712.86 499.88 505.40 536.59 583.06 528.81 521.76 497.44 342.62 452.09 1979 666.53 706.72 512.95 511.74 546.60 566.09 517.28 449.16 502.43 343.52 469.16 1980 693.18 707.88 519.73 518.18 551.50 586.94 530.76 517.07 507.54 347.97 473.74 1981 693.78 726.47 534.51 531.20 555.15 584.92 535.52 542.92 504.86 347.81 494.22 1982 680.37 721.36 527.83 528.42 554.31 599.40 546.92 556.66 497.68 348.35 487.97 1983 680.30 722.33 527.81 537.65 552.00 603.00 543.49 564.34 498.07 348.02 468.34 1984 696.71 714.56 519.28 537.54 550.17 601.11 540.23 570.93 508.65 353.10 470.95 1985 713.03 720.79 525.50 543.20 550.83 600.72 559.90 561.15 507.49 362.26 476.93 1986 727.63 751.56 525.42 554.71 534.21 674.40 567.92 558.69 507.55 357.97 485.91 1987 739.10 756.00 529.36 555.06 528.16 692.75 578.20 559.12 510.44 357.73 487.79 1988 647.14 766.91 538.55 551.88 526.22 683.02 589.89 563.87 509.15 362.25 484.68 1989 661.49 768.33 543.57 556.02 551.44 678.68 608.96 572.87 510.12 369.55 488.01 1990 710.95 780.63 557.59 561.32 556.17 679.75 627.09 583.62 518.80 370.19 500.09 8 North consisting of 25 countries (U.S. and Canada from the American continent, Japan and Korea on the Western Pacific Rim, and 21 countries in Western and Southern Europe), the South with 9 countries (Argentina, Chile, and Uruguay from the Southern Cone of the American continent, Australia and New Zealand on the Western Pacific Rim, and South Africa, Botswana, Lesotho, and Swaziland from the Southern tip of Africa. He measured income inequality as the natural logarithm of the ratio of arithmetic mean income to geometric mean income which was additively decomposable. He concluded that international inequality increased substantially from 1960 to 1980, and that regional inequality dominated the average within-region inequality. In 1960 the inequality in the North exceeded that in any other region, but Northern inequality declined very rapidly so that it was second lowest in 1985. In contrast to the North, Tropical Africa and Asia showed substantial increases in inequality. Berry et al. (1991) conducted an extensive analysis on world income inequality. They analyzed over 100 countries during 1950-1977. They used data from World Bank Tables (1976, 1980a), World Bank Atlas (1988), World Development Report (1980b, 1987, 1988), and the Summers and Heston (1988) data set. They computed Theils entropy index, Atkinsons inequality, and the Gini coefficient. The major difference in their study was that they computed inequalities for gross national product (GNP) and consumption measured as a percentage of GNP to study changes in welfare. The underlying logic being that the distribution of consumption was less unequal across countries and the savings rate was below average for the poorer countries. Berry et al. (1991) contended that marginal propensities to consume decrease with decreasing income 74 Table 4.5 Levels of Observed Income (YÂ¡, i=l to 22) in the 22 OECD Countries, 1955-1990 Year USA Canada Japan Austria Belgium Denmark Finland France Germany Greece Ireland 1 2 3 4 5 6 7 8 9 10 11 12 1955 9593 7012 2125 3921 5094 5453 4598 4944 5185 1688 2969 1956 9584 7459 2260 4061 5208 5572 4675 5267 5444 1819 2896 1957 9530 7363 2401 4296 5294 5780 4666 5477 5667 1936 2861 1958 9278 7225 2511 4458 5172 5837 4595 5550 5814 2007 2843 1959 9718 7330 2706 4605 5307 6349 4910 5685 6196 2064 3030 1960 9776 7288 3033 5176 5583 6751 5367 6013 6637 2088 3184 1961 9835 7298 3436 5420 5841 7134 5755 6287 6888 2312 3348 1962 10234 7645 3643 5512 6104 7505 5825 6608 7099 2330 3482 1963 10514 7914 3983 5718 6305 7394 5911 6869 7209 2574 3632 1964 10928 8284 4449 6015 6687 8124 6233 7279 7641 2798 3787 1965 11492 8709 4600 6178 6860 8433 6607 7540 7999 3066 3862 1966 11999 9142 5041 6475 7027 8559 6690 7893 8088 3181 3862 1967 12160 9279 5547 6636 7252 8775 6752 8203 8001 3316 4014 1968 12555 9635 6223 6887 7509 9030 6837 8498 8479 3550 4355 1969 12806 10034 6842 7207 7965 9607 7522 9062 9080 3907 4657 1970 12725 10175 7500 7565 8453 9675 8247 9621 9557 4234 4884 1971 13041 10665 7700 7905 8686 9861 8358 9897 9695 4516 4822 1972 13632 11192 8224 8351 9067 10348 8861 10177 10020 4883 5028 1973 14226 11917 8769 8746 9681 10628 9425 10608 10433 5235 5596 1974 13909 12298 8503 9047 10092 10417 9799 10781 10291 4971 5701 1975 13479 12348 8572 8981 9793 10185 9767 10467 10127 5198 5756 1976 14087 12996 8871 9423 10341 10898 9510 10945 10784 5414 5805 1977 14655 13246 9193 9851 10428 11014 9466 11098 11097 5511 6243 1978 15303 13691 9549 9806 10695 11085 9554 11365 11444 5786 6628 1979 15408 14191 9982 10281 10955 11426 10358 11708 11980 5894 6806 1980 15097 14231 10292 10586 11354 11234 10985 11798 12013 5895 6785 1981 15339 14681 10602 10456 10967 10997 11013 11758 11862 5877 6964 1982 14612 13799 10849 10508 11108 11383 11339 11981 11706 5936 7023 1983 15039 14176 11042 10741 11009 11682 11577 11921 11988 5899 6875 1984 16154 15047 11456 10918 11295 12314 11841 12012 12337 5963 7084 1985 16559 15695 12004 11172 11324 12884 12128 12186 12543 6184 7215 1986 16885 16155 12240 11306 11552 13428 12283 12505 12832 6221 7144 1987 17332 16759 12703 11510 11910 13364 12745 12753 13006 6197 7423 1988 17975 17393 13475 11968 12534 13376 13499 13222 13544 6404 7753 1989 18354 17690 14045 12378 13097 13579 14371 13664 13937 6622 8406 1990 18399 1741? 1483$ 12858 13600 138Q1 14219 13934 14498 $$79 9080 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy HUMAN CAPITAL, CONVERGENCE, AND INCOME INEQUALITY: A LATENT VARIABLE APPROACH By Sri Devi Deepak August 1995 Chairman: James L. Seale, Jr., Major Department: Food and Resource Economics Convergence in income and its determinants, for 22 OECD countries during 1955- 1990, was analyzed using a latent variable approach and via Theils inequality index. Income was specified as a function of human capital, international openness, government expenditure, and investment expenditure drawing on the theoretical underpinnings from standard macroeconomic theory and from recent developments in economic growth theory. Human capital, which cannot be observed directly, was treated as a latent variable. Theils inequality index was computed for income and its determinants. The latent variable model was estimated using maximum likelihood. The results of this estimation showed that the effects on income levels, of human capital, international openness, investment expenditure, and government expenditure were statistically significant and positive. Human capital had the greatest positive effect xii ACKNOWLEDGMENTS I would like to thank my supervisory committee for their tremendous help and guidance. I also thank Dr. Henri Theil for providing me with the opportunity to assist him in his research which culminated in this dissertation. In particular, I would like to thank Dr. James L. Seale, Jr., and Dr. Charles B. Moss for their individual attention, time, and patience which helped me a great deal in completing this dissertation. I thank Dr. Max R. Langham, Dr. Gary F. Fairchild, and Dr. Douglas G. Waldo for their insightful suggestions in writing this dissertation. I especially thank my husband, Dr. M. S. Deepak, for his support and encouragement during the course of my research. I appreciate the wonderful support from the staff of the FRE Systems Support Center for their indispensable, patient, and highly efficient assistance during the arduous months of writing this dissertation. I thank Dr. John R. Gordon for all his support during the course of my program. I thank Ms. Rosemarie T. Wolfendale, Ms. Shirley A. Johnson, and Ms. Shirley T. Harris for their help and kindness throughout my program. I also thank the staff of the Documentation Division and Reference Section of the University of Florida Library (West) for their expert guidance and support for the collection of some parts of the data for my dissertation. in 65 1955 1960 1965 1970 1975 1980 1985 1990 Year Figure 4.1 Average Level of Human Capital (HOEcd) in the 22 OECD Countries, 1955-1990 19 average human capital agents. Convergence arises because below-average human capital agents gain most from learning. Glomm and Ravikumar (1992) studied the effect of endogenous growth on income inequality by using an overlapping generations model with heterogenous agents in which human capital investment through formal schooling was the engine of growth. They used simple functional forms for preferences (logarithmic), production technologies (linear), learning technology (Cobb-Douglas), and income distribution (lognormal) to highlight the distinction between the economies with public education and those with private education. They found that income inequality (measured by the standard deviation of the lognormally distributed incomes) declined more rapidly under public education. On the other hand, private education yielded greater per capita incomes unless the initial income inequality was sufficiently high. They also concluded that societies would choose public education if a majority of agents have incomes below average. Lucas (1993) made a case study of the economic growth of Philippines and South Korea as a key to emphasize the effect of on-the-job human capital accumulation on growth. With this modification to the neoclassical model, an economy with a human capital stock lower than the world average would grow faster than an above average economy. His theory indicated that, relative to the worlds income and human capital, a countrys human capital converged to 1 which implied that relative incomes converge to 1 at the same rate. He also observed that convergence is more likely over subsets of countries or regions of countries, where factor and final goods mobility is high. He concluded that the main engine of economic growth was the accumulation of human CHAPTER 4 INCOME AND HUMAN CAPITAL IN THE OECD COUNTRIES In this chapter, levels of per capita income in 22 OECD countries are estimated (as a function of human capital, international openness, investment and government expenditures) and analyzed. Several studies analyzing the relationship between growth with human capital and income convergence have used multiple regression techniques (Barro, 1991; Barro and Sala-i-Martin, 1992; Mankiw et al., 1992) and mathematical optimization techniques (Lucas, 1988, 1993). Tallman and Wang (1992) reviewed neoclassical and endogenous growth models to argue that improvements in formulating human capital measures in growth models could help establish a stronger link between human capital and growth. Weatherspoon (1993) used Theils inequality index to measure inequality in income, industrial employment, investment expenditure, and government expenditure for the G-7 and 14 OECD countries during 1950-1985. He then used cointegration analysis to test for a long-run relationship among these inequalities. The basic premises of the model for estimation were derived from the national income identity for an open economy and the development of endogenous growth models. The national income identity states that national income is a function of consumption, 42 APPENDIX A SEVEN REGIONS OF THE WORLD The 22 countries in the North include USA, Canada, Japan, South Korea, and 18 European countries: Austria, Belgium, Denmark, Finland, France, Germany (W), Greece, Iceland, Ireland, Italy, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, UK. The six countries in the South are Australia, New Zealand, Chile, Argentina, Uruguay, and South africa. The 43 countries of Tropical Africa are Algeria, Angola, Benin, Botswana, Burkina Faso, Burundi, Cameroon, Cape Verde, Central African Republic, Chad, Comoros, Congo, Egypt, Ethiopia, Gabon, Gambia, Ghana, Guinea, Guinea-Bissau, Ivory Coast, Kenya, Liberia, Madagascar, Malawi, Mali, Mauritania, Morocco, Mozambique, Namibia, Niger, Nigeria, Rwanda, Senegal, Sierra Leone, Somalia, Swaziland, Tanzania, Togo, Tunisia, Uganda, Zaire, Zambia, Zimbabwe. The 22 countries of Tropical America are Barbados, Bolivia, Brazil, Colombia, Costa Rica, Dominican Republic, Ecuador, El Salvador, Guatemala, Guyana, Haiti, Honduras, Jamaica, Mexico, Nicaragua, Panama, Paraguay, Peru, Puerto Rico, Surinam, Trinidad and Tobago, Venezuela. The six countries of South-West Asia are Iran, Iraq, Israel, Jordan, Syria, Turkey. The six countries of South-Central Asia are Bangladesh, India, Myanmar, Nepal, Pakistan, Sri Lanka. The eight countries of South- East Asia are Hong Kong, Indonesia, Malaysia, Papua New Guinea, Philippines, Singapore, Taiwan, Thailand. 119 25 3.1 Penn World Tables The PWT data efforts date back to 1978 with the formation of the International Comparison Project (ICP) (Kravis et al., 1978a). This project attempted to compile Real Gross Domestic Product Per Capita (RGDP) for more than 100 countries where RGDP is the gross domestic product per capita adjusted for differences in the purchasing power of currencies. The objective of the ICP was to approximately fill the gap in the world statistical system arising from the absence of comparative data on "real" GDP per capita. The motivation for this project came from the widely accepted fact that the exchange-rate conversions of the GDPs of different countries to a common currency such as the United States dollar did not yield a reliable basis for international comparisons. The compilations in the ICP were based on the "nominal" values of the gross product obtained from a countrys national accounts. Therefore, the comparisons based on nominal values gave systematically incorrect estimates as exchange rates deviated from the conversion factors in systematic ways. The PWT data were constructed from intertemporal and interspatial extrapolations on ICP and non-ICP data and were compiled in a manner consistent with the national income identity. Thus, the nature of compilation of the PWT data makes them very valuable for empirical research. However, to comprehend the nature of the PWT data and appreciate the benefits from using PWT data over the ICP data, one needs to understand the construction and development of the ICP data. Sections 3.1.1 to 3.1.5 discuss the ICP data briefly. 82 y USA v Japan Canada y AustrI a r Nstherlands t Norway r Portugal r Spain Figure 4.5 (Contd) I dedicate this dissertation to my parents, Mahalakshmi and Krishna Murthy Duwuri. Without their encouragement, blessings, and high expectations I could not have attained this level of education. 95 Y Figure 4.7 Relationship Between Average Levels of Observed Income (Y0ECD) and Human Capital (Hqecd) in the 22 OECD Countries, 1955-1990 Figure 4.6 Comparing Countrywise Levels of Estimated Income (YÂ¡, i=l to 22) and Average Level of Estimated Income (YOECD) in the 22 OECD Countries, 1955-1990 A Yqegd o o o A o- YÂ¡ 60 country were weighted by their respective populations to yield an average per capita income and average per capita level of human capital for the 22 OECD countries as a group, 1 OECD , OECD h n Â£ L A7 * where Y0ecd was the per capita income of the group of 22 OECD countries, nÂ¡ (i = l to 22) was the population of country i, YÂ¡ (i= 1 to 22) was the per capita income of country i, Hoecd was the per capita level of human capital for the 22 OECD countries as a group, Hj (j = 1 to 22) was the per capita level of human capital of country j, and N was the total population in the 22 countries. Similarly, average per capita levels of observed income (Yoecd), openness (0OECD), investment (IOEcd) and government (GOECd) expenditures were computed for the group of 22 countries. Table 4.3 tabulates estimated levels of human capital for the 22 OECD countries individually. For the purposes of estimation, this variable was specified to be distributed as N(0,1) to ease interpretation of results. However, while reporting the results for this variable, it was rescaled to bring it to a form comparable with that of the other variables in the model. Therefore, it has to be noted that when the values in Table 4.3 are expressed as deviations from their mean, they are still distributed as N(0,1). Table 4.4 summarizes the computations of average levels of per capita human capital, openness, investment and government expenditures for the 22 OECD countries. Column 2 of this table gives the values of average level of human capital. Therefore, the value of human 87 y Australia r New Zealand Figure 4.5 (Contd) 2 convergence). Though Kuznets studies income inequality within an economy, the implications of his theory have led to many studies testing Kuznets hypothesis across countries. From the survey of recent literature on convergence and income inequality, four types of studies have emerged: those that measure income inequality directly (Wright, 1978; Bomschier, 1983; Branco and Williamson, 1988; Theil, 1989; Berry et al., 1991; Oshima,1992; Ram, 1992; Theil and Deepak, 1993a, 1993b, 1993c, 1994; Moss et al., 1993; Seale et al., 1994; Theil and Seale, 1994), those employing regression analysis (Ram, 1988, 1989a, 1989b; Barro, 1991; Barro and Sala-i-Martin, 1992; Mankiw et al., 1992), those based on growth models (Lucas, 1988, 1993; Rebelo, 1990; Tamura, 1991; Glomm and Ravikumar, 1992; Romer, 1994), and those using time-series techniques (Weatherspoon, 1993; Weatherspoon et al., 1994). This survey shows that there is evidence that, in terms of income inequality, rich countries are converging, poor countries are diverging, and the level of affluence increases with increasing distance from the equator (Theil, 1989; Seale et al., 1994; Theil and Deepak, 1994; Theil and Seale, 1994; Moss et al., 1993). However, till recently, though researchers have failed to reject the Kuznets hypothesis to a large extent, they failed to define, with any certainty, the determinants of convergence (or divergence). Of those that have analyzed or explored the determinants of convergence, Barro (1991), Barro and Sala-i-Martin (1992), and Mankiw et al. (1992) found, empirically, that human capital tended to be an important factor in determining convergence. Lucas APPENDIX B EUROPE, AFRICA, AND SOUTHERN CONE The first region constituting Western Europe, Mediterranean Europe and Mediterranean Africa consists of Europes core: UK, France, Switzerland, Germany (W), and the three Benelux countries; 11 countries around the core: Austria, Denmark, Finland, Greece, Iceland, Ireland, Italy, Norway, Portugal, Spain, Sweden; countries of North Africa: Algeria, Egypt, Morocco, Tunisia. The second region constitutes South Africa: Chad, Mali, Mauritania, Niger, Sudan; and its Northern neighbors: Namibia, Botswana, Zimbabwe, Swaziland, Mozambique, Angola, Zambia, Malawi, Tanzania. The third region constitutes USA, Mexico, and Central America (Costa Rica, El Salvador, Guatemala, Honduras, Nicaragua, Panama). The fourth region constitutes the Southern Cone of South America: Argentina, Chile, Uruguay; and its Northern neighbors: Brazil, Bolivia, Paraguay, Peru. 120 86 19,000 10,000 5. 000 Y 15,000 10,000 5.000 Sweden y Turkey Switzerland r UK \ Figure 4.5 (Contd) 22 and 14 OECD countries were becoming more equal in terms of income, investment expenditure, government expenditure, and industrial employment. The survey of the above literature on income convergence suggested that testing for convergence (or divergence) with a combination of the theories on income inequality and economic growth would prove to be an exercise that could expand the horizons of contemporary research on the subject. The evidence also suggests that though researchers have failed to reject the Kuznets hypothesis to a large extent, they, however, failed to define, with any certainty, the determinants of convergence (or divergence) until recently. This study expanded on the above mentioned studies (Barro, 1991; Mankiw et al., 1992; Weatherspoon, 1993) and incorporated the aspects of the theory of endogenous growth to explain the process of convergence (or divergence). Barro (1991) analyzed convergence in 98 countries during 1960-1985 by studying the relationship between growth rates in per capita income, levels of per capita income, and initial level of human capital (proxied by school enrollment ratios in 1960). He found that, holding levels of human capital constant, the growth rate in per capita income was inversely related to the level of per capita income. Further, holding the initial level od per capita income constant, Barro found that there was a positive relationship between the growth rate of income and level of human capital. Therefore, in his study, convergence was evident only in countries with high levels of initial human capital and per capita income. This study carried Barros research a step forward by analyzing the effects of levels of human capital, openness, investment and government expenditures on the levels 128 Kravis, I. B., A. Heston, and R. Summers (1978b)." Real GDP Per Capita for more than One Hundred Countries. The Economic Journal, 88, pp. 215-242. Kravis, I. B., A. Heston, and R. Summers (1982). World Product and Income: International Comparisons of Gross Product. Baltimore, MD: The Johns Hopkins University Press. Kravis, I. B., Z. Kenessey, A. Heston, and R. Summers (1975). A System of International Comparisons of Gross Product and Purchasing Power. Baltimore, MD: The Johns Hopkins University Press. Krugman, P.R. and M. Obstfeld (1991). International Economics: Theory and Policy. New York: HarperCollins Publishers Inc. Kuznets, S. (1955). "Economic Growth and Income Inequality." The American Economic Review, 45(1), pp. 1-28. Livada, A. (1991). "Income Inequality in Greece: A Statistical and Econometric Analysis." Oxford Bulletin of Economics and Statistics, 53(1), pp. 69-82. Lucas, R.E., Jr. (1988). "On the Mechanics of Development." Journal of Monetary Economics, 22, pp. 3-42. Lucas, R.E. Jr. (1993). "Making a Miracle." Econometrica, 61(2), pp. 51-272. Mankiw, N.G., D. Romer, D.N. Weil (1992). "A Contribution to the Empirics of Economic Growth." Quarterly Journal of Economics, pp. 407-437. Morrisson, C. (1987). Domestic Income Distribution and the Structure of Foreign Trade. Mimeo, Paris University. Moss, C.B., H. Theil, and S.D. Deepak (1993). "The GDPs and Populations of the G-7 Countries, 1950-1990." International Working Paper Series IW93-26, Food and Resource Economics Department, University of Florida, Gainesville. Oshima, H. T. (1992). "Kuznets Curve and Asian Income Distribution Trends." Hitotsubashi Journal of Economics, 33, pp. 95-111. Papnek, G.F. and O. Kyn (1986). The Effect on Income Distribution of Development, the Growth Rate and Economic Strategy." Journal of Development Economics, 23, pp. 55-65. Paukert, F. (1973). "Income Distributions at Different Levels of Development: A Survey of the Evidence." International Labour Review, 108, pp. 97-125. APPENDIX F CHANGE IN INEQUALITY A time-differential of Their s inequality index is derived here that links changes in inequality to changes in income and population. If J is defined as in equation (5.1), then J can also be written as Â¡-1 = Â£ Pi to y* i-l (F.l) - k + In Â£ Nfi Â£ PlJn Z, j-1 /-I where ZÂ¡ is the GDP of country i. Taking partial derivatives with respect to ZÂ¡ we get _a/ dz, N, Ei z, ' E ",2, y-i dZ, 1 Â£ njzj J-1 = y{-Pt Pi (F.2) which is the covariance of the population levels and income shares. Similarly, we derive another expression with respect to population shares a/ din N, P, (= 1 -ln(5) J). (F.3) Therefore we finally arrive at an expression for dJ as E i-l + E Z, z. 1) 1 hi ^ J ) (ln M) Z (F.4) Writing this in time differential form we get 124 Figure 4.8 Country wise Relationship Between Levels of Observed Income (YÂ¡, i = 1 to 22) and Human Capital (HÂ¡, i=l to 22) in the 22 OECD Countries, 1955-1990 23 of per capita income. A multiple-variable indicator was used to estimate the level of human capital via a latent variable approach. The per capita income, estimated as a function of human capital (as a latent variable), was then analyzed for convergence with help of Theils inequality index. This study also analyzed the convergence behavior in the determinants of income. 10 though small in magnitude, traced along with the U-shaped profile propounded by Kuznets. Further, a simple quadratic form in terms of time fitted the data extremely well. Inequality indices for 1977 and 1988 were computed after adjusting for interstate price-level changes. These revealed large reductions in the indices and a virtual disappearance of the increase in inequality after 1978. A decomposition of the index showed that income changes accounted for most of the inequality change in each decade. Lastly, the six most influential states in terms of their impact on interstate inequality were tabulated for 1950, 1959, 1969, 1979, and 1989. Three of these states had below average income and three had above-average income. New York and California from the above-average group and Alabama and Mississippi from the below-average group contributed the largest components to interstate inequality. Moss et al. (1993) used the Summers and Heston (1993) data to analyze income changes in the G-7 countries (USA, Canada, Japan, UK, West Germany, France and Italy), for the period 1950 to 1988, using Theils measure of income inequality. They found that for the G-7 as a whole, per capita GDP increased almost threefold in that period, while the inequality among the seven countries declined dramatically. They concluded that Japans increasing affluence toward European levels was the reason for this dramatic decline in inequality. The income inequality among the G-7 countries declined almost uninterruptedly. Since the G-7 can be viewed as affluent, this evidence is in favor of convergence. Theil and Deepak (1993a, 1993b, 1993c, 1994) used Theils inequality index to measure income inequality across countries and regions during the period 1950-1990. 62 Table 4.3 (Contd) Year Italy Netherlands Norway Portugal Spain Sweden Switzerland Turkey UK Australia New Zealand 13 14 15 16 17 18 19 20 21 22 23 24 1955 331.69 387.65 369.76 302.72 304.64 356.34 379.20 305.88 366.63 377.34 384.82 1956 332.99 358.23 375.19 303.03 304.25 357.78 383.72 305.73 367.25 375.56 383.52 1957 338.74 403.86 385.55 303.43 305.68 361.66 388.59 307.68 386.70 375.39 389.24 1958 340.30 400.95 396.23 303.47 306.10 375.89 393.28 309.11 386.51 356.72 390.79 1959 346.20 411.51 408.68 307.95 310.10 382.47 400.10 308.38 394.62 397.66 392.38 1960 362.77 430.81 412.09 310.79 312.65 385.01 418.17 307.88 398.33 401.59 408.11 1961 394.38 443.53 419.48 310.45 309.40 454.59 427.01 312.21 428.33 407.55 412.65 1962 412.17 457.44 435.86 310.24 312.28 469.33 502.07 312.63 441.10 410.54 416.94 1963 420.84 469.24 459.55 310.32 315.20 515.63 499.15 314.19 448.74 416.22 420.43 1964 424.72 497.04 469.63 309.02 326.20 532.84 489.88 314.24 459.24 430.10 431.38 1965 435.90 507.57 477.49 310.06 322.89 550.21 510.01 318.24 472.68 439.84 443.82 1966 402.44 482.81 498.20 310.47 324.68 573.75 473.64 321.32 486.48 448.65 455.63 1967 422.03 499.82 465.19 308.62 327.69 609.66 476.95 320.98 456.49 437.98 435.13 1968 418.82 514.62 472.63 310.08 331.45 589.34 481.09 321.37 441.23 441.38 433.72 1969 412.48 536.25 485.50 310.52 343.25 612.96 489.60 320.43 463.59 453.87 445.53 1970 418.96 566.04 475.48 344.71 349.06 607.67 504.84 318.42 465.84 467.55 467.46 1971 433.78 577.41 498.15 320.11 350.46 611.03 516.44 329.93 479.56 486.13 491.89 1972 447.85 580.25 537.61 323.25 362.35 616.59 525.98 343.37 510.94 503.22 493.82 1973 465.31 595.38 547.16 330.08 342.92 619.65 547.24 343.63 518.19 514.77 503.62 1974 466.93 616.54 547.84 337.18 342.41 621.22 556.23 347.47 508.71 572.59 517.70 1975 452.12 632.23 560.07 350.53 350.36 624.59 549.00 351.19 512.18 579.36 511.79 1976 465.95 638.83 602.11 361.16 354.27 639.36 550.67 354.51 515.58 576.52 498.16 1977 469.70 641.12 606.20 358.85 351.87 659.77 557.14 357.76 507.12 533.92 497.65 1978 457.17 651.91 639.41 368.42 365.75 693.12 552.77 335.58 507.69 461.35 496.76 1979 485.58 657.63 646.36 365.01 367.76 704.35 555.29 334.37 510.46 573.66 488.09 1980 495.49 631.94 627.18 378.35 368.12 716.36 570.91 323.64 513.97 575.46 507.46 1981 494.27 625.45 614.41 384.84 369.16 716.65 566.32 325.69 504.40 580.05 513.52 1982 493.64 610.86 618.17 388.61 372.25 711.18 567.00 325.73 504.66 579.13 504.23 1983 482.30 585.12 631.95 375.45 375.32 689.90 573.76 331.59 505.21 585.15 502.49 1984 499.41 584.82 637.16 378.64 386.77 691.67 572.21 323.98 501.98 626.88 503.87 1985 500.03 591.31 643.34 381.79 388.56 681.16 569.92 321.14 500.43 629.52 486.85 1986 505.76 599.99 674.67 381.72 389.01 683.17 583.93 320.59 512.98 595.49 523.13 1987 512.33 618.00 694.03 389.90 395.06 683.35 583.05 316.55 519.16 567.55 533.16 1988 521.26 602.00 700.72 403.04 427.52 654.16 596.18 317.65 525.44 565.52 541.48 1989 527.79 594.71 725.45 410.67 442.02 694.70 598.70 317.49 525.93 581.28 579.73 J990 446.14 ...m2} 738.22 4WQ 447.71 715.51 337.99 536.10 -52192 607.98 44 The layout of this chapter is as follows: Section 4.1 introduces a general latent variable model, Section 4.2 gives the estimation procedures, section 4.3 describes the empirical research model, Section 4.4 gives the results of estimation, Section 4.5 tabulates the results from estimation of per capita income and analyzes the effects of human capital, openness, investment and government expenditures on income, and Section 4.6 concludes this chapter. 4.1 General Latent Variable Model The full latent variable model consists of a system of structural equations. These equations contain random variables, structural parameters, and sometimes nonrandom variables. The three types of random variables are latent, observed, and distur bance/error variables. The nonrandom variables are explanatory variables whose values remain the same in repeated random sampling (fixed or nonstochastic variables). The links between the variables are summarized in the structural parameters. The structural parameters are invariant constants that provide the "causal" relation between variables. The system of structural equations has two major subsystems: the latent variable model and the measurement model. 4,1,1 Structural Equations of the Model The first component of the structural equations is the latent variable model which encompasses the structural equations that summarize the relationships between latent variables: 64 capital was increasing over time implying that the level of human capital has been increasing over time for the 22 OECD countries. From columns 3 to 5 of this table, it can be seen that average per capita levels of openness, investment and government expenditures, respectively, were also increasing over time though at different rates. Figures 4.1 and 4.2 depict these patterns clearly. These results indicate that the per capita income could be expected to increase over time as evidence from literature had suggested (Barro, 1991; Mankiw et al., 1992). Further, comparing the estimated levels of human capital in the individual countries to the average level (from Table 4.3, Table 4.4, and Figure 4.3) revealed that six countries (USA, Canada, Denmark, Netherlands, Norway, and Sweden) had above average levels, nine countries (Japan, Austria, West Germany, Greece, Ireland, Italy, Portugal, Spain, and Turkey) had below-average levels, and seven countries (Belgium, Finland, France, Switzerland, UKD, Australia, and New Zealand) tracked the average closely. Tables 4.5 and 4.6 give the values of observed and estimated income for the 22 countries separately. Columns 2 and 3 of Table 4.7 give the average levels of per capita observed and estimated incomes (YOECD and YOECD) for the 22 countries. At a glance, this table reveals that (i) income (observed and estimated) was increasing over time, and (ii) the estimated income values fit the observed income values quite closely. Further, from this table and Figure 4.4, the estimated income is initially lower than the observed income. Towards the end of the period the estimated income is lower than the observed 73 A 1B55 1900 1 005 1970 1075 1990 1095 1990 roor 1955 1000 1905 1070 1975 1000 1996 1090 Figure 4.3 (Contd) 55 2(6) r$r/ + y A3rr/ a* where 4 was the variance-covariance matrix of Â£, Y is the variance in i\, and 0S is the variance-covariance matrix of x. For the purposes of estimation, the data were treated as deviations from their means. In this model, the variance parameter of H, normalized to one to facilitate estimation. This implied that H N(0,1) which eased the statistical inference of the human capital variable. The variance parameters of O, I, and G were treated as fixed as in regular regression analysis. Additionally, mu)-= 1 $12 *13 *14 hi $12 *23 *24 >31 $31 *33 *34 J41 $42 *43 *44 where 2 = *22 *23 *24 *32 *33 *34 $41 *43 4*44 was the matrix of variance-covariance between the observed O, I, and G. Therefore 4>2 = S2 from the sample variance matrix (Section 4.2). Further, the restriction that 4>n = 4 matrix looked like 2The model was estimated with and without the restriction that 0. The likelihood ratio test failed to reject the restriction at a=0.05 level of signifi cance. 98 t Belgium Denmark Y France Figure 4.8 (Contd) 71 1055 1800 1870 1855 1080 1805 1870 1875 1880 1805 1080 y*ar 1800 1905 1970 1075 1900 1985 1990 1955 1060 1905 1070 1975 1080 1905 1090 Figure 4.3 (Contd) 12 temperate and tropical zones, is used to summarize the data on individual countries. The seven regions account for nearly 90 percent of the inequality among these countries in each year. Another classification, based on the position of countries with respect to the European Union, is applied to 18 countries in Western Europe. Five journeys around the world were described; the main result was that affluence tended to decline when the traveler moved from temperate zones (in either the Northern or the Southern Hemi sphere) toward the Equator. Another topic considered was that of the G-7 countries, the populations of which are all concentrated in the temperate zones of the Northern Hemisphere. Also, attention was paid to Kuznets hypothesis of divergence-convergence in a cross-country context. Seale et al. (1994) relate regional growth and the inequality across countries for four regions of the noncommunist world: the North, Sub-Saharan Africa, South-Central Asia, and South-East Asia (Appendix E). Their results indicate strong convergence in the North and strong divergence in South-East Asia, whereas the case of South-Central Asia is unclear. In the case of Sub-Saharan Africa, there is growth with divergence, in agreement with Kuznets hypothesis, but thereafter negative growth with convergence, which is a digression from the hypothesis. 2.2 Studies Using Regression Analysis Wright (1978) examined the validity of Kuznets hypothesis versus the institutionalist hypothesis. The institutionalist hypothesis states that institutional structures and government policies are the chief determinants of income inequality. 107 5.4 Properties of Inequality Index Anand and Kanbur (1993) present a formalization of the Kuznets process, a general analysis of distributional change under this process, and derive the functional forms of and conditions for a turning point in the inequality-development relationship for six commonly used indices of inequality. They used data on a cross-section of 60 developing and developed countries to estimate the functional form appropriate for each index. They divided the countries into regions or sectors. Assuming that during the course of development, the population is seen as shifting from a low-mean income and low-inequality sector to a high-mean income and high-inequality sector, the sectoral mean incomes and inequality levels remaining unchanged over time, they found that the estimated functional forms on the cross-section data rejected the formalization of the Kuznets process. If the Kuznets process is being invoked as the theoretical underpinning of the inequality-development relationship, the right index must be used with the right functional form for estimation purposes. Four properties for a consistent inequality measure are (Livada, 1991): symmetry, mean independence, population homogeneity, and the Pigou-Dalton condition. Symmetry is equivalent to saying that the social aspects of a country are irrelevant in measuring inequality. Mean independence states that if all incomes are raised or lowered in the same proportion, the inequality measure remains invariant. This means that inequality measures depend on relative rather than absolute incomes. According to population homogeneity the inequality does not change when r populations (each containing n individuals) with identical income distributions are combined into a single population. 13 Wright used a gini coefficient inequality measure to calculate the inequality in GDP per capita among 56 countries. He concluded that the cross-sectional data demonstrated that (1) inequality varies among countries at all levels; (2) variation in and level of inequality are higher among LDCs; and (3) an institutionalist variable in regressions explains far more income variation among countries than income levels. Further, the divergence- convergence hypothesis lends itself to the conservative argument that redistribution is growth reducing, while growth itself will take a country to the declining side of the "parabola of skewness" more quickly. In the institutionalist view, reduction in inequality depends on modifications in the institutions and policies which generate it. Bomschier (1983) outlined explanations of international differences in personal income distribution that were formulated within the "world economy" and the "level of development" paradigm. He constructed the Gini index of personal income inequality for 72 countries using Ballmer-Cao and Schiedegger (1979) data. He concluded that income inequality does not vary directly with development, but with surplus, power and the structural position within the world economy. Thus less developed countries do not automatically decrease their inequality in the process of development. Ram (1988) studied the validity of Kuznets hypothesis by extending his study to cover several countries. His hypothesis stated that intercountry inequality across nations would first increase with secular economic growth, then start to decline at some point. His sample consisted of 32 countries (24 less developed countries (LDCs) and 8 developed countries (DCs)) which were market economies from the Summers and Heston (1984) data. Average per capita world GDP was used as a proxy for the level of 77 Table 4.6 (Contd) Year Italy Netherlands Norway Portugal Spain Sweden Switzerland Turkey UK Australia New Zealand 13 14 15 16 17 18 19 20 21 22 23 24 1955 5514.50 6761.07 6879.14 3496.76 4154.43 7108.71 7561.72 3414.31 6425.34 7567.93 7558.55 1956 5616.18 7047.60 6901.59 3541.06 4273.60 7187.11 8070.87 3393.72 6428.86 7098.84 7356.73 1957 5759.19 7145.70 7023.27 3662.69 4347.88 7400.04 8292.34 3452.85 6470.64 7138.92 7548.77 1958 5839.59 6508.60 7118.70 3647.72 4437.20 7423.03 7270.51 3573.08 6356.64 7580.42 7386.45 1959 6055.31 6758.36 7029.04 3677.37 4195.03 7713.27 8003.70 3521.09 6535.10 7766.33 7406.19 1960 6442.15 7370.55 7091.86 3842.95 4428.09 8142.62 8941.58 3497.43 6859.13 8093.10 7724.47 1961 6776.73 7479.49 7335.40 3936.88 4744.29 8275.88 9879.31 3535.21 6944.07 7427.64 7948.30 1962 7045.08 7496.60 7518.77 4044.50 5037.56 8484.43 10049.39 3559.44 6867.64 8044.59 7727.73 1963 7280.21 7540.08 7818.13 4051.94 5183.93 8776.99 10202.12 3619.89 6977.25 8298.72 8039.51 1964 7073.67 8286.94 8047.35 4192.83 5369.73 9359.02 10650.08 3615.21 7505.48 9141.70 8480.51 1965 6862.33 8298.91 8490.24 4344.59 5695.40 9694.52 10383.50 3607.71 7540.31 9047.85 9035.77 1966 7026.56 8446.75 8763.60 4371.80 5956.59 9707.09 10352.28 3783.92 7569.48 9237.11 9373.24 1967 7415.75 8679.98 9267.23 4551.64 5981.79 9820.19 10538.43 3792.00 7842.00 9359.99 8423.46 1968 7725.67 9076.96 8927.22 4663.85 6154.58 10005.72 10613.29 3857.47 8048.96 10072.69 7855.90 1969 8080.35 9322.70 8773.81 4697.28 6550.74 10495.52 11000.04 3871.74 8022.79 10094.58 8451.74 1970 8285.84 9858.17 9703.44 5133.54 6564.79 11195.16 11968.42 3971.13 8112.43 10313.45 8635.92 1971 8099.61 9854.17 10290.76 5353.00 6488.51 10799.98 12288.69 4022.07 8151.34 10055.65 8873.53 1972 8188.95 9620.69 9792.39 5674.61 6926.45 10739.39 12281.15 4018.74 8206.72 9960.23 9102.80 1973 8749.94 9961.44 10575.86 6050.50 7326.57 10806.09 12471.45 4111.00 8898.46 10710.92 10378.71 1974 9094.63 10031.39 11434.80 6023.27 7704.65 11538.59 12733.36 4330.91 8739.38 10375.24 11628.59 1975 8082.09 9388.14 11898.73 5348.78 7520.06 11968.17 10492.99 4575.98 8402.93 10265.50 9477.74 1976 8719.65 9692.64 12698.49 5499.49 7522.21 12012.85 10345.06 4635.13 8808.67 10668.22 9654.53 1977 8582.75 9953.71 12620.92 5937.58 7377.18 11193.17 10510.39 4753.86 8833.51 10157.11 9173.52 1978 8659.04 10099.50 11452.81 6080.71 7181.22 10659.18 10886.45 4401.60 8935.18 10924.31 8669.24 1979 9040.00 10094.41 11836.86 6338.60 7117.27 11524.19 11772.88 4373.65 9105.01 10836.91 9161.81 1980 9614.07 10059.33 12499.27 6646.20 7231.59 12007.89 12898.39 4493.28 8561.56 11264.17 8887.32 1981 9186.62 9236.36 12431.43 6720.56 6932.34 11323.30 12464.35 4550.63 8275.17 11672.49 9615.32 1982 9102.17 9197.88 12551.77 6866.36 7012.02 11349.49 12082.08 4472.75 8559.19 10360.03 9792.81 1983 8966.55 9399.59 12512.59 6361.93 6939.45 11364.74 12315.54 4446.91 8916.61 11041.76 10009.04 1984 9382.49 9711.55 13562.74 6030.39 6860.76 11867.01 12676.62 4447.12 9217.27 11559.96 10643.78 1985 9516.06 10044.66 13426.96 6034.15 6991.38 12532.75 13094.06 4573.56 9326.63 11868.55 10347.82 1986 9561.95 9839.58 14580.95 6246.56 7358.05 12415.50 14069.76 4711.67 9413.30 11481.07 10231.82 1987 9830.04 9478.05 14141.08 6313.00 7943.62 12770.99 14695.97 4782.81 9799.56 11820.12 10206.83 1988 10188.1 9696.20 13655.62 6407.80 8555.98 13139.43 15114.09 4678.83 10445.90 12812.30 10172.23 1989 10385.1 10488.43 13175.96 6635.07 9218.02 13906.96 15871.16 4583.14 10691.44 12842.90 11339.54 1990 10422.5 10779.49 , Â¡2649.94 6878.67 9597.00 13863.07 16119.85 4793.40 10450.70 11730 73 11109.94 37 and government (G) expenditures at 1985 international prices. The growth rates for their components from the national accounts data and their change in international prices of the components between 1975 and 1985 or 1980 and 1985 were used. The changes in international prices were estimated from the benchmark estimates and the deflator for the numeraire country, the U.S. The 1975 and 1970 data were also re-analyzed. The May 1990 national accounts data were used for these revisions. The Geary-Khamis method was then used to aggregate the data. After the aggregation and re-estimations of the benchmark data, the non- benchmark countries RGDP per capitas were estimated. A post-allowance PPP was computed by dividing the national currency by the PPP implicit in the post adjustment index. A structural relationship was found in the benchmark countries between PPP and its post-allowance PPP. This relationship was used to estimate non-benchmark countries missing PPPs from their post-allowance PPPs. There were 81 benchmark countries and 57 non-benchmark countries that had to be estimated. The authors performed 12 different regressions for the benchmark studies and then these were used to obtain the non-benchmark estimates. Geary-Khamis method was used to aggregate the data resulting in consistent national absorption for all countries. It was still apparent that RGDP for poor and African countries were less accurate than estimates for rich countries. 15 inequality increased since 1960, there was a noticeable deceleration in the rate of increase of inequality. Ram (1989b) attempted to study the effect of education on income inequality in LDCs. Firstly, upon reviewing the literature in this area he found contradicting evidence of the influence of education on inequality. Chiswick (1971, 1974), Chiswick and Mincer (1972), Chenery and Syrquim (1975), and Ahluwalia (1976) contended that education did influence income inequality, while Fields (1980), Psacharopoulos and Woodhall (1985), and Morrisson (1987) concluded that there was no clear evidence that education had an effect on income inequality. These contradictory results prompted Ram to conduct his study using two sets of data that yielded contradictory results. His study concluded that the effect of education on income inequality was ambiguous. He concluded that the nature of the data could be a major factor for the contradictory and inconclusive nature of the results. Barro (1991) used the neoclassical growth models developed by Solow (1956), Cass (1965), and Koopmans (1965), and the recent theories of economic growth as proposed by Lucas (1988), Rebelo (1990), Romer (1989), and Becker, Murphy, and Tamura (1990) as a guide to test convergence in real per capita GDP for 98 countries during the period 1960 to 1985. His results suggested that poor countries tend to catch up with rich countries if the poor countries have high per capita human capital in relation to their level of per capita GDP, but not otherwise. He observed that countries with high human capital have low fertility rates and high ratios of physical investment to GDP. 30 measurement. The difference is that the ratios in the EKS method are unweighted, unlike in time-series measurement. The general representation of the mini-Laspeyres index is * P n pu 1Jm (3.3) where c and d are two different countries and m is the number of characteristic items in category a. Similarly, the mini-Paasche index is obtained as * P ny* M *tcj v* (3.4) This method does not pick one base country, and thus, a matrix of mini-Laspeyres indices is created between countries with a diagonal of ones. The same is true for the mini-Paasche indices. Once the mini-Laspeyres and mini-Paasche indices are computed, the mini-Fisher price indices are constructed. The latter indices are the unweighted geometric means of the former two indices Ki (i O'* (3-5) The matrix of mini-Fisher indices is not transitive, and the EKS method is applied to make them so. The equation for the EKS method is 91 y Germany Yr y Ireland VNT r Greece Ymr y Italy Figure 4.6 (Contd) 104 (1990) who concluded that human capital accumulation was vital to the growth of an economy. Table 4.8 Summary of Cross-Country Analyses for the 22 OECD Countries, 1955-1990 Y above Y Y below Y Tracks Yngr-p 6; above Hqecd Denmark Norway Sweden USA Canada Netherlands H; below Hqecd Germany Greece Ireland Italy Portugal Spain Turkey Austria Japan Tracks Hqecd Australia Finland France Switzerland Belgium New Zealand UK 68 USA ia5; nao isas wo is?s isao isas ns Canada Austria CHAPTER 5 INEQUALITY IN THE OECD COUNTRIES Historically, inequality measures have been used to study convergence (or divergence). Basic statistical tools such as graphs (e.g., histograms and Lorenz curves), measures of dispersion (e.g., variance and coefficient of variation), and indices (e.g., gini coefficient and Their s inequality index) have been used to analyze income inequality between and among groups. Using these tools, researchers have tried to determine if two income groups grew closer (convergence) or moved away from each other (divergence). 5.1 Graphical Inequality A histogram may be used to depict a frequency distribution of incomes of people at various levels. The Lorenz curve depicts a relationship between cumulative shares of income (on the vertical axis) against cumulative population shares (on the horizontal axis). Since these shares vary between 1 and 0, a person with all the income would be along the vertical axis, and if incomes were equal then the curve is a 45 diagonal. 105 51 Hi = I* C, y = Aytij + e (4.14) x = l where x is a perfect measure of Â£ and only one latent variable, rÂ¡u is present. Then rj, is directly affected by one or more x variables, and it is indicated by one or more y variables. Identification of the MIMIC models that conform to (4.14) follows if p (the number of ys) is two or greater and q (the number of xs) is one or more, provided rÂ¡Â¡ is assigned a scale. Therefore, the MIMIC rule for the model in (4.14) above with p > 2 and q ^ 1 is a sufficient condition for identification but not a necessary one. 4.2 Estimation The hypothesis for the generalized latent variable model is E = E(0). Given the sample covariance matrix of the observed variables, S, 0 has to be chosen such that E(0) is close to S. Theoretically, this means that we need to minimize E(0) to get consistent estimators of 0. Three such minimizing fitting functions are: the maximum likelihood (ML) function; the unweighted least squares (ULS) function; and the generalized least squares (GLS) function APPENDIX E FOUR REGIONS REVISITED The 18 European countries in the North are Austria, Belgium, Denmark, Finland, France, Germany (W), Greece, Iceland, Ireland, Italy, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, UK. The 37 countries of Sub-Saharan Africa are Angola, Benin, Botswana, Burkina Faso, Burundi, Cameroon, Cape Verde, Central African Republic, Chad, Congo, Ethiopia, Gabon, Gambia, Ghana, Guinea, Guinea-Bissau, Ivory Coast, Kenya, Madagascar, Malawi, Mali, Mauritania, Mozam bique, Namibia, Niger, Nigeria, Rwanda, Senegal, Sierra Leone, Somalia, Swaziland, Tanzania, Togo, Uganda, Zaire, Zambia, Zimbabwe. The five countries of South- Central Asia are Bangladesh, India, Myanmar, Pakistan, Sri Lanka. The eight countries of South-East Asia are Hong Kong, Indonesia, Malaysia, Papua New Guinea, Philippines, Singapore, Taiwan, Thailand. 123 45 n Bn + r{ + c (41) where 77 is an m x 1 vector of latent endogenous random variables; Â£ is an n x 1 vector of latent exogenous random variables; B is the m x m coefficient matrix showing the influence of the latent endogenous variables on each other; r is the m x n coefficient matrix for the effects of Â£ on rÂ¡, and contains no zero elements. The matrix (I B) is nonsingular. The diagonal of B is always zero, f is the disturbance vector that is assumed to have an expected value of zero [ E(f) = 0 ], homoscedastic, nonautocorrelat- ed, and which is uncorrelated with Â£. The second component of the structural system is the measurement model: y V + e (4.2) x = A,Â£ + 6 (4.3) where y (p x 1) and x (q x 1) vectors are observed variables. Aj(p x m) and Ax (q x n) are the coefficient matrices that show the relation of y to tj and x to Â£, respectively, e (p x 1) and 5 (q x 1) are the errors of measurement for y and x, respectively. The errors of measurement are assumed to be uncorrelated with Â£ and f and with each other. The expected value of e and 5 are zero. To simplify matters rj, Â£, y, and x are written as deviations from their means. Further, Â£ cannot influence any y directly; if the x and y vectors contain measurement errors, these errors cannot influence one another directly. 49 be greater than or equal to the number of unknown parameters in 0. In other words, the necessary but not sufficient condition of identification is: / < (p + q) (p + q + 1) (4-13) 2 The nonredundant elements of E = E(0) imply (p + q)(p + q + l)/2 equations. If the number of unknowns in 0 exceeds the number of equations, identification is not possible. Two-Step Rule Under this rule (Bollen, 1989), the first step is to treat the model as a confirmato ry factor analysis. This implies that the original y and x are treated as x variables, and the original rj and Â£ are treated as Â£ variables. The only relationships between latent variables that are of concern are their variances and covariances (<Â£). In short, B, T, and 'k elements of equation (4.1) are ignored. This model is identified if a unique solution exists for the structural parameters Ax, 4>, and 05 such that no vectors 7! and y2 exist that make E(0,) = E(02) unless 0, = 02. If the model is identified at this juncture then we move to the next step. The second step examines the latent variable equation of the original model given by (4.1) and is treated as a structural equations model with observable variables having no measurement error. Next it is determined whether B, T, and Â¥ are identified ignoring the measurement parameters considered in the first step (Ax, 4, and 04). This is achieved by verifying the identification of equation (4.1) using the order and rank conditions prescribed for systems of equations (Bollen, 1989). The order condition is 52 = log|S(0)| + tri 52Tl(0) > log|S| (p+i) Fou = (1/2) ir{[/- 22(0)5 (4.15) Fuu = (1/2) ft* {[5 22(0)f). Each of these functions is minimized with respect to 8. Further, the estimated values of the four explanatory variables are obtained by minimizing the weighted squared errors as proposed by Bartlett (1938): (4.16) The estimated or predicted per capita income is computed as: (4.17) s = n. 4.3 Empirical Model The research model in question had one endogenous variable (per capita income (Y)), one exogenous latent variable (human capital (H)), and three exogenous variables (investment expenditure (I), government expenditure (G), and international openness (O)). Income was the real gross domestic product per capita, international openness was measured as the real per capita level of exports and imports, and government and investment expenditures were measured at real per capita levels (Chapter 3, Section 3.4). Income, international openness, investment and government expenditures were assumed to be observed without error for the purposes of estimation. I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Z Z* James L. Seale, Jr., Cha Professor of Food and Resource Economics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Charles B. Moss, Cochair, Associate Professor of Food and Resource Economics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Max R. I^angham, Professor of Food and Resource Economics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Gary'F. Fairchild, Professor of Food and Resource Economics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Douglas G. Waldo, Associate Professor of Economics 54 [Yi Y* Y3 Y4] (4.18) where income was assumed to be observed without error (rÂ¡=y). The measurement model for estimation, similar to equation (4.3), was PE Xj 0 0 0 *1 CN x2 0 0 0 ES x3 0 0 0 H ET x4 0 0 0 V + 64 I O 0 0 m 0 G 65 / oox6o G 0 0 0 x7 67 (4.19) where the matrix on the left-hand side consisting of PE, CN, ES, ET, O, I, G vectors corresponded to x. Ax was the first matrix on the right side with factor loadings wherein which X5, Xg, and X7 were normalized to a value of one for purposes of estimation. Â£ corresponded with the matrix of exogenous latent variables wherein which Â£, was H and Â£2, Â£3, and Â£4 were assumed to be directly observable as O, I, and G, respectively. Therefore, 55 = 86 = ^ = 0 for estimation, f was the vector of errors in rj(=y). From equations (4.6) to (4.8) and equation (4.10), we could derive the implied covariance matrix for the observed y and x variables as a function of the model parameters: 90 i Denmark rmr France Ymmr Figure 4.6 (Contd) 106 5.2 Inequality via Measures of Dispersion The variance of n observations or income values, yÂ¡, with mean p can be written as <-) (yrvt n The square root of the variance is the standard deviation which could also be used as a measure of inequality. Dividing the standard deviation by the mean (p.) yields the coefficient of variation. 5.3 Inequality Indices The Gini coefficient (G) is computed based on the Lorenz curve G -4- \y, -y,\. 2n \i m j-i In graphical terms, the Gini coefficient measures the ratio of the area between the diagonal and the Lorenz Curve to the total area beneath the diagonal. Theils income inequality index or entropy index is based on an information measure developed by Shannon (1949). Shannons measure determines the information content in any given signal. Theil (1967) expands on this tool to measure change in the posterior distribution associated with a given signal. In terms of income inequality, the objective is to determine whether the information regarding a country can be used to predict the level of income. This index is described in detail later in this chapter. Germany re I and 19/000 10,000 5.000 Y 19,000 10,000 5.000 Greece Ymr y Italy Figure 4.5 (Contd) 103 the relationship between observed income and human capital for the 22 countries individually. This analysis showed that all countries showed clear evidence of a positive relationship between income and human capital. The analyses of the individual countries (Table 4.8) revealed that four countries (United States, Denmark, Norway, and Sweden) were the only ones that had above- average human capital and income; six countries (Greece, Ireland, Italy, Portugal, Spain, and Turkey) had below-average human capital and income; and only three countries (Belgium, UK, and New Zealand) had levels of human capital and income that tracked the average levels reasonably well. 4.6 Summary From the analyses in Sections 4.4 and 4.5 above the major points to note were: (i) the data fits the model reasonably well; (ii) all four determinants of income had positive effects; (iii) both observed and estimated income for the 22 OECD countries was increasing over time; (iv) estimated income and human capital have a significant positive relationship; (v) human capital had the greatest positive effect on income; (v) the income elasticity with respect to human capital was positive and greater than those with respect to openness, investment and government expenditures; and (vi) all four determinants depict an increasing trend. Therefore, the results from this study imply that human capital contributes positively to economic growth and is a key determinant of income. These results correspond to the contemporary evidence presented by Barro (1991), Mankiw et al. (1992), Tallman and Wang, (1992), Lucas (1988, 1993), and Romer 21 Thus, the evidence from the inequality studies (Theil, 1989; Theil and Deepak, 1993a, 1993b, 1993c, 1994; Theil and Seale, 1994; Seale et al., 1994; Weatherspoon, 1993; Weatherspoon et al., 1994) seems to suggest that poor economies are diverging, rich economies are converging, and there is inconclusive evidence in certain cases. Neoclassical growth models (Barro, 1991; Barro and Sala-i-Martin, 1992; Mankiw et al., 1992) favor convergence and endogenous growth models (Lucas, 1988 & 1993; Romer, 1994; and Tamura, 1991) lean toward ambiguity. The OECD countries were chosen for two main reasons: the evidence from the literature supports convergence (or divergence) for these countries and the availability of reliable data. In summary, the research by Theil and Deepak (1993a, 1993b, 1993c, 1994), Moss et al. (1993), Seale et al. (1994), and Theil and Seale (1994) determined that during the period 1950-1990 the income of the G-7, non-EU, and EU Center countries increased while the inequality declined almost uninterruptedly favoring the convergence component of Kuznets hypothesis; the income for EU Periphery countries increased but inequality fluctuated during 1950-1970 without a clear trend and then decreased showing evidence of transition from divergence to convergence components of Kuznets hypothesis; the North, consisting of 22 countries, also showed evidence of convergence and in the case of the countries in South, the results were inconclusive. In the process of analyzing convergence across 98 countries, Barro (1991) concluded that the evidence from 20 OECD countries was stronger because these countries had higher per capita incomes and had similar basic economic and political institutions. Further, Weatherspoon (1993) and Weatherspoon et al. (1994) found that, in the long run, the G-7 118 expenditure. Further, the inequalities in the determinants were slowing down the rate of convergence in terms of income for these countries. Thus, the results from this study present an encouraging picture for ongoing research in this area of international economics. A multiple indicator for the level of human capital variable had not been previously estimated. Though international openness was also a good candidate for being measured as a latent variable, the lack of theoretical and quantifiable information on feasible indicators or proxies for this variable prompted its use as an observable variable for the purposes of this study. Though data are scarce, reliable and lengthy information on investments in research and development, science and technology, womens education and development, and health and environmental care over time and across countries, along with factors for international openness, may provide opportunities to further extend what has been accomplished in this study. 94 y Australia y New Zealand lar Figure 4.6 (Contd) 57 variable), international openness, investment and government expenditures had positive and statistically significant effects on income for the 22 OECD countries. These results complied with the theoretical underpinnings from basic macroeco nomic and growth theories which indicate that growth in income was positively correlated with accumulation of capital and growth in international trade. The greatest positive effect on income was imposed by the level of human capital implying that human capital was a key determinant of income in the 22 OECD countries. This result tallied with the results put forth by Barro (1991), Mankiw et al. (1992), Tallman and Wang (1992), and Lucas (1988, 1993). The positive effect of international openness was as predicted by Romer (1990) who proposed that growth in international trade yielded positive dividends for economic growth. Mankiw et al. (1992) found that, in an augmented Solow model, a higher savings rate led to higher income and higher level of human capital. Barro (1991) found that growth in income was positively related to investment expenditures. Thus, the positive effects of investment and government expenditures were not surprising. Further, the elasticities in average income (Column 5) with respect to average levels of human capital, openness, investment and government expenditures are all positive. This also lends support to the above analysis that income is positively influenced by all the four factors and especially human capital followed by investment expenditure, government expenditure, and openness in that order. 66 H, Oj I, G Figure 4.2 Average Level of Human Capital (HOECd), International Openness (0OECD), Investment (Ioecd) and Government (GOECd) Expenditures in the 22 OECD Countries, 1955-1990 28 The three categories of data used for classification were GDP or expenditure data, price data for each item for which a price could be identified, and quantity data for the items for which prices could not be identified. The expenditure data were obtained from the U. N. national accounts data. Once the base data were collected, there were steps and alternatives to calculating purchasing power parities (PPPs) for each country. 3.1.2 Purchasing Power Parities Purchasing power parity (PPP) is the number of currency units required to buy goods equivalent to what can be bought with a unit of currency of the base country (Kravis et al., 1982). From the several methods that can be used to calculate PPPs, the most frequently used by the ICP were the country-product-dummy (CPD) and Elteto- Koves-Szulc (EKS) methods. These two methods are identical if all the prices for every item in each country are available. In that event, the PPPs obtained from both methods are geometric means of all the prices in the detailed category a for country c (Kravis et al., 1975). The geometric mean in country c is obtained as A 1, (3.1) gu; (jj V Â¡-i-v" l-l where PÂ¡ c is the price of the item i in country c and m is the number of items. 89 USA Y* Japan * Canada rr * Austria tmr 26 3.1.1 International Comparison Project Phase I of the international comparison project (ICP) began with a pilot study in 1967, initiated by Kravis et al. (1975), at the University of Pennsylvania, which resulted in data collection for 10 countries for 1970 (Table 3.1). Two successive volumes, Phase II and Phase III, were published in 1978 and 1982. Phase II compiled data for an additional six countries and corrected the data from Phase I. Phase III compiled data, for 1975, for an additional 18 countries taking the count to 34 countries. Phase IV of this project, with 60 countries in 1980, was completed in two stages by the Statistical Office of the United Nations Secretariat (1985 and 1987). However, seven countries from Phase III withdrew from the study during this period. Therefore, there were 10, 16, 34, and 60 countries, in Phases I, II, III, and IV, respectively. In the first stage of the ICP, a classification system for gross domestic product (GDP) was developed which divided each countrys GDP into numerous detailed categories. GDP data were then collected for each category. Further, prices and quantities for each item within a category were also gathered. The classification system follows the scheme proposed by the system of national accounts (SNA). This classification system was improved upon to facilitate international comparability of the data (Kravis et al., 1975). In Phases I and II, there were a total of 153 detailed categories: 110 for consumption, 38 for capital formation, and five for government. Phases II and IV have 151 detailed categories: 108 for consumption, 38 for capital formation, and five for government. 16 Barro and Sala-i-Martin (1992) used the neoclassical growth models developed by Ramsey (1928), Solow (1956), Cass (1965), and Koopmans (1965) to test for convergence across the 48 contiguous U.S. states using personal income since 1840 and gross state product since 1963. Their results indicated that the 48 states provided clear evidence of convergence, but the results could be reconciled quantitatively with the neoclassical model only if diminishing returns to capital set in slowly. The results for per capita GDP from a broad sample of countries were similar if a set of variables that proxy for differences in steady-state characteristics were held constant. Mankiw et al. (1992) examined whether the Solow growth model was consistent with the international variation in the standard of living. They showed that an augmented Solow model that included accumulation of human capital provided an excellent description of the cross-country data. While testing the convergence-divergence hypothesis, they concluded that holding population growth and capital accumulation constant, countries converge at a rate the augmented Solow model would predict. 2.3 Studies Using Models of Economic Growth The research on economic growth predominantly focuses on long-run economic progress, and the dominant sources are the neoclassical growth models developed by, to name a few, Solow (1956), Swan (1956), Ramsey (1928), Cass (1965), and Koopmans (1965). In general, the unexplained portions of growth were attributed to the area of technical progress which was treated as exogenous by the neoclassicalists. These models assumed that output can be produced using combinations of physical capital and labor in 70 Figure 4.3 (Contd) 116 capital, this study used a multiple indicator, constituted by per capita levels of public expenditure on education, consumption of newsprint, and shares of population with secondary school and university education, for measuring human capital. Further, this study used the Theil inequality index to analyze convergence in the OECD countries and Barro used the relationship between growth rates and levels of income and human capital. This study also differed from Weatherspoons in terms of methodology. While Weatherspoon used cointegration analysis, this study used a latent variable approach to analyze the effect, if any, of four factors of economic growth: human capital, internation al openness, investment and government expenditures on income convergence. Income was estimated as a function of human capital, investment expenditure, government expenditure, and international openness drawing upon the theoretical underpinnings from standard macroeconomic theory and from recent developments in the theory of human capital accumulation. The scope of the study was to cover 22 OECD countries. The OECD countries were chosen based on the existing evidence of income convergence and the availability of relevant data for these countries. Estimating income as a function of human capital prompted the use of a latent variable model since human capital was not a directly observable variable. The classical econometric treatment assumes that the observed variables are measured without error. Latent variable models incorporate measurement error in the observed variables into the process of estimation. Cointegration analysis requires time-series data over long periods of time and thus was not a very feasible methodology for this study. 50 a necessary condition which requires that the number of variables excluded from the equation to be identified are at least p-1. The rank condition is necessary and sufficient for identification and requires that the ith equation, of a system of equations, is identified if the rank of CÂ¡ is equal to p-1, where c = [(I-B) | -T]. If the first step shows that the measurement parameters are identified and the second step shows that the latent variable model parameters are also identified, then this is sufficient to identify the model. This is so since the first step establishes that all parameters in the measurement model are identified, including the covariance matrix of the latent variables. The second step establishes whether B, T, and Â¥ are functions of the identified covariance matrix of the latent variables. Since this is a sufficient condition for identification, a model could fail to meet it and still be identified. However, this rule exemplifies the possibility that constraints on the latent variable relations can assist the identification of measurement parameters such that even if a model failed the two-step rule, it could still be possible to find unique solutions for the unknown parameters. MIMIC Rule The models referred to as MIMIC (Bollen, 1989) contain observed variables that are Multiple Indicators and Multiple Causes of a single latent variable. However, the MIMIC rule applies only to models in a certain form (as below) making its applicability narrow in range. The equations in this model are: 101 * Sweden Y Turkey Y Switzer land Y UK H M Figure 4.8 (Contd) 76 Table 4.6 Levels of Estimated Income (YÂ¡, i=l to 22) in the 22 OECD Countries, 1955-1990 Year USA Canada Japan Austria Belgium Denmark Finland France Germany Greece Ireland 1 2 3 4 5 6 7 8 9 10 11 12 1955 8797.69 7116.97 4038.78 5327.55 5671.12 6032.36 6374.98 5683.44 6628.47 3531.65 4623.24 1956 8637.34 7824.74 4148.52 5207.65 5946.81 6263.32 6490.69 6121.38 6694.42 3639.48 4398.68 1957 8436.04 7544.98 4307.19 5421.78 5934.50 6506.80 6454.31 6249.57 6799.50 3713.47 4248.08 1958 8218.77 7153.03 4255.03 5519.17 5648.53 6292.25 6357.49 6315.97 6894.39 3790.09 4227.04 1959 8628.63 7239.31 4429.87 5600.65 5936.59 7144.40 6721.90 6402.74 7326.36 3856.12 4575.81 1960 8483.06 7050.75 4755.62 6234.38 6190.28 7613.40 7347.89 6742.16 7772.61 3947.30 4557.86 1961 8521.46 7050.09 5273.65 6370.57 6522.87 7796.35 7725.27 6932.05 7955.89 4147.62 4723.25 1962 8935.43 7316.07 5271.99 6320.02 6693.47 8272.63 7637.64 7174.07 8138.33 4148.63 4905.94 1963 9133.11 7418.17 5581.54 6418.88 6812.69 7867.55 7438.75 7335.22 8148.59 4354.87 5074.60 1964 9332.10 7721.68 5944.82 6831.17 7371.19 8922.02 7872.45 7782.97 8631.33 4638.66 5288.94 1965 9856.74 8231.13 5957.18 6908.21 7410.78 9235.22 8457.64 7917.41 8968.40 4899.57 5504.39 1966 10299.42 8642.58 6295.01 7264.04 7709.33 9219.50 8445.61 8252.59 8854.63 4802.35 5334.12 1967 10331.44 8437.64 6862.08 7269.07 7789.29 9410.94 8286.44 8457.28 8467.51 4856.57 5357.39 1968 10532.81 8618.33 7531.19 7443.00 7893.71 9647.26 8272.43 8750.92 8977.94 5035.37 5780.74 1969 10636.95 8995.37 8094.23 7690.30 8364.08 10436.75 8887.99 9331.40 9571.26 5470.91 6275.80 1970 10203.61 8879.80 8851.45 8195.68 8744.25 10588.66 10112.14 9611.99 10022.87 5707.66 6296.25 1971 10547.50 9205.15 8838.86 8342.88 8725.22 10695.33 10128.13 9811.41 10035.28 5870.57 6383.02 1972 10819.83 9474.53 9262.94 8763.83 8817.44 11167.47 9979.98 10070.31 10222.53 6170.95 6739.54 1973 11236.85 10063.55 9930.74 9174.50 9457.27 11697.15 10612.11 10644.95 10495.48 6933.55 7227.47 1974 10873.34 10643.88 9536.70 9358.21 10062.62 11292.97 11927.11 10790.15 9898.08 6254.53 7311.30 1975 9925.54 10595.93 9161.95 8856.20 9359.77 10365.30 11790.14 9810.48 9569.17 6301.13 6675.96 1976 10536.42 10883.38 9357.72 9467.20 9835.78 11502.90 10532.63 10483.50 10311.68 6358.53 7080.00 1977 11149.81 10963.09 9512.81 9796.58 9897.80 11375.29 10394.50 10533.35 10328.23 6391.36 7556.63 1978 11651.37 11043.70 9836.68 9553.50 10094.09 11341.32 9957.54 10500.77 10603.72 6584.79 7946.65 1979 11524.01 11791.15 10292.94 9990.30 10267.71 11673.53 11196.24 10934.63 11394.51 6857.86 8509.57 1980 10894.44 11922.47 10258.34 10442.76 10605.87 11036.71 12143.36 11053.39 11350.51 6713.87 7962.20 1981 11217.49 12640.43 10409.11 9974.28 9685.97 10338.71 11730.88 10656.76 10760.96 6370.28 8208.75 1982 10297.43 11176.82 10368.57 9584.59 9735.14 10872.61 12005.92 10852.26 10453.89 6224.60 8339.24 1983 10716.03 11505.48 10207.74 9565.95 9426.59 10877.70 12084.13 10472.86 10825.97 6230.87 7930.94 1984 12233.18 12068.64 10547.37 10109.63 9865.05 11701.00 12097.55 10438.05 11078.58 6155.06 7981.83 1985 12341.98 12587.89 10923.03 10279.05 9596.10 12315.43 12218.77 10596.14 11095.94 6381.61 7739.18 1986 12431.93 12995.84 11149.17 10333.99 9737.85 13001.85 12098.57 10993.89 11303.91 6152.73 7609.92 1987 12713.03 13706.89 11673.59 10465.21 10165.98 12496.88 12614.49 11340.79 11405.95 5922.22 7403.36 1988 12901.95 14384.36 12683.65 10963.91 10864.08 12157.62 13618.65 11851.40 11920.22 6357.50 7361.64 1989 13126.17 14823.41 13458.70 11311.00 11700.46 12447.88 15031.49 12241.81 12404.95 6414.57 8116.47 1999 12992.92 HUMS 14379.56 11864.18 .1212$ 12111.65 14497.3ft ..iwi-n 12945.13 6372.22 8777.88 80 income and the gap is widening. This gap could be due to the pooling of data which makes the estimation process insensitive to country specific effects. The values from Tables 4.5 and 4.6 and Figure 4.5 depict the relationship between observed and estimated income for the 22 countries individually. These comparisons indicated that the model underestimates the income of three countries (USA, Canada, Switzerland), overestimates the income for five countries (Greece, Ireland, Norway, Portugal, Turkey), and fits well for the remaining 14 (Japan, Austria, Belgium, Denmark, Finland, France, Germany, Italy, Netherlands, Spain, Sweden, UKD, Australia, New Zealand). Comparing Figures 4.1, 4.2, and 4.4, it was seen that international openness, investment and government expenditures, in their average levels, had increasing trends. This result also implied that the OECD countries were increasing their trading activities and investments over time. Yet again, comparing values from Tables 4.6 and 4.7 (Column 3), and Figure 4.6 revealed that the estimated incomes of nine countries (USA, Denmark, Finland, France, Germany, Norway, Sweden, Switzerland, Australia) were above-average, six countries (Greece, Ireland, Italy, Portugal, Spain, Turkey) were below-average, and seven countries (Canada, Japan, Austria, Belgium, Netherlands, UKD, New Zealand) moved closely with the average of the group of 22 countries. Figure 4.7 depicts the relationship between YOBcd and Hoecd (Table 4.7, column 3 and Table 4.4, column 2, respectively) as a positive and increasing one implying that human capital did have a significant and positive effect on per capita income for the 22 OECD countries. Similarly, using the values in Tables 4.3 and 4.6, Figure 4.8 depict 75 Table 4.5 (Contd) Year Italy Netherlands Norway Portugal Spain Sweden Switzerland Turkey UK Australia New Zealand 13 14 15 16 17 18 19 20 21 22 23 24 1955 3645 5365 5112 1543 2669 6549 8310 1429 5968 7312 6834 1956 3773 5626 5214 1602 2850 6702 8754 1410 6020 7155 6736 1957 3904 5682 5361 1678 2943 6840 8903 1655 6105 7140 6970 1958 4042 5424 5391 1685 3056 6954 8443 1752 6092 7485 6893 1959 4277 5637 5501 1774 2940 7282 9026 1664 6314 7807 7007 1960 4636 6122 5665 1869 3196 7492 9639 1604 6548 7879 7920 1961 4993 6269 5914 2004 3573 7857 10328 1613 6690 7678 8025 1962 5285 6445 6141 2077 3912 8129 10581 1651 6697 8089 8109 1963 5580 6616 6433 2197 4207 8495 10849 1794 6927 8485 8340 1964 5657 7158 6727 2253 4413 9025 11258 1798 7276 8981 8634 1965 5765 7431 7029 2415 4692 9285 11425 1793 7378 8955 8991 1966 6085 7562 7296 2479 4988 9370 11580 1970 7482 9282 9084 1967 6499 7887 7667 2659 5163 9603 11794 2000 7665 9503 8664 1968 6863 8335 7739 2934 5429 9893 12062 2089 7934 10240 8577 1969 7270 8778 8035 3017 5864 10295 12612 2142 8001 10556 9094 1970 7669 9228 8129 3323 6017 10643 13274 2179 7695 10917 9352 1971 7689 9493 8433 3759 6173 10621 13681 2343 8312 11039 9686 1972 7815 9711 8827 3998 6653 10808 13945 2441 8963 11288 9966 1973 8383 10096 9174 4479 7116 11194 14254 2454 9410 11675 10656 1974 8788 10411 9593 4704 7454 11548 14454 2646 9156 11517 11159 1975 8354 10291 9915 4363 7389 11825 13228 2832 9014 11616 10468 1976 8909 10739 10590 4526 7531 11873 13058 2998 9300 11865 10580 1977 9104 10939 10872 4733 7589 11528 13388 3102 9550 11750 9968 1978 9371 11147 11288 4775 7544 11613 13423 3019 9912 12279 9924 1979 9930 11325 11807 4914 7458 12073 13825 2930 10220 12332 10259 1980 10445 11323 12249 5048 7495 12290 14653 2853 10028 12622 10260 1981 10382 11105 12290 5092 7319 12165 14704 2843 9933 12828 10747 1982 10349 10891 12257 5194 7351 12274 14446 2847 10126 12168 10686 1983 10369 11005 12779 5105 7378 12479 14514 2885 10536 12840 10805 1984 10649 11317 13557 4952 7403 12999 14722 2996 10781 13349 11322 1985 10895 11570 14227 5026 7547 13313 15209 3059 11137 13662 11324 1986 11199 11736 14821 5250 7820 13558 15657 3281 11580 13755 11430 1987 11547 11747 14918 5615 8321 13931 15934 3423 12151 14190 11498 1988 12021 11987 14752 5990 8809 14231 16320 3395 12751 14659 11481 1989 12367 12434 14647 6281 9305 14534 16799 3370 13050 14904 11811 1990 12557 12m 14891 W5 9664 14495 17007 3711 130$3 14304 11540 TABLE OF CONTENTS page DEDICATION ACKNOWLEDGMENTS iii LIST OF TABLES viii LIST OF FIGURES x ABSTRACT xii CHAPTERS 1. INTRODUCTION 1 2. EVIDENCE OF CONVERGENCE 6 2.1 Studies Using Inequality Measures 7 2.2 Studies Using Regression Analysis 12 2.3 Studies Using Models of Economic Growth 16 2.4 Studies Using Time-Series Analysis 20 3. DATA 24 3.1 Penn World Tables 25 3.1.1 International Comparison Project 26 3.1.2 Purchasing Power Parities 28 3.1.3 Country-Product-Dummy Method 29 3.1.4 Elteto-Koves-Szulc Method 29 3.1.5 The Geary-Khamis Method 31 v 63 Table 4.4 Average Per Capita Levels of Human Capital (Hqecd), International Openness (Oqecd) Investment Expenditure (Ioecd)> and Government Expenditure (GOECd) in the 22 OECD Countries, 1955-1990 Year Human Capital International Openness Investment Expenditure Government Expenditure Hqecd Goecd Ioecd Goecd 1 2 3 4 5 1955 372.83 1283.14 1430.91 804.33 1956 375.89 1365.37 1457.26 808.44 1957 383.16 1422.75 1450.56 823.91 1958 384.16 1315.70 1404.01 828.75 1959 393.24 1393.18 1541.13 840.97 1960 416.43 1542.55 1639.43 852.70 1961 415.14 1568.23 1720.29 889.76 1962 431.45 1602.20 1815.93 927.39 1963 441.45 1675.17 1898.90 948.58 1964 453.25 1790.54 2066.63 964.09 1965 466.20 1865.29 2183.51 986.99 1966 471.55 1959.88 2287.96 1041.05 1967 450.93 2002.95 2316.70 1098.33 1968 458.80 2179.37 2476.89 1122.68 1969 474.78 2364.32 2646.05 1132.43 1970 481.22 2542.15 2703.16 1150.82 1971 493.73 2608.37 2757.89 1166.60 1972 501.24 2717.41 2882.64 1175.46 1973 519.74 3088.94 3149.99 1194.64 1974 519.92 3715.18 3017.30 1220.03 1975 518.27 3341.05 2633.05 1248.78 1976 521.36 3638.81 2870.10 1271.79 1977 534.82 3722.07 2973.74 1285.45 1978 543.37 3717.13 3074.45 1318.60 1979 542.60 4094.06 3176.32 1342.82 1980 557.36 4368.00 3060.20 1360.88 1981 561.50 4435.24 3016.31 1375.90 1982 556.70 4269.67 2789.60 1392.52 1983 556.29 4254.21 2844.59 1419.41 1984 562.79 4665.34 3187.09 1450.12 1985 568.16 4733.06 3254.57 1489.07 1986 574.88 4402.15 3329.83 1530.81 1987 580.36 4519.56 3487.03 1560.68 1988 557.26 4795.09 3733.70 1583.16 1989 565.66 5158.82 3949.07 1585.50 1990 581.93 5276.98 4003.32 1610.41 83 r Belgium Denmark Finland y France Figure 4.5 (Contd) 79 Y, Y Figure 4.4 Average Levels of Observed and Estimated Income, YOECd and YOECD, in the 22 OECD Countries, 1955-1990 APPENDIX D WESTERN PACIFIC REGION The Western Pacific region consists of 15 non-Communist countries: Australia, Fiji, Hong Kong, Indonesia, Japan, Malaysia, New Zealand, Papua New Guinea, Philippines, Singapore, Solomon Islands, South Korea, Taiwan, Thailand, Western Samoa. 122 32 non-negative international prices and PPPs. The CPD or EKS method can be used to produce the detailed category PPPs for the Geary-Khamis method. These PPPs are transitive and are relative to the U.S. dollar. Detailed categories are indicated by the subscript a = 1,..., A. The volume of detailed category a in country c is (3.7) where Ea c is the per capita expenditure (in national currency) on detailed category a in country c. This volume is expressed in U.S. dollars. However, these volumes are not additive over the detailed categories. This method introduces the international price Pa of each detailed category and the overall purchasing power parity tc of each country c. Pa is written as N E p e=l N c-1 which is equivalently written as N If r.v. E<Â£.A> where v. m E (3.8) C-1 while xc is defined as A c A which is also 20 capital and the main source of differences in living standards among nations was differences in human capital. Romer (1994) studied the origins of endogenous growth models and traced them back to the question of whether per capita income in different countries was converging. He observed that the most important policy questions about growth pertain to institutional arrangements for gaining access to knowledge and the production and use of new knowledge. 2.4 Studies Using Time-Series Analysis Weatherspoon (1993), and Weatherspoon et al. (1994) tested the convergence of the G-7 countries using Theils inequality (entropy) index on income and three other potential factors of influence on economic growth: government expenditure, investment expenditure, and industrial employment. Pairwise convergence was supported for all four variables for the time period of 1950 to 1988. It was determined that the inequality in all four variables for the G-7 countries has declined from 1950-1988. This suggests that the G-7 countries are becoming more equal in terms of the above-mentioned variables. The inequality-transformed variables were then tested for multiple cointegrat ion using an 1(2) procedure due to Johansen (1992). Multiple cointegration was supported for three out of four relationships suggesting that there exists a long-run equilibrium relationship among the inequalities in income, investment expenditure, and industrial employment. 46 4.1.2 Implied Covariance Matrix Covariance is a central concept for the above models: the covariance algebra helps in deriving properties of the latent and measurement models; and determine factors that influence sample covariances which in turn can affect parameter estimates. Two covariance matrices are part of the latent variable model: 4> (n x n), a symmetric matrix, is the covariance matrix of the latent exogenous variables^ s); Â¥ (m x m) is the covariance matrix of the errors in the latent variable model. Thus, the covariance matrix for r\ is a function of B, T, 4, and For the measurement model, 0, (q x q) and 0t (p x p) are the covariance matrices of the errors of measurement 8 and e, respectively. Specifically, 4 = E(Â£H, = E(ft), a = E(55), and 0f = E(ee). The sample covariance matrix is crucial to the estimates of structural equation models since factors that affect this matrix have the potential to affect the parameter estimates. The nx(p + q) sample covariance matrix is computed as (4.4) T where z is [y x]. The population covariance matrix is denoted by E. is the covariance matrix of y, E is the covariance matrix of x, EyX and E^ are the covariance matrices of y with x and x with y, respectively. Let 6 denote the vector of unknown parameters. Then, Eyy (0) is SJd) = Efyy') = Ay E(rÂ¡rl') + 0, (4.5) Substituting the reduced form of equation (4.1) 9 and, therefore, lower savings rates in poorer countries contributed to greater inequality worldwide. They also conducted similar analyses with and without the nonmarket economies which showed that inequality in the world began increasing in the mid-sixties and continued increasing until 1986. In addition, they divided the worlds inequality into deciles and showed that the income shares of the bottom half remained unchanged while the top decile gained at the expense of the sixth, seventh, and eighth deciles. Oshima (1992) tested the Kuznets hypothesis for the Asian countries. He found that though there is an upward and then a downward trend in income inequality in most Asian countries, the peak in the trend appears much earlier in the stage of development in Asia than in the West. In Asia, the peak is reached when the economy is still predominantly agricultural with per capita incomes much lower than in the West where the peak was reached when the economy was predominantly industrial. Hence, the forces and mechanics underlying Asian trends are different from the West, although those underlying Japans trends are similar to those of the West. He concluded the reason for this difference is that Asia (with the exception of Japan) never went through the first industrial revolution of the 19th century. Ram (1992) used an inequality index, prescribed by Bourguignon (1979), to measure the regional and interstate income inequalities in the United States. The data mainly consisted of the U.S. Bureau of Economic Analysis (1989a, 1989b, 1990) estimates of state personal income per capita and total personal income. The data were available from 1950 through 1989 and covered 50 states (including Alaska and Hawaii and 48 others) and District of Columbia. He found that interstate income inequality, 97 y USA T Japan y Canada T Austria 38 3.4 Data for Estimation A supplement to the PWT5 data set, PWT 5.5, was compiled by Summers and Heston in 1993. This data set, in 1985 international prices, spans the years 1950-1990 for most countries. The information necessary for this study were extracted from this data set. A description of the variables tabulated in this document are listed in Table 3.2. Data on population (POP) and GDP per capita (RGDPCH) for the 22 OECD countries during 1955-1990 were used in estimation as tabulated. Shares of real investment and real government expenditures (iÂ¡ and gj) for country j (j = 1 to 22) were used to compute per capita levels of real investment and government expenditures, IÂ¡ and Gj, respectively. lj = ij RGDPCHj Gj = gj RGDPCHj International openness, 0Â¡, which represents the per capita level of exports and imports was compiled using OPENj variable as follows Oj = OPENj RGDPCHj where OPENj = {EXPORTSj 4- IMPORTSj} / CGDPj and CGDPj is the per capita nominal income in country j. Both the UNESCO series, Basic Facts and Figures (1951-1961) and the Statistical Yearbook (1963-1993), income and population figures from the Summers and Heston (1993) data were used to compile information on the four indicators of human capital for Ill J Figure 5.1 Observed and Estimated Income Inequality (Jy, Jy) in the 22 OECD Countries, 1955-1990 113 j Figure 5.2 Inequality in Estimated Income (Jy), Human Capital (Jh), International Openness (J0), Investment (Jj) and Government (Jq) Expenditures in 22 OECD Countries, 1955-1990 27 Table 3.1 Countries Represented in the International Comparison Project Africa Asia Eurft&fi Countries represented in Phase I Kenya Columbia India France United States Japan W. Germany Hungary Italy United Kingdom Countries added in Phase II Iran Belgium S. Korea Malaysia Philippines Netherlands Countries added in Phase III Malawi Brazil Pakistan Austria Zambia Jamaica Sri Lanka Denmark Mexico Syria Ireland Uruguay Thailand Luxembourg Poland Romania Spain Yugoslavia Countries added in Phase IV Botswana Argentina Hong Kong Finland Cameroon Bolivia Indonesia Greece Ethiopia Canada Israel Norway Ivory Coast Chile Portugal Madagascar Costa Rica Mali Dominican Rep. Morocco Ecuador Nigeria El Salvador Senegal Gaulemala Tanzania Honduras Tunisia Panama Zimbabwe Paraguay Peru Venezuela Countries deleted in Phase IV Jamaica Iran Romania Mexico Malaysia Syria Source: Theil et al. 1989, p. 2. < fe HUMAN CAPITAL, CONVERGENCE, AND INCOME INEQUALITY: A LATENT VARIABLE APPROACH By SRI DEVI DEEPAK DISSERTATION PRESENTED TO THE GRADUATE SCHOOL THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1995 I dedicate this dissertation to my parents, Mahalakshmi and Krishna Murthy Duwuri. Without their encouragement, blessings, and high expectations I could not have attained this level of education. ACKNOWLEDGMENTS I would like to thank my supervisory committee for their tremendous help and guidance. I also thank Dr. Henri Theil for providing me with the opportunity to assist him in his research which culminated in this dissertation. In particular, I would like to thank Dr. James L. Seale, Jr., and Dr. Charles B. Moss for their individual attention, time, and patience which helped me a great deal in completing this dissertation. I thank Dr. Max R. Langham, Dr. Gary F. Fairchild, and Dr. Douglas G. Waldo for their insightful suggestions in writing this dissertation. I especially thank my husband, Dr. M. S. Deepak, for his support and encouragement during the course of my research. I appreciate the wonderful support from the staff of the FRE Systems Support Center for their indispensable, patient, and highly efficient assistance during the arduous months of writing this dissertation. I thank Dr. John R. Gordon for all his support during the course of my program. I thank Ms. Rosemarie T. Wolfendale, Ms. Shirley A. Johnson, and Ms. Shirley T. Harris for their help and kindness throughout my program. I also thank the staff of the Documentation Division and Reference Section of the University of Florida Library (West) for their expert guidance and support for the collection of some parts of the data for my dissertation. in The financial support from the Food and Resource Economics Department and Dr. James L. Seale, Jr., is greatly appreciated. IV TABLE OF CONTENTS page DEDICATION ACKNOWLEDGMENTS iii LIST OF TABLES viii LIST OF FIGURES x ABSTRACT xii CHAPTERS 1. INTRODUCTION 1 2. EVIDENCE OF CONVERGENCE 6 2.1 Studies Using Inequality Measures 7 2.2 Studies Using Regression Analysis 12 2.3 Studies Using Models of Economic Growth 16 2.4 Studies Using Time-Series Analysis 20 3. DATA 24 3.1 Penn World Tables 25 3.1.1 International Comparison Project 26 3.1.2 Purchasing Power Parities 28 3.1.3 Country-Product-Dummy Method 29 3.1.4 Elteto-Koves-Szulc Method 29 3.1.5 The Geary-Khamis Method 31 v 3.2 Extrapolations with ICP Data 33 3.3 Mark 5 Data Set 35 3.4 Data for Estimation 38 4. INCOME AND HUMAN CAPITAL IN THE OECD COUNTRIES 42 4.1 General Latent Variable Model 44 4.1.1 Structural Equations of the Model 44 4.1.2 Implied Covariance Matrix 46 4.1.3 Identification 48 4.2 Estimation 51 4.3 Empirical Model 52 4.4 Parameter Estimates of the Latent Variable Model 56 4.5 Income and Human Capital in OECD Countries 59 4.6 Summary 103 5. INEQUALITY IN THE OECD COUNTRIES 105 5.1 Graphical Inequality 105 5.2 Inequality via Measures of Dispersion 106 5.3 Inequality Indices 106 5.4 Properties of Inequality Index 107 5.5 Theils Inequality Index 108 5.6 Inequality in OECD Countries 109 5.7 Summary 114 6. SUMMARY AND CONCLUSIONS 115 APPENDICES A SEVEN REGIONS OF THE WORLD 119 B EUROPE, AFRICA, AND SOUTHERN CONE 120 vi C WESTERN EUROPE 121 D WESTERN PACIFIC REGION 122 E FOUR REGIONS REVISITED 123 F CHANGE IN INEQUALITY 124 REFERENCES 126 BIOGRAPHICAL SKETCH 133 vii LIST OF TABLES Table Bags 3.1 Countries Represented in the International Comparison Project 27 3.2 Description of Variables in PWT 5.5 File 39 4.1 Parameter Estimates of the Latent Variable Model for 22 OECD Countries, 1955-1990 58 4.2 Parameter Estimates of the Measurement Model for 22 OECD Countries, 1955-1990 59 4.3 Estimated Levels of Human Capital (HÂ¡, i=l to 22) in the 22 OECD Countries, 1955-1990 61-62 4.4 Average Per Capita Levels of Human Capital (Hqecd), International Openness (0OECD), Investment Expenditure (IOECd)> and Government Expenditure (GOEcd) in the 22 OECD Countries, 1955-1990 63 4.5 Levels of Observed Income (YÂ¡, i=l to 22) in the 22 OECD Countries, 1955-1990 74-75 4.6 Levels of Estimated Income (YÂ¡, i= 1 to 22) in the 22 OECD Countries, 1955-1990 76-77 4.7 Average Levels of Observed and Estimated Income Per Capita (YOECD, YOECD) in the 22 OECD Countries, 1955-1990 78 4.8 Summary of Cross-Country Analyses for the 22 OECD Countries, 1955-1990 104 viii 5.1 Average Inequality in Observed Income (JY), Estimated Income (JY), Human Capital (Jh), International Openness (JQ), Investment Expenditure (JO, and Government Expenditure (JG) in the 22 OECD Countries, 1955-1990 110 IX LIST OF FIGURES Figure Eage 4.1 Average Level of Human Capital (HOECd) in the 22 OECD Countries, 1955-1990 65 4.2 Average Level of Human Capital (Hoecd), International Openness (0OECD), Investment (Iobcd) Government (GOEcd) Expenditures in the 22 OECD Countries, 1955-1990 66 4.3 Comparing Countrywise Levels of Human Capital (Hj, i=l to 22) and Average Level of Human Capital (Hoecd) hi the 22 OECD Countries, 1955-1990 68-73 4.4 Average Levels of Observed and Estimated Income, Yoecd mid Yq^^, in the 22 OECD Countries, 1955-1990 79 4.5 Comparing Countrywise Levels of Observed Income (YÂ¡, i=l to 22) and Estimated Income (YÂ¡, i=l to 22) in the 22 OECD Countries, 1955-1990 82-87 4.6 Comparing Countrywise Levels of Estimated Income (YÂ¡, i=l to 22) and Average Level of Estimated Income (YOECD) in the 22 OECD Countries, 1955-1990 89-94 4.7 Relationship Between Average Levels of Observed Income (YOECD) and Human Capital (HOECD) in the 22 OECD Countries, 1955-1990 95 x 4.8 Country wise Relationship Between Levels of Observed Income (YÂ¡, i=l to 22) and Human Capital (HÂ¡, i=l to 22) in the 22 OECD Countries, 1955-1990 97-102 5.1 Observed and Estimated Income Inequality (JY, JY) in the 22 OECD Countries, 1955-1990 Ill 5.2 Inequality in Estimated Income (JY), Human Capital (Jh), International Openness (JQ), Investment (J,) and Government (JG) Expenditures in the 22 OECD Countries, 1955-1990 113 xi Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy HUMAN CAPITAL, CONVERGENCE, AND INCOME INEQUALITY: A LATENT VARIABLE APPROACH By Sri Devi Deepak August 1995 Chairman: James L. Seale, Jr., Major Department: Food and Resource Economics Convergence in income and its determinants, for 22 OECD countries during 1955- 1990, was analyzed using a latent variable approach and via Theils inequality index. Income was specified as a function of human capital, international openness, government expenditure, and investment expenditure drawing on the theoretical underpinnings from standard macroeconomic theory and from recent developments in economic growth theory. Human capital, which cannot be observed directly, was treated as a latent variable. Theils inequality index was computed for income and its determinants. The latent variable model was estimated using maximum likelihood. The results of this estimation showed that the effects on income levels, of human capital, international openness, investment expenditure, and government expenditure were statistically significant and positive. Human capital had the greatest positive effect xii indicating that it was a key determinant of income levels for the OECD countries. Further, all the determinants were increasing over time at an average per capita level. Estimated income per capita and Theils income inequality index were computed using the estimated human capital, the other three determinants and the parameters of estimation. The results of these computations indicated that the estimated income fitted the observed income closely and that both the observed and estimated incomes were increasing during 1955-1990. Theils inequality index was then used to measure observed and estimated inequalities in income, human capital, international openness, investment expenditure, and government expenditure. The evidence from the income inequality analysis is in favor of the convergence component of Kuznets hypothesis. Further, the analyses of the inequalities in income, human capital, openness, investment and government expenditures revealed that the OECD countries, as a group, were moving closer in terms of income, openness and government expenditure. However, these countries are diverging in terms of human capital and investment expenditure. xiii CHAPTER 1 INTRODUCTION Since the time of Adam Smith (1937) varying rates of economic growth have puzzled economists; thus, for the past several decades this issue has been the focus of research for economists. Three salient and apparent features of studies on economic growth are (a) long-run growth of per capita income has been sustained at a positive rate for many countries; (b) rates of growth vary across countries; and (c) methodologies vary for measuring and explaining economic growth and disparity. The principal question asked was whether countries varied greatly in their growth rates and whether these differences were the outcome of random processes. Further, the phenomenon of accelerated growth of poorer economies causing them to "converge" in per capita income level with that of the richer economies and the factors affecting this growth have become the focus of developmental and international economists. By convergence we refer to the process of the faster growth of relatively poor countries to enable them to "converge" with the growth of relatively rich countries. The divergence-convergence hypothesis originated in neoclassical economics with Kuznets inverted-U theory (1955) which states that, in the process of economic development, inequality within a country initially increases in the early stages, stabilizes at some peak level, then declines as the latter stages of development occur (divergence followed by 1 2 convergence). Though Kuznets studies income inequality within an economy, the implications of his theory have led to many studies testing Kuznets hypothesis across countries. From the survey of recent literature on convergence and income inequality, four types of studies have emerged: those that measure income inequality directly (Wright, 1978; Bomschier, 1983; Branco and Williamson, 1988; Theil, 1989; Berry et al., 1991; Oshima,1992; Ram, 1992; Theil and Deepak, 1993a, 1993b, 1993c, 1994; Moss et al., 1993; Seale et al., 1994; Theil and Seale, 1994), those employing regression analysis (Ram, 1988, 1989a, 1989b; Barro, 1991; Barro and Sala-i-Martin, 1992; Mankiw et al., 1992), those based on growth models (Lucas, 1988, 1993; Rebelo, 1990; Tamura, 1991; Glomm and Ravikumar, 1992; Romer, 1994), and those using time-series techniques (Weatherspoon, 1993; Weatherspoon et al., 1994). This survey shows that there is evidence that, in terms of income inequality, rich countries are converging, poor countries are diverging, and the level of affluence increases with increasing distance from the equator (Theil, 1989; Seale et al., 1994; Theil and Deepak, 1994; Theil and Seale, 1994; Moss et al., 1993). However, till recently, though researchers have failed to reject the Kuznets hypothesis to a large extent, they failed to define, with any certainty, the determinants of convergence (or divergence). Of those that have analyzed or explored the determinants of convergence, Barro (1991), Barro and Sala-i-Martin (1992), and Mankiw et al. (1992) found, empirically, that human capital tended to be an important factor in determining convergence. Lucas 3 (1988, 1993) also concluded that, with the inclusion of human capital in the production function, an economy with a human capital stock lower than the world average would grow faster than an above average economy. Tallman and Wang (1992), reviewing studies using theories of neoclassical and endogenous growth, concluded that accumula tion of human capital yielded positive dividends in terms of income and thus standards of living. This study expands on the above mentioned research and attempts to explain the process of convergence (or divergence) via factors that influence economic growth. While Weatherspoon (1993) used cointegration analysis to test for a long-term relationship in inequality among income, investment and government expenditures, and industrial employment, this study uses the latent variable model approach to analyze convergence in income levels and via directly measuring income inequality using Theils (1989) inequality index. Specifically, per capita incomes (determined by per capita levels of human capital, international openness, investment and government expenditures) for 22 member countries of the Organization of Economic Cooperation and Development (OECD) ( USA, Canada, Japan, Austria, Belgium, Denmark, Finland, France, West Germany, Greece, Ireland, Italy, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, Turkey, UK, Australia, New Zealand) were estimated via a latent variable model (Bollen, 1989) with human capital as the latent variable. An inequality index as derived by Theil (1989) was then used to measure the inequality in per capita income and its 4 determinants. The results from the above computations were used to analyze the effect(s) of determinants of growth on patterns, if any, of convergence (or divergence). The next chapter gives a brief overview of existing evidence on conver gence (or divergence). The literature is divided into four groups: studies using inequality measures, studies using regression analysis, studies using models of economic growth, and studies using time-series analysis. By and large, the studies using inequality measures and time-series analysis failed to reject Kuznets hypothesis, while the studies using growth theories either rejected or were inconclusive in testing the inverted-U hypothesis. The regression studies show some evidence in support of convergence- divergence hypothesis. Chapter 3 deals with the data used for the analysis of this study and includes a description of the compilation of purchasing power parity data by Summers and Heston (1993) in forming the Penn World Table (Mark 5). This chapter also details the other two sources of data: Statistical Yearbook, UNESCO (1963-1993), and Basic Facts and Figures, UNESCO (1951-1962) for compiling information for the indicators of human capital in the 22 OECD countries (two countries from Asia [Japan and Turkey], two from the Western Pacific Rim [Australia, New Zealand], 16 from Europe [Austria, Belgium, Denmark, Finland, France, Greece, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, and UK], and two countries from North America [USA and Canada]). Chapter 4 presents the generalized latent variable model (Bollen, 1989), and tabulates the results of estimation of per capita income. The chapter concludes with a brief study of the patterns in observed and estimated per capita incomes and the 5 explanatory variables for the 22 OECD countries. These trends are then compared and contrasted with evidence from literature. Chapter 5 describes Theils inequality index and presents the computations of inequalities using income, human capital, international openness, investment and government expenditures. The patterns of convergence (if any) are studied and analyzed. These results are also compared and contrasted with evidence from past studies. Chapter 6 summarizes and concludes the study. CHAPTER 2 EVIDENCE OF CONVERGENCE The interest in studying convergence has been derived from the basic relationship between development and income distribution. To achieve convergence the poorer countries need to increase their productivity at a rate greater than that in richer countries (Barro and Sala-i-Martin, 1992). The importance of the pattern of income distribution during various stages of development and the lack of adequate time-series data for most developing countries culminated in many studies which attempt to test Kuznets hypothesis with varying methodologies. The predominant methodologies used include inequality measures (Theil, 1989; Berry et al., 1991; Oshima, 1992; Ram, 1992; Moss et al., 1993; Theil and Deepak, 1993a, 1993b, 1993c, 1994; Theil and Seale, 1994; and Seale et al., 1994), regression analysis (Wright, 1978; Bomschier, 1983; Branco and Williamson, 1988; Ram, 1988, 1989a, 1989b; Barro, 1991; Barro and Sala-i-Martin, 1992; Mankiw et al., 1992), theories of growth (Lucas, 1988, 1993; Rebelo, 1990; Tamura, 1991; Glomm and Ravikumar, 1992; Romer, 1994), and time-series analysis (Weatherspoon, 1993; Weatherspoon et al., 1994). Since the recent developments in endogenous economic growth research (Romer, 1989), growth in income is no longer treated as a random process but as something that is systematically related to other factors in the economy (Grossman and Helpman, 1991). 6 7 Summers and Heston (1988) plot the growth rates of 114 countries between 1960 and 1985 against the level of per capita income in 1960. This plot did not depict any strong correlation between initial levels of income and growth during the period, but revealed the variation in growth rates between countries. In the past, growth patterns in the world could not be studied effectively due to data constraints. But the Penn World Table (PWT) time-series data for various economic indicators compiled by Summers and Heston (1991) have changed the scenario to a large extent. 2,1 Studies Using Inequality Measures The simplest inequality measures are estimates of statistical dispersion like variance, standard deviation, and the coefficient of variation. A commonly used inequality measure is the gini coefficient which is based on the Lorenz curve (Anand and Kanbur, 1993). This statistic measures the ratio of the area between the diagonal and the Lorenz curve to the total area below the diagonal. Another measure is the Theil entropy index (also known as Theils inequality index) which measures inequality by taking the logarithm of the ratio of the arithmetic mean income to the geometric mean income. The appropriateness of the inequality index to be used depends on the objective of the study as well as the properties of the index (Chapter 5, Section 5.4). For example, Theil (1989) used a decomposable inequality index to better assess its behavior internationally as well as regionally. Theil (1989) used the Summers and Heston (1988) data set spanning 1950-1985 to assess the economic development in five regions of the noncommunist world: the 8 North consisting of 25 countries (U.S. and Canada from the American continent, Japan and Korea on the Western Pacific Rim, and 21 countries in Western and Southern Europe), the South with 9 countries (Argentina, Chile, and Uruguay from the Southern Cone of the American continent, Australia and New Zealand on the Western Pacific Rim, and South Africa, Botswana, Lesotho, and Swaziland from the Southern tip of Africa. He measured income inequality as the natural logarithm of the ratio of arithmetic mean income to geometric mean income which was additively decomposable. He concluded that international inequality increased substantially from 1960 to 1980, and that regional inequality dominated the average within-region inequality. In 1960 the inequality in the North exceeded that in any other region, but Northern inequality declined very rapidly so that it was second lowest in 1985. In contrast to the North, Tropical Africa and Asia showed substantial increases in inequality. Berry et al. (1991) conducted an extensive analysis on world income inequality. They analyzed over 100 countries during 1950-1977. They used data from World Bank Tables (1976, 1980a), World Bank Atlas (1988), World Development Report (1980b, 1987, 1988), and the Summers and Heston (1988) data set. They computed Theils entropy index, Atkinsons inequality, and the Gini coefficient. The major difference in their study was that they computed inequalities for gross national product (GNP) and consumption measured as a percentage of GNP to study changes in welfare. The underlying logic being that the distribution of consumption was less unequal across countries and the savings rate was below average for the poorer countries. Berry et al. (1991) contended that marginal propensities to consume decrease with decreasing income 9 and, therefore, lower savings rates in poorer countries contributed to greater inequality worldwide. They also conducted similar analyses with and without the nonmarket economies which showed that inequality in the world began increasing in the mid-sixties and continued increasing until 1986. In addition, they divided the worlds inequality into deciles and showed that the income shares of the bottom half remained unchanged while the top decile gained at the expense of the sixth, seventh, and eighth deciles. Oshima (1992) tested the Kuznets hypothesis for the Asian countries. He found that though there is an upward and then a downward trend in income inequality in most Asian countries, the peak in the trend appears much earlier in the stage of development in Asia than in the West. In Asia, the peak is reached when the economy is still predominantly agricultural with per capita incomes much lower than in the West where the peak was reached when the economy was predominantly industrial. Hence, the forces and mechanics underlying Asian trends are different from the West, although those underlying Japans trends are similar to those of the West. He concluded the reason for this difference is that Asia (with the exception of Japan) never went through the first industrial revolution of the 19th century. Ram (1992) used an inequality index, prescribed by Bourguignon (1979), to measure the regional and interstate income inequalities in the United States. The data mainly consisted of the U.S. Bureau of Economic Analysis (1989a, 1989b, 1990) estimates of state personal income per capita and total personal income. The data were available from 1950 through 1989 and covered 50 states (including Alaska and Hawaii and 48 others) and District of Columbia. He found that interstate income inequality, 10 though small in magnitude, traced along with the U-shaped profile propounded by Kuznets. Further, a simple quadratic form in terms of time fitted the data extremely well. Inequality indices for 1977 and 1988 were computed after adjusting for interstate price-level changes. These revealed large reductions in the indices and a virtual disappearance of the increase in inequality after 1978. A decomposition of the index showed that income changes accounted for most of the inequality change in each decade. Lastly, the six most influential states in terms of their impact on interstate inequality were tabulated for 1950, 1959, 1969, 1979, and 1989. Three of these states had below average income and three had above-average income. New York and California from the above-average group and Alabama and Mississippi from the below-average group contributed the largest components to interstate inequality. Moss et al. (1993) used the Summers and Heston (1993) data to analyze income changes in the G-7 countries (USA, Canada, Japan, UK, West Germany, France and Italy), for the period 1950 to 1988, using Theils measure of income inequality. They found that for the G-7 as a whole, per capita GDP increased almost threefold in that period, while the inequality among the seven countries declined dramatically. They concluded that Japans increasing affluence toward European levels was the reason for this dramatic decline in inequality. The income inequality among the G-7 countries declined almost uninterruptedly. Since the G-7 can be viewed as affluent, this evidence is in favor of convergence. Theil and Deepak (1993a, 1993b, 1993c, 1994) used Theils inequality index to measure income inequality across countries and regions during the period 1950-1990. 11 Firstly, they categorized 113 countries into seven regions-North, South, Tropical Africa, Tropical America, South-East Asia, South-Central Asia, South-West Asia (see Appendix A for countries within each region)for the period 1950-1990. They found that the North was converging, South-East Asia was diverging, South-Central Asia presented no evidence of convergence or divergence, and the inequality values of sub-Saharan Africa tended to increase from the mid-1960s until the late 1970s and to decline thereaftera pattern in favor of the Kuznets hypothesis. Secondly, they compared the inequality in Western Europe, Mediterranean Europe and Mediterranean Africa; South Africa and its neighbors; USA, Mexico, and Central America; the Southern Cone of South America and its neighbors (Appendix B). The results indicate a strong tendency toward more poverty when moving from temperate zones toward the Equator. Thirdly, they considered three regions in Western Europe consisting of 18 countriesnon-EU, EU Center, and EU Periphery (see Appendix C for countries within each region)-and found that the income inequalities in the regions of EU and EU Center declined by more than 90%. This result was also in favor of convergence. In the case of the EU Periphery, the first 20 years provide evidence of transition from divergence to convergence. Lastly, they considered 15 noncommunist countries (Appendix D) in the Western Pacific and found that there was a strong tendency to greater poverty in movement toward the Equator from the temperate zones in the North or South. Theil and Seale (1994) used the purchasing power parity (PPP) based data for gross domestic products to assess the affluence of more than 100 non-communist countries in 1950-1990. A seven-region classification, based on the distinction between 12 temperate and tropical zones, is used to summarize the data on individual countries. The seven regions account for nearly 90 percent of the inequality among these countries in each year. Another classification, based on the position of countries with respect to the European Union, is applied to 18 countries in Western Europe. Five journeys around the world were described; the main result was that affluence tended to decline when the traveler moved from temperate zones (in either the Northern or the Southern Hemi sphere) toward the Equator. Another topic considered was that of the G-7 countries, the populations of which are all concentrated in the temperate zones of the Northern Hemisphere. Also, attention was paid to Kuznets hypothesis of divergence-convergence in a cross-country context. Seale et al. (1994) relate regional growth and the inequality across countries for four regions of the noncommunist world: the North, Sub-Saharan Africa, South-Central Asia, and South-East Asia (Appendix E). Their results indicate strong convergence in the North and strong divergence in South-East Asia, whereas the case of South-Central Asia is unclear. In the case of Sub-Saharan Africa, there is growth with divergence, in agreement with Kuznets hypothesis, but thereafter negative growth with convergence, which is a digression from the hypothesis. 2.2 Studies Using Regression Analysis Wright (1978) examined the validity of Kuznets hypothesis versus the institutionalist hypothesis. The institutionalist hypothesis states that institutional structures and government policies are the chief determinants of income inequality. 13 Wright used a gini coefficient inequality measure to calculate the inequality in GDP per capita among 56 countries. He concluded that the cross-sectional data demonstrated that (1) inequality varies among countries at all levels; (2) variation in and level of inequality are higher among LDCs; and (3) an institutionalist variable in regressions explains far more income variation among countries than income levels. Further, the divergence- convergence hypothesis lends itself to the conservative argument that redistribution is growth reducing, while growth itself will take a country to the declining side of the "parabola of skewness" more quickly. In the institutionalist view, reduction in inequality depends on modifications in the institutions and policies which generate it. Bomschier (1983) outlined explanations of international differences in personal income distribution that were formulated within the "world economy" and the "level of development" paradigm. He constructed the Gini index of personal income inequality for 72 countries using Ballmer-Cao and Schiedegger (1979) data. He concluded that income inequality does not vary directly with development, but with surplus, power and the structural position within the world economy. Thus less developed countries do not automatically decrease their inequality in the process of development. Ram (1988) studied the validity of Kuznets hypothesis by extending his study to cover several countries. His hypothesis stated that intercountry inequality across nations would first increase with secular economic growth, then start to decline at some point. His sample consisted of 32 countries (24 less developed countries (LDCs) and 8 developed countries (DCs)) which were market economies from the Summers and Heston (1984) data. Average per capita world GDP was used as a proxy for the level of 14 development and Theils income inequality measure was used to study income inequality. In addition, Ram used a Kuznets type quadratic regression to determine the relationship between the level of income and development, which represents development and inequality. The equation is J,-b + bj, btf u, where J is the measure of world inequality and Y is the natural logarithm of the average real GDP per capita. The last term is the disturbance term assumed to have the standard properties for best linear unbiased estimates. Ram found that the hypothesis was well supported when both LDCs and DCs were included in the sample and there is very little support when only LDCs were considered. Branco and Williamson (1988) also tested Kuznets hypothesis by analyzing development and income distribution. This study was unique in that it developed an absolute per capita income measure for the poorest 40% of the population in 68 countries. Their measure was the percent of income of the poorest 40% of a nations population in 1970 divided by 40% of the 1970 population, then multiplied by the real per capita GDP of that nation in 1970 (Summers and Heston, 1984). Their findings suggested that the poorest 40% of the population lose income both relatively and absolutely in the early stages of economic development; thereafter, there are gains in income although with diminishing marginal returns at the highest levels of development. Ram (1989a) also extended his 1988 study to the world economy inclusive of 115 market economies drawn from the Summers and Heston (1984) data for the years 1960- 1980. Using the same structure of the model as before, found that though world income 15 inequality increased since 1960, there was a noticeable deceleration in the rate of increase of inequality. Ram (1989b) attempted to study the effect of education on income inequality in LDCs. Firstly, upon reviewing the literature in this area he found contradicting evidence of the influence of education on inequality. Chiswick (1971, 1974), Chiswick and Mincer (1972), Chenery and Syrquim (1975), and Ahluwalia (1976) contended that education did influence income inequality, while Fields (1980), Psacharopoulos and Woodhall (1985), and Morrisson (1987) concluded that there was no clear evidence that education had an effect on income inequality. These contradictory results prompted Ram to conduct his study using two sets of data that yielded contradictory results. His study concluded that the effect of education on income inequality was ambiguous. He concluded that the nature of the data could be a major factor for the contradictory and inconclusive nature of the results. Barro (1991) used the neoclassical growth models developed by Solow (1956), Cass (1965), and Koopmans (1965), and the recent theories of economic growth as proposed by Lucas (1988), Rebelo (1990), Romer (1989), and Becker, Murphy, and Tamura (1990) as a guide to test convergence in real per capita GDP for 98 countries during the period 1960 to 1985. His results suggested that poor countries tend to catch up with rich countries if the poor countries have high per capita human capital in relation to their level of per capita GDP, but not otherwise. He observed that countries with high human capital have low fertility rates and high ratios of physical investment to GDP. 16 Barro and Sala-i-Martin (1992) used the neoclassical growth models developed by Ramsey (1928), Solow (1956), Cass (1965), and Koopmans (1965) to test for convergence across the 48 contiguous U.S. states using personal income since 1840 and gross state product since 1963. Their results indicated that the 48 states provided clear evidence of convergence, but the results could be reconciled quantitatively with the neoclassical model only if diminishing returns to capital set in slowly. The results for per capita GDP from a broad sample of countries were similar if a set of variables that proxy for differences in steady-state characteristics were held constant. Mankiw et al. (1992) examined whether the Solow growth model was consistent with the international variation in the standard of living. They showed that an augmented Solow model that included accumulation of human capital provided an excellent description of the cross-country data. While testing the convergence-divergence hypothesis, they concluded that holding population growth and capital accumulation constant, countries converge at a rate the augmented Solow model would predict. 2.3 Studies Using Models of Economic Growth The research on economic growth predominantly focuses on long-run economic progress, and the dominant sources are the neoclassical growth models developed by, to name a few, Solow (1956), Swan (1956), Ramsey (1928), Cass (1965), and Koopmans (1965). In general, the unexplained portions of growth were attributed to the area of technical progress which was treated as exogenous by the neoclassicalists. These models assumed that output can be produced using combinations of physical capital and labor in 17 variable proportions, and the production function was subjected to a technological factor. Thus, two exogenous processes, population growth and technological progress, determined the economys growth rate. In recent times with the development of endogenous growth models, the premises of neoclassical growth theory have come under serious scrutiny, thus creating the need for new techniques of measurement and analysis of the growth process. Endogenous growth models indicate that endogenizing technical progress via human capital accumulation allows an economy to grow endogenously and thus results in better measurement (Lucas 1988, 1993) and understanding of determinants of economic growth and the disparities in growth rates. The neoclassical growth model predicts a zero growth rate of output per unit of input in the long run, since the output growth rate is entirely determined by exogenous factors like the population growth rate and the rate of technical progress. However, in the endogenous growth models, the growth rate of output per capita is a positive constant because human capital accumulation results in endogenous technical progress. The underlying fact is that neoclassical models fix the rate of growth and allow the marginal product of capital to vary, whereas the endogenous models fix the marginal product of capital but allow the rate of economic growth to be endogenous. Lucas (1988) considered the prospects for constructing a neoclassical theory of growth and trade that was consistent with some of the main features of economic development. He studied three models to account for the disparities in growth rates across economies: a model emphasizing physical capital accumulation and technological 18 change, a model emphasizing human capital accumulation through schooling, and a model emphasizing specialized human capital accumulation through learning by doing. He concluded that, with the inclusion of human capital in the production function, economies that are initially poor will remain relatively poor, though their long-run rate of income growth will be as that of initially wealthier economies. If traded goods are included in the model, the long-run relationship between the two kinds of capital implies the same marginal productivity of physical capital, no matter what the level of capital that has been accumulated. If labor is mobile, it will flow in general from poor countries to wealthy ones. Rebelo (1990) described a class of endogenous growth models that have constant returns to scale technologies. He hypothesized that this class of models rationalizes the existence of permanent cross-country differences in growth rates as being, at least partly, a result of differences in government policies. His analysis revealed that small differences in policy regimes could easily mean the difference between growth and stagnation. Tamura (1991) developed an endogenous growth model that produced conver gence in per capita income and growth rates of output. His analysis was based on the premises that agents have identical preferences and access to identical technologies of production and investment, but differing levels of human capital. He concluded that a spillover effect of human capital in the investment technology provides below-average human capital agents with a higher rate of return on investment than above-average human capital agents; thus, below-average human capital agents grow faster than above- 19 average human capital agents. Convergence arises because below-average human capital agents gain most from learning. Glomm and Ravikumar (1992) studied the effect of endogenous growth on income inequality by using an overlapping generations model with heterogenous agents in which human capital investment through formal schooling was the engine of growth. They used simple functional forms for preferences (logarithmic), production technologies (linear), learning technology (Cobb-Douglas), and income distribution (lognormal) to highlight the distinction between the economies with public education and those with private education. They found that income inequality (measured by the standard deviation of the lognormally distributed incomes) declined more rapidly under public education. On the other hand, private education yielded greater per capita incomes unless the initial income inequality was sufficiently high. They also concluded that societies would choose public education if a majority of agents have incomes below average. Lucas (1993) made a case study of the economic growth of Philippines and South Korea as a key to emphasize the effect of on-the-job human capital accumulation on growth. With this modification to the neoclassical model, an economy with a human capital stock lower than the world average would grow faster than an above average economy. His theory indicated that, relative to the worlds income and human capital, a countrys human capital converged to 1 which implied that relative incomes converge to 1 at the same rate. He also observed that convergence is more likely over subsets of countries or regions of countries, where factor and final goods mobility is high. He concluded that the main engine of economic growth was the accumulation of human 20 capital and the main source of differences in living standards among nations was differences in human capital. Romer (1994) studied the origins of endogenous growth models and traced them back to the question of whether per capita income in different countries was converging. He observed that the most important policy questions about growth pertain to institutional arrangements for gaining access to knowledge and the production and use of new knowledge. 2.4 Studies Using Time-Series Analysis Weatherspoon (1993), and Weatherspoon et al. (1994) tested the convergence of the G-7 countries using Theils inequality (entropy) index on income and three other potential factors of influence on economic growth: government expenditure, investment expenditure, and industrial employment. Pairwise convergence was supported for all four variables for the time period of 1950 to 1988. It was determined that the inequality in all four variables for the G-7 countries has declined from 1950-1988. This suggests that the G-7 countries are becoming more equal in terms of the above-mentioned variables. The inequality-transformed variables were then tested for multiple cointegrat ion using an 1(2) procedure due to Johansen (1992). Multiple cointegration was supported for three out of four relationships suggesting that there exists a long-run equilibrium relationship among the inequalities in income, investment expenditure, and industrial employment. 21 Thus, the evidence from the inequality studies (Theil, 1989; Theil and Deepak, 1993a, 1993b, 1993c, 1994; Theil and Seale, 1994; Seale et al., 1994; Weatherspoon, 1993; Weatherspoon et al., 1994) seems to suggest that poor economies are diverging, rich economies are converging, and there is inconclusive evidence in certain cases. Neoclassical growth models (Barro, 1991; Barro and Sala-i-Martin, 1992; Mankiw et al., 1992) favor convergence and endogenous growth models (Lucas, 1988 & 1993; Romer, 1994; and Tamura, 1991) lean toward ambiguity. The OECD countries were chosen for two main reasons: the evidence from the literature supports convergence (or divergence) for these countries and the availability of reliable data. In summary, the research by Theil and Deepak (1993a, 1993b, 1993c, 1994), Moss et al. (1993), Seale et al. (1994), and Theil and Seale (1994) determined that during the period 1950-1990 the income of the G-7, non-EU, and EU Center countries increased while the inequality declined almost uninterruptedly favoring the convergence component of Kuznets hypothesis; the income for EU Periphery countries increased but inequality fluctuated during 1950-1970 without a clear trend and then decreased showing evidence of transition from divergence to convergence components of Kuznets hypothesis; the North, consisting of 22 countries, also showed evidence of convergence and in the case of the countries in South, the results were inconclusive. In the process of analyzing convergence across 98 countries, Barro (1991) concluded that the evidence from 20 OECD countries was stronger because these countries had higher per capita incomes and had similar basic economic and political institutions. Further, Weatherspoon (1993) and Weatherspoon et al. (1994) found that, in the long run, the G-7 22 and 14 OECD countries were becoming more equal in terms of income, investment expenditure, government expenditure, and industrial employment. The survey of the above literature on income convergence suggested that testing for convergence (or divergence) with a combination of the theories on income inequality and economic growth would prove to be an exercise that could expand the horizons of contemporary research on the subject. The evidence also suggests that though researchers have failed to reject the Kuznets hypothesis to a large extent, they, however, failed to define, with any certainty, the determinants of convergence (or divergence) until recently. This study expanded on the above mentioned studies (Barro, 1991; Mankiw et al., 1992; Weatherspoon, 1993) and incorporated the aspects of the theory of endogenous growth to explain the process of convergence (or divergence). Barro (1991) analyzed convergence in 98 countries during 1960-1985 by studying the relationship between growth rates in per capita income, levels of per capita income, and initial level of human capital (proxied by school enrollment ratios in 1960). He found that, holding levels of human capital constant, the growth rate in per capita income was inversely related to the level of per capita income. Further, holding the initial level od per capita income constant, Barro found that there was a positive relationship between the growth rate of income and level of human capital. Therefore, in his study, convergence was evident only in countries with high levels of initial human capital and per capita income. This study carried Barros research a step forward by analyzing the effects of levels of human capital, openness, investment and government expenditures on the levels 23 of per capita income. A multiple-variable indicator was used to estimate the level of human capital via a latent variable approach. The per capita income, estimated as a function of human capital (as a latent variable), was then analyzed for convergence with help of Theils inequality index. This study also analyzed the convergence behavior in the determinants of income. CHAPTER 3 DATA The three sources of data for this dissertation were the Supplement to Mark 5 or the Penn World Tables (PWT 5.5) compiled by Summers and Heston (1993), Basic Facts and Figures compiled by UNESCO (1951-1962), and The Statistical Yearbook compiled by UNSECO (1963-1993). The data on income, population, international openness, government expenditure, and investment expenditure were extracted from the Summers and Heston data. The data on the four indicators for human capital-public expenditure on education as a percentage of income, per capita consumption of newsprint, levels of education at the secondary school and university levels-were compiled from the two UNESCO series. The data span 36 years, 1955 to 1990. Though there are 24 countries in the OECD group, the data for Iceland and Luxembourg were insufficient to include them in this study. Due to the nature and complexity of the PWT data, their compilation procedure is discussed in this chapter. For greater details of construction of these data, please refer to Weatherspoon (1993) who discussed this subject at great length. 24 25 3.1 Penn World Tables The PWT data efforts date back to 1978 with the formation of the International Comparison Project (ICP) (Kravis et al., 1978a). This project attempted to compile Real Gross Domestic Product Per Capita (RGDP) for more than 100 countries where RGDP is the gross domestic product per capita adjusted for differences in the purchasing power of currencies. The objective of the ICP was to approximately fill the gap in the world statistical system arising from the absence of comparative data on "real" GDP per capita. The motivation for this project came from the widely accepted fact that the exchange-rate conversions of the GDPs of different countries to a common currency such as the United States dollar did not yield a reliable basis for international comparisons. The compilations in the ICP were based on the "nominal" values of the gross product obtained from a countrys national accounts. Therefore, the comparisons based on nominal values gave systematically incorrect estimates as exchange rates deviated from the conversion factors in systematic ways. The PWT data were constructed from intertemporal and interspatial extrapolations on ICP and non-ICP data and were compiled in a manner consistent with the national income identity. Thus, the nature of compilation of the PWT data makes them very valuable for empirical research. However, to comprehend the nature of the PWT data and appreciate the benefits from using PWT data over the ICP data, one needs to understand the construction and development of the ICP data. Sections 3.1.1 to 3.1.5 discuss the ICP data briefly. 26 3.1.1 International Comparison Project Phase I of the international comparison project (ICP) began with a pilot study in 1967, initiated by Kravis et al. (1975), at the University of Pennsylvania, which resulted in data collection for 10 countries for 1970 (Table 3.1). Two successive volumes, Phase II and Phase III, were published in 1978 and 1982. Phase II compiled data for an additional six countries and corrected the data from Phase I. Phase III compiled data, for 1975, for an additional 18 countries taking the count to 34 countries. Phase IV of this project, with 60 countries in 1980, was completed in two stages by the Statistical Office of the United Nations Secretariat (1985 and 1987). However, seven countries from Phase III withdrew from the study during this period. Therefore, there were 10, 16, 34, and 60 countries, in Phases I, II, III, and IV, respectively. In the first stage of the ICP, a classification system for gross domestic product (GDP) was developed which divided each countrys GDP into numerous detailed categories. GDP data were then collected for each category. Further, prices and quantities for each item within a category were also gathered. The classification system follows the scheme proposed by the system of national accounts (SNA). This classification system was improved upon to facilitate international comparability of the data (Kravis et al., 1975). In Phases I and II, there were a total of 153 detailed categories: 110 for consumption, 38 for capital formation, and five for government. Phases II and IV have 151 detailed categories: 108 for consumption, 38 for capital formation, and five for government. 27 Table 3.1 Countries Represented in the International Comparison Project Africa Asia Eurft&fi Countries represented in Phase I Kenya Columbia India France United States Japan W. Germany Hungary Italy United Kingdom Countries added in Phase II Iran Belgium S. Korea Malaysia Philippines Netherlands Countries added in Phase III Malawi Brazil Pakistan Austria Zambia Jamaica Sri Lanka Denmark Mexico Syria Ireland Uruguay Thailand Luxembourg Poland Romania Spain Yugoslavia Countries added in Phase IV Botswana Argentina Hong Kong Finland Cameroon Bolivia Indonesia Greece Ethiopia Canada Israel Norway Ivory Coast Chile Portugal Madagascar Costa Rica Mali Dominican Rep. Morocco Ecuador Nigeria El Salvador Senegal Gaulemala Tanzania Honduras Tunisia Panama Zimbabwe Paraguay Peru Venezuela Countries deleted in Phase IV Jamaica Iran Romania Mexico Malaysia Syria Source: Theil et al. 1989, p. 2. 28 The three categories of data used for classification were GDP or expenditure data, price data for each item for which a price could be identified, and quantity data for the items for which prices could not be identified. The expenditure data were obtained from the U. N. national accounts data. Once the base data were collected, there were steps and alternatives to calculating purchasing power parities (PPPs) for each country. 3.1.2 Purchasing Power Parities Purchasing power parity (PPP) is the number of currency units required to buy goods equivalent to what can be bought with a unit of currency of the base country (Kravis et al., 1982). From the several methods that can be used to calculate PPPs, the most frequently used by the ICP were the country-product-dummy (CPD) and Elteto- Koves-Szulc (EKS) methods. These two methods are identical if all the prices for every item in each country are available. In that event, the PPPs obtained from both methods are geometric means of all the prices in the detailed category a for country c (Kravis et al., 1975). The geometric mean in country c is obtained as A 1, (3.1) gu; (jj V Â¡-i-v" l-l where PÂ¡ c is the price of the item i in country c and m is the number of items. 29 3.1.3 Countrv-Product-Dummv Method The CPD is based on the assumption that the natural logarithm of the price of the item i in country c includes an item effect and a country effect; PPPs are estimated by least squares; and the relationship is stochastic. The CPD equation is (3.2) 1/m (lnC/y) = A, Be * where Pic is the price of the item i in country c, m is the number of items, eÂ¡c is normally distributed with mean zero and variance o2, AÂ¡ is the item effect on the price i in country c, and Bc is the country effect on the price. In most cases this method is normalized with U. S. as the base country. 3.1.4 Elteto-Koves-Szulc Method The EKS method consists of four steps: calculate "Laspeyres" and "Paasche" type price indices; calculate "Fisher" binary price indices; fill in the Fisher matrix if needed; and finally, build an EKS matrix of transitive parities. All calculations in the EKS method are based on the prices of the "characteristic" items. A characteristic item of a country is one that is considered to be purchased frequently within that country. Each country nominates at least one such product within each detailed category. The characteristic item chosen must also be priced in at least one other country. The price indices calculated in the first step of the EKS method are not true Laspeyres and Paasche indices and thus, they are called mini-Laspeyres and mini-Paasche price indices due to their similarity to the Laspeyres and Paasche indices in time-series 30 measurement. The difference is that the ratios in the EKS method are unweighted, unlike in time-series measurement. The general representation of the mini-Laspeyres index is * P n pu 1Jm (3.3) where c and d are two different countries and m is the number of characteristic items in category a. Similarly, the mini-Paasche index is obtained as * P ny* M *tcj v* (3.4) This method does not pick one base country, and thus, a matrix of mini-Laspeyres indices is created between countries with a diagonal of ones. The same is true for the mini-Paasche indices. Once the mini-Laspeyres and mini-Paasche indices are computed, the mini-Fisher price indices are constructed. The latter indices are the unweighted geometric means of the former two indices Ki (i O'* (3-5) The matrix of mini-Fisher indices is not transitive, and the EKS method is applied to make them so. The equation for the EKS method is 31 EKStj i Fm ti n -? C_1 li/- where t c/L (3.6) This is the PP for the detailed category a between countries c and d. The last step of the EKS method is to choose one country as a base country so that it can be compared with the CPD results. A base country can be chosen by observing the values in any of the country columns of the EKS matrix. If all the prices of items are available and are characteristic items, then the EKS method is the same as equation (3.1) if Pic is replaced with a price index. Without the basic prices, the CPD method does not equal a geometric mean and neither does the EKS method. This is due to the fact that the respective price indices in these methods cannot be computed with missing prices. An illustration to demonstrate the computations of PPPs is given in Kravis et al. (1975). 3.1.5 The Gearv-Khamis Method After estimating the PPPs, the second stage of the ICP was initiated. The Geary- Khamis method provides multilateral base-invariant price and volume comparisons at the various levels of aggregation for all countries, where the volumes are expressed in "international dollars". These volumes are additive across expenditure categories, while prices are obtained by dividing expenditures in national currency by those in international dollars. Geary suggested a system of homogeneous linear equations to calculate the international prices and PPPs simultaneously. Khamis proved that this system yielded 32 non-negative international prices and PPPs. The CPD or EKS method can be used to produce the detailed category PPPs for the Geary-Khamis method. These PPPs are transitive and are relative to the U.S. dollar. Detailed categories are indicated by the subscript a = 1,..., A. The volume of detailed category a in country c is (3.7) where Ea c is the per capita expenditure (in national currency) on detailed category a in country c. This volume is expressed in U.S. dollars. However, these volumes are not additive over the detailed categories. This method introduces the international price Pa of each detailed category and the overall purchasing power parity tc of each country c. Pa is written as N E p e=l N c-1 which is equivalently written as N If r.v. E<Â£.A> where v. m E (3.8) C-1 while xc is defined as A c A which is also 33 GDPÂ£I* Â£>K (3'9) -1 where GDPC (the gross domestic product of country c in national currency) is equal to GDF< IX, -1 It can be readily verified that (3.8) and (3.9) constitute a linear system of equations with (A + N 1) unknowns in P and l/xc (xc = 1 for c= U.S.) (Theil et al., 1989). The product P0Va>c is interpreted as real expenditure per capita in international dollars on category a in country c, and this product is additive over all categories. Let S be any grouping of such categories, then the sum over the categories within this group S of the real expenditure gives the real gross domestic product (RGDP) per capita in international dollars on S in country c. If S consists of all detailed categories, this sum is GDP per capita in c. Further discussions of intricacies in construction can be found in Weatherspoon (1993). 3.2 Extrapolations with ICP Data There are five publications of the extrapolations on the different phases of the ICP, the first by Kravis et al. (1978b), and the rest by Summers and Heston also known as the Mark 1 (1980), Mark 3 (1984), Mark 4 (1988), and Mark 5 (1991) (MARK 2 was not published, but used by Kravis et al. 1982). This study used data from a supplement to the MARK 5 data compiled by Summers and Heston in 1993. Therefore, only the 34 MARK 5 data is discussed at length. For detailed discussions of the other data sets, please see Weatherspoon (1993). The purpose of the first paper by Kravis et al. (1978b) was to fill the gap in the world statistical system for comparative data on "real" GDP per capita for a large number of countries. The contribution of the second paper by Summers and Heston (1980) was that they extrapolated the data for the ICP and non-ICP countries forward and backward through time. The third publication by Kravis et al. (1982) had two benchmark years, 1970 and 1975, unlike the previous papers which had only 1970. The fourth publication also by Summers and Heston (1988) was basically an update of the MARK 3 data set. The regression equation used to summarize the 1970 and 1975 cross-section relationship in Mark 3 (Summers and Heston, 1984) study was Inr = ax(Inwp + o2(lnp2 + a3(ln(0Pp + <41> where rx = ( DAj/PPPDAj) / DAUS and ^ = ( DAj/XRÂ¡ )/DAus. pppDA xs the purchasing power parity over domestic absorption, and XRj is the exchange rate. They are both expressed in national currency units of the jth country per U.S. dollars. OPj is the measure of relative openness of the jth economy defined as ((Exports, + ImportSj)/GDPj) / ((Exportsus + Importsus)/GDPus ), an average of the ratio for five years before the cross-section year. The as have the same expected signs as in Kravis et al. (1978b). 35 In Summers and Heston (1980), RGDPj t was based on constant prices while in Mark 3, international trade was incorporated into RGDP. The extrapolations in this data set were also treated differently and were computed at a greater disaggregated level. Data on consumption, gross domestic investment, government expenditure, and the net foreign balance, culled out from the U.N. constant-price series, were used to get real individual components expressed in 1975 international dollars for each of the years between 1950 and 1980. Mark 4 (Summers and Heston, 1988) updated the Mark 3 set. The major effort behind this project was to make the data more consistent, that is, the estimates need to adhere to the national income identity which states that total product equals total income generated by the production of the product. The implementation of consistency was done via an error-in-variables model. The objective was to adjust both the benchmark and national accounts data to make them consistent. The maximum likelihood procedure used to solve this model corrected the data sources so that they were consistent. However, a weakness of this procedure was that the asymptotic properties of maximum likelihood were not applicable. Mark 4 did not incorporate the openness variable since the exchange rates were greatly volatile during the 1970s. 3.3 Mark 5 Data Set MARK 5 covered 139 countries and RGDP per capita was obtained by extrapolating cross-section comparisons interspatially to non-benchmark countries and intertemporally to other years. This data set was based on ICP data from four 36 benchmark years: 1970, 1975, 1980, and 1985. Eighty-one countries participated in these benchmark studies and 47 participated in more than one study. Therefore, the need for relying on non-benchmark estimating methods was reduced. The national accounts data have also improved by using the World Banks archive data. The methodology for obtaining RGDP per capita for a large number of countries has improved. All these factors make the MARK 5 the most accurate data published in recent times. The four ICP benchmark studies, Phases II to V, used in this study were all compiled in different ways and have different countries participating in different years. This is why the data needed to be made intertemporal and interspatial. Since the Phase V data were not published at that time, the authors had to calculate the RGDPs on their own using raw data from the U.N. and The World Bank. The countries that participated in the 1985 benchmark comparisons form five groups: 22 OECD countries, 11 Asian countries including Japan, 22 African countries, five European Group II countries including Finland and Austria, and a group of Caribbean countries. The Caribbean countries comparisons were not complete at that time. The Geary-Khamis method was implemented for the OECD and Asian countries. The African countries, Hungary, Poland, and Yugoslavia all had data that allowed them to be linked to the OECD and Asian countries. The total number of countries from Phase V used in this study was 57. A different method was used for those countries which did not participate in the 1985 benchmark study, but which had participated in a previous benchmark study. The procedure was to value their 1975 or 1980 estimates of consumption (C), investment (I), 37 and government (G) expenditures at 1985 international prices. The growth rates for their components from the national accounts data and their change in international prices of the components between 1975 and 1985 or 1980 and 1985 were used. The changes in international prices were estimated from the benchmark estimates and the deflator for the numeraire country, the U.S. The 1975 and 1970 data were also re-analyzed. The May 1990 national accounts data were used for these revisions. The Geary-Khamis method was then used to aggregate the data. After the aggregation and re-estimations of the benchmark data, the non- benchmark countries RGDP per capitas were estimated. A post-allowance PPP was computed by dividing the national currency by the PPP implicit in the post adjustment index. A structural relationship was found in the benchmark countries between PPP and its post-allowance PPP. This relationship was used to estimate non-benchmark countries missing PPPs from their post-allowance PPPs. There were 81 benchmark countries and 57 non-benchmark countries that had to be estimated. The authors performed 12 different regressions for the benchmark studies and then these were used to obtain the non-benchmark estimates. Geary-Khamis method was used to aggregate the data resulting in consistent national absorption for all countries. It was still apparent that RGDP for poor and African countries were less accurate than estimates for rich countries. 38 3.4 Data for Estimation A supplement to the PWT5 data set, PWT 5.5, was compiled by Summers and Heston in 1993. This data set, in 1985 international prices, spans the years 1950-1990 for most countries. The information necessary for this study were extracted from this data set. A description of the variables tabulated in this document are listed in Table 3.2. Data on population (POP) and GDP per capita (RGDPCH) for the 22 OECD countries during 1955-1990 were used in estimation as tabulated. Shares of real investment and real government expenditures (iÂ¡ and gj) for country j (j = 1 to 22) were used to compute per capita levels of real investment and government expenditures, IÂ¡ and Gj, respectively. lj = ij RGDPCHj Gj = gj RGDPCHj International openness, 0Â¡, which represents the per capita level of exports and imports was compiled using OPENj variable as follows Oj = OPENj RGDPCHj where OPENj = {EXPORTSj 4- IMPORTSj} / CGDPj and CGDPj is the per capita nominal income in country j. Both the UNESCO series, Basic Facts and Figures (1951-1961) and the Statistical Yearbook (1963-1993), income and population figures from the Summers and Heston (1993) data were used to compile information on the four indicators of human capital for Table 3.2 Description of Variables in PWT 5.5 File Description 39 Variable POP Population in 000 s RGDPCH Real GDP per capita in constant dollars (Chain Index) (expressed in international prices, base 1985.) c Real Consumption share of GDP [%] (1985 intl.prices) i Real Investment share of GDP [%] (1985 inti, prices) g RGDPL Real Government share of GDP [%] (1985 inti, prices) Real GDP per capita (Laspeyres index) (1985 inti, prices) RGDPTT Real GDP per capita in constant dollars adjusted for changes in terms of trade (1985 international prices for domestic absorption and current prices for exports and imports.) Y CGDP relative to U.S. [%] (U.S. = 100, current inti, prices) CGDP Real GDP per capita (current inti, prices) cc Real Consumption share of GDP [%] (current inti, prices) ci Real Investment share of GDP [%] (current inti, prices) eg Real Government share of GDP [%] (current inti, prices) p Price level GDP [%] (PPP GDP/ U.S. dollar exchange rate) PC Price level Consumption [%] ([PPP of C]/XR) PI Price level Investment [%] ([PPP of I]/XR) PG Price level Government [%] ([PPP of G]/XR) XR Exchange Rate with U.S. dollar RGDPEA Real GDP per Equivalent Adult (1985 inti, prices) RGDPW Real GDP per Worker (1985 inti, prices) OPEN Openness (Exports + Imports) / Nominal GDP Summers and Heston, 1993. 40 the 22 OECD countries during 1955-1990. Per capita public expenditure on education (PE) for country i (i= 1 to 22) was compiled as PEÂ¡ = pe; RGDPCH, where peÂ¡ was the public expenditure on education as a percentage of income. Per capita consumption of newsprint (CNÂ¡) for country i, expressed in metric tons, was compiled directly as tabulated in the UNESCO series1. Education at the secondary school level (ESÂ¡) and university (or equivalent) level (ETÂ¡) in country i were compiled as ESi = esÂ¡ / POPi ETÂ¡ = etÂ¡ / POPÂ¡ where esÂ¡ was the total number of people with secondary school education, etÂ¡ was the total number of people with university (or equivalent) education, and POPÂ¡ was the population in country i. Thus, the variables represent the shares of the population with education at the secondary and university levels, respectively. In total, the data set used in the estimation of the research model had 36 observations per country i (i= 1 to 22)for each of the 22 OECD countries (36 x 22 = 792 total observations) for each of the eight variables: income (Y), per capita public expenditure on education (PEÂ¡), per capita consumption of news print (CN), education at secondary school level (ESÂ¡), education at university (or equivalent) level (ETÂ¡), per 1 The data for CN in 1986, for all the countries, was not available and was substituted by the average value of 1985 and 1987. 41 capita international openness (0Â¡), per capita investment expenditure (y, and per capita government expenditure (G). CHAPTER 4 INCOME AND HUMAN CAPITAL IN THE OECD COUNTRIES In this chapter, levels of per capita income in 22 OECD countries are estimated (as a function of human capital, international openness, investment and government expenditures) and analyzed. Several studies analyzing the relationship between growth with human capital and income convergence have used multiple regression techniques (Barro, 1991; Barro and Sala-i-Martin, 1992; Mankiw et al., 1992) and mathematical optimization techniques (Lucas, 1988, 1993). Tallman and Wang (1992) reviewed neoclassical and endogenous growth models to argue that improvements in formulating human capital measures in growth models could help establish a stronger link between human capital and growth. Weatherspoon (1993) used Theils inequality index to measure inequality in income, industrial employment, investment expenditure, and government expenditure for the G-7 and 14 OECD countries during 1950-1985. He then used cointegration analysis to test for a long-run relationship among these inequalities. The basic premises of the model for estimation were derived from the national income identity for an open economy and the development of endogenous growth models. The national income identity states that national income is a function of consumption, 42 43 investment and government expenditures, and volume of exports and imports. International trade is one of the key determinants of economic interaction among countries and countries gain from trading goods and services by taking advantage of the differences between their endowments and by achieving economies of scale in production. These gains from trade are reflected in the growth (or decline) of national income. Further, the national income accounts provide information essential for studying the disparities in income among rich and poor countries (Krugman and Obstfeld, 1991). Growth theorists (Barro, 1991; Mankiw et al., 1992; Lucas, 1988, 1993; Romer, 1989, 1994; Tallman and Wang, 1992) have shown that accumulation of human capital is beneficial to the economy as a whole and the individual within the economy. Therefore, income was specified as a function of human capital, international openness, government expenditure, and investment expenditure. The model is discussed further in Section 4.2 of this chapter. The objective of this study was to analyze the nature of the influence (if any) of factors of economic growth (especially human capital) on income for the 22 OECD countries (in Chapter 1) during 1955-1990. The classical econometric treatment assumes that the observed variables, endogenous and exogenous, are measured without error. Latent variable models, on the other hand, incorporate measurement error in the observed variables into the estimation process. These errors can be correlated, and multiple indicators can measure the unobservable variable. Therefore, as the level of human capital is not directly observable, this study estimated income using a latent variable model (Bollen, 1989) with human capital as the latent variable. 44 The layout of this chapter is as follows: Section 4.1 introduces a general latent variable model, Section 4.2 gives the estimation procedures, section 4.3 describes the empirical research model, Section 4.4 gives the results of estimation, Section 4.5 tabulates the results from estimation of per capita income and analyzes the effects of human capital, openness, investment and government expenditures on income, and Section 4.6 concludes this chapter. 4.1 General Latent Variable Model The full latent variable model consists of a system of structural equations. These equations contain random variables, structural parameters, and sometimes nonrandom variables. The three types of random variables are latent, observed, and distur bance/error variables. The nonrandom variables are explanatory variables whose values remain the same in repeated random sampling (fixed or nonstochastic variables). The links between the variables are summarized in the structural parameters. The structural parameters are invariant constants that provide the "causal" relation between variables. The system of structural equations has two major subsystems: the latent variable model and the measurement model. 4,1,1 Structural Equations of the Model The first component of the structural equations is the latent variable model which encompasses the structural equations that summarize the relationships between latent variables: 45 n Bn + r{ + c (41) where 77 is an m x 1 vector of latent endogenous random variables; Â£ is an n x 1 vector of latent exogenous random variables; B is the m x m coefficient matrix showing the influence of the latent endogenous variables on each other; r is the m x n coefficient matrix for the effects of Â£ on rÂ¡, and contains no zero elements. The matrix (I B) is nonsingular. The diagonal of B is always zero, f is the disturbance vector that is assumed to have an expected value of zero [ E(f) = 0 ], homoscedastic, nonautocorrelat- ed, and which is uncorrelated with Â£. The second component of the structural system is the measurement model: y V + e (4.2) x = A,Â£ + 6 (4.3) where y (p x 1) and x (q x 1) vectors are observed variables. Aj(p x m) and Ax (q x n) are the coefficient matrices that show the relation of y to tj and x to Â£, respectively, e (p x 1) and 5 (q x 1) are the errors of measurement for y and x, respectively. The errors of measurement are assumed to be uncorrelated with Â£ and f and with each other. The expected value of e and 5 are zero. To simplify matters rj, Â£, y, and x are written as deviations from their means. Further, Â£ cannot influence any y directly; if the x and y vectors contain measurement errors, these errors cannot influence one another directly. 46 4.1.2 Implied Covariance Matrix Covariance is a central concept for the above models: the covariance algebra helps in deriving properties of the latent and measurement models; and determine factors that influence sample covariances which in turn can affect parameter estimates. Two covariance matrices are part of the latent variable model: 4> (n x n), a symmetric matrix, is the covariance matrix of the latent exogenous variables^ s); Â¥ (m x m) is the covariance matrix of the errors in the latent variable model. Thus, the covariance matrix for r\ is a function of B, T, 4, and For the measurement model, 0, (q x q) and 0t (p x p) are the covariance matrices of the errors of measurement 8 and e, respectively. Specifically, 4 = E(Â£H, = E(ft), a = E(55), and 0f = E(ee). The sample covariance matrix is crucial to the estimates of structural equation models since factors that affect this matrix have the potential to affect the parameter estimates. The nx(p + q) sample covariance matrix is computed as (4.4) T where z is [y x]. The population covariance matrix is denoted by E. is the covariance matrix of y, E is the covariance matrix of x, EyX and E^ are the covariance matrices of y with x and x with y, respectively. Let 6 denote the vector of unknown parameters. Then, Eyy (0) is SJd) = Efyy') = Ay E(rÂ¡rl') + 0, (4.5) Substituting the reduced form of equation (4.1) 47 n 0 in E(ijrj) and simplifying we get 2^(0) = Ay (/-B)1 (Tr/ + T) [(/-B)-1]' Ay + 0t (4-6> which shows that the covariance of y is a complex function of six of the eight model parameter matrices or vectors. Similarly, 2^(0) = E(yx) = A, (/-B)"1 T sw(6) = 2^0)' A.sr' [(/--]' 4 Further, 2(0) = Â£(') A, Â£(((') K+% (49) Substituting for E(Â£Â£') we have S(0) A,A^ e, <410> Therefore, the covariance matrix 2 (0) for the observed y and x variables as a function of the model parameters is 2(0) V0> V0> .Ve> s(0) (4.11) which can also be written as 48 Ay(/-2*r1(Tr/ + et ai-m-'rvK (412) A^crlc/-^)^ + e6 4.1.3 Identification Investigations of identification (Bollen, 1989) begin with one or more equations relating known and unknown parameters. Known parameters are those that are known to be identified such as variances and covariances for which consistent sample estimators are readily available. The unknown parameters are those whose identification status is not known and the researcher must establish whether unique values exist for these. The unknown parameters are from the structural equation model. Identification is demonstrated by showing that the unknown parameters are functions only of the identified parameters and that these functions lead to unique solutions. If this can be done, the unknown parameters are identified; otherwise one or more parameters are unidentified. Therefore, the objective is to solve for the unknown parameters in terms of the identifiable parameters. The parameters in 0 are globally identified if no vectors 0j and 02 exist such that E (0t) = E (02) unless 0! = 02. t-Rule Let p+q be the number of observed variables, and t be the number of free and unconstrained elements in 0. The t-rule for identification (Bollen, 1989) is that the number of nonredundant elements in the covariance matrix of the observed variables must 49 be greater than or equal to the number of unknown parameters in 0. In other words, the necessary but not sufficient condition of identification is: / < (p + q) (p + q + 1) (4-13) 2 The nonredundant elements of E = E(0) imply (p + q)(p + q + l)/2 equations. If the number of unknowns in 0 exceeds the number of equations, identification is not possible. Two-Step Rule Under this rule (Bollen, 1989), the first step is to treat the model as a confirmato ry factor analysis. This implies that the original y and x are treated as x variables, and the original rj and Â£ are treated as Â£ variables. The only relationships between latent variables that are of concern are their variances and covariances (<Â£). In short, B, T, and 'k elements of equation (4.1) are ignored. This model is identified if a unique solution exists for the structural parameters Ax, 4>, and 05 such that no vectors 7! and y2 exist that make E(0,) = E(02) unless 0, = 02. If the model is identified at this juncture then we move to the next step. The second step examines the latent variable equation of the original model given by (4.1) and is treated as a structural equations model with observable variables having no measurement error. Next it is determined whether B, T, and Â¥ are identified ignoring the measurement parameters considered in the first step (Ax, 4, and 04). This is achieved by verifying the identification of equation (4.1) using the order and rank conditions prescribed for systems of equations (Bollen, 1989). The order condition is 50 a necessary condition which requires that the number of variables excluded from the equation to be identified are at least p-1. The rank condition is necessary and sufficient for identification and requires that the ith equation, of a system of equations, is identified if the rank of CÂ¡ is equal to p-1, where c = [(I-B) | -T]. If the first step shows that the measurement parameters are identified and the second step shows that the latent variable model parameters are also identified, then this is sufficient to identify the model. This is so since the first step establishes that all parameters in the measurement model are identified, including the covariance matrix of the latent variables. The second step establishes whether B, T, and Â¥ are functions of the identified covariance matrix of the latent variables. Since this is a sufficient condition for identification, a model could fail to meet it and still be identified. However, this rule exemplifies the possibility that constraints on the latent variable relations can assist the identification of measurement parameters such that even if a model failed the two-step rule, it could still be possible to find unique solutions for the unknown parameters. MIMIC Rule The models referred to as MIMIC (Bollen, 1989) contain observed variables that are Multiple Indicators and Multiple Causes of a single latent variable. However, the MIMIC rule applies only to models in a certain form (as below) making its applicability narrow in range. The equations in this model are: 51 Hi = I* C, y = Aytij + e (4.14) x = l where x is a perfect measure of Â£ and only one latent variable, rÂ¡u is present. Then rj, is directly affected by one or more x variables, and it is indicated by one or more y variables. Identification of the MIMIC models that conform to (4.14) follows if p (the number of ys) is two or greater and q (the number of xs) is one or more, provided rÂ¡Â¡ is assigned a scale. Therefore, the MIMIC rule for the model in (4.14) above with p > 2 and q ^ 1 is a sufficient condition for identification but not a necessary one. 4.2 Estimation The hypothesis for the generalized latent variable model is E = E(0). Given the sample covariance matrix of the observed variables, S, 0 has to be chosen such that E(0) is close to S. Theoretically, this means that we need to minimize E(0) to get consistent estimators of 0. Three such minimizing fitting functions are: the maximum likelihood (ML) function; the unweighted least squares (ULS) function; and the generalized least squares (GLS) function 52 = log|S(0)| + tri 52Tl(0) > log|S| (p+i) Fou = (1/2) ir{[/- 22(0)5 (4.15) Fuu = (1/2) ft* {[5 22(0)f). Each of these functions is minimized with respect to 8. Further, the estimated values of the four explanatory variables are obtained by minimizing the weighted squared errors as proposed by Bartlett (1938): (4.16) The estimated or predicted per capita income is computed as: (4.17) s = n. 4.3 Empirical Model The research model in question had one endogenous variable (per capita income (Y)), one exogenous latent variable (human capital (H)), and three exogenous variables (investment expenditure (I), government expenditure (G), and international openness (O)). Income was the real gross domestic product per capita, international openness was measured as the real per capita level of exports and imports, and government and investment expenditures were measured at real per capita levels (Chapter 3, Section 3.4). Income, international openness, investment and government expenditures were assumed to be observed without error for the purposes of estimation. 53 The indicators for human capital were levels of per capita public expenditure on education (PE), per capita consumption of newsprint (CN), shares of population with high school education (ES), and shares of population with university or equivalent education (ET). In a review of growth models, Tallman and Wang (1992) concluded that there were potential gains from greater emphasis on higher education, which improved learning efficiency on the job and yielded significant positive external effects. This improvement in on-the-job learning was also important for promoting perpetual economic growth, adding significantly to individual human capital stock as well as to the stock of societys knowledge that may improve the quality of life (Lucas, 1993). Therefore, since PE gave an indication of the level of investment in human capital, CN indicated a level of reading, and ES and ET denoted the shares of educated population, they were feasible choices for indicators of human capital accumulation. Further, the availability of data was yet another reason for the choice of indicators. Therefore, there were 36 observations for each of the eight variables (Y, PE, CN, ES, ET, O, I, and G) and for each of the 22 OECD countries. Since the intention was to study the convergence behavior of these countries as a group, the data were pooled making the total number of observations in each vector to be 792. Therefore, using equations (4.1), the latent variable model for estimation was 54 [Yi Y* Y3 Y4] (4.18) where income was assumed to be observed without error (rÂ¡=y). The measurement model for estimation, similar to equation (4.3), was PE Xj 0 0 0 *1 CN x2 0 0 0 ES x3 0 0 0 H ET x4 0 0 0 V + 64 I O 0 0 m 0 G 65 / oox6o G 0 0 0 x7 67 (4.19) where the matrix on the left-hand side consisting of PE, CN, ES, ET, O, I, G vectors corresponded to x. Ax was the first matrix on the right side with factor loadings wherein which X5, Xg, and X7 were normalized to a value of one for purposes of estimation. Â£ corresponded with the matrix of exogenous latent variables wherein which Â£, was H and Â£2, Â£3, and Â£4 were assumed to be directly observable as O, I, and G, respectively. Therefore, 55 = 86 = ^ = 0 for estimation, f was the vector of errors in rj(=y). From equations (4.6) to (4.8) and equation (4.10), we could derive the implied covariance matrix for the observed y and x variables as a function of the model parameters: 55 2(6) r$r/ + y A3rr/ a* where 4 was the variance-covariance matrix of Â£, Y is the variance in i\, and 0S is the variance-covariance matrix of x. For the purposes of estimation, the data were treated as deviations from their means. In this model, the variance parameter of H, normalized to one to facilitate estimation. This implied that H N(0,1) which eased the statistical inference of the human capital variable. The variance parameters of O, I, and G were treated as fixed as in regular regression analysis. Additionally, mu)-= 1 $12 *13 *14 hi $12 *23 *24 >31 $31 *33 *34 J41 $42 *43 *44 where 2 = *22 *23 *24 *32 *33 *34 $41 *43 4*44 was the matrix of variance-covariance between the observed O, I, and G. Therefore 4>2 = S2 from the sample variance matrix (Section 4.2). Further, the restriction that 4>n = 4 matrix looked like 2The model was estimated with and without the restriction that 0. The likelihood ratio test failed to reject the restriction at a=0.05 level of signifi cance. 56 1 0 0 0 4 = 0 4*22 4*23 4*24 0 4*32 4*33 4*34 0 4*42 4*43 4*44 (4.21) From equations (4.15) to (4.17) above, the empirical system of equations consisted of eight coefficients 7Â¡ (i=l to 4), and (j= 1 to 4)) and five variances (E(fn, E(<5j5j) (j = l to 4) that were to be estimated. Therefore, the number of unrestricted unknowns in the 6 vector of the empirical model were 13 and the t-rule value computed using equation (4.13) was 36. The empirical model, described by equations 4.15 and 4.16, was in the MIMIC form with p=l and q=7 y = r? C y = n (4.22) x = + 6 Therefore the necessary and sufficient conditions for identification were met for this model. 4.4 Parameter Estimates of the Latent Variable Model The maximum likelihood function FML as given in the previous section was used to estimate the parameters of this model. Table 4.1 gives the estimated parameters for the latent variable model (from equation 4.18) and their asymptotic standard errors of estimation. These results clearly indicate that human capital (as measured by a latent 57 variable), international openness, investment and government expenditures had positive and statistically significant effects on income for the 22 OECD countries. These results complied with the theoretical underpinnings from basic macroeco nomic and growth theories which indicate that growth in income was positively correlated with accumulation of capital and growth in international trade. The greatest positive effect on income was imposed by the level of human capital implying that human capital was a key determinant of income in the 22 OECD countries. This result tallied with the results put forth by Barro (1991), Mankiw et al. (1992), Tallman and Wang (1992), and Lucas (1988, 1993). The positive effect of international openness was as predicted by Romer (1990) who proposed that growth in international trade yielded positive dividends for economic growth. Mankiw et al. (1992) found that, in an augmented Solow model, a higher savings rate led to higher income and higher level of human capital. Barro (1991) found that growth in income was positively related to investment expenditures. Thus, the positive effects of investment and government expenditures were not surprising. Further, the elasticities in average income (Column 5) with respect to average levels of human capital, openness, investment and government expenditures are all positive. This also lends support to the above analysis that income is positively influenced by all the four factors and especially human capital followed by investment expenditure, government expenditure, and openness in that order. 58 Table 4.1 Parameter Estimates of the Latent Variable Model for 22 OECD Countries, 1955-1990. Variables Parameters Estimates Standard Elasticities Errors 1 2 3 4 5 H 7i 11.79 0.75 0.65 0 72 0.08 0.01 0.03 I 73 1.58 0.04 0.46 G 74 1.46 0.10 0.43 ECw) i 56.04 0.26 Table 4.2 gives the estimated parameters for the measurement model (from equation 4.19) and their standard errors of estimation. The factor loadings were all positive and statistically different from zero (a = .05). This result was as expected since the indicators contributed to the accumulation of human capital (Barro, 1991; Mankiw et al., 1991; Tallman and Wang, 1992; and Lucas, 1988, 1993). Increased public expenditure on education positively influences human capital accumulation since this investment results in improvement of level of schooling, improvement in skills, and level of technology; increased consumption of newsprint denotes an increasing level of reading which in turn could indicate increases in the level of educated population; increasing shares of educated population at the secondary school and university levels indicates growth in an educated and skilled population. An increase in all four variables does indicate a better level of living standard. Table 4.2 Parameter Estimates of the Measurement Model for 22 OECD Countries, 1955-1990. 59 Variables Parameters Estimates Standard Errors 1 2 3 4 PE x, 2.65 0.08 CN X2 1.04 0.04 ES X3 1.43 0.08 ET X4 0.97 0.03 E(5,6,) 1.51 0.06 EW) 22 0.54 0.02 E(5,63) e33 3.55 0.05 E(6A) Bu 0.28 0.02 4.5 Income and Human Capital in OECD Countries Using Bartletts method (equation 4.16) and the estimated parameters (Table 4.2), A we can compute the per capita value for human capital, H: = 2.7 / 1.5 -1 '2.7' -> '2.7 / 1.5 -1 PE 1.0 0 0.5 1.0 1.0 0 0.5 CN 1.4 0 0 3.6 1.4 1.4 0 0 3.6 ES 1 0 0 0 0.3 1 1 1 0 0 0 s ET (4.23) Using equation (4.17) and the parameters of estimation from Table 4.1, per capita incomes of the 22 OECD countries are computed: t = 11.79 + 0.08 O + 1.58 I + 1.46 G <4-24) These computations yield 792 values for human capital and per capita income for the 22 countries. Therefore, the estimation of the model yielded 36 values for each variable for each country. The values of estimated per capita income and human capital for each 60 country were weighted by their respective populations to yield an average per capita income and average per capita level of human capital for the 22 OECD countries as a group, 1 OECD , OECD h n Â£ L A7 * where Y0ecd was the per capita income of the group of 22 OECD countries, nÂ¡ (i = l to 22) was the population of country i, YÂ¡ (i= 1 to 22) was the per capita income of country i, Hoecd was the per capita level of human capital for the 22 OECD countries as a group, Hj (j = 1 to 22) was the per capita level of human capital of country j, and N was the total population in the 22 countries. Similarly, average per capita levels of observed income (Yoecd), openness (0OECD), investment (IOEcd) and government (GOECd) expenditures were computed for the group of 22 countries. Table 4.3 tabulates estimated levels of human capital for the 22 OECD countries individually. For the purposes of estimation, this variable was specified to be distributed as N(0,1) to ease interpretation of results. However, while reporting the results for this variable, it was rescaled to bring it to a form comparable with that of the other variables in the model. Therefore, it has to be noted that when the values in Table 4.3 are expressed as deviations from their mean, they are still distributed as N(0,1). Table 4.4 summarizes the computations of average levels of per capita human capital, openness, investment and government expenditures for the 22 OECD countries. Column 2 of this table gives the values of average level of human capital. Therefore, the value of human 61 Table 4.3 Estimated Levels of Human Capital (HÂ¡, i=l to 22) in the 22 OECD Countries, 1955-1990 Year USA Canada Japan Austria Belgium Denmark Finland France Germany Greece Ireland 1 2 3 4 5 6 7 8 9 10 11 12 1955 450.18 373.93 335.50 350.76 333.01 368.62 376.09 339.33 363.01 304.13 332.65 1956 450.04 378.99 341.50 348.17 341.72 376.54 400.37 362.12 366.43 304.87 331.72 1957 459.95 402.90 344.42 343.18 354.48 379.60 408.97 356.55 369.38 306.26 331.27 1958 455.57 417.21 348.60 345.01 396.00 380.44 398.57 357.38 373.51 306.70 331.04 1959 470.54 432.82 352.79 362.30 406.66 387.97 411.26 358.91 381.03 309.38 333.44 1960 537.94 454.01 352.96 366.80 414.59 393.88 428.20 367.16 382.18 310.34 339.02 1961 491.22 467.99 362.01 366.12 431.15 412.96 448.71 396.54 395.88 311.16 343.84 1962 522.35 513.72 370.20 377.72 437.30 470.06 459.36 399.26 398.99 311.29 337.93 1963 544.43 509.49 378.75 385.14 415.85 473.04 468.49 395.62 403.32 314.98 352.12 1964 554.28 525.79 390.27 396.65 473.62 499.85 473.26 420.87 415.60 324.14 364.58 1965 576.34 573.77 395.25 406.40 429.11 529.92 479.00 431.08 430.32 321.20 371.79 1966 584.25 625.58 402.99 426.43 450.93 556.03 488.89 440.45 434.88 322.19 370.34 1967 551.46 578.06 382.49 409.69 423.12 496.46 465.22 405.97 403.21 318.36 361.21 1968 569.28 581.66 388.50 416.64 436.17 512.54 459.64 435.61 406.50 321.38 368.51 1969 598.91 608.68 397.84 425.03 456.79 530.09 479.01 448.39 417.86 327.02 378.91 1970 606.59 624.61 410.59 428.66 428.48 550.00 493.68 421.61 438.75 323.35 384.86 1971 624.13 636.52 419.49 437.67 432.18 577.22 493.20 425.25 459.12 323.56 385.54 1972 628.82 632.31 427.99 452.08 438.21 567.77 498.46 432.78 445.75 324.07 393.21 1973 654.12 654.18 440.13 462.83 480.79 571.16 518.54 506.64 455.91 328.17 406.46 1974 640.86 647.12 458.16 475.44 519.14 589.24 520.06 485.71 469.24 332.11 410.72 1975 609.82 662.52 472.41 487.67 523.56 594.19 534.03 515.66 493.19 333.82 435.72 1976 613.42 676.93 471.93 497.17 536.38 631.60 549.25 534.00 465.41 335.45 428.17 1977 648.37 694.28 481.83 498.94 550.21 572.90 544.50 537.35 491.30 336.18 440.59 1978 675.54 712.86 499.88 505.40 536.59 583.06 528.81 521.76 497.44 342.62 452.09 1979 666.53 706.72 512.95 511.74 546.60 566.09 517.28 449.16 502.43 343.52 469.16 1980 693.18 707.88 519.73 518.18 551.50 586.94 530.76 517.07 507.54 347.97 473.74 1981 693.78 726.47 534.51 531.20 555.15 584.92 535.52 542.92 504.86 347.81 494.22 1982 680.37 721.36 527.83 528.42 554.31 599.40 546.92 556.66 497.68 348.35 487.97 1983 680.30 722.33 527.81 537.65 552.00 603.00 543.49 564.34 498.07 348.02 468.34 1984 696.71 714.56 519.28 537.54 550.17 601.11 540.23 570.93 508.65 353.10 470.95 1985 713.03 720.79 525.50 543.20 550.83 600.72 559.90 561.15 507.49 362.26 476.93 1986 727.63 751.56 525.42 554.71 534.21 674.40 567.92 558.69 507.55 357.97 485.91 1987 739.10 756.00 529.36 555.06 528.16 692.75 578.20 559.12 510.44 357.73 487.79 1988 647.14 766.91 538.55 551.88 526.22 683.02 589.89 563.87 509.15 362.25 484.68 1989 661.49 768.33 543.57 556.02 551.44 678.68 608.96 572.87 510.12 369.55 488.01 1990 710.95 780.63 557.59 561.32 556.17 679.75 627.09 583.62 518.80 370.19 500.09 62 Table 4.3 (Contd) Year Italy Netherlands Norway Portugal Spain Sweden Switzerland Turkey UK Australia New Zealand 13 14 15 16 17 18 19 20 21 22 23 24 1955 331.69 387.65 369.76 302.72 304.64 356.34 379.20 305.88 366.63 377.34 384.82 1956 332.99 358.23 375.19 303.03 304.25 357.78 383.72 305.73 367.25 375.56 383.52 1957 338.74 403.86 385.55 303.43 305.68 361.66 388.59 307.68 386.70 375.39 389.24 1958 340.30 400.95 396.23 303.47 306.10 375.89 393.28 309.11 386.51 356.72 390.79 1959 346.20 411.51 408.68 307.95 310.10 382.47 400.10 308.38 394.62 397.66 392.38 1960 362.77 430.81 412.09 310.79 312.65 385.01 418.17 307.88 398.33 401.59 408.11 1961 394.38 443.53 419.48 310.45 309.40 454.59 427.01 312.21 428.33 407.55 412.65 1962 412.17 457.44 435.86 310.24 312.28 469.33 502.07 312.63 441.10 410.54 416.94 1963 420.84 469.24 459.55 310.32 315.20 515.63 499.15 314.19 448.74 416.22 420.43 1964 424.72 497.04 469.63 309.02 326.20 532.84 489.88 314.24 459.24 430.10 431.38 1965 435.90 507.57 477.49 310.06 322.89 550.21 510.01 318.24 472.68 439.84 443.82 1966 402.44 482.81 498.20 310.47 324.68 573.75 473.64 321.32 486.48 448.65 455.63 1967 422.03 499.82 465.19 308.62 327.69 609.66 476.95 320.98 456.49 437.98 435.13 1968 418.82 514.62 472.63 310.08 331.45 589.34 481.09 321.37 441.23 441.38 433.72 1969 412.48 536.25 485.50 310.52 343.25 612.96 489.60 320.43 463.59 453.87 445.53 1970 418.96 566.04 475.48 344.71 349.06 607.67 504.84 318.42 465.84 467.55 467.46 1971 433.78 577.41 498.15 320.11 350.46 611.03 516.44 329.93 479.56 486.13 491.89 1972 447.85 580.25 537.61 323.25 362.35 616.59 525.98 343.37 510.94 503.22 493.82 1973 465.31 595.38 547.16 330.08 342.92 619.65 547.24 343.63 518.19 514.77 503.62 1974 466.93 616.54 547.84 337.18 342.41 621.22 556.23 347.47 508.71 572.59 517.70 1975 452.12 632.23 560.07 350.53 350.36 624.59 549.00 351.19 512.18 579.36 511.79 1976 465.95 638.83 602.11 361.16 354.27 639.36 550.67 354.51 515.58 576.52 498.16 1977 469.70 641.12 606.20 358.85 351.87 659.77 557.14 357.76 507.12 533.92 497.65 1978 457.17 651.91 639.41 368.42 365.75 693.12 552.77 335.58 507.69 461.35 496.76 1979 485.58 657.63 646.36 365.01 367.76 704.35 555.29 334.37 510.46 573.66 488.09 1980 495.49 631.94 627.18 378.35 368.12 716.36 570.91 323.64 513.97 575.46 507.46 1981 494.27 625.45 614.41 384.84 369.16 716.65 566.32 325.69 504.40 580.05 513.52 1982 493.64 610.86 618.17 388.61 372.25 711.18 567.00 325.73 504.66 579.13 504.23 1983 482.30 585.12 631.95 375.45 375.32 689.90 573.76 331.59 505.21 585.15 502.49 1984 499.41 584.82 637.16 378.64 386.77 691.67 572.21 323.98 501.98 626.88 503.87 1985 500.03 591.31 643.34 381.79 388.56 681.16 569.92 321.14 500.43 629.52 486.85 1986 505.76 599.99 674.67 381.72 389.01 683.17 583.93 320.59 512.98 595.49 523.13 1987 512.33 618.00 694.03 389.90 395.06 683.35 583.05 316.55 519.16 567.55 533.16 1988 521.26 602.00 700.72 403.04 427.52 654.16 596.18 317.65 525.44 565.52 541.48 1989 527.79 594.71 725.45 410.67 442.02 694.70 598.70 317.49 525.93 581.28 579.73 J990 446.14 ...m2} 738.22 4WQ 447.71 715.51 337.99 536.10 -52192 607.98 63 Table 4.4 Average Per Capita Levels of Human Capital (Hqecd), International Openness (Oqecd) Investment Expenditure (Ioecd)> and Government Expenditure (GOECd) in the 22 OECD Countries, 1955-1990 Year Human Capital International Openness Investment Expenditure Government Expenditure Hqecd Goecd Ioecd Goecd 1 2 3 4 5 1955 372.83 1283.14 1430.91 804.33 1956 375.89 1365.37 1457.26 808.44 1957 383.16 1422.75 1450.56 823.91 1958 384.16 1315.70 1404.01 828.75 1959 393.24 1393.18 1541.13 840.97 1960 416.43 1542.55 1639.43 852.70 1961 415.14 1568.23 1720.29 889.76 1962 431.45 1602.20 1815.93 927.39 1963 441.45 1675.17 1898.90 948.58 1964 453.25 1790.54 2066.63 964.09 1965 466.20 1865.29 2183.51 986.99 1966 471.55 1959.88 2287.96 1041.05 1967 450.93 2002.95 2316.70 1098.33 1968 458.80 2179.37 2476.89 1122.68 1969 474.78 2364.32 2646.05 1132.43 1970 481.22 2542.15 2703.16 1150.82 1971 493.73 2608.37 2757.89 1166.60 1972 501.24 2717.41 2882.64 1175.46 1973 519.74 3088.94 3149.99 1194.64 1974 519.92 3715.18 3017.30 1220.03 1975 518.27 3341.05 2633.05 1248.78 1976 521.36 3638.81 2870.10 1271.79 1977 534.82 3722.07 2973.74 1285.45 1978 543.37 3717.13 3074.45 1318.60 1979 542.60 4094.06 3176.32 1342.82 1980 557.36 4368.00 3060.20 1360.88 1981 561.50 4435.24 3016.31 1375.90 1982 556.70 4269.67 2789.60 1392.52 1983 556.29 4254.21 2844.59 1419.41 1984 562.79 4665.34 3187.09 1450.12 1985 568.16 4733.06 3254.57 1489.07 1986 574.88 4402.15 3329.83 1530.81 1987 580.36 4519.56 3487.03 1560.68 1988 557.26 4795.09 3733.70 1583.16 1989 565.66 5158.82 3949.07 1585.50 1990 581.93 5276.98 4003.32 1610.41 64 capital was increasing over time implying that the level of human capital has been increasing over time for the 22 OECD countries. From columns 3 to 5 of this table, it can be seen that average per capita levels of openness, investment and government expenditures, respectively, were also increasing over time though at different rates. Figures 4.1 and 4.2 depict these patterns clearly. These results indicate that the per capita income could be expected to increase over time as evidence from literature had suggested (Barro, 1991; Mankiw et al., 1992). Further, comparing the estimated levels of human capital in the individual countries to the average level (from Table 4.3, Table 4.4, and Figure 4.3) revealed that six countries (USA, Canada, Denmark, Netherlands, Norway, and Sweden) had above average levels, nine countries (Japan, Austria, West Germany, Greece, Ireland, Italy, Portugal, Spain, and Turkey) had below-average levels, and seven countries (Belgium, Finland, France, Switzerland, UKD, Australia, and New Zealand) tracked the average closely. Tables 4.5 and 4.6 give the values of observed and estimated income for the 22 countries separately. Columns 2 and 3 of Table 4.7 give the average levels of per capita observed and estimated incomes (YOECD and YOECD) for the 22 countries. At a glance, this table reveals that (i) income (observed and estimated) was increasing over time, and (ii) the estimated income values fit the observed income values quite closely. Further, from this table and Figure 4.4, the estimated income is initially lower than the observed income. Towards the end of the period the estimated income is lower than the observed 65 1955 1960 1965 1970 1975 1980 1985 1990 Year Figure 4.1 Average Level of Human Capital (HOEcd) in the 22 OECD Countries, 1955-1990 66 H, Oj I, G Figure 4.2 Average Level of Human Capital (HOECd), International Openness (0OECD), Investment (Ioecd) and Government (GOECd) Expenditures in the 22 OECD Countries, 1955-1990 Figure 4.3 Comparing Country wise Levels of Human Capital (HÂ¡, i = l to 22) and Average Level of Human Capital (HOECD) in the 22 OECD Countries, 1955-1990 H; *- Ho, BCD 68 USA ia5; nao isas wo is?s isao isas ns Canada Austria 69 Figure 4.3 (Contd) 70 Figure 4.3 (Contd) 71 1055 1800 1870 1855 1080 1805 1870 1875 1880 1805 1080 y*ar 1800 1905 1970 1075 1900 1985 1990 1955 1060 1905 1070 1975 1080 1905 1090 Figure 4.3 (Contd) Sweden 1933 1060 HW3 1070 ir75 1060 T003 1000 Yar 10 1000 1903 1970 1073 1900 1905 1990 900 700 800 300 400 300 A H 800 700 600 500 400 300 Figure 4.3 (Contd) 73 A 1B55 1900 1 005 1970 1075 1990 1095 1990 roor 1955 1000 1905 1070 1975 1000 1996 1090 Figure 4.3 (Contd) 74 Table 4.5 Levels of Observed Income (YÂ¡, i=l to 22) in the 22 OECD Countries, 1955-1990 Year USA Canada Japan Austria Belgium Denmark Finland France Germany Greece Ireland 1 2 3 4 5 6 7 8 9 10 11 12 1955 9593 7012 2125 3921 5094 5453 4598 4944 5185 1688 2969 1956 9584 7459 2260 4061 5208 5572 4675 5267 5444 1819 2896 1957 9530 7363 2401 4296 5294 5780 4666 5477 5667 1936 2861 1958 9278 7225 2511 4458 5172 5837 4595 5550 5814 2007 2843 1959 9718 7330 2706 4605 5307 6349 4910 5685 6196 2064 3030 1960 9776 7288 3033 5176 5583 6751 5367 6013 6637 2088 3184 1961 9835 7298 3436 5420 5841 7134 5755 6287 6888 2312 3348 1962 10234 7645 3643 5512 6104 7505 5825 6608 7099 2330 3482 1963 10514 7914 3983 5718 6305 7394 5911 6869 7209 2574 3632 1964 10928 8284 4449 6015 6687 8124 6233 7279 7641 2798 3787 1965 11492 8709 4600 6178 6860 8433 6607 7540 7999 3066 3862 1966 11999 9142 5041 6475 7027 8559 6690 7893 8088 3181 3862 1967 12160 9279 5547 6636 7252 8775 6752 8203 8001 3316 4014 1968 12555 9635 6223 6887 7509 9030 6837 8498 8479 3550 4355 1969 12806 10034 6842 7207 7965 9607 7522 9062 9080 3907 4657 1970 12725 10175 7500 7565 8453 9675 8247 9621 9557 4234 4884 1971 13041 10665 7700 7905 8686 9861 8358 9897 9695 4516 4822 1972 13632 11192 8224 8351 9067 10348 8861 10177 10020 4883 5028 1973 14226 11917 8769 8746 9681 10628 9425 10608 10433 5235 5596 1974 13909 12298 8503 9047 10092 10417 9799 10781 10291 4971 5701 1975 13479 12348 8572 8981 9793 10185 9767 10467 10127 5198 5756 1976 14087 12996 8871 9423 10341 10898 9510 10945 10784 5414 5805 1977 14655 13246 9193 9851 10428 11014 9466 11098 11097 5511 6243 1978 15303 13691 9549 9806 10695 11085 9554 11365 11444 5786 6628 1979 15408 14191 9982 10281 10955 11426 10358 11708 11980 5894 6806 1980 15097 14231 10292 10586 11354 11234 10985 11798 12013 5895 6785 1981 15339 14681 10602 10456 10967 10997 11013 11758 11862 5877 6964 1982 14612 13799 10849 10508 11108 11383 11339 11981 11706 5936 7023 1983 15039 14176 11042 10741 11009 11682 11577 11921 11988 5899 6875 1984 16154 15047 11456 10918 11295 12314 11841 12012 12337 5963 7084 1985 16559 15695 12004 11172 11324 12884 12128 12186 12543 6184 7215 1986 16885 16155 12240 11306 11552 13428 12283 12505 12832 6221 7144 1987 17332 16759 12703 11510 11910 13364 12745 12753 13006 6197 7423 1988 17975 17393 13475 11968 12534 13376 13499 13222 13544 6404 7753 1989 18354 17690 14045 12378 13097 13579 14371 13664 13937 6622 8406 1990 18399 1741? 1483$ 12858 13600 138Q1 14219 13934 14498 $$79 9080 75 Table 4.5 (Contd) Year Italy Netherlands Norway Portugal Spain Sweden Switzerland Turkey UK Australia New Zealand 13 14 15 16 17 18 19 20 21 22 23 24 1955 3645 5365 5112 1543 2669 6549 8310 1429 5968 7312 6834 1956 3773 5626 5214 1602 2850 6702 8754 1410 6020 7155 6736 1957 3904 5682 5361 1678 2943 6840 8903 1655 6105 7140 6970 1958 4042 5424 5391 1685 3056 6954 8443 1752 6092 7485 6893 1959 4277 5637 5501 1774 2940 7282 9026 1664 6314 7807 7007 1960 4636 6122 5665 1869 3196 7492 9639 1604 6548 7879 7920 1961 4993 6269 5914 2004 3573 7857 10328 1613 6690 7678 8025 1962 5285 6445 6141 2077 3912 8129 10581 1651 6697 8089 8109 1963 5580 6616 6433 2197 4207 8495 10849 1794 6927 8485 8340 1964 5657 7158 6727 2253 4413 9025 11258 1798 7276 8981 8634 1965 5765 7431 7029 2415 4692 9285 11425 1793 7378 8955 8991 1966 6085 7562 7296 2479 4988 9370 11580 1970 7482 9282 9084 1967 6499 7887 7667 2659 5163 9603 11794 2000 7665 9503 8664 1968 6863 8335 7739 2934 5429 9893 12062 2089 7934 10240 8577 1969 7270 8778 8035 3017 5864 10295 12612 2142 8001 10556 9094 1970 7669 9228 8129 3323 6017 10643 13274 2179 7695 10917 9352 1971 7689 9493 8433 3759 6173 10621 13681 2343 8312 11039 9686 1972 7815 9711 8827 3998 6653 10808 13945 2441 8963 11288 9966 1973 8383 10096 9174 4479 7116 11194 14254 2454 9410 11675 10656 1974 8788 10411 9593 4704 7454 11548 14454 2646 9156 11517 11159 1975 8354 10291 9915 4363 7389 11825 13228 2832 9014 11616 10468 1976 8909 10739 10590 4526 7531 11873 13058 2998 9300 11865 10580 1977 9104 10939 10872 4733 7589 11528 13388 3102 9550 11750 9968 1978 9371 11147 11288 4775 7544 11613 13423 3019 9912 12279 9924 1979 9930 11325 11807 4914 7458 12073 13825 2930 10220 12332 10259 1980 10445 11323 12249 5048 7495 12290 14653 2853 10028 12622 10260 1981 10382 11105 12290 5092 7319 12165 14704 2843 9933 12828 10747 1982 10349 10891 12257 5194 7351 12274 14446 2847 10126 12168 10686 1983 10369 11005 12779 5105 7378 12479 14514 2885 10536 12840 10805 1984 10649 11317 13557 4952 7403 12999 14722 2996 10781 13349 11322 1985 10895 11570 14227 5026 7547 13313 15209 3059 11137 13662 11324 1986 11199 11736 14821 5250 7820 13558 15657 3281 11580 13755 11430 1987 11547 11747 14918 5615 8321 13931 15934 3423 12151 14190 11498 1988 12021 11987 14752 5990 8809 14231 16320 3395 12751 14659 11481 1989 12367 12434 14647 6281 9305 14534 16799 3370 13050 14904 11811 1990 12557 12m 14891 W5 9664 14495 17007 3711 130$3 14304 11540 76 Table 4.6 Levels of Estimated Income (YÂ¡, i=l to 22) in the 22 OECD Countries, 1955-1990 Year USA Canada Japan Austria Belgium Denmark Finland France Germany Greece Ireland 1 2 3 4 5 6 7 8 9 10 11 12 1955 8797.69 7116.97 4038.78 5327.55 5671.12 6032.36 6374.98 5683.44 6628.47 3531.65 4623.24 1956 8637.34 7824.74 4148.52 5207.65 5946.81 6263.32 6490.69 6121.38 6694.42 3639.48 4398.68 1957 8436.04 7544.98 4307.19 5421.78 5934.50 6506.80 6454.31 6249.57 6799.50 3713.47 4248.08 1958 8218.77 7153.03 4255.03 5519.17 5648.53 6292.25 6357.49 6315.97 6894.39 3790.09 4227.04 1959 8628.63 7239.31 4429.87 5600.65 5936.59 7144.40 6721.90 6402.74 7326.36 3856.12 4575.81 1960 8483.06 7050.75 4755.62 6234.38 6190.28 7613.40 7347.89 6742.16 7772.61 3947.30 4557.86 1961 8521.46 7050.09 5273.65 6370.57 6522.87 7796.35 7725.27 6932.05 7955.89 4147.62 4723.25 1962 8935.43 7316.07 5271.99 6320.02 6693.47 8272.63 7637.64 7174.07 8138.33 4148.63 4905.94 1963 9133.11 7418.17 5581.54 6418.88 6812.69 7867.55 7438.75 7335.22 8148.59 4354.87 5074.60 1964 9332.10 7721.68 5944.82 6831.17 7371.19 8922.02 7872.45 7782.97 8631.33 4638.66 5288.94 1965 9856.74 8231.13 5957.18 6908.21 7410.78 9235.22 8457.64 7917.41 8968.40 4899.57 5504.39 1966 10299.42 8642.58 6295.01 7264.04 7709.33 9219.50 8445.61 8252.59 8854.63 4802.35 5334.12 1967 10331.44 8437.64 6862.08 7269.07 7789.29 9410.94 8286.44 8457.28 8467.51 4856.57 5357.39 1968 10532.81 8618.33 7531.19 7443.00 7893.71 9647.26 8272.43 8750.92 8977.94 5035.37 5780.74 1969 10636.95 8995.37 8094.23 7690.30 8364.08 10436.75 8887.99 9331.40 9571.26 5470.91 6275.80 1970 10203.61 8879.80 8851.45 8195.68 8744.25 10588.66 10112.14 9611.99 10022.87 5707.66 6296.25 1971 10547.50 9205.15 8838.86 8342.88 8725.22 10695.33 10128.13 9811.41 10035.28 5870.57 6383.02 1972 10819.83 9474.53 9262.94 8763.83 8817.44 11167.47 9979.98 10070.31 10222.53 6170.95 6739.54 1973 11236.85 10063.55 9930.74 9174.50 9457.27 11697.15 10612.11 10644.95 10495.48 6933.55 7227.47 1974 10873.34 10643.88 9536.70 9358.21 10062.62 11292.97 11927.11 10790.15 9898.08 6254.53 7311.30 1975 9925.54 10595.93 9161.95 8856.20 9359.77 10365.30 11790.14 9810.48 9569.17 6301.13 6675.96 1976 10536.42 10883.38 9357.72 9467.20 9835.78 11502.90 10532.63 10483.50 10311.68 6358.53 7080.00 1977 11149.81 10963.09 9512.81 9796.58 9897.80 11375.29 10394.50 10533.35 10328.23 6391.36 7556.63 1978 11651.37 11043.70 9836.68 9553.50 10094.09 11341.32 9957.54 10500.77 10603.72 6584.79 7946.65 1979 11524.01 11791.15 10292.94 9990.30 10267.71 11673.53 11196.24 10934.63 11394.51 6857.86 8509.57 1980 10894.44 11922.47 10258.34 10442.76 10605.87 11036.71 12143.36 11053.39 11350.51 6713.87 7962.20 1981 11217.49 12640.43 10409.11 9974.28 9685.97 10338.71 11730.88 10656.76 10760.96 6370.28 8208.75 1982 10297.43 11176.82 10368.57 9584.59 9735.14 10872.61 12005.92 10852.26 10453.89 6224.60 8339.24 1983 10716.03 11505.48 10207.74 9565.95 9426.59 10877.70 12084.13 10472.86 10825.97 6230.87 7930.94 1984 12233.18 12068.64 10547.37 10109.63 9865.05 11701.00 12097.55 10438.05 11078.58 6155.06 7981.83 1985 12341.98 12587.89 10923.03 10279.05 9596.10 12315.43 12218.77 10596.14 11095.94 6381.61 7739.18 1986 12431.93 12995.84 11149.17 10333.99 9737.85 13001.85 12098.57 10993.89 11303.91 6152.73 7609.92 1987 12713.03 13706.89 11673.59 10465.21 10165.98 12496.88 12614.49 11340.79 11405.95 5922.22 7403.36 1988 12901.95 14384.36 12683.65 10963.91 10864.08 12157.62 13618.65 11851.40 11920.22 6357.50 7361.64 1989 13126.17 14823.41 13458.70 11311.00 11700.46 12447.88 15031.49 12241.81 12404.95 6414.57 8116.47 1999 12992.92 HUMS 14379.56 11864.18 .1212$ 12111.65 14497.3ft ..iwi-n 12945.13 6372.22 8777.88 77 Table 4.6 (Contd) Year Italy Netherlands Norway Portugal Spain Sweden Switzerland Turkey UK Australia New Zealand 13 14 15 16 17 18 19 20 21 22 23 24 1955 5514.50 6761.07 6879.14 3496.76 4154.43 7108.71 7561.72 3414.31 6425.34 7567.93 7558.55 1956 5616.18 7047.60 6901.59 3541.06 4273.60 7187.11 8070.87 3393.72 6428.86 7098.84 7356.73 1957 5759.19 7145.70 7023.27 3662.69 4347.88 7400.04 8292.34 3452.85 6470.64 7138.92 7548.77 1958 5839.59 6508.60 7118.70 3647.72 4437.20 7423.03 7270.51 3573.08 6356.64 7580.42 7386.45 1959 6055.31 6758.36 7029.04 3677.37 4195.03 7713.27 8003.70 3521.09 6535.10 7766.33 7406.19 1960 6442.15 7370.55 7091.86 3842.95 4428.09 8142.62 8941.58 3497.43 6859.13 8093.10 7724.47 1961 6776.73 7479.49 7335.40 3936.88 4744.29 8275.88 9879.31 3535.21 6944.07 7427.64 7948.30 1962 7045.08 7496.60 7518.77 4044.50 5037.56 8484.43 10049.39 3559.44 6867.64 8044.59 7727.73 1963 7280.21 7540.08 7818.13 4051.94 5183.93 8776.99 10202.12 3619.89 6977.25 8298.72 8039.51 1964 7073.67 8286.94 8047.35 4192.83 5369.73 9359.02 10650.08 3615.21 7505.48 9141.70 8480.51 1965 6862.33 8298.91 8490.24 4344.59 5695.40 9694.52 10383.50 3607.71 7540.31 9047.85 9035.77 1966 7026.56 8446.75 8763.60 4371.80 5956.59 9707.09 10352.28 3783.92 7569.48 9237.11 9373.24 1967 7415.75 8679.98 9267.23 4551.64 5981.79 9820.19 10538.43 3792.00 7842.00 9359.99 8423.46 1968 7725.67 9076.96 8927.22 4663.85 6154.58 10005.72 10613.29 3857.47 8048.96 10072.69 7855.90 1969 8080.35 9322.70 8773.81 4697.28 6550.74 10495.52 11000.04 3871.74 8022.79 10094.58 8451.74 1970 8285.84 9858.17 9703.44 5133.54 6564.79 11195.16 11968.42 3971.13 8112.43 10313.45 8635.92 1971 8099.61 9854.17 10290.76 5353.00 6488.51 10799.98 12288.69 4022.07 8151.34 10055.65 8873.53 1972 8188.95 9620.69 9792.39 5674.61 6926.45 10739.39 12281.15 4018.74 8206.72 9960.23 9102.80 1973 8749.94 9961.44 10575.86 6050.50 7326.57 10806.09 12471.45 4111.00 8898.46 10710.92 10378.71 1974 9094.63 10031.39 11434.80 6023.27 7704.65 11538.59 12733.36 4330.91 8739.38 10375.24 11628.59 1975 8082.09 9388.14 11898.73 5348.78 7520.06 11968.17 10492.99 4575.98 8402.93 10265.50 9477.74 1976 8719.65 9692.64 12698.49 5499.49 7522.21 12012.85 10345.06 4635.13 8808.67 10668.22 9654.53 1977 8582.75 9953.71 12620.92 5937.58 7377.18 11193.17 10510.39 4753.86 8833.51 10157.11 9173.52 1978 8659.04 10099.50 11452.81 6080.71 7181.22 10659.18 10886.45 4401.60 8935.18 10924.31 8669.24 1979 9040.00 10094.41 11836.86 6338.60 7117.27 11524.19 11772.88 4373.65 9105.01 10836.91 9161.81 1980 9614.07 10059.33 12499.27 6646.20 7231.59 12007.89 12898.39 4493.28 8561.56 11264.17 8887.32 1981 9186.62 9236.36 12431.43 6720.56 6932.34 11323.30 12464.35 4550.63 8275.17 11672.49 9615.32 1982 9102.17 9197.88 12551.77 6866.36 7012.02 11349.49 12082.08 4472.75 8559.19 10360.03 9792.81 1983 8966.55 9399.59 12512.59 6361.93 6939.45 11364.74 12315.54 4446.91 8916.61 11041.76 10009.04 1984 9382.49 9711.55 13562.74 6030.39 6860.76 11867.01 12676.62 4447.12 9217.27 11559.96 10643.78 1985 9516.06 10044.66 13426.96 6034.15 6991.38 12532.75 13094.06 4573.56 9326.63 11868.55 10347.82 1986 9561.95 9839.58 14580.95 6246.56 7358.05 12415.50 14069.76 4711.67 9413.30 11481.07 10231.82 1987 9830.04 9478.05 14141.08 6313.00 7943.62 12770.99 14695.97 4782.81 9799.56 11820.12 10206.83 1988 10188.1 9696.20 13655.62 6407.80 8555.98 13139.43 15114.09 4678.83 10445.90 12812.30 10172.23 1989 10385.1 10488.43 13175.96 6635.07 9218.02 13906.96 15871.16 4583.14 10691.44 12842.90 11339.54 1990 10422.5 10779.49 , Â¡2649.94 6878.67 9597.00 13863.07 16119.85 4793.40 10450.70 11730 73 11109.94 78 Table 4.7 Average Levels of Observed and Estimated Income Per Capita (YOECD, YOECD) in the 22 OECD Countries, 1955-1990 Year Observed Estimated Income Income 1955 5603.64 6335.28 1956 5723.63 6389.51 1957 5813.63 6406.68 1958 5798.50 6332.68 1959 6061.19 6573.94 1960 6287.77 6759.70 1961 6497.31 6945.81 1962 6763.09 7155.94 1963 7021.29 7324.48 1964 7380.76 7622.04 1965 7682.17 7846.86 1966 8013.23 8098.39 1967 8232.08 8229.28 1968 8624.72 8532.40 1969 8994.56 8829.64 1970 9216.68 8961.31 1971 9480.43 9076.73 1972 9914.48 9296.54 1973 10402.89 9778.07 1974 10335.40 9653.87 1975 10127.53 9060.21 1976 10562.65 9491.47 1977 10867.58 9682.47 1978 11232.67 9889.26 1979 11497.94 10113.69 1980 11512.11 9979.04 1981 11599.01 9937.19 1982 11398.71 9590.19 1983 11633.87 9715.47 1984 12163.43 10333.14 1985 12495.18 10502.00 1986 12786.72 10656.12 1987 13162.41 10957.08 1988 13699.01 11398.60 1989 14076.57 11770.50 L22Q L4317.18 11902.49 79 Y, Y Figure 4.4 Average Levels of Observed and Estimated Income, YOECd and YOECD, in the 22 OECD Countries, 1955-1990 80 income and the gap is widening. This gap could be due to the pooling of data which makes the estimation process insensitive to country specific effects. The values from Tables 4.5 and 4.6 and Figure 4.5 depict the relationship between observed and estimated income for the 22 countries individually. These comparisons indicated that the model underestimates the income of three countries (USA, Canada, Switzerland), overestimates the income for five countries (Greece, Ireland, Norway, Portugal, Turkey), and fits well for the remaining 14 (Japan, Austria, Belgium, Denmark, Finland, France, Germany, Italy, Netherlands, Spain, Sweden, UKD, Australia, New Zealand). Comparing Figures 4.1, 4.2, and 4.4, it was seen that international openness, investment and government expenditures, in their average levels, had increasing trends. This result also implied that the OECD countries were increasing their trading activities and investments over time. Yet again, comparing values from Tables 4.6 and 4.7 (Column 3), and Figure 4.6 revealed that the estimated incomes of nine countries (USA, Denmark, Finland, France, Germany, Norway, Sweden, Switzerland, Australia) were above-average, six countries (Greece, Ireland, Italy, Portugal, Spain, Turkey) were below-average, and seven countries (Canada, Japan, Austria, Belgium, Netherlands, UKD, New Zealand) moved closely with the average of the group of 22 countries. Figure 4.7 depicts the relationship between YOBcd and Hoecd (Table 4.7, column 3 and Table 4.4, column 2, respectively) as a positive and increasing one implying that human capital did have a significant and positive effect on per capita income for the 22 OECD countries. Similarly, using the values in Tables 4.3 and 4.6, Figure 4.8 depict Figure 4.5 Comparing Country wise Levels of Observed Income (YÂ¡, i=l to 22) and Estimated Income (YÂ¡, i=l to 22) in the 22 OECD Countries, 1955-1990 o o o Yj A o- YÂ¡ 82 y USA v Japan Canada y AustrI a 83 r Belgium Denmark Finland y France Figure 4.5 (Contd) Germany re I and 19/000 10,000 5.000 Y 19,000 10,000 5.000 Greece Ymr y Italy Figure 4.5 (Contd) r Nstherlands t Norway r Portugal r Spain Figure 4.5 (Contd) 86 19,000 10,000 5. 000 Y 15,000 10,000 5.000 Sweden y Turkey Switzerland r UK \ Figure 4.5 (Contd) 87 y Australia r New Zealand Figure 4.5 (Contd) Figure 4.6 Comparing Countrywise Levels of Estimated Income (YÂ¡, i=l to 22) and Average Level of Estimated Income (YOECD) in the 22 OECD Countries, 1955-1990 A Yqegd o o o A o- YÂ¡ 89 USA Y* Japan * Canada rr * Austria tmr 90 i Denmark rmr France Ymmr Figure 4.6 (Contd) 91 y Germany Yr y Ireland VNT r Greece Ymr y Italy Figure 4.6 (Contd) 92 t Netherlands w r Norway T Spain Figure 4.6 (Contd) 93 r Sweden r Turkey r Switzerland UK Figure 4.6 (Contd) 94 y Australia y New Zealand lar Figure 4.6 (Contd) 95 Y Figure 4.7 Relationship Between Average Levels of Observed Income (Y0ECD) and Human Capital (Hqecd) in the 22 OECD Countries, 1955-1990 Figure 4.8 Country wise Relationship Between Levels of Observed Income (YÂ¡, i = 1 to 22) and Human Capital (HÂ¡, i=l to 22) in the 22 OECD Countries, 1955-1990 97 y USA T Japan y Canada T Austria 98 t Belgium Denmark Y France Figure 4.8 (Contd) Y Germany Ire I and 15,000 y Greece Y Italy H Figure 4.8 (Contd) 100 Y Netherlands H y Norway Spain Figure 4.8 (Contd) 101 * Sweden Y Turkey Y Switzer land Y UK H M Figure 4.8 (Contd) 102 Y Austro Mo T New Zen Iand Figure 4.8 (Contd) 103 the relationship between observed income and human capital for the 22 countries individually. This analysis showed that all countries showed clear evidence of a positive relationship between income and human capital. The analyses of the individual countries (Table 4.8) revealed that four countries (United States, Denmark, Norway, and Sweden) were the only ones that had above- average human capital and income; six countries (Greece, Ireland, Italy, Portugal, Spain, and Turkey) had below-average human capital and income; and only three countries (Belgium, UK, and New Zealand) had levels of human capital and income that tracked the average levels reasonably well. 4.6 Summary From the analyses in Sections 4.4 and 4.5 above the major points to note were: (i) the data fits the model reasonably well; (ii) all four determinants of income had positive effects; (iii) both observed and estimated income for the 22 OECD countries was increasing over time; (iv) estimated income and human capital have a significant positive relationship; (v) human capital had the greatest positive effect on income; (v) the income elasticity with respect to human capital was positive and greater than those with respect to openness, investment and government expenditures; and (vi) all four determinants depict an increasing trend. Therefore, the results from this study imply that human capital contributes positively to economic growth and is a key determinant of income. These results correspond to the contemporary evidence presented by Barro (1991), Mankiw et al. (1992), Tallman and Wang, (1992), Lucas (1988, 1993), and Romer 104 (1990) who concluded that human capital accumulation was vital to the growth of an economy. Table 4.8 Summary of Cross-Country Analyses for the 22 OECD Countries, 1955-1990 Y above Y Y below Y Tracks Yngr-p 6; above Hqecd Denmark Norway Sweden USA Canada Netherlands H; below Hqecd Germany Greece Ireland Italy Portugal Spain Turkey Austria Japan Tracks Hqecd Australia Finland France Switzerland Belgium New Zealand UK CHAPTER 5 INEQUALITY IN THE OECD COUNTRIES Historically, inequality measures have been used to study convergence (or divergence). Basic statistical tools such as graphs (e.g., histograms and Lorenz curves), measures of dispersion (e.g., variance and coefficient of variation), and indices (e.g., gini coefficient and Their s inequality index) have been used to analyze income inequality between and among groups. Using these tools, researchers have tried to determine if two income groups grew closer (convergence) or moved away from each other (divergence). 5.1 Graphical Inequality A histogram may be used to depict a frequency distribution of incomes of people at various levels. The Lorenz curve depicts a relationship between cumulative shares of income (on the vertical axis) against cumulative population shares (on the horizontal axis). Since these shares vary between 1 and 0, a person with all the income would be along the vertical axis, and if incomes were equal then the curve is a 45 diagonal. 105 106 5.2 Inequality via Measures of Dispersion The variance of n observations or income values, yÂ¡, with mean p can be written as <-) (yrvt n The square root of the variance is the standard deviation which could also be used as a measure of inequality. Dividing the standard deviation by the mean (p.) yields the coefficient of variation. 5.3 Inequality Indices The Gini coefficient (G) is computed based on the Lorenz curve G -4- \y, -y,\. 2n \i m j-i In graphical terms, the Gini coefficient measures the ratio of the area between the diagonal and the Lorenz Curve to the total area beneath the diagonal. Theils income inequality index or entropy index is based on an information measure developed by Shannon (1949). Shannons measure determines the information content in any given signal. Theil (1967) expands on this tool to measure change in the posterior distribution associated with a given signal. In terms of income inequality, the objective is to determine whether the information regarding a country can be used to predict the level of income. This index is described in detail later in this chapter. 107 5.4 Properties of Inequality Index Anand and Kanbur (1993) present a formalization of the Kuznets process, a general analysis of distributional change under this process, and derive the functional forms of and conditions for a turning point in the inequality-development relationship for six commonly used indices of inequality. They used data on a cross-section of 60 developing and developed countries to estimate the functional form appropriate for each index. They divided the countries into regions or sectors. Assuming that during the course of development, the population is seen as shifting from a low-mean income and low-inequality sector to a high-mean income and high-inequality sector, the sectoral mean incomes and inequality levels remaining unchanged over time, they found that the estimated functional forms on the cross-section data rejected the formalization of the Kuznets process. If the Kuznets process is being invoked as the theoretical underpinning of the inequality-development relationship, the right index must be used with the right functional form for estimation purposes. Four properties for a consistent inequality measure are (Livada, 1991): symmetry, mean independence, population homogeneity, and the Pigou-Dalton condition. Symmetry is equivalent to saying that the social aspects of a country are irrelevant in measuring inequality. Mean independence states that if all incomes are raised or lowered in the same proportion, the inequality measure remains invariant. This means that inequality measures depend on relative rather than absolute incomes. According to population homogeneity the inequality does not change when r populations (each containing n individuals) with identical income distributions are combined into a single population. 108 The Pigou-Dalton condition requires income inequality to increase whenever an income transfer is made from a poor country to a richer country. 5.5 Theils Inequality Index TheiTs index satisfies the four properties of any inequality measure: symmetry, mean independence, population homogeneity, and the Pigou-Dalton condition. Further, this index yields a statistic and is additively decomposable. Theils income inequality measures inequality by taking the logarithm of the ratio of the arithmetic mean income to the geometric mean income. When this measure is applied to per capita incomes of n countries, it can be written as J = ^ pÂ¡Lo%(p/y) where pÂ¡ is the world population share of country i, and yÂ¡ is its world income share. An advantage of J is its additive decomposition, that is, if R,,...,R<3 are regions such that each country is in exactly one region, Pg and Yg are the population and income shares of region Rg: Pg = sum, pÂ¡ and Yg = sumÂ¡ yÂ¡, where the summations are over i E Rg, then j. Â£ r, if w (5 2) which measures the inequality among regions, while J, (p/^piogJO/iy/Cy/i-,)] <5-3> measures the inequality among the countries of region Rg. The additive decomposition is then 109 J = JR + J, where J = ^ P^If Thus, total inequality among the n countries equals regional inequality plus the average within-region inequality, the average being a weighted average with the population shares Pj,...,PG as weights. Note that these weights are identical to those of the regional per capita incomes. 5.6 Inequality in the OECD Countries The analysis in this section is based on the observed and estimated inequalities computed for the 22 OECD countries during 1955-1990. Using equation (5.1) the observed and estimated income inequalities, JY and JY, respectively, were computed. For the observed index, JY, Summers and Heston (1993) data for income and population were used. Using the population data from the same source and estimated income computed via a latent variable model (Chapter 4, equation 4.24), the estimated inequality, JY, was computed using equation (5.1). The results of the computations of observed and estimated income inequality are given by Table 5.1 and depicted in Figure 5.1. At a glance, from Columns 2 and 3 of the table and from the figure, it was seen that the gap between JY and JY was quite wide initially and began to lessen over time. Again this could be attributed to the reduction in nonsystematic errors in the process of empirical estimation and the inability of the process to capture country-specific effects. JY decreased initially and then levelled off at a value of 0.03 depicting a pattern of convergence, in terms of income, and indicating that the OECD countries were moving closer as a group. 110 Table 5.1 Average Inequality in Observed Income (JY), Estimated Income (JY), Human Capital (Jh), International Openness (J0), Investment (Jj) and Government (JG) Expenditures in the 22 OECD Countries, 1955-1990 Year Observed Income Estimated Income Human Capital International Openness Investment Expenditure Government Expenditure Jy Jy J Jo Ji Jo 1 2 3 4 5 6 7 1955 0.1615 0.0462 0.0093 0.3027 0.2189 0.1830 1956 0.1526 0.0424 0.0087 0.2949 0.1901 0.1832 1957 0.1386 0.0372 0.0096 0.2859 0.1490 0.1896 1958 0.1264 0.0342 0.0088 0.3002 0.1350 0.1838 1959 0.1290 0.0380 0.0100 0.2830 0.1497 0.1735 1960 0.1181 0.0331 0.0186 0.2691 0.1221 0.1632 1961 0.1047 0.0280 0.0109 0.2364 0.0952 0.1598 1962 0.1031 0.0306 0.0142 0.2289 0.1024 0.1563 1963 0.0952 0.0291 0.0162 0.2254 0.0946 0.1446 1964 0.0925 0.0288 0.0158 0.2282 0.0887 0.1397 1965 0.0954 0.0322 0.0182 0.2182 0.0986 0.1347 1966 0.0909 0.0319 0.0197 0.2037 0.0875 0.1419 1967 0.0850 0.0287 0.0172 0.2061 0.0757 0.1477 1968 0.0798 0.0272 0.0183 0.2063 0.0717 0.1443 1969 0.0750 0.0259 0.0211 0.2174 0.0714 0.1378 1970 0.0693 0.0228 0.0211 0.2041 0.0656 0.1308 1971 0.0664 0.0240 0.0220 0.1904 0.0693 0.1174 1972 0.0656 0.0240 0.0206 0.1807 0.0697 0.1158 1973 0.0654 0.0235 0.0224 0.1736 0.0654 0.1107 1974 0.0604 0.0208 0.0198 0.1641 0.0554 0.1076 1975 0.0559 0.0171 0.0159 0.1549 0.0463 0.1001 1976 0.0563 0.0189 0.0164 0.1607 0.0474 0.0954 1977 0.0575 0.0201 0.0189 0.1648 0.0485 0.0916 1978 0.0620 0.0246 0.0226 0.1796 0.0671 0.0875 1979 0.0627 0.0250 0.0218 0.1915 0.0682 0.0869 1980 0.0615 0.0229 0.0234 0.1569 0.0657 0.0833 1981 0.0641 0.0246 0.0233 0.1494 0.0740 0.0831 1982 0.0591 0.0212 0.0220 0.1497 0.0645 0.0840 1983 0.0617 0.0231 0.0218 0.1518 0.0682 0.0849 1984 0.0672 0.0300 0.0234 0.1456 0.0869 0.0887 1985 0.0682 0.0298 0.0252 0.1545 0.0832 0.0918 1986 0.0660 0.0292 0.0271 0.1537 0.0777 0.0916 1987 0.0650 0.0297 0.0283 0.1399 0.0795 0.0918 1988 0.0670 0.0313 0.0182 0.1338 0.0856 0.0917 1989 0.0678 0.0332 0.0190 0.1357 0.0922 0.0899 1990 0.0625 0.0324 0.0230 0.1271 0.0907 0.0865 Ill J Figure 5.1 Observed and Estimated Income Inequality (Jy, Jy) in the 22 OECD Countries, 1955-1990 112 Columns 4 to 7 of Table 5.1 give the inequalities in human capital, J, international openness, JQ, investment expenditure, Jr, and government expenditure, JQ. The inequalities in human capital and investment expenditure depicted decreasing trends initially and then increased indicating that the OECD countries were converging in terms of these variables initially but have commenced to diverge in terms of human capital and investment expenditure. However, inequality in openness and government expenditure decreased indicating that the OECD countries were converging in terms of these variables. A graphic comparison of inequalities in income and its determinants of income is given by Figure 5.2. This figure showed that inequality in income and human capital were converging and were almost identical during 1970-1983 and 1986-87. The inequality in openness was larger in value than any other variable and was decreasing over time. Inequality in investment expenditure was decreasing initially and then increased from 1979 onwards. Inequality in government expenditure was decreasing over time and intersected with that of investment expenditure in 1987. These results point to the fact that the convergence in income is contributed by all its determinants. Thus, the low rate of convergence in income could be due to the rapid rate of convergence in openness, a high rate of divergence (from 1979 onwards) in investment expenditure, a modest rate of convergence in government expenditure, and a slow rate of divergence in human capital (which influenced income more positively than the other determinants). 113 j Figure 5.2 Inequality in Estimated Income (Jy), Human Capital (Jh), International Openness (J0), Investment (Jj) and Government (Jq) Expenditures in 22 OECD Countries, 1955-1990 114 5.1 Summary From Section 5.4, the declining income inequality (observed and estimated) indicates that the countries in the OECD group are growing closer together in income. This evidence is in favor of the convergence component of the "extended" Kuznets hypothesis. The slow rate of convergence in income could be attributed to the accelerated convergence in terms of openness offset by divergence in terms of investment expenditure and low rate of convergence in terms of human capital. Barro (1991) concluded that convergence in the OECD countries was clearly evident since these countries had high levels of per capita income and were similar in terms of economic and political institutions. Adding to this conclusion, this study showed that convergence in these countries was also a result of the influence of increasing levels of human capital and international openness. An attempt was also made to analyze the change in inequality using a time-differential to the Theil index (Appendix F). However, the results from the analysis of the time-differential were inconclusive for the purposes of this study. CHAPTER 6 SUMMARY AND CONCLUSIONS Simon Kuznets (1955) hypothesized that, as an agrarian society becomes more urbanized and affluent, income inequality initially increases and then decreases (divergence followed by convergence). It is true that Kuznets discusses inequality within one country, not across countries, but several authors have extended the convergence- divergence hypothesis to the cross-country level. For example, Paukert (1973), Ahluwalia (1976), Papanek and Kyn (1986), Ram(1989), Theil (1989), Theil and Deepak (1993a, 1993b, 1993c, and 1994), Seale et al (1994), Moss et al (1993), and Theil and Seale (1994) have used cross-country time-series data to test Kuznets divergence- convergence hypothesis. The evidence from these studies suggests that rich countries are converging in terms of income and the countries with higher levels of human capital tend to converge faster. However, in most cases the analysis was based on either an inequality index or theories of economic growth, the exception being Weatherspoon who performed cointegration analysis on inequalities in income, investment and government expenditures, and industrial employment. The objective of this study was to expand on research by Barro (1991) and Weatherspoon (1993) by including indicators for international trade and human capital into the analysis. While Barro used school enrollment ratios as a proxy for human 115 116 capital, this study used a multiple indicator, constituted by per capita levels of public expenditure on education, consumption of newsprint, and shares of population with secondary school and university education, for measuring human capital. Further, this study used the Theil inequality index to analyze convergence in the OECD countries and Barro used the relationship between growth rates and levels of income and human capital. This study also differed from Weatherspoons in terms of methodology. While Weatherspoon used cointegration analysis, this study used a latent variable approach to analyze the effect, if any, of four factors of economic growth: human capital, internation al openness, investment and government expenditures on income convergence. Income was estimated as a function of human capital, investment expenditure, government expenditure, and international openness drawing upon the theoretical underpinnings from standard macroeconomic theory and from recent developments in the theory of human capital accumulation. The scope of the study was to cover 22 OECD countries. The OECD countries were chosen based on the existing evidence of income convergence and the availability of relevant data for these countries. Estimating income as a function of human capital prompted the use of a latent variable model since human capital was not a directly observable variable. The classical econometric treatment assumes that the observed variables are measured without error. Latent variable models incorporate measurement error in the observed variables into the process of estimation. Cointegration analysis requires time-series data over long periods of time and thus was not a very feasible methodology for this study. 117 Tallman and Wang (1992) reviewed neoclassical and endogenous growth theories and concluded that higher levels of education could positively influence the accumulation of human capital and thus the standard of living in an economy. Lucas (1993) concluded that countries with high rates of human capital accumulation could sustain greater rates of growth. Barro (1991) deduced that growth in income converged faster at higher levels of human capital. This study used public expenditure on education, consumption of newsprint, education at high school and university levels as observable variables for human capital. All these factors contribute positively to accumulation of human capital. The latent variable model was estimated using maximum likelihood and the estimated values of the four factors of growth were obtained using Bartletts method (1938). The results from estimation showed that the data fit the model reasonably well and that income and its determinants were growing over time. Therefore, the factors of growth specified for this study did appear to contribute to growth in income. These results comply with contemporary evidence (Barro, 1991; Mankiw et al., 1992). Theils inequality index was then used to measure observed and estimated inequalities for the OECD countries. The evidence from the inequality analysis was in favor of the convergence component of Kuznets hypothesis for income, international openness, and government expenditures and favors the divergence component in terms of human capital and investment expenditure. These results suggested that the OECD countries were growing closer together in terms of income, international openness, and government expenditure and moving away in terms of human capital and investment 118 expenditure. Further, the inequalities in the determinants were slowing down the rate of convergence in terms of income for these countries. Thus, the results from this study present an encouraging picture for ongoing research in this area of international economics. A multiple indicator for the level of human capital variable had not been previously estimated. Though international openness was also a good candidate for being measured as a latent variable, the lack of theoretical and quantifiable information on feasible indicators or proxies for this variable prompted its use as an observable variable for the purposes of this study. Though data are scarce, reliable and lengthy information on investments in research and development, science and technology, womens education and development, and health and environmental care over time and across countries, along with factors for international openness, may provide opportunities to further extend what has been accomplished in this study. APPENDIX A SEVEN REGIONS OF THE WORLD The 22 countries in the North include USA, Canada, Japan, South Korea, and 18 European countries: Austria, Belgium, Denmark, Finland, France, Germany (W), Greece, Iceland, Ireland, Italy, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, UK. The six countries in the South are Australia, New Zealand, Chile, Argentina, Uruguay, and South africa. The 43 countries of Tropical Africa are Algeria, Angola, Benin, Botswana, Burkina Faso, Burundi, Cameroon, Cape Verde, Central African Republic, Chad, Comoros, Congo, Egypt, Ethiopia, Gabon, Gambia, Ghana, Guinea, Guinea-Bissau, Ivory Coast, Kenya, Liberia, Madagascar, Malawi, Mali, Mauritania, Morocco, Mozambique, Namibia, Niger, Nigeria, Rwanda, Senegal, Sierra Leone, Somalia, Swaziland, Tanzania, Togo, Tunisia, Uganda, Zaire, Zambia, Zimbabwe. The 22 countries of Tropical America are Barbados, Bolivia, Brazil, Colombia, Costa Rica, Dominican Republic, Ecuador, El Salvador, Guatemala, Guyana, Haiti, Honduras, Jamaica, Mexico, Nicaragua, Panama, Paraguay, Peru, Puerto Rico, Surinam, Trinidad and Tobago, Venezuela. The six countries of South-West Asia are Iran, Iraq, Israel, Jordan, Syria, Turkey. The six countries of South-Central Asia are Bangladesh, India, Myanmar, Nepal, Pakistan, Sri Lanka. The eight countries of South- East Asia are Hong Kong, Indonesia, Malaysia, Papua New Guinea, Philippines, Singapore, Taiwan, Thailand. 119 APPENDIX B EUROPE, AFRICA, AND SOUTHERN CONE The first region constituting Western Europe, Mediterranean Europe and Mediterranean Africa consists of Europes core: UK, France, Switzerland, Germany (W), and the three Benelux countries; 11 countries around the core: Austria, Denmark, Finland, Greece, Iceland, Ireland, Italy, Norway, Portugal, Spain, Sweden; countries of North Africa: Algeria, Egypt, Morocco, Tunisia. The second region constitutes South Africa: Chad, Mali, Mauritania, Niger, Sudan; and its Northern neighbors: Namibia, Botswana, Zimbabwe, Swaziland, Mozambique, Angola, Zambia, Malawi, Tanzania. The third region constitutes USA, Mexico, and Central America (Costa Rica, El Salvador, Guatemala, Honduras, Nicaragua, Panama). The fourth region constitutes the Southern Cone of South America: Argentina, Chile, Uruguay; and its Northern neighbors: Brazil, Bolivia, Paraguay, Peru. 120 APPENDIX C WESTERN EUROPE There are 18 countries constituting Western Europe which is divide into three regions. One is non-EU, consisting of six countries: Austria, Finland, Iceland, Norway, Sweden, Switzerland. Another is the EU Center, consisting of eight countries: Belgium, Denmark, France, Germany (W), Italy, Luxembourg, Netherlands, UK. The third is the EU Periphery, consisting of four countries: Greece, Ireland, Portugal, Spain. 121 APPENDIX D WESTERN PACIFIC REGION The Western Pacific region consists of 15 non-Communist countries: Australia, Fiji, Hong Kong, Indonesia, Japan, Malaysia, New Zealand, Papua New Guinea, Philippines, Singapore, Solomon Islands, South Korea, Taiwan, Thailand, Western Samoa. 122 APPENDIX E FOUR REGIONS REVISITED The 18 European countries in the North are Austria, Belgium, Denmark, Finland, France, Germany (W), Greece, Iceland, Ireland, Italy, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, UK. The 37 countries of Sub-Saharan Africa are Angola, Benin, Botswana, Burkina Faso, Burundi, Cameroon, Cape Verde, Central African Republic, Chad, Congo, Ethiopia, Gabon, Gambia, Ghana, Guinea, Guinea-Bissau, Ivory Coast, Kenya, Madagascar, Malawi, Mali, Mauritania, Mozam bique, Namibia, Niger, Nigeria, Rwanda, Senegal, Sierra Leone, Somalia, Swaziland, Tanzania, Togo, Uganda, Zaire, Zambia, Zimbabwe. The five countries of South- Central Asia are Bangladesh, India, Myanmar, Pakistan, Sri Lanka. The eight countries of South-East Asia are Hong Kong, Indonesia, Malaysia, Papua New Guinea, Philippines, Singapore, Taiwan, Thailand. 123 APPENDIX F CHANGE IN INEQUALITY A time-differential of Their s inequality index is derived here that links changes in inequality to changes in income and population. If J is defined as in equation (5.1), then J can also be written as Â¡-1 = Â£ Pi to y* i-l (F.l) - k + In Â£ Nfi Â£ PlJn Z, j-1 /-I where ZÂ¡ is the GDP of country i. Taking partial derivatives with respect to ZÂ¡ we get _a/ dz, N, Ei z, ' E ",2, y-i dZ, 1 Â£ njzj J-1 = y{-Pt Pi (F.2) which is the covariance of the population levels and income shares. Similarly, we derive another expression with respect to population shares a/ din N, P, (= 1 -ln(5) J). (F.3) Therefore we finally arrive at an expression for dJ as E i-l + E Z, z. 1) 1 hi ^ J ) (ln M) Z (F.4) Writing this in time differential form we get 124 125 AJ, = o; p,-) (Â£>z, P; dz i*i /-i * [>; p; p; on ^ y; >] (mv, p; ay 1-1 pÂ¡t imX where Pit = | \Pu + />* J y | [y*+ y^-il. DZ^ = te. Zj ln Zj.j , IW* = ln Nu lnATft_, , " Pu J, = E P* 111 w y* Therefore the change in income inequality can be written as U H A2, = E O. P.'XOZ* E?; oz*> <-l /-I E O#' P.' P#> O'.' / p,) Oxiw, Ep.' "#) i-i y-i (F.5) (F.6) (F.7) REFERENCES Ahluwalia, M.S. (1976). "Income Distribution and Development: Stylized Facts." American Economic Review, 66, pp. 128-135. Anand, S. and S.M.R. Kanbur (1993). 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"The GDPs of Seven Major Regions, 1950-1990." Empirical Economics, 19, pp. 517-522. Theil, H., and S.D. Deepak (1993a). "How Affluent Are the Neighbors of Affluent Countries ?" International Working Paper Series IW93-21, Food and Resource Economics Department, University of Florida, Gainesville. 131 Theil, H., and S.D. Deepak (1993b). "The GDPs of Three Regions in Western Europe, 1950-1990." International Working Paper Series IW93-24, Food and Resource Economics Department, University of Florida, Gainesville. Theil, H., and S.D. Deepak (1993c). "Visiting the GDPs of the Western Pacific." International Working Paper Series IW93-24, Food and Resource Economics Department, University of Florida, Gainesville. Theil, H., and J.L. Seale, Jr. (1994). "The Geographic Distribution of World Income, 1950-1990." De Economist, 142, pp. 387-419. UNESCO, "Basic Facts and Figures, 1951-1962." Paris: UNESCO. UNESCO, "Statistical Yearbook, 1963-1993." Paris: UNESCO. United Nations, (1965). Report of the Thirteenth Session. New York: Statistical Commission, United Nations, April 20-May 7. United Nations, (1985). World Comparisons of Purchasing Power and Real Product for 1980: Part One: Summary Results for 60 Countries. New York: The Statistical Office of the United Nations Secretariat. United Nations, (1987). World Comparisons of Purchasing Power and Real Product for 1980: Part Two: Detailed Results for 60 Countries. New York: The Statistical Office of the United Nations Secretariat. U. S. Bureau of Economic Analysis (1989a), Survey of Current Business, Department of Commerce, Regional Perspectives. 69, pp. 35-36. U.S. Bureau of Economic Analysis (1989b). State Personal Income by State: 1929-1987. Washington : Government Printing Office. U.S. Bureau of Economic Analysis (1990). "Regional per capita Income in 1989." News, (BEA 90-14), April 1990. Weatherspoon, D.D. (1993). "Cross Country Convergence of Gross Domestic Products and Associated Factors: A Cointegration Approach." Ph D dissertation, Food and Resource Economics Department, University of Florida, Gainesville. Weatherspoon, D.D., J.L. Seale, Jr., and C.B. Moss (1994). "Convergence of the G-7: A Cointegration Approach." Paper presented at the International Symposium on Economic Modelling sponsored by The World Bank and the Center for Economic Modelling, London University, Washington,DC. 132 World Bank (1976). World Tables. Washington, DC: Johns Hopkins University Press. World Bank (1980a). World Tables. Washington, DC: Johns Hopkins University Press. World Bank (1980b). World Development Report 1980. Washington, DC: Johns Hopkins University Press. World Bank (1987). World Development Report 1987. Washington, DC: Johns Hopkins University Press. World Bank (1988). World Development Report 1988. Washington, DC: Johns Hopkins University Press. World Bank (1988). World Bank Atlas. Washington, DC: Johns Hopkins University Press. Wright, C.L. (1978). "Income Inequality and Economic Growth: Examining the Evidence." The Journal of Developing Areas, 13, pp. 49-66. BIOGRAPHICAL SKETCH Sri Devi Deepak of Hyderabad, India, completed her B.A. degree in mathematics, applied mathematics, and statistics at Osmania University, Hyderabad, in 1980. She received the National Merit Scholarship for graduate education for securing second rank in the B.A. examination. She completed her masters degree in business administration at Osmania University, Hyderabad, in 1982. Sri Devi worked as a Young Professional at Andhra Pradesh Industrial and Technical Consultancy Organisation, Hyderabad, India, for two years November 1982 to December 1984. Upon being selected via a national level examination, she served as an Assistant Development Officer in the National Bank for Agriculture and Rural Development (NABARD) for four yearstwo years at their Head Office in Bombay (December 1984 to January 1987) and two years at their Regional Office in Bangalore (January 1987 to March 1989). She came to the United States in April 1989 and commenced her doctoral program at the University of Florida in the Spring semester of 1990. Sri Devi has accepted a fellowship at Columbia Business School, New York, to pursue her second doctoral degree in Marketing starting Fall 1995. 133 I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Z Z* James L. Seale, Jr., Cha Professor of Food and Resource Economics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Charles B. Moss, Cochair, Associate Professor of Food and Resource Economics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Max R. I^angham, Professor of Food and Resource Economics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Gary'F. Fairchild, Professor of Food and Resource Economics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Douglas G. Waldo, Associate Professor of Economics This dissertation was submitted to the Graduate Faculty of the College of Agriculture and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. r\ August, 1995 tr o Dean, College of Agriculture Dean, Graduate School 92 t Netherlands w r Norway T Spain Figure 4.6 (Contd) 58 Table 4.1 Parameter Estimates of the Latent Variable Model for 22 OECD Countries, 1955-1990. Variables Parameters Estimates Standard Elasticities Errors 1 2 3 4 5 H 7i 11.79 0.75 0.65 0 72 0.08 0.01 0.03 I 73 1.58 0.04 0.46 G 74 1.46 0.10 0.43 ECw) i 56.04 0.26 Table 4.2 gives the estimated parameters for the measurement model (from equation 4.19) and their standard errors of estimation. The factor loadings were all positive and statistically different from zero (a = .05). This result was as expected since the indicators contributed to the accumulation of human capital (Barro, 1991; Mankiw et al., 1991; Tallman and Wang, 1992; and Lucas, 1988, 1993). Increased public expenditure on education positively influences human capital accumulation since this investment results in improvement of level of schooling, improvement in skills, and level of technology; increased consumption of newsprint denotes an increasing level of reading which in turn could indicate increases in the level of educated population; increasing shares of educated population at the secondary school and university levels indicates growth in an educated and skilled population. An increase in all four variables does indicate a better level of living standard. 31 EKStj i Fm ti n -? C_1 li/- where t c/L (3.6) This is the PP for the detailed category a between countries c and d. The last step of the EKS method is to choose one country as a base country so that it can be compared with the CPD results. A base country can be chosen by observing the values in any of the country columns of the EKS matrix. If all the prices of items are available and are characteristic items, then the EKS method is the same as equation (3.1) if Pic is replaced with a price index. Without the basic prices, the CPD method does not equal a geometric mean and neither does the EKS method. This is due to the fact that the respective price indices in these methods cannot be computed with missing prices. An illustration to demonstrate the computations of PPPs is given in Kravis et al. (1975). 3.1.5 The Gearv-Khamis Method After estimating the PPPs, the second stage of the ICP was initiated. The Geary- Khamis method provides multilateral base-invariant price and volume comparisons at the various levels of aggregation for all countries, where the volumes are expressed in "international dollars". These volumes are additive across expenditure categories, while prices are obtained by dividing expenditures in national currency by those in international dollars. Geary suggested a system of homogeneous linear equations to calculate the international prices and PPPs simultaneously. Khamis proved that this system yielded 5 explanatory variables for the 22 OECD countries. These trends are then compared and contrasted with evidence from literature. Chapter 5 describes Theils inequality index and presents the computations of inequalities using income, human capital, international openness, investment and government expenditures. The patterns of convergence (if any) are studied and analyzed. These results are also compared and contrasted with evidence from past studies. Chapter 6 summarizes and concludes the study. 3 (1988, 1993) also concluded that, with the inclusion of human capital in the production function, an economy with a human capital stock lower than the world average would grow faster than an above average economy. Tallman and Wang (1992), reviewing studies using theories of neoclassical and endogenous growth, concluded that accumula tion of human capital yielded positive dividends in terms of income and thus standards of living. This study expands on the above mentioned research and attempts to explain the process of convergence (or divergence) via factors that influence economic growth. While Weatherspoon (1993) used cointegration analysis to test for a long-term relationship in inequality among income, investment and government expenditures, and industrial employment, this study uses the latent variable model approach to analyze convergence in income levels and via directly measuring income inequality using Theils (1989) inequality index. Specifically, per capita incomes (determined by per capita levels of human capital, international openness, investment and government expenditures) for 22 member countries of the Organization of Economic Cooperation and Development (OECD) ( USA, Canada, Japan, Austria, Belgium, Denmark, Finland, France, West Germany, Greece, Ireland, Italy, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, Turkey, UK, Australia, New Zealand) were estimated via a latent variable model (Bollen, 1989) with human capital as the latent variable. An inequality index as derived by Theil (1989) was then used to measure the inequality in per capita income and its 127 Bourguignon, F. (1979). "Decomposable Inequality Measures." Econometrica, 47(4), pp. 901-920. Cass, D. (1965). "Optimum Growth in an Aggregative Model of Capital Accumulation." Review of Economic Studies, 32, pp. 233-240. Chenery, H. and M. Syrquim (1975). Patterns of Development, 1950-1970. London: Oxford University Press. Chiswick, B.R. (1971). "Earnings Inequality and Economic Development." Quarterly Journal of Economics, 85, pp. 21-39. Chiswick, B.R. (1974). Income Inequality: Regional Analysis Within a Human Capital Framework. New York: National Bureau of Economic Research, Columbia University Press. Chiswick, B.R. and J. Mincer (1972). "Time-Series Changes in Personal Income Inequality in the United States from 1939, with Projections to 1985." Journal of Political Economy, 80, pp. 534-566. Dollar, D. (1992). "Outward-oriented Developing Economics Really Do Grow More Rapidly: Evidence from 95 LDCs, 1976-1985." Economic Development and Cultural Change, pp. 523-544. Fields, G.S. (1980). Poverty, Inequality and Development. London: Cambridge University Press. Glomm, G., and B. Ravikumar (1992)." Public versus Private Investment in Human Capital: Endogenous Growth and Income Inequality." Journal of Political Economy, 100(4), pp. 818-834. Grossman, G.M., and E. Helpman (1991). Innovation and Growth in the Global Economy. Cambridge, MA: The MIT Press. Johansen, S. (1992). "A Representation of Vector Autoregressive Processes Integrated of Order 2." Econometric Theory, 8, pp. 188-202. Koopmans, T.C. (1965). "On the Concept of Optimal Growth." in The Econometric Approach to Development. Amsterdam: North-Holland Publishing Company. Kravis, I. B., A. Heston, and R. Summers (1978a). International Comparisons of Real Product and Purchasing Power. Baltimore, MD: The Johns Hopkins University Press. 4 determinants. The results from the above computations were used to analyze the effect(s) of determinants of growth on patterns, if any, of convergence (or divergence). The next chapter gives a brief overview of existing evidence on conver gence (or divergence). The literature is divided into four groups: studies using inequality measures, studies using regression analysis, studies using models of economic growth, and studies using time-series analysis. By and large, the studies using inequality measures and time-series analysis failed to reject Kuznets hypothesis, while the studies using growth theories either rejected or were inconclusive in testing the inverted-U hypothesis. The regression studies show some evidence in support of convergence- divergence hypothesis. Chapter 3 deals with the data used for the analysis of this study and includes a description of the compilation of purchasing power parity data by Summers and Heston (1993) in forming the Penn World Table (Mark 5). This chapter also details the other two sources of data: Statistical Yearbook, UNESCO (1963-1993), and Basic Facts and Figures, UNESCO (1951-1962) for compiling information for the indicators of human capital in the 22 OECD countries (two countries from Asia [Japan and Turkey], two from the Western Pacific Rim [Australia, New Zealand], 16 from Europe [Austria, Belgium, Denmark, Finland, France, Greece, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, and UK], and two countries from North America [USA and Canada]). Chapter 4 presents the generalized latent variable model (Bollen, 1989), and tabulates the results of estimation of per capita income. The chapter concludes with a brief study of the patterns in observed and estimated per capita incomes and the 125 AJ, = o; p,-) (Â£>z, P; dz i*i /-i * [>; p; p; on ^ y; >] (mv, p; ay 1-1 pÂ¡t imX where Pit = | \Pu + />* J y | [y*+ y^-il. DZ^ = te. Zj ln Zj.j , IW* = ln Nu lnATft_, , " Pu J, = E P* 111 w y* Therefore the change in income inequality can be written as U H A2, = E O. P.'XOZ* E?; oz*> <-l /-I E O#' P.' P#> O'.' / p,) Oxiw, Ep.' "#) i-i y-i (F.5) (F.6) (F.7) APPENDIX C WESTERN EUROPE There are 18 countries constituting Western Europe which is divide into three regions. One is non-EU, consisting of six countries: Austria, Finland, Iceland, Norway, Sweden, Switzerland. Another is the EU Center, consisting of eight countries: Belgium, Denmark, France, Germany (W), Italy, Luxembourg, Netherlands, UK. The third is the EU Periphery, consisting of four countries: Greece, Ireland, Portugal, Spain. 121 CHAPTER 6 SUMMARY AND CONCLUSIONS Simon Kuznets (1955) hypothesized that, as an agrarian society becomes more urbanized and affluent, income inequality initially increases and then decreases (divergence followed by convergence). It is true that Kuznets discusses inequality within one country, not across countries, but several authors have extended the convergence- divergence hypothesis to the cross-country level. For example, Paukert (1973), Ahluwalia (1976), Papanek and Kyn (1986), Ram(1989), Theil (1989), Theil and Deepak (1993a, 1993b, 1993c, and 1994), Seale et al (1994), Moss et al (1993), and Theil and Seale (1994) have used cross-country time-series data to test Kuznets divergence- convergence hypothesis. The evidence from these studies suggests that rich countries are converging in terms of income and the countries with higher levels of human capital tend to converge faster. However, in most cases the analysis was based on either an inequality index or theories of economic growth, the exception being Weatherspoon who performed cointegration analysis on inequalities in income, investment and government expenditures, and industrial employment. The objective of this study was to expand on research by Barro (1991) and Weatherspoon (1993) by including indicators for international trade and human capital into the analysis. While Barro used school enrollment ratios as a proxy for human 115 40 the 22 OECD countries during 1955-1990. Per capita public expenditure on education (PE) for country i (i= 1 to 22) was compiled as PEÂ¡ = pe; RGDPCH, where peÂ¡ was the public expenditure on education as a percentage of income. Per capita consumption of newsprint (CNÂ¡) for country i, expressed in metric tons, was compiled directly as tabulated in the UNESCO series1. Education at the secondary school level (ESÂ¡) and university (or equivalent) level (ETÂ¡) in country i were compiled as ESi = esÂ¡ / POPi ETÂ¡ = etÂ¡ / POPÂ¡ where esÂ¡ was the total number of people with secondary school education, etÂ¡ was the total number of people with university (or equivalent) education, and POPÂ¡ was the population in country i. Thus, the variables represent the shares of the population with education at the secondary and university levels, respectively. In total, the data set used in the estimation of the research model had 36 observations per country i (i= 1 to 22)for each of the 22 OECD countries (36 x 22 = 792 total observations) for each of the eight variables: income (Y), per capita public expenditure on education (PEÂ¡), per capita consumption of news print (CN), education at secondary school level (ESÂ¡), education at university (or equivalent) level (ETÂ¡), per 1 The data for CN in 1986, for all the countries, was not available and was substituted by the average value of 1985 and 1987. 110 Table 5.1 Average Inequality in Observed Income (JY), Estimated Income (JY), Human Capital (Jh), International Openness (J0), Investment (Jj) and Government (JG) Expenditures in the 22 OECD Countries, 1955-1990 Year Observed Income Estimated Income Human Capital International Openness Investment Expenditure Government Expenditure Jy Jy J Jo Ji Jo 1 2 3 4 5 6 7 1955 0.1615 0.0462 0.0093 0.3027 0.2189 0.1830 1956 0.1526 0.0424 0.0087 0.2949 0.1901 0.1832 1957 0.1386 0.0372 0.0096 0.2859 0.1490 0.1896 1958 0.1264 0.0342 0.0088 0.3002 0.1350 0.1838 1959 0.1290 0.0380 0.0100 0.2830 0.1497 0.1735 1960 0.1181 0.0331 0.0186 0.2691 0.1221 0.1632 1961 0.1047 0.0280 0.0109 0.2364 0.0952 0.1598 1962 0.1031 0.0306 0.0142 0.2289 0.1024 0.1563 1963 0.0952 0.0291 0.0162 0.2254 0.0946 0.1446 1964 0.0925 0.0288 0.0158 0.2282 0.0887 0.1397 1965 0.0954 0.0322 0.0182 0.2182 0.0986 0.1347 1966 0.0909 0.0319 0.0197 0.2037 0.0875 0.1419 1967 0.0850 0.0287 0.0172 0.2061 0.0757 0.1477 1968 0.0798 0.0272 0.0183 0.2063 0.0717 0.1443 1969 0.0750 0.0259 0.0211 0.2174 0.0714 0.1378 1970 0.0693 0.0228 0.0211 0.2041 0.0656 0.1308 1971 0.0664 0.0240 0.0220 0.1904 0.0693 0.1174 1972 0.0656 0.0240 0.0206 0.1807 0.0697 0.1158 1973 0.0654 0.0235 0.0224 0.1736 0.0654 0.1107 1974 0.0604 0.0208 0.0198 0.1641 0.0554 0.1076 1975 0.0559 0.0171 0.0159 0.1549 0.0463 0.1001 1976 0.0563 0.0189 0.0164 0.1607 0.0474 0.0954 1977 0.0575 0.0201 0.0189 0.1648 0.0485 0.0916 1978 0.0620 0.0246 0.0226 0.1796 0.0671 0.0875 1979 0.0627 0.0250 0.0218 0.1915 0.0682 0.0869 1980 0.0615 0.0229 0.0234 0.1569 0.0657 0.0833 1981 0.0641 0.0246 0.0233 0.1494 0.0740 0.0831 1982 0.0591 0.0212 0.0220 0.1497 0.0645 0.0840 1983 0.0617 0.0231 0.0218 0.1518 0.0682 0.0849 1984 0.0672 0.0300 0.0234 0.1456 0.0869 0.0887 1985 0.0682 0.0298 0.0252 0.1545 0.0832 0.0918 1986 0.0660 0.0292 0.0271 0.1537 0.0777 0.0916 1987 0.0650 0.0297 0.0283 0.1399 0.0795 0.0918 1988 0.0670 0.0313 0.0182 0.1338 0.0856 0.0917 1989 0.0678 0.0332 0.0190 0.1357 0.0922 0.0899 1990 0.0625 0.0324 0.0230 0.1271 0.0907 0.0865 35 In Summers and Heston (1980), RGDPj t was based on constant prices while in Mark 3, international trade was incorporated into RGDP. The extrapolations in this data set were also treated differently and were computed at a greater disaggregated level. Data on consumption, gross domestic investment, government expenditure, and the net foreign balance, culled out from the U.N. constant-price series, were used to get real individual components expressed in 1975 international dollars for each of the years between 1950 and 1980. Mark 4 (Summers and Heston, 1988) updated the Mark 3 set. The major effort behind this project was to make the data more consistent, that is, the estimates need to adhere to the national income identity which states that total product equals total income generated by the production of the product. The implementation of consistency was done via an error-in-variables model. The objective was to adjust both the benchmark and national accounts data to make them consistent. The maximum likelihood procedure used to solve this model corrected the data sources so that they were consistent. However, a weakness of this procedure was that the asymptotic properties of maximum likelihood were not applicable. Mark 4 did not incorporate the openness variable since the exchange rates were greatly volatile during the 1970s. 3.3 Mark 5 Data Set MARK 5 covered 139 countries and RGDP per capita was obtained by extrapolating cross-section comparisons interspatially to non-benchmark countries and intertemporally to other years. This data set was based on ICP data from four 5.1 Average Inequality in Observed Income (JY), Estimated Income (JY), Human Capital (Jh), International Openness (JQ), Investment Expenditure (JO, and Government Expenditure (JG) in the 22 OECD Countries, 1955-1990 110 IX 4.8 Country wise Relationship Between Levels of Observed Income (YÂ¡, i=l to 22) and Human Capital (HÂ¡, i=l to 22) in the 22 OECD Countries, 1955-1990 97-102 5.1 Observed and Estimated Income Inequality (JY, JY) in the 22 OECD Countries, 1955-1990 Ill 5.2 Inequality in Estimated Income (JY), Human Capital (Jh), International Openness (JQ), Investment (J,) and Government (JG) Expenditures in the 22 OECD Countries, 1955-1990 113 xi C WESTERN EUROPE 121 D WESTERN PACIFIC REGION 122 E FOUR REGIONS REVISITED 123 F CHANGE IN INEQUALITY 124 REFERENCES 126 BIOGRAPHICAL SKETCH 133 vii < fe HUMAN CAPITAL, CONVERGENCE, AND INCOME INEQUALITY: A LATENT VARIABLE APPROACH By SRI DEVI DEEPAK DISSERTATION PRESENTED TO THE GRADUATE SCHOOL THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1995 14 development and Theils income inequality measure was used to study income inequality. In addition, Ram used a Kuznets type quadratic regression to determine the relationship between the level of income and development, which represents development and inequality. The equation is J,-b + bj, btf u, where J is the measure of world inequality and Y is the natural logarithm of the average real GDP per capita. The last term is the disturbance term assumed to have the standard properties for best linear unbiased estimates. Ram found that the hypothesis was well supported when both LDCs and DCs were included in the sample and there is very little support when only LDCs were considered. Branco and Williamson (1988) also tested Kuznets hypothesis by analyzing development and income distribution. This study was unique in that it developed an absolute per capita income measure for the poorest 40% of the population in 68 countries. Their measure was the percent of income of the poorest 40% of a nations population in 1970 divided by 40% of the 1970 population, then multiplied by the real per capita GDP of that nation in 1970 (Summers and Heston, 1984). Their findings suggested that the poorest 40% of the population lose income both relatively and absolutely in the early stages of economic development; thereafter, there are gains in income although with diminishing marginal returns at the highest levels of development. Ram (1989a) also extended his 1988 study to the world economy inclusive of 115 market economies drawn from the Summers and Heston (1984) data for the years 1960- 1980. Using the same structure of the model as before, found that though world income 100 Y Netherlands H y Norway Spain Figure 4.8 (Contd) 78 Table 4.7 Average Levels of Observed and Estimated Income Per Capita (YOECD, YOECD) in the 22 OECD Countries, 1955-1990 Year Observed Estimated Income Income 1955 5603.64 6335.28 1956 5723.63 6389.51 1957 5813.63 6406.68 1958 5798.50 6332.68 1959 6061.19 6573.94 1960 6287.77 6759.70 1961 6497.31 6945.81 1962 6763.09 7155.94 1963 7021.29 7324.48 1964 7380.76 7622.04 1965 7682.17 7846.86 1966 8013.23 8098.39 1967 8232.08 8229.28 1968 8624.72 8532.40 1969 8994.56 8829.64 1970 9216.68 8961.31 1971 9480.43 9076.73 1972 9914.48 9296.54 1973 10402.89 9778.07 1974 10335.40 9653.87 1975 10127.53 9060.21 1976 10562.65 9491.47 1977 10867.58 9682.47 1978 11232.67 9889.26 1979 11497.94 10113.69 1980 11512.11 9979.04 1981 11599.01 9937.19 1982 11398.71 9590.19 1983 11633.87 9715.47 1984 12163.43 10333.14 1985 12495.18 10502.00 1986 12786.72 10656.12 1987 13162.41 10957.08 1988 13699.01 11398.60 1989 14076.57 11770.50 L22Q L4317.18 11902.49 47 n 0 in E(ijrj) and simplifying we get 2^(0) = Ay (/-B)1 (Tr/ + T) [(/-B)-1]' Ay + 0t (4-6> which shows that the covariance of y is a complex function of six of the eight model parameter matrices or vectors. Similarly, 2^(0) = E(yx) = A, (/-B)"1 T sw(6) = 2^0)' A.sr' [(/--]' 4 Further, 2(0) = Â£(') A, Â£(((') K+% (49) Substituting for E(Â£Â£') we have S(0) A,A^ e, <410> Therefore, the covariance matrix 2 (0) for the observed y and x variables as a function of the model parameters is 2(0) V0> V0> .Ve> s(0) (4.11) which can also be written as 34 MARK 5 data is discussed at length. For detailed discussions of the other data sets, please see Weatherspoon (1993). The purpose of the first paper by Kravis et al. (1978b) was to fill the gap in the world statistical system for comparative data on "real" GDP per capita for a large number of countries. The contribution of the second paper by Summers and Heston (1980) was that they extrapolated the data for the ICP and non-ICP countries forward and backward through time. The third publication by Kravis et al. (1982) had two benchmark years, 1970 and 1975, unlike the previous papers which had only 1970. The fourth publication also by Summers and Heston (1988) was basically an update of the MARK 3 data set. The regression equation used to summarize the 1970 and 1975 cross-section relationship in Mark 3 (Summers and Heston, 1984) study was Inr = ax(Inwp + o2(lnp2 + a3(ln(0Pp + <41> where rx = ( DAj/PPPDAj) / DAUS and ^ = ( DAj/XRÂ¡ )/DAus. pppDA xs the purchasing power parity over domestic absorption, and XRj is the exchange rate. They are both expressed in national currency units of the jth country per U.S. dollars. OPj is the measure of relative openness of the jth economy defined as ((Exports, + ImportSj)/GDPj) / ((Exportsus + Importsus)/GDPus ), an average of the ratio for five years before the cross-section year. The as have the same expected signs as in Kravis et al. (1978b). 114 5.1 Summary From Section 5.4, the declining income inequality (observed and estimated) indicates that the countries in the OECD group are growing closer together in income. This evidence is in favor of the convergence component of the "extended" Kuznets hypothesis. The slow rate of convergence in income could be attributed to the accelerated convergence in terms of openness offset by divergence in terms of investment expenditure and low rate of convergence in terms of human capital. Barro (1991) concluded that convergence in the OECD countries was clearly evident since these countries had high levels of per capita income and were similar in terms of economic and political institutions. Adding to this conclusion, this study showed that convergence in these countries was also a result of the influence of increasing levels of human capital and international openness. An attempt was also made to analyze the change in inequality using a time-differential to the Theil index (Appendix F). However, the results from the analysis of the time-differential were inconclusive for the purposes of this study. 69 Figure 4.3 (Contd) 129 Psacharopolous, G., and A.M. Amagada (1986). "The Educational Composition of the Labor Force: An International Comparison." International Labor Review, 125(5), pp. 561-574. Psacharopolous, G., and M. Woodhall (1985). Education for Development. New York: Oxford University Press. Ram, R. (1988). "Economic Development and Income Inequality: Further Evidence on the U-Curve Hypothesis." World Development, 10(11), pp. 1371-1375. Ram, R. (1989a). "Level of Development and Income Inequality: An Extension of Kuznets-Hypothesis to the World Economy." Kyklos, 42(1), pp. 73-88. Ram, R. (1989b). "Can Educational Expansion Reduce Income Inequality in Less- Developed Countries?" Economics of Educational Review, 8(2), pp. 185-195. Ram, R. (1992). "Interstate Income Inequality in the United States: Measurement, Modelling, and Some Characteristics." Review of Income and Wealth, 38(1), pp. 39-48. Ramsey, F.P. (1928). "A Mathematical Theory of Saving." Economic Review, 38, pp. 543-59. Rebelo, S. (1990). "Long-Run Policy Analysis and Long-run Growth." Journal of Political Economy, 99(3), pp. 500-521. Romer, P.M. (1989). "Capital Accumulation in the Theory of Long-Run Growth." in Modem Business Cycle Theory. Cambridge, MA: Harvard University Press, pp. 51-127. Romer, P.M. (1994). "The Origins of Endogenous Growth." Journal of Economic Perspectives, 8(1), pp. 3-22. Seale, J.L., Jr., H. Theil and S.D. Deepak (1994). "Growth and its Disparity in Rich and Poor Regions." Economics Letters, 45, pp. 467-470. Shannon, C.E. (1949). The Mathematical Theory of Communication. Urbana: The University of Illinois Press. Smith, A. (1937). An Inquiry into the Nature and Causes of the Wealth of Nations. New York: The Modem Library. Solow, R.M. (1956). "A Contribution to the Theory of Economic Growth." Quarterly Journal of Economics, 70, pp. 65-94. 18 change, a model emphasizing human capital accumulation through schooling, and a model emphasizing specialized human capital accumulation through learning by doing. He concluded that, with the inclusion of human capital in the production function, economies that are initially poor will remain relatively poor, though their long-run rate of income growth will be as that of initially wealthier economies. If traded goods are included in the model, the long-run relationship between the two kinds of capital implies the same marginal productivity of physical capital, no matter what the level of capital that has been accumulated. If labor is mobile, it will flow in general from poor countries to wealthy ones. Rebelo (1990) described a class of endogenous growth models that have constant returns to scale technologies. He hypothesized that this class of models rationalizes the existence of permanent cross-country differences in growth rates as being, at least partly, a result of differences in government policies. His analysis revealed that small differences in policy regimes could easily mean the difference between growth and stagnation. Tamura (1991) developed an endogenous growth model that produced conver gence in per capita income and growth rates of output. His analysis was based on the premises that agents have identical preferences and access to identical technologies of production and investment, but differing levels of human capital. He concluded that a spillover effect of human capital in the investment technology provides below-average human capital agents with a higher rate of return on investment than above-average human capital agents; thus, below-average human capital agents grow faster than above- 43 investment and government expenditures, and volume of exports and imports. International trade is one of the key determinants of economic interaction among countries and countries gain from trading goods and services by taking advantage of the differences between their endowments and by achieving economies of scale in production. These gains from trade are reflected in the growth (or decline) of national income. Further, the national income accounts provide information essential for studying the disparities in income among rich and poor countries (Krugman and Obstfeld, 1991). Growth theorists (Barro, 1991; Mankiw et al., 1992; Lucas, 1988, 1993; Romer, 1989, 1994; Tallman and Wang, 1992) have shown that accumulation of human capital is beneficial to the economy as a whole and the individual within the economy. Therefore, income was specified as a function of human capital, international openness, government expenditure, and investment expenditure. The model is discussed further in Section 4.2 of this chapter. The objective of this study was to analyze the nature of the influence (if any) of factors of economic growth (especially human capital) on income for the 22 OECD countries (in Chapter 1) during 1955-1990. The classical econometric treatment assumes that the observed variables, endogenous and exogenous, are measured without error. Latent variable models, on the other hand, incorporate measurement error in the observed variables into the estimation process. These errors can be correlated, and multiple indicators can measure the unobservable variable. Therefore, as the level of human capital is not directly observable, this study estimated income using a latent variable model (Bollen, 1989) with human capital as the latent variable. xml version 1.0 encoding UTF-8 REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd INGEST IEID ESMB2U8UM_2OZ1OB INGEST_TIME 2015-03-31T18:42:26Z PACKAGE AA00029820_00001 AGREEMENT_INFO ACCOUNT UF PROJECT UFDC FILES 53 The indicators for human capital were levels of per capita public expenditure on education (PE), per capita consumption of newsprint (CN), shares of population with high school education (ES), and shares of population with university or equivalent education (ET). In a review of growth models, Tallman and Wang (1992) concluded that there were potential gains from greater emphasis on higher education, which improved learning efficiency on the job and yielded significant positive external effects. This improvement in on-the-job learning was also important for promoting perpetual economic growth, adding significantly to individual human capital stock as well as to the stock of societys knowledge that may improve the quality of life (Lucas, 1993). Therefore, since PE gave an indication of the level of investment in human capital, CN indicated a level of reading, and ES and ET denoted the shares of educated population, they were feasible choices for indicators of human capital accumulation. Further, the availability of data was yet another reason for the choice of indicators. Therefore, there were 36 observations for each of the eight variables (Y, PE, CN, ES, ET, O, I, and G) and for each of the 22 OECD countries. Since the intention was to study the convergence behavior of these countries as a group, the data were pooled making the total number of observations in each vector to be 792. Therefore, using equations (4.1), the latent variable model for estimation was 36 benchmark years: 1970, 1975, 1980, and 1985. Eighty-one countries participated in these benchmark studies and 47 participated in more than one study. Therefore, the need for relying on non-benchmark estimating methods was reduced. The national accounts data have also improved by using the World Banks archive data. The methodology for obtaining RGDP per capita for a large number of countries has improved. All these factors make the MARK 5 the most accurate data published in recent times. The four ICP benchmark studies, Phases II to V, used in this study were all compiled in different ways and have different countries participating in different years. This is why the data needed to be made intertemporal and interspatial. Since the Phase V data were not published at that time, the authors had to calculate the RGDPs on their own using raw data from the U.N. and The World Bank. The countries that participated in the 1985 benchmark comparisons form five groups: 22 OECD countries, 11 Asian countries including Japan, 22 African countries, five European Group II countries including Finland and Austria, and a group of Caribbean countries. The Caribbean countries comparisons were not complete at that time. The Geary-Khamis method was implemented for the OECD and Asian countries. The African countries, Hungary, Poland, and Yugoslavia all had data that allowed them to be linked to the OECD and Asian countries. The total number of countries from Phase V used in this study was 57. A different method was used for those countries which did not participate in the 1985 benchmark study, but which had participated in a previous benchmark study. The procedure was to value their 1975 or 1980 estimates of consumption (C), investment (I), BIOGRAPHICAL SKETCH Sri Devi Deepak of Hyderabad, India, completed her B.A. degree in mathematics, applied mathematics, and statistics at Osmania University, Hyderabad, in 1980. She received the National Merit Scholarship for graduate education for securing second rank in the B.A. examination. She completed her masters degree in business administration at Osmania University, Hyderabad, in 1982. Sri Devi worked as a Young Professional at Andhra Pradesh Industrial and Technical Consultancy Organisation, Hyderabad, India, for two years November 1982 to December 1984. Upon being selected via a national level examination, she served as an Assistant Development Officer in the National Bank for Agriculture and Rural Development (NABARD) for four yearstwo years at their Head Office in Bombay (December 1984 to January 1987) and two years at their Regional Office in Bangalore (January 1987 to March 1989). She came to the United States in April 1989 and commenced her doctoral program at the University of Florida in the Spring semester of 1990. Sri Devi has accepted a fellowship at Columbia Business School, New York, to pursue her second doctoral degree in Marketing starting Fall 1995. 133 130 Summers, R., and A. Heston (1984). "Improved International Comparisons of Real Product and its Composition: 1950-1980." The Review of Income and Wealth, 30, pp. 207-262. Summers, R., and A. Heston (1988). "A new Set of International Comparisons of Real Product and Price Levels Estimates for 130 Countries, 1950-1985." The Review of Income and Wealth, 34, pp. 1-25. Summers, R., and A. Heston (1991). "The Penn World Table (Mark 5): An Expanded Set of International Comparisons. 1950-1988" Quarterly Journal of Economics, pp. 327-368. Summers, R., and A. Heston (1993). New Computer Diskette Supplement (MARK 5.5) to The Penn World Table (Mark 5): An Expanded Set of International Comparisons. 1950-1988: Quarterly Journal of Economics, pp. 327-368. Summers, R., I. Kravis, and A. Heston (1980). "International Comparisons of Real Product and its Composition: 1950-1977." The Review of Income and Wealth, 26, pp. 327-368. Swan, T.W. (1956). "Economic Growth and Capital Accumulation." Economic Record, 32, pp. 334-61. Tallman, E.W., and P. Wang (1992). "Human Capital Investment and Economic Growth: New Routes in Theory Address Old Questions." Economic Review, pp. 1-12. Tamura, R. (1991). "Income Convergence in an Endogenous Growth Model." Journal of Political Economy, 99(3), pp. 522-540. Theil, H. (1967). Economics and Information Theory. Amsterdam: North-Holland Publishing Company. Theil, H. (1989). "The Development of International Inequality." Journal of Econometrics, 42, pp. 145-155. Theil, H., and S.D. Deepak (1994). "The GDPs of Seven Major Regions, 1950-1990." Empirical Economics, 19, pp. 517-522. Theil, H., and S.D. Deepak (1993a). "How Affluent Are the Neighbors of Affluent Countries ?" International Working Paper Series IW93-21, Food and Resource Economics Department, University of Florida, Gainesville. LIST OF TABLES Table Bags 3.1 Countries Represented in the International Comparison Project 27 3.2 Description of Variables in PWT 5.5 File 39 4.1 Parameter Estimates of the Latent Variable Model for 22 OECD Countries, 1955-1990 58 4.2 Parameter Estimates of the Measurement Model for 22 OECD Countries, 1955-1990 59 4.3 Estimated Levels of Human Capital (HÂ¡, i=l to 22) in the 22 OECD Countries, 1955-1990 61-62 4.4 Average Per Capita Levels of Human Capital (Hqecd), International Openness (0OECD), Investment Expenditure (IOECd)> and Government Expenditure (GOEcd) in the 22 OECD Countries, 1955-1990 63 4.5 Levels of Observed Income (YÂ¡, i=l to 22) in the 22 OECD Countries, 1955-1990 74-75 4.6 Levels of Estimated Income (YÂ¡, i= 1 to 22) in the 22 OECD Countries, 1955-1990 76-77 4.7 Average Levels of Observed and Estimated Income Per Capita (YOECD, YOECD) in the 22 OECD Countries, 1955-1990 78 4.8 Summary of Cross-Country Analyses for the 22 OECD Countries, 1955-1990 104 viii 109 J = JR + J, where J = ^ P^If Thus, total inequality among the n countries equals regional inequality plus the average within-region inequality, the average being a weighted average with the population shares Pj,...,PG as weights. Note that these weights are identical to those of the regional per capita incomes. 5.6 Inequality in the OECD Countries The analysis in this section is based on the observed and estimated inequalities computed for the 22 OECD countries during 1955-1990. Using equation (5.1) the observed and estimated income inequalities, JY and JY, respectively, were computed. For the observed index, JY, Summers and Heston (1993) data for income and population were used. Using the population data from the same source and estimated income computed via a latent variable model (Chapter 4, equation 4.24), the estimated inequality, JY, was computed using equation (5.1). The results of the computations of observed and estimated income inequality are given by Table 5.1 and depicted in Figure 5.1. At a glance, from Columns 2 and 3 of the table and from the figure, it was seen that the gap between JY and JY was quite wide initially and began to lessen over time. Again this could be attributed to the reduction in nonsystematic errors in the process of empirical estimation and the inability of the process to capture country-specific effects. JY decreased initially and then levelled off at a value of 0.03 depicting a pattern of convergence, in terms of income, and indicating that the OECD countries were moving closer as a group. Table 4.2 Parameter Estimates of the Measurement Model for 22 OECD Countries, 1955-1990. 59 Variables Parameters Estimates Standard Errors 1 2 3 4 PE x, 2.65 0.08 CN X2 1.04 0.04 ES X3 1.43 0.08 ET X4 0.97 0.03 E(5,6,) 1.51 0.06 EW) 22 0.54 0.02 E(5,63) e33 3.55 0.05 E(6A) Bu 0.28 0.02 4.5 Income and Human Capital in OECD Countries Using Bartletts method (equation 4.16) and the estimated parameters (Table 4.2), A we can compute the per capita value for human capital, H: = 2.7 / 1.5 -1 '2.7' -> '2.7 / 1.5 -1 PE 1.0 0 0.5 1.0 1.0 0 0.5 CN 1.4 0 0 3.6 1.4 1.4 0 0 3.6 ES 1 0 0 0 0.3 1 1 1 0 0 0 s ET (4.23) Using equation (4.17) and the parameters of estimation from Table 4.1, per capita incomes of the 22 OECD countries are computed: t = 11.79 + 0.08 O + 1.58 I + 1.46 G <4-24) These computations yield 792 values for human capital and per capita income for the 22 countries. Therefore, the estimation of the model yielded 36 values for each variable for each country. The values of estimated per capita income and human capital for each 93 r Sweden r Turkey r Switzerland UK Figure 4.6 (Contd) 3.2 Extrapolations with ICP Data 33 3.3 Mark 5 Data Set 35 3.4 Data for Estimation 38 4. INCOME AND HUMAN CAPITAL IN THE OECD COUNTRIES 42 4.1 General Latent Variable Model 44 4.1.1 Structural Equations of the Model 44 4.1.2 Implied Covariance Matrix 46 4.1.3 Identification 48 4.2 Estimation 51 4.3 Empirical Model 52 4.4 Parameter Estimates of the Latent Variable Model 56 4.5 Income and Human Capital in OECD Countries 59 4.6 Summary 103 5. INEQUALITY IN THE OECD COUNTRIES 105 5.1 Graphical Inequality 105 5.2 Inequality via Measures of Dispersion 106 5.3 Inequality Indices 106 5.4 Properties of Inequality Index 107 5.5 Theils Inequality Index 108 5.6 Inequality in OECD Countries 109 5.7 Summary 114 6. SUMMARY AND CONCLUSIONS 115 APPENDICES A SEVEN REGIONS OF THE WORLD 119 B EUROPE, AFRICA, AND SOUTHERN CONE 120 vi LIST OF FIGURES Figure Eage 4.1 Average Level of Human Capital (HOECd) in the 22 OECD Countries, 1955-1990 65 4.2 Average Level of Human Capital (Hoecd), International Openness (0OECD), Investment (Iobcd) Government (GOEcd) Expenditures in the 22 OECD Countries, 1955-1990 66 4.3 Comparing Countrywise Levels of Human Capital (Hj, i=l to 22) and Average Level of Human Capital (Hoecd) hi the 22 OECD Countries, 1955-1990 68-73 4.4 Average Levels of Observed and Estimated Income, Yoecd mid Yq^^, in the 22 OECD Countries, 1955-1990 79 4.5 Comparing Countrywise Levels of Observed Income (YÂ¡, i=l to 22) and Estimated Income (YÂ¡, i=l to 22) in the 22 OECD Countries, 1955-1990 82-87 4.6 Comparing Countrywise Levels of Estimated Income (YÂ¡, i=l to 22) and Average Level of Estimated Income (YOECD) in the 22 OECD Countries, 1955-1990 89-94 4.7 Relationship Between Average Levels of Observed Income (YOECD) and Human Capital (HOECD) in the 22 OECD Countries, 1955-1990 95 x 41 capita international openness (0Â¡), per capita investment expenditure (y, and per capita government expenditure (G). Y Germany Ire I and 15,000 y Greece Y Italy H Figure 4.8 (Contd) 102 Y Austro Mo T New Zen Iand Figure 4.8 (Contd) indicating that it was a key determinant of income levels for the OECD countries. Further, all the determinants were increasing over time at an average per capita level. Estimated income per capita and Theils income inequality index were computed using the estimated human capital, the other three determinants and the parameters of estimation. The results of these computations indicated that the estimated income fitted the observed income closely and that both the observed and estimated incomes were increasing during 1955-1990. Theils inequality index was then used to measure observed and estimated inequalities in income, human capital, international openness, investment expenditure, and government expenditure. The evidence from the income inequality analysis is in favor of the convergence component of Kuznets hypothesis. Further, the analyses of the inequalities in income, human capital, openness, investment and government expenditures revealed that the OECD countries, as a group, were moving closer in terms of income, openness and government expenditure. However, these countries are diverging in terms of human capital and investment expenditure. xiii 131 Theil, H., and S.D. Deepak (1993b). "The GDPs of Three Regions in Western Europe, 1950-1990." International Working Paper Series IW93-24, Food and Resource Economics Department, University of Florida, Gainesville. Theil, H., and S.D. Deepak (1993c). "Visiting the GDPs of the Western Pacific." International Working Paper Series IW93-24, Food and Resource Economics Department, University of Florida, Gainesville. Theil, H., and J.L. Seale, Jr. (1994). "The Geographic Distribution of World Income, 1950-1990." De Economist, 142, pp. 387-419. UNESCO, "Basic Facts and Figures, 1951-1962." Paris: UNESCO. UNESCO, "Statistical Yearbook, 1963-1993." Paris: UNESCO. United Nations, (1965). Report of the Thirteenth Session. New York: Statistical Commission, United Nations, April 20-May 7. United Nations, (1985). World Comparisons of Purchasing Power and Real Product for 1980: Part One: Summary Results for 60 Countries. New York: The Statistical Office of the United Nations Secretariat. United Nations, (1987). World Comparisons of Purchasing Power and Real Product for 1980: Part Two: Detailed Results for 60 Countries. New York: The Statistical Office of the United Nations Secretariat. U. S. Bureau of Economic Analysis (1989a), Survey of Current Business, Department of Commerce, Regional Perspectives. 69, pp. 35-36. U.S. Bureau of Economic Analysis (1989b). State Personal Income by State: 1929-1987. Washington : Government Printing Office. U.S. Bureau of Economic Analysis (1990). "Regional per capita Income in 1989." News, (BEA 90-14), April 1990. Weatherspoon, D.D. (1993). "Cross Country Convergence of Gross Domestic Products and Associated Factors: A Cointegration Approach." Ph D dissertation, Food and Resource Economics Department, University of Florida, Gainesville. Weatherspoon, D.D., J.L. Seale, Jr., and C.B. Moss (1994). "Convergence of the G-7: A Cointegration Approach." Paper presented at the International Symposium on Economic Modelling sponsored by The World Bank and the Center for Economic Modelling, London University, Washington,DC. CHAPTER 2 EVIDENCE OF CONVERGENCE The interest in studying convergence has been derived from the basic relationship between development and income distribution. To achieve convergence the poorer countries need to increase their productivity at a rate greater than that in richer countries (Barro and Sala-i-Martin, 1992). The importance of the pattern of income distribution during various stages of development and the lack of adequate time-series data for most developing countries culminated in many studies which attempt to test Kuznets hypothesis with varying methodologies. The predominant methodologies used include inequality measures (Theil, 1989; Berry et al., 1991; Oshima, 1992; Ram, 1992; Moss et al., 1993; Theil and Deepak, 1993a, 1993b, 1993c, 1994; Theil and Seale, 1994; and Seale et al., 1994), regression analysis (Wright, 1978; Bomschier, 1983; Branco and Williamson, 1988; Ram, 1988, 1989a, 1989b; Barro, 1991; Barro and Sala-i-Martin, 1992; Mankiw et al., 1992), theories of growth (Lucas, 1988, 1993; Rebelo, 1990; Tamura, 1991; Glomm and Ravikumar, 1992; Romer, 1994), and time-series analysis (Weatherspoon, 1993; Weatherspoon et al., 1994). Since the recent developments in endogenous economic growth research (Romer, 1989), growth in income is no longer treated as a random process but as something that is systematically related to other factors in the economy (Grossman and Helpman, 1991). 6 7 Summers and Heston (1988) plot the growth rates of 114 countries between 1960 and 1985 against the level of per capita income in 1960. This plot did not depict any strong correlation between initial levels of income and growth during the period, but revealed the variation in growth rates between countries. In the past, growth patterns in the world could not be studied effectively due to data constraints. But the Penn World Table (PWT) time-series data for various economic indicators compiled by Summers and Heston (1991) have changed the scenario to a large extent. 2,1 Studies Using Inequality Measures The simplest inequality measures are estimates of statistical dispersion like variance, standard deviation, and the coefficient of variation. A commonly used inequality measure is the gini coefficient which is based on the Lorenz curve (Anand and Kanbur, 1993). This statistic measures the ratio of the area between the diagonal and the Lorenz curve to the total area below the diagonal. Another measure is the Theil entropy index (also known as Theils inequality index) which measures inequality by taking the logarithm of the ratio of the arithmetic mean income to the geometric mean income. The appropriateness of the inequality index to be used depends on the objective of the study as well as the properties of the index (Chapter 5, Section 5.4). For example, Theil (1989) used a decomposable inequality index to better assess its behavior internationally as well as regionally. Theil (1989) used the Summers and Heston (1988) data set spanning 1950-1985 to assess the economic development in five regions of the noncommunist world: the 17 variable proportions, and the production function was subjected to a technological factor. Thus, two exogenous processes, population growth and technological progress, determined the economys growth rate. In recent times with the development of endogenous growth models, the premises of neoclassical growth theory have come under serious scrutiny, thus creating the need for new techniques of measurement and analysis of the growth process. Endogenous growth models indicate that endogenizing technical progress via human capital accumulation allows an economy to grow endogenously and thus results in better measurement (Lucas 1988, 1993) and understanding of determinants of economic growth and the disparities in growth rates. The neoclassical growth model predicts a zero growth rate of output per unit of input in the long run, since the output growth rate is entirely determined by exogenous factors like the population growth rate and the rate of technical progress. However, in the endogenous growth models, the growth rate of output per capita is a positive constant because human capital accumulation results in endogenous technical progress. The underlying fact is that neoclassical models fix the rate of growth and allow the marginal product of capital to vary, whereas the endogenous models fix the marginal product of capital but allow the rate of economic growth to be endogenous. Lucas (1988) considered the prospects for constructing a neoclassical theory of growth and trade that was consistent with some of the main features of economic development. He studied three models to account for the disparities in growth rates across economies: a model emphasizing physical capital accumulation and technological 56 1 0 0 0 4 = 0 4*22 4*23 4*24 0 4*32 4*33 4*34 0 4*42 4*43 4*44 (4.21) From equations (4.15) to (4.17) above, the empirical system of equations consisted of eight coefficients 7Â¡ (i=l to 4), and (j= 1 to 4)) and five variances (E(fn, E(<5j5j) (j = l to 4) that were to be estimated. Therefore, the number of unrestricted unknowns in the 6 vector of the empirical model were 13 and the t-rule value computed using equation (4.13) was 36. The empirical model, described by equations 4.15 and 4.16, was in the MIMIC form with p=l and q=7 y = r? C y = n (4.22) x = + 6 Therefore the necessary and sufficient conditions for identification were met for this model. 4.4 Parameter Estimates of the Latent Variable Model The maximum likelihood function FML as given in the previous section was used to estimate the parameters of this model. Table 4.1 gives the estimated parameters for the latent variable model (from equation 4.18) and their asymptotic standard errors of estimation. These results clearly indicate that human capital (as measured by a latent 112 Columns 4 to 7 of Table 5.1 give the inequalities in human capital, J, international openness, JQ, investment expenditure, Jr, and government expenditure, JQ. The inequalities in human capital and investment expenditure depicted decreasing trends initially and then increased indicating that the OECD countries were converging in terms of these variables initially but have commenced to diverge in terms of human capital and investment expenditure. However, inequality in openness and government expenditure decreased indicating that the OECD countries were converging in terms of these variables. A graphic comparison of inequalities in income and its determinants of income is given by Figure 5.2. This figure showed that inequality in income and human capital were converging and were almost identical during 1970-1983 and 1986-87. The inequality in openness was larger in value than any other variable and was decreasing over time. Inequality in investment expenditure was decreasing initially and then increased from 1979 onwards. Inequality in government expenditure was decreasing over time and intersected with that of investment expenditure in 1987. These results point to the fact that the convergence in income is contributed by all its determinants. Thus, the low rate of convergence in income could be due to the rapid rate of convergence in openness, a high rate of divergence (from 1979 onwards) in investment expenditure, a modest rate of convergence in government expenditure, and a slow rate of divergence in human capital (which influenced income more positively than the other determinants). This dissertation was submitted to the Graduate Faculty of the College of Agriculture and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. r\ August, 1995 tr o Dean, College of Agriculture Dean, Graduate School CHAPTER 1 INTRODUCTION Since the time of Adam Smith (1937) varying rates of economic growth have puzzled economists; thus, for the past several decades this issue has been the focus of research for economists. Three salient and apparent features of studies on economic growth are (a) long-run growth of per capita income has been sustained at a positive rate for many countries; (b) rates of growth vary across countries; and (c) methodologies vary for measuring and explaining economic growth and disparity. The principal question asked was whether countries varied greatly in their growth rates and whether these differences were the outcome of random processes. Further, the phenomenon of accelerated growth of poorer economies causing them to "converge" in per capita income level with that of the richer economies and the factors affecting this growth have become the focus of developmental and international economists. By convergence we refer to the process of the faster growth of relatively poor countries to enable them to "converge" with the growth of relatively rich countries. The divergence-convergence hypothesis originated in neoclassical economics with Kuznets inverted-U theory (1955) which states that, in the process of economic development, inequality within a country initially increases in the early stages, stabilizes at some peak level, then declines as the latter stages of development occur (divergence followed by 1 117 Tallman and Wang (1992) reviewed neoclassical and endogenous growth theories and concluded that higher levels of education could positively influence the accumulation of human capital and thus the standard of living in an economy. Lucas (1993) concluded that countries with high rates of human capital accumulation could sustain greater rates of growth. Barro (1991) deduced that growth in income converged faster at higher levels of human capital. This study used public expenditure on education, consumption of newsprint, education at high school and university levels as observable variables for human capital. All these factors contribute positively to accumulation of human capital. The latent variable model was estimated using maximum likelihood and the estimated values of the four factors of growth were obtained using Bartletts method (1938). The results from estimation showed that the data fit the model reasonably well and that income and its determinants were growing over time. Therefore, the factors of growth specified for this study did appear to contribute to growth in income. These results comply with contemporary evidence (Barro, 1991; Mankiw et al., 1992). Theils inequality index was then used to measure observed and estimated inequalities for the OECD countries. The evidence from the inequality analysis was in favor of the convergence component of Kuznets hypothesis for income, international openness, and government expenditures and favors the divergence component in terms of human capital and investment expenditure. These results suggested that the OECD countries were growing closer together in terms of income, international openness, and government expenditure and moving away in terms of human capital and investment |