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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 inlaws 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. JongYing 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 . . KuznetsType 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 CountryProductDummy Method . 3.3.3 EltetoKovesSzulc Method .. ... 3.4 3.5 3.6 Estimating Purchasing Power Parity . The GearyKhamis 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 G7 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 G7 . . 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 DickeyFuller (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 DickeyFuller 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 G7 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 MiniLaspeyres Price Ratio Matrix . 3.4 MiniFisher 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 (G7 Countries) . . 5.2 Government, Investment, and the Number of People Employed in Industry Inequalities (G7 Countries) . . 5.3 Investment Expenditure per Capita, and the Rate of Investment Expenditures for the G7 . . 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 G7 . . Estimates of Gamma from the G7 . . 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 G7 . 6.2 Total Government Inequality for the G7 . 6.3 Total Investment Inequality for the G7 . 6.4 Total Industrial Employment Inequality for the G7 . . 6.5 Total Income Inequality for the G7 Second Differenced. . . 6.6 Total Government Inequality for the G7 Second Differenced. . . 6.7 Total Investment Inequality for the G7 Second Differenced. . . 6.8 Total Industrial Employment Inequality for the G7 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 G7 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 G7 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 G7 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 G7 sample, suggesting that there exists a longrun 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 longrun equilibrium when innovations occur. The G7 equilibrium was stable without government expenditure while the OECD sample was stable with government expenditure. This may suggest that the OECD countries excluding the G7 rely on government expenditures for economic growth and stabilization of their economies. CHAPTER 1 INTRODUCTION Crosscountry 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 SalaiMartin, 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 G7 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 longrun 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 G7 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 G7 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 G7 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 38year 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 G7 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 G7 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 (divergenceconvergence theory). This theory has since been expanded to crosscountry 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 crosscountry interpretation of Kuznets hypothesis is not directly tested in this dissertation. However, if the G7 and the OECD countries are found to be converging, then the 4 results may support Kuznets crosscountry hypothesis since the G7 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 longrun 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 crosscountry 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 SalaiMartin, 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 divergenceconvergence 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 SaliiMartin, 1992; and BaradaranShoraka, 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 timeseries 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 timeseries). Baumol analyzed the G7 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 reexamined 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 shortrun, and in the longrun, 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 longrun 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 KuznetsType 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 coreperiphery 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 engagedin 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. 559587. 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 "TwentyFive 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 variablesthat 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 (196080) 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 subSaharan Africa. Some of the contributing reasons were the agriculture and debt crisis, and the rapid population growth.6 The middleincome 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 middleincome 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 BaradaranShoraka (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 timeseries implications from the model. The only significant relationship he found was the positive relationship between the average growth rate and the 1960 school enrollment. BaradaranShoraka (1992) using the same variable as Barro found the same result which supported Romer's argument. 27 BaradaranShoraka (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 BaradaranShoraka 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 nonCommunist 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 interregional 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 '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, BaradaranShoraka (1992) conducted a similar study with a few of the variables measured differently and found the same results as Barro. Barro and SalaiMartin (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 SalaiMartin (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 SalaiMartin (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 ofparticipating 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. Nonnarrowly 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 comparisonresistant goods. Comparisonresistant goods are goods and services that cannot be put into a category based on their characteristics. Some examples of comparisonresistant 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 comparisonresistant 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 countryproductdummy (CPD) and EltetoKovesSzulc (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 CountryProductDummy 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 logprice of i in c, but that coefficient is not used in this study (Theil et al. 1989, p. 8). 3.3.3 EltetoKovesSzulc 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 pricedata 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 miniLaspeyres and miniPaasche price ratios due to their similarity to the Laspeyres and Paasche timeseries 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. 4243). The miniLaspeyres 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 miniLaspeyres equation is: ic (3.3) L",d = i / = Pid where i = 1,...,m characteristic items in detailed category a. The miniPaasche formula is the reciprocal of the transposed miniLaspeyres 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 miniLaspeyres is created between countries with a diagonal of ones, the same is true for the miniPaasche 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 miniLaspeyres and miniPaasche 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 miniFisher binary price ratios. The miniFisher ratios are unweighted geometric means of the miniLaspeyres and miniPaasche price ratios. The equation for the miniFisher price ratios is: (3.5) Fc,d = (La,d ,d)12 where F,d is the miniFisher price ratio for detailed category a between countries c and d. Note that F,d F, = 1. However, the matrix of miniFisher 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 miniFisher ratios can be calculated. Hence, there would exist a full matrix of miniFisher ratios. The EKS method is then applied to the miniFisher 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 miniFisher 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. 4445). 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 miniFisher 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 miniPaasche, 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 n1 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 miniPaasche price ratios. The miniLaspeyres 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 miniPaasche matrix is just the inverse of the numbers in Table 3.3, that is Pu,. = 1/L,, the miniPaasche matrix will not be shown. Table 3.3 MiniLaspeyres 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 miniLaspeyres and miniPaasche price ratios are calculated, the miniFishers are estimated. Table 3.4 shows the results of the miniFisher calculations. There are no missing miniFisher 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 miniFisher 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 miniFisher 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 miniFisher ratios then the above procedure is applied until the matrix has no missing data. Table 3.4 MiniFisher 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 miniFisher 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 GearyKhamis method. The second stage of the estimation process is discussed next. 3.5 The GearyKhamis Method The objective of the GearyKhamis method is to provide multilateral baseinvariant 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 nonnegative international prices and PPPs. Thus, Geary and Khamis are responsible for this model. The derivation of the GearyKhamis method follows. The CPD or EKS method can be used to produce the detailed category PPP's for the GearyKhamis 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 GearyKhamis 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 GearyKhamis 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 GearyKhamis formula is straight forward. For the comparisonresistant 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 comparisonresistant 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 GearyKhamis 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 GearyKhamis 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. 5056); 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 GearyKhamis 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 GearyKhamis 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 GearyKhamis 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 GearyKhamis 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 containsfor 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 GearyKhamis 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 augmentedpricetableau 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 GearyKhamis 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 GearyKhamis 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 exchangerate converted figures and those which Kravis et al. (1978a) obtained using the GearyKhamis 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 exchangerate conversions greatly underestimate the true quantities of services in low income countries relative to those in highincome countries. (Kravis et al. 1982, p. 23) In addition, exchange rates have been variable since the switchover 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 Cooperative 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 GearyKhamis 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 chainlinkprocedure. 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 chainlinkprocedure 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 GearyKhamis 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 nonparticipating 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 GearyKhamis 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 nonICP countries. Lastly, an extrapolation is made to get RGDPC for later years. The shortcut 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 nonbenchmark countries. However, the authors caution that the nonICP 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 whichwere 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 exchangerateconverted 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 includedinthe 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 nontraded goods industries in high productivity countries; because international differences in productivity are smaller in nontraded goods industries (largely personal services) than in traded goods industries (largely commodities), the nontraded goods will be higher in 73 high productivity (high incomes) countries; and lastly, the high prices of nontraded 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 nontraded 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 nontraded 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 nontraded goods prices will be pulled up to the price levels of the highincome 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 nonbenchmark 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 nonICP countries as before. What is new in this paper is that the extrapolations for the ICP and nonICP 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 constantprice value of GDP,, in national currency and POPj, refers to the population. By using the constantprice 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. 332340). The crosssection 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 crosssection 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 pricelevel 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. constantprice 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 1970derived and 1975 crosssection 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 crosssection 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 nonAfrican 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 invariables 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 19751980 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 lowercase symbols x,, x2, x3, g,, and g2 stand for estimated values equivalent to their corresponding uppercase letters and are obtained from 84 benchmark studies or the national accounts. The errorsin 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 variancecovariance 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 rikk, 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. 543546). However, it is claimed that the maximum likelihood estimates are of the same varianceminimizing estimates obtained from averaging all possible unbiased point estimates. The data from Phases II, III, and IV and the U.N. constantprice series are made consistent by following the errorsinvariable approach. The nonbenchmark 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 nonbenchmark 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 postallowance price index. The two indexes that compose the postallowance 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 nonprofit 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 crosssection 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. Eightyone countries participated in these benchmark studies and 47 participated in more than one benchmark study. Thus, the need for relying on nonbenchmark 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 GearyKhamis 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 GearyKhamis 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 reanalyzed. The May 1990 national accounts data were used to revise those years. The GearyKhamis method was then implemented to aggregate the data. 90 After the benchmark data were aggregated, reestimated, and made consistent, the nonbenchmark 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 highranking 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 