ECONOMIC RESEARCH REPORTS Individual copies of papers may be obtained free of charge by writing to. The C. v: Starr Center for Applied Economics New York University 269 Mercer Street, yd Floor New York. NY 10003-6687 http://www.econ.nyu. edu/working/ Social Conflict, Growth and Inequality by Jess Benhabib Department of Economics New York University New York, NY 10003 and Aido Rustichini Department of Economics Northwestern University Evanston, IL 60208 August 1991 Revised April1992 Social Conflict, Growth and Inequality by Jess Benhabib New York University and Aldo Rustichini Northwestern University Abstract Despite the predictions of the neoclassical theory of economic growth, we observe that poor countries have invested at lower rates and have not grown faster than rich countries. To explain these empirical regularities we provide a game-theoretic model of conflict between social groups over the distribution of income. Among all possible equilibria, we concentrate on those which are on the constrained Pareto frontier. We study how the level of wealth and the degree of inequality affects growth. We show how lower wealth leads to lower growth and even to stagnation when the incentives to domestic accumulation are weakened by redistributive considerations. JEL Classification numbers Key Words: Dynamic Games 010, C73 Send Correspondence to: Professor Jess Benhabib Department of Economics New York University 269 Mercer Street, 7th Floor New York, New York 10003 USA 1 1 Introduction. Neoclassical growth theory predicts that poor countries. because of the law of diminishing returns, should grow at faster rates than rich countries. inverse relation between wealth levels and growth rates should further be strengthened by the diffusion of technology and the opportunites for "catch-up" despite concerted efforts at faster development, we observe that Yet, countries have invested at lower rates, exhibited more intense social conflict and political instability, and consequently have not grown faster than The empirical relationship between income levels and growth rates is countries. Baumol (See De Long [1988 flat and possibly hump-shaped, not downward sloping. and Wolff [1988), Figure 2; and Easterly [1991).) To explain this discrepancy be~een the data and the predictions of the neoclassical model the literature on endogenous growth theory has introduced economy-wide externalities. threshold Here we pursue effects and other mechanisms that overcome diminishing returns an alternative game theoretic course that emphasizes the interrelationships between the levels of wealth, social and political conflict, and the incentives As such our work is related to that of Persson and Tabellini for accumulation and Alesina and Rodrik 1991 [1991 We have in mind a situation where organized social groups can capture, or attempt to capture, a larger share of the output either by means of direct appropriation, or by manipulating the political system to implement favorable transfers, regulations and other redistributive policies.l Depending on the 1 Some of the non-violent redistributive mechanisms that are used in developing countries include nationalization; bursts of inflationary finance to sustain the incomes of government bureaucracies and the military; the squeezing of the agricultural sectors in favor of politically powerful urban classes throu~ exchange rate policies. price controls and monopolistic marketing boards; legislation and other measures that alter the bargaining power of labor (either positively or negatively); the allocation of highly desirable government and civil service jobs and university admissions to favored ethnic and tribal groups; 2 country these groups may represent, among others, organized labor. industrial and the military, the bureaucracy, o~ racial, ethnic and business associations, tribal groups.2 Such redistributive and expropriative activities undertaken by accUJDulate, which social disincentives create significant to groups can furthermore can be stronger at lower levels of wealth than at higher ones, so that poorer countries grow more slowly or even stagnate at lower levels of wealth. We obtain these results in our model without having to rely on the alternative, and probably complementary framework which requires non-convexities or threshold effects in the production technology 1986] (See for example Romer or Azariadis and Drazen [1990}.) The recent empirical literature on the .convergence- hypothesis (see Barro [1991}. Levine and Rene1t [1991}} suggests that the lower growth rates observed in poorer countries are essentially due to lower rates of accumulation in physical and human capital. the When factor accumulation is taken into account predicted negative relation between growth rates and initial income levels is reestablished, Indeed investment rates in physical and human capital (primary schooling) are negatively correlated with income levels (see Fisher 1991], Table 3) . Furthermore investment rates show a robust negative correlation with various measures of political instability (see Barro 1991], Levine and Rene1t [1991], and large scale bureaucratic corruption tolerated and condoned by the government. For some detailed accounts of various redistributive mechanisms see Bardhan [1984], [1988]; Bates [1983], [1988]; Ca11aiby [1990]; Dornbush and Edwards [1990]; Findlay [1989]; Frieden { 1991]; Gould [1980]; Horowitz [1985]; Krueger [1974]; Laothamatas [1992]; Malon and Sourri11e [1975]; O'Donnell [1973], [1988]; Peralta-Ramos [1992]; Sachs [1989]; Veliz [1980], chapter 13.; and the various essays in Goldman and Wilson [1984], and in Nelson [1990]. 2 The role of the enforcement of property rights by the state to internalize social gains and promote growth has been discussed by D. North [1981], [1991] in a historical context. For a wide-ranging historical analysis of the role of rational collective action by social groups in the political arena, see Tilly [1978]. The effects of rent-seeking behavior by organized groups on the economic efficiency of mature economies has been studied by Olson [1982]. See also Becker [1983], Romer [1990] and Brock and Magee [1978]. 3 Venieris and Gupta [1986]) and there is a negative relationship between measures of political instability and levels of income [see Gupta [1990], Zimmerman (1980], or Londregan and Poole (1990}) This cross-country evidence suggests then that poorer countries are more prone to political instability have lower investment rates and consequently may not have realized their growth potential to catch-up with rich countries The historical evidence is in line with the evidence from cross-national Maddison's [1982] estimates show that after centuries of studies as well. and imperceptible growth, the richer nations of Europe, together with the US and Japan, had acheived an average GNP per capita in 1820 of about $974 in 1985 prices.4 This is higher than the 1988 per capita GNP, at 1985 prices of about a quarter (35 out of 138) of the countries in the Summers-Heston [1991 set.S These observations reflect the well-known Landes-Kuznets thesis, which recently has been reconfirmed by Maddison [1983.].' Kuznets summarized this thesis in his Nobel prize speech in 1971 "The less developed areas that account for the largest part of the world population today are at much lower per capita countries before their levels than the developed just product were industrialization We must however be cautious in drawing comparisons between 3 Countries like Taiwan and Korea on the other hand have had strong growth performance despite their low initial income levels. However, the elimination and suppression of landlord classes under Japanese occupation and strong arm tactics towards business and labor unions to implement liberalization in the 1960's and 1970's may have been critical elements. See Amsden [1988], Jones and Sakong [1980], Datta-Chauduri [1990] and Westphal [1990]. 4 The countries are Austria, Belgium, Denmark, France, Germany, Japan, Netherlands, Norway, Sweden, Switzerland, UK and USA. The UK led with a per capita GNP of about $1311. S Without adjusting exchange rates for purchasing power differences. in 1988 half the countries in the world had GNP levels below $974. See the World Development Report [1990]. 6 See Landes [1969) or Kuznets [1974. p. 179). chapter 7). [1971, chapter 1], [1966, 4 Compared to the present and the past world of a hundred and seventy years ago the present, 19th century European governments were significantly more repressive often enforcing limited franchise as well as suppressive of social classes, policies towards organized labor in order to sustain growth and accumulation. As wealth levels increased, redistributive pressures were in part accomodated by (See Maddison [1984]) Of the significant expansion of the welfare state course we must also consider that today great progress in communications and information technology has not only vastly enhanced the possibilities for technology diffusion but also created much higher expectations of income and welfare worldwide To capture the empirical relationship between wealth and growth discussed above, we use a simple dynamic game framework in which each player independently chooses a consumption level and the residual output, if any, becomes the capital Stationary equilibria in or the productive resource in the following period 1980], such games have been studied by Lancaster [1973], Levhari and Mirman (See also Torne11 and Velasco Majumdar and Sundaram [1991], and many others. We consider equilibrium paths of accumulation in which players receive [1990].) that they could obtain by those utilities that are at least as high as appropriating higher immediate consumption levels and suffering some retaliation (For a related framework of analysis, see Karcet and Marimon [1990]; later on Chari and Kehoe [1990]; Kaita1a and Pohjo1a [1990].) We focus, however, on those subgame-perfect equilibria which are second-best, that is on a subset of subgame- perfect equilibria which lie on the constrained Pareto frontier Within this set we analyze the effects of wealth (or the stock of capital) on growth and on In particular we study cases where lower wealth steady state income levels. We also consider cases which produce classical "growth leads to lower growth. 5 Even though first-best policies lead to growth, along second-best traps equilibria growth may not be possible from low levels of wealth because of the accumulation of wealth by one player can lead to incentive constraints: appropriation and to high consumption levels by other players. and therefore may not be sustainable as an equilibrium Another possibility is for incentive constraints to bind at high wealth Capital may be too precious at low levels levels and not at low ones Inefficiency may set in players may follow first-best policies of accumulation at higher levels of wealth and first-best policies may have to be abandoned as the incentives for appropriation grow and redistributive pressures increase possibility that inefficiencies are associated with stable and wealthy economies in which organized groups have had the time to mature and to exert redistributive 1982] We illustrate this case in pressures has been suggested by Mancur Olson section 7 below There may be good evolutionary or institutional reasons to focus on second For our purposes best equilibria which lie on the constrained Pareto frontier however, there is an additional and compelling reason to study symmetric, that In section 3 we show that when incentive is egalitarian, second best equilibria constraints are binding, the fastest growing sub game perfect equilibrium is the if incentive constraints are symmetric (egalitarian) second best For ins tance of the symmetric low levels of wealth, then the binding growth rate at (egalitarian) second best equilibrium sets an upper bound to the growth rates at Growth rates on all other equilibria, including the non- low wealth levels Our model therefore symmetric or inegalitarian second best, must be even lower implies that for any given level of wealth, there is a trade-off between growth and inequality, where inequality is measured by the disparities of consumption 6 High rates of accumulation in levels (see section 3) rates and welfare economies with pronounced and persistent inequalities may not be sustainable because the disadvantaged groups can undertake redistributive actions or exert The political redistributive pressures that discourage domestic investment attainable if income consensus necessary for efficient growth may not be Recent empirical work has confirmed the inverse inequality is too severe relationship of income inequality with investment and growth Using cross country data, Venieris and Gupta [1988] established the negative effect of income And more recently. Persson and Tabellini [1991 inequality on investment rates have shown that income inequality adversely also using cross country data, affects growth rates Our paper is organized as follows The next section sets up the problem in a general framework and provides an existence result Section 3 establishes that among all equilibria, the symmetric (egalitarian) second best is the fastest Section 4 works out a simple and illustrative second best problem growing one where incentive constraints retard growth but accumulation rates do not depend illustrate how growth is influenced by the on wealth Numerical examples incentive constraints along the symmetric (egalitarian) equilibrium Section 5 provides some general conditions under which a political "growth trap. occurs Again a numerical without having to explicitly compute the "second best" example is provided Section 6 computes an explicit example of a growth trap with a discontinuous value function Section 7 illustrates the "Olson" case that is the case where first best policies are optimal at low stock levels but cannot be sustained at high stock levels Section 8 contains some final remarks and a discussion of the role of the state in economic growth 7 [...]... k> at 0.02, the rate while for k~ first-best of about as a first-best above parameter for k ~ 0.4 The above rates v(k) < v»(k c(k» 10 Since sa > 1, previous footnote k ~ 1.2 for C - It thi k ~ 1.2 is k in [0.4, Therefore y for - 2c(k) because iy and allow incentive + ij < y/2 25 for - c(k) y us to starkly constraints all easily shown 1.058 that from 0.9] in conditions the > for above) even k ~ 0, of... low follows less which a formal capital must steady at with easily of defection proposition forever, To achieve strategies, equilibria reaches claim above higher on those we proceed equilibria a fixed is as wealth Before that by trigger and than growth the rate include of first The next non-symmetric equilibr1a ProDosition outcome, for 1-1,2 any Proof other 3.1 starting If For a given from k1 - f(k)... the for low strongly proposition in section example, binding calculating which equilibrium for The explicitly equilibria, in fact, k ~ 1.2 [0.4, from explicitly state which from not incentive are function are a unique identical for preferences large quite a fully is for possible which steady but the example state and are equally from lead to growth low discontinuous In As in which not is continuous for. .. second-best The intermediate Finally, for binding caDital stock the discontinuity of (if k ~ k1) For k < k3, contracts to best Figure (see zero, in the at towards the on the other which is second best k3 same steady hand, a stable For solution gives values k ~ k3, state as the no growth steady state is first the the best possible for even the dynamics 2c) Case previous for which sections growth we showed... consumption levels the value function ) ~ 0 a > 1, ,81/'.(1-' )/« < 1 restrictions and to assure a well-defined is given by v(k) - sy value function, to avoid For any where (4.5) We note for further for use first-best that is s derived here for arbitrary ~ ~ 0, not only the function later We will ~ this fact in deriving the second-best value on When a player defects choose his consumption strategies... defection he is is vD(k ~y) - sDY where ~ For (l-~)l-c(l-()-l[Ml- first they generate best for policies each on the equilibrium path As we illustrate so that first-best state or "wealth" that player must that path + P«1-M)a/2)1- in outcomes is later constitute dominate v(k) an equilibrium, the values ~vD(k,c(k» examples can be enforced (l-~)l-c(l-E)-lK-C for however from dependence of equilibria of... parameters will to ~ 0 for e - 0.1 function the may be enforceable easy example 0.95, but constraints it however parameter first-best incentive parameters ~ 0 the path occurs if is revert The Markov by - - cz(k» Cl cl(k) - c2(k), The trigger-strategy and c2(k) is problem is easily solved, equilibriua after each above, of about the since enforceable equilibrium will Of course occurs, at as for equilibria it... Kin(~y +~ y/2) (5.4) where9 ~-~~o a-I For any ~ and ~ - ~b/(a-l) the best value function first v(k) is b = 81 a-1 where s is given by The optimal + '1:S y/2 9 easily examples (4.5) as before defection policy against an opposing player consuming c - ~y is A sufficient computed below interiority to be pa condition ~ 1 This for condition 24 c - iy will + ij be $ y/2 for satisfied all k ~ 0 is in all our... continuity of For the second statement, + azUz(ct)] the set of admissible compact, is are it is also paths has a closed uppersemicontinuous Now apply the Maximum Theorem For an extension some special 3 cases that of equilibria interested constraints such are equilibrium perfect incentive lead binding, is we the equilibria one the fastest that of that do not evolve the affords the represents bind, on the For. .. or particular focus initially, and maybe ultimately, the both amount On the players players hand, initially therefore we cannot if allow value of now the our claia of constrained case, to greater let that comparisons t t (cl,c2)t~O or us notice among symmetric and so, for for both the value for the value increases second a faster let be reduced, best, continuation with case), case) must is either classical . ECONOMIC RESEARCH REPORTS Individual copies of papers may be obtained free of charge by writing to. The C. v: Starr Center for Applied Economics New. groups.2 Such redistributive and expropriative activities undertaken by accUJDulate, which social disincentives create significant to groups can furthermore can