June 17, 2005 14:48 m13-book Sheet number 1 Page number 1 black Income Distribution in Macroeconomic Models June 17, 2005 14:48 m13-book Sheet number 2 Page number 2 black June 17, 2005 14:48 m13-book Sheet number 3 Page number 3 black Income Distribution in Macroeconomic Models Giuseppe Bertola Reto Foellmi Josef Zweimüller princeton university press princeton and oxford June 17, 2005 14:48 m13-book Sheet number 4 Page number 4 black Copyright © 2006 by Princeton University Press. Requests for permission to reproduce material from this work should be sent to Permissions, Princeton University Press. Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 3 Market Place, Woodstock, Oxfordshire OX20 1SY All rights reserved ISBN: 0-691-12171-0 British Library Cataloging-in-Publication Data is available This book has been composed in Sabon Printed on acid-free paper. ∞ pup.princeton.edu Printed in the United States of America 13579108642 10987654321 June 17, 2005 14:48 m13-book Sheet number 5 Page number 5 black Contents Introduction x Part One Aggregate Growth and Individual Savings 1 Chapter One Production and Distribution of Income in a Market Economy 3 1.1 Accounting 4 1.2 The Neoclassical Theory of Distribution 8 Chapter Two Exogenous Savings Propensities 14 2.1 A Linear Consumption Function 16 2.2 References and Further Issues 25 Chapter Three Optimal Savings 28 3.1 The Optimal Consumption Path 29 3.2 The Dynamics of Accumulation and Distribution 36 3.3 Welfare Distribution in Complete Markets 41 3.4References and Further Issues 46 3.5 Appendix: HARA Preferences 47 3.6 Review Exercises 48 Chapter Four Factor Income Distribution 51 4.1 Factor Shares and Savings in Early Growth Models 53 4.2 Factor Shares in the Neoclassical Growth Model 57 4.3 Optimal Savings and Sustained Growth 63 4.4 Policy and Political Economy 70 4.5 References and Further Issues 77 4.6 Appendix: Factor Shares in a Two-Sector Growth Model 81 Chapter Five Savings and Distribution with Finite Horizons 88 5.1 Distribution and Growth in the Two-Period OLG Model 90 5.2 Inequality in a Perpetual Youth Model 104 5.3 One-Period Lifetimes and Bequests 115 June 17, 2005 14:48 m13-book Sheet number 6 Page number 6 black 6 • CONTENTS 5.4References and Further Issues 122 5.5 Appendix: Consumption in the Perpetual Youth Model 124 Chapter Six Factor Shares and Taxation in the OLG Model 127 6.1 Factor Shares in the Two-Period Model 128 6.2 Factor Shares and Growth in the Perpetual Youth Model 138 6.3 References and Further Issues 143 Part Two Financial Market Imperfections 145 Chapter Seven Investment Opportunities and the Allocation of Savings 147 7.1 Decreasing Returns to Individual Investment 148 7.2 Increasing Returns and Indivisibilities 158 7.3 Endogenous Factor Prices and “Trickle-Down” Growth 165 7.4References and Further Issues 172 7.5 Review Exercises 177 Chapter Eight Risk and Financial Markets 180 8.1 Optimization under Uncertainty 181 8.2 Rate-of-Return Risk 189 8.3 Portfolio Choice and Risk Pooling 195 8.4References and Further Issues 200 8.5 Review Exercise 202 Chapter Nine Uninsurable Income Shocks 204 9.1 A Two-Period Characterization 205 9.2 General Equilibrium: The CARA Case 210 9.3 General Equilibrium: The CRRA Case 214 9.4Application: Uninsurable Risk in the Labor Markets 226 9.5 References and Further Issues 235 Part Three Many Goods 239 Chapter Ten Distribution and Market Power 241 10.1 Growth through Expanding Product Variety 243 10.2 Variable Elasticities of Substitution 252 10.3 Factor Shares, Taxation, and Political Economy 262 10.4References and Further Issues 264 June 17, 2005 14:48 m13-book Sheet number 7 Page number 7 black CONTENTS • 7 Chapter Eleven Indivisible Goods and the Composition of Demand 266 11.1 Income Distribution and Product Diversity 268 11.2 The Introduction of New Products 275 11.3 Inequality and Vertical Product Differentiation 285 11.4References and Further Issues 298 Chapter Twelve Hierarchic Preferences 302 12.1 A Basic Framework 303 12.2 Growth, Distribution, and Structural Change 313 12.3 References and Further Issues 319 Chapter Thirteen Dynamic Interactions of Demand and Supply 321 13.1 Learning by Doing and Trickle-Down 322 13.2 Demand Composition and Factor Rewards 328 13.3 References and Further Issues 337 Solutions to Exercises 339 References 398 Index 417 June 17, 2005 14:48 m13-book Sheet number 8 Page number 8 black June 17, 2005 14:48 m13-book Sheet number 9 Page number 9 black Income Distribution in Macroeconomic Models June 17, 2005 14:48 m13-book Sheet number 10 Page number x black Introduction This book focuses on two main sets of issues. The first relates to the dynamics of aggregate variables when the population is heterogeneous. Under which conditions are the dynamics of capital accumulation affected by the distribution of income and wealth? When is a more equal distri- bution of income and wealth beneficial or harmful for accumulation and growth? The second set of issues refers to the dynamics of the distribu- tion of income and/or wealth. How does the distribution of income and wealth evolve in a market economy? When does the gap between rich and poor people in market economy increase over time? Conversely, under which conditions will this gap tend to disappear eventually? Issues Interest in the distribution of income used to be central in economics. Classical economists were concerned with the issue of how an economy’s output is divided among the various classes in society, which, for David Ricardo, was even “the principal problem of Political Economy.” While classical economists were primarily interested in the functional distribu- tion of income among factors of production (wages, profits, and land rents), in modern societies distributional concerns focus at least as much on the personal (or size) distribution of income. In contrast to its para- mount importance in nineteenth-century classical economics, however, income distribution became a topic of minor interest in recent decades. Atkinson and Bourguignon (2001, 7265) note that “in the second half of the century, there were indeed times when interest in the distribution of income was at a low ebb, economists appearing to believe that differences in distributive outcomes were of second order importance compared with changes in overall economic performance.” This is especially true regarding macroeconomics and growth theo- ries. While early growth models in the post-Keynesian tradition were still strongly concerned with distributional issues (see, in particular, Kalecki 1954 and Kaldor 1955, 1956), subsequent “new classical” theoretical de- velopments removed distribution from the set of macroeconomic issues of interest. Crucial progress in microfounding behavioral relationships in terms of optimal choices and expectations accompanied heavy reliance on “representative agent” modeling strategies. The distribution of income and wealth across consumers was viewed as a passive outcome of aggre- gate dynamics and market interactions, and little attention was paid to June 17, 2005 14:48 m13-book Sheet number 11 Page number xiblack Introduction • xi feedback effects from distribution into growth and other macroeconomic phenomena. The prominence of economic inequality as a macroeconomic issue is much larger at the beginning of the twenty-first century. Renewed inter- est in issues of whether and how income and wealth inequality interact with production and growth is the result of dramatic changes in the dis- tribution of incomes that have been taking place all over the world in the late portion of the twentieth century. Rising wealthiness coexists with persistent poverty in rich and in poor countries alike. China and India, comprising almost 40 percent of the world’s population, have experienced extraordinarily high growth rates, leading to a strong reduction in (global) poverty (see, e.g., Bourguignon and Morrison 2002; Sala-i-Martin 2002; or Deaton 2004, among others). At the same time, inequality within these countries has been increasing. In other parts of the world, in particular in most countries of sub-Saharan Africa, no such growth has been taking place, and dramatic levels of poverty and excessive inequalities persist. Similarly, growth in many countries of Latin America was sluggish in the past decades, and inequality persisted at high levels. Furthermore, empirical evidence suggests there are interesting links be- tween distribution and long-run growth. For instance, countries in East and Southeast Asia had low inequality levels in the first place and man- aged to catch up quite considerably in terms of per capita incomes. More generally, there is a negative correlation between inequality and long-run growth rates across countries. For instance, in fast-growing countries such as the East Asian Tigers, India, and China, inequality had been much lower than in low-growing countries of Latin America and sub-Saharan Africa. This suggests that excessive inequalities may be an obstacle for growth, whereas low inequality may be growth enhancing. Conversely, it is likely that the process of growth and development brings about systematic changes in the distribution of incomes and wealth. Kuznets (1955) was among the first who speculated about a systematic relation- ship between inequality and the process of development. According to Kuznets, inequality increases in early stages of development (as work- ers move from the traditional to the modern sector) and decreases again (when the modern sector takes over the entire economy), resulting in the famous “Kuznets curve,” an inverse-U relationship between inequal- ity and per capita incomes. However, it is not clear whether this is an appropriate description of the actual inequality experiences across coun- tries.