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Human capital, convergence, and income inequality

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Human capital, convergence, and income inequality a latent variable approach
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Deepak, Sri Devi
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xiii, 133 leaves : ill. ; 29 cm.

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Capital investments ( jstor )
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Government expenditures ( jstor )
Human capital ( jstor )
Income estimates ( jstor )
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Dissertations, Academic -- Food and Resource Economics -- UF
Food and Resource Economics thesis, Ph. D
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Thesis (Ph. D.)--University of Florida, 1995.
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Includes bibliographical references (leaves 126-132).
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Typescript.
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Vita.
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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







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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)




Full Text
Figure 4.5 Comparing Country wise Levels of Observed Income (Y¡, i=l to 22) and
Estimated Income (Y¡, i=l to 22) in the 22 OECD Countries, 1955-1990
o
o
o
Yj
A
o- Y¡


33
GDP£I* £>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 (H¡, 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, e¡c is
normally distributed with mean zero and variance o2, A¡ 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 = ^ p¡Lo%(p/y)
where p¡ is the world population share of country i, and y¡ 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, p¡ and Yg = sum¡ y¡, where the summations are over i E
Rg, then
j. £ 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 (H¡, 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 (Y¡, 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
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12543
6184
7215
1986
16885
16155
12240
11306
11552
13428
12283
12505
12832
6221
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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
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1483$
12858
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$$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 (Y¡, 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- Y¡


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
£
L A7 *
where Y0ecd was the per capita income of the group of 22 OECD countries, n¡ (i = l to
22) was the population of country i, Y¡ (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
¡-1
= £ Pi to y*
i-l
(F.l)
- k + In £ Nfi £ PlJn Z,
j-1 /-I
where Z¡ is the GDP of country i. Taking partial derivatives with respect to Z¡ we get
_a/
dz,
N,
Ei
z,
' E ",2,
y-i
dZ, 1
£ 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) Z,
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 (Y¡, i = 1 to
22) and Human Capital (H¡, 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* (4.20)
where 4 was the variance-covariance matrix of £, 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, u, 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,
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 =
i3 = 0i4 = 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 n = n = u =
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
, ¡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 £ and only one latent variable, r¡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 r¡¡ 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; £ 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 £ on r¡, 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 £.
The second component of the structural system is the measurement model:
y V + e
(4.2)
x = A,£ + 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 £, 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 £ and f and with each other.
The expected value of e and 5 are zero. To simplify matters rj, £, y, and x are written
as deviations from their means. Further, £ 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 £ are treated as £ variables. The only relationships between latent
variables that are of concern are their variances and covariances (<£). 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 ¥ 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 (r¡=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. £
corresponded with the matrix of exogenous latent variables wherein which £, was H and
£2, £3, and £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, y¡, 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 ¡-i-v"
l-l
where P¡ 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 C¡ 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 ¥ 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 (Y¡, 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<£.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); ¥ (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(£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(r¡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 (i¡ and gj) for country j (j = 1 to 22) were
used to compute per capita levels of real investment and government expenditures, I¡ and
Gj, respectively.
lj = ij RGDPCHj
Gj = gj RGDPCHj
International openness, 0¡, 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 (H¡, 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 (Y¡, i=l to 22) in
the 22 OECD Countries, 1955-1990 74-75
4.6 Levels of Estimated Income (Y¡, 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 (Y¡, i=l to 22) and Estimated Income
(Y¡, i=l to 22) in the 22 OECD Countries,
1955-1990 82-87
4.6 Comparing Countrywise Levels of Estimated
Income (Y¡, 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 (Y¡, i=l to 22) and Human Capital
(H¡, 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 ¡-i-v"
l-l
where P¡ 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, e¡c is
normally distributed with mean zero and variance o2, A¡ 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<£.A> where v. m E
(3.8)
C-1
while xc is defined as
A
c
A
which is also

33
GDP£I* £>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/XR¡ )/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 (i¡ and gj) for country j (j = 1 to 22) were
used to compute per capita levels of real investment and government expenditures, I¡ and
Gj, respectively.
lj = ij RGDPCHj
Gj = gj RGDPCHj
International openness, 0¡, 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
PE¡ = pe; RGDPCH,
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 series1. Education at the secondary
school level (ES¡) and university (or equivalent) level (ET¡) in country i were compiled
as
ESi = es¡ / POPi
ET¡ = et¡ / POP¡
where es¡ was the total number of people with secondary school education, et¡ 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
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 (0¡), 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; £ 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 £ on r¡, 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 £.
The second component of the structural system is the measurement model:
y V + e
(4.2)
x = A,£ + 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 £, 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 £ and f and with each other.
The expected value of e and 5 are zero. To simplify matters rj, £, y, and x are written
as deviations from their means. Further, £ 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); ¥ (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(£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(r¡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 and
sw(6) = 2^0)' A.sr' [(/--]' 4
Further,
2(0) = £(') A, £(((') K+% (49)
Substituting for E(££') 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 £ are treated as £ variables. The only relationships between latent
variables that are of concern are their variances and covariances (<£). 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 ¥ 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 C¡ 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 ¥ 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 £ and only one latent variable, r¡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 r¡¡ 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 (r¡=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. £
corresponded with the matrix of exogenous latent variables wherein which £, was H and
£2, £3, and £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* (4.20)
where 4 was the variance-covariance matrix of £, 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, u, 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,
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 =
i3 = 0i4 = 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 n = n = u =
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 7¡ (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
£
L A7 *
where Y0ecd was the per capita income of the group of 22 OECD countries, n¡ (i = l to
22) was the population of country i, Y¡ (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 (H¡, 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 (H¡, 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 (Y¡, 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 (Y¡, 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
, ¡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 (Y¡, i=l to 22) and
Estimated Income (Y¡, i=l to 22) in the 22 OECD Countries, 1955-1990
o
o
o
Yj
A
o- Y¡

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 (Y¡, 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- Y¡

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 (Y¡, i = 1 to
22) and Human Capital (H¡, 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, y¡, 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 = ^ p¡Lo%(p/y)
where p¡ is the world population share of country i, and y¡ 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, p¡ and Yg = sum¡ y¡, where the summations are over i E
Rg, then
j. £ 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
¡-1
= £ Pi to y*
i-l
(F.l)
- k + In £ Nfi £ PlJn Z,
j-1 /-I
where Z¡ is the GDP of country i. Taking partial derivatives with respect to Z¡ we get
_a/
dz,
N,
Ei
z,
' E ",2,
y-i
dZ, 1
£ 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) Z,
1 hi ^ J ) (ln M)
Z
(F.4)
Writing this in time differential form we get
124

125
AJ, = o; p,-) (£>z, P; dz
i*i /-i
* [>; p; p; on ^ y; >] (mv, p; ay
1-1 p¡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)

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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,-) (£>z, P; dz
i*i /-i
* [>; p; p; on ^ y; >] (mv, p; ay
1-1 p¡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
PE¡ = pe; RGDPCH,
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 series1. Education at the secondary
school level (ES¡) and university (or equivalent) level (ET¡) in country i were compiled
as
ESi = es¡ / POPi
ET¡ = et¡ / POP¡
where es¡ was the total number of people with secondary school education, et¡ 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
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 (Y¡, i=l to 22) and Human Capital
(H¡, 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 and
sw(6) = 2^0)' A.sr' [(/--]' 4
Further,
2(0) = £(') A, £(((') K+% (49)
Substituting for E(££') 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/XR¡ )/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.


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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 (H¡, 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 (Y¡, i=l to 22) in
the 22 OECD Countries, 1955-1990 74-75
4.6 Levels of Estimated Income (Y¡, 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 (Y¡, i=l to 22) and Estimated Income
(Y¡, i=l to 22) in the 22 OECD Countries,
1955-1990 82-87
4.6 Comparing Countrywise Levels of Estimated
Income (Y¡, 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 (0¡), 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 7¡ (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