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## Material Information- Title:
- Cross country convergence of gross domestic products and associated factors a cointegration approach
- Creator:
- Weatherspoon, Dave D
- Publication Date:
- 1993
- Language:
- English
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- x, 220 leaves : ill. ; 29 cm.
## Subjects- Subjects / Keywords:
- Countries ( jstor )
Employment ( jstor ) Financial investments ( jstor ) Government expenditures ( jstor ) Gross domestic product ( jstor ) Income inequality ( jstor ) Investment income ( jstor ) Mathematical variables ( jstor ) Prices ( jstor ) Public investments ( jstor ) Dissertations, Academic -- Food and Resource Economics -- UF Food and Resource Economics thesis Ph. D - Genre:
- bibliography ( marcgt )
non-fiction ( marcgt )
## Notes- Thesis:
- Thesis (Ph. D.)--University of Florida, 1993.
- Bibliography:
- Includes bibliographical references (leaves 211-219).
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- Typescript.
- General Note:
- Vita.
- Statement of Responsibility:
- by Dave D. Weatherspoon.
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- University of Florida
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- Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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31303705 ( OCLC ) AKC9900 ( NOTIS )
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CROSS COUNTRY CONVERGENCE OF GROSS DOMESTIC PRODUCTS AND ASSOCIATED FACTORS: A COINTEGRATION APPROACH By DAVE D. WEATHERSPOON 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 1993 ACKNOWLEDGEMENTS First, I would like to thank my wife for her support and encouragement throughout this process. She provided me with the incentives and assistance necessary to complete this degree. I appreciate the standards of excellence expected and portrayed by my parents. The supportive discussions with them as well as my in-laws and siblings made this process somewhat easier. I will always be indebted to my forefathers who stood up for their rights so that people like myself can enter and finish at any higher educational institution in the United States. The many hours of individual attention Dr. James Seale, Jr., provided me during my course of study are much appreciated. I would also like to acknowledge the extra efforts of Dr. Charles Moss in helping me complete this degree. The additional suggestions during the preparation of this dissertation by Dr. Jong-Ying Lee, Dr. Gary Fairchild, Dr. Douglas Waldo, Dr. M. Langham, and Dr. Henri Theil are much appreciated. The financial support as a McKnight Doctoral Fellow from the Florida Endowment Fund for Higher Education made this all possible. The additional financial support by Dr. James Seale, Jr., and Dr. Henri Theil is much appreciated. TABLE OF CONTENTS page ACKNOWLEDGEMENTS . ... ii LIST OF TABLES . . vi LIST OF FIGURES .. . ABSTRACT . . * viii . ix CHAPTERS 1 INTRODUCTION . . 2 CONVERGENCE . . 2.1 2.2 2.3 2.4 2.5 2.6 Overview of Convergence . Historical Evidence . Kuznets-Type Studies . LDC Growth and Poverty . Human Capital . Contemporary Evidence .. . 1 *6 S6 S8 . 11 . 15 . 24 . 27 3 THE INTERNATIONAL COMPARISON PROJECT AND ITS' USEFULNESS IN EXAMINING CONVERGENCE . 3.1 Overview of the Construction of the ICP 3.2 The Geographic Expansion of the ICP: Phases I to IV . 3.3 The Data . . 3.3.1 The Methodology of Calculating Purchasing Power Parity . 3.3.2 Country-Product-Dummy Method . 3.3.3 Elteto-Koves-Szulc Method .. ... 3.4 3.5 3.6 Estimating Purchasing Power Parity . The Geary-Khamis Method . Calculating PPP's for Comparison Resistant Goods . 3.7 Regionalism .. . 3.8 Phase III Results Compared with Exchange Rates . 3.9 Phase IV Further Considered. . . 33 . 33 * 34 . 36 S. 40 S. 41 . 42 . 46 . 52 S. 55 . 56 * 59 * 62 "' r 3.9.1 Other Methods Used in Phase IV . 3.9.2 Linking the Regions of Phase IV . 4 EXTRAPOLATIONS. . . 4.1 The Beginning of Extrapolations with ICP Data . . 4.2 Mark 1 . . 4.3 Mark 3 . . 4.4 Mark 4 . . 4.5 Mark 5 . . 4.6 The Centrally Planned Economies ... 5 INEQUALITY IN THE G-7 AND OECD. . 5.1 Inequality Measures. . 5.1.1 Graphical Inequality. . 5.1.2 Inequality Indices. . 5.1.3 Properties of an Inequality Index . 5.2 Income Inequality in the G-7 . 5.3 Variables of Interest . 5.3.1 Inequality in Government Expenditure. . 5.3.2 Inequality in Investment Expenditure. . 5.3.3 Inequality in Industrial Employment . 5.4 Inequality in Selected OECD Countries . 5.4.1 Income Inequality in the OECD Countries. . 5.4.2 Inequality of Government Expenditure in the OECD . 5.4.3 Investment Inequality in the OECD . 5.4.4 OECD Inequality in Industrial Employment. . 5.5 Summary of the Inequality Results. . 6 COINTEGRATION . . 6.1 An Overview of Cointegration . 6.2 Unit Root Tests . 6.2.1 Augmented Dickey-Fuller (ADF) Test. . 6.2.2 Phillips Test . 6.2.3 Unit Root Results . 6.3 Pairwise Cointegration . 6.3.1 Durban Watson . iv . 63 * 65 . 70 . 70 . 76 . 77 . 82 . 87 . 93 . 96 . 96 . 96 . 97 .100 .102 .106 .107 .111 .113 .114 .115 .119 .122 .124 .125 .127 .127 .131 .132 .137 .139 .141 .141 6.3.2 Augmented Dickey-Fuller Cointegration Test ..142 6.3.3 Pairwise Cointegration Results. ... ..143 6.4 Johansen's Multiple Cointegration Test ... .146 6.4.1 I(1) Procedure. .146 6.4.2 1(2) Procedure. .154 6.4.3 G-7 Multiple Cointegration Results. .161 6.4.4 OECD Multiple Cointegration Results .170 6.4.5 Other 7 Multiple Cointegration Results ... .178 6.5 Summary and Interpretation ... .182 7 SUMMARY AND CONCLUSION. .190 APPENDICES A PRICES PER KILOGRAM OF FRESH VEGETABLES AND ESTIMATED PPP'S IN 10 COUNTRIES FOR 1970. .197 B SUPERCOUNTRY WEIGHTING. .199 C EKS CALCULATIONS .. 202 D FIXITY. . ... ... .205 E DATA AVAILABILITY .. ... 207 F EXTRAPOLATIONS OF INDUSTRIAL DATA .... .... .209 REFERENCES . .. .. .. 211 BIOGRAPHICAL SKETCH. . .220 LIST OF TABLES Table 3.1 Countries Represented in the International Comparison Project. . 3.2 Fresh Vegetables for 4 Countries and Items in 1970 . . 3.3 Mini-Laspeyres Price Ratio Matrix . 3.4 Mini-Fisher Ratios . 3.5 Transitive PPP's from the EKS Method. . 3.6 GDP Per Capita for 34 Countries in 1975 . 3.7 The Organizations that Performed the Calculations and the Countries Involved in Each Group for Phase IV. . 5.1 Income Per Capita and Income Inequality (G-7 Countries) . 5.2 Government, Investment, and the Number of People Employed in Industry Inequalities (G-7 Countries) . 5.3 Investment Expenditure per Capita, and the Rate of Investment Expenditures for the G-7 . 5.4 Income Per Capita and Income Inequality (OECD Countries) . 5.5 Government, Investment, and the Number of People Employed in Industry Inequalities (OECD Countries) . 5.6 Investment Expenditure per Capita, and the Rate of Investment Expenditure for the OECD. . . 6.1 Unit Root Tests . vi page S 35 S 47 S 49 S 50 S. .. 51 S. .. 60 S 64 . .103 . .108 . .112 S .117 S .120 . .123 . .140 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 vii Pairwise Tests for Cointegration. . Johansen's Multiple Cointegration Test. . Cointegrating Vectors and Adjustment Coefficients from the G-7 . Estimates of Gamma from the G-7 . Johansen's Multiple Cointegration Test (OECD) . Cointegrating Vectors and Adjustment Coefficients from the OECD. . Estimates of Gamma from the OECD. . Johansen's Multiple Cointegration Test (Other 7). Summary of Integration and Cointegration Analysis. . . . .144 . .162 . .165 . .169 . .172 . .174 . .177 . .179 . .183 LIST OF FIGURES Figure 6.1 Total Income Inequality for the G-7 . 6.2 Total Government Inequality for the G-7 . 6.3 Total Investment Inequality for the G-7 . 6.4 Total Industrial Employment Inequality for the G-7 . 6.5 Total Income Inequality for the G-7 Second Differenced. . 6.6 Total Government Inequality for the G-7 Second Differenced. . 6.7 Total Investment Inequality for the G-7 Second Differenced. . 6.8 Total Industrial Employment Inequality for the G-7 Second Differenced . page . 133 S. .. 133 S. .. 134 . 134 . 135 . 135 . 136 . 136 viii 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 CROSS COUNTRY CONVERGENCE OF GROSS DOMESTIC PRODUCTS AND ASSOCIATED FACTORS: A COINTEGRATION APPROACH By Dave D. Weatherspoon December 1993 Chairman: James L. Seale, Jr., Major Department: Food and Resource Economics The convergence of income in the G-7 and selected OECD countries was tested using Theil's inequality (entropy) index between the years of 1950 to 1988. Theil's inequality index was also applied to three potential factors of influence on economic growth. These factors were government expenditure, investment expenditure, and the number of people employed in industry. The financial indicator variables were adjusted for purchasing power parity based on Summers and Heston's 1991 data series. The derivation of this data set is also discussed in this dissertation. The results of the convergence test confirmed that all four inequality indices were declining. This suggested that income, government expenditure, investment expenditure, and industrial employment are converging within the G-7 and within the selected OECD countries. The inequality indices were then tested to determine if they move together over time. Pairwise and multiple cointegration tests were conducted on the inequality indices that were found to be 1(2). In general, there was support for pairwise cointegration of all the variables for the G-7 and the selected OECD countries. Johansen's 1(2) method was used to test multiple cointegration. Multiple cointegration was supported for three of the four variables for the G-7 sample, suggesting that there exists a long-run equilibrium among the inequality in income, investment expenditure, and the number of people employed in industry. The OECD selected sample supported multiple cointegration of all four variables. It was also determined that industrial employment was the primary factor in the sample that adjusts to return the four inequality indices to their long-run equilibrium when innovations occur. The G-7 equilibrium was stable without government expenditure while the OECD sample was stable with government expenditure. This may suggest that the OECD countries excluding the G-7 rely on government expenditures for economic growth and stabilization of their economies. CHAPTER 1 INTRODUCTION Cross-country economic convergence means that a group of countries are becoming closer in terms of income. This definition is usually operationalized as the faster rate of productivity growth by less productive countries (Barro and Sala-i-Martin, 1992). The result of which is the faster rate of income growth of relatively poor countries than relatively rich countries. Worldwide income growth and the factors that influence this growth have been of interest for quite some time. The interest in the economic welfare of current and future trading partners is one reason why the U.S. in particular is concerned with the area of economic growth and convergence. The literature has supported the idea that the high income countries are converging (Grier and Tullock, 1989 and Goa et al., 1992). However, none of the studies can definitively state the factors in these economies that are causing convergence. Therefore, the objective of this study is to determine a method of measuring convergence, test the method on a group of countries, and determine the factors that influence convergence over time. There are two hypotheses being tested in this dissertation. First, it is hypothesized that the G-7 and the 1 2 selected OECD countries are converging in terms of income.' Theil's inequality measure is used to test this hypothesis. The second hypothesis is that the inequality of income has a long-run relationship with the inequality of other factors in the economy. The factors considered to influence the convergence of income across countries are the inequalities in government expenditure, investment expenditure, and the number of people employed in industry. This hypothesis is tested by using pairwise cointegration analysis and Johansen's multiple cointegration technique. The G-7 and OECD countries were chosen for this study for several reasons. The most important factor is the availability and the superior quality of their data. The fact that the G-7 and OECD countries are some of the most powerful countries economically in the world also influenced this decision. The growth rate of per capital income for the G-7 and OECD has been sustained at a positive rate for a long time period. In fact, per capital income in both groups increased almost threefold during the 38-year period from 1950 to 1988. These positive growth rates are not considered to be a random process but are believed to be systematically related to other factors in the economy (Grossman and Helpman, 1991). 'The G-7 countries are Canada, W. Germany, Italy, Japan, the U.K., the U.S., and France. The selected 14 OECD countries are Austria, Belgium, Denmark, the Netherlands, Norway, Ireland, Spain, and the G-7 countries. 3 This analysis is not the first attempt to associate economic growth and convergence to specific factors in an economy. One of the models that influenced the way economists approached the idea of convergence was put forth by Solow (1956). Solow (1956) and the generalized neoclassical growth model by Brock and Mirman (1972) implied that economies with identical technology and preferences will converge regardless of initial conditions. The driving force in both models was technology. Several empirical studies have shown that the world is not converging in terms of income and only recently have the theoretical models begun to challenge the cross- country implications of Solow's model (Romer, 1986; and Lucas, 1989). Another approach was put forth by Kuznets (1955). He approached convergence in an indirect manner by relating personal income to economic development. Specifically, Kuznets' (1955) hypothesis was that income inequality within a country first increased then decreased as development proceeded (divergence-convergence theory). This theory has since been expanded to cross-country analysis where the hypothesis is that countries first diverge then converge in terms of income inequality as development occurs (Wright 1978, Branco and Williamson 1988, and Ram 1988 and 1989a). The cross-country interpretation of Kuznets hypothesis is not directly tested in this dissertation. However, if the G-7 and the OECD countries are found to be converging, then the 4 results may support Kuznets cross-country hypothesis since the G-7 and OECD countries are developed countries. The literature concerning the convergence or divergence of the countries around the world is discussed in Chapter 2. There are two main reasons why the topic of convergence and economic growth are important. First, the factors that cause convergence or economic growth have not been exclusively identified. Second, the quality of international data have been improved recently. The problem in the past with output and income data from different countries was that international comparisons require the data to be converted to a common currency by using official exchange rates. Official exchange rates do not reflect the relative purchasing powers of different currencies. For example, the official exchange rate does not reflect domestic services since they are not traded internationally (i.e. haircuts, house cleaning, etc.) (Kravis et al. 1975, 1978a, and 1982). Hence, errors are introduced into international comparisons when exchange rates are used. This problem has been addressed and much improved by Summers and Heston (1988 and 1991). They developed a data series that is based on purchasing power parity. This data set along with others are used to test the hypotheses stated above. The format of this dissertation is as follows. Chapter 2 includes a literature review on convergence while Chapters 5 3 and 4 include a discussion on the methodology used to calculate gross domestic product without using exchange rates. Specifically, the international comparison project (ICP) methodology is addressed in Chapter 3. Then the data series by Summers and Heston, which is based on the ICP, is addressed. The convergence of income, government expenditure, investment expenditure, and the number of people employed in industry is tested using Theil's inequality index in Chapter 5. Theil's decomposable index allows one to determine which countries are driving the convergence. Then, these four inequality indices are tested for cointegration using pairwise cointegration and Johansen's 1(2) multiple cointegration test in Chapter 6. This method determines if there exists a long- run equilibrium among the four indices. If the series are cointegrated, then the four inequality indices cannot drift apart in the long-run given that there are no structural changes. Chapter 7 presents the summary and conclusion of this dissertation. CHAPTER 2 CONVERGENCE 2.1 Overview of Convergence The meaning of cross-country convergence in its simplest form is that the income level of countries are becoming closer. To get this result the less productive countries must increase their productivity growth rate at a faster rate than the more productive countries (Barro and Sala-i-Martin, 1992). The result is that income grows at a faster rate in relatively poor countries than in relatively rich countries. There has been an interest in reducing the income gap (convergence) between the developed countries (DCs) and the lesser developed countries (LDCs) for some time (Berry et al., 1991). The Pearson Commission (1969) was set up to address the income gap problem. Specifically, the commission was to identify ways to reduce the income gap between the developed and the developing countries (Berry et al., 1991). Kuznets (1955) influenced many researchers to explore convergence through his hypothesis. Kuznets' hypothesis (also known as the divergence-convergence theory) basically states that income inequality within a country increases in the early stages of economic development, stabilizes at some peak level, then declines as the latter stages of development occur. 7 Kuznets was writing about a single country; however, this hypothesis was quickly expanded to address international development. Many studies attempt to directly and indirectly prove or disprove Kuznets' hypothesis with income inequality measures (Wright, 1978; Branco and Williamson, 1988; Ram, 1988, 1989a) or with regression analysis (Grier and Tullock, 1989; Barro, 1991; Barro and Sali-i-Martin, 1992; and Baradaran-Shoraka, 1992). However, the results of all of these studies have been inconclusive. Three observations about economic growth in the world economy frame the phenomenon examined in this study. First, the growth of per capital income has been sustained at a positive rate for many countries for a long time period. Second, the performance of countries has varied across countries and time. These two observations lead to the conjecture that growth in income is not a random process. They are believed to be systematically related to other factors in the economy (Grossman and Helpman, 1991). The third observation deals with the ability to study the growth patterns around the world. Convergence of the world cannot be thoroughly studied over long periods of time due to data constraints. However, there are data available for many countries starting in the 1950s. These data are largely due to the efforts of Summers and Heston (1991) who developed a time-series for several economic indicators for most of the 8 world for the years 1950 through 1988.' In the studies mentioned above, the data of Summers and Heston as well as other sources are used to analyze convergence from a historical point of view. The international comparison studies conducted prior to this data set were misspecified due to the use of exchange rates (Kravis et al. 1975, 1978a, and 1982). There have been two main approaches to studying convergence, inequality measures and regression analysis.2 The review of the studies that follow represent both approaches. The first section covers studies that analyze what happened in the past. 2.2 Historical Evidence Machinery investment and productivity growth have been strongly associated over the past century in countries where adequate data exist (Canada, Germany, Italy, Japan, the United Kingdom, and the United States). In the recent past, the same association holds for more countries (De Long, 1992). The real question is whether high machinery investment causes rapid growth? Baumol (1986) showed that industrialized market economies supported convergence using data from 1870 to 1979 (the data 'The development of the Summers and Heston data series is discussed in the next two chapters. 2A summary of the inequality measures is given in Chapter 5. 9 are not time-series). Baumol analyzed the G-7 countries along with Australia for this time period. To extend his analysis to a larger number of countries, he used the Summers and Heston data from 1950 to 80. In this data set, the variable used was output per capital. The results showed that convergence is not supported when LDCs are included in the analysis. The results of a similar study conducted by Dollar and Wolff (1988) supported Baumol's 1986 results of convergence. In a follow up article criticizing Baumol's (1986) findings, De Long (1988) showed that Baumol's study was flawed. He commented that Baumol only used successful countries (selection bias). In response to De Long's article, Baumol and Wolff (1988) admitted to data mining in previous studies. When they re-examined the results, it appeared that a small group of countries began to converge in 1860. Since then, more countries have joined the group according to Baumol. De Long (1992) reviewed the issue of productivity growth and machinery investment similar to that done by Baumol. De Long studied six countries (Canada, Germany, Italy, Japan, the United Kingdom, and the United States) from 1870 to 1980, and then a large number of countries on all six continents from 1950 to 1980. He divided up his study into 15 year periods to offset any cycles and the effects of wars. This study showed a strong positive relationship between growth and machinery 10 investment. He cautions that these countries are all wealthy and that the regression may have captured "luck" instead of the intended relationship. The results may have been different if more countries were included. In addition, De Long examined the effects that political stability and investment in education had on growth. All of the countries sampled had been stable politically and had invested heavily in education. He also argued that just the presence of high tech machinery may have provided a higher level of education. In testing these relationships, he found little evidence supporting the education or political stability influence on growth. De Long (1992) concluded that when a broader group of countries is considered, there is little evidence of convergence in the short-run, and in the long-run, the regressions may not be accurate. Alam (1992), however, cautions that De Long needed to use other variables to indicate productivity. Hanson (1988) examined the convergence of LDCs before World War I. This study is interesting for two reasons. First, historical studies of this type conducted on LDCs are rare. Second, the long period of analysis from 1913 to 1980 is impressive. Hanson corrected the historical data by extrapolating Summers and Heston's (1984) data backwards and combining other data sets. He also compared other data sets to that of Summers and Heston. Unfortunately, his results were inconclusive. 11 To summarize, there appears to be a long-run relationship between investment in machinery and growth. The only countries that appear to be converging are a few industrialized countries. The LDCs appear to be caught in a circle of poverty (Alam and Naseer, 1992). It is clear that human capital is considered an important variable with respect to growth, and that the relationship may be that higher equipment investment drives faster growth (Adams, 1990; De Long and Summers, 1991). 2.3 Kuznets-Type Studies As mentioned before, Kuznets hypothesized (divergence- convergence theory) that income inequality increases in the early stages of economic development, stabilizes at some peak level, then declines as the latter stages of development occur. A few of the many studies that have tested this hypothesis in the international context using various methods are discussed next. It will become clear that there are no definite answers as to whether Kuznets' hypothesis is indeed correct. Wright (1978) analyzed whether the institutionalist or Kuznets' hypothesis was correct. The institutionalist hypothesis states that institutional structures and governmental policies are the chief determinants of income inequality. Wright conducted his analysis using a Gini coefficient inequality measure. He calculated the income inequality of the GDP per capital for 56 countries. He 12 concluded that the data did not support Kuznets' hypothesis. Instead, he found that the level of inequality was higher in the LDCs than the developed countries. Wright concluded that his results supported the institutionalist hypothesis. Hence, the reduction of income inequality among countries is dependent on modifications of institutions and policies. Ram (1989a) extends Kuznets' hypothesis to the world system. He hypothesizes that intercountry (world) inequality across sovereign nation states would first increase with secular economic growth, then start to decline at some point. He tested this hypothesis using 115 market economies for the years 1960 to 1980 from the Summers and Heston 1984 data set. Average (per capital) world GDP was used as a proxy for the level of development and Theil's income inequality (J) measure was used to analyze the inequality (see Section 5.1.2 for Theil's 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 (2.1) J, = Bo + B, LRY, + B2 (LRY,)2 + u, where J is the measure of the world inequality and LRY is the natural logarithm of the average real GDP per capital. The last term is the disturbance term with the standard properties (zero mean and a constant variance). He found that world income inequality has increased since 1960. However, the rate 13 of increase has slowed. The regression results supported the hypothesis that world inequality may first increase and then decline with world economic growth. Hence, Ram's study supports the idea of divergence then convergence of real GDP worldwide. A partial contrast of the above results is provided by Ram in 1988. In this paper, Ram (1988) tests Kuznets' hypothesis for 32 counties, 8 developed countries and 24 LDCs. The estimated equation in this paper is the same as the one used in his 1989a paper. Ram (1988) finds support for Kuznets' hypothesis when all of the countries are present. However, when only the LDCs are present, the results do not support Kuznets' hypothesis. 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 capital income measure for the poorest 40% of the population in 68 countries. Their measure was the percent of income of the poorest 40% of the nation's population in 1970 divided by 40% of the 1970 population, then multiplied by the real GDP per capital of a nation in 1970 (Summers and Heston, 1984 data set). Bronco and Williamson (1988) felt that this dependent variable portrayed the situation of the poorest 40% in different countries. The independent variable was the energy consumption per capital in 1970 (measured in kilograms of coal equivalents). This variable is supposedly a better indicator 14 of industrial development across nations than GNP per capital. They estimated linear, quadratic, logarithmic, and log quadratic models to determine the best fit and also to prove or disprove Kuznets' hypothesis. Their results supported Kuznets hypothesis. Therefore, the countries are expected to diverge, then converge in terms of income as development occurs. Bornschier (1983) reinterpreted Kuznets' theory by combining two paradigms of world economy and the level of development. Briefly, the world development paradigm is the core-periphery division of labor, which has come about due to multinational corporations. The core specializes in control over capital, technology, innovation processes, and the production of the most advanced products, which embodies the most human capital. -The periphery is engaged-in standardized and routine industrial production for domestic or maybe world markets. In a sense the multinational corporations have created a world division of labor. The core countries are basically the industrial countries, and the periphery are the countries with the raw materials.3 The level of development paradigm is basically Kuznets' hypothesis. Both of these paradigms have different ideas on how development takes place. Bornschier (1983) combined the two approaches with the following deviations from the original hypotheses: the 3For a more detailed explanation of this theory see Amin, 1974, pp. 559-587. 15 countries on the periphery, which were still considered agrarian based, had the most income inequality; the countries that assumed less importance for agrarian production had lower inequality; and the core countries within the world economy had the lowest income inequality. He showed that developing countries did not automatically decrease their income inequality with increased development. In addition, the reduction of inequality was found to be dependent on the type of production (services, agriculture, and industry) in which they were involved. Several of the studies supported the divergence- convergence theory (Kuznets' hypothesis) and others did not. The studies that included the LDCs were also contradictory. In the study by Bornschier (1983), the author implied that the type of development countries pursued affectedthe reduction in income inequality. He indicated that if a country has less emphasis on agrarian development, then that country is expected to converge faster than a country that promotes agricultural development. This may or may not be the actual case, but it introduces the idea of what has happened within the LDCs. 2.4 LDC Growth and Poverty Morawetz (1977) addressed the issue of growth in chapter 2 of his book entitled "Twenty-Five Years of Economic Development 1950 to 1975." The questions he posed were: "How rapidly were GNP per capital and population expected to grow in 16 1950, and how has their actual growth compared with these expectations." He commenced by stating that the status of development in Africa, Asia, and Latin America was not considered before 1950. The reason for this was that the industrialized countries were just getting over the war, and were still concerned with reconstruction in Europe. The few researchers who thought about the economic development of the LDCs had no hope for their short and medium term future. The industrialized countries only attained 2% growth (per capital) on average during that period. Therefore, the developing countries were not expected to perform as well as the industrialized countries. In addition, it was perceived that the population growth in the developing countries was high while their GNP growth was low. Morawetz stated that no statistical work had been done on the LDCs. Hence, he conducted a statistical analysis on the LDCs to determine their economic growth status. His results indicated that the disparity between the rich and poor developing countries had increased significantly between 1950 to 1975. However, at the aggregate level, it was not true that the richest of the developing countries were getting richer and the poor were getting poorer. When the developing countries regional averages of income per capital in 1950 were examined, the richest regions (Latin America and the Middle East) had grown five to six times faster than the poorest region (South Asia). By 1975 this gap had increased to 13 17 times for the Middle East and seven times faster for Latin America than South Asia. When the LDCs were compared to the developed countries, it was shown that China, East Asia and the Middle East narrowed the gap, while the gap was widened for South Asia, Africa, and Latin America. However, the ranking of 80 individual developing countries remained stable from 1950 to 1975. Morawetz (1977) regressed 16 indexes of basic needs on GNP per capital growth to get a better understanding of how the change in relative GNP per capital affected poverty. Morawetz used 16 different regression equations to analyze the problem. The factors that were found to be significantly related to GNP per capital growth were three nutrition indicators, infant mortality, and the percentage of dwellings with access to electricity. Some of the other variables-that were included in the analysis but were not significantly related to the growth in GNP per capital were four indicators for education: adult literacy rate, primary school enrollment ratio, secondary school enrollment ratio, and vocational school enrollments as a percent of secondary school enrollments. Another study on the LDCs was conducted by Zind (1991). He tried to determine if the LDCs were converging in terms of income, and assess the key variables that influenced convergence such as government policies, population growth, and investment levels. The Summers and Heston 1984 (1960-80) data set was used for the comparison of 89 LDCs. His test was 18 a simple regression of real income per capital annual growth rate against per capital income in 1960. In his model a negative coefficient indicated convergence. When all of the countries were included, there was no evidence of convergence. Reducing the number of countries to 30, results indicated convergence at the 10% level; reducing the countries further to 19 yielded convergence at the 5% level. These 19 countries were the most developed countries in the LDC sample. In addition, he found that the other variables (the relative size of government, population growth and investment level), contributed to convergence in the most developed countries. Dollar (1992) basically answered the question of how the slowest growing countries in the LDC category could increase their growth. Asian (16 countries) LDCs grew at an average rate of 3.4%, while this occurred at 0.4% in Africa '(43 countries), and only 0.3% in Latin America (24 countries) (Dollar, 1992). Using the data of Summers and Heston (1984), he showed that outward oriented countries had lower prices than inward oriented countries.4 He believes that the price level was a reflection of the protectionist policies in the different countries. The Asian countries had the lowest price levels, followed by Latin America and Africa. He also considered the variation in exchange rates where the Asian countries had the lowest variation. He created an index of 4Inward oriented countries are countries that have protectionist trade policies. Outward oriented countries are countries that have relatively open trade policies. 19 outward orientation based on the variation of the exchange rate. This index was found to be highly correlated with per capital GDP growth. He concluded that Africa and Latin America could increase their growth through trade liberalization, devaluation of their real exchange rates, and by maintaining a stable exchange rate. Berry et al. (1991) conducted an extensive analysis on world income inequality. They analyzed over 100 countries from the time period of 1950 to 1977. The data came from World Bank Tables, World Bank Atlas, World Development Report, and the Summers and Heston data set. Their objective was to determine what had happened to income inequality in the world. They applied Theil's entropy, Atkinson's inequality, and the Gini coefficient measure (see Chapter 5 for definitions of these inequality indices). The uniqueness of this study was that they applied these inequality measures to gross national product (GNP) and consumption measured as a percentage of GNP to determine changes in welfare. The idea behind using the inequality of consumption was that the distribution of consumption was less unequal than that for income for two reasons. First, the savings rate was below average in many of the poorer countries. Second, the intracountry distribution of consumption was generally less unequal than the income distribution. Berry et al. (1991) attributed this to the fact that the marginal propensities to consume fall with income and that high income families do most 20 of the saving. The fact that the savings rate was lower than average in the poorer countries contributes more to worldwide inequality than the second reason, regardless of whether income or consumption was used. They conducted the analysis with and without the non- market economies for which the data were considered to be inaccurate (Berry et al., 1991; Summers and Heston, 1991). The results of their study showed that the 1950s and early 1960s were stable around the world in terms of income. Between 1964 and 1972 there was a large increase in world inequality, which gradually continued to increase until 1986.5 The consumption ratio also indicated a worsening of inequality from 1950 to 1986. The other unique aspect of this paper was that they broke the world's inequality into deciles. Using this method they were able to show that the bottom half of the world's population income shares remained unchanged, while the top decile gained at the expense of the sixth, seventh, and eighth decile. In addition, the middle deciles gained in the 1950s and 1960s, only to lose it in the 1970s and 1980s. During this time period, the richest two deciles increased their share of world consumption from 68.5% to 71.6% at the expense of the seven lowest deciles. 5They initially stated that this study was from 1950 - 1977. That is the case for their analysis which includes the communist countries. After 1977, they were not able to get adequate data for the communist countries; hence, they left them out of the analysis from 1950 86. 21 The change in inequality in the 1980s was due to slow growth particularly among the low income countries which had zero growth during the period of 1980 to 1985. Most of these countries were in sub-Saharan Africa. Some of the contributing reasons were the agriculture and debt crisis, and the rapid population growth.6 The middle-income countries were not as progressive in terms of economic growth with the industrialized countries, while the average income of the less developed countries (LDCs) increased. The South Asian countries (India, Pakistan, Bangladesh, Sri Lanka, and Nepal) on the other hand grew faster between 1980 and 1985 than between 1965 and 1980. The fastest growth occurred in the newly industrialized countries and the OPEC countries. However, their presence did not reduce inequality much because of the relatively small population. In general, the population has grown faster in the poor and middle-income countries than in the rich ones. Berry et al. (1991) suggest that the slow economic growth and the population boom in the poorest countries had increased the absolute number of poor around the world (income below $200 U.S. 1970 dollars). However, to give a full picture, the share of the total population that was considered poor had decreased. The results of Berry et al. about the poverty line can be disputed. Atkinson (1987) examined the issue of measuring 6Theil's entropy measure is sensitive to population changes. An increase in population increases the inequality measure if income is held constant. 22 poverty. Specifically, he researched the poverty line, indexes on poverty, and the relationship between poverty and inequality. The choice of the poverty level could influence the results on whether countries were becoming closer in terms of the absolute number of people in poverty. However, the choice of the poverty line would have no effect on the income inequality measures. Ahluwalia et al. (1979) made some predictions concerning the future. Their approach to studying growth and poverty in the LDCs was threefold. First, they estimated the absolute poverty in the developing countries and the relationship between income distribution and the rising levels of output. Second, an analysis of the past trends in growth and poverty for certain countries was conducted, the results of which were projected into the future based on the policies at that time. Lastly, the changes in poverty were considered when income growth was accelerated, the distribution of income was improved, and the reduction of fertility was implemented. This analysis was based on 36 countries, all of which were LDC market economies. These countries GDPs per capital were adjusted for purchasing power parity using what was referred to as the Kravis adjustment factor.7 Ahlualia et al. (1979) used Theil's inequality index to analyze the trends in inequality and poverty from 1960 to 1975 7The Kravis adjustment factor was an attempt by Ahlualia et al. to adjust the data for purchasing power parity estimates by Kravis et al. 1975 and 1978a. 23 among the LDCs. The results indicated that the inequality among the LDCs increased during this period. In addition, they projected the inequality level to the year 2000. They expect the income inequality to increase from .67 in 1975 to .77 in the year 2000. The reason for the divergence will increasingly be due to the wider distribution of income among the countries (from 37% to 50% respectively).s They predict that India and Bangladesh will have higher growth than the other LDCs. Therefore, a large percent of the increase in inequality in the LDCs will be due to the economic events in India and Bangladesh. The worsening of the internal distribution of income is what Ahlualia et al. (1979) attributed to the lack of growth in the poorest of the LDCs. The middle group of LDCs are not expected by these authors to reduce their inequality. A listing of the poorest LDCs and middle LDCs is presented in Ahluwalia et al. (1979). They expect the relative level of poverty to decrease and the absolute level of poverty in the year 2000 to be 600 million. The studies in this section clearly state that the LDCs are diverging instead of converging. There were several reasons given for their slow growth: debt crisis, population 8Income inequality increases if the income of the different countries continue to grow further apart. That is the case with India and Bangladesh. They are increasing the inequality because they continue to grow faster than the other DCs. Hence, creating a greater dispersion (increasing inequality). 24 growth, agricultural based economies, and restrictive trade. Two variables that have been related to convergence in the other two sections were also found to influence convergence in the LDCs: government expenditure and investment. 2.5 Human Capital The effect of human capital on economic growth is uncertain. Human capital in this text is considered to be a set of specialized skills that agents can acquire by devoting time to schooling or special training (Grossman and Helpman, 1991). The more training an individual receives the more human capital that individual acquires. Human capital has become more important in the literature recently. The endogenous growth models show that increasing returns are possible with a constant return to scale model if human capital is included (Romer, 1990). In contrast, the older exogenous growth models assumed that growth is attributed to exogenous technological change (Solow, 1956). The key to endogenous growth models is the idea of learning by doing. Romer (1990) showed that the rate of growth and technology was a function of total human capital in an economy. The initial human capital level affects the rate of growth in the different countries. Romer's approach led to the suggestion that countries will diverge. Unlike Romer, Lucas (1988) mathematically showed that human capital has spillover effects which drive growth (unbounded growth). However, his conclusion was that there will be no convergence 25 or divergence, but that countries will grow uniformly. Grossman and Helpman (1991) agree with Lucas; however, they assume that a finite population can only accumulate a bounded quantity of human capital. Glomm and Ravikumar (1992) examined the implications of public investment in human capital on growth and the evolution of income inequality. Using an overlapping generations model, they showed that public education reduced income inequality faster than private education. However, private education yielded higher per capital incomes except when the initial income inequality was sufficiently large. The main objective in the study reported by Ram (1989b) was to explain the role of schooling in reducing income inequality and poverty in LDCs. The first part of Ram's paper reviewed past literature on this subject. The review of literature as cited by Ram (1989b) showed the following: Chiswick (1971, 1974) found that income inequality was reduced as educational inequality was reduced (based on nine countries); Chiswick and Mincer (1972) found that in the U.S., inequality in schooling did influence income inequality, even though it had a minimal affect; Adelman and Morris (1973), Chenery and Syrquim (1975), and Ahluwalia (1976) showed that for 43 developing countries, 55 LDCs and 60 various countries, respectively, education reduced income inequality. Contradictory later findings were also cited. These were the 26 work of Fields (1980), Psacharopoulos and Woodhall (1985), and Morrison (1987). The above literature was puzzling to Ram. Hence, he used the data from Psacharopoulos and Arriagada (1986) and Summers and Heston (1984) for his analysis. His income inequality variable was a Gini coefficient, and the independent variable was mean education level of the labor force. He found little evidence that the education level affected income inequality, even for the LDCs. Ram concluded that based on both empirical evidence and theory, the effects of education on income inequality were ambiguous. Problems with the data (e.g. inconsistency or missing information) may have affected the ability to effectively test the relationship between educational inequality and income inequality. Barro (1991) and Baradaran-Shoraka (1992) did empirical studies on the effect of human capital on growth. Barro used several proxies for human capital: secondary school enrollment in the year of 1960 and 1985, primary school enrollment in the year of 1960 and 1985, and adult literacy in the year of 1960. The data were pooled for this analysis. Therefore, there were no time-series implications from the model. The only significant relationship he found was the positive relationship between the average growth rate and the 1960 school enrollment. Baradaran-Shoraka (1992) using the same variable as Barro found the same result which supported Romer's argument. 27 Baradaran-Shoraka (1992) went one step further to create an education data set that had four data points, which supposedly included mean years of schooling of the total population aged 25 years and older, and years of schooling for young workers for the period of 1969 to 1985. His results indicated that the variable for human capital was positively and significantly related to growth, which again supported Romer's argument. It must be noted, however, that Baradaran-Shoraka was only able to conduct this analysis for 50 countries due to data limitations. The theoretical arguments put forth about the relationship between convergence and education are inconclusive. In addition, the empirical studies are also inconclusive. The small data sample appears to be the major limiting factor. 2.6 Contemporary Evidence The first contemporary study reviewed here was done by Theil. Theil (1989) conducted a study from 1960 to 1985 using the Summers and Heston 1988 data set. Theil's entropy index was used to measure the inequality among the North, South, and the Tropical Middle (Tropical America, Asia, and Africa).9 This analysis was based solely on non-Communist countries. Theil noted that the population has decreased in the North and the South while it has increased dramatically in the tropical 9See Theil (1989) for details of the breakdown of the country categories. 28 middle countries. The ranking of real GDP places the regions in descending order as stated above. The results showed that world income inequality has increased over the 25 years. Using the decomposability of his index, he showed that 80% of the world inequality was due to inter-regional inequality.10 It has also been shown that the inequality within the North started with the most inequality and decreased dramatically by 1985. The South's within inequality fluctuated, but stayed relatively low while Tropical America's was relatively low and continued to decrease. Tropical Asia started out high and increased its inequality while Tropical Africa started out the second lowest in inequality and ended with the highest inequality. Tropical Africa's inequality increased approximately three times while the North almost halved its inequal-ity; These results showed that the world is not converging. However, there are some regions of the world which are converging, the North and Tropical America. Grier and Tullock (1989) investigated postwar economic growth for 113 countries from 1950 to 1981. The 1984 data set of Summers and Heston was used in this study. They averaged the data for every five years and pooled the data into OECD countries and the rest of the world (ROW). This decision was made after tests confirmed that the OECD countries and ROW should not be pooled. They regressed their five year average 'OFor a discussion on the decomposability of Theil's index see Chapter 5. 29 growth in real GDP against the following variables: initial real GDP, government as a percent of real GDP, population growth, standard deviation of real GDP as a percent, inflation, and the standard deviation for inflation. Convergence was supported only in the OECD sample. There was no evidence to support the idea that Africa, Asia, and the Americas are converging. The variable that was significantly related to the average five year growth was government. This relationship was negative for all regions except Asia. Barro (1991) used a simple multiple regression technique to analyze the convergence of 98 countries from 1960 to 1985, and the factors that influenced it. He regressed the average growth rate from 1960 to 1985 on several independent variables: real GDP in 1960, and 1970; square root of real GDP in 1960; secondary school enrollment in 1950, and 1960; primary school enrollment in 1950, and 1960; average government expenditure between 1970 and 1985 as a percent of real GDP; number of revolutions and coups per year; number of assignations per million population per year; and the magnitude of the deviation of 1960 purchasing power parity value for the investment deflator. He also ran regressions using fertility as a dependent variable on some of the independent variables. The last regression was run with investment as the dependent variable. The results from this set of regressions, 29 in all, indicated that a few variables were significantly related to 30 growth. The starting point of human capital was shown to be positively related to growth. This suggested that poor countries with high human capital per person would eventually converge with rich countries in terms of real GDP. The second relationship was a negative one with government. This was interpreted by Barro (1991) as the distortions governmental policies (high taxes) introduce and offset private investment growth. Lastly, the political instability was negatively related to growth and investment. The more unstable a country is politically, the less investment and growth are likely to occur. In support of Barro's findings, Baradaran-Shoraka (1992) conducted a similar study with a few of the variables measured differently and found the same results as Barro. Barro and Sala-i-Martin (1992) also conducted a similar study to Barro's 1991 study. In this study they used a neoclassical growth model to analyze the convergence of 98 market economies from 1960 to 1985 (data set of Summers and Heston, 1988). They were trying to test B convergence which is a term that Barro defined as countries converging in terms of income over time." In this model, the log change in GDP per capital (growth rate) was used as its dependent variable. A description of the rest of the equation was detailed, intricate and well illustrated in Barro and Sala-i-Martin (1992). The independent variables were a constant and the log "The other type of convergence Barro defines is a convergence. This type of convergence refers to the dispersion in income across countries reducing over time. 31 of 1960 per capital GDP. Analysis showed that there was little to no relationship between the growth rate and the log of 1960 per capital GDP. This finding indicated that the initially rich countries grew at a faster rate than the poor countries (divergence). However, the first part of their analysis was conducted on just the U.S. states, where they found convergence taking place. Barro and Sala-i-Martin (1992) extended their analysis to include primary and secondary school enrollment rates in 1960, the average ratio of government consumption expenditure to GDP, proxies for political stability, and a measure of market distortions based on purchasing power parity ratios for investment goods. When this was done, the model indicated convergence conditionally. This meant that to get convergence, the following variables had to held constant: initial school enrollment and the ratio of government consumption to GDP. In this section, the income inequality studies indicated that world divergence was taking place, but some regions were converging (the North and Tropical America). The growth studies also showed divergence in the world. However, the OECD countries were found to be converging. In addition, several other variables were found to be significantly related to growth: government expenditure, human capital (education), and political instability. In the next two chapters the development of the Summers and Heston data series on which 32 most of the studies in this section based their analysis will be discussed. CHAPTER 3 THE INTERNATIONAL COMPARISON PROJECT AND IT'S USEFULNESS IN EXAMINING CONVERGENCE 3.1 Overview of the Construction of the ICP The objective of the International Comparison Project (ICP) was to establish a system of comparisons of real product and purchasing power for a large number of countries. The reason for this is that it was realized that the use of exchange rates to conduct international comparisons introduced errors into the analysis. For example, a 1954 study by Gilbert and Kravis found that $1000 in US currency, when converted to sterling at the official exchange rate, bought a basket of U.K. goods 64% larger than the $1000 could have purchased in the United States. This problem was recognized by the Statistical Commission of the United Nations. The issue was discussed in 1965, at the United Nations' thirteenth session, and it was concluded that using exchange rates for currency conversion was inadequate for many uses of international data (U.N. Statistical Commission, 1965). The United Nations and the University of Pennsylvania started the "International Comparisons Project" in 1968. Initial funding came from the World Bank, Ford Foundation, some of the countries involved in 34 the first set of data collection, U.S. Agency for International Development, and the U.S. Social Science Research Council. Kravis et al. (1975) published the first results of these efforts which is referred to as Phase I. In this seminal attempt, the methodology developed is presented, and actual comparisons are made for several countries. Since Phase I, several other successive Phases have been published. Each successive Phase increased the number of countries and refined the methodology for calculating gross domestic product for each country. The countries involved in the first four Phases are discussed in the next section. 3.2 The Geographic Expansion of the ICP: Phases I to IV Phase I of the international comparison project (ICP) began with a pilot study in 1967 (which included data collection for six countries) and included data collection for 10 countries for 1970. The project was initiated by Irving Kravis, Zoltan Kenessey, Alan Heston, and Robert Summers, all at the University of Pennsylvania, and their results in 1975. The countries included in 1970 are shown at the top of Table 3.1. These authors later published two successive volumes, 1978a and 1982, referred to as Phases II and III, respectively. Phase II added six new countries to the ICP. These are listed in Table 3.1 under countries added in Phase II. Phase II provides data for 1970 and 1973, but much of the Table 3.1 Countries Represented in the International Comparisons Project Africa America Asia Europe Countries represented in Phase I Columbia United States India Japan France W. Germany Hungary Italy United Kingdom Countries added in Phase II Iran S. Korea Malaysia Philippines Countries added in Phase III Pakistan Sri Lanka Syria Thailand Belgium Netherlands Austria Denmark Ireland Luxembourg Poland Romania Spain SYugoslavia Countries added in Phase IV Argentina Bolivia Canada Chile Costa Rica Dominican Rep. Ecuador El Salvador Guatemala Honduras Panama Paraguay Peru Venezuela Jamaica Mexico Countries deleted in Phase IV Iran Malaysia Syria Thailand Sore Tfel tal 98,p.2 Malawi Zambia Brazil Jamaica Mexico Uruguay Botswana Cameroon Ethiopia Ivory Coast Madagascar Mali Morocco Nigeria Senegal Tanzania Tunisia Zimbabwe Hong Kong Indonesia Israel Finland Greece Norway Portugal Romania Kenya Source: Theil et al. 1989, p. 2. 36 1973 data were based on extrapolations; hence 1970 will be the main focus. Phase II also made corrections on Phase I data; hence Phase II has the most accurate data for 1970. Phase III added 18 countries which are reported in Table 3.1 under countries added in Phase III. The data are for 1975. Phase IV results were published in two different volumes (United Nations, 1985 and 1987). Phase IV is different from the previous three phases in two ways. First, the study was completed by the Statistical Office of the United Nations Secretariat, and 33 countries were added in this Phase (see Table 3.1, countries added in Phase IV). Second, there are seven countries that participated in Phase III that withdrew in Phase IV. These countries are also reported in Table 3.1 under Countries deleted in Phase IV. This makes the total number of-participating countries in Phase IV equal to 60. In Phases I, II, III, and IV, we have 10, 16, 34, and 60 participating countries, respectively. In Phase IV (including the seven deleted countries), there are 15 countries in Africa, 20 in the America's, 13 in Asia, and 19 in Europe. In all of these countries detailed data were collected. The type of data and the method in which they were collected follows. 3.3 The Data There are two main steps to obtaining the type of data the ICP needed. First, a classification system was developed for gross domestic product (GDP) so that each countries GDP could be divided into detailed categories. After the detailed 37 categories were defined, GDP data were collected at the detailed category level, prices for each item within the detailed categories, and quantity data for the items which price data could not be obtained. The classification system follows the scheme proposed by the system of national accounts (SNA). Some improvements were made to this classification system to enhance the international comparability of the data (Kravis et al. 1975, p. 26). The format the ICP settled on for phases I and II was a total of 153 detailed categories, 110 for consumption, 38 for capital formation, and five for government. Phases III and IV have 151 detailed categories, 108 for consumption, 38 for capital formation, and five for government.1 Once the classification system was determined the next issue was the collection of the data. There were three categories of data used; GDP or expenditure data for the detailed categories, price data for each item for which a price could be identified, and quantity data for those items for which price data could not be collected. The collection of the expenditure data was simple: the data were taken from the U.N. national accounts data. Therefore, expenditure data are not discussed in detail here but the price and quantity data collection are. 'In Phase IV, the European countries had more detailed categories than the 151 categories and the African countries had less. However, the systems were similar making it possible to use the 151 detailed category system. 38 Accurate price data were very difficult to obtain for each item, within every category, in each country. The difficulty was that some items are not found in every country, and if found in all of the countries, matching the qualities of the item was complex. To ensure that the items specified were the same, the U.N. sent price specialists to the different countries to directly compare the qualities of the items in question. An example of the specifications used by the ICP was: fresh chicken eggs, size large (weighing at least 680.4 grams per dozen), white or brown shell, not of the best quality, but close to it. The less than best quality's white is less thick and higher than the best quality. The best qualities yolk must be firm, high, and not easily broken (Kravis et al. 1982, p. 38). In this example of the egg specifications, it can- -be. assumed- that if-- these specifications were met in any country, the quality is the same for those countries. For most of the food groups, the specifications were met. As mentioned before the U.N. sends price experts to resolve questions about matching qualities. For example, the visits helped clear up misunderstandings from the use of different terminology. In Japan, "cashmere" refers to a weave rather than yarn, as in the U.S. and Europe. In England, "ox liver" is used rather than "beef liver," the American terminology (Kravis et al. 1982, p. 38). These types of goods 39 were referred to as narrowly defined goods. They could be classified by their characteristics and uses. Non-narrowly defined goods are the items for which prices cannot be collected in a systematic way in all of the countries. For these items quantity data were collected. These items were called comparison-resistant goods. Comparison-resistant goods are goods and services that cannot be put into a category based on their characteristics. Some examples of comparison-resistant goods are services rendered by teachers, physicians, and the government. Dissimilar to most commodities, services constitute a heterogeneous collection of final products, and the production of each is necessarily simultaneous with its consumption; consequently, no service can be stocked. For example, to compare teachers and physicians around the world is difficult. The problem is how can the quality and productivity of a teacher or physicians be measured. However, indicators of quality and productivity can be obtained. For example, these indicators for teaching services would include the level of education, average income, number of students in a classroom, or the amount of educational inputs available to and used by the teacher. For doctor's services, the number of patients seen or the number of operations in a day may be indicators of their quality and productivity. Government services are also hard to measure. The amount of capital available to the worker may help indicate their productivity. 40 Once the base data were collected, there were several steps and alternatives to calculating purchasing power parities (PPPs) for each country. The first step was to calculate the PPPs for each country with respect to a base country. Then, the real GDP was calculated using those PPPs. The calculation of the PPPs for comparison-resistant goods is discussed in Section 3.6 while that for the narrowly defined goods is discussed next. 3.3.1 The Methodology of Calculating Purchasing Power Parities Purchasing power parity (PPP) is the number of currency units required to buy goods equivalent to what can be bought with one unit of the currency of the base country (Kravis et al. 1982, p. 383). From the base data that are collected purchasing power parities can be calculated. There are several ways to calculate PPPs, but the methods most commonly used by the ICP are the country-product-dummy (CPD) and Elteto-Koves-Szulc (EKS) methods. The CPD and EKS methods are exactly the same if all of the prices for every item in each country are present. In that case, the resulting PPP's from the CPD and EKS are just geometric means of all of the prices in detailed category a for country c (Kravis et al. 1975, p. 60). The equation for the geometric mean of all the prices in country c is: (3.1) GM- = [ Pic ]v i = l,...,m where P,, is the price of the ith item in country c. 3.3.2 Country-Product-Dummy Method The derivation of the CPD method from this representation is simple. The CPD method is derived by making the following assumptions: the natural logarithm of the price for the ith item in country c is composed of an item effect and a country effect; the PPP's are estimated by least squares; and the relationship is stochastic. Then the CPD equation becomes: (3.2) 1/m [ln(Pi,,)] = A, + B, + ei,,. The symbol e,c represents a normally distributed variable with mean zero and variance a2. A, is the coefficient which represents the item effect on the price of item i in country c. B, is the coefficient that represents the country effect on the price. In most cases this method is' normalized by a base country, usually the U.S. In summary, the CPD method describes the natural logarithm of the price of item i in country c with respect to a base country d as the sum of an item effect A,, and a country effect B,. The coefficient Be is the mean over all items of the log of the price of item i in country c and is interpreted as the logarithm of the PPP for that country's currency relative to the base country (U.S.). Also, Ai is equal to the mean over c of the log-price of i in c, but that coefficient is not used in this study (Theil et al. 1989, p. 8). 3.3.3 Elteto-Koves-Szulc Method To derive the EKS method it takes four steps2. The steps are: calculate "Laspeyres" and "Paasche" type price ratios; calculate Fisher binary price ratios; fill in the Fisher matrix if needed; and then build an EKS matrix of transitive parities. Only the equations will be shown here, an actual example will be given in the next section. Before the derivation of the EKS method the concept of characteristic items must be introduced. A characteristic item is an item that is considered to be purchased frequently within that country. Each country is asked to nominate at least one product within every detailed category which it regards as a characteristic item. The characteristic item chosen must also be priced in at least one other country. This is done so that the most consistent price-data is used in the EKS calculations. It will become clear that all calculations in the EKS method are based on the prices of the characteristic items. The first step of the EKS method is to calculate the Laspeyres and Paasche type price ratios. These ratios are not true Laspeyres and Paasche ratios and are often referred to as mini-Laspeyres and mini-Paasche price ratios due to their similarity to the Laspeyres and Paasche time-series measurement. The difference is that these are unweighted 2We would like to thank Ms. Harary at the OECD, Economic Statistics and National Accounts Division for providing unpublished material on the EKS method. 43 price ratios whereas Laspeyres and Paasche are weighted indexes (Ward, 1985, pp. 42-43). The mini-Laspeyres formula is a price ratio of the characteristic item between two countries, if the base country has only one characteristic item. If there are more than one characteristic items in the base country, a geometric mean is taken of all of the price ratios3. The general representation of the equation for the mini-Laspeyres equation is: ic (3.3) L",d = i / = Pid where i = 1,...,m characteristic items in detailed category a. The mini-Paasche formula is the reciprocal of the transposed mini-Laspeyres price ratios. The equation for the mini- Paasche price ratios is: 1= I Pi,d (3.4) Pdc =[ i / / L ,d This method does not pick one base country; therefore, a matrix of mini-Laspeyres is created between countries with a diagonal of ones, the same is true for the mini-Paasche ratios. 3To calculate the geometric mean the base country's characteristic item or items determine the relative parity ratios. The comparison country's price does not have to be a characteristic item in order to calculate the geometric mean. 44 Once the mini-Laspeyres and mini-Paasche ratios are computed, the Fisher binary type price ratios are constructed. Just as before these are not true Fisher binaries because they are based on unweighted price ratios. Therefore, these Fisher type price ratios will be referred to as mini-Fisher binary price ratios. The mini-Fisher ratios are unweighted geometric means of the mini-Laspeyres and mini-Paasche price ratios. The equation for the mini-Fisher price ratios is: (3.5) Fc,d = (La,d ,d)12 where F,d is the mini-Fisher price ratio for detailed category a between countries c and d. Note that F,d F, = 1. However, the matrix of mini-Fisher ratios are not transitive. Transitivity means that F,/Fc, : F~,d Hence, to make the mini- Fisher ratios transitive, the EKS method is applied. Given that all of the price ratios are present, all of the mini-Fisher ratios can be calculated. Hence, there would exist a full matrix of mini-Fisher ratios. The EKS method is then applied to the mini-Fisher ratios. The equation for the EKS method is: F" (3.6) EKS,d = ,d2 1/n where e f cd. :=l F d, EKS",d is the PPP for the detailed category a between countries c and d. This procedure uses direct mini-Fisher price ratios F,d and indirect ratios F, and F*, which use country e as the 45 bridge country between countries c and d. This method replaces each direct ratio by the geometric mean of itself and all corresponding indirect ratios that can be obtained using as many of the other countries as possible for bridges. The EKS gives the direct ratio twice the weight of each indirect ratio since Fd/F, Fc/F,c is the same as Fc,d. The resulting transformed ratios are all transitive. The overall transitive parity between any individual pair of countries is therefore significantly dependent on the indirect ratios involving prices in all other countries (Ward, 1985, pp. 44-45). 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 be observing the values in any of the country columns of the EKS matrix. To make the EKS equivalent to a geometric- mean is -simple. The EKS formula itself is a geometric mean. If all of the prices of the items are all present and all characteristic items, then the EKS method is the same as equation (3.1) if Pi, is replaced with a price ratio. The reason is that the indirect mini- Fishers and the direct mini-Fisher ratios are equal, that is F ,e/Fd,e = F,d. This section shows how the CPD and EKS method calculate PPP's for a detailed category when all of the prices are present. Also, it is proven that the CPD equals EKS which equals the geometric mean when all of the prices are present and all of them are characteristic items. The next section 46 illustrates the situation where there are missing prices, which is the case for most detailed categories. 3.4 Estimating Purchasing Power Parities In many detailed categories, there are several missing prices. Without the basic prices, the CPD method does not equal a geometric mean and neither does the EKS method. In fact with the EKS method the mini-Paasche, Laspeyre, and Fisher ratios cannot be calculated when there are missing prices. In this case it should be clear that the CPD method does not equal the EKS method, although they should deviate minimally from one another. This section addresses the procedures the ICP used to estimate the PPP's via the CPD and EKS methods when there were missing price data Estimating PPP's with the CPD method is the same as in section 3.3. Equation 3.3 normalized by the U.S. price is the equation used to estimate the B,'s. To illustrate this procedure part of the data from the fresh vegetables detailed category for 1970 is used (Kravis et al. 1975, p. 59). The data for four countries and four goods are shown in Table 3.2. The full matrix for fresh vegetables for 10 countries and 20 countries in 1970 is shown in Appendix A4. If the prices of vegetables in their respective national currencies in Table 3.2 are considered to be a detailed 4The PPP's and Al's estimated by Kravis et al. 1975 are also included in Appendix A. Table 3.2 Fresh Vegetables for 4 Countries and Items in 1970 United United Japan Kenya Kingdom States (Yen) (Shilling) (Pound) (Dollar) Lettuce 218.1* 0.62 0.5* Mushrooms 0.54* 1.9 Onions, yellow 98.6* 0.77 0.13 0.35* Tomatoes 160.9 1.19* 0.31* 0.92* Source: Kravis et al. 1975, p. 59. *The starred items are the characteristic items for each country5. category, then the vector for the dependent variable using the U.S. as a base country is equal to: ln(218.1/.5) ln(98.6/.35) ln(160.9/.92) ln(.62/.5) ln(.77/.35) ln(1.19/.92) ln(.54/1.9) ln(.13/.35) ln(.31/.92). Kravis et al. 1975, 1978a, and 1982 weighted each price ratio with the reciprocal of the number of prices in the numerator country by the base country (4/3), and by the supercountry expenditure (see Appendix B). The independent variables (dummy variables) for this equation, constructing the country dummy then the item dummy, are: 5These items are not the actual characteristic items they are chosen for illustration purposes only. 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1. This system cannot be estimated because each row for each independent variable sums to 1. That means there is an adding up problem. To solve this problem one of the items has to be dropped. No information is lost when this is done, redundant information is eliminated from the system. Once one of the columns from the item dummy is eliminated the regression can be estimated. The results from this setup having dropped item 2 and weighted the price ratio by (4/3)6 are Bp.U.s = 5.62 BKn.Us = 0.41 BUK.,U.S = -0.99. These results are the natural logarithm of the PPP between country c and the U.S. To get the PPP, the exponential of BC is taken. The PPP's are 275.89, 1.51, and 0.37, respectively. There are n-1 PPP's because the U.S. is used as the base country. The explanation of these numbers are given after the EKS results are calculated and compared with the CPD results. 6The supercountry weighted is not used in this example. 49 The first step of the EKS method is to create the mini- Laspeyres price ratios. For simplicity, Ld will now be expressed as LCId and the same for the mini-Paasche price ratios. The mini-Laspeyres matrix is shown in Table 3.3. All calculations for the EKS example are shown in Appendix C. In this.matrix the base country is given by the columns, the rows are the numerator countries. Since the mini-Paasche matrix is just the inverse of the numbers in Table 3.3, that is Pu,. = 1/L,, the mini-Paasche matrix will not be shown. Table 3.3 Mini-Laspeyres Price Ratio Matrix Japan Kenya U.K. U.S. Japan 1_0 135.21 519.03 278.02 Kenya 0.0047 1.0 2.48 1.52 U.K. 0.0013 0.26 1.0 0.35 U.S. 0.0029 0.77 3.23 1.0 After the mini-Laspeyres and mini-Paasche price ratios are calculated, the mini-Fishers are estimated. Table 3.4 shows the results of the mini-Fisher calculations. There are no missing mini-Fisher ratios in this example. If there were, a bridge country method would have been implemented to fill in the missing values. For example, if the mini-Fisher price ratio between countries c and d (F d) is missing, but the 50 ratios between countries c and e, and d and e exist, then the mini-Fisher price ratio for countries c and d can be calculated by dividing F", by F,,. Country e is the bridge country that links countries c and d. If more than one bridge country is available, then a simple geometric mean is taken of all of the indirect estimates. If there are still missing mini-Fisher ratios then the above procedure is applied until the matrix has no missing data. Table 3.4 Mini-Fisher Ratios Japan Kenya U.K. U.S. Japan 1.0 169.61 631.87 309.63 Kenya 0.0059 1.0 3.09 1.41 U.K. 0.0016 0.32 1.0 0.33 U.S. 0.0032 0.71 3.04 1.0 The final step in calculating the PPP's is to implement the EKS method. The EKS method uses the direct and indirect mini-Fisher ratios to make these parities transitive. The matrix of transitive PPP's are shown in Table 3.5. The EKS results are implicitly weighted because only the characteristic items are used for base countries in the calculations. Table 3.5 Transitive PPP's from the EKS method Japan Kenya U.K. U.S. Japan 1.0 189.58 667.53 262.67 Kenya 0.0053 1.0 3.50 1.39 U.K. 0.0015 0.28 1.0 0.40 U.S. 0.0038 0.72 3.53 1.0 To compare the EKS results with those from the CPD, the U.S. column is used because the CPD used the U.S. as its base country. The values from the CPD compared with the EKS for fresh vegetables in 1970 for 4 countries and items are as follows: CPD EKS Japan/U.S. 275.89 262.67 Kenya/U.S. 1.51 1.39 U.K./U.S. 0.37 0.40. The differences between these numbers are negligible. Most of the variance could be due to weights and rounding error. The interpretation of the PPP's estimated by both methods is that one dollar's worth of fresh vegetables in the U.S. equals between 262.67 275.89 yen worth of fresh vegetables in Japan, 1.39 1.51 shillings worth of fresh vegetables in Kenya, and 0.37 0.40 pounds worth of fresh vegetables in the United Kingdom. 52 The CPD method was used in Phases I, II, and III. The CPD and EKS methods were used in Phase IV. The reasons for using the different methods in the different Phases will be discussed in Chapter 4. Once the PPPs were estimated, they were used in the Geary-Khamis method. The second stage of the estimation process is discussed next. 3.5 The Geary-Khamis Method The objective of the Geary-Khamis method is to provide 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 can be obtained by dividing expenditures in national currency by those in international dollars. The method was first introduced by Geary who suggested that a system of homogeneous linear equations be used. These equations are used to calculate the international prices and the PPPs simultaneously. Subsequently, Khamis shows that the system yields non-negative international prices and PPPs. Thus, Geary and Khamis are responsible for this model. The derivation of the Geary-Khamis method follows. The CPD or EKS method can be used to produce the detailed category PPP's for the Geary-Khamis method. These PPP's are transitive and relative to the U.S. dollar. Detailed categories are indicated by the subscript a = 1, ..., A. Let Ec be the per 53 capital expenditure (in national currency) on detailed category a in country c. The equation for the volume of detailed category a in country c is (3.7) V., = E.,/PPP,,. V., is expressed in U.S. dollars. Although (3.7) achieves the goal of expressing all expenditures in the same currency ( U.S. dollars), the V.,'s have the problem that they are not additive over detailed categories. To achieve such additivity, the Geary-Khamis method introduces the international price P. of each detailed category and the overall purchasing power parity ir of each country c. The definition of P. is N E' (E;; w *** *** 7tj c=1 Pa = N E V., c=1 or, equivalently, N N (3.8) PaVa = Z (Ec/7c) where V, = E Vc c=l c=l while 7, is defined as A Z E,, a=l 7r =_____ A E PVa a=I or, equivalently, as A (3.9) GDP(1/ir) = E P.V., a=1 where GDPc (the gross domestic product of country c in national currency) is equal to the sum over a = 1, ..., A of E.. It is readily verified that (3.8) and (3.9) constitute a linear system in the A + N -1 unknown P, and 1/w, ( c = 1 for c = U.S.) (Theil et al. 1989, Appendix A). The product PV., is interpreted as real expenditure per capital in international dollars on detailed category a in country c. This product is additive over detailed categories. Let S be any grouping of such categories; then the sum over a E S of PV., is real expenditure per capital or real gross domestic product (RGDP) per capital in international dollars on S in c. If S consists of all detailed categories, this sum is GDP per capital in c. The exposition given on the CPD, EKS, and Geary-Khamis methods is a general overview on how PPP's for the detailed categories and overall, international prices, and RGDP are 55 calculated. The next section deals with calculating PPP's for the comparison resistant goods. 3.6 Calculating PPP's for Comparison Resistant Goods In the previous sections the procedure for calculating PPP's for narrowly defined goods was discussed. In this section, the calculations for PPP's of comparison resistant goods are discussed. The procedure for calculating these PPP's to use in the Geary-Khamis formula is straight forward. For the comparison-resistant goods and services (i.e., services of teachers, physicians, dentists, hospitals, nurses, and government employees), neither the CPD or EKS method was used. Quantity comparisons for these categories were based on a method called "direct quantity" comparisons. For example, for teachers of first, second, and third level students, the quantity comparisons were based on the number of standardized persons engaged in providing the services. For physicians, dentists, technicians, midwives, and the like, the ICP quantity comparisons were based on the number of physicians, dentists, and nurses, respectively. For Phases I and II, it was assumed that all equally qualified personnel in these comparison-resistant categories have the same productivity. In Phases III and later, this assumption was abandoned, and adjustments were made. In educational services, the modifications improve the estimates of teacher inputs by introducing education level and the number of students as a further dimension of productivity. In 56 medical care and government services, adjustments are made for the differences in the productivity of inputs for broad groups of countries and by making adjustments for capital per worker. After the adjusted final quantity ratios are derived, the PPPs used for the Geary-Khamis method are considered to be indirect PPP's. These PPPs are found by dividing the expenditure ratios by the adjusted quantity ratios. From there, the Geary-Khamis method is applied as before. The reader who is interested in these and similar issues should consult the original source: the work of national and U.N. price experts (Kravis et al. 1982, p. 38); prices of construction and consumer durables (Kravis et al. 1982, pp. 50-56); and the treatment of services (Kravis et al. 1982, Chapter 5). 3.7 Regionalism Regionalism is a new issue beginning in Phase III. The previous Phases I and II were limited to a small number of heterogenous countries. Thus, there is little point in considering whether comparisons could be improved by identifying relative homogeneous subsets of countries. The Geary-Khamis method was applied to the entire set of countries without any effort to distinguish such subsets or to take them into account in the index number calculations. This symmetrical treatment of all countries is called the "universal" approach. 57 As the number of countries increased significantly in Phase III, it became necessary to consider whether applying the CPD or the Geary-Khamis methods in successive stages would improve the comparisons. The first step would be to look at the level of sets of relatively homogeneous countries and, thereafter, at the regional level. Thus, countries in different regions are compared through regional linkages. The most obvious basis for identifying homogeneous sets of countries is geographic closeness. This basis for grouping countries assumes that these countries have close political and cultural ties as well as similar customs. Although ad- hoc, there are some good reasons for using this approach. Europe and Latin America, for example, are similar in the way they classify daily business and the way they deal with the changes in -the political, social, and economic arenas., In addition, there are usually regional organizations with the sole responsibility of economic development for that region. For the actual calculations for Phase III, the ICP opted to use what is called a modified "universal" approach. This approach has some regionalism aspects which are introduced via the organization of the price inputs for the Geary-Khamis calculations. The objective is to retain base country invariance or to at least allow all countries within each region to influence the world comparisons while retaining the intraregional PPPs and quantity relationships for the detailed categories and for GDP as a whole. 58 The modified universal approach has 3 steps. First, the CPD method is applied at the regional level to fill in the missing prices. Second, the CPD method is applied again, this time on all countries in the study. Lastly, the PPPs from the second stage CPD are used as direct inputs to the Geary-Khamis method. The first stage CPD takes advantage of the regional similarities in price structures to cope with a major problem in deriving the set of PPPs. The problem is primarily incomplete, overlapping sets of price comparisons among the participating countries. The first CPD estimation operates at the regional level to fill in for each country's missing entries in the vector of item prices. All items for which at least two countries in the region provided prices are included. Therefore, this tableau contains-for each region, a full vector of prices, for each country, for all items priced by two or more countries in the region. Note that if the CPD is run on the augmented price tableau for a given region, it would yield the same PPPs as those produced by the original incomplete tableau of prices. Thus, the tableau retains the characteristics of the original tableau. After each country's price vector has been completed to match the other country's in the same region, a second CPD is run. This CPD is calculated for all 34 countries (Phase III), where these PPPs are used as the direct price inputs for the Geary-Khamis calculation covering all the countries. This 59 approach embodies a regional element in deriving the category PPPs, but the aggregation of the PPPs across categories is of the universal mode. The results of this new approach relative to the approach used in Phases I and II, which is based on direct price inputs of all countries regardless of the region, are improved. The augmented-price-tableau enhances the influence of intraregional price relationships. The missing prices are explicitly filled in on the basis of intraregional price relationships versus being estimated on the basis of price relationships in all countries like the universal approach does. The last step is to put the PPPs derived from the two- stage CPD method into the Geary-Khamis equations. Calculations for all 34 countries (Phase III) were completed using this method. The results from this approach are discussed next. 3.8 Phase III Results Compared with Exchange Rates Using the two stage CPD method to obtain the PPPs for the detailed categories and then implementing the Geary-Khamis method, the international prices and GDPs per capitas are calculated. Table 3.6 provides the results of these efforts for gross domestic product for the year 1975 (Phase III). The 34 countries are listed in the order of declining GDP per capital in international dollars. Table 3.6 GDP Per Capita for 34 Countries in 1975 International Same, Exchange rate Country dollars U.S.=100b converted (1) (2) (3) (4) United States Germany Denmark Luxembourg France Belgium Netherlands Austria Japan United Kingdom Spain Italy Poland Hungary Ireland Uruguay Iran Yugoslavia Mexico Romania Brazil Syria Jamaica Colombia Malaysia Korea Philippines Thailand Zambia Sri Lanka Pakistan Kenya India Malawi 7176.0 5952.7 5910.9 5883.4 5876.9 5574.1 5397.2 4994.8 4906.7 4587.9 4010.2 3861.1 3597.9 3558.9 3048.8 2844.3 2704.6 2591.4 2487.3 2386.8 1811.2 1794.2 1722.6 1608.7 1540.6 1484.1 946.3 936.1 737.8 667.7 590.3 470.5 470.5 351.7 100.0 83.0 82.4 92.0 81.9 77.7 75.2 69.6 68.4 63.9 55.9 53.8 50.1 49.6 42.5 39.6 . 37-.7, 36.1 34.7 33.3 25.2 25.0 24.0 22.4 21.5 20.7 13.2 13.0 10.3 9.3 8.2 6.6 6.6 4.9 100.0 94.7 104.5 90.2 89.6 87.8 84.5 69.8 62.3 57.6 41.0 47.9 36.0 29.6 37.2 18.2 22.1 23.2 20.4 24.3 16.0 10.0 19.6 7.9 10.9 8.1 5.2 5.0 6.9 2.6 2.6 3.4 2.0 1.9 p. 12. aSummed over all 151 detailed categories. bSource: Kravis, Heston, and Summers 1982, 61 The differences between the exchange-rate converted figures and those which Kravis et al. (1978a) obtained using the Geary-Khamis method are substantial. These differences increase as real GDP per capital decreases. This is readily seen in columns 3 and 4 of Table 3.6 where the PPP based estimates of GDP per capital are compared with the exchange rate based estimates (both are a percentage of U.S. value). The use of exchange rates tend to overstate the poverty of poor nations considerably. For example, when we use exchange rates, the ratio of the U.S. GDP per capital to its Indian counterpart is 100/2.0 = 50, but it is only 100/6.6 or about 15 when we use the Kravis approach. One reason for this dispersion is that services tend to be cheaper relative to commodities in poorer countries, and services -make up a small- portion of international trade. Hence, exchange rates understate the value of services in low income countries. Services, which are nontraded goods, are cheap in low- income countries; hence exchange-rate conversions greatly underestimate the true quantities of services in low- income countries relative to those in high-income countries. (Kravis et al. 1982, p. 23) In addition, exchange rates have been variable since the switch-over to floating exchange rates in 1973. However, there is no reason why the consumption expenditures in national currencies should reflect this variability exactly. Converting these expenditures by such wildly fluctuating exchange rates would yield highly spurious results. 3.9 Phase IV Further Considered After Phase III regionalism plays a bigger role in the ICP. Regionalism complicated things in many ways. Therefore, Phase IV is discussed explicitly. Phase IV as mentioned before is different from the other Phases. The information on Phase IV is presented in "World Comparisons of Purchasing Powers and Real Product for 1980: Phase IV of the International Comparison Project." This manuscript has two parts: "Part I: Summary Results for 60 Countries"; and "Part II: Detailed Results for 60 Countries." These papers are published by the Statistical Office of the United Nations Secretariat (UNSOS), Statistical Office of the European Communities (EUROSTAT), and the Organization for Economic Co-operative and Development (OECD). This work is discussed here to -address several problems (i.e., decentralization, regionalism, and fixity) and the additional problems they create. The other reason for Phase IV's importance is that it increased the number of benchmark countries to 60. Phase IV is similar in many ways to the previous Phases, so only the deviations from those Phases will be discussed below. After Phase III, the ICP was decentralized, which meant that various regional and country groups assumed major responsibilities while the Statistical Office of the United Nations Secretariat was responsible for linking the work of the various regions. There were seven organization that 63 carried out the work for the country groups: Statistical Office of the European Communities (EUROSTAT), Economic Commission for Europe (ECE), OECD, Economic Commission for Africa (ECA), Economic Commission for Latin America and the Caribbean (ECLAC), Economic and Social Commission for Asia and the Pacific (ESCAP), and UNSOS. With the decentralization, each group carried out its own estimations within its region; this is referred to as regionalism. This definition supersedes the definition in section 3.7 for Phase IV and later. Table 3.7 shows the countries involved in each group as well as the organization that did the calculations. After the comparisons within each region are accomplished, then the regions are compared at the world level. 3.9.1 Other Methods Used in Phase IV With the decentralization 'and- regionalism of Phase IV, one problem is that each region can choose any method they preferred to calculate the PPPs. Europe Group 2 and ECIEL decided not to use the CPD or EKS method. The European group implemented a method called the "STAR" system. It is not clear what the ECIEL group did to calculate their PPPs. The star system used by Europe group 2 has Austria as the base country for that group. They carried out four separate binary comparisons with the four countries representing the outer points of the star. The detailed category PPPs for each country are only estimated with respect to Austria. The PPPs for any two countries are derived from the two sets of binary Table 3.7 The Organizations that Performed the Calculations and the Countries Involved in Each Group for Phase IV. EUROSTAT ECE ECA/EUROSTAT ESCAP/UNSOS ECIEL/ECLAC OECD -----------Europe-------- Group 1 Group 2 Africa Asia Latin America OECD Belgium Austria Botswana Hong Kong Argentina Canada Denmark Finland Cameroon India Bolivia Japan France Hungary Ethiopia Indonesia Brazil Norway Germany Poland Ivory Coast Pakistan Chile U.S. Greece Yugoslavia Kenya Philippines Colombia Italy Madagascar Korea Costa Rica Ireland Malawi Sri Lanka Dom. Rep. Luxembourg Mali Ecuador Netherlands Morocco El Salvador United Kingdom Nigeria Guatemala Portugal Senegal .. Honduras Spain U.R. of Tunisia Mexico Israel Tanzania Panama Zambia Paraguay Zimbabwe Peru Uruguay Venezuela Source: United Nations, 1985 and 1987. PPPs (i.e. country C and D's binary PPPS with country B and D's binary PPPs). Using this method, transitivity is not a problem since no direct comparisons are made between the points of the star. Thus, the EKS system is not necessary. The Geary-Khamis method is used to aggregate the categories and calculate GDP as a whole. The weights (expenditure and 65 prices (PPPs) of the countries covered) of the five countries are taken into account (The Statistical Office of the United Nations Secretariat 1987, p. 5). There is less information on what the ECIEL region did. However, it is clear that neither the CPD nor the EKS method was implemented. It has been ECIEL's practice that each country provides prices for every item in the detailed categories. PPPs are then derived that are transitive across all countries by obtaining the geometric mean of the price ratios of each country to any one of the countries chosen as the numeraire. All that can be said about this method is that, if all countries provide prices for all of the commodities, then all of the other methods reduce to a geometric mean, when estimating PPPs for the detailed categories (The Statistical Office of the United Nations Secretariat 1987, p. 11). 3.9.2 Linking the Regions of Phase IV After the PPPs for the detailed categories were estimated, the problem was to link all of the country groups together. The main problem was that each region had a different base country. In addition, the Europeans (both groups) have approximately 320 detailed categories while the other groups typically have approximately 150; the African and Latin American countries have a more condensed system. Fortunately, the European, African, and Latin American groups 66 were able to make their respective detailed categories compatible with those of the world comparisons. Linking the various country groups requires that the prices of the overlapping items between countries across the different country groups be compared. In order for this to work, there must be at least one country in each group which has prices for each detailed category so that the PPPs can be estimated to link the countries. When comparing Europe Groups 1 and 2, for example, only Austria has sufficient prices to link Group 2 to 1. However, this was sufficient to link the Europe Group 2 countries with the world comparisons. There are 20 countries that serve as liaisons like Austria. These countries act only as a set of countries whose item prices for comparable goods and services serve as the basis for linking the country groups. These countries are called "core" countries. The core countries are: France, Spain, Israel, and the United Kingdom (Europe Group 1) ; Austria (Europe Group 2); United States, Canada, and Japan (OECD); Brazil, Colombia, Uruguay, Dominican Republic, and Guatemala (ECLAC); Hong Kong, Indonesia, Korea, Pakistan, and Sri Lanka (ESCAP); and Kenya and Senegal (ECA). The CPD method was used for the core countries where the item prices for the 20 core countries were used as inputs. The expenditure weights used by some of the country groups were also incorporated into the CPD estimation procedure. When the CPDs were estimated for each of the detailed 67 categories, PPPs between each core country and the United States, which was the numeraire country, were provided. The next problem was how to link these PPPs with the other countries in these regions. The method used to link the PPPs to the other countries is a type of chain-link-procedure. Using the African countries as an example, the detailed category PPPs exist and for the core countries of Kenya and Senegal, both with respect to the African numeraire and with respect to the United States. The ratio of the geometric means of the core country to the African PPPs provided a factor which, when multiplied times the detailed category PPPs within Africa for all of the African countries, aligned these parities with respect to the United States dollar. This procedure preserves the relationship between the basic PPPs for all countries as originally obtained in the African comparisons, including Kenya and Senegal. This is the fixity principle (see Appendix D). The chain-link-procedure was applied to Latin America, Europe Group 2, and the OECD countries. In the case of the ESCAP countries, there was no reason to do the chain link method since the base country for that group was the U.S. For India and the Philippines, a slightly different procedure was used since the price information for these countries became available too late to include in the core country CPDs. The item prices were directly compared to the item price estimates 68 that were a part of the CPD output for each detailed category. The geometric means of these item price ratios, which were based in national currency units per dollar for each detailed category, were used as the PPPs. All methods in which the expenditure and PPPs at the detailed categories were obtained have been discussed. These calculations were the basic inputs to the aggregation procedure. The Geary-Khamis method was used just as in the previous Phases for the aggregation of the data. The use of supercountry weighting was also retained. It was important that the results for countries participating in several phases of the ICP not be influenced by the addition of new countries. Hence, the world comparisons utilized a system of supercountry weights where the dollar GDP of non-participating countries was assigned to participating countries on- the basis fof geographical proximity and the level of per capital income. The problem with the Phase IV data are that the fixity principle is imposed (see Appendix D). Fixity adversely affects the data if one is interested in world comparisons. That is why there are two data sets for Phase IV. The first set is for researchers who are interested in world comparisons and the other, which preserves fixity, is for intraregional comparisons. The first set is made available by the U.N. Statistical Office upon request by the researcher. The other data set which has fixity imposed is in the Phase IV 69 publication. The calculations in this thesis were all based on the data that do not impose the fixity principle. To calculate RGDP per capital for each country with respect to the U.S. without fixity, the calculations must be done like the Phases previous to Phase IV. That is, estimate the PPPs with the CPD or EKS method using the U.S. as a base country, then apply the Geary-Khamis method. CHAPTER 4 EXTRAPOLATIONS 4.1 The Beginning of Extrapolations with ICP Data There are five publications of the extrapolations on the different phases of the ICP. The first publication is by Kravis et al. (1978b). All of the rest are by Summers et al. (1980 also known as Mark 1,1 1984 Mark 3, 1988 Mark 4, and 1991 MARK 5). These publications sought a way to approximate real gross domestic product (RGDP) per capital for virtually all the countries in the world and for every year from 1950 to 1988. This method is referred to as the "short cut" method. During the years following the first publication in 1978, the methodology and the quality of the data from the Mark's have improved. The purpose of the first paper, "Real GDP Per Capita for More than One Hundred Countries," by Kravis et al. (1978b) was to close a gap that the world statistical system had been unable to fill. At that time, there were no comparative data on "real" GDP per capital (gross domestic product per capital adjusted for differences in the purchasing power of currencies) for a large number of countries. In this paper, 'Mark 2 was not published but it was used in Kravis, Heston, and Summers (1982). 71 Kravis et al. (1978b) develop a method to calculate these real GDP per capital (RGDPC) by using the detailed comparisons of the 16 countries in Phase II. The structural information from this method allows the RGDPCs to be calculated for non-ICP countries. Lastly, an extrapolation is made to get RGDPC for later years. The short-cut method that Kravis et al. (1978b) developed concentrates on the relationship found in the 16 countries between RGDPC and certain independent variables. These structural relationships were used to estimate other years and non-benchmark countries. However, the authors caution that the non-ICP RGDPC's were approximations, and that it would be some time before more exact comparisons would be available for a large number of countries. Nonetheless, their numbers are superior to exchange rate converted GDPs per capital which-were used prior to PPP conversions. The model Kravis et al. (1978a) used to find the structural relationships was PI, (4.1) In rj = a+ + a2 In nj + 3 (In nj)2 + a4 In PIus OP. + a5 In ___ = 1,..., 16 OPus where j represents countries, rj = Rj/Rus, nj = Nj/Ns, R is real GDP per capital (adjusted for purchasing power), and N is nominal or exchange-rate-converted GDP per capital. The 72 variables OP (openness) and PI (price isolation) come from international trade theory and will be covered in more detail later (Kravis et al. 1978b, p. 219). The relationship between r and n has been discussed in Chapter 3 so it should not be a surprise that a2 is expected to be between 0 and 1. The value of al is expected to be 0 because r should equal 1 when n, OP, and the PI ratios equal 1, which is the case for the base country. The a3 coefficient is expected to be negative since its corresponding variable is the square of a. That is the square of a negative number is positive, and ln(n) is negative while ln(n)2 is positive; hence, r and ln(n)2 are negatively related. The expected signs of OP and PI as well as the variables themselves are discussed next. The reason why OP and PI are included-in-the model is because Kravis et al. (1978b) were influenced by the productivity differential model. This model is most clearly stated by Harrod and Balassa cited by Kravis et al. (1978b). It states: international trade tends to equalize the prices of traded goods; given equal prices, wages will be high in high productivity countries; internal factor mobility will lead to high wages also in non-traded goods industries in high productivity countries; because international differences in productivity are smaller in non-traded goods industries (largely personal services) than in traded goods industries (largely commodities), the non-traded goods will be higher in 73 high productivity (high incomes) countries; and lastly, the high prices of non-traded goods have little if any impact on the exchange rate and thus make possible a difference between the overall purchasing power of the currency and the exchange rate. The influence of this model led the authors to attempt to account for the differences in countries openness to trade. The degree to which each country's price level is influenced by foreign prices is measured by the variable "openness" (OP). This variable basically measures the exposure to world markets. OP is calculated by the average ratio of exports plus imports to GDP for the years 1965 to 1973. The period for which the data are used is completely arbitrary and taken directly from the World Bank Tables, 1976 (Washington D.C.: International Bank for Reconstruction and Development, 1976). The expected sign for a5 is ambiguous. The relationship between OP and r is negative if the following is correct: the more open an economy, the higher its prices are for non-traded goods, making the difference between n and r smaller. The relationship is not clear if the lack of openness is due to protective commercial policies which could lead to higher prices for non-traded goods (Kravis et al. 1978b, p. 223). PI stands for price isolation. The assumption is that the influence of external factors on a country's price level at a particular moment in time can be inferred from how closely its time to time movements over some preceding period 74 are correlated with time to time movements of "world" prices. The world price index (implicit deflator) is created by placing countries whose currencies the International Monetary Fund (IMF) have defined the value of a unit of Special Drawing Rights (SDRs) on a common base. These are converted to dollars by division by an appropriate index of exchange rates. The world index is then constructed by aggregating the SDR country indices using weights which reflect the importance assigned to each currency by the IMF in its initial calculation of the value of an SDR unit in mid 1974. The implicit deflator is then adjusted for each individual country to a common base period and correct exchange rate changes. The final step is to calculate the price isolation index using the formula, 1970 (4.2) PI = t= (WDt CD)2/8 where WD is the world price index and CD the country price index, both based on the average over the period 1963 to 1970. Eight of the ICP countries are included in the set of countries that the IMF uses in its SDR calculations. Thus PI can be summarized as the mean squared difference for the years 1963 to 1970 between the country's GDP implicit deflator and a "world" average GDP implicit deflator. The sign for a4 is ambiguous like a,, and for similar reasons. PI and r could be positively related if the 75 following line of reasoning is consistent with what has actually happened. The reasoning is, the greater the price isolation, the less a country's non-traded goods prices will be pulled up to the price levels of the high-income countries; thus a larger real income (r) is associated with a given nominal income (n). However, these affects can be negated by combining different micro and macro economic policies which is why the sign is ambiguous (Kravis et al. 1978b, p. 223). The question is empirical and one can only estimate the equation and see what signs and magnitudes the parameters have. All of the values for the variables are known for the 16 ICP countries, but r is not known for the other countries. Hence, the model was run for those 16 countries to obtain the structural relationships between RGDPC and the other variables. The resulting signs for this model are a2 positive, a3 negative, a4 positive, and a5 is negative. The parameter estimates and their respective standard errors can be found in Kravis et al. (1978b, p. 226). After calculating r for the non-benchmark countries for 1973, extrapolations have to be made to other years. The method of extrapolation is setup to incorporate the impact on real income through the changes in the terms of trade. This is done by treating the net foreign balance component of GDP separately from "domestic absorption." For domestic absorption (DA), the per capital quantity change between the benchmark year and the year of extrapolation for 76 each country is estimated by deflating consumption, capital formation, and government by the implicit deflator for these sectors. This results in the value of DA in the extrapolation year being expressed in international dollars of the benchmark year. The net foreign balance was then valued in benchmark year international dollars and added to the figure for DA to obtain GDP per capital in international dollars. Finally, this sum was compared to the corresponding U.S. total to form the extrapolation year index for real per capital GDP (Kravis et al. 1978b, p. 229). The results of this task were estimates for 1973 and 1974. 4.2 Mark 1 The second paper by Summers et al. (1980) is entitled, "International Comparisons of Real Product and its Composition: 1950 to 1977." This study includes 119 countries of which 16 are from the ICP Phase I data set. The same equation (4.1) is used to calculate r for the ICP countries and the structural relationships found from those calculations, are used to calculate r for the non-ICP countries as before. What is new in this paper is that the extrapolations for the ICP and non-ICP countries are done forward and backward through time. To calculate RGDPj, before and after 1970 is relatively easy since all of the results are in 1970 dollars (benchmark year). R is calculated the same as previously (r, = 77 RGDPj,/RGDPus,70) for the year 1970 only. The RGDPJ, for the other years is obtained using the jth country's constant price series (in domestic currency units) for GDP as indicated in the equation below, GDPj,t /POPjt (4.3) RGDPj, = (RGDPj7o) GDPj70 /POPj,70 where GDP is a constant-price value of GDP,, in national currency and POPj, refers to the population. By using the constant-price valuation, changes in terms of trade facing the jth country between the tth year and 1970 are neglected. RGDP is calculated for all 119 countries from 1950 to 1977 using these methods. 4.3 Mark 3 The third paper, "Improved International Comparisons of Real Product and its Composition: 1950 1980" written in 1984 by Summers and Heston, is referred to as Mark 3. Mark 2 was not published but it was used by Kravis, Heston, and Summers (1982). Mark 3 was different from Mark 1 and Kravis et al. (1978b) because it utilized the data from Phase III. This data set included 34 countries for the year 1975. This difference and the fact that there were two benchmark years of data (i.e., 1970 and 1975) resulted in the authors using a different method for calculating the RGDPs in Mark 3. 78 The first change from the earlier papers was that a slightly different functional form for the regression was used. However, before that is addressed, the data need to be considered. There are two benchmark years of data to utilize. The approach used by Summers and Heston in this paper is a modification of the approach used in Phase III (Extensions beyond the ICP countries, pp. 332-340). The cross-section regressions for the two years were run in terms of per capital DA instead of per capital GDP as done previously. The slightly different functional form for the regressions was that the openness variable in the equation used to summarize the 1970 and 1975 data was introduced additively compared to an interaction term. Furthermore, the constant terms in both years were suppressed since they were not significantly different from -zero,. .-..These -modifications simplify the equation and make the actual and estimated values for the numeraire country the same (U.S.). Lastly, the results obtained from the two benchmark years were combined to get a single 1975 estimate. Weights were also devised to take into account the relative precision of the two cross sections. The regression equation used to summarize the 1970 and 1975 cross-section relationships is (4.4) In r, = a, (ln n) + a2 (In n)2 + a3 (In OPj) + u where r = (DAj/PPPA)/DAus and n = (DA,/XR,)/DAus. pppDA is the purchasing power parity over domestic absorption, and XRj the exchange rate. Each is expressed in national currency units of the jth country per U.S. dollars. OP, is the measure of relative openness of the jth economy which was defined as ((Exportsj + Imports))/GDP) / ((Exportss + Importsus)/GDPus), an average of the ratio for five years before the cross- section year. Before further definitions are given it should be stated that the a's have the same expected signs as they did in Kravis et al. (1978b). The XR, 7 variable was defined by a weighted geometric mean of the 1975 exchange rate and the real exchange rates of 1974 and 1976. This was done due to the volatility of the exchange rates for several countries. The equation for XRj, is then (4.5) XR,7s = (Pj,75n4XR ,74) (XRj7s) '' (Pj,75n6XRj76) where Pj,. measures the change in the relative price levels of domestic absorption of the jth country and the U.S. between t and t'. X is a weight for the 1974 to 1976 exchange rates. No averaging implies X = 0 and equal weighting implies X = 2/3. The weighting question is resolved by running a non- 80 linear least squares regression on the data. For 1975, the results indicate that X is not significantly different from zero so XRj.7 only depended on XR,7s. The year 1970 was different in that X was large. Hence, its value was set at 2/3. Thus, XR,,7 is just a simple geometric mean of XRP70 and the price-level adjusted values of XR,. and XR,7,. In Summers and Heston (1980), RGDP,, is based on constant- prices whereas in Mark 3, international trade was incorporated into RGDP. The net foreign balance was converted by the exchange rate on the grounds that, at the margin, this is the conversion factor for an increment to the net foreign balance. This is equivalent to setting the international price of a dollar's worth of net balance to 1. Thus, RGDPj7 = r75 (DAus,75 + NFBj,7/XR,7s) where NFBi,7 is the net foreign balance in 1975 for the jth country. Rj,7 is defined as the geometric mean of ri from equation 4.4 for the years 1970 and 1975 for all 85 countries. The extrapolations in Mark 3 were also treated differently and were calculated at a more disaggregated level. The tapes of the U.N. constant-price series for consumption, gross domestic investment, government, and the net foreign balance were used to get real individual components expressed in 1975 international dollars for each of the years between 1950 and 1980. Thus, RGDP, was obtained by summing the components, where the net foreign balance exports and imports in 1975 were converted to dollars at current exchange rates. 81 The new disaggregate procedure insures that the price weights used for consumption, investment, and government in each year in each country reflected 1975 international prices rather than the individual country's relative prices. The imprecision of the RGDP estimates varied considerably from country to country and from year to year. Therefore, the authors classified a countries' estimates into four quality classes: A (best), B (better), C (good), and D (fair). The classifications stemmed from the main source of the imprecisions in the estimation process. First, imprecisions were inherent in the ICP benchmark estimates as qualified in Phase III (Table 3.6). Second, the estimation of the cross- section regression introduced some error. Third, the authors did not know what weights to use in averaging the 1970-derived and 1975 cross-section estimates of r'. The authors find several general relationships with respect to the imprecision of their estimates. The ICP imprecision was inversely correlated with real income; so was the error term in the cross-section regression. Also Ceteris paribus, benchmark countries were rated higher than non- benchmark countries; higher income countries were rated higher than lower income countries; and African countries were rated lower than non-African countries. All of these things should be taken into account when observing the RGDPs. Later, the quality grading of the data will become crucial. 4.4 Mark 4 The fourth paper by Summers and Heston (1988) was basically an update to Mark 3. The new issue in this paper was consistency. Consistency means that the estimates must obey the national income identity that total product equals total income generated by the production of the product. The reason this becomes an issue in Mark 4 was that the discrepancies between Mark 3 and Phase IV were large for the 1980 RGDP per capital estimates. In addition, the ICP closely followed a system called the System of Real National Accounts (SRNA). The basic rule of SRNA was that entries should obey all temporal identities. The identity that is being violated when Phase IV and Mark 3 estimates of RGDP for 1980 do not match is that the value at time period two (t2) equals the value at time period one (t,) times the growth rate between the two time periods. To illustrate this point, consider two countries, A and the U.S. Suppose the 1980 Phase IV RGDP estimate of Country A is 66% of the U.S.'s 1980 RGDP. How could this be resolved if the Phase III 1975 relative RGDP value was 65%, and country A had a 4% growth rate while the U.S. had a 1% growth rate? This is why consistency has to be applied.2 2Stone, Champernowne, and Meade (1942) developed a similar method to make their estimates conform to the national income accounting identity. 83 The implementation of consistency is done via an errors- in-variables model. The objective of this model is to adjust both the benchmark and national accounts data to make them consistent. To continue with the two country example, this model would make the Phase IV estimate equal to the Phase III estimate multiplied by the 1975-1980 growth rate. The likelihood function for this model is (4.6) In L(X,,X2,X3G,G,G2/x1,x2,x3,g1,g2;S)= K 1/2 In C 3 3 -1/2 E Xij, (In xi In X,) (In x In X) I5 5 5 + E E X (n gi.3 In G3) (In g.3 In G,3) 4 4 where the X's are true values of a country's output at a particular level of aggregation (e.g., consumption) expressed in per capital terms and relative to corresponding values for the U.S. for the three time points, t,, t2, and t3. The G's are the true values of the country's growth rates for the same aggregate as the X's, expressed in the same per capital units relative to the U.S. for the (tM, t2) and (t2, t3) periods, respectively. Therefore, the temporal identity requires that X, = X, (G,) and X3 = X2 (G2). The lower-case symbols x,, x2, x3, g,, and g2 stand for estimated values equivalent to their corresponding upper-case letters and are obtained from 84 benchmark studies or the national accounts. The errors-in- variables specification is then x = Xi (vi) i = 1, 2, 3 9g = G, (v4) and g2 = G2 (vS). The five v's are joint random variables with a multivariate lognormal distribution n(0,E ). The a priori information about the relative accuracies of the data sources were introduced through the specification of the entries in E which is the variance-covariance matrix of the v's. The information is parameterized in the form of a five element vector (ki, k2, k3, r,, r2) and an assumed pattern of independence among the v's. The variances among the v's associated with the g's (growth rate v's) were all assumed to be the same and equal to 1. The v's associated with the x's (benchmark v's) were expressed relative to the variances of the growth rate v's and are called k's. The correlation between v, and v2 and also between v, and v3 was given by r,; the correlation between v, and v3, because of the longer time interval, was assumed to equal r2; the correlation between the two growth rate v's was given by r2; and the benchmark and growth rate v's were assumed to be independent. All of these assumptions imply that E has the form x o where k, rAVk r-ikk, EX= k21 l ,= rtick r k, rk3k and 1 r2 r2 1 The Xis in equation 4.6 are just the elements in '-. This maximum likelihood procedure corrects the data sources so that they are consistent. The only problem is that the maximum likelihood asymptotic properties cannot be claimed for this estimation. The reason is that additional parameters are added as more time points were introduced, an estimation problem called the incidental parameter problem (Judge et al. 1980, pp. 543-546). However, it is claimed that the maximum likelihood estimates are of the same variance-minimizing estimates obtained from averaging all possible unbiased point estimates. The data from Phases II, III, and IV and the U.N. constant-price series are made consistent by following the errors-in-variable approach. The non-benchmark countries do not need this. They are just aligned appropriately with the benchmark country estimates. With the consistent data, the 86 1980 RGDP for the benchmark and non-benchmark countries are computed similar to the way they are computed for the base year (1975) in Mark 3. There are a few differences from Mark 3 other than consistency in the manner in which the RGDP's were calculated. Mark 4 drops the openness variable. The exchange rates were too volatile throughout the late 1970's, and the openness variable was no longer significantly related to RGDP by 1980 so it was not used in Mark 4. Dummy variables for Africa were also introduced to allow for divergence. The last adjustment came with the replacement in the equation of exchange rates with a combination of price indexes called the international post-allowance price index. The two indexes that compose the post-allowance index were the International Civil Service Commission index and the Employment Conditions Abroad index. The International Civil Service Commission index is published in the Monthly Bulletin of Statistics of the United Nations Statistical Office and uses New York city as a base. The Employment Conditions Abroad index is an organization based in London with members including multinational firms, governments, and non-profit international agencies. This organization produces a number of binary indexes. The extrapolations forward and backward were accomplished by following the procedures used in Mark 3 precisely. The preciseness of the estimates were also graded A to D using the same standards developed in Mark 3. This was done for 130 87 countries for the years 1950 to 1985. The estimates for RGDP still suffer from large errors for low income countries and African countries. 4.5 Mark 5 The most current paper written updating these data is by Summers and Heston (1991). Their data for RGDP per capital was used in this thesis for analysis. Mark 5 covered 139 countries and RGDP per capital was obtained by extrapolating these cross-section comparisons interspacially to non- benchmark countries and then intertemporally to other years. Mark 5 is arguably the best of the Marks and utilizes ICP data from 4 benchmark years: 1970, 1975, 1980, and 1985. Eighty-one countries participated in these benchmark studies and 47 participated in more than one benchmark study. Thus, 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. Most of all, the methodology for obtaining RGDP per capital for a large number of countries has improved. Hence, all of these factors make Mark 5 the most accurate and most recently published international comparisons data of this type. The four ICP benchmark studies, Phases II V, used in this study were all compiled in different ways and have different countries participating in different years. This is why the data have to be made consistent. Consistency, as discussed in the previous review of Mark 4, is calculated the 88 same way in Mark 5 (using equation 4.6). What needs to be addressed is the benchmark data itself. The biggest problem with the benchmark data was that Phase V had not been published by the time Mark 5 was published.3 Summers and Heston calculated the RGDPs on their own, using only the raw data provided by the U.N. and World Bank. The method used by Summers and Heston to calculate the values in Mark 5 are discussed next. There are three main changes to the Phase IV results for this paper. First, Phase IV introduces the issue of fixity. It should be clear that the 1980 values mentioned here do not use the fixity principle. Instead, the Geary-Khamis method is used for all 60 countries. However, there is an allowance made for supercountry weighting. Second, the 1980 estimates that underlay the Mark 4 estimates were recalculated using national accounts data of May, 1990 which are the latest current national accounts data for the countries. The U.N. in some cases used national accounts data that are available for 1982 or 1983. Third, there was a slightly different treatment of two categories, change in stocks and compensation of government employees. They also used a slightly different normalization procedure which only affects the valuation of the net foreign balance. 3Actually Phase V was never published, instead the U.N. decided to publish regional data (i.e. OECD, EUROSTAT, ECA, ESCAP, and ECIEL) (see Table 3.7). 89 The countries that participate in the 1985 benchmark comparisons fall into five groups: 22 OECD countries, 11 Asian countries including Japan, 22 African countries, 5 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 have data that allow the authors to link them to the OECD and Asian countries. The total number of countries from Phase V used in this study is 57. Once again fixity was not imposed on these results. A different method was used for those countries that did not participate in the 1985 benchmark study, but did participate in a previous benchmark study. The procedure was to value their 1975 or 1980 benchmark estimates of C, I, and G 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 to revise those years. The Geary-Khamis method was then implemented to aggregate the data. 90 After the benchmark data were aggregated, re-estimated, and made consistent, the non-benchmark countries RGDP per capitas were estimated. The same equation used in Mark 4 was also used in Mark 5 with some minor changes. The left hand side variable was r* which was per capital domestic currency DA converted to international dollars expressed relative to the U. S. Mark 4 used a post adjustment index to estimate the real domestic absorption of each country. This estimate was obtained by dividing the national currency DA by the PPP implicit in the post adjustment index. The post allowance index was made up of two indexes for Mark 4 and three for Mark 5. The International Civil Service Commission index (variable ruj) and the Employment Conditions Abroad index (variable rcAj) was used as post adjustment indexes in Mark 4. Mark 5 used both of those indexes and another index produced by the U.S. State Department. The U.S. State Department provides housing or a separate housing allowance indexes (variable rusj). This was an area in which the data were less reliable (including the ICP data). Hence, the added information from this index was used. All of the post allowance indexes were designed to supplement salaries in a way that equalize real incomes of high-ranking civil servants and business executives assigned to different foreign countries. Each of these indexes have shortcomings. The most notable was that all of the countries were not included in any of these indexes. A structural relationship, however, was |

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xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd INGEST IEID EW19RPOLF_R5C82J INGEST_TIME 2011-09-29T19:48:28Z PACKAGE AA00004740_00001 AGREEMENT_INFO ACCOUNT UF PROJECT UFDC FILES CROSS COUNTRY CONVERGENCE OF GROSS DOMESTIC PRODUCTS AND ASSOCIATED FACTORS: A COINTEGRATION APPROACH By DAVE D. WEATHERSPOON 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 1993 ACKNOWLEDGEMENTS First, I would like to thank my wife for her support and encouragement throughout this process. She provided me with the incentives and assistance necessary to complete this degree. I appreciate the standards of excellence expected and portrayed by my parents. The supportive discussions with them as well as my in-laws and siblings made this process somewhat easier. I will always be indebted to my forefathers who stood up for their rights so that people like myself can enter and finish at any higher educational institution in the United States. The many hours of individual attention Dr. James Seale, Jr., provided me during my course of study are much appreciated. I would also like to acknowledge the extra efforts of Dr. Charles Moss in helping me complete this degree. The additional suggestions during the preparation of this dissertation by Dr. Jong-Ying Lee, Dr. Gary Fairchild, Dr. Douglas Waldo, Dr. M. Langham, and Dr. Henri Theil are much appreciated. The financial support as a McKnight Doctoral Fellow from the Florida Endowment Fund for Higher Education made this all possible. The additional financial support by Dr. James Seale, Jr., and Dr. Henri Theil is much appreciated. ii TABLE OF CONTENTS page ACKNOWLEDGEMENTS ii LIST OF TABLES vi LIST OF FIGURES viii ABSTRACT ix CHAPTERS 1 INTRODUCTION 1 2 CONVERGENCE 6 2.1 Overview of Convergence 6 2.2 Historical Evidence 8 2.3 Kuznets-Type Studies 11 2.4 LDC Growth and Poverty 15 2.5 Human Capital 24 2.6 Contemporary Evidence ..... 27 3 THE INTERNATIONAL COMPARISON PROJECT AND ITS' USEFULNESS IN EXAMINING CONVERGENCE 33 3.1 Overview of the Construction of the ICP .... 33 3.2 The Geographic Expansion of the ICP: Phases I to IV 34 3.3 The Data 3 6 3.3.1 The Methodology of Calculating Purchasing Power Parity 40 3.3.2 Country-Product-Dummy Method 41 3.3.3 Elteto-Koves-Szulc Method 42 3.4 Estimating Purchasing Power Parity 46 3.5 The Geary-Khamis Method 52 3.6 Calculating PPP's for Comparison Resistant Goods 55 3.7 Regionalism 56 3.8 Phase III Results Compared with Exchange Rates 59 3.9 Phase IV Further Considered 62 3.9.1 Other Methods Used in Phase IV 63 3.9.2 Linking the Regions of Phase IV 65 4 EXTRAPOLATIONS 70 4.1 The Beginning of Extrapolations with ICP Data 70 4.2 Mark 1 76 4.3 Mark 3 77 4.4 Mark 4 82 4.5 Mark 5 87 4.6 The Centrally Planned Economies 93 5 INEQUALITY IN THE G-7 AND OECD 96 5.1 Inequality Measures 96 5.1.1 Graphical Inequality 96 5.1.2 Inequality Indices 97 5.1.3 Properties of an Inequality Index . . . .100 5.2 Income Inequality in the G-7 102 5.3 Variables of Interest 106 5.3.1 Inequality in Government Expenditure. . .107 5.3.2 Inequality in Investment Expenditure. . .111 5.3.3 Inequality in Industrial Employment . . .113 5.4 Inequality in Selected OECD Countries 114 5.4.1 Income Inequality in the OECD Countries 115 5.4.2 Inequality of Government Expenditure in the OECD 119 5.4.3 Investment Inequality in the OECD . . . .122 5.4.4 OECD Inequality in Industrial Employment 124 5.5 Summary of the Inequality Results 125 6 COINTEGRATION 127 6.1 An Overview of Cointegration 127 6.2 Unit Root Tests 131 6.2.1 Augmented Dickey-Fuller (ADF) Test. . . .132 6.2.2 Phillips Test 137 6.2.3 Unit Root Results 139 6.3 Pairwise Cointegration 141 6.3.1Durban Watson 141 IV 6.3.2 Augmented Dickey-Fuller Cointegration Test 142 6.3.3 Pairwise Cointegration Results 143 6.4 Johansen's Multiple Cointegration Test 146 6.4.1 1(1) Procedure 14 6 6.4.2 1(2) Procedure 154 6.4.3 G-7 Multiple Cointegration Results. . . .161 6.4.4 OECD Multiple Cointegration Results . . .170 6.4.5 Other 7 Multiple Cointegration Results 178 6.5 Summary and Interpretation 182 7 SUMMARY AND CONCLUSION 190 APPENDICES A PRICES PER KILOGRAM OF FRESH VEGETABLES AND ESTIMATED PPP'S IN 10 COUNTRIES FOR 1970 197 B SUPERCOUNTRY WEIGHTING 199 C EKS CALCULATIONS 2 02 D FIXITY 205 E DATA AVAILABILITY 2 07 F EXTRAPOLATIONS OF INDUSTRIAL DATA 209 REFERENCES 211 BIOGRAPHICAL SKETCH 220 v LIST OF TABLES Table page 3.1 Countries Represented in the International Comparison Project 35 3.2 Fresh Vegetables for 4 Countries and Items in 1970 47 3.3 Mini-Laspeyres Price Ratio Matrix 49 3.4 Mini-Fisher Ratios 50 3.5 Transitive PPP's from the EKS Method 51 3.6 GDP Per Capita for 34 Countries in 1975 60 3.7 The Organizations that Performed the Calculations and the Countries Involved in Each Group for Phase IV 64 5.1 Income Per Capita and Income Inequality (G-7 Countries) 103 5.2 Government, Investment, and the Number of People Employed in Industry Inequalities (G-7 Countries) 108 5.3 Investment Expenditure per Capita, and the Rate of Investment Expenditures for the G-7 112 5.4 Income Per Capita and Income Inequality (OECD Countries) 117 5.5 Government, Investment, and the Number of People Employed in Industry Inequalities (OECD Countries) 120 5.6 Investment Expenditure per Capita, and the Rate of Investment Expenditure for the OECD 123 6.1 Unit Root Tests 140 vi 6.2 Pairwise Tests for Cointegration 144 6.3 Johansen's Multiple Cointegration Test 162 6.4 Cointegrating Vectors and Adjustment Coefficients from the G-7 165 6.5 Estimates of Gamma from the G-7 169 6.6 Johansen's Multiple Cointegration Test (OECD) . . . .172 6.7 Cointegrating Vectors and Adjustment Coefficients from the OECD 174 6.8 Estimates of Gamma from the OECD 177 6.9 Johansen's Multiple Cointegration Test (Other 7). . .179 6.10 Summary of Integration and Cointegration Analysis 183 vii LIST OF FIGURES Figure page 6.1 Total Income Inequality for the G-7 133 6.2 Total Government Inequality for the G-7 13 3 6.3 Total Investment Inequality for the G-7 134 6.4 Total Industrial Employment Inequality for the G-7 134 6.5 Total Income Inequality for the G-7 Second Differenced 135 6.6 Total Government Inequality for the G-7 Second Differenced 135 6.7 Total Investment Inequality for the G-7 Second Differenced 136 6.8 Total Industrial Employment Inequality for the G-7 Second Differenced 136 viii 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 CROSS COUNTRY CONVERGENCE OF GROSS DOMESTIC PRODUCTS AND ASSOCIATED FACTORS: A COINTEGRATION APPROACH By Dave D. Weatherspoon December 1993 Chairman: James L. Seale, Jr., Major Department: Food and Resource Economics The convergence of income in the G-7 and selected OECD countries was tested using Theil's inequality (entropy) index between the years of 1950 to 1988. Theil's inequality index was also applied to three potential factors of influence on economic growth. These factors were government expenditure, investment expenditure, and the number of people employed in industry. The financial indicator variables were adjusted for purchasing power parity based on Summers and Heston's 1991 data series. The derivation of this data set is also discussed in this dissertation. The results of the convergence test confirmed that all four inequality indices were declining. This suggested that income, government expenditure, investment expenditure, and industrial employment are converging within the G-7 and within the selected OECD countries. The inequality indices were then tested to determine if they move together over time. Pairwise and multiple cointegration tests were conducted on the inequality indices that were found to be 1(2). In general, there was support for pairwise cointegration of all the variables for the G-7 and the selected OECD countries. Johansen's 1(2) method was used to test multiple cointegration. Multiple cointegration was supported for three of the four variables for the G-7 sample, suggesting that there exists a long-run equilibrium among the inequality in income, investment expenditure, and the number of people employed in industry. The OECD selected sample supported multiple cointegration of all four variables. It was also determined that industrial employment was the primary factor in the sample that adjusts to return the four inequality indices to their long-run equilibrium when innovations occur. The G-7 equilibrium was stable without government expenditure while the OECD sample was stable with government expenditure. This may suggest that the OECD countries excluding the G-7 rely on government expenditures for economic growth and stabilization of their economies. x CHAPTER 1 INTRODUCTION Cross-country economic convergence means that a group of countries are becoming closer in terms of income. This definition is usually operationalized as the faster rate of productivity growth by less productive countries (Barro and Sala-i-Martin, 1992). The result of which is the faster rate of income growth of relatively poor countries than relatively rich countries. Worldwide income growth and the factors that influence this growth have been of interest for quite some time. The interest in the economic welfare of current and future trading partners is one reason why the U.S. in particular is concerned with the area of economic growth and convergence. The literature has supported the idea that the high income countries are converging (Grier and Tullock, 1989 and Goa et al., 1992). However, none of the studies can definitively state the factors in these economies that are causing convergence. Therefore, the objective of this study is to determine a method of measuring convergence, test the method on a group of countries, and determine the factors that influence convergence over time. There are two hypotheses being tested in this dissertation. First, it is hypothesized that the G-7 and the 1 2 selected OECD countries are converging in terms of income.1 Theil's inequality measure is used to test this hypothesis. The second hypothesis is that the inequality of income has a long-run relationship with the inequality of other factors in the economy. The factors considered to influence the convergence of income across countries are the inequalities in government expenditure, investment expenditure, and the number of people employed in industry. This hypothesis is tested by using pairwise cointegration analysis and Johansen's multiple cointegration technique. The G-7 and OECD countries were chosen for this study for several reasons. The most important factor is the availability and the superior quality of their data. The fact that the G-7 and OECD countries are some of the most powerful countries economically in the world also influenced this decision. The growth rate of per capita income for the G-7 and OECD has been sustained at a positive rate for a long time period. In fact, per capita income in both groups increased almost threefold during the 38-year period from 1950 to 1988. These positive growth rates are not considered to be a random process but are believed to be systematically related to other factors in the economy (Grossman and Helpman, 1991). â€˜The G-7 countries are Canada, W. Germany, Italy, Japan, the U.K., the U.S., and France. The selected 14 OECD countries are Austria, Belgium, Denmark, the Netherlands, Norway, Ireland, Spain, and the G-7 countries. 3 This analysis is not the first attempt to associate economic growth and convergence to specific factors in an economy. One of the models that influenced the way economists approached the idea of convergence was put forth by Solow (1956). Solow (1956) and the generalized neoclassical growth model by Brock and Mirman (1972) implied that economies with identical technology and preferences will converge regardless of initial conditions. The driving force in both models was technology. Several empirical studies have shown that the world is not converging in terms of income and only recently have the theoretical models begun to challenge the crossÂ¬ country implications of Solow's model (Romer, 1986; and Lucas, 1989). Another approach was put forth by Kuznets (1955). He approached convergence in an indirect manner by relating personal income to economic development. Specifically, Kuznets' (1955) hypothesis was that income inequality within a country first increased then decreased as development proceeded (divergence-convergence theory). This theory has since been expanded to cross-country analysis where the hypothesis is that countries first diverge then converge in terms of income inequality as development occurs (Wright 1978, Branco and Williamson 1988, and Ram 1988 and 1989a). The cross-country interpretation of Kuznets hypothesis is not directly tested in this dissertation. However, if the G-7 and the OECD countries are found to be converging, then the 4 results may support Kuznets cross-country hypothesis since the Gâ€”7 and OECD countries are developed countries. The literature concerning the convergence or divergence of the countries around the world is discussed in Chapter 2. There are two main reasons why the topic of convergence and economic growth are important. First, the factors that cause convergence or economic growth have not been exclusively identified. Second, the quality of international data have been improved recently. The problem in the past with output and income data from different countries was that international comparisons require the data to be converted to a common currency by using official exchange rates. Official exchange rates do not reflect the relative purchasing powers of different currencies. For example, the official exchange rate does not reflect domestic services since they are not traded internationally (i.e. haircuts, house cleaning, etc.) (Kravis et al. 1975, 1978a, and 1982). Hence, errors are introduced into international comparisons when exchange rates are used. This problem has been addressed and much improved by Summers and Heston (1988 and 1991). They developed a data series that is based bn purchasing power parity. This data set along with others are used to test the hypotheses stated above. The format of this dissertation is as follows. Chapter 2 includes a literature review on convergence while Chapters 5 3 and 4 include a discussion on the methodology used to calculate gross domestic product without using exchange rates. Specifically, the international comparison project (ICP) methodology is addressed in Chapter 3. Then the data series by Summers and Heston, which is based on the ICP, is addressed. The convergence of income, government expenditure, investment expenditure, and the number of people employed in industry is tested using Theil's inequality index in Chapter 5. Theil's decomposable index allows one to determine which countries are driving the convergence. Then, these four inequality indices are tested for cointegration using pairwise cointegration and Johansen's 1(2) multiple cointegration test in Chapter 6. This method determines if there exists a long- run equilibrium among the four indices. If the series are cointegrated, then the four inequality indices cannot drift apart in the long-run given that there are no structural changes. Chapter 7 presents the summary and conclusion of this dissertation. CHAPTER 2 CONVERGENCE 2.1 Overview of Convergence The meaning of cross-country convergence in its simplest form is that the income level of countries are becoming closer. To get this result the less productive countries must increase their productivity growth rate at a faster rate than the more productive countries (Barro and Sala-i-Martin, 1992) . The result is that income grows at a faster rate in relatively poor countries than in relatively rich countries. There has been an interest in reducing the income gap (convergence) between the developed countries (DCs) and the lesser developed countries (LDCs) for some time (Berry et al., 1991). The Pearson Commission (1969) was set up to address the income gap problem. Specifically, the commission was to identify ways to reduce the income gap between the developed and the developing countries (Berry et al., 1991). Kuznets (1955) influenced many researchers to explore convergence through his hypothesis. Kuznets' hypothesis (also known as the divergence-convergence theory) basically states that income inequality within a country increases in the early stages of economic development, stabilizes at some peak level, then declines as the latter stages of development occur. 6 7 Kuznets was writing about a single country; however, this hypothesis was quickly expanded to address international development. Many studies attempt to directly and indirectly prove or disprove Kuznets' hypothesis with income inequality measures (Wright, 1978; Branco and Williamson, 1988; Ram, 1988, 1989a) or with regression analysis (Grier and Tullock, 1989; Barro, 1991; Barro and Sali-i-Martin, 1992; and Baradaran-Shoraka, 1992). However, the results of all of these studies have been inconclusive. Three observations about economic growth in the world economy frame the phenomenon examined in this study. First, the growth of per capita income has been sustained at a positive rate for many countries for a long time period. Second, the performance of countries has varied across countries and time. These two observations lead to the conjecture that growth in income is not a random process. They are believed to be systematically related to other factors in the economy (Grossman and Helpman, 1991). The third observation deals with the ability to study the growth patterns around the world. Convergence of the world cannot be thoroughly studied over long periods of time due to data constraints. However, there are data available for many countries starting in the 1950s. These data are largely due to the efforts of Summers and Heston (1991) who developed a time-series for several economic indicators for most of the 8 world for the years 1950 through 1988.1 In the studies mentioned above, the data of Summers and Heston as well as other sources are used to analyze convergence from a historical point of view. The international comparison studies conducted prior to this data set were misspecified due to the use of exchange rates (Kravis et al. 1975, 1978a, and 1982). There have been two main approaches to studying convergence, inequality measures and regression analysis.2 The review of the studies that follow represent both approaches. The first section covers studies that analyze what happened in the past. 2.2 Historical Evidence Machinery investment and productivity growth have been strongly associated over the past century in countries where adequate data exist (Canada, Germany, Italy, Japan, the United Kingdom, and the United States). In the recent past, the same association holds for more countries (De Long, 1992) . The real question is whether high machinery investment causes rapid growth? Baumol (1986) showed that industrialized market economies supported convergence using data from 1870 to 1979 (the data â€˜The development of the Summers and Heston data series is discussed in the next two chapters. 2A summary of the inequality measures is given in Chapter 5. 9 are not time-series) . Baumol analyzed the G-7 countries along with Australia for this time period. To extend his analysis to a larger number of countries, he used the Summers and Heston data from 1950 to 80. In this data set, the variable used was output per capita. The results showed that convergence is not supported when LDCs are included in the analysis. The results of a similar study conducted by Dollar and Wolff (1988) supported Baumol's 1986 results of convergence. In a follow up article criticizing Baumol's (1986) findings, De Long (1988) showed that Baumol's study was flawed. He commented that Baumol only used successful countries (selection bias). In response to De Long's article, Baumol and Wolff (1988) admitted to data mining in previous studies. When they re-examined the results, it appeared that a small group of countries began to converge in 1860. Since then, more countries have joined the group according to Baumol. De Long (1992) reviewed the issue of productivity growth and machinery investment similar to that done by Baumol. De Long studied six countries (Canada, Germany, Italy, Japan, the United Kingdom, and the United States) from 1870 to 1980, and then a large number of countries on all six continents from 1950 to 1980. He divided up his study into 15 year periods to offset any cycles and the effects of wars. This study showed a strong positive relationship between growth and machinery 10 investment. He cautions that these countries are all wealthy and that the regression may have captured "luck" instead of the intended relationship. The results may have been different if more countries were included. In addition, De Long examined the effects that political stability and investment in education had on growth. All of the countries sampled had been stable politically and had invested heavily in education. He also argued that just the presence of high tech machinery may have provided a higher level of education. In testing these relationships, he found little evidence supporting the education or political stability influence on growth. De Long (1992) concluded that when a broader group of countries is considered, there is little evidence of convergence in the short-run, and in the long-run, the regressions may not be accurate. Alam (1992), however, cautions that De Long needed to use other variables to indicate productivity. Hanson (1988) examined the convergence of LDCs before World War I. This study is interesting for two reasons. First, historical studies of this type conducted on LDCs are rare. Second, the long period of analysis from 1913 to 1980 is impressive. Hanson corrected the historical data by extrapolating Summers and Heston's (1984) data backwards and combining other data sets. He also compared other data sets to that of Summers and Heston. Unfortunately, his results were inconclusive. 11 To summarize, there appears to be a long-run relationship between investment in machinery and growth. The only countries that appear to be converging are a few industrialized countries. The LDCs appear to be caught in a circle of poverty (Alam and Naseer, 1992). It is clear that human capital is considered an important variable with respect to growth, and that the relationship may be that higher equipment investment drives faster growth (Adams, 1990; De Long and Summers, 1991). 2.3 Kuznets-Type Studies As mentioned before, Kuznets hypothesized (divergence- convergence theory) that income inequality increases in the early stages of economic development, stabilizes at some peak level, then declines as the latter stages of development occur. A few of the many studies that have tested this hypothesis in the international context using various methods are discussed next. It will become clear that there are no definite answers as to whether Kuznets' hypothesis is indeed correct. Wright (1978) analyzed whether the institutionalist or Kuznets' hypothesis was correct. The institutionalist hypothesis states that institutional structures and governmental policies are the chief determinants of income inequality. Wright conducted his analysis using a Gini coefficient inequality measure. He calculated the income inequality of the GDP per capita for 56 countries. He 12 concluded that the data did not support Kuznets' hypothesis. Instead, he found that the level of inequality was higher in the LDCs than the developed countries. Wright concluded that his results supported the institutionalist hypothesis. Hence, the reduction of income inequality among countries is dependent on modifications of institutions and policies. Ram (1989a) extends Kuznets' hypothesis to the world system. He hypothesizes that intercountry (world) inequality across sovereign nation states would first increase with secular economic growth, then start to decline at some point. He tested this hypothesis using 115 market economies for the years 1960 to 1980 from the Summers and Heston 1984 data set. Average (per capita) world GDP was used as a proxy for the level of development and Theil's income inequality (J) measure was used to analyze the inequality (see Section 5.1.2 for Theil's 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 (2.1) J, = B0 + B, LRYt + B2 (LRYt)2 + ut where J is the measure of the world inequality and LRY is the natural logarithm of the average real GDP per capita. The last term is the disturbance term with the standard properties (zero mean and a constant variance) . He found that world income inequality has increased since 1960. However, the rate 13 of increase has slowed. The regression results supported the hypothesis that world inequality may first increase and then decline with world economic growth. Hence, Ram's study supports the idea of divergence then convergence of real GDP worldwide. A partial contrast of the above results is provided by Ram in 1988. In this paper, Ram (1988) tests Kuznets' hypothesis for 32 counties, 8 developed countries and 24 LDCs. The estimated equation in this paper is the same as the one used in his 1989a paper. Ram (1988) finds support for Kuznets' hypothesis when all of the countries are present. However, when only the LDCs are present, the results do not support Kuznets' hypothesis. 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 the nation's population in 1970 divided by 40% of the 1970 population, then multiplied by the real GDP per capita of a nation in 1970 (Summers and Heston, 1984 data set). Bronco and Williamson (1988) felt that this dependent variable portrayed the situation of the poorest 40% in different countries. The independent variable was the energy consumption per capita in 1970 (measured in kilograms of coal equivalents). This variable is supposedly a better indicator 14 of industrial development across nations than GNP per capita. They estimated linear, quadratic, logarithmic, and log quadratic models to determine the best fit and also to prove or disprove Kuznets' hypothesis. Their results supported Kuznets hypothesis. Therefore, the countries are expected to diverge, then converge in terms of income as development occurs. Bornschier (1983) reinterpreted Kuznets' theory by combining two paradigms of world economy and the level of development. Briefly, the world development paradigm is the core-periphery division of labor, which has come about due to multinational corporations. The core specializes in control over capital, technology, innovation processes, and the production of the most advanced products, which embodies the most human capital. The periphery is engaged in standardized and routine industrial production for domestic or maybe world markets. In a sense the multinational corporations have created a world division of labor. The core countries are basically the industrial countries, and the periphery are the countries with the raw materials.3 The level of development paradigm is basically Kuznets' hypothesis. Both of these paradigms have different ideas on how development takes place. Bornschier (1983) combined the two approaches with the following deviations from the original hypotheses: the 3For a more detailed explanation of this theory see Amin, 1974, pp. 559-587. 15 countries on the periphery, which were still considered agrarian based, had the most income inequality; the countries that assumed less importance for agrarian production had lower inequality; and the core countries within the world economy had the lowest income inequality. He showed that developing countries did not automatically decrease their income inequality with increased development. In addition, the reduction of inequality was found to be dependent on the type of production (services, agriculture, and industry) in which they were involved. Several of the studies supported the divergence- convergence theory (Kuznets' hypothesis) and others did not. The studies that included the LDCs were also contradictory. In the study by Bornschier (1983), the author implied that the type of development countries pursued affected the reduction in income inequality. He indicated that if a country has less emphasis on agrarian development, then that country is expected to converge faster than a country that promotes agricultural development. This may or may not be the actual case, but it introduces the idea of what has happened within the LDCs. 2.4 LDC Growth and Poverty Morawetz (1977) addressed the issue of growth in chapter 2 of his book entitled "Twenty-Five Years of Economic Development 1950 to 1975." The questions he posed were: "How rapidly were GNP per capita and population expected to grow in 16 1950, and how has their actual growth compared with these expectations." He commenced by stating that the status of development in Africa, Asia, and Latin America was not considered before 1950. The reason for this was that the industrialized countries were just getting over the war, and were still concerned with reconstruction in Europe. The few researchers who thought about the economic development of the LDCs had no hope for their short and medium term future. The industrialized countries only attained 2% growth (per capita) on average during that period. Therefore, the developing countries were not expected to perform as well as the industrialized countries. In addition, it was perceived that the population growth in the developing countries was high while their GNP growth was low. Morawetz stated that no statistical work had been done on the LDCs. Hence, he conducted a statistical analysis on the LDCs to determine their economic growth status. His results indicated that the disparity between the rich and poor developing countries had increased significantly between 1950 to 1975. However, at the aggregate level, it was not true that the richest of the developing countries were getting richer and the poor were getting poorer. When the developing countries regional averages of income per capita in 1950 were examined, the richest regions (Latin America and the Middle East) had grown five to six times faster than the poorest region (South Asia) . By 1975 this gap had increased to 13 17 times for the Middle East and seven times faster for Latin America than South Asia. When the LDCs were compared to the developed countries, it was shown that China, East Asia and the Middle East narrowed the gap, while the gap was widened for South Asia, Africa, and Latin America. However, the ranking of 80 individual developing countries remained stable from 1950 to 1975. Morawetz (1977) regressed 16 indexes of basic needs on GNP per capita growth to get a better understanding of how the change in relative GNP per capita affected poverty. Morawetz used 16 different regression equations to analyze the problem. The factors that were found to be significantly related to GNP per capita growth were three nutrition indicators, infant mortality, and the percentage of dwellings with access to electricity. Some of the other variables that were included in the analysis but were not significantly related to the growth in GNP per capita were four indicators for education: adult literacy rate, primary school enrollment ratio, secondary school enrollment ratio, and vocational school enrollments as a percent of secondary school enrollments. Another study on the LDCs was conducted by Zind (1991). He tried to determine if the LDCs were converging in terms of income, and assess the key variables that influenced convergence such as government policies, population growth, and investment levels. The Summers and Heston 1984 (1960-80) data set was used for the comparison of 89 LDCs. His test was 18 a simple regression of real income per capita annual growth rate against per capita income in 1960. In his model a negative coefficient indicated convergence. When all of the countries were included, there was no evidence of convergence. Reducing the number of countries to 30, results indicated convergence at the 10% level; reducing the countries further to 19 yielded convergence at the 5% level. These 19 countries were the most developed countries in the LDC sample. In addition, he found that the other variables (the relative size of government, population growth and investment level), contributed to convergence in the most developed countries. Dollar (1992) basically answered the question of how the slowest growing countries in the LDC category could increase their growth. Asian (16 countries) LDCs grew at an average rate of 3.4%, while this occurred at 0.4% in Africa (43 countries), and only 0.3% in Latin America (24 countries) (Dollar, 1992). Using the data of Summers and Heston (1984), he showed that outward oriented countries had lower prices than inward oriented countries.4 He believes that the price level was a reflection of the protectionist policies in the different countries. The Asian countries had the lowest price levels, followed by Latin America and Africa. He also considered the variation in exchange rates where the Asian countries had the lowest variation. He created an index of 4Inward oriented countries are countries that have protectionist trade policies. Outward oriented countries are countries that have relatively open trade policies. 19 outward orientation based on the variation of the exchange rate. This index was found to be highly correlated with per capita GDP growth. He concluded that Africa and Latin America could increase their growth through trade liberalization, devaluation of their real exchange rates, and by maintaining a stable exchange rate. Berry et al. (1991) conducted an extensive analysis on world income inequality. They analyzed over 100 countries from the time period of 1950 to 1977. The data came from World Bank Tables, World Bank Atlas, World Development Report, and the Summers and Heston data set. Their objective was to determine what had happened to income inequality in the world. They applied Theil's entropy, Atkinson's inequality, and the Gini coefficient measure (see Chapter 5 for definitions of these inequality indices). The uniqueness of this study was that they applied these inequality measures to gross national product (GNP) and consumption measured as a percentage of GNP to determine changes in welfare. The idea behind using the inequality of consumption was that the distribution of consumption was less unequal than that for income for two reasons. First, the savings rate was below average in many of the poorer countries. Second, the intracountry distribution of consumption was generally less unequal than the income distribution. Berry et al. (1991) attributed this to the fact that the marginal propensities to consume fall with income and that high income families do most 20 of the saving. The fact that the savings rate was lower than average in the poorer countries contributes more to worldwide inequality than the second reason, regardless of whether income or consumption was used. They conducted the analysis with and without the non- market economies for which the data were considered to be inaccurate (Berry et al.f 1991; Summers and Heston, 1991). The results of their study showed that the 1950s and early 1960s were stable around the world in terms of income. Between 1964 and 1972 there was a large increase in world inequality, which gradually continued to increase until 1986.5 The consumption ratio also indicated a worsening of inequality from 1950 to 1986. The other unique aspect of this paper was that they broke the world's inequality into deciles. Using this method they were able to show that the bottom half of the world's population income shares remained unchanged, while the top decile gained at the expense of the sixth, seventh, and eighth decile. In addition, the middle deciles gained in the 1950s and 1960s, only to lose it in the 1970s and 1980s. During this time period, the richest two deciles increased their share of world consumption from 68.5% to 71.6% at the expense of the seven lowest deciles. 5They initially stated that this study was from 1950 - 1977. That is the case for their analysis which includes the communist countries. After 1977, they were not able to get adequate data for the communist countries; hence, they left them out of the analysis from 1950 - 86. 21 The change in inequality in the 1980s was due to slow growth particularly among the low income countries which had zero growth during the period of 1980 to 1985. Most of these countries were in sub-Saharan Africa. Some of the contributing reasons were the agriculture and debt crisis, and the rapid population growth.6 The middle-income countries were not as progressive in terms of economic growth with the industrialized countries, while the average income of the less developed countries (LDCs) increased. The South Asian countries (India, Pakistan, Bangladesh, Sri Lanka, and Nepal) on the other hand grew faster between 1980 and 1985 than between 1965 and 1980. The fastest growth occurred in the newly industrialized countries and the OPEC countries. However, their presence did not reduce inequality much because of the relatively small population. In general, the population has grown faster in the poor and middle-income countries than in the rich ones. Berry et al. (1991) suggest that the slow economic growth and the population boom in the poorest countries had increased the absolute number of poor around the world (income below $200 U.S. 1970 dollars). However, to give a full picture, the share of the total population that was considered poor had decreased. The results of Berry et al. about the poverty line can be disputed. Atkinson (1987) examined the issue of measuring 6Theil's entropy measure is sensitive to population changes. An increase in population increases the inequality measure if income is held constant. 22 poverty. Specifically, he researched the poverty line, indexes on poverty, and the relationship between poverty and inequality. The choice of the poverty level could influence the results on whether countries were becoming closer in terms of the absolute number of people in poverty. However, the choice of the poverty line would have no effect on the income inequality measures. Ahluwalia et al. (1979) made some predictions concerning the future. Their approach to studying growth and poverty in the LDCs was threefold. First, they estimated the absolute poverty in the developing countries and the relationship between income distribution and the rising levels of output. Second, an analysis of the past trends in growth and poverty for certain countries was conducted, the results of which were projected into the future based on the policies at that time. Lastly, the changes in poverty were considered when income growth was accelerated, the distribution of income was improved, and the reduction of fertility was implemented. This analysis was based on 36 countries, all of which were LDC market economies. These countries GDPs per capita were adjusted for purchasing power parity using what was referred to as the Kravis adjustment factor.7 Ahlualia et al. (1979) used Theil's inequality index to analyze the trends in inequality and poverty from 1960 to 1975 7The Kravis adjustment factor was an attempt by Ahlualia et al. to adjust the data for purchasing power parity estimates by Kravis et al. 1975 and 1978a. 23 among the LDCs. The results indicated that the inequality among the LDCs increased during this period. In addition, they projected the inequality level to the year 2000. They expect the income inequality to increase from .67 in 1975 to .77 in the year 2000. The reason for the divergence will increasingly be due to the wider distribution of income among the countries (from 37% to 50% respectively).8 They predict that India and Bangladesh will have higher growth than the other LDCs. Therefore, a large percent of the increase in inequality in the LDCs will be due to the economic events in India and Bangladesh. The worsening of the internal distribution of income is what Ahlualia et al. (1979) attributed to the lack of growth in the poorest of the LDCs. The middle group of LDCs are not expected by these authors to reduce their inequality. A listing of the poorest LDCs and middle LDCs is presented in Ahluwalia et al. (1979). They expect the relative level of poverty to decrease and the absolute level of poverty in the year 2000 to be 600 million. The studies in this section clearly state that the LDCs are diverging instead of converging. There were several reasons given for their slow growth: debt crisis, population â€œincome inequality increases if the income of the different countries continue to grow further apart. That is the case with India and Bangladesh. They are increasing the inequality because they continue to grow faster than the other DCs. Hence, creating a greater dispersion (increasing inequality). 24 growth, agricultural based economies, and restrictive trade. Two variables that have been related to convergence in the other two sections were also found to influence convergence in the LDCs: government expenditure and investment. 2.5 Human Capital The effect of human capital on economic growth is uncertain. Human capital in this text is considered to be a set of specialized skills that agents can acquire by devoting time to schooling or special training (Grossman and Helpman, 1991). The more training an individual receives the more human capital that individual acquires. Human capital has become more important in the literature recently. The endogenous growth models show that increasing returns are possible with a constant return to scale model if human capital is included (Romer, 1990). In contrast, the older exogenous growth models assumed that growth is attributed to exogenous technological change (Solow, 1956). The key to endogenous growth models is the idea of learning by doing. Romer (1990) showed that the rate of growth and technology was a function of total human capital in an economy. The initial human capital level affects the rate of growth in the different countries. Romer's approach led to the suggestion that countries will diverge. Unlike Romer, Lucas (1988) mathematically showed that human capital has spillover effects which drive growth (unbounded growth). However, his conclusion was that there will be no convergence 25 or divergence, but that countries will grow uniformly. Grossman and Helpman (1991) agree with Lucas; however, they assume that a finite population can only accumulate a bounded quantity of human capital. Glomm and Ravikumar (1992) examined the implications of public investment in human capital on growth and the evolution of income inequality. Using an overlapping generations model, they showed that public education reduced income inequality faster than private education. However, private education yielded higher per capita incomes except when the initial income inequality was sufficiently large. The main objective in the study reported by Ram (1989b) was to explain the role of schooling in reducing income inequality and poverty in LDCs. The first part of Ram's paper reviewed past literature on this subject. The review of literature as cited by Ram (1989b) showed the following: Chiswick (1971, 1974) found that income inequality was reduced as educational inequality was reduced (based on nine countries); Chiswick and Mincer (1972) found that in the U.S., inequality in schooling did influence income inequality, even though it had a minimal affect; Adelman and Morris (1973), Chenery and Syrquim (1975), and Ahluwalia (1976) showed that for 43 developing countries, 55 LDCs and 60 various countries, respectively, education reduced income inequality. Contradictory later findings were also cited. These were the 26 work of Fields (1980) , Psacharopoulos and Woodhall (1985) , and Morrison (1987). The above literature was puzzling to Ram. Hence, he used the data from Psacharopoulos and Arriagada (1986) and Summers and Heston (1984) for his analysis. His income inequality variable was a Gini coefficient, and the independent variable was mean education level of the labor force. He found little evidence that the education level affected income inequality, even for the LDCs. Ram concluded that based on both empirical evidence and theory, the effects of education on income inequality were ambiguous. Problems with the data (e.g. inconsistency or missing information) may have affected the ability to effectively test the relationship between educational inequality and income inequality. Barro (1991) and Baradaran-Shoraka (1992) did empirical studies on the effect of human capital on growth. Barro used several proxies for human capital: secondary school enrollment in the year of 1960 and 1985, primary school enrollment in the year of 1960 and 1985, and adult literacy in the year of 1960. The data were pooled for this analysis. Therefore, there were no time-series implications from the model. The only significant relationship he found was the positive relationship between the average growth rate and the I960 school enrollment. Baradaran-Shoraka (1992) using the same variable as Barro found the same result which supported Romer's argument. 27 Baradaran-Shoraka (1992) went one step further to create an education data set that had four data points, which supposedly included mean years of schooling of the total population aged 25 years and older, and years of schooling for young workers for the period of 1969 to 1985. His results indicated that the variable for human capital was positively and significantly related to growth, which again supported Romer's argument. It must be noted, however, that Baradaran-Shoraka was only able to conduct this analysis for 50 countries due to data limitations. The theoretical arguments put forth about the relationship between convergence and education are inconclusive. In addition, the empirical studies are also inconclusive. The small data sample appears to be the major limiting factor. 2.6 Contemporary Evidence The first contemporary study reviewed here was done by Theil. Theil (1989) conducted a study from 1960 to 1985 using the Summers and Heston 1988 data set. Theil's entropy index was used to measure the inequality among the North, South, and the Tropical Middle (Tropical America, Asia, and Africa).9 This analysis was based solely on non-Communist countries. Theil noted that the population has decreased in the North and the South while it has increased dramatically in the tropical 9See Theil (1989) for details of the breakdown of the country categories. 28 middle countries. The ranking of real GDP places the regions in descending order as stated above. The results showed that world income inequality has increased over the 25 years. Using the decomposability of his index, he showed that 80% of the world inequality was due to inter-regional inequality.10 It has also been shown that the inequality within the North started with the most inequality and decreased dramatically by 1985. The South's within inequality fluctuated, but stayed relatively low while Tropical America's was relatively low and continued to decrease. Tropical Asia started out high and increased its inequality while Tropical Africa started out the second lowest in inequality and ended with the highest inequality. Tropical Africa's inequality increased approximately three times while the North almost halved its inequality; These results showed- that the world is not converging. However, there are some regions of the world which are converging, the North and Tropical America. Grier and Tullock (1989) investigated postwar economic growth for 113 countries from 1950 to 1981. The 1984 data set of Summers and Heston was used in this study. They averaged the data for every five years and pooled the data into OECD countries and the rest of the world (ROW). This decision was made after tests confirmed that the OECD countries and ROW should not be pooled. They regressed their five year average 10For a discussion on the decomposability of Theil's index see Chapter 5. 29 growth in real GDP against the following variables: initial real GDP, government as a percent of real GDP, population growth, standard deviation of real GDP as a percent, inflation, and the standard deviation for inflation. Convergence was supported only in the OECD sample. There was no evidence to support the idea that Africa, Asia, and the Americas are converging. The variable that was significantly related to the average five year growth was government. This relationship was negative for all regions except Asia. Barro (1991) used a simple multiple regression technique to analyze the convergence of 98 countries from 1960 to 1985, and the factors that influenced it. He regressed the average growth rate from 1960 to 1985 on several independent variables: real GDP in 1960, and 1970; square root of real GDP in 1960; secondary school enrollment in 1950, and 1960; primary school enrollment in 1950, and 1960; average government expenditure between 1970 and 1985 as a percent of real GDP; number of revolutions and coups per year; number of assignations per million population per year; and the magnitude of the deviation of 1960 purchasing power parity value for the investment deflator. He also ran regressions using fertility as a dependent variable on some of the independent variables. The last regression was run with investment as the dependent variable. The results from this set of regressions, 29 in all, indicated that a few variables were significantly related to 30 growth. The starting point of human capital was shown to be positively related to growth. This suggested that poor countries with high human capital per person would eventually converge with rich countries in terms of real GDP. The second relationship was a negative one with government. This was interpreted by Barro (1991) as the distortions governmental policies (high taxes) introduce and offset private investment growth. Lastly, the political instability was negatively related to growth and investment. The more unstable a country is politically, the less investment and growth are likely to occur. In support of Barro's findings, Baradaran-Shoraka (1992) conducted a similar study with a few of the variables measured differently and found the same results as Barro. Barro and Sala-i-Martin (1992) also conducted a similar study to Barro's 1991 study. In this study they used a neoclassical growth model to analyze the convergence of 98 market economies from 1960 to 1985 (data set of Summers and Heston, 1988). They were trying to test B convergence which is a term that Barro defined as countries converging in terms of income over time.11 In this model, the log change in GDP per capita (growth rate) was used as its dependent variable. A description of the rest of the eguation was detailed, intricate and well illustrated in Barro and Sala-i-Martin (1992) . The independent variables were a constant and the log â€œThe other type of convergence Barro defines is a convergence. This type of convergence refers to the dispersion in income across countries reducing over time. 31 of 1960 per capita GDP. Analysis showed that there was little to no relationship between the growth rate and the log of 1960 per capita GDP. This finding indicated that the initially rich countries grew at a faster rate than the poor countries (divergence). However, the first part of their analysis was conducted on just the U.S. states, where they found convergence taking place. Barro and Sala-i-Martin (1992) extended their analysis to include primary and secondary school enrollment rates in 1960, the average ratio of government consumption expenditure to GDP, proxies for political stability, and a measure of market distortions based on purchasing power parity ratios for investment goods. When this was done, the model indicated convergence conditionally. This meant that to get convergence, the following variables had to held constant: initial school enrollment and the ratio of government consumption to GDP. In this section, the income inequality studies indicated that world divergence was taking place, but some regions were converging (the North and Tropical America). The growth studies also showed divergence in the world. However, the OECD countries were found to be converging. In addition, several other variables were found to be significantly related to growth: government expenditure, human capital (education), and political instability. In the next two chapters the development of the Summers and Heston data series on which 32 most of the studies in this section based their analysis will be discussed. CHAPTER 3 THE INTERNATIONAL COMPARISON PROJECT AND IT'S USEFULNESS IN EXAMINING CONVERGENCE 3.1 Overview of the Construction of the ICP The objective of the International Comparison Project (ICP) was to establish a system of comparisons of real product and purchasing power for a large number of countries. The reason for this is that it was realized that the use of exchange rates to conduct international comparisons introduced errors into the analysis. For example, a 1954 study by Gilbert and Kravis found that $1000 in US currency, when converted to sterling at the official exchange rate, bought a basket of U.K. goods 64% larger than the $1000 could have purchased in the United States. This problem was recognized by the Statistical Commission of the United Nations. The issue was discussed in 1965, at the United Nations' thirteenth session, and it was concluded that using exchange rates for currency conversion was inadequate for many uses of international data (U.N. Statistical Commission, 1965). The United Nations and the University of Pennsylvania started the "International Comparisons Project" in 1968. Initial funding came from the World Bank, Ford Foundation, some of the countries involved in 33 34 the first set of data collection, U.S. Agency for International Development, and the U.S. Social Science Research Council. Kravis et al. (1975) published the first results of these efforts which is referred to as Phase I. In this seminal attempt, the methodology developed is presented, and actual comparisons are made for several countries. Since Phase I, several other successive Phases have been published. Each successive Phase increased the number of countries and refined the methodology for calculating gross domestic product for each country. The countries involved in the first four Phases are discussed in the next section. 3.2 The Geographic Expansion of the ICP: Phases I to IV Phase I of the international comparison project (ICP) began with a pilot study in 1967 (which included data collection for six countries) and included data collection for 10 countries for 1970. The project was initiated by Irving Kravis, ZoltÃ¡n Kenessey, Alan Heston, and Robert Summers, all at the University of Pennsylvania, and their results in 1975. The countries included in 1970 are shown at the top of Table 3.1. These authors later published two successive volumes, 1978a and 1982, referred to as Phases II and III, respectively. Phase II added six new countries to the ICP. These are listed in Table 3.1 under countries added in Phase II. Phase II provides data for 1970 and 1973, but much of the 35 Table 3.1 Countries Represented in the International Comparisons Project Africa America Asia Europe Countries represented in Phase I Kenya Columbia India France United States Japan U. Germany Hungary Italy United Kingdom Comtries added in Phase II I ran Belgium S. Korea Netherlands Malaysia Philippines Comtries added in 1 Phase III Malawi Brazil Pakistan Austria Zambia Jamaica Sri Lanka Denmark Mexico Syria Ireland Uruguay Thai land Luxembourg Poland Romania Spain " ' Â»r! . * *. â€¢ ' . ' â€¢ * â€¢ *: - â€˜r * ^ Yugoslavia Comtries added in Phase IV Botswana Argentina Hong Kong Finland Cameroon Bolivia Indones i a Greece Ethiopia Canada Israel Norway Ivory Coast Chi le Portugal Madagascar Costa Rica Mali Dominican Rep. Morocco Ecuador Nigeria El Salvador Senegal Guatemala Tanzania Honduras Tunisia Panama Zimbabwe Paraguay Peru Venezuela Comtries deleted in Phase IV Jamaica I ran Romania Mexico Malaysia Syria Thai land Source: Theil et al. 1989, p~. 27 36 1973 data were based on extrapolations; hence 1970 will be the main focus. Phase II also made corrections on Phase I data; hence Phase II has the most accurate data for 1970. Phase III added 18 countries which are reported in Table 3.1 under countries added in Phase III. The data are for 1975. Phase IV results were published in two different volumes (United Nations, 1985 and 1987). Phase IV is different from the previous three phases in two ways. First, the study was completed by the Statistical Office of the United Nations Secretariat, and 33 countries were added in this Phase (see Table 3.1, countries added in Phase IV). Second, there are seven countries that participated in Phase III that withdrew in Phase IV. These countries are also reported in Table 3.1 under Countries deleted in Phase IV. This makes the total number of participating countries in Phase IV equal to 60. In Phases I, II, III, and IV, we have 10, 16, 34, and 60 participating countries, respectively. In Phase IV (including the seven deleted countries), there are 15 countries in Africa, 20 in the America's, 13 in Asia, and 19 in Europe. In all of these countries detailed data were collected. The type of data and the method in which they were collected follows. 3.3 The Data There are two main steps to obtaining the type of data the ICP needed. First, a classification system was developed for gross domestic product (GDP) so that each countries GDP could be divided into detailed categories. After the detailed 37 categories were defined, GDP data were collected at the detailed category level, prices for each item within the detailed categories, and guantity data for the items which price data could not be obtained. The classification system follows the scheme proposed by the system of national accounts (SNA). Some improvements were made to this classification system to enhance the international comparability of the data (Kravis et al. 1975, p. 26). The format the ICP settled on for phases I and II was a total of 153 detailed categories, 110 for consumption, 38 for capital formation, and five for government. Phases III and IV have 151 detailed categories, 108 for consumption, 38 for capital formation, and five for government.1 Once the classification system was determined the next issue was the collection of the data. There were three categories of data used; GDP or expenditure data for the detailed categories, price data for each item for which a price could be identified, and quantity data for those items for which price data could not be collected. The collection of the expenditure data was simple: the data were taken from the U.N. national accounts data. Therefore, expenditure data are not discussed in detail here but the price and quantity data collection are. 'in Phase IV, the European countries had more detailed categories than the 151 categories and the African countries had less. However, the systems were similar making it possible to use the 151 detailed category system. 38 Accurate price data were very difficult to obtain for each item, within every category, in each country. The difficulty was that some items are not found in every country, and if found in all of the countries, matching the qualities of the item was complex. To ensure that the items specified were the same, the U.N. sent price specialists to the different countries to directly compare the qualities of the items in question. An example of the specifications used by the ICP was: fresh chicken eggs, size large (weighing at least 680.4 grams per dozen), white or brown shell, not of the best quality, but close to it. The less than best quality's white is less thick and higher than the best quality. The best qualities yolk must be firm, high, and not easily broken (Kravis et al. 1982, p. 38). In this example of the egg specifications, . it -can - -be >â€¢assumed- that, if - these specifications were met in any country, the quality is the same for those countries. For most of the food groups, the specifications were met. As mentioned before the U.N. sends price experts to resolve questions about matching qualities. For example, the visits helped clear up misunderstandings from the use of different terminology. In Japan, "cashmere" refers to a weave rather than yarn, as in the U.S. and Europe. In England, "ox liver" is used rather than "beef liver," the American terminology (Kravis et al. 1982, p. 38). These types of goods 39 were referred to as narrowly defined goods. They could be classified by their characteristics and uses. Non-narrowly defined goods are the items for which prices cannot be collected in a systematic way in all of the countries. For these items quantity data were collected. These items were called comparison-resistant goods. Comparison-resistant goods are goods and services that cannot be put into a category based on their characteristics. Some examples of comparison-resistant goods are services rendered by teachers, physicians, and the government. Dissimilar to most commodities, services constitute a heterogeneous collection of final products, and the production of each is necessarily simultaneous with its consumption; consequently, no service can be stocked. For example, to compare teachers and physicians around the world is difficult. The problem is how can the quality and productivity of a teacher or physicians be measured. However, indicators of quality and productivity can be obtained. For example, these indicators for teaching services would include the level of education, average income, number of students in a classroom, or the amount of educational inputs available to and used by the teacher. For doctor's services, the number of patients seen or the number of operations in a day may be indicators of their quality and productivity. Government services are also hard to measure. The amount of capital available to the worker may help indicate their productivity. 40 Once the base data were collected, there were several steps and alternatives to calculating purchasing power parities (PPPs) for each country. The first step was to calculate the PPPs for each country with respect to a base country. Then, the real GDP was calculated using those PPPs. The calculation of the PPPs for comparison-resistant goods is discussed in Section 3.6 while that for the narrowly defined goods is discussed next. 3.3.1 The Methodology of Calculating Purchasing Power Parities Purchasing power parity (PPP) is the number of currency units required to buy goods equivalent to what can be bought with one unit of the currency of the base country (Kravis et al. 1982, p. 383). From the base data that are collected purchasing power parities can be calculated. There are several ways to calculate PPPs, but the methods most commonly used by the ICP are the country-product-dummy (CPD) and Elteto-Koves-Szulc (EKS) methods. The CPD and EKS methods are exactly the same if all of the prices for every item in each country are present. In that case, the resulting PPP's from the CPD and EKS are just geometric means of all of the prices in detailed category a for country c (Kravis et al. 1975, p. 60). The equation for the geometric mean of all the prices in country c is: (3.1) GMâ€œ = [ f| Pi>c ]1/m i = 1, . . . ,m 41 where Pic is the price of the ith item in country c. 3.3.2 Countrv-Product-Dummv Method The derivation of the CPD method from this representation is simple. The CPD method is derived by making the following assumptions: the natural logarithm of the price for the ith item in country c is composed of an item effect and a country effect; the PPP's are estimated by least squares; and the relationship is stochastic. Then the CPD equation becomes: (3.2) l/m [In(Pjc) ] = A( + Bc + eic. The symbol eic represents a normally distributed variable with mean zero and variance a2. AÂ¡ is the coefficient which represents the item effect on the price of item i in country c. Bc is the coefficient that represents the country effect on the price. In most cases this method is normalized by a base country, usually the U.S. In summary, the CPD method describes the natural logarithm of the price of item i in country c with respect to a base country d as the sum of an item effect AÂ¡, and a country effect Bc. The coefficient Bc is the mean over all items of the log of the price of item i in country c and is interpreted as the logarithm of the PPP for that country's currency relative to the base country (U.S.). Also, AÂ¡ is equal to the mean over c of the log-price of i in c, but that coefficient is not used in this study (Theil et al. 1989, p. 8). 42 3.3.3 Elteto-Koves-Szulc Method To derive the EKS method it takes four steps2. The steps are: calculate "Laspeyres" and "Paasche" type price ratios; calculate Fisher binary price ratios; fill in the Fisher matrix if needed; and then build an EKS matrix of transitive parities. Only the equations will be shown here, an actual example will be given in the next section. Before the derivation of the EKS method the concept of characteristic items must be introduced. A characteristic item is an item that is considered to be purchased frequently within that country. Each country is asked to nominate at least one product within every detailed category which it regards as a characteristic item. The characteristic item chosen must also be priced in at least one other country. This is done so that the most consistent price data is used in the EKS calculations. It will become clear that all calculations in the EKS method are based on the prices of the characteristic items. The first step of the EKS method is to calculate the Laspeyres and Paasche type price ratios. These ratios are not true Laspeyres and Paasche ratios and are often referred to as mini-Laspeyres and mini-Paasche price ratios due to their similarity to the Laspeyres and Paasche time-series measurement. The difference is that these are unweighted 2We would like to thank Ms. Harary at the OECD, Economic Statistics and National Accounts Division for providing unpublished material on the EKS method. 43 price ratios whereas Laspeyres and Paasche are weighted indexes (Ward, 1985, pp. 42-43). The mini-Laspeyres formula is a price ratio of the characteristic item between two countries, if the base country has only one characteristic item. If there are more than one characteristic items in the base country, a geometric mean is taken of all of the price ratios3. The general representation of the equation for the mini-Laspeyres equation is: (3.3) 0, 1/m where i = 1,...,m characteristic items in detailed category a. The mini-Paasche formula is the reciprocal of the transposed mini-Laspeyres price ratios. The equation for the mini- Paasche price ratios is: (3.4) pa * d,c 0, i,d l,C 1/m = l/L c,d ' This method does not pick one base country; therefore, a matrix of mini-Laspeyres is created between countries with a diagonal of ones, the same is true for the mini-Paasche ratios. 3To calculate the geometric mean the base country's characteristic item or items determine the relative parity ratios. The comparison country's price does not have to be a characteristic item in order to calculate the geometric mean. 44 Once the mini-Laspeyres and mini-Paasche ratios are computed, the Fisher binary type price ratios are constructed. Just as before these are not true Fisher binaries because they are based on unweighted price ratios. Therefore, these Fisher type price ratios will be referred to as mini-Fisher binary price ratios. The mini-Fisher ratios are unweighted geometric means of the mini-Laspeyres and mini-Paasche price ratios. The equation for the mini-Fisher price ratios is: (3.5) Fâ€œd = (Lâ€œd * Pâ€œd),/2 where Fâ€œd is the mini-Fisher price ratio for detailed category a between countries c and d. Note that Fâ€œd * Fdc = 1. However, the matrix of mini-Fisher ratios are not transitive. Transitivity means that Fâ€œe/Fde f Fâ€œd. Hence, to make the mini- Fisher ratios transitive, the EKS method is applied. Given that all of the price ratios are present, all of the mini-Fisher ratios can be calculated. Hence, there would exist a full matrix of mini-Fisher ratios. The EKS method is then applied to the mini-Fisher ratios. The equation for the EKS method is: (3.6) EKS c,d Fct 2 c,d 1/n where e f cd. EKSâ€œd is the PPP for the detailed category a between countries c and d. This procedure uses direct mini-Fisher price ratios Fâ€œd and indirect ratios Fâ€œe and Fdc which use country e as the 45 bridge country between countries c and d. This method replaces each direct ratio by the geometric mean of itself and all corresponding indirect ratios that can be obtained using as many of the other countries as possible for bridges. The EKS gives the direct ratio twice the weight of each indirect ratio since Fâ€œd/FÂ£d * Fâ€œc/Fdc is the same as F"d2. The resulting transformed ratios are all transitive. The overall transitive parity between any individual pair of countries is therefore significantly dependent on the indirect ratios involving prices in all other countries (Ward, 1985, pp. 44-45). 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 be observing the values in any of the country columns of the EKS matrix. To make the EKS equivalent to a geometric mean is simple. The EKS formula itself is a geometric mean. If all of the prices of the items are all present and all characteristic items, then the EKS method is the same as equation (3.1) if Pic is replaced with a price ratio. The reason is that the indirect mini- Fishers and the direct mini-Fisher ratios are equal, that is rc,e/rd,e rc,d* This section shows how the CPD and EKS method calculate PPP's for a detailed category when all of the prices are present. Also, it is proven that the CPD equals EKS which equals the geometric mean when all of the prices are present and all of them are characteristic items. The next section 46 illustrates the situation where there are missing prices, which is the case for most detailed categories. 3.4 Estimating Purchasing Power Parities In many detailed categories, there are several missing prices. Without the basic prices, the CPD method does not equal a geometric mean and neither does the EKS method. In fact with the EKS method the mini-Paasche, Laspeyre, and Fisher ratios cannot be calculated when there are missing prices. In this case it should be clear that the CPD method does not equal the EKS method, although they should deviate minimally from one another. This section addresses the procedures the ICP used to estimate the PPP's via the CPD and EKS methods when there were missing price data Estimating PPP's with the CPD method is the same as in - - r - r . . â€¢ section 3.3. Equation 3.3 normalized by the U.S. price is the equation used to estimate the Bc's. To illustrate this procedure part of the data from the fresh vegetables detailed category for 1970 is used (Kravis et al. 1975, p. 59). The data for four countries and four goods are shown in Table 3.2. The full matrix for fresh vegetables for 10 countries and 20 countries in 1970 is shown in Appendix A4. If the prices of vegetables in their respective national currencies in Table 3.2 are considered to be a detailed 4The PPP's and AÂ¡'s estimated by Kravis et al. 1975 are also included in Appendix A. 47 Table 3.2 Fresh Vegetables for 4 Countries and Items in 1970 Japan (Yen) Kenya (Shilling) United Kingdom (Pound) United States (Dollar) Lettuce 218.1* 0.62 0.5* Mushrooms - - 0.54* 1.9 Onions, yellow 98.6* 0.77 0.13 0.35* Tomatoes 160.9 1.19* 0.31* 0.92* Source: Kravis et al. 1975, p. 59. *The starred items are the characteristic items for each country5. category, then the vector for the dependent variable using the U.S. as a base country is equal to: In (218.1/ . 5) In(98.6/.35) In(160.9/.92) In(.62/.5) In(.77/.35) In(1.19/.92) In(.54/1.9) In(.13/.35) ln(.31/.92). Kravis et al. 1975, 1978a, and 1982 weighted each price ratio with the reciprocal of the number of prices in the numerator country by the base country (4/3), and by the supercountry expenditure (see Appendix B) . The independent variables (dummy variables) for this equation, constructing the country dummy then the item dummy, are: 5These items are not the actual characteristic items they are chosen for illustration purposes only. 48 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 10 10 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 10 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1. This system cannot be estimated because each row for each independent variable sums to 1. That means there is an adding up problem. To solve this problem one of the items has to be dropped. No information is lost when this is done, redundant information is eliminated from the system. Once one of the columns from the item dummy is eliminated the regression can be estimated. The results from this setup having dropped item 2 and weighted the price ratio by (4/3)6 are BjÂ»p,u.s. = 5.62 Â®Ken,U.S. = 0.41 Â®u.k.,u.s. = â€œ 0.99. These results are the natural logarithm of the PPP between country c and the U.S. To get the PPP, the exponential of Bc is taken. The PPP's are 275.89, 1.51, and 0.37, respectively. There are n-1 PPP's because the U.S. is used as the base country. The explanation of these numbers are given after the EKS results are calculated and compared with the CPD results. 6The supercountry weighted is not used in this example. 49 The first step of the EKS method is to create the mini- Laspeyres price ratios. For simplicity, Lâ€œd will now be expressed as Lc/d and the same for the mini-Paasche price ratios. The mini-Laspeyres matrix is shown in Table 3.3. All calculations for the EKS example are shown in Appendix C. In this matrix the base country is given by the columns, the rows are the numerator countries. Since the mini-Paasche matrix is just the inverse of the numbers in Table 3.3, that is Pjap/Us = 1 /Lus/jap, the mini-Paasche matrix will not be shown. Table 3.3 Mini-Laspeyres Price Ratio Matrix Japan Kenya U.K. U.S. Japan 1.0 135.21 519.03 278.02 Kenya 0.0047 1.0 2.48 1.52 U.K. 0.0013 0.26 1.0 0.35 U.S. 0.0029 0.77 3.23 1.0 After the mini-Laspeyres and mini-Paasche price ratios are calculated, the mini-Fishers are estimated. Table 3.4 shows the results of the mini-Fisher calculations. There are no missing mini-Fisher ratios in this example. If there were, a bridge country method would have been implemented to fill in the missing values. For example, if the mini-Fisher price ratio between countries c and d (Fâ€œd) is missing, but the 50 ratios between countries c and e, and d and e exist, then the mini-Fisher price ratio for countries c and d can be calculated by dividing Fâ€œe by Fjc. Country e is the bridge country that links countries c and d. If more than one bridge country is available, then a simple geometric mean is taken of all of the indirect estimates. If there are still missing mini-Fisher ratios then the above procedure is applied until the matrix has no missing data. Table 3.4 Mini-Fisher Ratios Japan Kenya U.K. U.S. Japan 1.0 169.61 631.87 309.63 Kenya 0.0059 1.0 3.09 1.41 U.K. 0.0016 0.32 1.0 0.33 U.S. 0.0032 0.71 3.04 1.0 The final step in calculating the PPP's is to implement the EKS method. The EKS method uses the direct and indirect mini-Fisher ratios to make these parities transitive. The matrix of transitive PPP's are shown in Table 3.5. The EKS results are implicitly weighted because only the characteristic items are used for base countries in the calculations. 51 Table 3.5 Transitive PPP's from the EKS method Japan Kenya U.K. U.S. Japan 1.0 189.58 667.53 262.67 Kenya 0.0053 1.0 3.50 1.39 U.K. 0.0015 0.28 1.0 0.40 U.S. 0.0038 0.72 3.53 1.0 To compare the EKS results with those from the CPD, the U.S. column is used because the CPD used the U.S. as its base country. The values from the CPD compared with the EKS for fresh vegetables in 1970 for 4 countries and items are as follows: CPD EKS Japan/U.S. 275.89 262.67 Kenya/U.S. 1.51 1.39 U.K./U.S. 0.37 0.40. The differences between these numbers are negligible. Most of the variance could be due to weights and rounding error. The interpretation of the PPP's estimated by both methods is that one dollar's worth of fresh vegetables in the U.S. equals between 262.67 - 275.89 yen worth of fresh vegetables in Japan, 1.39 - 1.51 shillings worth of fresh vegetables in Kenya, and 0.37 - 0.40 pounds worth of fresh vegetables in the United Kingdom. 52 The CPD method was used in Phases I, II, and III. The CPD and EKS methods were used in Phase IV. The reasons for using the different methods in the different Phases will be discussed in Chapter 4. Once the PPPs were estimated, they were used in the Geary-Khamis method. The second stage of the estimation process is discussed next. 3.5 The Gearv-Khamis Method The objective of the Geary-Khamis method is to provide 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 can be obtained by dividing expenditures in national currency by those in international dollars. The method was first introduced by Geary who suggested that a system of homogeneous linear equations be used. These equations are used to calculate the international prices and the PPPs simultaneously. Subsequently, Khamis shows that the system yields non-negative international prices and PPPs. Thus, Geary and Khamis are responsible for this model. The derivation of the Geary-Khamis method follows. The CPD or EKS method can be used to produce the detailed category PPP's for the Geary-Khamis method. These PPP's are transitive and relative to the U.S. dollar. Detailed categories are indicated by the subscript a = 1, ..., A. Let Eac be the per 53 capita expenditure (in national currency) on detailed category a in country c. The equation for the volume of detailed category a in country c is (3.7) Va,c = Ea c/PPPa c. Vac is expressed in U.S. dollars. Although (3.7) achieves the goal of expressing all expenditures in the same currency ( U.S. dollars), the Vac's have the problem that they are not additive over detailed categories. To achieve such additivity, the Geary-Khamis method introduces the international price Pa of each detailed category and the overall purchasing power parity 7rc of each country c. The definition of Pa is N r (E;c7Tfcyâ€¢ C=1 Pa = N 2 VÂ«,c C=1 or, equivalently, N N (3.8) PaVa = Z (Eac/7Tc) where Va = E Va>c c=l c=l while nâ€ž is defined as 54 A 2 Eâ€ž,c a=l = A E P V Â« a,c a=l or, equivalently, as A (3.9) GDPc (1/ttc) = E PaVa c a=l where GDPC (the gross domestic product of country c in national currency) is equal to the sum over a = 1, ..., A of Eac. It is readily verified that (3.8) and (3.9) constitute a linear system in the A + N -1 unknown Pa and l/nc (7rc = 1 for c = U.S.) (Theil et al. 1989, Appendix A). The product PaVac is interpreted as real expenditure per capita in international dollars on detailed category a in country c. This product is additive over detailed categories. Let S be any grouping of such categories; then the sum over a e S of PaVac is real expenditure per capita or real gross domestic product (RGDP) per capita in international dollars on S in c. If S consists of all detailed categories, this sum is GDP per capita in c. The exposition given on the CPD, EKS, and Geary-Khamis methods is a general overview on how PPP's for the detailed categories and overall, international prices, and RGDP are 55 calculated. The next section deals with calculating PPP's for the comparison resistant goods. 3.6 Calculating PPP's for Comparison Resistant Goods In the previous sections the procedure for calculating PPP's for narrowly defined goods was discussed. In this section, the calculations for PPP's of comparison resistant goods are discussed. The procedure for calculating these PPP's to use in the Geary-Khamis formula is straight forward. For the comparison-resistant goods and services (i.e., services of teachers, physicians, dentists, hospitals, nurses, and government employees), neither the CPD or EKS method was used. Quantity comparisons for these categories were based on a method called "direct quantity" comparisons. For example, for teachers of first, second, and third level students, the Â¡ o? i<â€¢ â€¢ or | - -. . â– ; i r â€¢ â€¢ j i - *;' â€¢ Â¡ â€¢'* Â»vr y â€¢ â€¢ â€¢j ; * * : '*'â€™* quantity comparisons were based on the number of standardized persons engaged in providing the services. For physicians, dentists, technicians, midwives, and the like, the ICP quantity comparisons were based on the number of physicians, dentists, and nurses, respectively. For Phases I and II, it was assumed that all equally qualified personnel in these comparison-resistant categories have the same productivity. In Phases III and later, this assumption was abandoned, and adjustments were made. In educational services, the modifications improve the estimates of teacher inputs by introducing education level and the number of students as a further dimension of productivity. In 56 medical care and government services, adjustments are made for the differences in the productivity of inputs for broad groups of countries and by making adjustments for capital per worker. After the adjusted final quantity ratios are derived, the PPPs used for the Geary-Khamis method are considered to be indirect PPP's. These PPPs are found by dividing the expenditure ratios by the adjusted quantity ratios. From there, the Geary-Khamis method is applied as before. The reader who is interested in these and similar issues should consult the original source: the work of national and U.N. price experts (Kravis et al. 1982, p. 38); prices of construction and consumer durables (Kravis et al. 1982, pp. 50-56); and the treatment of services (Kravis et al. 1982, Chapter 5). r 1 â€¢ â€¢ '. â€¢ " i?â– â€¢ . â€¢ â€¢ â€¢ â€¢<> 'â€¢ n vi â– â€¢ â€¢ -1 â€¢ *n 3.7 Regionalism Regionalism is a new issue beginning in Phase III. The previous Phases I and II were limited to a small number of heterogenous countries. Thus, there is little point in considering whether comparisons could be improved by identifying relative homogeneous subsets of countries. The Geary-Khamis method was applied to the entire set of countries without any effort to distinguish such subsets or to take them into account in the index number calculations. This symmetrical treatment of all countries is called the "universal" approach. 57 As the number of countries increased significantly in Phase III, it became necessary to consider whether applying the CPD or the Geary-Khamis methods in successive stages would improve the comparisons. The first step would be to look at the level of sets of relatively homogeneous countries and, thereafter, at the regional level. Thus, countries in different regions are compared through regional linkages. The most obvious basis for identifying homogeneous sets of countries is geographic closeness. This basis for grouping countries assumes that these countries have close political and cultural ties as well as similar customs. Although ad- hoc, there are some good reasons for using this approach. Europe and Latin America, for example, are similar in the way they classify daily business and the way they deal with the changes in the political, social, and economic arenas. - In addition, there are usually regional organizations with the sole responsibility of economic development for that region. For the actual calculations for Phase III, the ICP opted to use what is called a modified "universal" approach. This approach has some regionalism aspects which are introduced via the organization of the price inputs for the Geary-Khamis calculations. The objective is to retain base country invariance or to at least allow all countries within each region to influence the world comparisons while retaining the intraregional PPPs and quantity relationships for the detailed categories and for GDP as a whole. 58 The modified universal approach has 3 steps. First, the CPD method is applied at the regional level to fill in the missing prices. Second, the CPD method is applied again, this time on all countries in the study. Lastly, the PPPs from the second stage CPD are used as direct inputs to the Geary-Khamis method. The first stage CPD takes advantage of the regional similarities in price structures to cope with a major problem in deriving the set of PPPs. The problem is primarily incomplete, overlapping sets of price comparisons among the participating countries. The first CPD estimation operates at the regional level to fill in for each country's missing entries in the vector of item prices. All items for which at least two countries in the region provided prices are included. Therefore, this tableau contains for each region, a full vector of prices, for each country, for all items priced by two or more countries in the region. Note that if the CPD is run on the augmented price tableau for a given region, it would yield the same PPPs as those produced by the original incomplete tableau of prices. Thus, the tableau retains the characteristics of the original tableau. After each country's price vector has been completed to match the other country's in the same region, a second CPD is run. This CPD is calculated for all 34 countries (Phase III), where these PPPs are used as the direct price inputs for the Geary-Khamis calculation covering all the countries. This 59 approach embodies a regional element in deriving the category PPPs, but the aggregation of the PPPs across categories is of the universal mode. The results of this new approach relative to the approach used in Phases I and II, which is based on direct price inputs of all countries regardless of the region, are improved. The augmented-price-tableau enhances the influence of intraregional price relationships. The missing prices are explicitly filled in on the basis of intraregional price relationships versus being estimated on the basis of price relationships in all countries like the universal approach does. The last step is to put the PPPs derived from the two- stage CPD method into the Geary-Khamis equations. Calculations for all 34 countries (Phase III> were completed using this method. The results from this approach are discussed next. 3.8 Phase III Results Compared with Exchange Rates Using the two stage CPD method to obtain the PPPs for the detailed categories and then implementing the Geary-Khamis method, the international prices and GDPs per capitas are calculated. Table 3.6 provides the results of these efforts for gross domestic product for the year 1975 (Phase III) . The 34 countries are listed in the order of declining GDP per capita in international dollars. 60 Table 3.6 GDP Per Capita for 34 Countries in 1975 Country (1) International dollars* (2) Same, U. S.=100b (3) Exchange rate converted1* (4) United States 7176.0 100.0 100.0 Germany 5952.7 83.0 94.7 Denmark 5910.9 82.4 104.5 Luxembourg 5883.4 92.0 90.2 France 5876.9 81.9 89.6 Belgium 5574.1 77.7 87.8 Netherlands 5397.2 75.2 84.5 Austria 4994.8 69.6 69.8 Japan 4906.7 68.4 62.3 United Kingdom 4587.9 63.9 57.6 Spain 4010.2 55.9 41.0 Italy 3861.1 53.8 47.9 Poland 3597.9 50.1 36.0 Hungary 3558.9 49.6 29.6 Ireland 3048.8 42.5 37.2 Uruguay 2844.3 39.6 18.2 Iran --â€¢â€¢'2704.6 37.7-i 22.1 Yugoslavia 2591.4 36.1 23.2 Mexico 2487.3 34.7 20.4 Romania 2386.8 33.3 24.3 Brazil 1811.2 25.2 16.0 Syria 1794.2 25.0 10.0 Jamaica 1722.6 24.0 19.6 Colombia 1608.7 22.4 7.9 Malaysia 1540.6 21.5 10.9 Korea 1484.1 20.7 8.1 Philippines 946.3 13.2 5.2 Thailand 936.1 13.0 5.0 Zambia 737.8 10.3 6.9 Sri Lanka 667.7 9.3 2.6 Pakistan 590.3 8.2 2.6 Kenya 470.5 6.6 3.4 India 470.5 6.6 2.0 Malawi 351.7 4.9 1.9 â€œSummed over all 151 detailed categories. bSource: Kravis, Heston, and Summers 1982, p. 12 61 The differences between the exchange-rate converted figures and those which Kravis et al. (1978a) obtained using the Geary-Khamis method are substantial. These differences increase as real GDP per capita decreases. This is readily seen in columns 3 and 4 of Table 3.6 where the PPP based estimates of GDP per capita are compared with the exchange rate based estimates (both are a percentage of U.S. value). The use of exchange rates tend to overstate the poverty of poor nations considerably. For example, when we use exchange rates, the ratio of the U.S. GDP per capita to its Indian counterpart is 100/2.0 = 50, but it is only 100/6.6 or about 15 when we use the Kravis approach. One reason for this dispersion is that services tend to be cheaper relative to commodities in poorer countries, and services make up a small portion of international trade. Hence, exchange rates understate the value of services in low income countries. Services, which are nontraded goods, are cheap in low- income countries; hence exchange-rate conversions greatly underestimate the true quantities of services in low- income countries relative to those in high-income countries. (Kravis et al. 1982, p. 23) In addition, exchange rates have been variable since the switch-over to floating exchange rates in 1973. However, there is no reason why the consumption expenditures in national currencies should reflect this variability exactly. Converting these expenditures by such wildly fluctuating exchange rates would yield highly spurious results. 62 3.9 Phase IV Further Considered After Phase III regionalism plays a bigger role in the ICP. Regionalism complicated things in many ways. Therefore, Phase IV is discussed explicitly. Phase IV as mentioned before is different from the other Phases. The information on Phase IV is presented in "World Comparisons of Purchasing Powers and Real Product for 1980: Phase IV of the International Comparison Project." This manuscript has two parts: "Part I: Summary Results for 60 Countries"; and "Part II: Detailed Results for 60 Countries." These papers are published by the Statistical Office of the United Nations Secretariat (UNSOS), Statistical Office of the European Communities (EUROSTAT), and the Organization for Economic Co-operative and Development (OECD). This work is discussed here to address several problems- (i.e., decentralization, regionalism, and fixity) and the additional problems they create. The other reason for Phase IV's importance is that it increased the number of benchmark countries to 60. Phase IV is similar in many ways to the previous Phases, so only the deviations from those Phases will be discussed below. After Phase III, the ICP was decentralized, which meant that various regional and country groups assumed major responsibilities while the Statistical Office of the United Nations Secretariat was responsible for linking the work of the various regions. There were seven organization that 63 carried out the work for the country groups: Statistical Office of the European Communities (EUROSTAT), Economic Commission for Europe (ECE), OECD, Economic Commission for Africa (ECA), Economic Commission for Latin America and the Caribbean (ECLAC), Economic and Social Commission for Asia and the Pacific (ESCAP), and UNSOS. With the decentralization, each group carried out its own estimations within its region; this is referred to as regionalism. This definition supersedes the definition in section 3.7 for Phase IV and later. Table 3.7 shows the countries involved in each group as well as the organization that did the calculations. After the comparisons within each region are accomplished, then the regions are compared at the world level. 3.9.1 Other Methods Used in Phase IV With the decentralization and regionalism of Phase IV, one problem is that each region can choose any method they preferred to calculate the PPPs. Europe Group 2 and ECIEL decided not to use the CPD or EKS method. The European group implemented a method called the "STAR" system. It is not clear what the ECIEL group did to calculate their PPPs. The star system used by Europe group 2 has Austria as the base country for that group. They carried out four separate binary comparisons with the four countries representing the outer points of the star. The detailed category PPPs for each country are only estimated with respect to Austria. The PPPs for any two countries are derived from the two sets of binary 64 Table 3.7 The Organizations that Performed the Calculations and the Countries Involved in Each Group for Phase IV. EUROSTAT ECE ECA/EUROSTAT ESCAP/UNSOS ECIEL/ECLAC OECD Europe- Group 1 Group 2 Africa Asia Latin America OECD Belgium Austria Botswana Hong Kong Argentina Canada Denmark Finland Cameroon India Bolivia Japan France Hungary Ethiopia Indonesia Brazil Norway Germany Poland Ivory Coast Pakistan Chile U.S. Greece Yugoslavia Kenya Philippines Colombia Italy Madagascar Korea Costa Rica Ireland Malawi Sri Lanka Dorn. Rep. Luxembourg Mal i Ecuador Netherlands Morocco El Salvador United Kingdom Nigeria Guatemala Portugal Senegal - â– â€¢ ~ â€¢ â€¢ -Honduras â€¢ - S TV Spain U.R. of Tunisia Mexico Israel Tanzania Panama Zambia Paraguay Zimbabwe Peru Uruguay Venezuela Source: United Nations, 1985 and 1987. PPPs (i.e. country C and D's binary PPPS with country B and D's binary PPPs). Using this method, transitivity is not a problem since no direct comparisons are made between the points of the star. Thus, the EKS system is not necessary. The Geary-Khamis method is used to aggregate the categories and calculate GDP as a whole. The weights (expenditure and 65 prices (PPPs) of the countries covered) of the five countries are taken into account (The Statistical Office of the United Nations Secretariat 1987, p. 5). There is less information on what the ECIEL region did. However, it is clear that neither the CPD nor the EKS method was implemented. It has been ECIEL's practice that each country provides prices for every item in the detailed categories. PPPs are then derived that are transitive across all countries by obtaining the geometric mean of the price ratios of each country to any one of the countries chosen as the numeraire. All that can be said about this method is that, if all countries provide prices for all of the commodities, then all of the other methods reduce to a geometric mean, when estimating PPPs for the detailed categories (The Statistical Office of the United Nations Secretariat 1987, p. 11). 3.9.2 Linking the Regions of Phase IV After the PPPs for the detailed categories were estimated, the problem was to link all of the country groups together. The main problem was that each region had a different base country. In addition, the Europeans (both groups) have approximately 320 detailed categories while the other groups typically have approximately 150; the African and Latin American countries have a more condensed system. Fortunately, the European, African, and Latin American groups 66 were able to make their respective detailed categories compatible with those of the world comparisons. Linking the various country groups requires that the prices of the overlapping items between countries across the different country groups be compared. In order for this to work, there must be at least one country in each group which has prices for each detailed category so that the PPPs can be estimated to link the countries. When comparing Europe Groups 1 and 2, for example, only Austria has sufficient prices to link Group 2 to 1. However, this was sufficient to link the Europe Group 2 countries with the world comparisons. There are 20 countries that serve as liaisons like Austria. These countries act only as a set of countries whose item prices for comparable goods and services serve as the basis for linking the country groups. These countries are called "core" countries. The core countries are: France, Spain, Israel, and the United Kingdom (Europe Group 1) ; Austria (Europe Group 2) ; United States, Canada, and Japan (OECD); Brazil, Colombia, Uruguay, Dominican Republic, and Guatemala (ECLAC); Hong Kong, Indonesia, Korea, Pakistan, and Sri Lanka (ESCAP); and Kenya and Senegal (ECA). The CPD method was used for the core countries where the item prices for the 20 core countries were used as inputs. The expenditure weights used by some of the country groups were also incorporated into the CPD estimation procedure. When the CPDs were estimated for each of the detailed 67 categories, PPPs between each core country and the United States, which was the numeraire country, were provided. The next problem was how to link these PPPs with the other countries in these regions. The method used to link the PPPs to the other countries is a type of chain-link-procedure. Using the African countries as an example, the detailed category PPPs exist and for the core countries of Kenya and Senegal, both with respect to the African numeraire and with respect to the United States. The ratio of the geometric means of the core country to the African PPPs provided a factor which, when multiplied times the detailed category PPPs within Africa for all of the African countries, aligned these parities with respect to the United States dollar. This procedure preserves the relationship between the basic PPPs for all countries as originally obtained in the African comparisons, including Kenya and Senegal. This is the fixity principle (see Appendix D) . The chain-link-procedure was applied to Latin America, Europe Group 2, and the OECD countries. In the case of the ESCAP countries, there was no reason to do the chain link method since the base country for that group was the U.S. For India and the Philippines, a slightly different procedure was used since the price information for these countries became available too late to include in the core country CPDs. The item prices were directly compared to the item price estimates 68 that were a part of the CPD output for each detailed category. The geometric means of these item price ratios, which were based in national currency units per dollar for each detailed category, were used as the PPPs. All methods in which the expenditure and PPPs at the detailed categories were obtained have been discussed. These calculations were the basic inputs to the aggregation procedure. The Geary-Khamis method was used just as in the previous Phases for the aggregation of the data. The use of supercountry weighting was also retained. It was important that the results for countries participating in several phases of the ICP not be influenced by the addition of new countries. Hence, the world comparisons utilized a system of supercountry weights where the dollar GDP of non-participating countries was assigned to participating countries on the basis of geographical proximity and the level of per capita income. The problem with the Phase IV data are that the fixity principle is imposed (see Appendix D) . Fixity adversely affects the data if one is interested in world comparisons. That is why there are two data sets for Phase IV. The first set is for researchers who are interested in world comparisons and the other, which preserves fixity, is for intraregional comparisons. The first set is made available by the U.N. Statistical Office upon request by the researcher. The other data set which has fixity imposed is in the Phase IV 69 publication. The calculations in this thesis were all based on the data that do not impose the fixity principle. To calculate RGDP per capita for each country with respect to the U.S. without fixity, the calculations must be done like the Phases previous to Phase IV. That is, estimate the PPPs with the CPD or EKS method using the U.S. as a base country, then apply the Geary-Khamis method. CHAPTER 4 EXTRAPOLATIONS 4.1 The Beginning of Extrapolations with ICP Data There are five publications of the extrapolations on the different phases of the ICP. The first publication is by Kravis et al. (1978b). All of the rest are by Summers et al. (1980 also known as Mark l,1 1984 Mark 3, 1988 Mark 4, and 1991 MARK 5). These publications sought a way to approximate real gross domestic product (RGDP) per capita for virtually all the countries in the world and for every year from 1950 to 1988. This method is referred to as the "short cut" method. During the years following the first publication in 1978, the methodology and the guality of the data from the Mark's have improved. The purpose of the first paper, "Real GDP Per Capita for More than One Hundred Countries," by Kravis et al. (1978b) was to close a gap that the world statistical system had been unable to fill. At that time, there were no comparative data on "real" GDP per capita (gross domestic product per capita adjusted for differences in the purchasing power of currencies) for a large number of countries. In this paper, â€˜Mark 2 was not published but it was used in Kravis, Heston, and Summers (1982). 70 71 Kravis et al. (1978b) develop a method to calculate these real GDP per capita (RGDPC) by using the detailed comparisons of the 16 countries in Phase II. The structural information from this method allows the RGDPCs to be calculated for non-ICP countries. Lastly, an extrapolation is made to get RGDPC for later years. The short-cut method that Kravis et al. (1978b) developed concentrates on the relationship found in the 16 countries between RGDPC and certain independent variables. These structural relationships were used to estimate other years and non-benchmark countries. However, the authors caution that the non-ICP RGDPC's were approximations, and that it would be some time before more exact comparisons would be available for a large number of countries. Nonetheless, their numbers are superior to exchange rate converted GDPs per capita which were used prior to PPP conversions. The model Kravis et al. (1978a) used to find the structural relationships was PIi (4.1) In rj = a, + a2 In n; + a3 (In nj)2 + a4 In Plus 0Pj + a5 In j = 1,..., 16 where j represents countries, ri = Rj/Rus, nj = Nj/Nus, R is real GDP per capita (adjusted for purchasing power) , and N is nominal or exchange-rate-converted GDP per capita. The 72 variables OP (openness) and PI (price isolation) come from international trade theory and will be covered in more detail later (Kravis et al. 1978b, p. 219). The relationship between r and n has been discussed in Chapter 3 so it should not be a surprise that a2 is expected to be between 0 and 1. The value of a, is expected to be 0 because r should equal 1 when n, OP, and the PI ratios equal 1, which is the case for the base country. The a3 coefficient is expected to be negative since its corresponding variable is the square of a2 That is the square of a negative number is positive, and ln(n) is negative while ln(n)2 is positive; hence, r and ln(n)2 are negatively related. The expected signs of OP and PI as well as the variables themselves are discussed next. The reason why OP and PI are included "inâ€œthe model is because Kravis et al. (1978b) were influenced by the productivity differential model. This model is most clearly stated by Harrod and Balassa cited by Kravis et al. (1978b). It states: international trade tends to equalize the prices of traded goods; given equal prices, wages will be high in high productivity countries; internal factor mobility will lead to high wages also in non-traded goods industries in high productivity countries; because international differences in productivity are smaller in non-traded goods industries (largely personal services) than in traded goods industries (largely commodities), the non-traded goods will be higher in 73 high productivity (high incomes) countries; and lastly, the high prices of non-traded goods have little if any impact on the exchange rate and thus make possible a difference between the overall purchasing power of the currency and the exchange rate. The influence of this model led the authors to attempt to account for the differences in countries openness to trade. The degree to which each country's price level is influenced by foreign prices is measured by the variable "openness" (OP). This variable basically measures the exposure to world markets. OP is calculated by the average ratio of exports plus imports to GDP for the years 1965 to 1973. The period for which the data are used is completely arbitrary and taken directly from the World Bank Tables, 1976 (Washington D.C.: International Bank for Reconstruction and Development, 1976). The expected sign for a5 is ambiguous. The relationship between OP and r is negative if the following is correct: the more open an economy, the higher its prices are for non-traded goods, making the difference between n and r smaller. The relationship is not clear if the lack of openness is due to protective commercial policies which could lead to higher prices for non-traded goods (Kravis et al. 1978b, p. 223). PI stands for price isolation. The assumption is that the influence of external factors on a country's price level at a particular moment in time can be inferred from how closely its time to time movements over some preceding period 74 are correlated with time to time movements of "world" prices. The world price index (implicit deflator) is created by placing countries whose currencies the International Monetary Fund (IMF) have defined the value of a unit of Special Drawing Rights (SDRs) on a common base. These are converted to dollars by division by an appropriate index of exchange rates. The world index is then constructed by aggregating the SDR country indices using weights which reflect the importance assigned to each currency by the IMF in its initial calculation of the value of an SDR unit in mid 1974. The implicit deflator is then adjusted for each individual country to a common base period and correct exchange rate changes. The final step is to calculate the price isolation index using the formula, 1970 (4.2) PI = y (WD, - CD,)2/8, t= 1963 where WD is the world price index and CD the country price index, both based on the average over the period 1963 to 1970. Eight of the ICP countries are included in the set of countries that the IMF uses in its SDR calculations. Thus PI can be summarized as the mean squared difference for the years 1963 to 1970 between the country's GDP implicit deflator and a "world" average GDP implicit deflator. The sign for a4 is ambiguous like a5, and for similar reasons. PI and r could be positively related if the 75 following line of reasoning is consistent with what has actually happened. The reasoning is, the greater the price isolation, the less a country's non-traded goods prices will be pulled up to the price levels of the high-income countries; thus a larger real income (r) is associated with a given nominal income (n). However, these affects can be negated by combining different micro and macro economic policies which is why the sign is ambiguous (Kravis et al. 1978b, p. 223). The question is empirical and one can only estimate the equation and see what signs and magnitudes the parameters have. All of the values for the variables are known for the 16 ICP countries, but r is not known for the other countries. Hence, the model was run for those 16 countries to obtain the structural relationships between RGDPC and the other variables. The resulting signs for this model are a2 positive, a3 negative, a4 positive, and a5 is negative. The parameter estimates and their respective standard errors can be found in Kravis et al. (1978b, p. 226). After calculating r for the non-benchmark countries for 1973, extrapolations have to be made to other years. The method of extrapolation is setup to incorporate the impact on real income through the changes in the terms of trade. This is done by treating the net foreign balance component of GDP separately from "domestic absorption." For domestic absorption (DA), the per capita quantity change between the benchmark year and the year of extrapolation for 76 each country is estimated by deflating consumption, capital formation, and government by the implicit deflator for these sectors. This results in the value of DA in the extrapolation year being expressed in international dollars of the benchmark year. The net foreign balance was then valued in benchmark year international dollars and added to the figure for DA to obtain GDP per capita in international dollars. Finally, this sum was compared to the corresponding U.S. total to form the extrapolation year index for real per capita GDP (Kravis et al. 1978b, p. 229). The results of this task were estimates for 1973 and 1974. 4.2 Mark 1 The second paper by Summers et al. (1980) is entitled, "International Comparisons of Real Product and its Composition: 1950 to 1977." This study includes 119 countries of which 16 are from the ICP Phase I data set. The same equation (4.1) is used to calculate r for the ICP countries and the structural relationships found from those calculations, are used to calculate r for the non-ICP countries as before. What is new in this paper is that the extrapolations for the ICP and non-ICP countries are done forward and backward through time. To calculate RGDPJt before and after 1970 is relatively easy since all of the results are in 1970 dollars (benchmark year) . R is calculated the same as previously (rjt = 77 RGDPj,/RGDPUS70) for the year 197 0 only. The RGDPj, for the other years is obtained using the jth country's constant price series (in domestic currency units) for GDP as indicated in the equation below, GDPj t /POPj t (4.3) RGDPj, = (RGDPj 70) , GDPjjo /POPjjo where GDP is a constant-price value of GDPjt in national currency and POPjt refers to the population. By using the constant-price valuation, changes in terms of trade facing the jth country between the tth year and 1970 are neglected. RGDP is calculated for all 119 countries from 1950 to 1977 using these methods. 4.3 Mark 3 The third paper, "Improved International Comparisons of Real Product and its Composition: 1950 - 1980" written in 1984 by Summers and Heston, is referred to as Mark 3. Mark 2 was not published but it was used by Kravis, Heston, and Summers (1982). Mark 3 was different from Mark 1 and Kravis et al. (1978b) because it utilized the data from Phase III. This data set included 34 countries for the year 1975. This difference and the fact that there were two benchmark years of data (i.e., 1970 and 1975) resulted in the authors using a different method for calculating the RGDPs in Mark 3. 78 The first change from the earlier papers was that a slightly different functional form for the regression was used. However, before that is addressed, the data need to be considered. There are two benchmark years of data to utilize. The approach used by Summers and Heston in this paper is a modification of the approach used in Phase III (Extensions beyond the ICP countries, pp. 332-340). The cross-section regressions for the two years were run in terms of per capita DA instead of per capita GDP as done previously. The slightly different functional form for the regressions was that the openness variable in the eguation used to summarize the 1970 and 197 5 data was introduced additively compared to an interaction term. Furthermore, the constant terms in both years were suppressed since they were not significantly different from zero. - These modifications simplify the eguation and make the actual and estimated values for the numeraire country the same (U.S.). Lastly, the results obtained from the two benchmark years were combined to get a single 1975 estimate. Weights were also devised to take into account the relative precision of the two cross sections. The regression eguation used to summarize the 1970 and 1975 cross-section relationships is (4.4) In rj = a, (In nj) + a2 (In n-)2 + a3 (In OPj) + Uj where 79 rj = (DAj/PPPj*A) /DAUS and nj = (DtyXRj) /DAUS. pppDA tj^e pUrchasing power parity over domestic absorption, and XRj the exchange rate. Each is expressed in national currency units of the jth country per U.S. dollars. OPj is the measure of relative openness of the jth economy which was defined as ((ExportSj + ImportSj)/GDPj) / ( (Exportsus + Importsus) /GDPUS) , an average of the ratio for five years before the cross- section year. Before further definitions are given it should be stated that the a's have the same expected signs as they did in Kravis et al. (1978b). The XR-75 variable was defined by a weighted geometric mean of the 1975 exchange rate and the real exchange rates of 1974 and 1976. This was done due to the volatility of the exchange rates for several countries. The equation for XRj75 is then (4.5) XR:.75 = (Pj>75/74XRj 74) m (XRj 75) 1_X (Pj,75/76^Rj.76) ^ where PJt/t. measures the change in the relative price levels of domestic absorption of the jth country and the U.S. between t and t' . X is a weight for the 1974 to 1976 exchange rates. No averaging implies X = 0 and equal weighting implies X = 2/3. The weighting question is resolved by running a non- 80 linear least squares regression on the data. For 1975, the results indicate that X is not significantly different from zero so XRj75 only depended on XRj75. The year 197 0 was different in that X was large. Hence, its value was set at 2/3. Thus, XRj70 is just a simple geometric mean of XRj70 and the price-level adjusted values of XRj69 and XRj_7,. In Summers and Heston (1980), RGDPJt is based on constant- prices whereas in Mark 3, international trade was incorporated into RGDP. The net foreign balance was converted by the exchange rate on the grounds that, at the margin, this is the conversion factor for an increment to the net foreign balance. This is equivalent to setting the international price of a dollar's worth of net balance to 1. Thus, RGDPj75 = râ€75 (DAUS75 + NFBj75/XRj75) where NFBj75 is the net foreign balance in 1975 for the jth country. R-â€™75 is defined as t:he geometric mean of rj from equation 4.4 for the years 1970 and 1975 for all 85 countries. The extrapolations in Mark 3 were also treated differently and were calculated at a more disaggregated level. The tapes of the U.N. constant-price series for consumption, gross domestic investment, government, and the net foreign balance were used to get real individual components expressed in 1975 international dollars for each of the years between 1950 and 1980. Thus, RGDPj was obtained by summing the components, where the net foreign balance exports and imports in 1975 were converted to dollars at current exchange rates. 81 The new disaggregate procedure insures that the price weights used for consumption, investment, and government in each year in each country reflected 1975 international prices rather than the individual country's relative prices. The imprecision of the RGDP estimates varied considerably from country to country and from year to year. Therefore, the authors classified a countries' estimates into four quality classes: A (best), B (better), C (good), and D (fair). The classifications stemmed from the main source of the imprecisions in the estimation process. First, imprecisions were inherent in the ICP benchmark estimates as qualified in Phase III (Table 3.6). Second, the estimation of the cross- section regression introduced some error. Third, the authors did not know what weights to use in averaging the 1970-derived and 1975 cross-section estimates of r'. The authors find several general relationships with respect to the imprecision of their estimates. The ICP imprecision was inversely correlated with real income; so was the error term in the cross-section regression. Also Ceteris paribus, benchmark countries were rated higher than nonÂ¬ benchmark countries; higher income countries were rated higher than lower income countries; and African countries were rated lower than non-African countries. All of these things should be taken into account when observing the RGDPs. Later, the quality grading of the data will become crucial. 82 4.4 Mark 4 The fourth paper by Summers and Heston (1988) was basically an update to Mark 3. The new issue in this paper was consistency. Consistency means that the estimates must obey the national income identity that total product equals total income generated by the production of the product. The reason this becomes an issue in Mark 4 was that the discrepancies between Mark 3 and Phase IV were large for the 1980 RGDP per capita estimates. In addition, the ICP closely followed a system called the System of Real National Accounts (SRNA). The basic rule of SRNA was that entries should obey all temporal identities. The identity that is being violated when Phase IV and Mark 3 estimates of RGDP for 1980 do not match is that the value at time period two (t2) equals the value at time period one (t,) times the growth rate between the two time periods. To illustrate this point, consider two countries, A and the U.S. Suppose the 1980 Phase IV RGDP estimate of Country A is 66% of the U.S.'s 1980 RGDP. How could this be resolved if the Phase III 1975 relative RGDP value was 65%, and country A had a 4% growth rate while the U.S. had a 1% growth rate? This is why consistency has to be applied.2 2Stone, Champernowne, and Meade (1942) developed a similar method to make their estimates conform to the national income accounting identity. 83 The implementation of consistency is done via an errors- in-variables model. The objective of this model is to adjust both the benchmark and national accounts data to make them consistent. To continue with the two country example, this model would make the Phase IV estimate equal to the Phase III estimate multiplied by the 1975-1980 growth rate. The likelihood function for this model is (4.6) In L(X1,X2,X3,G1,G2/x1,x2,x3,g1,g2; Â£ ) = K - 1/2 In Â£ -1/2 3 3 E E X::, (In X: - In XÂ¡) (In Xj - In XÂ¡) i i j i j 5 5 + E E X1J (In gÂ¡.3 - In GÂ¡.3) (In g^ - In G^) 4 4 where the X's are true values of a country's output at a particular level of aggregation (e.g., consumption) expressed in per capita terms and relative to corresponding values for the U.S. for the three time points, t,, t2, and t3. The G's are the true values of the country's growth rates for the same aggregate as the X's, expressed in the same per capita units relative to the U.S. for the (t,, t2) and (t2, t3) periods, respectively. Therefore, the temporal identity requires that X2 = X, (G,) and X3 = X2 (G2) . The lower-case symbols x,, x2, x3, g,, and g2 stand for estimated values equivalent to their corresponding upper-case letters and are obtained from 84 benchmark studies or the national accounts. The errors-in- variables specification is then Xj = XÂ¡ (vÂ¡) i = 1, 2, 3 g, = G, (v4) and g2 = G2 (v5) . The five v's are joint random variables with a multivariate lognormal distribution n(0,Â£). The a priori information about the relative accuracies of the data sources were introduced through the specification of the entries in E which is the variance-covariance matrix of the v's. The information is parameterized in the form of a five element vector (kw k2, k3, r,, r2) and an assumed pattern of independence among the v's. The variances among the v's associated with the g's (growth rate v's) were all assumed to be the same and equal to 1. The v's associated with the x's (benchmark v's) were expressed relative to the variances of the growth rate v's and are called k's. The correlation between v, and v2 and also between v2 and v3 was given by r,; the correlation between v, and v3, because of the longer time interval, was assumed to equal r\', the correlation between the two growth rate v's was given by r2; and the benchmark and growth rate v's were assumed to be independent. All of these assumptions imply that E has the form E - [ E' Â° 1 L o eJ 85 where *1 r,Vk, k2 r fvOc, k 3 rykÂ¡ k2 k2 rÂ¿\/k2k3 r^/k, k3 rjVkjkj k3 and The XÂ¡jS in equation 4.6 are just the elements in Â£'*. This maximum likelihood procedure corrects the data sources so that they are consistent. The only problem is that the maximum likelihood asymptotic properties cannot be claimed for this estimation. The reason is that additional parameters â– â– t I i : â€¢ â€¢ - â– â€¢ â€¢ â– are added as more time points were introduced, an estimation problem called the incidental parameter problem (Judge et al. 1980, pp. 543-546). However, it is claimed that the maximum likelihood estimates are of the same variance-minimizing estimates obtained from averaging all possible unbiased point estimates. The data from Phases II, III, and IV and the U.N. constant-price series are made consistent by following the errors-in-variable approach. The non-benchmark countries do not need this. They are just aligned appropriately with the benchmark country estimates. With the consistent data, the 86 1980 RGDP for the benchmark and non-benchmark countries are computed similar to the way they are computed for the base year (1975) in Mark 3. There are a few differences from Mark 3 other than consistency in the manner in which the RGDP's were calculated. Mark 4 drops the openness variable. The exchange rates were too volatile throughout the late 1970's, and the openness variable was no longer significantly related to RGDP by 1980 so it was not used in Mark 4. Dummy variables for Africa were also introduced to allow for divergence. The last adjustment came with the replacement in the equation of exchange rates with a combination of price indexes called the international post-allowance price index. The two indexes that compose the post-allowance index were the International Civil Service Commission index and the Employment Conditions Abroad index. The International Civil Service Commission index is published in the Monthly Bulletin of Statistics of the United Nations Statistical Office and uses New York city as a base. The Employment Conditions Abroad index is an organization based in London with members including multinational firms, governments, and non-profit international agencies. This organization produces a number of binary indexes. The extrapolations forward and backward were accomplished by following the procedures used in Mark 3 precisely. The preciseness of the estimates were also graded A to D using the same standards developed in Mark 3. This was done for 130 87 countries for the years 1950 to 1985. The estimates for RGDP still suffer from large errors for low income countries and African countries. 4.5 Mark 5 The most current paper written updating these data is by Summers and Heston (1991). Their data for RGDP per capita was used in this thesis for analysis. Mark 5 covered 139 countries and RGDP per capita was obtained by extrapolating these cross-section comparisons interspacially to nonÂ¬ benchmark countries and then intertemporally to other years. Mark 5 is arguably the best of the Marks and utilizes ICP data from 4 benchmark years: 1970, 1975, 1980, and 1985. Eighty-one countries participated in these benchmark studies and 47 participated in more than one benchmark study. Thus, 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. Most of all, the methodology for obtaining RGDP per capita for a large number of countries has improved. Hence, all of these factors make Mark 5 the most accurate and most recently published international comparisons data of this type. The four ICP benchmark studies, Phases II - V, used in this study were all compiled in different ways and have different countries participating in different years. This is why the data have to be made consistent. Consistency, as discussed in the previous review of Mark 4, is calculated the 88 same way in Mark 5 (using equation 4.6). What needs to be addressed is the benchmark data itself. The biggest problem with the benchmark data was that Phase V had not been published by the time Mark 5 was published.3 Summers and Heston calculated the RGDPs on their own, using only the raw data provided by the U.N. and World Bank. The method used by Summers and Heston to calculate the values in Mark 5 are discussed next. There are three main changes to the Phase IV results for this paper. First, Phase IV introduces the issue of fixity. It should be clear that the 1980 values mentioned here do not use the fixity principle. Instead, the Geary-Khamis method is used for all 60 countries. However, there is an allowance made for supercountry weighting. Second, the 1980 estimates that underlay the Mark 4 estimates were recalculated using national accounts data of May, 1990 which are the latest current national accounts data for the countries. The U.N. in some cases used national accounts data that are available for 1982 or 1983. Third, there was a slightly different treatment of two categories, change in stocks and compensation of government employees. They also used a slightly different normalization procedure which only affects the valuation of the net foreign balance. Actually Phase V was never published, instead the U.N. decided to publish regional data (i.e. OECD, EUROSTAT, ECA, ESCAP, and ECIEL) (see Table 3.7). 89 The countries that participate in the 1985 benchmark comparisons fall into five groups: 22 OECD countries, 11 Asian countries including Japan, 22 African countries, 5 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 have data that allow the authors to link them to the OECD and Asian countries. The total number of countries from Phase V used in this study is 57. Once again fixity was not imposed on these results. A different method was used for those countries that did not participate in the 1985 benchmark study, but did participate in a previous benchmark study. The procedure was to value their 1975 or 1980 benchmark estimates of C, I, and G 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 to revise those years. The Geary-Khamis method was then implemented to aggregate the data. 90 After the benchmark data were aggregated, re-estimated, and made consistent, the non-benchmark countries RGDP per capitas were estimated. The same equation used in Mark 4 was also used in Mark 5 with some minor changes. The left hand side variable was r* which was per capita domestic currency DA converted to international dollars expressed relative to the U. S. Mark 4 used a post adjustment index to estimate the real domestic absorption of each country. This estimate was obtained by dividing the national currency DA by the PPP implicit in the post adjustment index. The post allowance index was made up of two indexes for Mark 4 and three for Mark 5. The International Civil Service Commission index (variable r^j and the Employment Conditions Abroad index (variable rECAJ) was used as post adjustment indexes in Mark 4. Mark 5 used both of those indexes and another index produced by the U.S. State Department. The U.S. State Department provides housing or a separate housing allowance indexes (variable russj) . This was an area in which the data were less reliable (including the ICP data). Hence, the added information from this index was used. All of the post allowance indexes were designed to supplement salaries in a way that equalize real incomes of high-ranking civil servants and business executives assigned to different foreign countries. Each of these indexes have shortcomings. The most notable was that all of the countries were not included in any of these indexes. A structural relationship, however, was 91 found in the benchmark countries between PPP and its post allowance PPP. This structural relationship was exploited to estimate the non-benchmark countries missing PPPs from their post allowance PPPs. There were 81 benchmark countries and 57 non-benchmark countries that have to be estimated. The authors estimate 12 different regressions for the non-benchmark countries. The expected sign of the parameters are given in the equation. The equations are (4.7) In â€¢ = - â€œi + â€œ2 In r^ (4.8) In â€¢ rj = - â€œi + 0-2 In rECAJ (4.9) In â€¢ rj = â€œi + a2 In rUSSj (4.10) In â€¢ = - + Â°2 In r^ + a3 rECAj (4.11) In â€¢ rj = a. + a2 In rUNj + â€œ3 russj (4.12) In â€¢ = a, + a2 In russ,j + a-3 rECA j (4.13) In â€¢ = a, + a2 In rUN,j + â€œ3 AD (4.14) In â€¢ rj = a. + a2 In r ECA j + â€œ3 AD (4.15) In * rj = a. + a2 In rUSSj + a3 AD (4.16) In â€¢ rj = ai + a2 In r UN j + a3 rECA,j â€œ a4 AD (4.17) In â€¢ rj = ai + tt2 In rUN j + â€œ3 russj â€œ4 AD (4.18) In â€¢ rJ = a. + a2 In russ,j + a3 rECAj Â«4 AD. The AD variable represents a dummy variable for Africa. If the non-benchmark country have all of the post adjustment indexes, equation (4.12) and (4.18) were used. If only two indexes were available for the countries, one of the equations 92 from (4.10) - (4.12) or (4.16) - (4.18) was used, and if only one index was available, equations (4.7) - (4.9) or (4.13) - (4.15) were used. Thus, there were two alternative estimates of DA for non-benchmark countries for 1985, and the results have to be merged. The first equations to be estimated from equations (4.12) - (4.18) were those that showed a significant relationship between their squared residuals (SR) and the level of per capita domestic absorption relative to the U.S. (rj) . That is, the squared residuals from equations (4.12) - (4.18) were estimated first if they were found to be related to the dependent variable in equations (4.12) - (4.18). The calibrated equations used to estimate the SR value for each non-benchmark country are (4.19) SR85j = .076 (.012) - .108 rj (.033): n = 77 (4.20) SR80j = .036 (.008) - .029 rj (.019): n = 66. The reciprocal of each SR estimate was used to weight the two estimated rj for the non-benchmark countries. The resulting average domestic absorption relative to the U.S. was then the base for all 1985 estimates. The final step was to merge the non-benchmark with the benchmark data. A Geary-Khamis aggregation was performed, producing consistent national absorption for all of the countries. This procedure was different to that used in Marks 3 and 4. The benchmark values were not necessarily preserved for the benchmark countries in the base year for Mark 5. 93 Grades were also given in Mark 5; this will be covered in Section 5.1. It is still apparent that estimates of RGDP for poor and African countries were less accurate than estimates for rich countries. 4.6 The Centrally Planned Economies Some background information is needed on the centrally planned economies before the reasons why they were dropped from this thesis were given. Hungary is the first centrally planned economy (CPE) to participate in the ICP benchmark studies (1970). No CPEs were added to the 1975 benchmark study. The three that were added in 1980 are Poland, Romania, and Yugoslavia. None were added in 1985, but one was deleted, Romania. Romania is deleted because its results could not be extrapolated due to the lack of necessary national time-series * I - . â€¢ . ' . ' ' . I â€˜ '.! â€¢ â€¢ . â€¢ _ data. CPE's were not included in the Marks until Mark 3. In that paper nine CPE's were added: Hungary, Poland, Romania, Yugoslavia, China, Soviet Union, Bulgaria, Czechoslovakia, and the Democratic Republic of Germany. The estimates of the first four were based on the ICP. The rest were based on various data sources. The same nine CPEs were estimated in Mark 4. Mark 5 is different. Only four of the CPEs have full representation: China, Hungary, Poland, and Yugoslavia. Each of these countries have data over time. The estimates for these four countries were carried out the same way as the 94 market economies. The other 5 countries included in Marks 3 and 4 were dropped from Mark 5 for two main reasons. They did not have data over time, and there was a consensus among CPE specialists that both the levels and growth rates in those economies were overstated. China also has a problem, which necessitated treating it different from the other CPEs included in Mark 5. The published growth rates for China are high (the World Bank accepts a per capita figure of 5.4% from 1965 to 1988 (World Development Report 1990, p. 187) implying a doubling every 13 years. This was what Summers and Heston 1991 (Appendix B, p. 20) have to say about China's growth rate. When Kravis initially published an estimate of China as 12.3% of the U.S. in 1975 (India was 6.6%), it was criticized as too high but the critics did not offer reasons to change it. However, that figure coupled with - China's growth rate would have put China well over 20% of the U.S. in 1988, which most observers do believe is too high. Our conjecture is that Chinese growth rates are too high because they are heavily based on growth in physical output figures rather than deflated expenditure series. ...we have extrapolated the Kravis PPPs forward to 1985 and used that as the basis for making China's estimates for that year because we feel this more closely approximates a correct deflation procedure...This procedure puts China at about 13% of the U.S. in 1988, and almost 3 times the level of India. This differential with India may be high because the benchmark estimate for India in 1985 was unusually low (its consumption per capita was less than Bangladesh!) compared to earlier benchmarks, so that our best guess is that China would be somewhat over twice India rather than three times India. Again, the user is warned... Given the aforementioned problems with China, it was dropped from this thesis. The opinion that the remaining three CPEs, Hungary, Poland, and Yugoslavia, may have similar problems 95 resulted in them being dropped from this thesis. The RGDP data for the CPEs calculated by Summers and Heston (1991) were not used in this thesis. CHAPTER 5 INEQUALITY IN THE G-7 AND OECD 5.1 Inequality Measures There are basically two types of inequality indices; graphical (histogram, Pen's Parade, and the Lorenz Curve), and measures (variance, coefficient of variation, gini coefficient, and Theil's entropy index). These measures analyze the dispersion between individuals or groups. From these measures, researchers can determine if the two groups are becoming closer (convergence) or further apart (divergence). These measures are typically used to determine the inequality in income, as several studies in the Convergence chapter reviewed. However, the initial use of these measures was on domestic issues. The graphical inequalities and inequality measures are discussed followed by the necessary properties of an inequality index. Then the inequality index that was chosen for this study is discussed. 5.1.1 Graphical Inequality A common graphical inequality index is the histogram. A histogram shows the number of people with income in a particular range (Osberg, 1991). The first step with this technique is to determine the number of intervals in the 96 97 range, then create a frequency table showing how many people fall into each range (class frequency). After the intervals have been decided two more steps are needed to construct a frequency histogram. Next a graph with the class intervals on the X axis and the frequencies on the Y axis is produced. Lastly, a rectangle over each class interval with a height equal to the number of measurements falling in a given subinterval is drawn (Ott, 1984). There are several variations of the histogram (relative, log, and Pen's Parade), but they are all based on the same steps outlined above. The other graphical index is the Lorenz Curve (LC). The Lorenz Curve basically plots the cumulative population share on the X axis against the cumulative income share on the Y axis (Osberg, 1991). If one person had all of the income then the -curve would actually be represented by the axis. If everyone had the same income, then the curve would be a diagonal line (the X and Y axis range is from 0 to 1). This graphical representation of inequality can be transformed to be a measure. The measures are discussed next. 5.1.2 Inequality Indices There are several inequality measures. The most commonly used in statistics of dispersion within a distribution is variance (V). The equation for variance is n V = (1/n) Â£ (Yi - y.)2 i=l (5.1) 98 where yÂ¡ is a vector of n income values with a mean n. The square root of V is the standard deviation which is also used as an inequality measure. Another variant of V is to divide the standard deviation by /Â¿. This is referred to as the coefficient of variation (Osberg, 1991). A commonly used inequality statistic is the Gini coefficient (G) which is based on the Lorenz Curve. The formula for G is n n (5.2) G = [l/(2n2M) ] 2 Z | yÂ¡ - Yj | i=l i=j where | . | represents the absolute value of the difference between all pairs of income (Osberg, 1991). In graphical terms, this inequality statistic measures the ratio of the area between the diagonal and the Lorenz Curve to the total area below the diagonal. The last index discussed here is Theil's entropy index (T) also referred to as Theil's inequality index.1 Theil's index is based on an information measure developed by Shannon (1949). Shannon cited by Moss and Mulkey (1993), wanted to determine how much information content exists in a given signal. Theil further developed this idea to measure the change in the posterior distribution associated with a given â€˜There are several derivatives of Theil's inequality index. These indices are referred to as the entropy family of indices and have similar properties to Theil's index. Another family of indices with similar properties to Theil's is the Atkinson's family of indices (Osberg, 1991). 99 signal (Theil, 1967). In terms of income inequality, the approach is to determine whether the information regarding a country can be used to predict the level of income. Theil's income inequality measures inequality by taking the logarithm of the ratio of the arithmetic mean income to geometric mean income (Theil 1989b, and 1979).2 When this measure is applied to n countries, it can be written as n (5.3) J = E pÂ¡ log(Pi/yj) , i=l where Pi is the population share of country i and yÂ¡ is its income share (the shares of i is the total n population and in total n income, respectively). The advantage of using J is its convenient additive decomposition. For example, let R,,...,Rg represent regions so that each country is in only one region. Let Pg and Yg be the population and income shares of region R^P^E^ and Yg=Eiyi, where the summations are over iGRg (g=l,...,G). Then the extension of equation (5.3) to regions is G (5.4) JR = E Pg log (Pg/Yg) , g=l which measures the inequality between the two regions, while 2A11 logarithms in this paper are natural logarithms. 100 (5.5) Jg = SÃÃ©r. (Pi/Pg) lÂ°g[ (Pi/Pg) / (Yi/^g) ] measures the inequality among the countries of region . It is then easily verified that n (5.6) J = JR+ Jâ€™ where J* = S PgJgf g=i which is an additive decomposition expressing total inequality J among the n countries as the sum of regional inequality JR and the average within-region inequality J*. This average is a weighted average with weights proportional to the populations. 5.1.3 Properties of an Inequality Index The determination of which inequality index to use is dependent on the objective of the study as well as the properties of the index. The objective of this study is to calculate a consistent statistic for inequality over time. Given the objective, the graphical representations are eliminated. The statistical measures need to meet certain criteria to be considered consistent estimators. There are four properties an inequality measure should satisfy. These properties are: symmetry, mean independence, population homogeneity, and the Pigou-Dalton condition. Symmetry is also referred to as anonymity which means that the social aspects of the country are irrelevant in calculating the inequality measure. Both mean independence and income- 101 homogeneous of degree zero state that if all incomes are multiplied by the same scalar the ineguality measure should be invariant. Population homogeneity requires that the inequality measure be invariant to replications of the sample distribution. More precisely, given two identical populations X, and X2 with identical income distributions, the inequality measure would be the same for X, and X2 as well as when the X's are merged. An inequality measure satisfies the Pigou-Dalton condition, also known as the principle of transfer condition, if the level of inequality decreases when income is transferred from a rich country to a poor country (Bourguignon, 1979; Osberg, 1991). The inequality index that is used to analyze convergence in this dissertation is Theil's income inequality index. There aire three main reasons for this choice. First, Theil's index meets all four criteria for an inequality index (symmetry, mean-independence, population homogeneity, and the Pigou-Dalton condition). Second, this index yields a statistic (not a graphical representation). Thirdly, this index, or some derivative thereof, is the only additively decomposable inequality index (equation (5.6))(Osberg, 1991). Bourguignon (1979) defines additive decomposability as a measure that the total inequality of a population, can be broken down into a weighted average of the inequality existing within subgroups of the population, and the inequality existing between them. 102 Theil's Inequality index is the optimal inequality index for this study. This index meets all four properties and produces a consistent statistic. The decomposability of the index was used to determine the drivinq forces behind the changes in inequality. 5.2 Income Inequality in the G-7 In this section Theil's inequality index is applied to the Summers and Heston 1991 data. Summers and Heston data were used for an analysis of income changes in the G-7 countries (USA, Canada, Japan, UK, W. Germany, France and Italy) (Gao et al. 1992). Theil (1989b) did a similar analysis of inequality on a much larger group of countries, based on earlier data from Summers and Heston. This dissertation focuses on the G-7 because of their increased importance in recent years and the fact that the data for these countries are relatively accurate. For simplicity the word "income" is substituted for real gross domestic product per capita. Hence, when income inequality is referred to, it represents the inequality of real gross domestic product per capita. Column 2 of Table 5.1 shows per capita income of the combined G-7 from 1950-1988. Income per capita is obtained by weighting the per capita incomes of the seven countries in each year proportionally to their populations. Note that the G-7 per capita income increased almost threefold during the 38-year period. 103 Table 5.1 Income per Capita and Income Inequality (G-7 Countries) Per Capita Income Income Inequality Year (1) North All G-7 America (2) (3) Other Five (4) All G-7 (5) Regional (6) Average Within Region (7) (6) as a percentage of (5) (8) North America (9) Other Five (10) 1950 5019 8520 2889 0.2182 0.1432 0.0750 0.6562 0.0018 0.1195 1951 5258 8820 3069 0.2023 0.1366 0.0658 0.6752 0.0023 0.1048 1952 5400 8964 3188 0.1888 0.1310 0.0578 0.6938 0.0018 0.0925 1953 5586 9164 3346 0.1811 0.1246 0.0565 0.6880 0.0020 0.0906 1954 5617 8976 3496 0.1660 0.1092 0.0567 0.6578 0.0024 0.0911 1955 5972 9497 3725 0.1628 0.1076 0.0552 0.6609 0.0025 0.0887 1956 6105 9573 3873 0.1520 0.1007 0.0513 0.6625 0.0017 0.0831 1957 6201 9552 4025 0.1396 0.0919 0.0477 0.6583 0.0018 0.0775 1958 6165 9297 4113 0.1260 0.0819 0.0441 0.6500 0.0016 0.0719 1959 6468 9694 4337 0.1209 0.0797 0.0412 0.6592 0.0022 0.0670 1960 6706 9782 4656 0.1036 0.0679 0.0356 0.6554 0.0024 0.0577 1961 6898 9826 4932 0.0867 0.0586 0.0281 0.6758 0.0026 0.0452 1962 7167 10210 5114 0.0840 0.0590 0.0250 0.7023 0.0024 0.0403 1963 7429 10491 5353 0.0767 0.0559 0.0209 0.7288 0.0022 0.0335 1964 7802 10923 5673 0.0705 0.0530 0.0176 0.7517 0.0021 0.0281 1965 8116 11447 5836 0.0735 0.0560 0.0174 0.7619 0.0021 0.0279 1966 8481 11954 6094 0.0695 0.0561 0.0134 0.8071 0.0021 0.0212 1967 8726 12143 6366 0.0608 0.0515 0.0093 0.8470 0.0021 0.0143 1968 9156 12557 6792 0.0534 0.0467 0.0068 0.8745 0.0021 0.0100 1969 9510 12816 7215 0.0461 0.0408 0.0053 0.8850 0.0017 0.0078 1970 9705 12710 7611 0.0367 â€¢ 0.0324 0.0043 0.8828 0.0015 0.0062- 1971 9914 12974 7777 0.0364 0.0323 0.0040 0.8873 0.0011 0.0061 1972 10290 13393 8118 0.0348 0.0309 0.0038 0.8879 0.0019 0.0052 1973 10820 13943 8627 0.0315 0.0284 0.0030 0.9015 0.0017 0.0039 1974 10720 13698 8627 0.0296 0.0264 0.0032 0.8918 0.0016 0.0044 1975 10540 13385 8532 0.0276 0.0250 0.0026 0.9057 0.0006 0.0040 1976 11047 14009 8941 0.0275 0.0249 0.0026 0.9054 0.0007 0.0039 1977 11461 14572 9236 0.0278 0.0257 0.0021 0.9244 0.0003 0.0034 1978 11900 15131 9573 0.0280 0.0259 0.0021 0.9250 0.0007 0.0031 1979 12231 15357 9964 0.0249 0.0231 0.0017 0.9277 0.0007 0.0025 1980 12277 15162 10171 0.0211 0.0197 0.0013 0.9336 0.0005 0.0020 1981 12434 15382 10267 0.0214 0.0202 0.0012 0.9439 0.0003 0.0018 1982 12262 14829 10362 0.0169 0.0159 0.0010 0.9408 0.0004 0.0014 1983 12584 15346 10526 0.0183 0.0176 0.0007 0.9617 0.0002 0.0010 1984 13164 16303 10811 0.0216 0.0209 0.0007 0.9675 0.0005 0.0008 1985 13399 16609 10976 0.0219 0.0213 0.0006 0.9726 0.0005 0.0006 1986 13833 17118 11339 0.0215 0.0211 0.0004 0.9813 0.0003 0.0005 1987 14232 17587 11670 0.0212 0.0209 0.0003 0.9858 0.0003 0.0002 1988 14759 18140 12161 0.0203 0.0199 0.0004 0.9802 0.0006 0.0002 104 This increase is in sharp contrast to the behavior of the inequality of the seven per capita incomes. The inequality measure has a lower bound of 0 but no upper bound. Zero represents the case where there exists no inequality. In column 5, inequality is measured using equation (5.3). The results in column 5 indicate that inequality declined drastically: from almost 0.22 in 1950 to about 0.02 in 1988, or more than 90 percent. Thus the G-7 countries became much more affluent on the average, and also much more "equal." How did this happen? First of all, Canada and the U.S. had the highest per capita incomes among the G-7 in each year. The second reason is illustrated by grouping the seven countries into two regions, R, is North America (USA and Canada), and R2 is the Other 5. Columns 3 and 4 contain their per capita incomes. In 1950, R2 was approximately one-third of RÂ¡; However, by 1988 R2 rose to be almost two-thirds of R,. Thus, the Other 5 succeeded in substantially narrowing the gap between themselves and North America. The last five columns of Table (5.1) provide an analogous extension of the inequality analysis. Columns 6 and 7 show that both the regional inequality JR and the average within- region inequality jâ€™ declined drastically. Initially, in 1950, total inequality J was almost 0.22 and about two-thirds of this was regional (see column 8) . Ten years later, in 1960, total inequality was reduced by more than 50 percent and the regional share of this was still about two-thirds. 105 Another 10 years later, in 1970, total inequality was reduced even more (by almost two-thirds), and the regional component increased to almost 90 percent. Then, in 1980, total inequality declined further to about 0.02, after which it ceased to decline, but the regional component increased further until about 98 percent in the late 1980's. Columns 9 and 10 contain the within-region inequalities Jg for North America (g=l) and the Other 5 (g=2). The North American figures are small and slightly irregular, implying that the U. S.-Canadian differences in per capita income are small and uninteresting. The decline of the inequality among the Other 5 was from 0.12 in 1950 to 0.0002 in 1988. This reflects the increase of Japan's affluence toward Western European levels. The results for the G-7 countries clearly indicate that these countries were converging over the time period of 1950 to 1988. Japan's rapid growth in income was one of the biggest influences in the decrease in inequality between the G-7 nations. Germany and Italy also grew at a faster rate than the other countries. Thus, they helped influence the convergence of the G-7 also. The next section analysis some of the factors that are expected to have influenced the convergence of the G-7 countries. 106 5.3 Variables of Interest The prior section determined that the G-7 countries have converged over the period between 1950 to 1988. This section uses the same inequality index (Theil's) to determine if the inequality in some other variables have also converged. Three of the variables that have been associated with the inequality of income, or growth are examined (see Chapter 2). The criterion for choosing these time-series, in addition to the hypothesized relationships, was that the data series needed to extend back to 1950. These two restrictions narrowed the variables down to: total government expenditure (G) , total investment (I), and the number of people employed in industry (E) (see Appendix E concerning other variables that would enhance this study). The data used in this dissertation are from two sources. The financial indicators came from the Summers and Heston (1991) data set (income, G, and I). The total population in each country also came from Summers and Heston (1991) data set. Summers and Heston defined government expenditure as public consumption and investment expenditure as private and public expenditure. The number of people employed in industry came from the OECD (1963, 1969, 1989, 1991a, and 1991b). The government and investment data in Summers and Heston data series were measured in terms of a ratio. Their variables were transformed from real government expenditure as a percent of income and real investment expenditure as a 107 percent of real income to total government expenditure and total investment expenditure. These variables were analyzed here with Theil's inequality index. In the case of the number of people employed in industry, several countries did not have a complete data series. When considering the G-7 countries, only Japan and Italy had incomplete series. The method of extrapolation to fill in the missing observations is presented in Appendix F. The results from applying Theil's inequality index on government and investment expenditure, and the number of people employed in industry are shown in Table (5.2). This table is arranged such that the total, regional, and within inequalities are presented for each variable. The average within inequality is not shown here; however, J - JR is equal to the- average within inequality as illustrated in equation (5.6). 5.3.1 Inequality in Government Expenditure The total inequalities of G, I, and E in Table 5.2 (columns 1, 5, and 9) appear to decline over time, similar to income inequality. Specifically the inequality in government expenditure decreased from .14 in 1950 to .05 in 1988, which is a 65% decrease. The 1950 value is much lower than the other values in the 1950's. In fact, the inequality in government expenditure only attains the 1950 value of 0.1374 in 1963, 13 years later. Therefore, consider the 1951 value, the inequality then declines by 78% compared to 65%. Either Table 5.2 Government, Investment, and the Number of People Employed in Industry Inequalities (G-7 Countries) Government Inequality Investment Inequality Industrial Employment Inequality Year J (1) Jr (2) N. Am. J0 (3) Other 5 (4) J (5) Jr (6) N. Am. Ju (7) Other 5 (8) J (9) Jr (10) N. Am. J, (11) Other 5 J. (12) 1950 0.1374 0.0633 0.0100 0.1130 0.2579 0.1602 0.0001 0.1571 0.0246 0.0002 0.0000 0.0392 1951 0.2152 0.1261 0.0142 0.1351 0.1675 0.1140 0.0000 0.0865 0.0297 0.0009 0.0002 0.0464 1952 0.2254 0.1412 0.0149 0.1272 0.1690 0.0981 0.0008 0.1144 0.0270 0.0012 0.0004 0.0415 1953 0.2333 0.1463 0.0166 0.1311 0.1736 0.0941 0.0011 0.1287 0.0281 0.0011 0.0005 0.0436 1954 0.2009 0.1200 0.0151 0.1225 0.1452 0.0640 0.0000 0.1324 0.0318 0.0042 0.0004 0.0447 1955 0.1893 0.1121 0.0135 0.1177 0.1561 0.0678 0.0000 0.1446 0.0329 0.0045 0.0004 0.0463 1956 0.1849 0.1062 0.0134 0.1207 0.1298 0.0545 0.0022 0.1223 0.0285 0.0053 0.0002 0.0380 1957 0.1900 0.1105 0.0163 0.1205 0.0918 0.0334 0.0027 0.0946 0.0276 0.0080 0.0001 0.0322 1958 0.1799 0.1081 0.0159 0.1084 0.0919 0.0246 0.0016 0.1104 0.0305 0.0132 0.0000 0.0286 1959 0.1685 0.0981 0.0173 0.1054 0.0875 0.0274 0.0004 0.0994 0.0278 0.0116 0.0002 0.0268 1960 0.1568 0.0888 0.0169 0.1021 0.0553 0.0096 0.0002 0.0760 0.0301 0.0145 0.0004 0.0257 1961 0.1527 0.0890 0.0142 0.0969 0.0291 0.0029 0.0000 0.0438 0.0332 0.0198 0.0003 0.0222 1962 0.1474 0.0873 0.0147 0.0908 0.0387 O.0O62 0.0000 0.0544 0.0308 0.0197 0.0002 0.0186 1963 0.1352 0.0810 0.0140 0.0816 0.0302 0.0062 0.0000 0.0403 0.0302 0.0202 0.0002 0.0166 1964 0.1297 0.0790 0.0143 0.0755 0.0200 0.0036 0.0001 0.0276 0.0215 0.0127 0.0004 0.0145 1965 0.1240 0.0761 0.0137 0.0713 0.0301 0.0101 0.0001 0.0336 0.0204 0.0109 0.0004 0.0158 1966 0.1328 0.0873 0.0144 0.0668 0.0247 0.0105 0.0003 0.0237 0.0177 0.0087 0.0004 0.0150 1967 0.1386 0.0929 0.0150 0.0668 0.0093 0.0045 0.0000 0.0080 0.0145 0.0082 0.0007 0.0102 1968 0.1342 0.0929 0.0136 0.0605 0.0060 0.0015 0.0000 0.0077 0.0147 0.0087 0.0008 0.0095 1969 0.1274 0.0882 0.0127 0.0576 0.0075 0.0002 0.0002 0.0123 0.0144 0.0084 0.0008 0.0095 1970 0.1149 0.0791 0.0085 0.0548 0.0115 0.0026 0.0001 0.0150 0.0164 0.0109 0.0008 0.0087 1971 0.1026 0.0682 0.0066 0.0538 0.0096 0.0003 0.0001 0.0158 0.0184 0.0136 0.0004 0.0079 1972 0.0952 0.0610 0.0060 0.0540 0.0116 0.0000 0.0000 0.0198 0.0159 0.0113 0.0004 0.0076 1973 0.0854 0.0520 0.0042 0.0538 0.0077 0.0000 0.0000 0.0131 0.0142 0.0093 0.0003 0.0081 1974 0.0833 0.0493 0.0034 0.0554 0.0092 0.0000 0.0010 0.0149 0.0132 0.0093 0.0001 0.0066 1975 0.0783 0.0438 0.0024 0.0571 0.0131 0.0007 0.0063 0.0168 0.0150 0.0121 0.0000 0.0051 1976 0.0697 0.0373 0.0019 0.0540 0.0080 0.0000 0.0029 0.0117 0.0110 0.0082 0.0000 0.0048 1977 0.0643 0.0350 0.0013 0.0493 0.0087 0.0012 0.0009 0.0123 0.0095 0.0068 0.0002 0.0045 1978 0.0597 0.0312 0.0012 0.0481 0.0107 0.0030 0.0001 0.0132 0.0075 0.0044 0.0004 0.0049 1979 0.0540 0.0267 0.0012 0.0462 0.0102 0.0012 0.0013 0.0146 0.0066 0.0033 0.0003 0.0054 1980 0.0507 0.0243 0.0010 0.0451 0.0159 0.0000 0.0035 0.0248 0.0074 0.0044 0.0001 0.0051 1981 0.0463 0.0222 0.0008 0.0412 0.0215 0.0017 0.0045 0.0311 0.0073 0.0042 0.0000 0.0055 1982 0.0456 0.0223 0.0006 0.0400 0.0152 0.0009 0.0030 0.0228 0.0103 0.0070 0.0002 0.0056 1983 0.0432 0.0211 0.0005 0.0381 0.0091 0.0002 0.0021 0.0139 0.0107 0.0066 0.0003 0.0070 1984 0.0441 0.0230 0.0008 0.0364 0.0141 0.0076 0.0001 0.0113 0.0091 0.0037 0.0005 0.0091 1985 0.0500 0.0292 0.0013 0.0356 0.0122 0.0051 0.0010 0.0118 0.0100 0.0036 0.0004 0.0120 1986 0.0483 0.0297 0.0016 0.0316 0.0117 0.0037 0.0019 0.0126 0.0101 0.0031 0.0003 0.0122 1987 0.0508 0.0305 0.0019 0.0344 0.0113 0.0032 0.0025 0.0122 0.0099 0.0027 0.0002 0.0126 1988 0.0480 0.0282 0.0015 0.0338 0.0105 0.0016 0.0037 0.0128 0.0114 0.0031 0.0001 0.0146 108 109 way, it is clear that the inequality in the level of government expenditure has declined over time. This suggests that the G-7 countries have been converging in their expenditure on public consumption. The question is, "why?" The decomposability of Theil's index gives some insights on why the G-7 are converging in terms of government expenditure. Column 2 shows the government regional inequality declines 56% from 1950 and 78% from 1951 to 1980 which is similar to the movements in total government inequality (i.e. the percentage decline). The inequality between the two regions has decreased significantly. The question is, How much of the regional inequality decline accounts for the reduction in total inequality? This question can be answered by dividing column 2 by column 1 (not shown). The result of this is that regional government inequality accounts for an average of 50% to 55% of the total government inequality. The amount of total inequality accounted for by regional inequality is fairly constant over time. Given those results, the within inequality values are analyzed to find the driving force behind the decline in government inequality. Column 3 contains the North American within inequality and column 4 contains the Other 5. The inequality between Canada and the U.S. has decreased 86% since 1950. The reason for this large decrease is due to Canada's increase in government expenditure per capita. In the 1950's and 60's, Canada's expenditure was only half of the U.S.'s. 110 The 1980's showed an increase to about 82% of the U.S.'s government expenditure per capita. Stated another way, between 1950 and 1988, Canada increased its expenditures three times while the U.S.'s only increased 1.5 times. The Other 5 countries only reduced their within inequality by 30% from 1950 to 1988. The U.K. had the largest initial level of expenditure in this group: 3.6 times larger than Japan, 2.6 times larger than Italy, 2.1 times larger than W. Germany, and 1.4 times larger than France. Over time this situation changed considerably with W. Germany and France having approximately the same per capita expenditure as the U.K.; Japan and Italy still lagged behind but closed the gap some. In 1988, Japan spent 1.9 times less, and Italy spent 1.2 less than the U.K. in terms of government expenditure per capita. However, the rate of increase for Japan (3.3 times their initial value) was similar to W. Germany (3.4), France (2.3), and Italy (3.6). In contrast, the U.K.'s rate of increase was only 1.7 times its initial value for 1950.3 Therefore, the convergence in terms of government expenditure appears to be due to the slow rate of increase in the U.S. and the U.K. and the fast rate of increase in government expenditure in the other countries. 3The growth rates for the U.S. and Canada during this time period were 1.9 and 2.8, respectively. Ill 5.3.2 Inequality in Investment Expenditure The decrease in the total inequality in investment is similar to the situation with income inequality. Column 5 of Table 5.2 shows that total investment inequality decreased by 96% from 1950 to 1988. Once again if the 1951 value is used, the reduction is still extremely high, 94%. Column 6 shows that regional inequality also decreased dramatically, 99%. The interesting fact about the drastic decrease in both the total and regional inequalities is that the majority of the reduction in total inequality is due to the average within inequality. The average within inequality accounts for the following percentage of the decrease in total investment inequality by decade: 64% in the 1950's, 76% in the 1960's, 91% in the 1970's, and 78% in the 1980's. The relatively dramatic rate of r convergence ^ is " largely due â€™ to - within inequality. The North American within inequality, however, is close to being nonexistent (Table 5.2, Column 7). Therefore, the reduction in inequality must be due to the within inequality in the Other 5 (Table 5.2, column 8). The Other 5 within inequality reduced 92% from 1950 to 1988, and 85% from 1951 to 1988. To determine which countries are responsible for this decrease, consider Table 5.3. This table illustrates each countries initial (1950) and final (1988) per capita investment expenditure and the rate of increase in investment, 112 the latter is defined as dividing the final expenditure by the initial expenditure. Table 5.3. Investment Expenditure per Capita, and the Rate of Investment Expenditure for the G-7 G-7 Countries Year Canada U.S. Japan U.K. W. Germany France Italy (1) (2) (3) (4) (5) (6) (7) (8) 1950 1562 1640 185 516 845 752 569 1988 4661 3513 3878 2465 3094 3050 2921 Rate of Investment Expenditure 3 2 21 4.8 4 3.7 5 The initial value for Japan is clearly significantly low in comparison to the other G-7 countries. However, their increase in the rate of expenditure on investment per capita (21 times initial value) has boosted them to being one of the top countries in terms of investment expenditure per capita. Hence, Japan's increase in investment expenditure is part of the reason for the large decrease in the total inequality of investment expenditure. The relatively fast rate of increase in investment expenditure in Italy and the U.K. is partly responsible for the reduction in the Other 5. In terms of the G-7, the relatively slow rate of increase of investment in the 113 U.S. and Canada allowed the other countries, all of which increased their expenditure at a faster rate, to catch up. 5.3.3 Inequality in Industrial Employment The total inequality in industrial employment is different than the other three inequalities. The total inequality in industrial employment has always been below 0.04 for the sample period which is small in comparison to the other three inequalities.4 The total inequality in industrial employment shown in column 9 of Table 5.2 decreased 54% from 1950 to 1988. If the 1951 value is taken, the decline in inequality is larger, 62%. Regional inequality for industrial employment in column 10 is also different from the other three inequality results. The regional inequality actually increases 94% from 1950 to 1988 and 71% for 1951 to 1988. The total industrial employment inequality is decreasing while the regional industrial employment inequality is increasing. To figure out what is occurring, consider the percent of total inequality due to regional inequality. In the 1950's regional inequality accounted for 18% of total inequality, 57% in the 1960's, 68% in the 1970's, and 46% in the 1980's. Hence, regional inequality became more important until the 1970's, then having an effect equal to that of the average within inequality by the 1980's. 4The industrial employment data for countries that have incomplete data for the number of people employed in industry were extrapolated as explained in Appendix E. 114 The within inequalities are straight forward. The North American (column 11) within inequality is basically nonÂ¬ existent. The Other 5 inequality is small, but its inequality is the largest out of all of the inequalities for industry. The inequality for the Other 5 decreased by 63% from 1950-88 and 68% from 1951-88. It is apparent that the regional inequality and the average within inequality are going in opposite directions. Given that the two (regional and average within) have basically an equal effect on total inequality, total inequality declines largely because of the reduction in the average within region inequality. In addition, after 1975 regional inequality starts to decline. In summary, the convergence in the number of people employed in industry is due to the reduction in inequality in the Other 5. The rate of increase in'industrial employment from 1950 to 1988 (final value divided by initial value) for each country was: Canada, 1.7; U.S., 1.5; Japan, 2.5; U.K., .77; W. Germany, 1.2; France, 1.1; and Italy, 1.3. Once again Japan's was largely responsible for the decrease in inequality. 5.4 Inequality in Selected OECD Countries In this section Theil's inequality index is applied to 14 of the Organization for Economic Co-operation and Development (OECD) countries (the U.S., Canada, Japan, the U.K., W. Germany, France, Italy, Austria, Belgium, Denmark, the 115 Netherlands, Norway, Ireland, and Spain).5 The reason for selecting 14 out of the 24 OECD for this analysis was solely based on the availability of data. The data for income from 1950 is available for most of these countries but the data is too sparse for the other three variables for the countries not included in this analysis. As in the G-7 case, the data for the 14 OECD countries, which will now be referred to as the OECD, were taken from the Summers and Heston 1991 data set, and the OECD statistics. The main reason for expanding this study to the OECD is to compare the results with those of the G-7. The comparison of the results from the G-7 and OECD is a way to check the performance of the instruments used in this study. In fact, it would be helpful if a larger group of countries could be included. > However, it was mention prior that the data limitations will not allow such a comparison. In the next section Theil's ineguality measure is applied to the 14 OECD countries data. 5.4.1 Income Inequality in the OECD Countries Column 2 of Table 5.4 shows per capita income of the combined OECD countries from 1950 to 1988. Income per capita 5The Signatories of the Convention on the OECD were Austria, Belgium, Canada, Denmark, France, the Federal Republic of Germany, Greece, Iceland, Ireland, Italy, Luxembourg, the Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, Turkey, the United Kingdom, and the United States. The list of countries that subsequently joined this Convention are given along with the date of accession: Japan (April, 1964) , Finland (January, 1969) , Australia (June, 1971), and New Zealand (May, 1973) (Ward, 1985). 116 is obtained by weighting the per capita incomes of the 14 countries in each year proportionally to their populations. Note that the OECD per capita income increased almost threefold during the 38-year period. As mentioned in section 5.2, the G-7 increased its income approximately threefold during the same time period. The Other 7 has increased its income by 3.3 times. Once again equation (5.3) is used to determine the movement of inequality in income over time. The results in column 5 indicate that inequality declined from 0.21 in 1950 to 0.03 in 1988, or 86 percent. Thus the OECD countries became much more affluent on the average, and also much more "equal." This is not surprising considering the G-7 accounts for most of the income and population. As in the G-7 analysis, the OECD countries were grouped into two regions. The first region was the G-7 and the second region was the Other 7 countries. Column 6 shows that regional inequality only reduced by 40% from 1950 to 1988. Column 8 confirms that regional inequality only accounted for a minimal part of the reduction in total income inequality in the 1950's. The percent of regional income inequality accounting for total income inequality grew every year to reach a maximum of 30% in 1988. However, average within- region inequality is responsible for the decrease in income inequality. The average within-region inequality (column 7) 117 Table 5.4 Income per Capita and Income Inequality (OECD Countries) Per Capita Income Income Inequality Year ALL OECD G-7 Other 7 ALL OECD Regional Average Within Region (6) as a percentage of (5) Ui thin G-7 Within Other 7 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) 1950 4749 5019 2897 0.2143 0.0146 0.1996 0.0683 0.2182 0.0725 1951 4976 5258 3038 0.1975 0.0145 0.1830 0.0735 0.2023 0.0498 1952 5109 5400 3096 0.1856 0.0148 0.1708 0.0800 0.1888 0.0460 1953 5282 5586 3164 0.1812 0.0154 0.1657 0.0851 0.1811 0.0589 1954 5340 5617 3404 0.1633 0.0121 0.1512 0.0742 0.1660 0.0479 1955 5672 5972 3566 0.1610 0.0127 0.1482 0.0791 0.1628 0.0457 1956 5808 6105 3714 0.1502 0.0118 0.1383 0.0789 0.1520 0.0418 1957 5907 6201 3816 0.1387 0.0113 0.1274 0.0814 0.1396 0.0407 1958 5878 6165 3834 0.1254 0.0108 0.1146 0.0861 0.1260 0.0330 1959 6153 6468 3893 0.1237 0.0122 0.1115 0.0986 0.1209 0.0437 1960 6383 6706 4067 0.1095 0.0118 0.0977 0.1080 0.1036 0.0553 1961 6588 6898 4348 0.0914 0.0101 0.0813 0.1109 0.0867 0.0427 1962 6855 7167 4589 0.0876 0.0095 0.0781 0.1081 0.0840 0.0353 1963 7111 7429 4801 0.0799 0.0091 0.0708 0.1138 0.0767 0.0280 1964 7475 7802 5101 0.0745 0.0086 0.0658 0.1158 0.0705 0.0317 1965 7783 8116 5360 0.0761 0.0082 0.0679 0.1081 0.0735 0.0273 1966 8132 8481 5586 0.0722 0.0083 0.0638 0.1155 0.0695 0.0228 1967 8367 8726 5754 0.0647 0.0083 0.0564 0.1282 0.0608 0.0242 1968 8772 9156 5988 0.0585 0.0086 0.0499 0.1472 0.0534 0.0241 1969 9129 9510 6350 0.0511 0.0078 0.0433 0.1531 0.0461 0.0229 1970 9331 9705 6604 0.0424 0.0071 0.0352 0.1683 0.0367 0.0245 1971- ' 9539 - - 9914 â€¢ 6803 â€¢â€¢ 8.0418 0.0068 â– - 0.0350 -r -0.1634 0.0364 â€¢ â€™-0.0248 1972 9911 10290 7137 0.0395 0.0065 0.0330 0.1636 0.0348 0.0201 1973 10425 10820 7534 0.0362 0.0063 0.0299 0.1748 0.0315 0.0180 1974 10373 10720 7831 0.0330 0.0048 0.0282 0.1459 0.0296 0.0178 1975 10203 10540 7736 0.0310 0.0047 0.0264 0.1505 0.0276 0.0173 1976 10681 11047 8012 0.0317 0.0050 0.0266 0.1589 0.0275 0.0206 1977 11061 11461 8145 0.0327 0.0057 0.0270 0.1736 0.0278 0.0209 1978 11460 11900 8248 0.0340 0.0065 0.0275 0.1911 0.0280 0.0233 1979 11765 12231 8362 0.0321 0.0070 0.0252 0.2165 0.0249 0.0274 1980 11822 12277 8495 0.0286 0.0065 0.0221 0.2282 0.0211 0.0297 1981 11953 12434 8429 0.0298 0.0072 0.0225 0.2431 0.0214 0.0308 1982 11800 12262 8406 0.0254 0.0068 0.0186 0.2688 0.0169 0.0309 1983 12091 12584 8463 0.0275 0.0075 0.0200 0.2722 0.0183 0.0331 1984 12621 13164 8616 0.0319 0.0085 0.0234 0.2660 0.0216 0.0369 1985 12841 13399 8719 0.0326 0.0087 0.0239 0.2662 0.0219 0.0392 1986 13256 13833 8979 0.0322 0.0088 0.0234 0.2722 0.0215 0.0379 1987 13639 14232 9237 0.0313 0.0088 0.0226 0.2791 0.0212 0.0331 1988 14143 14759 9554 0.0304 0.0088 0.0216 0.2908 0.0203 0.0314 118 has declined by 89%. Which region is responsible for this change? The G-7 movements in inequality for income were discussed in section 5.2. It was determined that Japan was the driving force behind the decline in income inequality for the G-7. Column 9 in Table 5.4 is the same as column 5 in Table 5.1. It was determined that the G-7 inequality declined 90%. Comparing this result with the Other 7's within-region inequality (column 10) which only decreased 57% indicates that the G-7 dominated the OECD results. Income inequality of the 14 selected OECD countries declined mainly due to the G-7 countries and their heavy weighting in the index. Although the Other 7 countries were converging, they were converging within themselves at a slower rate than the G-7.> The two regions, -G-7 and the Other 7 were also converging. It was determined in section 5.2 that the convergence of the G-7 was largely due to Japan's rapid income growth. Germany and Italy were also fast growers which helped in the convergence. The Other 7 on average grew faster than the G-7, but there were no extremely fast growers like Japan. Austria and Spain had the fastest growth rates in the Other 7 followed by Norway. The other countries grew at slower rates than the OECD average. Therefore, the countries largely responsible for convergence in the Other 7 were Austria, Spain, and Norway. Overall convergence is due to the fast income growth 119 of Japan, Germany, Italy, Austria, Spain, and Norway. The slow growth of the U.S. and Canada also helped the convergence of the OECD countries. In fact the U.S. had the slowest growth rates followed by Canada and the U.K. 5.4.2 Inequality of Government Expenditure in the OECD The total inequalities of G, I, and E in Table 5.5 (columns 1, 5, and 9) appear to decline over time, similar to income inequality. Specifically the inequality in government expenditure decreased from .17 in 1950 to .055 in 1988, which is approximately a 67% decrease. The inequality among the OECD countries started out higher than the inequality in the G-7. However, by 1988, the inequality in the OECD had decreased more than the inequality in the G-7 indicating that the Other 7 countries increased their expenditure at a faster rate. When the population weighted averages are considered these results are confirmed. The G-7 have increased their government expenditures 2.3 times over the 39 year period while the Other 7 have increased theirs by 3.4 times. The regional inequality, however, only accounted for a small percentage of the total inequality, 10 - 15% during the 39 year period. In addition, the regional inequality (Table 5.5, column 2) was fairly small when the within-region inequalities were considered. As mentioned in the G-7 discussion, total government inequality of the G-7 decreased 65% which was mainly due to the small increases in government expenditure in the U.S. and the U.K over time. Table 5.5 Government, Investment, and the Number of People Employed in Industry Inequalities (OECD Countries) Government Inequality Investment Inequality Industrial Employment Inequality G-7 Other 7 G-7 Other 7 G-7 Other 7 J Jr J, J. J Jr Jo J, J Jr J, J, Year LLL iUL (3) (Â¿0 (5) (6) (7) (8) (9) (10) (11) (12) 1950 0.1699 0.0264 0.1374 0.1848 0.2489 0.0072 0.2579 0.1302 0.0266 0.0003 0.0246 0.0381 1951 0.2446 0.0370 0.2152 0.1555 0.1647 0.0081 0.1675 0.0813 0.0348 0.0015 0.0297 0.0576 1952 0.2612 0.0435 0.2254 0.1645 0.1669 0.0087 0.1690 0.0829 0.0308 0.0015 0.0269 0.0457 1953 0.2700 0.0416 0.2333 0.1945 0.1715 0.0070 0.1736 0.1015 0.0306 0.0013 0.0281 0.0382 1954 0.2300 0.0322 0.2009 0.1765 0.1394 0.0026 0.1451 0.0787 0.0325 0.0006 0.0318 0.0329 1955 0.2170 0.0294 0.1893 0.1757 0.1497 0.0055 0.1561 0.0606 0.0325 0.0004 0.0329 0.0266 1956 0.2107 0.0280 0.1849 0.1670 0.1258 0.0042 0.1298 0.0635 0.0280 0.0004 0.0285 0.0210 1957 0.2142 0.0282 0.1900 0.1573 0.0915 0.0028 0.0918 0.0662 0.0271 0.0004 0.0276 0.0208 1958 0.2062 0.0288 0.1799 0.1596 0.0887 0.0031 0.0919 0.0407 0.0290 0.0002 0.0305 0.0168 1959 0.1954 0.0286 0.1685 0.1551 0.0923 0.0058 0.0874 0.0798 0.0267 0.0002 0.0278 0.0171 1960 0.1848 0.0271 0.1568 0.1643 0.0646 0.0040 0.0553 0.0984 0.0292 0.0003 0.0301 0.0203 1961 0.1809 0.0278 0.1527 0.1566 0.0349 0.0022 0.0291 0.0593 0.0316 0.0002 0.0332 0.0186 1962 0.1752 0.0271 0.1474 0.1529 0.0404 0.0017 0.0387 0.0388 0.0292 0.0001 0.0308 0.0164 1963 0.1609 0.0243 0.1352 0.1466 0.0318 0.0022 0.0302 0.0256 0.0284 0.0001 0.0302 0.0148 1964 0.1562 0.0240 0.1297 0.1509 0.0233 0.0010 0.0200 0.0389 0.0210 0.0004 0.0215 0.0143 1965 0.1496 0.0235 0.1240 0.1414 0.0301 0.0006 0.0301 0.0251 0.0199 0.0004 0.0204 0.0126 1966 0.1595 0.0256 0.1328 0.1425 0.0246 0.0004 0.0246 0.0206 0.0174 0.0005 0.0177 0.0114 1967 0.1651 0.C265 0.1386 0.1385 0.0124 0.0006 0.0093 0.0301 0.0145 0.0006 0.0145 0.0102 1968 0.1609 0.0263 0.1342 0.1373 0.0099 0.0012 0.0060 0.0283 0.0147 0.0007 0.0147 0.0091 1969 0.1524 0.0239 0.1274 0.1367 0.0104 0.0011 0.0075 0.0225 0.0143 0.0007 0.0143 0.0083 1970 0.1376 0.0209 0.1149 0.1292 0.0144 0.0007 0.0115 0.0303 0.0160 0.0006 0.0164 0.0081 1971 0.1247 0.0191 0.1026 0.1281 0.0139 0.0011 0.0096 0.0364 0.0176 0.0004 0.0183 0.0084 1972 0.1165 0.0178 0.0952 0.1240 0.0141 0.0014 0.0116 0.0210 0.0153 0.0005 0.0159 0.0073 1973 0.1055 0.0166 0.0854 0.1149 0.0106 0.0017 0.0077 0.0179 0.0140 0.0006 0.0142 0.0071 1974 0.1007 0.0151 0.0833 0.1028 0.0102 0.0004 0.0092 0.0140 0.0130 0.0006 0.0132 0.0068 1975 0.0949 0.0142 0.0783 0.0986 0.0135 0.0000 0.0131 0.0159 0.0143 0.0003 0.0150 0.0065 1976 0.0847 0.0121 0.0697 0.0932 0.0104 0.0005 0.0080 0.0235 0.0113 0.0006 0.0110 0.0084 1977 0.0784 0.0110 0.0643 0.0904 0.0122 0.0014 0.0087 0.0257 0.0101 0.0007 0.0095 0.0086 1978 0.0728 0.0095 0.0597 0.0896 0.0159 0.0034 0.0107 0.0255 0.0087 0.0012 0.0074 0.0083 1979 0.0664 0.0082 0.0540 0.0885 0.0173 0.0045 0.0102 0.0325 0.0085 0.0016 0.0066 0.0096 1980 0.0623 0.0072 0.0507 0.0867 0.0213 0.0030 0.0159 0.0363 0.0097 0.0019 0.0074 0.0106 1981 0.0583 0.0067 0.0463 0.0902 0.0300 0.0066 0.0215 0.0375 0.0105 0.0026 0.0073 0.0119 1982 0.0566 0.0063 0.0456 0.0849 0.0216 0.0039 0.0152 0.0359 0.0132 0.0026 0.0103 0.0130 1983 0.0537 0.0060 0.0432 0.0809 0.0191 0.0062 0.0091 0.0411 0.0140 0.0029 0.0107 0.0138 1984 0.0544 0.0065 0.0441 0.0760 0.0297 0.0093 0.0141 0.0665 0.0139 0.0038 0.0091 0.0164 1985 0.0596 0.0070 0.0500 0.0717 0.0276 0.0089 0.0122 0.0667 0.0152 0.0040 0.0100 0.0202 1986 0.0574 0.0071 0.0483 0.0657 0.0246 0.0067 0.0117 0.0641 0.0149 0.0037 0.0101 0.0198 1987 0.0580 0.0063 0.0508 0.0586 0.0220 0.0069 0.0113 0.0433 0.0135 0.0029 0.0099 0.0157 1988 0.0547 0.0061 0.0480 0.0536 0.0203 0.0067 0.0105 0.0369 0.0141 0.0024 0.0114 0.0143 120 121 The reduction in the within-region inequality of the Other 7 is a different story. The within-region inequality of the Other 7 decreased 71% from 1950 to 1988. The rate of increase in government expenditure for the G-7 countries was discussed in section 5.3.1; hence, this section will focus on the Other 7's. Government expenditure for the Other 7 increased from 1950 to 1988 by the following values: Spain, 5.8; Denmark, 4.8; Norway, 4.6; Belgium, 3.3; Ireland,2.8; Austria, 2.7; and the Netherlands, 2, respectively. Lastly, the 1950 government expenditure per capita for each country was: Netherlands $808; Denmark, $596; Austria, $555; Norway, $468; Belgium, $452; Ireland, $342; and Spain, $171, respectively. Considering the initial value and the rate of increased expenditureconvergence in the Other 7 wars due ta Spain and Norway's increased expenditure on public goods. The Netherlands slow rate of government expenditure also helped the countries to converge by allowing the other countries to catch up. Ireland appeared to be growing slow as well as having a small initial value. Therefore, Ireland may be slowing the convergence of the Other 7 countries. Denmark had a high rate of increased expenditure and had a relatively high expenditure in 1950, thus, this country is diverging instead of converging. Denmark may have slowed the rate of convergence in the Other 7 sample. Although there are 122 converging and diverging forces in the sample, the overall effect is that the Other 7 and OECD countries are converging. 5.4.3 Investment Inequality in the OECD Column 5 of Table 5.5 shows the dramatic decline in investment inequality. Investment inequality decreased by 92% from 1950 to 1988. Actually investment inequality reached its lowest level in 1968, from .25 in 1950 to .01 in 1968, a 96% decline in 19 years. The inequality increased slightly after 1968 to reach .02 in 1988. Hence, investment inequality increased by 51% from 1968 to 1988. Little of the total inequality was due to regional inequality until the late 1970's. The average regional inequality between the 1950 and the late 1970's is around 6%. After the late 1970's, total inequality due to regional inequality jumped to an average of 30%. .-StÂ±il,~regional inequality has remained low between the two regions during the whole time period. Within-region inequality appears to be the major reason for the reduction in total investment inequality. The G-7 section determines that the 96% decrease in inequality in the G-7 was mainly due to the rapid increase in investment by Japan. The within-region inequality for the Other 7 decreased by 72%. To extend Table 5.3, Table 5.6 is added to the text. Table 5.6 shows the initial, final, and the rate of investment expenditure per capita for the Other 7 countries. The initial values for the Other 7 were lower than the G- 7 on average. The average population weighted value for the 123 G-7 is $941 compared to the Other 7 value of $644 per capita. However, if Japan's initial value is removed, the G-7 level would be a little higher. Denmark, Norway, and the Netherlands have high initial values compared to the rest of the OECD with the exception of the U.S. and Canada. Just like the U.S. and Canada, Denmark and the Netherlands increased their expenditure on investment at a slower rate allowing other countries to catch up. Norway, however, increased its expenditure rate at a fairly fast rate (3.2) to end up as the second highest value for 1988. The average population weighted rate of investment expenditure for all 14 countries is 3.6. Using that value as a guide, the countries that have influenced convergence in the Other 7 can be determined. Table 5.6 Investment Expenditure per Capita, and the Rate of Investment Expenditure for the Other 7 Other 7 Countries Year (1) Austria (2) Belgium (3) Denmark (4) Nethrlds (5) Norway (6) Ireland (7) Spain (8) 1950 544 812 1120 1013 1394 488 341 1988 3534 2598 2473 2275 4404 1287 1921 Rate of Investment Expenditure 6.5 3.2 2.2 2.3 3.2 2.6 5.6 124 Austria and Spain had the fastest rates in investment expenditure for the Other 7 countries. Thus, their fast rate of increase in investment expenditure and the slow rate of Denmark and the Netherlands have influenced convergence in the Other 7. Convergence in terms of investment per capita in the OECD countries was supported by the fast rate of investment expenditure in Japan, Austria, Spain, Italy, and the U.K. The slow rate of investment expenditure in the U.S. and Canada (they had the slowest rate) helped the other countries to catch up, therefore, converge. 5.4.4 OECD Inequality in Industrial Employment The inequality in the number of people employed in industrial is shown in column 9 of Table 5.5.6 Total inequality has decreased 47% from 1950 to 1988. The lowest level of inequalityâ– occurred in 1979 among the 14 countries. As in the G-7 case, regional inequality has increased even though total inequality has decreased. The regional inequality has increased 88% (column 10), which means the two regions have grown further apart over time. However, regional inequality only accounts for less than 5% on average until the late 1970's. Then regional inequality jumps to almost 22% of total inequality. Once again within-region inequality is responsible for the reduction in total inequality. As noted in the G-7 6The countries that have incomplete data for the number of people employed in industry were extrapolated as explained in Appendix E. 125 section, inequality among the G-7 decreased 54% (reproduced in Table 5.5, column 11). The driving force behind the reduction in the G-7 is the rate of increase in the number of people employed in industry in Japan. The within-region inequality for the Other 7 decreased 62% from 1950 to 1988 (column 12). In summary, the convergence in the number of people employed in industry was due to the reduction in the within- region inequality. The rate of increase in industrial employment (final value divided by initial value) for each group was: G-7 (Canada, 1.7; U.S., 1.5; Japan, 2.5; U.K., .77; W. Germany, 1.2; France, 1.1; and Italy, 1.3), and the Other 7 (Austria, 1.2432; Belgium, 0.7; Denmark, 1.3; Netherlands, 1.0; Norway, 1.1; Ireland, 1.9; and Spain, 1.5). Once again Japan's was largely responsible for the decrease in the inequality of the G-7. The relatively fast rate of increase in industrial employment by Ireland and Spain have influenced the convergence of the Other 7. 5.5 Summary of the Inequality Results The overall summary of the findings is that convergence is supported for all four variables (income, government, investment, and the number of people employed in industry inequalities) for the G-7 and for the OECD countries. In general, convergence occurred at a faster rate in the income and investment variables. However, there was a relatively low level of inequality among the countries in terms of the number of people employed in industry. The next section analyzes 126 these results further by determining if there exists any long term relationships among these variables and the movement within them. CHAPTER 6 COINTEGRATION 6.1 An Overview of Cointecrration Cointegration is used in this analysis to determine the long-run relationships among the four inequality indices for the G-7 and selected OECD countries. Several studies in the Convergence section combined inequality measures with multiple regression techniques (Braun, 1988; Ram, 1989b; Ram, 1992; McGillivray, 1991; and Amos, 1991). This study, however attempts to establish the co-movement of these inequality indices over time. This objective is important because the long-run equilibrium has not previously been explained. The co-movements over time will explain the long-run equilibrium instead of the static equilibrium which regression analysis addresses. The most appropriate statistical method to establish the co-movements over time is cointegration analysis. Cointegration analysis will explain if there is or is not a long-run equilibrium, and which variables are included in that equilibrium. There are three basic differences between standard regression analysis and cointegration analysis. First, regression analysis establishes a linear or nonlinear 127 128 combination of the dependent variable and independent variables that must be equal to white noise.1 Cointegration analysis only requires that slow or trending movements in the dependent variable equal linear combinations of similar movements in the independent variable. The cointegrating relationship does not have to be purely random. It can be a stationary process. The second difference is that there is no need to designate a variable as exogenous. If the two series are found to be cointegrated, then the relationship is symmetric. That is, if y and x are cointegrated, then x and y are cointegrated (Engle and Yoo, 1991). In addition, regression analysis only describes the positive or negative influence of the dependent variable on the independent variable. The last reason cointegration analysis is used is to determine the long-run trends in the data series. Regular regression analysis produces spurious results if it is used on variables that have trends in them (Maddala, 1992) . In order to resolve this problem, the data need to be differenced or transformed until stationary, then regressed. However, when this is done all of the long-run information in the series is lost. Cointegration analysis on the contrary incorporates non-stationary levels data along with the differenced â€˜White noise in time series is a sequence of uncorrelated random variables with zero mean and identical finite variances (Judge et al., 1980). 129 stationary data.2 Therefore, the long-run information is not lost, and the regression is not spurious. Testing for cointegration begins with analyzing the residuals from a cointegrating regression for stationarity. Stationarity refers to a time-series having a constant mean and a bounded variance over time. If the residuals from a cointegrating equation are stationary, then the variables are cointegrated. If the residuals are not stationary, then any deviation between the series causes them to diverge infinitely as time approaches infinity, versus being stable when the residuals are stationary (Maddala 1992, Moss 1992). Stated another way, if two vectors are cointegrated, then any deviation between the two series dissipates quickly. However, if the two series are not cointegrated then a deviation persists.3 Three of the four variables (income, investment expenditure, and government expenditure) of interest in this dissertation have been tested for cointegration in other studies. The variables in those studies are defined 2The error correction model incorporates levels data with stationary data to describe the long-run relationships. The error correction model is explicitly or implicitly used in most multiple cointegration models. 3Cointegrated series have short memories meaning that any innovation in the model does not last long. Non-cointegrated series have long memories, that is innovations last a long time. For example, if the series are cointegrated, then old shocks in the series have no effect on the current values. 130 differently than in this dissertation, but there results will be helpful in interpreting the results from this dissertation. Kugler (1991) tested the multivariate cointegration of income, consumption, investment, and exports from 1970 to 1987 for seven countries: the U.S., Japan, Switzerland, W. Germany, the U.K., and France. Income was defined as GDP for all of the countries except the U.S. where GNP was used. Investment was defined as the gross fixed business investment for all of the countries except Switzerland where investment only covers equipment. The data came from the Quarterly National Accounts for each respective country. In general, Kugler found the time-series data to be 1(1). The multivariate cointegration results supported the relationships among income, consumption, and investment, but not exports. The U.K. had no statistically significant cointegrating relationships. Government expenditure has been tested for cointegration with income by MacDonald et al. (1989) . They conducted a study on the cointegration between the log of government expenditure and income for four countries: U.K., Canada, Germany, and the U.S. from 1965 to 1986. Income was defined as GDP less government expenditure. Both variables were deflated by their respective consumer price indexes. The data for the study came from the International Financial Statistics (quarterly data) . In general, they found that the log of government expenditure and income to be 1(1). Cointegration 131 was found between these two variables in three countries: Germany, the U.K., and the U.S. Canada's sample did not support cointegration between the log of government expenditure and income. Before the inequality indices can be tested for cointegration and compared with Kugler (1991) and MacDonald et al. 1989 certain requirements must be met. The next section covers those requirements and is followed by the derivation of the cointegration method. Then the results are presented and interpreted. 6.2 Unit Root Tests A necessary prerequisite of cointegration analysis is that the variables under consideration be integrated of the same order. This means that the variables being compared require the same number of differences to attain stationarity. A time-series variable is integrated of order d if the dth difference of x, is stationary, denoted 1(d). An 1(0) series means that the series is stationary without any differencing. In this case, the error term is white noise and there is no correlation between the error terms for all time t (Maddala, 1992) . Maddala (1992) suggests examining graph's of the time- series over time as well as using unit root tests to determine if a time-series is stationary. A stationary time-series is expected to have regular crossings of the mean. The graphs 132 for the inequality of income, government, investment, and the number of people employed in industry for the G-7 countries are shown in Figures 6.1 to 6.4. All four variables have a trend indicating that they are non-stationary. The problem is not that the data are non-stationary, but if a regression is run with one time-series being stationary and another being non-stationary, then the results would be spurious (Maddala 1992) . One way to correct the non-stationarity is to first difference or detrend the non-stationary variable. The data series were first differenced, but they still appeared to be non-stationary. Therefore the series was second differenced and are shown in Figures 6.5 to 6.8. It appears that all four data series are stationary after second differencing which means the series are integrated of order 2. 6.2.1 Augmented Dickev-Fuller ÃADF) Test The other way to determine the order of integration of a series is to use a unit root test. Two unit root tests will be applied to the data. The first test is the Augmented Dickey-Fuller (ADF) test. The model is k (6.1) y, = 7 + it + ay,., + Â£ Â©jAy,., + u, j=l where y, is the time-series, t is time, and u, is a covariance stationary process with zero mean. The Ay,., terms (lags) are Government Inequality Income Inequality 133 0.26 0.2 0.16 0.1 0.06 0 1060 I960 1970 1980 1988 Years FIGURE 6.1 Total Income Inequality for the G-7 FIGURE 6.2 Total Government Inequality for the G-7 Industry Inequality Investment Inequality 134 Years FIGURE 6.3 Total Investment Inequality for the G-7 FIGURE 6.4 Total Industrial Employment Inequality for the G-7 Government Inequality Income Inequality 135 FIGURE 6.5 Total Income Inequality for the G-7 Second Differenced 0.04 0.02 o Â«0.02) Â«0.04) Â«0.061 Â«0.081 1962 1960 1970 1980 1988 Years FIGURE 6.6 Total Government Inequality for the G-7 Second Differenced Industry Inequality Investment Inequality 136 FIGURE 6.7 Total Investment Inequality for the G-7 Second Differenced 1962 1900 1970 1900 1988 Years FIGURE 6.8 Total Industrial Employment Inequality for the G-7 Second Differenced 137 added to whiten the residuals (i.e. remove the autoregressive- moving-average (ARMA)). The number of lags is determined by comparing the significance levels as more lags are added. This method was chosen because the power of the unit root tests decrease when small samples are used and as more lags are added, degrees of freedom are also lost. The first step in the procedure is to estimate (6.1) with the hypothesis being that there is a unit root which means a = 1. A t-test is used as the criteria in determining if a = 1. This t-test does not have a limiting normal distribution (Engle and Granger, 1991). The distribution is skewed to the left and is referred to as a Dickey-Fuller distribution. The t-test is (6.2) t(l) = (a - l)/SE(a) where a is the ordinary least squares (OLS) estimate of (6.1), SE(Â¿) is the standard error of a, and the 1 represents the hypothesis that a is equal to 1. The critical values for this test are in Fuller (1976), where 6 is assumed to be zero. 6.2.2 Phillips Test The second unit root test is by Phillips (1987). The model is similar to the ADF model with less parameters. The model is (6.3) y, = ay,., + u, where all the symbols have the same meaning as equation (6.1), and the null hypothesis is the same as (6.1). The difference 138 from ADF is that this is a non-par ame trie procedure that uses the residuals from the first order model to correct the t- statistic. Phillips' new tests for unit roots are Zâ€ž and Zt. The Z(( statistic is a transformation of the standard estimator T(a - 1), and Z, is a transformation of the regression t- statistic. The equation for Za is T (6.4) Za = T (a - 1) - (1/ 2) (SjL - S*) / (T2 S y*,) t=l where T Sj = T-1 Z u? t=l and T L T S^L = T'1 Z u] + 2T"1 Z WtL Z utu,.T t=l T=1 t=T+l given that WtL = 1 - t/(L + 1) . The symbol T represents the sample size, L is referred to as the lag truncation number by Phillips (1987) . The lag truncation number represents the number of autocorrelations and is determined empirically. Since the sample autocorrelations of first differenced economic time-series decay quickly, the value of L will be small (Phillips, 1987). 139 SyL is a consistent estimator of a2 if the autocovariance increases as T approaches positive infinity, but the rate of increase is controlled so that L = 0(T1/4). is a consistent estimator of a2 when Ã¡ = 1. The other statistic which is a transformation of the t- statistic is T (6.5) Z, = (S yi,)1/2(Â¿ ~ 1) /STL - (1/2) (S^ - S2) t=l T [ sTL (T"2 s yt-i)1/2 ]'* â€¢ t=i All of the definitions are the same as in the Za statistic. To test the unit root hypothesis, the Za and Zt statistics are computed and compared with the critical values in Evans and Savin (1981) and Fuller (1976). 6.2.3 Unit Root Results The results of the G-7 in Table 6.1 for the ADF and Phillips unit root tests confirm the interpretation of the graphs. The unit root tests indicate that the inequality in income, investment, industry, and government are all 1(2). Both tests supported these results at the 1% level. In addition, increasing the number of lags (autocovariance terms for Phillips tests) in the model had no effect on the significance level for the 1(2) series. 140 Table 6.1. Unit Root Tests Tests Income G-7 Results Government Investment Industry ADF*,b 9.40 4.65 10.01 10.23 Phillips" 9.67 10.16 10.30 10.54 OECD Results Tests Income Government Investment Industry ADFab 10.38 8.30 11.21 10.08 Phillips" 10.68 8.54 11.53 10.37 Note: Only the second differenced results are reported. â€œThe reported values are for 0 lagged difference terms. bThe critical values for the Augmented Dickey-Fuller test and Phillips test are 3.56, and 2.94 for the 0.01, and 0.05 confidence levels respectively. cThe reported values are for 1 autocorrelation term. 141 The same tests were applied to the OECD data. The results are reported in Table 6.1. As expected these data were also found to be 1(2) for all of the variables. Given that all of the variables appear to be integrated of the same order, the long-run relationships can be estimated. Pairwise cointegration analysis will be conducted first, followed by multiple cointegration tests. 6.3 Pairwise Cointeqration for the G-7 Engle and Granger (1987) state that two 1(d) variables, x, and y,, are cointegrated of order (d,b) , if there exist a constant B f 0 such that ut = y, - a - Bx, is integrated of order (d - b), b > 0. If these restrictions are satisfied, then x, and y, are cointegrated which is written as CI(d,b). In this example, a is a constant and u, is the residual vector. The two tests that are used to determine pairwise cointegration are the Durbin Watson test and the Dickey-Fuller test. These test will be used on the following inequality measures: income - government expenditures, income investment expenditure, and income - the number of people employed in industry. 6.3.1 Durbin Watson The Durbin Watson pairwise cointegration vector is tested as (6.6) y, = Bxt + a + u, 142 where all of the variable and coefficients are defined in the prior section. After estimating (6.6), the Durbin Watson statistic is used to determine if the residuals are stationary. The Durbin Watson statistic is (6.7) DW = E (Ãš, - Ãº,.,)2/ E u2. The DW statistic approaches zero if the residuals contain a unit root. An autoregressive unit root in the residual is represented by ut = pu,_j + et, where p = 1. That is why DW approaches zero because DW a 2(1 - p). Therefore, the null hypothesis of non-cointegration means that DW = 0. Cointegration is supported if DW is significantly different than zero. 6.3.2 Augmented Dickey-Fuller Cointegration Test To explain the Augmented Dickey-Fuller cointegration (ADFC) test, the Dickey-Fuller (DFC) test for cointegration is first discussed. The DFC test uses the same regression as the Durbin Watson test. That is after (6.6) is estimated, the residuals are regressed on the lags of themselves using the following equation: (6.8) AÃš, = $ut., + et. Now the test for cointegration is a t-statistic for the $ coefficient. To extend this to the Augmented Dickey-Fuller test for cointegration, some terms are added so that the residuals are uncorrelated. The ADFC equation is 143 P . (6.9) Au, = $u,_, + Z ut.Â¡ + et i=l where p is selected to make e, white noise (see footnote 1 in this Chapter for a definition of white noise). Once again the ADFC is a t-statistic for the 4 coefficient. The null hypothesis is that 4=1, or non-cointegration. 6.3.3 Pairwise Cointegration Results The results from the two pairwise tests for the G-7 are somewhat inconsistent. Table 6.2 shows that the Durbin Watson statistic is significantly different from 0 at the 1% level for income inequality and investment expenditure inequality. Government inequality and the inequality of income are only significant at the 10% confidence level. The inequality of the number of people employed in industry and income inequality pair is not significantly different from zero for the Durbin Watson statistic. The Durbin Watson tests indicate that non-cointegration is rejected for investment and possibly government, but, cannot be rejected for the number of people employed in industry. The CADF tests reject non-cointegration for all three pairs. The government regression rejects non-cointegration at the 1% level, while the number of people employed in industry rejects non-cointegration at the 5% level. The investment regression rejects non-cointegration at the 10% level. 144 Table 6.2 Pairwise Tests for Cointegration G-7 Results Tests Government Investment Industry Durbin-Watson Regression3 0.374 0.524 0.263 Augmented Dickey-Fuller Regressionb,c 7.25 3.14 3.76 OECD Results Tests Government Investment Industry Durbin-Watson Regression3 0.296 0.429 0.471 Augmented Dickey-Fuller Regressionbc 6.07 2.76 4.27 â€œThe critical values for the Durbin-Watson regression are .511, .386, .322 for the 0.01, 0.05, and 0.10 confidence levels respectively (Engle and Granger, 1987) . bThe critical values for the Augmented Dickey-Fuller regression are 4.02, 3.4, and 3.09 for the 0.01, 0.05, and 0.10 confidence levels respectively. cThe reported values are for 0 lags. 145 The results for the OECD countries are similar to the outcome of the G-7 analysis. Table 6.2 shows that the Durbin Watson statistic is significantly different from 0 at the 5% level for the following pairs: income inequality and investment expenditure inequality, and income inequality and the inequality in the number of people employed in industry. The Durbin Watson statistic is not significantly different from zero for government inequality and the inequality of income. The Durbin Watson tests indicate that non-pairwise cointegration is rejected for investment and the number of people in industry, but cannot be rejected for the government. The CADF tests tells a different story from that of the Durbin Watson test results. The government and the number of people employed in industry regressions reject nonÂ¬ cointegration at the 1% level. The investment regression does not reject non-cointegration. It is fairly common in time-series studies to get two tests indicating two different results. In this case the small sample size may have a lot to do with these results. In general, the test results indicate that income inequality is cointegrated with the inequalities of the other three variables. This suggests that there exists a long-run equilibrium among income inequality and the inequality in government expenditure, inequality in investment expenditure, and inequality in the number of people employed in industry for the G-7 and OECD countries. The results from this 146 section do not prove the hypothesis of this thesis. The hypothesis of all four variables being cointegrated is what needs to be proved. These results only illustrate that two variables are cointegrated not all four. As a final step, this study analyzes whether multiple cointegration exists among the four variables. The methodology of the test to prove or disprove this hypothesis is discussed next. 6.4 Johansen's Multiple Cointeqration Test Johansen's cointegration test is a test for cointegration for a general vector autoregressive (VAR) model with p variables and k lags. The time-series are collected in a vector such as X( = [xlt, x2t, . . . , xpt] . It is assumed that the X('s are integrated of the same order. The test for 1(1) variables is discussed first followed by the case where the variables are 1(2). The 1(2) case is covered simply because all of the variables tested here seem to be 1(2). 6.4.1 Ifl) Procedure Johansen (1988) and Johansen and Juselius (1990) begin by defining a general polynomial distributed lag model for X, as k (6.10) X, = n + E 7TiXt.1 + e, t=l, . . . , T i=l where Â¿i is a constant and et is an independently identically 147 distributed p dimensional vector with zero mean and variance matrix A.4 Given this framework, the cointegrating matrix is (6.11) I â€”77,â€”7T2 . . . -7rk = n. The n matrix is therefore a p x p matrix. The number of cointegrating relationships among the variables in X is r, where r is the rank of w. If all of the variables are 1(1) then the most r can be is p-1. If n is expressed as (6.12) tt = aB' where a and B are p x r matrices, then the rows of B form r distinct cointegrating vectors. In order to implement this idea, Johansen (1988) put forth the following theorem. The maximum likelihood estimate of space spanned by B is the space spanned by the r canonical variates. These variates correspond to the r largest squared canonical correlations between the residuals of X,.k and AXt, which are corrected for the effect of the lagged differences of the X process. The likelihood ratio test statistic for the hypothesis that there are at most r cointegrating vectors is P (6.13) -21n(Qr) = -T X ln(l - XÂ¡) i=r+l 4In Johansen's 1988 paper /n is assumed to equal zero. The same assumption is made here. 148 where Ar+1,...,Ap are the p-r smallest canonical correlations. Johansen then shows that the likelihood ratio test has an asymptotic distribution for which a set of critical values can be tabulated which are correct for all models. The implementation of this theorem requires the reparameterization of (6.10) into a first differenced model (error correction model) k-1 (6.14) AX, = n + X TjAX,., + rkX,.k + e, i=l where rk = . . +7Tk. The equilibrium matrix 7r=aB' is equal to -rk. Therefore, B is the p x r matrix of cointegrating vectors, and a is a corresponding coefficient matrix. The loglikelihood representation of this model is T k-1 (6.15) In L(rÂ¡,rk,A) = -T/2 ln|A| -1/2 X (AX, - X AX,.^ t=l i=l k-1 - X,.krk) 'A-1 (AX, - z Ax^r, - xt.krk). i=l The parameters r,, . . . , rk., can be eliminated by partially maximizing (6.15) with respect to rÂ¡. The result of taking the partial maximization with respect to rÂ¡ is 149 (6.16) T k-l k-l ainL/dr, = 1/2 Z (E AX,_Â¡) 'A'1 (AX, - E AXt.iri - X,.krk) t=l i=l i=l T k-l k-l + 1/2 Z (AX, - Z AX,.^ - X,.krk) 'A1 (E AX,.Â¡) = 0. t=l i=l i=l This can be further reduced by multiplying (6.16) by 2, and A yields (6.17) T k-l k-l dlnL/dr, = Z (Z AX,.Â¡) ' (AX, - z Ax,.Â¡r, - x,.krk) t=l i+1 i+1 T k-l k-l + Z (AX, - Z AXj.jFi - X,_krk) ' (Z AX,.j) = 0. t=l i=l i=l If the matrices in (6.17) are multiplied out, the similar terms added, and then divide everything by two the result is T k-1 (6.18) E Z [ (AX^AX, - AX^AX^Tj - AX^rj ] = 0. t=l i=l Solving (6.18) for T, yields (6.19) T k-l r, = z z [ (Axi^x^Ax^Ax,,) -1 - (Ax,.iAx,.i) â€¢1Ax;.ixt.krk) ] t=l i=l Substituting aB' in for -rk makes (6.19) the same as regressing AX, + aB'X,.k on the lagged differences. Johansen (1988) suggests doing this procedure in two steps using OLS. First AX, is regressed on the lagged differences yielding 150 residuals R^, and then Xt.k is regressed on the lagged differences yielding residuals Rkt. After that is done the concentrated maximum likelihood function in terms of a, B, A is T (6.20)L (a, B, A) = | A | T/2exp [-1/2 Z (R^ + aB'Rkt) 'A'1 t=l (Rot + aB'Rkt) ] . If the log of (6.20) is taken, it yields T (6.21)In L(a,B,A) = -T/2 In|A| -1/2 Z (Rw + aB'RJ'A1 t=l (Rot + aB,Ria) â€¢ The objective is to maximize (6.21) with respect to a and A. The maximization with respect to a yields T (6.22)dlnL/da = -1/2 Z (B'Rkt) 'A'1 (R* + aB'Rkt) t=l T -1/2 Z (R^ + aB'Rkl) 'A'1 (B'Rkt) = 0. t=l Multiply (6.22) by -2, and A yields dlnL/da = Z (B'Rkt) ' (R^ + aB'Rkl) t=l (6.23) 151 T + 2 (R* + ctB'RJ ' (B' Rkl) = 0. t=l Now define the product moment matrices of the residuals as (6.24) SÂ¡j = T-1 Z RjtRj, and multiply the matrices in (6.23) to get (6.25) dlnL/da = Tâ€™S^B + T'crB'S^B + T-'S^B + T-'aB'S^B = 0 or equivalently 23^6 + 2aB,SkkB = 0. Solving for a yields (6.26) a (B) = -S^B (B' S^B). Now the consistent estimator for A must be derived. This is done by first rewriting (6.21) with equivalent trace (tr) notation. The result is T (6.27) In L(a,B,A) = -T/2 ln|A| -1/2 Z triR^ + aB'R^) ' t=l (Rq< + aB,Rkt) A-1. T Let Z = Z tr (R^ + aB^,) ' (RM + aB'Rkl) t=l and maximize with respect to A to get 152 (6.28) dlnL/dA = -T/2 tr A1 dA - 1/2 tr Z dA'1 = 0. Multiply (6.28) by 2 and manipulate the last term on the right hand side (Magnus, 1988) to get (6.29) dlnL/dA = -T tr A'1 dA + tr Z A1 (dA) A"1 = 0. This can be rewritten as (6.30) tr dA (TA_1 - A'1 Z A'1) = 0. where A'1 - A'1 Z A-1 is symmetric. The necessary condition for a maximum (Magnus, 1988) is (6.31) TAâ€™1 - A1 Z A1 = 0. That is T (6.32) A = 1/T Z = 1/T S trfR* + aB' RJ ' (RM + aB'Rkt) t=l and if the matrices in (6.32) are multiplied using the definition in (6.24), the result is (6.33) A = + 2aB' Sko + aB'S^Ba' = 0. Rearrange and substitute in for a (equation 6.26) to get (6.34) A = S, - 2SokB(B'SkkB)-1B'Sko + [ S^B (B' S^B) -1 ]B'S^B[S^B(B'S^B)1]' which reduces to 153 (6.35) A = - S^B (B' S^B) _1B' Sko. Solving (6.35) for B requires maximizing the following likelihood function (6.36) L-2T(B) = | A (B) | = | Sgg - SokB(B,SkkB)'1B'Sko| . To proceed in estimating B the following identity is applied (Johansen, 1988 and 1991c; Tso, 1981) (6.37) | - S^BiB'S^Br'B'Sj = ISoollB'S^B - B' Sko (SM) 'S^B | / IB'S^BI = I Soo I I B' (Skk - Sko ( Sqq) â€™â€™S^) B I / | B' S^B | . Maximizing the likelihood function in (6.36) is now reduced to minimizing the last term in (6.37) with respect to B. This minimization can be determined by solving the following eigenvalue problem (6.38) | - Sk0(S00) â€˜S0k) | = 0. Equation (6.38) yield the eigenvalues XÂ¡, . . . ,\p and eigenvectors V = (v,,...,vp) normalized such that V'S^V = I. The maximum likelihood estimator of B is now given by the first r rows of V, that is the first r eigenvectors of Sko (Soo) 'Sok with respect to S^. The eigenvectors are the canonical variates, and the corresponding eigenvalues are the 154 squared canonical correlations of R* with respect to R0. These eigenvalues are used to test how many cointegrating vectors exist. The likelihood ratio test that there are at most r cointegrating vectors is given in equation (6.13). The estimates of the other parameters are found by inserting the estimate of B into the respective equations. 6.4.2 1(2) Procedure The discussion in section 6.4.1 is correct for the situation where all of the variables are 1(1). However, all of the variables in this dissertation have been confirmed to be 1(2). Therefore, a few extensions have to be made to account for the I(2)-ness.5 Fortunately, the discussion in section 6.4.1 is basically correct for the 1(2) process with a few exceptions. The error correction model that anticipates 1(2) variables is k-2 (6.39) A2X, = Z + TAX,., + IIA2^., + et. i=l This model's error correction equation is similar to (6.14) but more complicated. The parameter restrictions for the 1(2) model are 5This section is based on Johansen's computer program and the following preprint articles: October, 1990; June, 1991; September, 1991; and October, 1992; and the published article by Johansen, 1992a. 155 (6.40) II = otB' (6.41) a}'TB} = 0r]' where a and B are p x r matrices of rank r and 0 and 77 are (p- r) x s matrices. Here s = 0,1,...,p-r, and aÂ± and BÂ± are orthogonal to a and B. This insures that the 1(1) processes is orthogonal to the 1(2) processes (i.e. no relationships exist between the 1(1) process and the 1(2) process). The general definition of 1 as a superscript is that a1' = (a'aj 'a, a'a1 = I, and a'ai = 0. The derivation of this model is similar to the derivation of the 1(1) model in the prior section. The first step is to arrange (6.39) into a loglikelihood function: T k-2 (6.42) In L(II,r,A) = -T/2 ln|A| -1/2 E [ (A2Xt - E AX^Tj t=l i=l k-2 -AX,.,r - Xl2II) 'A-1 (A2X, - E AX^Tj i=l - AXt.,r - X,2II) ] . The parameters rlf...,rk., can be eliminated by partially maximizing (6.42) with respect to T,. When that is done the result is T k-2 (6.43) ainL/ar, = 1/2 E E [ (A2Xt.Â¡) 'Aâ€˜(A2Xt - AX^T, - AX^T t=l i=l 156 - Xt.2II) + 1/2 (A2X, - AXt.Â¡Tj - AXt.,r - X,.2II) 'A1 (AX,,) = 0. To solve (6.43) for rÂ¡ multiply by - and A, then multiply the matrices out and add the like terms. When this is done the result is T k-2 (6.44) T, = Z Z[( A2x;,A2Xt) (A2x;â€žiA2X,.1) t=l i=l - (AXiAXj 'fAX^x^r) - (A2x;.iA2xt,)-,(A2x;,xt.2n) ]. Substituting aB' in for II makes (6.44) the same as regressing A2Xt, AX,.,r, and aB'Xt.2 on A2Xâ€ž, . . . , A2X,_k+2. This yields the residuals Rq,, Rlt, and R2t, and the residual product moment matrices which is the same as (6.24). The concentrated maximum loglikelihood function for the 1(2) model is then T (6.45) In L(a,B,A) = -T/2 ln|A| -1/2 Z [ (Re + TRlt t=l + aB'R2t)'A-â€˜ (Rw + rRu + aB'R2t) ] . However, instead of dealing with (6.45) Johansen (1992b) suggests manipulating the following regression equation Re = rRlt + aB'R2t + e,. (6.46) 157 From (6.46) the 1(1) and 1(2) analysis can be performed. The 1(1) model is given by eliminating the unrestricted parameter T and carrying out the analysis as in the previous section. The first step in calculating the 1(2) model is to get the values for r, a, and B from the 1(1) model with r unrestricted (6.46). To solve the 1(1) portion of the model, follow the steps outlined from equations (6.22) to (6.38) with the exception of the additional parameter F (Johansen, 1992b). Once the parameters and value of r are found, assume that they are fixed and multiply (6.46) by a1' and a}'. The results of multiplying (6.46) by a1' and a}' yields (6.47) a1' = a1' TR,, + B'R2t + aâ€˜'et, and (6.48) oÃ i 'Rot = o-i'rR,, + aj'e,. â€˜ 'â€¢' ' > * â€¢ i â– ! : â– . i* i . .i . â– . _ :)ni.rÂ¡ j â€¢ â€¢ i i â€¢: Ã ry. c t * The 1(2) model eigenvalue problem is based on solving (6.48) . That is because by multiplying by a}' makes sure that the 1(1) and 1(2) processes have no relationship. Define I = B'B' + BjBj/ and substitute this definition into (6.48) to get (6.49) = a*'r(Bâ€˜B' + B{Bx ') Râ€ž + a}'et. This equation can be rewritten as (6.50) ai'RÂ« = ai'TB^B'R,,) + was eliminated in the 1(1) model (equations (6.22) - (6.25)). 158 This is done by arranging (6.50) in maximum loglikelihood format and maximizing the eguation with respect to ai'TB1. The result of this expression is (6.51) ai'TB1 = -ax ' S10B (B' SnB) '* - 07, â€¢ (B^ Sâ€žB) (B' Sâ€žB) '. The actual eigenvalue problem is determined by solving for A. This is accomplished the same way as before. Maximize the likelihood representation of (6.50) in the trace format like eguations (6.27) to (6.31) where Z = [aj'R,* + a} 'TB1 (B'Rlt) + 07,' (B.'RJ ] ' [0^'Rq, + a} 'TB1 (B'Rn) + 07,' (Bx 'Rlt) ] . Solving this setup and substituting in (6.51) where needed the eigenvalue problem is (6.51) A = |pBx (Sâ€ž - SnB(B'S11B)1B'S11)Bi - [B;;(Sio - S,,B (B'SnB) 'B^Sjo) a* ] [aj' (So, - S10B(B'S11B)1B'SI0)al] [B;(Sio - SnB(B'S11B)1B'SI0)a-l] | = 0. The solution to (6.51) gives eigenvalues p, > ... > Pp_r > 0 and eigenvectors W = (w,, . . . ,Wp_r) normalized by W'[BX(Sâ€ž S,,B (B' SUB) â€˜B' S,,) Bx ] W = I. Note, B and Bx transform the differences which are 1(1) variables. The aj coefficient transforms the second differences which are stationary by assumption. The likelihood ratio test to determine the number of eigenvalues that are significantly different than zero is 159 p-r (6.52) -2 In (Qr,) = -T 2 ln(l - p,) i=s+l where s = (0,1,...,p-r-1). The maximum likelihood estimators (for fixed values r, a, and B) are rÂ¡ = (w,,...,w(), and 0 = [B1(S10 - S,,B (B' S,,B) '*B'S10) a} ]77. The variance matrix A is equal to (6.51) without the absolute value symbols and p. In summary, the steps that need to be taken to determine the number of 1(2) cointegrating equations using Johansen's method are: 1. Compute using OLS on the regression AXt on AX,^, ..., AXj. k+1/ and Rjrt from the regression X,_k on AXt.Â¡, . . . , AXt.k+1. 2. Compute the moment matrices S^, S^, and Sk0. 3. Solve the equation | Xs^ - S^ScJ-'S*) |=0, yielding p eigenvalues \ and determine the corresponding H- V-, .â€¢Â» y ( t I â€¢ 1 ,â€¢ - -j . , . eigenvector matrix V. Normalize V such that V 'S^V = I. 4. Determine the number of cointegrating vectors using the likelihood ratio test statistic for the hypothesis test that there are at most r cointegrating vectors: P -2ln(Qr ) = -T I In (1 - X.) i=r+l where Xr+1,...,Xp are the p-r smallest canonical correlations (eigenvalues). 5. Plug the in the value for a and B from the 1(1) model into the 1(2) model. Compute a new set of residuals by 160 regressing A2Xt, AXt.,r, and aB'X,.2 on A2Xn, . . . , A2Xt.k+2. This yields the residuals R^, Râ€ž, and R2t respectively. 6. Compute the moment matrices S10 and Sâ€ž. 7. Solve the following eigenvalue problem A= |pB^ (Sn - S11B(B'S11B)'1B,S11)Bi - [Bi(S10 - S,,B (B' SnB) '*B' S,0) a} ] [aj' (Soo - S10B (B' S,,B) "â€˜B' S10) a j ] [B; (S10 - S,,B (B/SI1B)'1B'S10) a| ] I = 0. where the eigenvalues are p, > ... > Pp_r > 0 and eigenvectors W = (w,,...,w ) are normalized by W'[B^(Sn - SuBÃB'SpBr'B'SuJBJW = I. 8. Determine the number of cointegrating vectors using the . . ' ... . r â€¢ - â€¢ .N i- L - Â» , . . 4. . , â€¢ likelihood ratio test statistic for the hypothesis test that there are at most p-r cointegrating vectors: p-r -21n(Qrs) = -T E ln(l - Pi) i=s+l where s = (0,1,...,p-r-1). 9. Given those results there are p-r-s 1(2) trends. The next section applies the 1(2) method on the inequalities calculated in Chapter 5. 161 6.4.3 G-7 Multiple Cointeqration Results This section tests the hypothesis that all four total inequalities (income, government expenditure, investment expenditure, and industrial employment) for the G-7 countries are cointegrated. It was determined in Chapter 5 that all four of these inequalities are converging for the G-7 and has since been hypothesized that these variables have a long-run equilibrium. That is the four inequality indices may drift apart in the short-run, but will return to the long-run equilibrium. The results from Johansen's test are shown in Table 6.3. First, the results of the eigenvalue problem (eq. 6.38) and the associated eigenvectors are presented. The value of r or the number of significant eigenvalues are determined by reading the Qr column from top to bottom and comparing the observed value with the 95% critical value (C,,.,) for p-r degrees of freedom. Once the value of r has been determined, then the value of s is chosen by reading the row associated with the selected r value in the Qrs rows. The observed values are compared with the critical values at the bottom of the table (Cp.r.s) . The value of s determines the number of 1(1) trends in the model. For example, if s is equal to one, then there is one 1(1) trend in the model. The trace statistic clearly rejects r = 0, since the test statistic is 80.87 and the 95% calculated critical value is only 49.09. The hypothesis H, of r < 1 is also clearly 162 Table 6.3 Johansen'sâ€ Multiple Cointegration Test (G-7) Eigenvalue (o) : 0.638 0.536 0.280 0.123 Eigenvectors 55.047 (B) : -251.057 107.747 224.610 -6.439 32.678 -12.882 -133.018 -32.331 177.140 -40.991 -106.753 125.960 283.937 -323.738 -17.699 Test Statistics p-r r Qr,s Qr Cp_r(95%) 4 0 103.411 s=0 48.233 S=1 16.545 s=2 3.056 s=3 80.870 49.097 3 1 71.819 s=0 27.182 S=1 1.756 s=2 44.241 31.618 2 2 36.999 s=0 2.303 S=1 16.567 17.652 1 3 29.536 s=0 4.742 8.106 p-r-s 4 3 2 1 Cp-r-s (95%) 49.097 31.618 17.652 8.106 163 rejected with the statistic being 44.24 and the critical value being 31.62. Therefore, r does not equal 0 or 1. The hypothesis H2 of r < 2 is a borderline case since the statistic 16.57 corresponds roughly to the 95% critical value 17.65 in the asymptotic distribution. The hypothesis that r = 2 cannot be rejected, determining that r = 2 means that there are two linear combinations of x, that are stationary. More will be stated about this after the value of s is determined. To determine the value of s, the row equal to r = 2 is read. The hypothesis H20 (i.e. r = 2 and s = 0) is rejected given the test statistic 37.00 and the critical value of 17.65. Therefore, s does not equal 0. The next test for s < 1 cannot be rejected. This is determined by comparing Q2, = 2.3 with the critical value of 8.11. Therefore, the number of common 1(2) trends in the data series is p-r-s = 1 and the number of common 1(1) trends is s = 1. Having decided that r = 2, the estimate of the two cointegrating vectors (B) are given by the first two columns of eigenvectors in Table 6.3. The complication is that since all of the variables are 1(2), the cointegrating vectors are 1(1).6 The vectors B'X, in this case are two linear combinations, and they are 1(1) (not stationary). However, this representation can be made stationary (1(0)) by including 6If all of the variables were 1(1) then the two cointegrating vectors would be stationary at the 1(0) level. 164 the differences, that is B'X, + /cB^'AX, (Johansen, 1991a and b). The k coefficient is equal to (a'a) â€˜a'TBj(B7'B7) 1 = a{'TB7 (Bj'B7)'1, a} = a(a'a)'1, and B7 = Bj^. The two normalized stationary relationships become (6.53) INC - .12 GOV, -.59 INV, + 2.29 IND, + 144.93 AINC + 78.33 AGOV, + 202.67 AINV, - 7.31 AIND, and (6.54) INC - .13 GOV, -.71 INV, - 1.13 IND, - 70.17 AINC - 37.93 AGOV, - 98.13 AINV, + 3.54 AIND,. The B vectors used in (6.53) and (6.54) are in Table 6.4, and are equal to the first two columns of the eigenvector in Table 6.3, with the exception of being normalized" by the income coefficient. These two equations represent the long- run equilibrium among the four inequality indices for the G-7. Given that there are two stationary relationships, the equilibrium can be thought of as a plane instead of a line in hyperspace.7 The next step is to use all the information from this estimation to determine which variable or variables are determining this equilibrium. The two normalized 7Hyperspace in this case refers to a four dimensional space with two stationary relationships forming an equilibrium within this space. Since there are two relationships, the equilibrium is a plane. 165 Table 6.4 Cointegrating Vectors and Adjustment Coefficients from the G-7 The estimates of the cointegrating vectors B, and the supplementary vectors Bj1' = (BiBi) 'B^rj, and B^ = B* Bj1' B l 1.0 1.0 5.509 10.533 -0.12 -0.13 -61.812 5.693 -0.59 -0.71 19.934 14.729 2.29 -1.13 -0.451 -0.531 The estimates the supplementary a of the cointegrating vectors a}1' = (aâ€™a1) a}1' vectors a, and â€˜a, and a2Â± = a1 -.002 .001 0.009 -0.011 . 001 -.001 0.008 0.006 -.007 -.002 -0.002 -0.001 -.001 . 000 0.002 0.034 'These B's are normalized by Income. 166 cointegrating vectors (Table 6.4) roughly have the following relationships (1,*,-1,*) and (1,*,-1,-1). The interpretation of the first vector is that income inequality and the inequality in investment are stationary and the other two variables do not affect this equilibrium. If either income or investment were removed from the equation, the result would be a non-stationary relationship. The other two inequalities do not contribute to this stationary equilibrium. The interpretation of the second vector is that the inequality in income, investment, and industrial employment form a stationary long-run equilibrium. In this case government expenditure inequality has no effect on this equilibrium. Determining the number of significant s's identifies how many common 1(1) processes there are in the model. It was found that there is one common 1(1) process. In addition, there is only one common 1(2) trend that drives all of the variables. To determine the common 1(1) trend is difficult. Therefore, the determination of the common 1(2) trend is addressed. The coefficient in Table 6.4 shows which variables are actually 1(2).8 The variable that has a coefficient closest to one or negative one is the common 1(2) trend. The BÂ¿ vector indicates that the inequality in the number of people 8To clarify the B's further, the px(r+s) matrix (B,B|) represents all possible cointegrating relationships. That is, (B,B})'Xt is either 1(1) or 1(0), whereas B^'Xt is an 1(2) process that does not cointegrate. 167 employed in industry is the 1(2) variable. That means that when an innovation occurs and the inequalities are out of equilibrium, the inequality in the number of people employed in industry adjusts to restore the equilibrium. The inequality in government expenditure is in equilibrium with the rest of the variables, but government does not contribute to this equilibrium. To develop this further, the interpretation of a is addressed. The coefficient a in Table 6.4 is interpreted as the weights with which the inequalities enter the system. The economic interpretation is that a represents the average speed of adjustment towards the estimated equilibrium. The small coefficients indicate a slow adjustment and a large coefficient represents a fast adjustment. The adjustment coefficients for a in Table 6.4 are small indicating that the inequalities of the variables adjust minimally to the deviations among the inequality in income, investment, and industry. This interpretation of a would be important if the variables were 1(1), however, they are 1(2). The important a in Table 6.4 is a\. a\ is interpreted as the linear combination that describes the common 1(2) trend. The heaviest weights are given to industrial employment and income. Industrial employment has the heaviest weight, hence, the I(2)-ness of the model is ascribed to the inequality of the number of people in industry. Thus, the number of people in industry is the variable that reacts the 168 most to innovations. In simpler terms, when a shock to one of the inequalities occurs which forces the inequalities out of equilibrium, the main force to restore the equilibrium comes from the inequality in industrial employment. The importance of the discussion on the a's and B's is that they help explain the equilibrium. It was determined that the common 1(2) trend in the model is the inequality in industrial employment. In addition, the inequality in industrial employment reacts first and the strongest to any innovation in the model. To complete the analysis the meaning of B}1' and a}1' is discussed. There exist other combinations in the model that reduce the 1(2) variables to an 1(1) relationship. That is what the B}1' vector represents. The 1(1) combination appears to be income, government, and investment. The a}1' vector indicates that the main force behind this relationship is the inequality of government and income. However, this combination does not cointegrate with the first differences of the variables by design of the model (Johansen, 1991) . These coefficients are not used in this thesis. The final table, Table 6.5, is provided to give the estimates of r. r is the coefficient of the lagged first difference term in the error correction model (eq. 6.39). These estimates allow the error correction model to be estimated, but are not utilized in this dissertation. The values of T are similar because there is only one parameter 169 restriction. This is due to the fact that the reduced rank hypothesis aj'rB1 = model are shown in Table 6.5 under the unrestricted results. The estimates for the 1(2) model are under the restricted heading. Table 6.5 Estimates of Gamma from the G-7 T Estimated from the 1(1) model (unrestricted) INC -1.043 -0.200 -0.073 -0.548 GOV 2.498 -1.191 -0.716 0.997 INV -0.121 -0.598 -1.833 -1.411 IND -0.735 0.141 0.075 ' .'-I ' ' "X â€” -1.494 r estimated from the 1(2) model (restricted) INC -0.895 -0.179 -0.070 -0.480 GOV 2.448 -1.198 -0.717 0.974 INV 0.148 -0.560 -1.827 -1.288 IND -0.825 0.128 0.073 -1.536 In summary, the stationary equilibrium is dependent on two stationary relationships. The first stationary relationship for the G-7 is described as the inequality in income and the inequality in investment expenditure. The 170 second relationship is the inequality in income, investment expenditure, and the number of people employed in industry. The inequality in industrial employment was determined to be the common 1(2) trend. That means that whenever an innovation occurs in one of the inequalities, and there is a deviation from the long-run equilibrium, industrial employment adjusts first to return the economy to the long-run equilibrium. This long-run equilibrium can be described but not represented graphically. The graphical representation is that of a plane in four dimensional space. The two stationary relationships create a plane in the four inequality variable space. This plane acts as an attractor every time the four inequities deviate from this equilibrium. 6.4.4 OECD Multiple Cointegration Results This section tests the hypothesis that all four total inequalities (income, government expenditure, investment expenditure, and the employment in industry) for the 14 OECD countries are cointegrated.9 It was determined in Chapter 5 that all four of these inequalities are converging for the OECD and was hypothesized that these variables have a long-run equilibrium. This hypothesis addresses the implications of adding more countries to the G-7 long-run equilibrium. 9The 14 OECD countries included in this analysis are the U.S., Canada, Japan, the U.K., W. Germany, France, Italy, Austria, Belgium, Denmark, the Netherlands, Norway, Ireland, and Spain. 171 The reason for adding more countries to the G-7 was to broaden the policy implications from this work. The G-7 countries are highly integrated meaning their economies are intertwined. Therefore, more countries are added to this system to determine if the eguilibrium is affected. The Other 7 countries are all fairly rich, and it would enhance the results of this dissertation if middle income countries could be included. Unfortunately, due to data constraints only seven more countries could be added (see APPENDIX E about data constraints). The additional seven countries that were added to the G-7 were Austria, Belgium, Denmark, the Netherlands, Norway, Ireland, and Spain. The results from the OECD analysis are similar to the G-7 in the sense that there appears to be two cointegrating vectors. This is not surprising considering that the G-7 dominates the 14 OECD countries. Table 6.6 contains the output from the Johansen's cointegration analysis. Once again, r = 2 and s = 1 cannot be rejected at the 95% significance level. Hence, there are two cointegrating vectors, one common 1(1) trend and one common 1(2) trend. Having decided that r = 2, the estimate of the two cointegrating vectors (B) are given by the first two columns of eigenvectors in Table 6.6. The two normalized stationary relationships for the OECD are (6.55) INC - .61 GOV, - .64 INV, - 5.27 IND, + 128.4 AINC 172 Table 6.6 Johansen's Multiple Cointegration Test (OECD) Eigenvalue (o): 0.688 0.504 0 .260 0.143 Eigenvectors (B): -35. 718 -225.140 133 .669 215.392 21. 627 23.452 -33 . 151 -111.575 22 . 905 154.150 -41 .214 -107.683 188. 173 179.047 -358 .899 31.076 Test Statistics â€¢ r - â€¢ . _ p-r r Qr,s O O ,r(95%) 4 0 99.633 46.278 16.756 2.807 83.555 49.097 s=0 s=l s=2 s=3 3 1 73.589 27.506 4.782 41.646 31.618 s=0 S=1 s=2 2 2 38.685 3.930 16.398 17.652 S=0 S=1 1 3 27.406 5.557 8.106 s=0 p-r-s 4 3 2 1 Cprs 49.097 31.618 17.652 8.106 (95%) 173 + 48.83 AGOV, + 184.39 AINV, -3.68 AIND, and (6.56) INC - .1 GOVt -.69 INV, - .80 IND, - 135.12 AlNC - 51.4 AGOV, - 194.1 AINV, + 3.88 AIND, The B vectors used in (6.55) and (6.56) are in Table 6.7. These two vectors are equal to the first two columns of the eigenvectors in Table 6.6, with the exception of being normalized by the income coefficient. The cointegrating 1(1) relationships are different than the G-7. Both eigenvectors appear to have strong relationships. The first eigenvector may have the following cointegrating relationship (1,-1,-1,*) and the second cointegrating relationship may be (1,*,-1,-1). The first vector indicates that income inequality, the inequality of government expenditure, and the inequality in investment expenditure form a stationary equilibrium. The second vector is the same as the G-7 case where income inequality, the inequality of investment expenditure, and the number of people employed in industry form a stationary equilibrium. The interesting development here is that government expenditure plays a more important role in the 14 OECD countries than in the G-7. 174 Table 6.7 Cointegrating Vectors and Adjustment Coefficients from the OECD The estimates of the cointegrating vectors B, and the supplementary vectors B{w = (BXBX) '*B^77, and Bx = Bxi/x B* Bj1' B 2 1 1.0 1.0 6.227 11.397 -0.61 -0.10 -54.325 4.334 -0.64 -0.69 10.174 16.366 -5.27 -0.80 6.187 -.327 The estimates the supplementary a of the cointegrating vectors aj1' = (axax) ai1' vectors a, and â– 'ax0, and ax = a1 -.002 .001 0.010 0.006 .000 -.002 0.004 0.010 -.007 -.001 -0.003 -0.006 -.001 . 000 -0.002 0.056 â€™These B's are normalized by Income. 175 The coefficient Bj in Table 6.7 shows which variables are actually 1(2).10 The variable that has a coefficient closest to one or negative one is the common 1(2) trend. The B\ vector indicates that the inequality in the number of people employed in industry is the 1(2) variable. That means when an innovation creates disequilibrium, the inequality in the number of people employed in industry adjusts in such a way that the four inequality indices return to their long-run equilibrium. This is the same as the G-7 case. The result that industrial employment is the main force is confirmed by in Table 6.7. As in the G-7 case, the heaviest weight is given to the inequality in industrial employment. Therefore, the stabilizing force in this model is the inequality in industrial employment. However, the second largest value for a2Â± is the inequality of government expenditure. Hence, when the economy is out of equilibrium, the inequality of government expenditure helps to return the economy to the long-run equilibrium. This result is contrary to the G-7 results where government expenditure was not important to the equilibrium process. To complete the analysis the meaning of B}1' and a}1' should be discussed. There exist other combinations in the model that reduce the 1(2) variables to an 1(1) relationship. 10To clarify the B's further, the px(r+s) matrix (B,Bj) represents all possible cointegrating relationships. That is, (BjBjj'X, is either 1(1) or 1(0), whereas B^')^ is an 1(2) process that does not cointegrate. 176 That is what the B}1' vector represents. The 1(1) combination appears to be income and government. The a}1' vector indicates that the force behind this relationship is the inequality of government expenditure and income which is the same as the G-7 case. As stated before, this combination does not cointegrate with the differences by design of the model (Johansen, 1991a). These coefficients are not directly used in this thesis. The final table, Table 6.8, is provided to give the estimates of T. T is the coefficient of the lagged first difference term in the error correction model (eq. 6.39). These estimates allow the error correction model to be estimated. These values are not utilized in this dissertation. The values of r are similar because there is only one parameter restriction. This is due to the fact that the reduced rank hypothesis aj'rB1 = 1(1) model is shown in Table 6.8 under the unrestricted results. The estimates for the 1(2) model are under the restricted heading. In summary, there appears to be two stationary relationships in the OECD sample. The first relationship includes the inequality in income, government expenditure, and investment expenditure. The second equilibrium is the same as the G-7 equilibrium: the inequality of income, investment expenditure, and the number of people employed in industry. 177 Table 6.8 Estimates of Gamma from the OECD T Estimated from the 1(1) model (unrestricted) INC -1.227 -.217 -.092 -.723 GOV 3 . Ill -1.250 -.942 1.690 INV -.793 -.496 -1.701 -1.733 IND -.448 . 101 . 071 -1.198 r Estimated from the 1(2) model (restricted) INC -1.096 -.219 -.096 -.730 GOV 2.927 -1.247 -.937 1.699 INV -.487 -.501 -1.710 -1.749 IND -.567 . 103 .075 -1.191 The inequality in industrial employment was determined to be the common 1(2) variable. In addition, whenever the economy deviates from the long-run equilibrium, industrial employment adjusts first to return the economy to the long-run equilibrium. Lastly, government expenditure is the second variable to assist in returning the economy to the long-run equilibrium. Given the fact that government expenditure is important in the 14 country OECD sample and not the G-7, some analysis should be done to determine the structure of the Other 7. 178 6.4.5 Other 7 Multiple Cointeqration Results The fact that the G-7 and the 14 selected countries of the OECD yield such different results the cointegration of the Other 7 is examined.11 This can be done simply due to the properties of Theil's inequality index. Theil's inequality index is additively decomposable. Therefore, the within- region inequalities for the Other 7 which are reported in Tables 5.4 and 5.5 are the same as the total inequality for the Other 7. Chapter 5 established that all four inequality indices were declining for the Other 7, indicating that these countries are converging in terms of income, government expenditure, investment expenditure, and industrial employment. Johansen's multiple cointegration analysis is applied to determine if there is a long-run relationship among the four inequalities for the Other 7. The results of Johansen's test are shown in Table 6.9. These results are different than the G-7 and 14 country OECD sample in that there appears to be only one cointegrating vector. Comparing the trace statistic of 59.43 with the 95% significance level of 49.1 assures that r is greater than zero. The hypothesis H, of r < 1 is a borderline case since the statistic is 31.5 and the critical value is 31.6. The test for the hypothesis that r < 2 is clearly rejected. â€œThe Other 7 countries are defined as Austria, Belgium, Denmark, the Netherlands, Norway, Ireland, and Spain. 179 Table 6.9 Johansen's Multiple Cointegration Test (Other 7) Eigenvalue (o): 0.539 0.490 0.170 0.015 Eigenvectors (B) : 112.726 -614.485 18.477 257.797 -27.867 -4.397 -11.576 -37.536 59.672 261.158 -118.687 -73.889 -455.087 109.353 265.419 0.401 Test p-r Statistics r Qm Qr Cp.r(95%) 4 0 102.093 56.855 21.615 6.947 59.429 49.097 3 s=0 1 S=1 66.834 s=2 31.603 s=3 10.371 31.514 31.618 2 2 s=0 S=1 22.096 s=2 7.561 7.257 17.652 1 3 s=0 S=1 4.611 s=0 0.561 8.106 p-r-s 4 ^p-r-s (95%) 3 2 1 49.097 31.618 17.652 8.106 180 Therefore, it is accepted that r = 1. That is, there exists one cointegrating vector in the Other 7 sample. The number of 1(1) and 1(2) trends can be determined after the value for s is determined. To determine the value of s, the row equal to r = 1 is read. The hypothesis H, 0 (i.e. r = 1 and s = 0) is rejected given the test statistic 66.83 and the critical value of 31.62. Therefore, s does not equal 0. The next test for s < 1 is also rejected. This is determined by comparing Q,, = 31.6 with the critical value of 17.7. The last hypothesis of s < 3 also cannot be rejected. The critical value for this hypothesis (H13 that is r = 1 and s = 3) is 8.1 and the statistic is 10.4. That means that r = 1, s = 3, and p-r-s = 0. The interpretation is that there is one cointegrating vector, three 1(1) trends, and no 1(2) trends in the model. In other words, this is an 1(1) model not 1(2) .12 The apparent stationary relationship is given by the first vector in B. The stationary relationship is formed by the inequality in investment expenditure and government expenditure. Normalizing this vector by investment expenditure the stationary relationship is then 1.88 INC - .467 GOV, + INV, + 7.63 INDt. 12The inequalities of the Other 7 data were confirmed to be 1(1) using the Augmented Dickey-Fuller and Phillips unit root tests. 181 Since the model is 1(1), this cointegrating relationship is 1(0). It is appropriate to state that the inequality in income and industrial employment are in equilibrium, but do not influence this equilibrium. These results are contrary to the G-7 results. In fact, these results indicate that the two groups are dissimilar. The G-7 sample clearly has an 1(2) trend while the Other 7 only has an 1(1) trend. The 14 country OECD sample has an 1(2) trend because when an 1(1) and 1(2) are added together the series becomes 1(2) (Engle and Granger, 1991). The differences between the Other 7 and G-7 indicates that there are underlying structural differences. In the G-7 case income, investment expenditure, and industrial employment create an equilibrium; where the Other 7's equilibrium is between investment and"government expenditure. < The OECD equilibrium may reflect the complexity of combining two equilibriums from different populations and creating one equilibrium. The OECD equilibrium has two stationary relationships; income, investment expenditure, and industrial employment, and income, government expenditure, and investment expenditure. The first vector mentioned appears to show the G-7 influence on the equilibrium and the latter shows the Other 7 influence on the equilibrium. The fact that the two groups of countries are structurally different may indicate that they should not be pooled. 182 There is no way to resolve this problem given the current techniques and data. Summers and Heston did an excellent job of creating a large data set that represented many of the countries in the world. Hopefully, as the World Bank takes over this task, they will improve the data as well as be able to extend the length of the data for more countries. This would allow the complex issue of what happens to the equilibrium as more countries are added to the system. 6.5 Summary and Interpretation The analysis began by confirming convergence among the G- 7 and the 14 selected OECD countries in terms of the inequality in income, government expenditure, investment expenditure, and in the number of people employed in industry. The next step was to determine if any of the movements were -* ' â€¢ â€¢ â€¢â– >*â€¢<* â€¢ ' Â» r â€¢ *, # â– i * Â» â– * | * r y . * v fr>; â– â€¢ â€¢ â€¢ â€¢ . â€¢ > cointegrated, that is, was there a long-run equilibrium among the variables of interest. A summary of the integration and multiple cointegration results are presented in Table 6.10. The order of integration in Table 6.10 (column 2) indicates that the country samples are not the same. The G-7 and the 14 OECD countries have an 1(2) structure while the Other 7 has an 1(1) structure. This indicates that the inequalities for the Other 7 are less disperse than the G-7 and OECD sample. The implication of the G-7 and Other 7 being integrated of different levels implies that the two groups have different structures. This becomes more clear as the cointegration analyses are summarized. Table 6.10 Summary of Integration and Cointegration Analysis Johansen's Multiple Cointegration Group of Countries ÃœJ Order of Integration L2J I(D Relationships UJ 1(2) Relationships LD G-7 1(2) fa. Income and Investment Industrial Employment b. Income, Investment, & Industrial Employment Industrial Employment OECD 1(2) a. Income, Government, & Investment Industrial Employment b. Income, Investment, & Industrial Employment Industrial Employment Other 7 KD Investment & Government N/A 183 184 The cointegration analysis of the G-7 found that there appears to be two cointegrating vectors (column 3) . These two stationary relationships (the inequality in income and investment expenditure; and the inequality of income, investment expenditure, and industrial employment) appear to form a long-run equilibrium. The long-run equilibrium for the 14 selected OECD countries also includes two stationary relationships (the inequality in income, government expenditure, and investment expenditure; and the inequality of income, investment expenditure, and industrial employment). The Other 7's equilibrium only consists of the inequality in government expenditure and investment expenditure. All of these relationships are 1(1). These long-run equilibriums are stationary as long as no structural changes take place. The last -column in Table 6.10 shows the -1(2) trend in each sample. The Other 7 does not have an 1(2) trend that is why N/A is placed there. The 1(2) trend for the OECD and G-7 is the inequality in industrial employment. The interpretation of these results and the relationships found in this study compared with others is discussed next. Several studies in the Convergence Chapter indicated that investment is influential to economic growth (Zind, 1991; Barro, 1991; Baradaran-Shoraka, 1992; and De Long, 1992). Kugler (1991) found a cointegrating relationship between income and investment expenditure. Although he used a few different countries than the G-7 sample, his results support 185 those of the G-7 in this dissertation. In fact, investment expenditure was shown to be cointegrated in all of the samples (G-7, OECD, and Other 7). The difficulty is in interpreting the results concerning the inequality of government expenditure. The inequality of government expenditure is in equilibrium with the other variables in the G-7; however, it does not influence this equilibrium. Although the inequality in government expenditure declines over time, its movements or changes over time do not appear to be similar to the other three inequality indices. MacDonald et al. (1989) showed that there was a long-run equilibrium between the log of government expenditure and income for three of the G-7 countries. In this dissertation, the G-7 pairwise cointegration results between the inequality in government expenditure and the inequality in income was also tested. Once again, the relationship between government and income is not overwhelmingly supported (significant at the 10% confidence level). There may be several reasons why MacDonald et al. (1989) found a relationship between government expenditure and income and no relationship was found in this dissertation. First, the data for the two studies came from different sources, and the MacDonald et al. data were not adjusted for purchasing power parity. Second, the variables were defined differently. In this dissertation, an index was created that represented all of the countries simultaneously. MacDonald et 186 al. (1989) actually tested the cointegration of income and government within each country. Therefore, their study did not deal with international relationships. Rather they just compared the cointegration results within the U.S. with those of the other three countries. Lastly, the objectives of the studies were different. In this dissertation an attempt to describe the co-movements of the inequalities of major factors in the G-7 economy was made. The MacDonald et al. study in contrast established a relationship within an economy of two major factors in the economy for four countries. The analysis is more complex when the Other 7 and the OECD are considered. These two groups supported the idea that government expenditures influence the equilibrium for the Other 7 and the 14 OECD countries. The fact that the G-7 equilibrium was stationary without government expenditure and the OECD had a stationary vector with government expenditure suggests two things. First, as more countries are added to the G-7 sample, government expenditure becomes more important. Second, the inequality in government expenditure changes over time, similarly to the changes in the other inequality indices for the 14 country sample. The Other 7 and OECD results are similar to what Barro (1991) and Baradaran-Shoraka (1992) found. Both of their studies found that government expenditure was significantly related to the growth rate of income for 98 countries. The Institutionalist idea of governmental policies being the chief 187 determinant of income inequality (Wright, 1978) was also supported with the Other 7 and OECD sample. Grier and Tullock (1989) found that OECD countries were converging in terms of income and that government expenditure was significantly related to the growth rate of income for the OECD and the rest of the world. The evidence that government expenditure is more important for the Other 7 is clear. Consider the eigenvector value for government expenditure. It was close to zero for the G-7. When the Other 7 were added to the G-7 sample, the coefficient for government expenditure increased to above 0.5. This suggests that adding seven countries, which on average are less endowed than the G-7, changed the equilibrium. The Other 7 countries are smaller in all terms than the G-7 (population, income,- government and investment expenditure, and the number of people employed in industry). However, they influenced the stationary equilibrium. This can be interpreted as the reliance of the Other 7 on government expenditure as a means of economic growth. If Section 5.4.2 is referred to, it is confirmed that the Other 7 increased government expenditures at a faster rate than the G-7. In addition, the multiple cointegration test for the Other 7 indicated that the only stationary equilibrium that existed was between the inequality in investment and government expenditure. 188 The way to interpret the government expenditure results is to look at the level of economic development of the group of countries in question. The Other 7 countries are less endowed than the G-7. They can be considered the second strata. The structures of the first strata (G-7) and the second strata (Other 7) are different. The second strata depends on investment and government expenditure for economic growth while the G-7 depend on investment expenditure and industrial employment for growth. However, the Other 7 are converging in terms of income with the G-7. Therefore, their dependence on investment and government expenditure should not be considered a suboptimal growth equilibrium. When these two groups are combined into 14 countries, the influence of both groups are reflected in the new equilibrium. The last set of.results to interpret are those concerning the industrial employment. It was determined that industrial employment was the 1(2) variable in the G-7 and OECD sample. In addition, the number of people employed in industry adjusts the quickest to correct short-run deviations from the long-run equilibrium. These deviations occur when innovations take place. This indicates that labor demand in the G-7 and OECD responds the most to innovations within the economies. These results are similar to what is discussed in several introductory macroeconomic text books about the relationship between income growth and the unemployment level (Baumol and Blinder, 1985; McConnell and Brue, 1990). That is, during 189 fast economic growth unemployment decreases and during slowdowns in growth, unemployment increases. It is clear that there exists a long-run eguilibrium among the ineguality in income, investment expenditure, and industrial employment for the G-7 and 14 country OECD sample. Investment expenditure and specifically industrial employment were extremely important when considering the convergence of those groups of countries. It was determined that the inequality in industrial employment was the major factor that adjusted when an innovation occurred for the G-7 and OECD. The Other 7, however, indicated the importance of government expenditure in their economy but not industrial employment. The Other 7 are an example of a group of countries that are converging with the G-7 although they have a different underlying structure. â€¢ i< â€¢- â€”. i >- â€¢â€” - â€” CHAPTER 7 SUMMARY AND DISCUSSION Two hypotheses were tested in this dissertation. The first hypothesis was to determine whether the countries in the G-7 and 14 selected OECD countries are converging in terms of income, government expenditure, investment expenditure, and industrial employment. This hypothesis was tested using Theil's inequality index. The second hypothesis tested whether the four inequality transformed variables have a long- run equilibrium (i.e. do they move together over time). This test required the use of cointegration analysis. The results from testing the first hypothesis were no surprise. Itâ€™was determined that the inequality in all four variables for the G-7, Other 7, and 14 OECD countries has declined over the period 1950 to 1988 suggesting convergence. A couple of other studies have shown that the richest countries in the world are converging in terms of income (Gao et al. 1992; Grier and Tullock, 1989). The new information came from the other variables that were tested for convergence. Government expenditure, investment expenditure, and industrial employment were all found to be converging for the G-7, Other 7, and the 14 190 191 countries of the OECD. The fact that the indices all declined gives support to the idea that they may be cointegrated (move together over time). The four inequality indices were then tested for cointegration. Before cointegration tests could be done, the level of integration was determined. The augmented Dickey- Fuller and Phillips tests showed that the four inequality indices were all 1(2) for the G-7 and the OECD. Given that the indices were all integrated of the same level, cointegration tests were conducted. The inequality transformed variables were tested for pairwise cointegration (Durbin Watson and Augmented Dickey- Fuller cointegration tests) where the inequality of income was regressed against the other three inequalities. In general the results indicated that all three pairs were cointegrated. These findings indicated that the inequality in income forms binary stationary equilibriums with the inequality in government expenditure, the inequality in investment expenditure, and the inequality in industrial employment. The stationary equilibriums were found in the G-7 and the 14 country OECD sample. These results were helpful in describing the co-movements in the inequalities. However, the hypothesis was that all four inequality indices were in equilibrium. To test that hypothesis, multiple cointegration was used. The samples were tested for multiple cointegration using Johansen's 1(2) method. The G-7 had two stationary long-run 192 relationships. The first cointegrating vector was between the inequality in income and investment expenditure. The second cointegrating vector was among the inequality in income, investment expenditure, and industrial employment. These results indicated that there is a long-run equilibrium among the indices that is stationary as long as no structural changes take place. The inequality of government expenditure is in equilibrium with the other variables in the G-7, but it does not influence this equilibrium. Although the inequality in government expenditure declines over time, its movements or changes over time do not appear to be similar to the other three inequality indices. It was also determined that industrial employment was the 1(2) variable in the G-7 model. Industrial employment adjusts the quickest out of the four inequality indices to correct short-run deviations from the long-run equilibrium. These deviations would occur when innovations take place. This suggests that labor demand in the G-7 responds to innovations within the economies. The G-7 was then combined with seven more countries from the OECD which are referred to as the Other 7 (Austria, Belgium, Denmark, the Netherlands, Norway, Ireland, and Spain). This 14 country OECD sample was assembled to broaden the policy implications from the results. The G-7 countries economies are highly integrated (i.e. intertwined). The obvious question is, "what happens to the G-7 equilibrium when 193 more countries are added?â€ The Other 7 countries are all fairly rich and it would enhance this dissertation if middle income countries could be included. Unfortunately, due to data constraints only seven more countries could be added (see APPENDIX E about data constraints). Given the argument above, the results from the 14 OECD countries cointegration test were similar to that of the G-7 in that there were two cointegrating vectors. The two cointegrating vectors were the inequality of income, government expenditure, and investment expenditure; and the inequality of income, investment expenditure, and the number of people employed in industry. These two stationary relationships appear to form a long-run equilibrium. The 1(2) variable in the OECD model was determined to be industrial employment and is interpreted in the same way as the G-7 case. The first cointegrating vector which included government expenditure added considerable information to the analysis. The fact that the G-7 equilibrium was stationary without government expenditure and the OECD had a stationary vector with government expenditure suggests two things. First, as more countries are added to the G-7 sample, government expenditure becomes more important. Second, the inequality in government expenditure changes over time similarly to the other inequality indices in the 14 country sample. Given that the results between the G-7 and the 14 OECD countries were different, cointegration tests were run on the 194 Other 7 sample. It was determined that the Other 7 inequality indices were all 1(1) indicating that the Other 7 has a different structure than the G-7. The long-run equilibrium in the Other 7 sample was between government expenditure and investment expenditure. This can be interpreted as the reliance of the Other 7 on government expenditure as a means of economic growth. When the inequality indices were consulted, it was confirmed that the Other 7 increased government expenditures at a faster rate than the G-7. The reliance of the Other 7 on government expenditure and investment expenditure is not necessarily a suboptimal long- run path simply because the Other 7 and G-7 are converging. This result just reflects the different ways growth can be accomplished given the economic strata of a country. It is clear that there exists a long-run equilibrium among the inequality in income, investment expenditure, and industrial employment for the G-7 and OECD sample. Investment expenditure and specifically industrial employment were extremely important when considering the convergence of countries. It was determined that the inequality in industrial employment was the major factor that adjusts when an innovation occurred. The implication from the government equilibrium, however, may be that as countries less endowed than the G-7 are considered, government expenditure may play a bigger role in the economy and in the influence of the convergence of countries in terms of income. 195 The implications of these results are potentially important when considering the economic growth in the middle income and possibly the lower income countries. The Other 7 results show that a country can converge with the G-7 without mimicking the structural setup of the G-7. If the low income countries devote increased expenditures on investment and government in per capita terms in an appropriate fashion, then they may begin to converge with the developed countries in terms of income per capita. These interesting issues should be pursued as the data becomes available for more countries. This dissertation would be enhanced if more countries had data for income adjusted for purchasing power parity that began in 1950. In addition, the other data series used (government expenditure, investment expenditure, and industrial employment) would need to begin in 1950. Another way to enhance this dissertation would be to include trade indicators and educational indicators over time. However the data for those variables only date back to the early 1960's for most countries. There are two limitations of this study. The first has already been discussed which is the lack of data. The second deals with the sample size. There are 39 observations for each country and all four indices in this study. That means the parameters are a third of the sample size. Therefore, some caution should be taken when considering the results of these tests. 196 In conclusion, both hypotheses were confirmed in this dissertation. The G-7 and OECD are converging in terms of income, government expenditure, investment expenditure, and industrial employment. These four variables are also cointegrated for the 14 country OECD sample and all but government expenditure is cointegrated in the G-7 sample. In addition, Industrial employment is the factor in the economy that adjusts when the inequalities deviate from their long-run equilibrium. Lastly, government expenditure may be a factor that contributes to economic growth for countries less endowed than the G-7. APPENDIX A PRICES PER KILOGRAM OF FRESH VEGETABLES AND ESTIMATED PPP'S IN 10 COUNTRIES FOR 1970 197 Columbia (Peso) France W. Germany Hungary India (Franc) (0. Mark) (Florint) (Rupee) 1. Artichokes - 2.75 3.26 - - 2. Beets 3.90 - - - - 3. Brussels sprouts - 2.35 1.69 - - 4. Cabbage 1.41 .98 .55 2.9 .91 5. Cauliflower 5.33 1.90 1.13 - 1.27 6. Carrots 2.10 .93 .86 3.2 .75 7. Celery, pascal 4.49 - - * - 8. Cucumbers - - - 4.7 .87 9. Eggplant - - - - .72 10. Escarole - 1.82 .98 - - 11. Green peppers 17.40 2.62 2.32 8.7 - 12. Kunde greens - - - - .56 13. Lettuce 4.82 3.23 2.27 9.3 - 14. Mushrooms - 7.90 5.60 - - 15. Onions, yellow 5.59 1.18 .86 4.8 .67 16. Radishes - - - - .55 17. Red cabbage - 1.27 .56 - - 18. Spinach 4.71 - - - - 19. Tomatoes 5.79 2.55 1.85 6.7 1.21 20. Yellow squash 2.29 - - 1.5 - Coefficient Bc 1.96 .92 .57 2.02 .34 Anti log (PPP's) 7.11 2.52 1.77 7.53 1.41 "This entry represents a correction of the corresponding figure in Kravis et Source: Kravis et al. 1975, p. 59. Italy Japan Kenya (Lira) (Yen) (Shilling) 646 - - 485 . _ 157 75.4 .47 195 156.6 2.58 172 115.1 2.58 173.3 212 186 195.4 - - - .79 239 218.1 .62 790 - - 127* 98.6 .77 m 133.8 - 226 160.9 1.19 5.68 5.32 .57 291.9 204.5 1.76 United Kingdom (Pound) Uni ted States (Dollar) Coeffic A. _ 2.22 .56 .07 .42 -.89 - 1.89 -.23 .08 .32 -1.02 .17 .63 -.18 .07 .39 -.67 - .44 -.59 - .61 -.39 - .59 -.63 - - -.41 - 1.16 .14 - .67 -.78 - .53 -.21 .54 1.95 1.00 .13 .35 -.66 - .88 -.68 - .12 -1.20 - 1.24 -.29 .31 .92 -.10 - .66 -1.22 -1.56 .00 .21 1.00 APPENDIX B SUPERCOUNTRY WEIGHTING A supercountry is a representative country assumed to have the some price and quantity structure of a group of countries (Kravis et al. 1975, p. 289). The objective of supercountry weighting is to assign to each country's price structure a weight that reflects its GDP as well as other countries in the world which were not included in the ICP. Supercountry weighting also insures that countries who participate in several phases of the ICP will not be influenced by the addition of new countries in later Phases. The world comparisons utilized a system of supercountry weights where the dollar GDP of non-participating countries is assigned to participating countries on the basis of geographical proximity and the level of per capita income. It must be made clear that the supercountry analysis is for estimating average prices only. The starting point of this procedure is the crossÂ¬ classification of all the countries of the world by region and by per capita nominal (exchange rate converted) GDP. Once the income class is selected, the aggregate population and nominal GDP of each cell is assigned to one of the 34 Phase III countries for example. The aggregate GDP is divided evenly 199 200 among the countries in the same cell, with the provision that no country receives less than its own GDP as a weight. The supercountry weighting is used with the CPD method. The prices of each item are weighted by the supercountry expenditure for that category and by the reciprocal of the number of items priced by country. Thus, the function of the supercountry weights is to assign each country's price structure a weight that reflects the importance of its GDP, as well as all the other countries in the world not included in the ICP for which the ICP country's price structure can be regarded as representative. From the weighted CPD method, the PPPs are obtained and the Geary-Khamis method applied. The aggregate GDP of the supercountry is used to weight the prices of the representative country in the process of deriving average international prices. Each country's own quantities (obtained from its expenditures and prices) are then valued at these supercountry-based average prices (for further discussion of supercountry weighting see Kravis et al. 1982, pp. 79-88). If the GDPs of countries not included in the ICP are appropriately assigned to ICP countries, the "true" world average price structure is obtained. Then, if more countries are subsequently added to the ICP set, the reassignment of supercountry weights should leave the average prices essentially unchanged. Thus, the extent to which the multilateral comparisons of the 10 countries of Phase I 201 remained approximately the same after the six countries were added in Phase II. This reassures the success of supercountry weighting. APPENDIX C EKS CALCULATIONS To calculate the mini-Laspeyres price ratios, the geometric mean of the characteristic items for the base country is taken. Table 3.2 in the text has the matrix of characteristic items. To derive the mini-Paasche price ratios, the inverse of the mini-Laspeyres price ratios are taken. For simplicity, Japan is country A, Kenya B, U.K. C, and the U.S. is country D. The mini-Laspeyres index is: ^A/A = 1 = 1 Lb/a [ (.62/218.1) *(.77/98.6) ]1/2 = 0.0047 ^C/A = .13/98.6 = 0.0013 ^D/A = [(. 5/218.1) *(.35/98.6) ]1/2 = 0.0029 ^A/B = 160.9/1.19 = 135.21 ^B/B = 1 = 1 kc/B = .31/1.19 = 0.26 ^D/B â€” .92/1.19 = 0.77 ^A/C = 160.9/.31 = 519.03 ^B/C = .77/.31 = 2.48 Lc/c = 1 = 1 ^D/C = [(1.9/.54)*(.92/.31)]m = 3.23 â– ^A/D = [ (218.1/. 5) *(98.6/. 35) *(160.9/. 92) ]1/3 â€” 278.02 ^B/D = [ (.62/. 5) *(.77/. 35) *(1.19/. 92) ]1/3 â€” 1.52 ^C/D = [(,13/.35)*(.31/.92)]m = 0.35 ^D/D = 1 = 1 The mini-Paasche index is: ^A/A = 1/La/a = 1 ^A/B = 1 / Lb/a = 212.77 ^A 1C = 1 / LC/a = 769.23 ^A/D = 1/Ld/a = 344.83 ^B/A = 1 / La/b = 0.0074 ^B/B = i / iâ€™B/B = i ^B/C = 1 / Lc/b =3.85 ^B/D = 1 / LD/B =1.3 Pc/A = 1 / LA/C = 0.0019 ^C/B = i / ^b/c = 0.4 202 203 â€™c/c - i / ^C/C â€” 1 C/D = i / i*D/C = 0.31 D/A = 1/La/d = 0.0036 D/B = 1 / iâ€™B/D ~ 0.66 D/C = 1 / i*C/D = 2.86 D/D = i / i'D/D = 1. To calculate the mini-Fishers, multiply the mini-Laspeyres times mini-Paasche and take the square root. For example: FB/A - (i'B/A . * Fb/a) 1/2 / thus the mini-Fishers ^A/A = (1 * l)m = 1 ^B/A = (.0047 * .0074)1/2 = 0.0059 ^C/A = (.0013 * .0019)1/2 = 0.0016 ^D/A = (.0029 * .0036)1/2 = 0.0032 ^A/B = (135.21 * 212.77)1/2 169.61 ^B/B = (1 * l)m = 1 ^C/B = (.2 6 * .4)1/2 = 0.32 Fd/B = (.77 * . 66)1/2 = 0.71 Fa/C â€” (519.03 * 769.23 )1/2 631.87 ^B/C = (2.48 * 3.85)1/2 = 3.09 FC/c = (1 * 1)1/2 = 1 Fd/c â€” (3.23 * 2.86) 1/2 = 3.04 Fa/d = (278.02 * 3 4 4.8 3 )1/2 = 309.63 Fb/d = (1.52 * 1.3)1/2 = 1.41 Fc/d = (.35 * . 31)1/2 = 0.33 Fd/d = (1 * l)m = 1. Then the calculation of the EKS method is completed by utilizing all the information available with the direct and indirect mini-Fisher ratios. The EKS equations are: eksa/a = [(l)2 * i * 1),/4 = 1 EKSa/b = [(169.61)2 * 631.87/3.09 * 309.63/1.41]1/4 = 189.58 EKSa/c = [(631.87)2 * 169.61/.32 * 309.63/.33]1/4 = 667.53 EKSa/d = [(309.63)2 * 169.61/.71 * 631.87/3.04 ]1/4 = 262.67 EKSb/a = [(.0059)2 * 3.09/631.87 * 1.41/309.63]1/4 â€” 0.0053 eksb/b = [(l)2 * 1 * 1]1/4 = 1 eksb/c = [(3.09)2 * .0059/.0016 * 1.41 / . 3 3 ]1/4 = 3.5 EKSb/d = ((1.41)2 * .0059/.0032 * 3.09 / 3.04 ]1/4 = 1.39 eksc/a = [(.0016)2 * .32/169.61 * . 33/309.63]1/4 = 0.0015 EKSc/b = [(â€¢32)2 * . 0016/.0059 * . 3 3 /1.41 ]1/4 = 0.28 EKSC/C = [(l)2 * 1 * 1]1/4 = 1 EKSC/D = [ ( . 3 3)2 * .0016/.0032 * .32/.71]I/4 EKSd/a = [ (. 0032 ) 2 * .71/169.61 * 3.04 / 631.87 ]1/4 EKSd/b = [ ( . 71) 2 * .0032/.0059 * 3.04 / 3.09 ]1/4 EKSD/C = [ (3.04)2 * .0032/.0016 * .71/.32]1'4 eksd/d = [ (l)2 * 1 * 1]1/4 204 = 0.4 = 0.0038 = 0.72 = 2.53 = 1. APPENDIX D FIXITY The fixity principle requires that any index calculated and published for a regional comparison remain unchanged when it is involved in other comparisons embracing a larger group of countries. Decentralization requires that all regions calculate everything as a region, but certain regions also want their results, when compared to the rest of the world, to exemplify the fixity principle. For example, if the European Community (EC) regional comparison results in the per capita GDP of France being 25.6% higher than Italy's, then all other comparisons, OECD or world comparison, must yield a France/Italy per capita GDP index of 1.256. (.it . * ! â€¢ â€¢ ' â€¢ 1 ' - n ' â€¢ . Â¡ | -â€¢ v._; < - - â€¢ ' This idea becomes a problem in Phase IV because there are several regions, each observing the fixity principle, and some of the countries belong to more than one country group. There are no resolutions on what is to be done if a country falls into more than one region or grouping. Austria and Finland are members of both the OECD and the Europe 2 group. However, it is possible to satisfy the requirements of fixity for these two countries in the world comparison, but not simultaneously for the two regional comparisons. There is no justifications for the subordination of one region to another (Kurabayashi 1986). 205 206 The cost of fixity, if strictly adhered to, is that only total GDP is comparable across regions. For any subdivisions of GDP such as household or food consumption, or fruit and vegetables, the quantity comparisons are affected by the fact that these aggregates are expressed in different regional (relative) prices. Therefore, one can not compare, for example, the food consumption volume between two countries in different regions. APPENDIX E DATA AVAILABILITY There are several other countries and variables that should be included in this study. However, the data are not available for the length of time needed for this type of study. Cointegration analysis requires a fairly long time- series . The variables that I would have liked to have included in this analysis was imports and exports and a variable representing education. The import-export data is important because the G-7 and OECD export a considerable amount of their produce. These exports as well as imports are included in the income of these countries. Therefore, it would be interesting to test to see if the inequality in "traded goods" are cointegrated with the inequality in income. The data from the OECD National Accounts for imports and exports only starts in 1960 for 13 of the 22 OECD countries. The second variable is important because several studies in Chapter 2 associated education with growth and income inequality. The other variable that would enhance this study would be a time-series for the education level of the work force. The inequality of the educational level of the work force may be cointegrated with the inequality of income. The 207 208 data from the OECD National Accounts has expenditures on education data starting from 1960. Only eight of the 22 OECD countries begin their series in that year. Lastly, it would be beneficial if more countries could be included in this analysis. Unfortunately, Summers and Heston (1991) data set includes over 100 countries but many of their time-series only start in the late 1950's or early 1960's. APPENDIX F EXTRAPOLATION OF INDUSTRIAL DATA Fourteen OECD countries were used in this analysis (Canada, the U.S, Japan, Austria, Belgium, Denmark, France, Germany, Ireland, Italy, Netherlands, Norway, Spain, and the U.K. The following countries did not have a complete data series for the number of people employed in industry: Japan (1950-52), Austria (1950-55), Denmark (1950-54), France (1950- 53), Ireland (1950-55), Italy (1950-53), and Spain (1951-55). The data for the years that were missing is indicated in parenthesis, next to the countries name. The method of extrapolation was based on multiple regression. The 'independent variables were the number of people employed in industry in the U.S., Canada, Germany, and the U.K. The independent country was the country with missing data. The equation was: Yit = a^Canada, + ai2U.St + ai3Germanyt + ai4U.K.t + ai5t + ai6t2 where YÂ¡ represents the number of people employed in country i, and t represents time. This equation was estimated for the period for which observations exist for country i. After the equation was estimated, the parameters were used to predict the missing values. The full equation was used for the 209 210 following countries: Austria, France, and Ireland. The following countries data was best fit when the time and time squared trend was removed from the model: Japan, Denmark, and Italy. 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The Statistical Office of the United Nations Secretariat, New York: United Nations, 1987. Ward, M., Purchasing Power Parities and Real Expenditures in the OECD. Paris, France: OECD, 1985. 219 World Bank, World Bank Tables. Washington D.C.: International Bank for Reconstruction and Development, 1976. World Bank, World Development Report. Brussels: World Bank, (1990), p. 187. Wright, C. L., "Income Inequality and Economic Growth: Examining the Evidence," The Journal of Developing areas 13(1978):49-66. Zind, R. G., "Income Convergence and Divergence Within and Between LDC Groups." World Development. 19(1991): 6, pp. 719-727. BIOGRAPHICAL SKETCH Dave Deniel Weatherspoon of Vandalia, Michigan, completed his B.S. degree in crop and soil science at Michigan State University in 1987. After working for six months as a consultant in the Caribbean Islands he returned to the U.S. to pursue a master's degree. Dave received his Master of Science degree in 1989 from Penn State University in agricultural economics with a specialty in international development. Dave was awarded the McKnight Doctoral Fellowship to attend the University of Florida where he pursued a Ph.D. in food and resource economics. His areas of specialty are International Trade and Demand Analysis. 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. nes L. Seale, 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. 'jfoh ^ 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. a Â¿ 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 Fi 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. Douglafs 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 reguirements for the degree of Doctor of Philosophy. December 1993 Dean, College of Agriculture Dean, Graduate School UNIVERSITY OF FLORIDA |