Mg“. u.._ yr “‘r .“W\MI‘EI‘iiiii‘ii‘ii‘“ £34» 9' .. fi This is to certify that the dissertation entitled THE IMPACT OF ECONOMIC GROWTH ON THE DISTRIBUTION OF INCOME IN THE LESS-DEVELOPED COUNTRIES presented by Abdollah Ferdowsi has been accepted towards fulfillment of the requirements for Ph. D. Economics degree in N em. ' Major professor Date August 12, 1982 MS U is an Affirmative Action/Equal Opportunity Institution 0-12771 MSU LIBRARIES “ RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES will be charged if book is returned after the date stamped below. THE IMPACT OF ECONOMIC GROWTH ON THE DISTRIBUTION OF INCOME IN THE LESS—DEVELOPED COUNTRIES By Abdollah Ferdowsi A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Economics 1982 3 Q l \"5 o ~--.2’~?“ ABSTRACT THE IMPACT OF ECONOMIC GROWTH ON THE DISTRIBUTION OF INCOME IN THE LESSQDEVELOPED COUNTRIES By Abdollah Ferdowsi The past three decades have been characterized by an unprecedented and unexpected rate of economic growth in many developing countries. Most developing countries focused their attention on policies aimed at increasing the level of output and they succeeded. The preoccupation with maximizing the rate of output growth took precedence over the concept of distribution of output among all segments of the population. The justification for growthvoriented policies is the so-called Kuznets' Hypothesis. It suggests that in the early stages of economic growth, the distribution of income tends to worsen, while at the later stages market forces and government's corrective action will improve the distribution of income in favor of the poor. A great deal of skepticism has been raised with regard to the inherent tendency and ability of market forces and governments to reduce the inequality in the distribution of income. The main objective of this dissertation is to empirie cally explore the relationship between income distribution and different socio—economic and structural changes which occure at different stages of economic growth. An unprecedented technique of estimation is used, i.e. the cubic spline function. The spline function is superior to the other form of specification in a sense which allows a curvature relationship between different variables. Based on the empirical finding, a set of policies are proposed to improve the distribution of income. It is argued that there is no need for sacrificing economic growth for an egalitarian distribution of income. By designing and implementing economic and social policies, a better distribution of income can accompany economic growth from the start. It is also argued that any policy which attempts to improve the distribution of income may prove impossible to implement unless the poor develop sufficient consciousness and organization to provide support for redistributive policies. TO MY PARENTS ii ACKNOWLEDGMENTS There are so many great peOple whom without their assistance and encouragement, it would be impossible to complete a program of graduate study, and it is with great pleasure that I take this opportunity to recognize and acknowledge their invaluable contributions toward the completion of this dissertation. I must first express my sincere gratitude to Professor Anthony Koo, Chairman of my dissertation committee, for his invaluable advice and guidance throughout this study. His willingness to devote immediate attention, prompt responses, perceptive comments, and general encouragement all made my work much easier. The other members of my committee: Professors Subbiah Kannappan, W. Paul Strassmann, and Edmund Sheehey were also extremely helpful in providing technical advice, insightful suggestions, and moral support. Other faculty members also provided assistance. In particular, Professor Daniel Suits, who stimulated my interest in applied econometrics. In addition, my special thanks to the members of my family for their generous moral and financial support throughout these years. Finally, I gratefully acknowledge the invaluable editorial assistance made by Monica Green and the expert typing of the manuscript by Terie Snyder. iii TABLE OF CONTENTS LIST OF TABLES. LIST OF FIGURES CHAPTER ONE - INTRODUCTION TWO - SURVEY OF LITERATURE 2.1 - Introduction. . . . . . . . . . . . 2.2 - Historical Presentation of. the Distribution of Income . 2.3 - Income Distribution in the Process of Economic Development. 2.” - Rise of Skepticism. 2.5 - Decomposition of the Gini Coefficient 2.6 - Conclusion. Footnotes THREE - DETERMINANTS OF INCOME DISTRIBUTION IN THE PROCESS OF ECONOMIC GROWTH 3.1 — Introduction. 3.2 - Functional Distribution of Income Under a Dualistic Economic Regime . . . . 3.3 - Distribution of Income and Education. 3.H - Inequal Distribution of Assets. . . 3.5 - Population Growth and Income Determination. 3.6 - Trade Policies and Income Distribution. 3.7 - Government Policies and Income Distribution Footnotes FOUR - EMPIRICAL EXPLORATION OF THE IMPACT OF ECONOMIC GROWTH ON INCOME DISTRIBUTION. ”.1 - Introduction. . . . . . . . . . . . . . u.2 - Method of Estimation. . . . . . . . . . . . u.3 - The Estimation Results. M. 3a - Per capita GDP and the Distribution Income . . . u. 3b - Rate of Growth Of GDP and Income Inequality . . . . . . . . . . . u. 3c - Dualistic Economic Development and Income Distribution. . . . . iv PAGE vi vii 0101 13 31 3M 37 39 H2 H2 U3 51 56 58 6” 66 71 73 73 76 79 79 83 87 CHAPTER PAGE FOUR - (cont‘d.) ° H.3d - Labor Share and Capital Formation. . . 9O 4.3e — Education and Income Distribution. . . 95 H.3f - Import-Export and Income Distribution. 100 n.3g — Indirect Taxes and the Gini Coefficients . . . . . . . . . . . . . 103 u.u-General Equation. . . . . . . . . . . . . . . 106 Footnotes. . . . . 111 FIVE - POLICY IMPLICATIONS TO IMPROVE THE DISTRIBUTION OF INCOME. . . . . . . . . . . . . . . . . . . 113 5. l-Introduction. . . . . 113 5. 2-Policy Intervention to Increase Labor Shares. 115 5. 3-Investment Policies and Income Distribution . 119 5.u-Capital Ownership and Inequality. . . . . . . 122 5.5-Policies to Promote Educational Level . . . . 126 5.6-Population Policies to Improve the Distribu— tion of Income. . . . . . . . . . . . . 131 5. 7-Tax Policies for Mobilizing Resources . . . . 13H 5. 8-Conclusion. . . . . . . . . . . . . . . . . . 135 Footnotes. 137 APPENDIX . . . . . . . . . . . . . . . . . . 139 BIBLIOGRAPHY lu5 LIST OF TABLES PAGE TABLE 2.1 - Share of Ordinal Groups Over Long Periods . . 1“ TABLE 2.2 - Cross—Country Regression Model. . . . . . . . 25 vi FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE LIST OF FIGURES PAGE .1 — Distribution of Income at Different Level of Percapita GDP. . . . . . . . . . . . . . 22 .2 - Skewness of the Lorenz Curve and its Relation to Development. . . . . . . . . . . . . . . 30 .l - Industrial Labor Market Under Dualistic Economic Regime . . . . . . . . . . . . . . us .2 - Rate of Population Growth and Level of Income. . . . . . . . . . . . . . . . . . . 60 .l - Piece-Wise Linear Relationship Between Gini Coefficient and Per-Capita Income . . . . . 78 .2 - Piece-Wise Polynomial Relationship Between Gini Coefficient and Per-Capita Income. . . 78 .3 - Estimated Gini at Different Per Capita Income 82 .H - Gini Coefficient and Percentage Rate of Growth of Output. . . . . . . . . . . . . . 86 .5 - Urbanization and Gini Coefficient . . . . . 89 .6 - Labor Share and Gini Ratio. . . . . . . . . 92 .7 - Capital Formation and Gini Ratio. . . . . . 9h .8 - School Enrollment Ratio and Gini Ratio. . . 98 .9 - Import and Estimated Gini Ratio . . . . . . 102 .10-Impact of Export on Gini Ratio. . . . . . . 10H .1l-Indirect Taxes and Gini Ratio . . . . . . . 107 vii CHAPTER ONE Introduction The past three decades have been characterized by an unprecedented and unexpected rate of economic growth in many deve10ping countries. Most deveIOping countries focused their attention on policies aimed at increasing the level of output and they succeeded. Between 1950 and 1975 the income per capita in these countries rose by 3.9 percent per year (including China). The preoccupation with maximizing rates of output growth took precedence over the concept of distribution of output among all segments of the population. The justification for growth-oriented policies is the so-called "trade-off" between economic growth and egalitarian distribution of income. It has been suggested that redistri- bution of income would lead to a smaller rate of growth of income. On the other hand, if growth is given primary emphasis, it creates a mechanism - higher productivity, rising demand for labor and consequent higher wages — through which the fruits of economic growth "trickles down" speedily. In other words, growth-oriented policies suggest that it is necessary first to build up the capital, infrastructure, and productive capacity of the economy and the fate of the poor should not be of great concern in the early stages of develOp- ment. The rational behind this justification is the Kuznets hypothesis suggesting that in the early stages of economic growth, the distribution of income tends to worsen, while at the later stages it eventually will improve. The strong implication of the Kuznets hypothesis is that inequality in the distribution of income is a necessary condition for economic growth and at the later stages, market forces and government's corrective actions will improve the distribution of income in favor of the poor. A great deal of skeptism, supported by recent empirical data, has been raised with regard to the inherent tendency, ability, and willingness of governments to take corrective action to reduce the inequality in the distribution of income. Landlords, politicians, and other rich elites do not save and invest substantial pr0porv tions of their incomes in the local economy. Much of their incomes are spent on imported luxury goods, lavish mansions, and foreign travels. Therefore, the growth—oriented strategies are really an inaccurate justification for policies which perpetuates the conditions of income inequality in the developing countries. V/Recognition of these facts make it essential to reorient develOpment priorities away from preoccupation with GNP growth and towards broader social objectives such as the provision of health, nutrition, education, and finally more equal distribution of income. Strategies designed to raise the level of living and incomes of the poor not only contribute to material well-being of the poor but also to higher productivity and income levels of the society as a whole. The main objective of this dissertation is to explore the relationship between economic growth and income distribu- tion. Chapter Two presents a review of the literature on distribution of income and its pattern in the course of economic growth in developing countries. It compares and contrasts different schools of thought as they have appeared in this field. Chapter Three deals with the important socio—economic and structural changes which occur at different stages of economic growth. After identifying these changes, inherent in the process of economic development it will be explained how these changes affect the distribution of income. Chapter Four concentrates on the empirical exploration of the impact of different variables on the distribution of income. It stressed that caution should be used in interpreting the results obtained from cross~sectiOnal data and applying these results to the long-term growth process for an individual country. High income inequality and substantial absolute poverty may create the conditions for ultimate rejection of the economic system by the frustrated masses and politically explosive people. Chapter Five deals with the policies to improve the distribution of income in favor of the poor. It is shown that there is no need for sacrificing economic growth to achieve an egalitarian distribution of income. By designing and implementing economic and social policies, both growth and distributional objectives can be achieved. Chapter Five also advises that any redistributive policy necessarily requires the political process that can generate more power for the poor in the society. The achievement of political power by the poor is a necessary first step toward a better design and implementation of redistributive policies. CHAPTER TWO SURVEY OF LITERATURE 2.1 - Introduction The issue of unequal distribution of income and wealth in a society has been of concern to mankind for centuries. This issue can be seen from a variety of perspectives. This chapter offers a brief review of the literature on the topics of income distribution and economic development. Section 2 presents a historical evolution of the distribution of income as it appears in the literature. Section 3 deals with the pattern of income distribution in the process of economic development. In this section the literature on the Kuznets' hypothesis is discussed. In Section N, the skepticism with regard to the validity of the Kuznet‘s hypothesis is introduced. Section 5 deals with the most recent approach to the relationship between income distribution and economic development, i.e., decomposition of the Gini coefficient. Finally, section 6 offers a brief conclusion. 2.2 - Historical Presentation of the DiStributiOn of Income The founders of classical economics were primarily concerned with the functional distribution of income, i.e. the distribution of income among the major factors of production. The concept of unequal distribution was considered only as a secondary issue. The beginnings of abstract studies of distribution were made by Physiocrats. Quesnay was mainly interested in distribution between social classes i.e. "sterile" and "productive" classes. Handicrafts and trades were considered the sterile occupations while agriculture was thought to be the only productive employment.1 In his Wealth of Nations, Adam Smith distinguished a threefold classification of the factors of production—land, labor and capital; and, naturally he distinguished three shares: rent, wages and profit. He wrote, "the whole annual produce...naturally divides itself into three parts, and constitutes a revenue to three orders of people; to those who live by rent, to those who live by wages and to those who live by profit. These are three great, original and constituent orders of civilized society. "2 Smith commented that pecuniary wages and profit could be different according to the differences arising from the nature of advantages and disadvantages of different employment. But he pointed out that the other source of differences in pecuniary wages and profit was due to the policy of EurOpe, "which.no-where leaves things at perfect liberty":31 The-Ricardian law of rent, which is the first example of the marginal method, defines rent as that portion of the product which is paid for the use of the better quality or powers of the soil. He argues that the rent of a given field is measured by the surplus of its produce over that obtainable with the same capital and labor from the poorest land in cultivation. Ricardo believed that wages were basically governed by subsistence level with some allowances for rising standards of living, a concept which he termed "natural price of labor". As population increases, which is assumed is inevitable, poorer soil is brought under cultivation. Consequently, the rent will rise, wages remain at the "natural price of labor" and profit will correspondingly decline. In 1898 John Stuart Mill published his Principles of Political Economy. In his book, he infused social and institutional concepts in the theory of distribution. He believed that unlike the law of production, those of distribution are the matter of human institution solely and "therefore depends on the laws and customs of society... these laws are consequences of the fundamental laws of human nature combined with the state of knowledge."u He stated that law in general, and particularly laws relating to prOperty, have profound effects upon the distribution of income among persons. Even though Mill modified the Ricardian schema by infusing social institutions, his analysis of distribution fundamentally was the same as that of other classical writers. None of the classical economists were concerned with economic equality itself. The main thrust of their thinking appeared to be concerned with the distribution of income among different factors of production. The Utopian socialists of the early nineteenth century, influenced by the events of the French Revolution, brought the idea of economic equality to the attention of economic theorists. They espoused a belief in the possibility of a large reconstruction and reorganization of human society. St. Simon advocated distribution based on a person's work and reorganizing production by "the union of all instruments of all labour in a social fund, which shall be exploited 5 I Fourier favored a more complex system by association." of distribution which demanded a comfortable minimum income to every person, including women and children more than five years old. In 1867 the first volume of Dasvxapital was published by Marx. This volume contains the clearest exposition of the Marxian system. As regards distribution, Marx followed Ricardo's doctrines. He argued that the wages of labor were determined by the amount of the necessities just enough to maintain the labor force. Wages can never rise above this subsistence level. But labor, Marx argues, creates the whole value of the product, and receives only subsistence wage. The difference is surplus value which is taken by the capitalists. Every increaSe in the laborer's efficiency, every improvement in the means of production, every new discovery of natural resources, every addition to capital by way of saving, only increases surplus value. It follows that economic progress, while leaving the condition of the laborer as miserable as ever, adds continually to the aggregate of surplus value, that is to say, to the aggregate income of the capitalist classes.6 As mentioned previously, classical economists also dealt with the issue of inequality in the distribution of wealth. To Smith, the differences in the nature of employment were partly due to the absence of perfect liberty. To John Stuart Mill it was the human institution, namely the law of the inheritance of wealth, which led to unequal distribution of income. And finally, Marx believed that concentration of capital, due to rapid accumulation of surplus, had to be blamed for income inequality in the society. However, it only was after the arrival of the "law of decreasing marginal utility" that it became possible to analyze the economic and welfare effects of income inequality. Jevons7 introduced a principle which later was called the law of diminishing marginal utility. The principle postulates that income and wealth are subject to diminishing marginal utility. From this principle arises a great concept, namely the extreme wastefulness of large inequality of income on economic welfare. The quantity of happiness for a man, who already has a great quantity of property in his possession, will decline as he acquires additional units of prOperty. This led Jevons to assert the great wastefulness of large inequality of income from the point of view of economic welfare. Ever since, it has been generally accepted that total economic welfare is increased with more equal 10 distribution of income. Another view on income distribution was suggested by Pareto. He pioneered the study of distribution of income between households without reference to social class to which they belonged,the size distribution of income. From this study, Pareto developed his famous law of distribution which is known as Pareto's law. The law states that in all places and at all times the distribution of income is given by a mathematical formula. The formula is, log y = A -eemeeegm50= .memcusx .m "woesom 3m am am m.m~ Hm mm was eccch m: m: a: mm a: om sou ace mH mH :a mm mm om ea Hm Hm ace mmmH mmmH ommH wmmH amaH mNmH mNmH MHmH "ccema "mcmeeow pmozlzcmaemw mm a: as mm m: sea ace :H eH 3a eH am am ace XMP .HOPMM OEOOrHH m.H: m.e: om as am Hm mm mm HON ace mH m.m~ me am Hm mm m: as am ace xMP whomon mEOUCH emmH asaH mmmH ezmH mmmH mamH mHmH ommH "cceca "accmcHx cceHca 3m 3m om m.aa How emcch a: m: as am How ace mH mH m.H~ m.m~ am ace XMe Hmempow ememm mEoocH mm mm mm mm ea am How emcsca a: m: a: as am :m sea ace om Ha Ha 3N m.ma om am ace XMe meomon mEoocH mmmH :mmH esmH HsmH mmmH mamH umceca "mcecem copes: mmHmHzm Qz< mMHHmmmooDm mDOHmmm mzoq mm>o mmDoxw A Hmma bu: 000H 000 -- 000 0H0H 000 0.0 HH.0 0.0 0.0 0.0 0.0 0.0 0.0 H0.0H 00.00 0.00 0H.00 0.0H H.0H 0.00 0.H0 00. 00. 00. 00. 00. 00. 00. 00. 000.00 000.00 000.00 000.00 000.00 000.00 000.00 000.00 00.0 0H.0H 00.0H . 00.0H 00.0 0H.0 H0 0- 00.00- 000.H0 000.H0 000.H0 000.H0 00.0 00.0 00.0 0H.0- 000.00 000.H0 000.00 000.00 00.0 0H.0 H0.0 00.0- 000.00 000.00 000.00 000.00 0H.H- 00.0- 00.0- 00.0 000.00 00.H0 000.00 000.00 00.0 00.0 0H.0 0H.0- 000.00 000.00 00H.H0 0H0.00 00.0 00.0 00. 00 0- 000.00 000.00 000.00 000.00 0H0.00 000.00 000.00 000.00 HH.0 00.0 0H.0 0H.0 H00.0 0H.0 HH.0- 00.0- 000.00 000.00 00H.00 000.00 00H.00 000.00 000.H0 000.00 00.0 00.0 0H.0H 00.0H 00.0 00.0 0H.0- 00.0H- 000.00 000.00 000.00 000.00 00H.00 000.00 00H.00 000.00 00.00- 00.00- 00.00- 00.H0- 00.0- H0.00- 00.00 00.00 0HH.00 000.00 00H.00 000.00 000.H0 000.00 000.00 000.00 00.00 00.00 00.0HH 00.00H 0H.H0 00.00 00.0 - 00.00- 000 .00 0000 .00 0c00 .00 0000 .0m 0c00 .00 0000 .00 0cH0 .00 0cH0 .0m ecooema o: ummsoq ucooemm om pmmsoq eccccca 00 chcHz ecooema cm 909 wmm Hzmozmmma 0mm: :0 mzm wweamo.emm0 owvmeomsv mo useoa mcecnsu Uomewpwm mum h m m mmeeecsoo pmeHmMUOm pom hassa .oa. coflmesmoa cone: mo oemsm .m mam c0 meswasoeewm mo oemnm .m cowemHsaoa no mums Aezoew .e pcwEHHoecw Hoonow memocooom .w mumm momemued .m mam mo meme zwsoew .2 «mazw meemmo Rom onH .m azm weflamo pom moH .N penumcoo .H - .I.Il LIIIIHLI‘NJHJ ‘hvl II"- Iul 1" moanmeem> aeoumcmflaxm Juno: ZOHmmmmwmm prZDOUImmomo ~.N mAm B , and if a < 8 then it is skewed toward (1, 1). He estimates the value of a and B for fifty countries and he shows that the ratio of 0/8 is greater than unity (a > 8) for all develOping countries or countries with Lorenz curves skewed toward (0, 0). But for most developed countries a/g ratio is smaller than one (a < 6), indicating that Lorenz curves are skewed toward (1, 1). Based on his finding, he concludes that "this observation supports Kuznets' hypothesis that the income share of the middle group is higher in the developed than in the develoPing countries."37 \/2.u - Rise of Skepticism One implication of the inverted Uvshape relationship is the nature of a trade off between equality and economic growth- Specifically, the worsening of inequality is inevitable in the early stages of economic growth, and then in the later stages, the fruit of economic growth will automatically trickle down to the poor. Also government may take an active role to correct the distribution of income in favor of the poor (as Kuznets pointed out). The inverted U-shape hypothesis implicitly accepts that in the poor society inequality can be eliminated only through 32 increased production. But the growth experience in most of the developing countries has revealed that the fruits of growth have been concentrated in the modern sector of the economy reinforcing inequalities in income, assets and power. At the same time the modern and industrial sector has not been able to absorb the rapidly growing labor force from the agricultural sector (as Lewis anticipated). After failure of growth-oriented strategies to achieve an equitable society and to reduce poverty, new strategies have been proposed. These new strategies are concerned with achieving more equality in distribution of income, with growth regarded as a necessary but not a sufficient condition. Stewart and Streeten are among those skeptical of growth-oriented strategies. They claim that government intervention, which was considered to be used to correct the distribution of income is in fact in favor of the upper-income groups rather than the poor. The reason which they offer is that government is comprised of the elite who are reluctant to take actions to correct the distribution of income. They write, "The elite, against whom redistri0 butive measures must be aimed,ftum1the personnel who administer the measures. They capture the machine and render it ineffective."38 They also argue that modern technology which is used in developing countries leads to inequal distribution of income. Modern technology needs a highly skilled 33 personnel, and efficient, disciplined and literate workers. In order to achieve these standards, public and private expenditure must be concentrated on the modern sector. Meanwhile, an unequal distribution of income is required for generating market for the goods produced by modern technology, i.e. goods produced for consumers with high incomes. By considering these factors, Stewart and Streeten refute the existence of an inverted Uvshape relationship. They conclude that "the high-growth policy thus tends not only to generate inequalities, but also to establish positions of power that make it extremely difficult to combat these inequalities by government redistribution policies."39 So they demand more direct actions to reduce inequality of income in the developing countries. They present a list of direct strategies to alleviate poverty and to reduce income inequality. They assert that progressive taxation of income has not been successful to correct inequality, so they suggest a policy for redistribution of existing assets. Redistribution of assets, they argue, includes policies of land reform, spread of ownership or nationalization of industries, and greater access of educational and health services to the poor. But they acknowledge that this strategy is a radical one and "it does not normally form part of the advice given to existing governments."1+0 The other strategy which they present is called 314 redistribution through growth. This strategy was originated by I.L.O., then was modified by Chenery and Ahluwalia.ul Chenery and Ahluwalia collaborated to construct a model which incorporated the distributional objectives into develOpment strategy. Their strategy is simply to transfer the extra income resulting from growth to the poor. Chenery and Ahluwalia assert that this strategy can achieve substantial improvements in pattern of concentration of assets and a considerable potential for raising the income of the poor. This form of redistribution involves the transfer of investment resources to low-income groups, providing the poor with a source of income. This strategy does not reduce the overall G.N.P. because "it means a lower rate of growth of incomes at the upper end, and a higher rate of growth at the lower end, without any absolute ~u2 . . fl reduct1on of 1ncome. 2.5 - Decomposition of the Gini CoeffiCient Perhaps one of the most interesting approaches to detect the relationship between economic growth and income distribution is the decomposition of Gini ratio. This approach was fruitfully used by John Fei, Gustav Ranis and Shirley Kuo.”3 Their purpose was to set out a methodology for the decomposition of family income inequality by distinguishing among different components of family incomes and their change in the process of economic development. As the measure of inequality, they chose the Gini 35 coefficient. They also assumed that the total income pattern of n families, Y = (Yl, Y2...Yn) have been comprised of different income components. For simplicity they assume that income of families are composed of wage, property income and transfer income. And consequently overall inequality measure, Gy, can be decomposed into the various sub Gi (i.e. Gw indicates the inequality in wages among families). In order to estimate overall inequality, they use the weighted sum of the factor Ginis: Gy = c G(Yl) + ¢ G(Y2) + ¢ G(Yr) l 2 . ... r . and pi can be defined as the distributive shares and is calculated as: ¢. = %; and § 0i = 1 1 The above formula simply states that total family income inequality, Gy, is the weighted average of the factor Ginis G(Yi). Depending on how G(Yi) affects the overall inequality, they distinguish among the different types of income components. They argue that type one income, prOperty income, is distributed less equally than total income (G1 > Gy). Type two income is distributed more equally than total income (G2 < Gy)' Wage income is considered as a type two income. They consider transfer income as type three income. The important feature of type three is its role to 36 narrow the inequality of income. As they point out "a large welfare budget (a large 0T) will certainly contribute to the overall equality rather than inequality,"uu so a negative sign has to be attached to ¢TG(YT). They also recognize the phenomenon of urbanization in a dualistic economy i.e. reallocation of labor from agricultural sector to industrial sector. They argue that if agricultural income is distributed more equally than total income, the phenomenon of urbanization will contribute (to a higher inequality of total income. But if agricultural income is distributed less equally than total income, its declining share would result in the equality of total income. They apply their model to Taiwan. Its economic structure was characterized by labor surplus dualistic economy. They point out that though Taiwan's family distribution of income in the 1950's was unfavorable to the poor, that distribution has improved substantially during two decades of rapid growth, The factors involved in this process, they assert, were a combination of activities to correct the distribution of income in urban and rural sector. In the rural sector these policies included agricultural reforms, rapid spread of secondary crops, rural industrial activities, reducing rent payments and more labor intensive cropping patterns. In the urban sector, they assert "that urban income inequality cannot decline very much until after the turning point."‘u'5 By 37 turning point, it is meant the end of surplus labor. In urban sector the policies have to be concerned with the rapid absorption of labor by using more labor intensive technology. Decomposition of overall inequality into factor components is a very useful method in detecting the source of income inequality and introducing policies to improve the distribution of income. The use of the method requires details and comprehensive data on different components of family incomes. The lack of data in most develOping countries hinders the application of this method. 2.6 - Conclusion In concluding, it will be helpful to classify different schools of thought as they appeared in this field. The classical economists were concerned with the distribution of income among workers, capitalists, and land owners. It was the prevailing approach until the beginning of the [present century. Around this period, Pareto suggested the size distribution of income. His statistical studies led him to assert that the inequality of income was a social constant determined by basic economic and social forces and this inequality could not be influenced by: differing national institutions and government policies. Kuznets (1955) pioneered a study which.negated Pareto's law. In his study, Kuznets developed a dynamic relationship between distribution of income by size and 38 different stages of economic growth. Based on provided data, he concluded that income inequality is not constant, as Pareto suggested, but it would increase in the early stages of economic growth, then decrease in later stages. This behavior in income inequality at different stages of economic growth is termed Kuznets' hypothesis and constituted a new intellectual school of thought. After this study, there have been a large number of studies that have accepted ”6 This hypothesis Kuznets' hypothesis as a general law. implies that the worsening of inequality is inevitable in the early stages of growth and then at the later stages, inequality will narrow down. This hypothesis implicitly accepts that in the poor society income inequality can be eliminated only through increases in production. It was this behavior in income inequality which led some development economists to emphasize the growth«oriented strategies with the presumption that an equitable society can be achieved automatically. FOOTNOTES CHAPTER TWO FOOTNOTES 1Hugh Dalton, Some Aspects of the Inequality of Incomes in Modern Communities (London: George Routledge and Sons, Ltd; New York: E.P. Dutton and Co., 1920) p. 38. 2Adam Smith, The Wealth of Nations, ed. Edwin Cannan (New York: The Modern Library, 1937) p. 52. 3 Ibid, p. 99. uJohn Stuart Mill, Principles of Political Economy, 2 Vol., Vol. 1 7th ed. (London: Longmans, Green, Reader and Dyer, 1871) p. 250. 5Thomas Kirkup, History of Socialism, 5th ed. rev. (London: A. and C. Black, 1913) p. 28. ‘— 6 Dalton, Some Aspects of the Inequality, p. 81. 7Jevons admits that he was not the first person to bring the subject of marginal utility. It had been already discovered by J. Benthan in his writing about "principles of utility". 8Dalton, Some Aspects of the Inequality, p. 100. gEdwin Cannan, "The Division of Income," Quarterly Journal of Economics, (May 1905) p. 368. if 10John Maynard Keynes, The General Theory of Employ— ment, Interest and Money, First Harbinger ed. (New York: Harcourt, Brace, and World, Inc., 196”) pl 372. ll Ibid, p. 373. 12Ibid. 13W. Arthur Lewis, "Economic Development with Unlimited Supplies of Labor;VThe Manchester SChoOl, 22 (May 195%) pp. 139—192. 39 NO 31Idem, "Inequality, Poverty and Development," p. 337. 321bid, p. 337. 33Char1es L. Wright, "Income Inequality and Economic Growth: Examining the Evidence," The Journal of Developing Areas (October 1978) pp. #9. 3D'Nanak C. Kakwani, Income Inequality and Poverpy: Methods of Estimation and Policy Applications (New York: Oxford University Press, Published for World Bank, 1980). 35 Ibid, p. 383. 36Kakwani imposes several restrictions on the formula: But R.H. Rasche, J. Gaffney, A.Y.C. Koo and N. Obst show that these restrictions are inadequate. Even with imposing these restrictions, Gini coefficient might be greater than one. For further details see Rasche, Gaffney, Koo and Obst, "Functional Forms for Estimating the Lorenz Curve," Michi an State University, Econometrics Workshop Papers No. 7706, (February 1978). 37 Kakwani, Income Inequality, p. 385. 38France Stewart and Paul Streeten, "New Strategies for Development: Poverty, Income Distribution and Growth," Oxford Economic Papers 28 (November 1976) p. 391. 39 Ibid, p. 393. 1+01131-1, p. 395. l“I'Montek S. Ahluwalia and Hollis Chenery, "A Model of Distribution and Growth," in RediStribution with Growth, ed. Hollis Chenery et a1., (London: Oxford University Press, 3rd Printingm 1976) pp. 209-235. 2Stewart and Streeten, "New Strategies," p. 395. uaJohn E. Fei, Gustave Ranis and Shirley Kuo, "Growth and the Family Distribution of Income by Factor Components," Quarterly'Journal 0f Edenomics (February 1978) pp. 17053. ””Ibid, p. 18. usIbid, p. 37. 6Sherman Robinson, "A Note on the U-Hypothesis Relating Income Inequality and Economic Development," American Economic Review (June 1976), p. #37. 91 luSimon Kuznets, "Economic Growth and Income Inequality," American Economic Review, HS (March 1955), pp. 1—28. 15Idem, "Quantitative Aspects of Economic Growth of Nations: VIII. Distribution of Income by Size," Economic DeveloPment and Cultural Change (January 1963, Part II), pp. 1-80. 16 Idem, "Economic Growth and Income Inequality," p. 19. 17Ibid, p. 7. 18Ibid. 19Ibid, p. 8. 2oIbid, p. 9. 21Ibid, p. 17. 22Irving B. Kravis, "International Differences in the Distribution of Income," The Review of Economics and Statistics (November 196077p. 909. 23Harry T. Oshima, "The International Comparison of Size Distribution of Family Income with Special Reference to Asia," The Review of Economics and StatistiCs (November 1962) p. 0H2. 2‘I‘Irma Adleman and Cynthia Taft Morris, An Anatomy of Patterns Of Income Dietribution in Developing Nations, Part III of the final report (Grant AID, Northwestern Univer- sity, 1971). 25Felix Paukert, "Income Distribution at Different Levels of Development: A Survey of Evidence," International Labor Review 108 (August—September 1973), p. 116. 26 Ibid, p. 120. 27Montek S. Ahluwalia, "Income Distribution and Development: Some Stylized Facts," American EconomiC'Review 66, No. 2 (May 1976) p. 128. 28Idem, "Inequality, Poverty and Development," Journal of Development EccncmicS 3 (December 1976) p. 309. 2g“Idem, "Income Distribution and Development," p. 131. 30 Ibid, p. 132. CHAPTER THREE DETERMINANTS OF INCOME DISTRIBUTION IN THE PROCESS OF ECONOMIC GROWTH V’There are many factors which affect the distribution of income and its pattern during the course of economic develOpment. To investigate the relationship between growth and income distribution, the best point of departure is the recognition of the main characteristic of an underdeveloped economy, that is, the socio-economical and structural changes which occur at different stages of economic growth. After identifying these changes, the second step will be to find how these changes affect income distribution. These main characteristics include a broad selection of variables that attempt not only to describe different aspects of a developing country, but also the trend in the _ distribution of income during the course of development. In Section 2 of this chapter, a dynamic production function is introduced. The production function explains the functional distribution of income between laborers and capitalists under a dualistic economic regime. In Section 3, the relationship between the distribution of human capital and income is considered. In Section u, the concentration of holdings of physical capital and its impact on income is analyzed. In Section 5, there is a discussion of the 92 H3 population growth and change in its age structure. Section 6 deals with the external aspects of the economy. The impact of trade policies on internal terms of trade and employment will be discussed. Finally, Section 7 is concerned with the government policies in attempting to achieve the distributive justice in the economy. 3.2 - Functional Distribution of Income Under a Dualistic Economic Regime ‘ Perhaps one of the most observable characteristics of many underdeveloped countries is the coexistence of a overpopulated agricultural sector and a rapidly growing modern or industrial sector. This phenomenon has been termed "dualistic development" in the literature. The agricultural sector is characterized by widespread disguised underemploy- ment with a high rate of population growth. In this sector the traditional techniques of production are being used. The industrial sector, on the other hand, enjoys advanced technology which is usually the result of foreign investments. In the process of economic growth as output per capita increases, it has been observed that output per capita in the industrial sector increases at a rate much higher than the output per capita in the agricultural sector.1 This uneven rate of growth in two sectors can be explained by the differences in income elasticity for agricultural products and industrial products. Income elasticity for food and other agricultural products are very low, whereas the inverse is true for industrial goods. nu As average income increases, the percentage change in demand for agricultural products is less than the percen- tage increase of income. Correspondingly, the percentage change in demand for industrial products is greater than ‘the percentage change in income. This phenomenon causes more demand for industrial products and less demand for agricultural products. Since demand for factors of production is derived demand, the differences in output demand lead to a rapid increase in demand for labor in the industrial sector. The agricultural sector will supply the greatest part of this labor to the industrial sector. The movement of the labor force from the agricultural sector to the industrial sector due to structural change in final output can be shown by a very simple graph. The graph.only presents the demand for labor in the industrial sector under the assumption of the dualistic economy with unlimited supply of labor (at least up to a certain level of employment). In Figure 3-01, the wage rate is measured on the vertical axis and the level of industrial employment on the horizontal axis. Demand for labor is downward sloping, reflecting the law of diminishing marginal product. The most important feature of this sector under the assumption of unlimited supply of labor is the labor supply curve. The supply of labor is perfectly elastic up to Lc and beyond LC it is upward sloping. The horizontal portion of labor supply reflects the rapid increase of labor from the agricultural \/ to the industrial sector. This prevents the institutionally US > '— ..-—-0--. Figure 3.l INDUSTRIAL LABOR MARKET UNDER DUALISTIC ECONOMIC REGIME 96 determined wage rate (Wi) to increase up to LC, where the unlimited supply of labor is eliminated.2 In the industrial sector, firms maximize their profit by employing labor where marginal revenue product of labor (demand for labor) is equal to the institutional wage rate. If demand for labor is DlL’ then the amount of employment will be Ll° Since wage is constant, this level of employment leads to the surplus or profit of WNA, and total wage income of OWALl. The amount of surplus will be the main source of investment and capital accumulation in the industrial sector. In the next period, this surplus will be added to capital stock which leads to a greater demand for labor (D2L) and the labor employment of L2. The new employment level will create ABMN amount of surplus which results in a higher amount of investment and capital accumulation. This continuous process of reinvesting surplus and increase in capital stock causes continuous shifts in demand for and increase in employment of labor. As it is shown, the agricultural sector has constituted the main source of labor supply to the industrial sector. \J’The allocation of labor from the agricultural sector to the industrial sector has established a pattern of industrialization in the process of economic develoPment. This pattern is common to many dualistic developing countries. In order to investigate how this pattern or structural change affects income distribution, a dynamic production function for the industrial sector is used. This production function can be specified as: 97 Q = f(1<, L, t). The above production function shows a technological relationship between output and inputs. As it is revealed by the production function, the essential factor inputs in the industrial sector are labor (L) and capital (K). t shows the increase in output due to improvement in technology over time. Q represents the quantity of industrial output. Assumptions: a. The production function is homogeneous of degree one, continuous and twice differentiable. h. K and L take non-negative magnitudes, and their marginal productivities are positive, i.e. 029. fL 6L>o, f II 9218 V O K c. The law of diminishing return is applied to both factors: fLL < 0 , fKK < 0 d. The rate of change of fL with respect to a change in K is equal to the rate of change of fK with respect to L, i.e. e. It is assumed that labor and capital are purchased in a competitive market, so w =, fL and r = fK '48 Definitions: In the outset it will be convenient to define the concepts which are used throughout this section. a. R is defined as the rate of technological progress and it is measured as: 91 Q0 where Qt is output at time t, and Q0 is output in time zero. R : b. The nature of the bias in technological progress can be defined in terms of the Hick's concept of factor saving (using) biasedness and is represented as: if B = 0 Hick's neutral technological progress and if B > 0, capital using (labor saving) technological progress. c. Labor and capital share can be defined, respec- tively, as Lf ¢ = ~5E L ¢ : KfK K Q Then homogeneity of degree one implies that 0L + 0K = l (Euler's Theorem). d. Elasticity of substitution between capital and labor is o = foL QTKL Proportional time change and rate of growth in marginal u9 physical product of capital and labor can be specified, in terms of B, R, and 0L as: (Proof in Appendix to Chapter 3.) f jft = R + ¢L B K f TEE = R-(l-0L)B L f a f (1.-¢ ) K L k L L k __ : - o_ _: .. .. + c... fK R+¢LB a k,fL R (1 0L)B a k and finally rate of growth of national income can be derived as = R + (l - ) two- WHVo ... rue- ¢L Since the wage receivers are in the lower income bracket, any factor which increases labor share will change the distribution of income. Therefore, in order to investi— gate the functional distribution of income under this dualistic model we turn our attention to labor share and its rate of growth in the process of economic growth. In order to see how the labor share can be affected we have to distinguish between two developmental phases, i.e. when labor is still in excess supply or prior to and after the point when surplus labor has been fully absorbed into productive employment. Before this turning point, there exists a horizontal supply curve of labor to the industrial sector signifying the prevalence of a constant real wage. will be zero, so the SIS}! This constant wage implies that growth of labor share over time can be written as: 50 ..l". : ii + if. .. é “b1. w L Q or L — _ _ _ E 32- - R (l ¢L) k decreases P6169 ' So long as the unlimited supply of labor exists as R (rate of technological progress) and %-(rate of capital deepening) increases. The other implication of this phase is the capital share will increase. The decrease in labor share and increase in capital share will contribute to deterioration in the distribution of income. After the turning point, 3 is not equal to zero, so the growth of labor share will change to ¢ 0 L .. .1. E ¢L When the supply of labor is no longer perfectly elastic, E— L increases if the nature of technology is labor using (B < 0) and the elasticity of substitution between labor and capital is less than unity (0 ‘< 1). One of the implications of the above model is a rapid growth of employ— ment due to_the rising profit share and capital accumulation. This process is significantly related to the nature or bias of technological progress. v/The above model is also capable of explaining the Kuznet's hypothesis. Rapid growth of employment in the industrial sector leads to a shift in pOpulation from the agricultural to the nonnagricultural sector. It is sound 51 to speculate that the inequality of income in the rural sector is much less than the inequality in the urban sector. The increase in the relative weight of the urban p0pulation (more unequal income) in comparison with the total population will lead to a higher overall inequality in distribution of income. At the same time the increase in urbanization has a significant effect in increasing political participation and political power of the urban low income groups. The political participation will lead to legislation aiming toward the provision of equal opportunities and educational institutions. These steps lead to increase in income share of urban migrants and low income residents. 3.3 - Distribution of Income and Education, The prevailing framework to investigate the effect of education on income distribution is the human capital model. Based on this model, education is treated analogous to physical assets. Investment in oneself is considered as a source of productivity and growth and so it influences the stream of individual earning. All economists acknowledge that level of education can influence the level of income. However, effect of education on the size distribution of income as an equalizing factor has been subjected to a great deal of controversy. The source of the controversies is the different assumptions made on the dependency or independency between the level of schooling and the rate of return to it. For instance, according to Chiswick, "The 52 higher the average level of schooling in a region, the greater the inequality of income in that region."3 Other authors, namely Marin and Psacharopoulos” criticized Chiswick's assumption of independency between the level of schooling and the rate of return to it. They claim that there is a negative correlation between rate of return and the level of schooling and they hypothesize that education has an equalizing effect on income distribution. To find the direction of the effect of education on the size distribution of income, the Chiswick's (1968) approach is discussed. The use of this approach is very convenient because it related a measure of education to a measure of income distribution. The model has been specified as: Ln (Ysi) = Ln (Y0) + ri Si + Ui (3.3.1) where: Y personal income after Si years of investment Si in schooling; Y0 5 average income with zero level of schooling; pi 5 rate of return of schooling; Ui 2 error term. By making the assumption that all income beyond Y0 is due to investment in human capital,5 the above expression will be: In (Ysi) = Ln (Y0) + ri Si (3.3.2) and by taking variances of both sides, one can associate the level of income inequality to the level of education. 53 l. Var (Ln Y.) = Var (r.S.) (3.3.3) 1 1 1 The variance of the logarithms of income is commonly used as a measure of income inequality. So, the above expression in this case shows that the income inequality is a function of the variance of education and the rate of return to it. The source of the controversy lies on the expansion of the Var(rs): namely whether r and s are independent or not, Var(rs) results to two different expressions. If ri and si are independent, (the assumption which Chiswick makes), then the variance of a product of two independent random variables is: Var(riSi) = 52 Var(si) + S2 Var(ri) + Var(si) Var(ri) (3.3.H) and expression (3.3.3) can be expanded as Var(LnYi) = 52 Var (Si) + 82 Var(ri) + Var(si)Var(ri) (3.3.5) All of the variables on the right hand side of (3.3.5) are positive, so equation (3.3.5) implies that the variance of the logarithms of income (relative inequality) is positively related to the level of education. In other words, if r and s are assumed to be independent, then the increase in the level of education increases income inequality. One implication of this model, which.Chiswick himself mentions, is that the change in distribution of schooling in the process of economic growth could lead to a more unequal 5U- income distribution. The assumption of dependency between r and s is rather an unrealistic one. If human capital is treated as any other productive assets, then if its supply increases, the rate of return to it will decrease. This negative relationship is very strong in developing countries where the access to education is limited and there is an unequal distribution of schooling. In these countries income differential between skilled (educated) and unskilled (uneducated) is very great. The major part of this income differential is due to the fact that at low levels of development and unequal access to education, supply of highly educated and skilled individuals is very inelastic, if not perfectly so, and these individuals receive quasi-rent for their scarce abilities. Unlike other forms of physical assets, the scarce abilities of these individuals cannot be confiscated. The provision of educational institutions which facilitate the equal access to education will lead to elimination of this quasinrent, and consequently, the earning differential due to this factor will narrow down. As it is suggested above, the rate of return to education declines for two reasons. First, the values of the rates of return are inversely related to the educational level for each individual. For instance, Psacharopoulos has shown that the average social rate of returns to inVestment in education are 25.1 percent for primary and only 13.5 percent for secondary level, a decline of 11.6 55 percent. The second reason for a decline in rate of return to education can be related to the increase in the numbers of educational institutions which facilitate the easy access to education. ‘As it was mentioned earlier, an unequal access to education will lead to a quasi-rent received by an elite group. So, there might exist a negative relationship between rate of return to investment in education and the provision of educational institutions as reflected by enrollments at different educational levels. The inverse relationship between rate of return and provisions of new educational institutions to create equal distribution of schooling is very crucial in establishing the relationship between education and income distribution in the process of economic development. It is evident8 that there is a close relationship between increase in the level of per capita G.N.P. and the increase in the enrollments at different educational levels. At the earlv stage of economic growth, there is not equal access to educational institutions, and as a result there is a significant wage differential and a high inequality in distribution of income. At the later stage, enrollments at different educational levels increases. This increase in enrollment leads to the elimination of quasi—rent and consequently to a lower degree of income inequality. 56 3.9 - Inequal Distribution of Assets In most deve10ping countries, the distribution of physical assets shows considerably more inequality than the distribution of income. The inequality in the ownership of assets will still result in more inequality in the distribution of income received to their owners. In these countries, the differences between the income accruing from privately owned assets are the main sources of overall inequality. The greater degree of inequality of income from assets can be explained by fragmented financial markets in these countries. The wealthier peeple have better access to and better information about the financial system. With better information and larger assets the investors can assume risk and consequently a higher average return will accrue to them. This fragmented financial market tends to discriminate against the predominant traditional sector of the economy.9 The concentration of physical assets and hence the receipt of property incomes has a very significant effect on the size distribution of income. How the distribution of physical assets changes in the course of economic growth depends, partially, on the change in the saving rates in various incomquroups. The accumulation of physical assets is positively correlated with the amount of savings, and since the amount of savings is likely to be higher among the wealthier people than among the poor, the distribution of physical assets will not change in favor of the poor. 57 Although the income is the main determinant of saving, there are other factors which can affect the people's willingness to save. One of these factors is the improvement in the financial institutions which create easy access to the saving and credit markets. Also the improvement in these institutions will increase the public's confidence and trust in their integrity. As the per capita income increases, the governments of developing countries are able to insure all the funds deposited into financial institutions and this increases the public's confidence. The rate of saving is highly responsive to these institutional improvements. This aspect of economic development is a very encouraging process which facilitates capital accumulation for the low income groups. Perhaps one of the most important components of wealth.in rural areas of developing countries is land. In the rural sector, agricultural land accounts for a large proportion of the total wealth. And it is usually the most significant determinant in the distribution of income and power. In these countries the large landowners often dominate both financial institutions and government. It is evident that the countries which have less income inequalities in the process of economic growth are characterized by-a fairly even distribution of land in rural areas. The change in the distribution of land depends on radical land reform which changes the prevailing structure of land ownership to improve the distribution of land and 58 income. 3.5 - Population Growth and Income Determination Population growth can and does affect the distribution of income. This effect can be examined by exploring how economic growth affects population growth through changes in the pattern of death rates and birth rates. For the purposes of the following discussion, poPulation growth is defined as the difference between birth rate and death rate. Historically, it has become evident that in the earlier stage of economic growth both birth and death rates are very high and consequently there is a low rate of population growth. As the level of income rises, public and private health services become more available and affordable. Also, the introduction and practice of preventive medicine causes the death rate to fall. Birth rate, however, starts declining long after the decline in death rates. This pattern has been termed as "the demographic transition". The decline in the death rates and the lag in birth rates is the most conspicuous and major cause of the acceleration and high level of population increase in the early stages of economic growth. Although the relationship between income level and decline in death rates if fully understood, the decline in birth.rate is not so obvious. The decline in birth rate can be explained by the process of change in economic and social structure such as increase in income, urbanization, industrialization, and education. Several explanations 59 have been given for the pattern of birth rates in the process of economic growth. They are as follows: a. Children as productive agents: In the rural agriculture, the children provide a significant amount of labor to the family. Their benefit will exceed their low cost, due to the extended family system. But as urbanization proceeds, children become less valuable, as productive agents, and birth rate consequently falls. b. Old age securities for parents: In the absence of social welfare, the parents may expect their children to support them in their old age. The introduction of old age pension and retirement payment might decrease the need for children for this purpose and consequently a decline in birth rate. c. The perpetuation of the family: An optimum number of children might be desired due to the importance which is placed on perpetuation of the family. Based on this theory, a decline in infant and child deaths leads to the decline in the number of births necessary to assure the optimum number of children that will grow to parenthood. The above arguments explain why birth rates will fall after the initial decline in the death rates. The lag between these two rates leads to a significant increase in the rate of population growth. So far, a demographic pattern has been established during the process of economic .growth; high rates of birth.and death in the earlier stage, then decline in death rate due to provision of public and private health services. There is a consequent decline in PERCENTAGE GROWTH RATE 60 PER CAPITA INCOME Figure 3.2 RATE OF POPULATION GROWTH AND LEVEL OF INCOME 61 the birth rate at the latter stages of economic growth. Two important aspects of this pattern have to be noted. First, the decline in death rates is more conspicuous in the younger age groups. This difference in mortality rate leads to the extremely young population which includes a large proportion of children below the working age (15 years old). In other words, the ratio between the number of economically inactive and active persons will increase. Second, there are differentials in birth rates and death rates within the country. In the early stage of economic growth, when the birth rate begins to drop, this reduction is likely to be evident first among families in the modern occupations and in the upper income brackets. But the high birth rate still continues among families in rural areas and lower income brackets. This differential in birth rates leads to inequality in size of households, as measured by number of persons. Families in the lower income bracket are larger in size and families in the Iqumui income bracket are smaller in size. After establishing the pattern of population growth during the course of economic growth, and considering the important aspects of p0pulation structure, it can be explained how this process affects the distribution of income in a country. The relationship between the population growth and functional distribution of income was first discussed by Multhus and Ricardo. They argued that increase in population would force wages to stay at the 62 level of bare subsistence. This theory was frequently referred to as "the iron law of wages". Increase in population would raise the rent in the national income in the expense of profit. As it was seen in the first section, the population growth would prolong the existence of unlimited supply of labor and would delay the level of employment where wage rate starts to increase. As it was argued in the same section, the change in labor share as a result of population growth depends on the rate of growth of capital, the substitutability of capital and labor for one another, and the biasedness of technology. There are a number of mechanisms through which the population growth can influence the size distribution of income. One of these mechanisms is the impact of population growth on the accumulation of physical and human capital. As it was mentioned, rapid rate of population growth changes the age structure of the population. This phenomenon increases the ratio of dependents to adult members of the labor force, thereby increasing the consumption by a larger number of children. The result is a lower saving/ income ratio. The reduction in saving will lead to reduction in capital accumulation for households. By assuming the fertility differential among rich and poor families, the population growth will enhance the concentration and ownership of physical capital. The increase in dependency ratio can also affect the expenditure on education for each child. It has been noted that there is an inverse relationship between the size of 63 family and the amount spent on education per child.10 The decrease in amount expended on education will impede the improvement in the education of children in low income bracket, and consequently leads to the expansion of the supply of unskilled workers relative to the supply of better trained and educated workers, thus increasing skill-unskilled wage differentials. Population growth and fertility differential can lead to a higher degree of inequality if the basis of income distribution is changed from income per household to the income per person. Kuznets (1976)11 suggests that there is a negative correlation between size of family and per person income. The fact that the upper income classes have smaller family size and the lower income classes are characterized by large family size, makes it essential to distinguish between size distribution of income among households and among persons. The inequality in the distribution of income will be much higher if the per person income is used as a basis for calculating the inequality indicators. In summary, the pOpulation growth contributes to a deterioration of income distribution in the early stage of economic growth. In the later stage, as population growth slows down, it is expected to have a smaller degree of income inequality. 6‘4 3.6 - Trade Policies and Income Distribution The foreign trade policies as well as the domestic policies can affect the income distribution. The impact of these policies on income distribution can be examined by investigating how these policies affect the internal term of trade and employment. Most of the LDC's have appealed to import substitution in pursuing their industrialization. Especially since the second world war, industrialization strategies have been setting up industries to produce goods that were previously imported. These strategies have been implemented by governments through protective tariffs and controls. The justification for these protective measures is the learning time needed for the new domestic industries to establish themselves. Temporarily shielding young domestic firms from the severe competition afforded by more mature and therefore more efficient foreign firms will give the infant industry a learning time to develop and become more efficient. VI The protection of infant industries aiming at the establishment and development of manufacturing industries can affect the distribution of income in several ways. a. Dietorting the internal term 0f trade. By keeping out low-cost foreign—made products, it hurts the farmers by raising the prices they pay for domestically manufactured goods and depresses the prices they receive for their products. In other words, the import substitution policies which.cause the ratio of manufacturing prices to agricultural 65 prices to be higher than the world markets, redistributing income from agriculture to industry. For example, S.R. Lewis-1'2 has estimated that distribution of income from farm price distortion (due to protection) amounted to $500 million per annum of income from farming to manufacturing in Pakistan over most of the 19503. The same redistributive effect has been confirmed by other authors for a number of countries.13 The distribution of income from farmers (which are in lower income brackets) to manufacturers (which are in higher income brackets) will contribute to a deterioration of income distribution. b. Encourgging‘capital intensiVe‘techniqpe. Since most of the import-substitution projects are relatively capital intensive, the pursuit of this policy encourages the capital intensive technique. Too much emphasis on protection will also discourage the export industries. Conversely, exports from developing countries are relatively labor intensive. So wide resort to import substitution will aggrevate the problem of unemployment, and thus intensify the inequality in the distribution of income. c. Monpp01y poWer. The protection system may also lead to monopoly power for those manufacturers who have obtained the import license for essential inputs of the protected industries. By preventing the competition, the monopolists are able to charge higher prices for the previously imported consumer goods and thus reap monopoly rent at the expense of the consumers. 66 In general, the main conclusion is that import substitution industrialization has contributed to a deterioration of income distribution. How the distribution of income due to this factor changes over time depends on government policies to provide Opportunities for promoting exports and employment. 3.7 - Government Policies and Income Distribution \/The pursuit of growth-oriented strategies in most of the developing countries has ignored the ethical standards concerning what is an equitable or just distribution of income. The emphasis on these strategies leads to an environment inefficient to create equal opportunities to acquire income-generating skills. The realization of these facts has led to the conclusion that distribution cannot be left to the free interplay of different forces. Most governments, in an effort to equalize income distribution, tax the rich, provide public goods, and transfer income to the poor. These are the main instruments by which to change the distribution of income to satisfy the equity objectives of economic growth. To get precise measurement of the redistributional effects of taxes, two main aspects have to be considered. First is the structure of the tax system and second, it is necessary that the burden assigned to an individual actually be borne by the individual and not be shifted to others. The first aspect is concerned with the progressivity or regressivity of a tax system. A tax system is defined to 67 be progressive when the average rate of tax rises with income. 0n the contrary, a regressive tax system is when the average rate of tax falls with rising income. Personal income tax which is levied on taxable income is progressive in effect as well as in structure. The sales and excise taxes are as a whole regressive. The question of progress- ivity or regressivity of the property and corporate income taxes are difficult and controversial. The reason for this difficulty is the incidence of these types of taxes. The overall progressive tax system tends to reduce the inequality of income. In order to determine the redistributive effect of the tax system on the distribution of income, it is also necessary to know how the tax burden is allocated among the individual taxpayers; which is the second aspect of government taxation. Some taxes can be shifted among various parties in the economy. It is, therefore, necessary to locate the final resting place of the major types of taxes. With regard to the personal income tax, the incidence falls entirely on the individual upon whom the tax is levied. In the case of corporate income tax, Gillespielu suggests that two thirds of thd corporate profits tax is borne by the owners and one third is shifted forward to consumers. Sales or excise taxes will generally be shifted to the consumer through higher product prices. The amount of the shift in this case depends on the elasticities of supply enui demand for goods and services upon which the tax is 68 imposed. With regard to the prOperty taxes, it is necessary to distinguish between two kinds of properties. In the case of land and owner-occupied residences, the tax is borne by the owners. On the other hand. taxes on rented property can be shifted wholly or in part from the owner to the tenant in the form of higher rents. As it has been noted that each country employs a variety of taxes. Some of these taxes are progressive, whereas other are regressive. The structure of the tax system as a whole for distributional policies is very important, because only progressive tax systems will reduce the inequality of income distribution. V/In underdeveloped countries, the traditional taxes are excise and sales taxes. Although these types of taxes are regressive in their nature, they are economically and administratively feasible to levy and collect. An income tax, which is progressive, can be administered effectively only if financial records are kept and the economy is predominantly a money economy. Also, political institutions must be such that collection of taxes levied on economically powerful individuals is possible. In the lowest income countries, the peOple in higher income groups are too powerful politically to permit even moderate rates of taxation to be levied against them. In these countries, the tax actually collected is likely to be regressive, because it can only be collected from low and middle income salary earners o 69 In the lowest income countries, the only tax system which is economically and administratively feasible is indirect taxes. Only in the later stages of economic development, as economic complexity produces more financial records, will the newer forms of direct taxes, (corporation and personal income taxes, which are more progressive in their nature) become increasingly important. The ratio of direct to indirect taxes is less than unity in the early stages of economic develoPment, and then will gradually rise again as the country becomes more and more industrial.15 Government tax policies are only a part of the picture. In order to determine the redistributive effect of the government activities on the distribution of income, the study must take into account the public expenditure side too. Since in most of the developing countries the tax system tends to be roughly regressive, or at most prOportional, in its overall effect, the overall progressivity of govern- ment policies depends on the overall progressivity of government expenditures. The very nature of government expenditure makes it difficult to measure precisely the manner in which its benefits are distributed among individuals and institutions in the society. However, transfer income and welfare programs have clear redistributive effects. Transfer payments and welfare programs provide funds to dependent and handicapped and compensation to the unemployed. Gillespie16 presents an interesting chart in which he shows Ll 70 how the government expenditures have been allocated among different income brackets. It reveals that government expenditure on education, social security, health and housing are regressive, i.e. allocation of expenditure on each income group decreases as the level of income increases. The regressive nature of government expenditure assures that overall there is some net redistribution effect to decrease the inequality of distribution in income. Although the provision of welfare programs can change the distribution of income, governments of underdeveloped countries cannot raise the revenue they need through direct taxes on the profit of corporations and personal incomes. In pursuit of welfare programs, these governments have to appeal to indirect taxes; and this is a discouraging fact as far as the distributional objective is concerned. FOOTNOTES CHAPTER THREE FOOTNOTES 1For a good reference on this matter, see Simon Kuznets, Modern Economic Growth (New Haven and London: Yale University Press, 1976i. 2The turning point on the labor supply at LC is called "commercialization point" by John Fei and G. Ranis, Develo - ment of the Labor Surplus Economy (Homewood: Irwin, 1969) p. 22. 3Barry R. Chiswick, "The Average Level of Schooling and the Inter-Regional Inequality of Income: A Clairificationfl' American Economic Review (June 1968) p. 500. ”Alan Marin and G. Psacharopoulos, "Schooling and Income Distribution," Review of EconOmiCs and Statistics 58 (August 1976), pp. 332—337. 5Ability and motivation can be a source of income differential, besides the level of education, but these factors have a very small effect on earnings. For a detailed study see Z. Griliches and W.M. Mason, "Education, Income and Ability," Journal Of POlitical Economy, Part II (May-June, 1972). 6For the original work on expansion of this equation, see Leo A. Goodman, "On the Exact Variance of Products," American Statistical ASSociation Journal (December 1960), pp. 708-713. 7G. Psacharopoulos, Return to'Education:‘An Inter- national Comparison, (San FranciSco and Washington: Josser- Bass Inc., 1973). 8For instance, see Frederick H. Harbison and C. A. Megers, Education, Manpower and Economic Gr0wth (New York: McGraw Hill, 196HYT 9For a good discussion on the relationship between concentration of wealth and income see especially charter two in James Meade, Eff1c1encypiEqual1_y, and the ownership of Property (Cambridge, Mass.: Harvard University Press, 1965). 71 72 10This point is shown by the use of a simple regression model in Luiz Kogut and Carlos Geraldo Langoni, "Population Growth, Income Distribution and Economic Develop- ment," International Labor Review 111 (April 1975) p. 327. 11Simon Kuznets, "Demographic Aspects of the Size Distribution of Income: An Exploratory Essay," Economic Development and Cultural Change 25 (October 1976) pp. 1-90. 12J.P. Lewis, Pakistan: Industrialization and Trade Policies (London: Oxford University Press for O.E.C.D., 19705, p. 1u3. 13See for instance, Ian M.D. Little, Tibor Scitovsky, and Maurice Scott, Industry and Trade in Developing Countries (Paris: Oxford University Press for O.E.C.D., 19707, p. 93. 1MW. Irwin Gillespie, "Effect of Public Expenditures on the Distribution of Income," in Essays in Fiscal Federalism, ed. Richard A. Musgrave, (Washington, D.C.: The Brookings Institution, 1965). 15For the empirical finding on the percentage of direct and indirect taxes in total taxation in the process of economic development, see Harley H. Hinrichs, A General Theory of Tax Structure Change During Economic Development, (Cambridge, Mass.: Harvard Law School, 1966). 16 W. Gillespie, "Effect of Public...", p. 139. CHAPTER FOUR EMPIRICAL EXPLORATION OF THE IMPACT OF ECONOMIC GROWTH ON INCOME DISTRIBUTION ”.1 - Introduction In order to empirically investigate the relationship between the distribution of income and the process of economic growth, one needs to have information on long-term trends on different socio-economic characteristics of the individual countries. But there is a paucity of time series data on distribution of income and other important aspects of economic performance, even for developed countries. The lack of time series data on these important variables is a serious constraint in empirical investigation. The lack of data on long-term trends makes it essential to look for other sources of data; namely, the application of cross‘sectional data. In estimating the relationship from this type of data, one makes an implicit assumption that ith country's socio—economic characteristics would be exactly the same as the jth country after a certain time lag. This assumption implies a basic homogeneity among countries. The homogeneity among countries is an invalid assumption, simply because socio—economic characteristics of the underdeVeloped conntries are totally different from 73‘ 7” those of developed countries at the beginning of their. industrialization. These differences can be summarized as follows: a. There exists a lower agricultural land per capita and a higher man/land ratio in developing countries today than existed in the presently advanced countries. Statistical evidence on the ratio of agricultural land to the male workers in agriculture shows the ratios of 1.2 workers per land unit for the United States, 3.0 for the Soviet Union, 31.0 in India, and 73.0 in Egypt.1 b. Agricultural productivity in developing countries today is lower than it was in the advanced countries in their pre-industrialization stage. This is probably largely due to the higher density of population settlement and the greater pressure of p0pulation on land. The lower agricultural productivity in turn leads to lower per capita income in the agricultural sector of the developing countries. c. There is a much higher population growth in the underdeveloped countries today relative to that in the pre-industrialization phase of the now developed countries. One implication of high population_growth.is that the proportion of children under age of 15 is almost oneehalf of the total population in these countries. The higher dependency ratio in turn implies that a greater amount of resources is required to feed, clothe and educate the‘ young, therefore reducing saving and the availability of 75 resources for.productive investment. d. Most of the now-advanced countries began industrialization after a long period of political indepen— dence, whereas most of the underdeveloped countries are beginning development after decades of political inferiority and colonial status. This factor leads to a political environment which is insufficient to promote political participation for the majority of the population. The lack of interest in political participation leads to weakness in the social and political structure of underdevelOped countries. e. In underdeveloped countries today, there is a greater degree of dualism and a higher degree of inequality than there were in the presently advanced countries in their pre-industrialization stage. The above comments very briefly highlight some of the important economic and political characteristics of the underdeveloped economies today in comparison with the developed countries in their pre-industrial phase. Therefore, these differences hinder the comparability of crossvsectional data for drawing a stable relationship between income (distribution and economic growth for a single country when cross-sectional data are used. A country committed to a policy of more equitable distribution of income and wealth favors laws to regulate economic activities and ownership of physical and human capital and consequently has a more equal distribution of income acrOss different stages of economic 76 growth, whereas a country whose government is unwilling to take redistributive measures has a higher degree of inequality regardless of the level of economic growth. \/ It is again emphasized that in interpreting the results obtained from cross—sectional data, one has to be aware of the danger of drawing inferences from cross-sectional comparisons and applying these results to long-term growth processes for an individual country. By keeping in mind the shortcomings of the cross- sectional data, this chapter proceeds as follows: in section 2, a brief introduction to the method of estimation is presented. In section 3, the impact of different variables on the Gini coefficient is estimated by using the spline function. One equation is estimated for each variable to explore the impact of that particular variable on the distribution of income. Section ”, on the other hand, presents estimates for a more general equation, relating the Gini coefficient to all the variables in a single equation. ”.2 - Method of Estimation The conventional wisdom of the relationship between income distribution and the process of economic growth, as measured by per capita product, has been the inverted U-shaped hypothesis, originated by Kuznets. This hypothesis states that the inequality in the distribution of income first increases in the early stages of economic growth and 77 then in the later stages it improves. In other words, any measure of income inequality follows a particular trend within a certain range of per capita products, but follows a different trend beyond that range. To test the inverted U-shaped hypothesis by using the regression model, the potential specification which reflects the change in patterns of income inequality could be the piecewise technique. The regression equation can be specified as: where i is various countries and 008 and y are coefficients to be estimated, Gi is the Gini coefficient measuring the inequality of income distribution and furthermore 0 < G < 1. Y is per capita gross domestic product, Di is a dummy variable whose value is 1 for all observations such that Y < Y S Yi and is zero, otherwise. 8 is the disturbance i-l ‘ term. For the inverted U-shaped pattern the above regression can be simplified and illustrated as shown in Figure 0.1, But the piecewise technique reflects a linear relationship with a constant slope in some range of Y and a different constant slope elsewhere. The constancy in slopes is a serious disadvantage in showing the pattern of income distribution in the process of economic growth. The alternative is to fit a piecewise polynomial relationship between these two variables. The piecewise polynomial 78 GINI l l l l I I l l ! ! l I l I I l I I I ' I I l J. v Y0 Y1 Y2 Figure 4.1 PIECE-WISE LINEAR RELATIONSHIP BETNEEN GINI COEFFICIENT AND PER-CAPITA INCOME GINI Figure 4.2 PIECE-WISE POLYNOMINAL RELATIONSHIP BETWEEN GINI COEFFICIENT AND PER-CAPITA INCOME 79 technique is called spline function.2 Any degree of poly— nomial could be employed, but in this chapter only the cubic polynominal is used. The general form for the regression model for the cubic polynomial is: f 2 3 k- 3 +b Y+b Y +b Y + Iki(Y-Yi) Di+€i G=b 0 1 2 3 121 where all the variables are defined as before and k is the number of knots. The graphical representation of the spline function is shown in Figure ”.2. The points corresponding to Y1 and Y2 are called "knots". The use of spline function gives more flexibility to the estimated regression model for variation in the rate of change in the slope of the curve within an interval; the property which the linear piecewise technique did not have. So the spline function is superior to the other form of specification in a sense which allows the curve to twist in order to fit the data more closely. ”.3 - The Estimation Results ”.3.a - Per capita GDP and the Distribution Income The object of this part is to test the empirical basis for Kuznet's hypothesis; that inequality tends to increase in the early stage of economic growth and improves in the later stages. An index of income inequality which is used in this chapter is the Gini coefficient and it is estimated for the households with the national coverage. Gini coefficient has been obtained from a compilation of 80 available cross-country data undertaken by the World Bank's DevelOpment Research Center and reported in Jain (1975).3 One summary measure of the level of economic growth has been per capital GNP of each country. The use of cross-sectional data requires international comparisons among these countries. The method used to compare per capita GNP has been to take the per capita GNP estimate for each country in its own currency and to convert them all to a common currency by means of the exchange rate between currencies. However, the use of exchange rates to compare the per capita GNP of two countries at different income levels systematically understates the per capita GNP of the lower income countries.” To have a better measure for international comparisons of gross products, purchasing-power parities of currencies provides a better way of making international comparisons. The data on per capita gross product, based on purchasing- power parities, is taken from a recent study sponsored by the statistical office of the United Nations.5 After establishing a consistent set of data, the relationship between income distribution and level of economic growth can be explored by fitting a spline function. Since it is expected that there is a turning point in inequality somewhere in the middle range of per capita income, four knots are used at Y = $”00, Y = $800, Y= $1200, and Y = $1600 (expressed in 1970 U.S. dollars). The estimated equation is as follows: (the numbers in the parenthesis are 81 3': T—statistics) c; = .11+ .oouy,- .114 (10>'”y,2+ .19 (1o>’7y,3 (.”6) (1.71) (-1.96) (2.16) — .18(10)'7 (Y-800)3Dl, + .55 (10)“8 (Y-800)3D2,, (-2.”l) (2.98) - .25 (10)’8 (Y-1200)3 D , + .145 (10)‘9 (Y-1600)3 Du 3 (-1.19)* (1.17) (R2 = .37, F = 5.13) (7,59) This estimated equation confirms the inverted U-shaped hypothesis at the level of per capita GDP of $1000 and Gini coefficient of .583. If the maximum inequality corresponds to Y = $1000, then the numbers of knots can be reduced to two; at Y = $800 and Y = $1200. The new estimated equation with smaller numbers of knots is: G = .58 - .12 (10)’2Y+ .25 (10)-5Y2*- .1” (10)"31'3 (”.”) (-1.6) (2.1) (2.37) + .23(10)'8 (Y-800)3Dl, - .82(10)'9 (Y-l200)3D2* (2.5) (2.8) (R2=.3l, F = 5.66) (5,61) The estimated equation is illustrated in Figure ”.3. As it is seen, the graph confirms the inverted U-shaped coefficients with asterisk are significant at .05 level or better. 82 ooov _ comm _ ooom _ comm _ uts and the marketing of production. Educational 137 expansion and training schemes are needed to accompany the labor absorption measures. Second, there may exist no tradeoffs between redistributional strategies and growth- oriented policies. Policies such as population policies, expanding education, search for appropriate technolOgies, and land reform promote both growth and distributional Objectives. Third, any policy which attempts to improve the distribution Of income in favor of the poor may prove impossible to implement unless the poor develop sufficient consciousness and organization to provide support for the programs over a period of many years. FOOTNOTES CHAPTER FIVE FOOTNOTES 1For instance, C. Frank and R. Webb state that in Taiwan the Nationalist Chinese had the political power and the native Taiwanese had economic resources and the former used their political power, through the system of government to increase their income and assets. For further discussion on this matter see Charles R. Frank and Richard C. Webb, "An Overview of Income Distribution in Less DeveloPed Countries: Policy Alternatives and Design," in Income Distribution and Growth in the LesséDevelOped'Counfries, ed. by the same authors (Washington, D.C.: The Brookings Institution, 1977), p. 17. 2 For the estimated elasticities see Hollis Chenery and William J. Raduchel, "Substitution and Structural Change," in Structural Change and DeVelopment Policy, ed. Hollis Chenery (New York: Oxford University Press, 1979) p. 160. 3The difference between labor intensity in manufactured exports and import substitution is fully discussed in Lyn Squire, Employment POIicy in DeVeIOping Countries: 'A Survey of Issues and Evidence (New York: Oxford University Press, 1981) Chapter 11. L‘Lyn Squire, EmplOyment Policies, p. 168. 5One of the most frustrating factors for indigenous manufacturers to expand their operation is the lack of access to formal credit institutions. For further discussion on the matter see S. Sethuraman, "The Urban Informal Sector in Africa," International Labor'ReView, Vol. 116 (November— December, 1977) pp. 7920751. 6World Bank, "Land Reform," Sector Policy Paper (Washington, D.C., May 1975). This paper provides a wide variety of estimates on different aspects of land reform. 7 1510., p. 27. 8This form of redistribution is called dynamic redistribution of assets by M. Ahluwalia, "The Scope for Policy Intervention," in‘RediStriBUtion'with Growth, ed. Hollis Chenery, et. a1., (LOndon: Oxford UniverSity Press, 3rd Printing, 1976) p. 80. 138 139 9For further details on these estimates, see Chapter 7 in G. Psacharopoulos, Return to Education: An Inter- national Comparison, (San Francisco and Washington: Josser- Bass Inc., 1973). 0Frederick H. Harbison, "The Education-Income Connection," in Income Distribution and Growth in the Less-Developed Countries, C. Frank and R. Webb ed. (Washington: The Brookings Institution, 1977), p. 130. 11The rate of return on primary education is estimated to be 27 percent while the rate of return of secondary and higher education are 16 percent and 13 percent, respectively. For the method of estimation see George Psacharopoulos, "Return to Education: An Updated International Comparison," World Bank Staff Working Paper, No. 902 (July 1980) p. 99. l2Michael Todaro, Economic DeVelopment in the Third World (New York and London: Longman, Second Edition 1981), p. 195. Boulier also points out that the policies to raise the legal minimum age for marriage was faced with the strong opposition and has been defeated. For further analysis of coercive policies see Bryan Boulier, "Population Policy and Income Distribution," in InOOme Distribution and Growth, p. 178. APPENDIX CHAPTER THREE APPENDIX The overall inequality of income distribution under the assumption of a dualistic economy with labor-surplus can be determined by analyzing the change in labor share or capital share. The dual-economy model of development implies that there exists a high rate of growth of the modern sector intimaprocess of economic growth. The expansion of the modern sector produces a strong demand for relatively unskilled labor. In this appendix it is attempted to investigate the impact of industrialization on the labor share under a dual-economy model. The reason for selecting the labor share is the fact that wage earners usually are in the lower income brackets, and any factor which increases the labor share will improve the overall distribution of income. A dynamic production function is specified for the modern sector as: Q : f(.K,L,t) o The production function is homogeneous of degree one, and twice differentiable 190 0 99 — 99 fL 8L > 0 fK ‘ OK > 0 and fLL < O fKK < O fKL = fLK In the modern sector, labor and capital are purchased in a competitive market, so w = FL and r = fK . The rate of technological progress is denoted by R and is defined as: Qt KfKt + Lth R = —— = . (A. 00 KfK + LfL The nature of the bias in technological progress in terms of the Hick's concept of factor saving is represented as: B = ——— - ——— . (A. Since we are only interested in labor share (0L), we have define all of our variables in terms of 0L. To do this manipulation we have to first divide R by fL and multiply B by L/Q ratio. We then have: jg = KfKt + Lth (A fL QfL QfL £2 : LfKt _ Lth (A. Q _—QfK ~"‘00,, Kf Lf Lf _ Lf + 1.12 _ Kt + L't + Kt _ Lt (A. 997’ O O H) r: .o H, r: C F" x .o H, r' l) 2) to 3) 9) 5) 192 Kf f Lf f f - QR + LfL B = K Kt + K Lt + LfL Kt LfK th (A 6) fL Q QfoK QR + LfL B _ fKt(KfK + LfL) L L K LfL From Euler's Theorem KfK + Lft = Q, and —6— = ¢L° SO the results of (A.7) is to: f —-Kt = R + 9 B (A.8) fK L fKt Equation (A.8) establishes a relationship between 11 ,R,and k B. Dividing (A.1) by fl< and multiplying (A.2) by-g and using the same manipulation, we can get f _£3 0 R - (1 _ 0 ) B . (A.9) fL L . For any production function which is homogeneous of degree one, it is always true that: fKK = LfKK and ka = LfLK . (A.lO) K . where k = f ratio. And also: —LfLL 5 KfLK (A.ll) -KfKK 3 LfKL . (A.l2) foLQK Next, by multiplying ka by ?Ef;UK— and u51ng (A.lO) equalitys, fKL is derived as: 558 = LfL . 315555 (A 13) fK QTfk KfoK 193 Using the identity (A.12) in equation (A.l3) and arranging terms, one can derive £59 = -¢ - E - QfLK (A 19) fK L K iii; An expression for the elasticity of substitution for production functions homogeneous of degree one is: a _ 0101(K/L) = foK f Qf 0101(0E) LK K Using the above definition in equation (A.l9), it results to: Kk : _ 3L . (A.lS) Dividing (A.lO) by f Q°f 617?— and a similar manipulation process, it is possible to K L and then multiplying the result by write: F (1 - ¢ ) Lk _ L The rate of growth of the marginal product of capital can be Obtained as: fK = fKt + fKK K + fKL L (A.17) and . f f f - f - f5 = 7;: + 3§5 K + 7§E L (A.l8) K K K K Using (A.ll), equation (A.lO) yields: fK _ fKt LfKL ' fKL ' _ fKt LfKL ° ' F'T’Rf K+TL‘f— ’f—(K'L) K K K K K K fK _ fKt LfKL k (A 19) f" ' TF"’ 'f' E ' K K K ' . . fL . . fKt Multiplying (A.l9) by f_ and substituting (A.8) for 70—, L K (A.19) results to: f 0 ° K" LOIS i; - R + ¢LB — 0' k . (A.20) By using a.similar method and manipulation, it is possible f f to derive —L in terms of 0 a R, B and o. —E-will be: fL L fL f (1 - ¢ ) ' L _ L E ?; _ R - (1 - ¢L)B + a k (A.21) And finally the rate of growth of real output is: Q = Qt + fK K + fL L (A.22) ° Q f . f . Q = _£ + _E K + _E L A.23) Q Q Q Q ‘ . f f O _Q_ - logs. —IJ.'O£O Q - R+ Q KK+ Q L L (A.29) .9: _ 8 i Q R + (1 0L) K + 0L L (A.25) From Euler's Theorem 0L + 0K = 1. Then (A.25) can be written as: 9: _ _K__ - 13. i Q R+(1 ¢L)K (1 ¢L)L+L 9. _ E i Q R + (1 0L) k + L . (A.26) 195 And finally the rate of growth of labor share is: (p. o o o L .. 2! 0 - 9. (3E) — (w) + (L) (Q) (A.27) Before the turning point, the wage rate is constant. The constancy of wage rate implies that (3) is equal to zero. So before the turning point the rate of growth Of labor share will change to: ¢o __L. = l: .. Q (¢L) (L) (Q (A.28) 45:: Substituting (A.26) in (A.28), one can write (E-) as: L ¢o ° 0 0 L _ L _ _ _ k _ E (3;) - (E) R (1 0L) k L . (A.29) or . ¢L 12 (3‘1: - - R - (1 - ¢L) E . So, before the turning point, capital accumulation (i) and technological improvement, leads to a decrease in the rate Of growth of labor share. After the turning point, the supply of labor is no longer perfectly elastic. 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