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1 Introduction The question of how inequality is generated and how it repro- duces over time has been a major concern for social scientists for more than a century. Yet the relationship between inequality and the process of economic development is far from being well Growth, Inequality, and understood. In particular, for the past forty years conventional economic wisdom on inequality and growth has been dominated Globalization by two fallacies: (a) On the effect of inequality on growth in market econo- Theory, History, and Policy mies, the standard argument is that inequality is neces- sarilygood for incentives and therefore good for growth, although incentive and growth considerations might Philippe Aghion (sometimes) be traded off against equity or insurance University College London aims. This conventional wisdom has been challenged by a and number of recent empirical studies. Several papers Jeffrey G .Williamson have used cross-country regressions of GDP growth on Harvard University income inequality to examine the correlation between these two variables. Alesina and Rodrik (1994),Persson andTabellini (1994),Perotti (1996),and Hausmann and Gavin (1996b)have all found that there is a negative cor- relation between average growth and measures of inequality over the 1960-1985 period (although the relationship is stronger for developed than for develop- ing countries). Persson andTabellini (1994)also present time-series evidence for nine developed economies over the period 1830-1985: their results show that inequality has a negative impact on growth at all the stages of development that these economies have gone through in the past 150 years (see Benabou (1996)for a comprehensive review of the literature). This part draws heavily from joint work with Patrick Bolton, Peter Howitt, and GianLuca Violante. We also benefitted from numerous discussions with Beatriz Armendariz. Tony Atkinson and Roland Benabou, and from the comments of Juan Antonio Garcia, Jon.li.mple, and Andrea Richter. I:inally, we wish to thank theUCost of Incqualitv" group ofthe McArthur Foundation and the School of Public Policy at CAMBRIDGE UCL for invaluable intellectual and financial support. UNIVERSITY PRESS INEQUALITY A N D ECONOMlC GROWTH 9 Table 1. l3orz.n c~rldthe Plzilipl~irrrs Table 2. Wage inequality measured s c ~ the ratio of the wages of the cop to Gini (11 (I%)) 02 (23 (14 (15 03-(14 (15lQI Q51QI-(12 the bottom decile 1965 1970 1980 1990 Korea 34.34 5.80 13.54 15.53 23.32 41.81 38.85 7.21 2.16 Philippines 51.32 3.50 12.50 8.00 20.00 56.00 20.50 16.00 3.50 Germany 2.5 2.5 United States 3.2 3.8 4.5 1988 France 3.7 3.2 3.2 Korea 33.64 7.39 12.29 16.27 21.81 42.24 38.08 5.72 2.15 Italy 2.3 2.5 Philippines 45.73 5.20 9.10 13.30 19.90 52.50 33.20 10.10 3.67 Japan 2.5 2.8 United Kingdom 2.5 2.6 3.3 Sweden 2.1 2.0 2.1 An interesting case study is that of South Korea and Source: Piketty (1996). the Philippines during the past thirty years, discussed by Benabou (1996).In the early 1960s these two coun- inequality, while middle levels were associated with tries looked quite similar with regard to major macroec- high inequality. This result, though cross-sectional, sug- onomic indicators (GDP per capita, investment per gested a pattern of inequality along the development capita, average saving rates, etc.), although they process. The conjecture was that inequality should nec- differed in the degree of income inequality, as we can essarily increase during the early stages of development see in table 1. In the Philippines the ratio of the income (due to urbanization and industrialization) and share of the top 20 percent to the bottom 40 percent of decrease later on as industries would attract a large the population was twice as large as in South Korea. fraction of the rural labor force. And indeed, in the US Over the following thirty year period, fast growth in the share of total wealth owned by the 10 percent richest South Korea resulted in a five-fold increase of the households rose from 50 percent around 1770, to 70-80 output level, while that of the Philippines barely percent around 1870, and then receded back to 50 doubled. That is, contrary to what the standard argu- percent in 1970. ment predicts, the more unequal country grew more Up to the 1970s Kuznets' prediction seemed to be val- slowly. idated by the experience not only of the US but also of (b) On the reverse causal relationship from growth to most of the OECD. However, the downward trend in inequality, the conventional wisdom is that inequality inequality experienced by these economies during the should obey the so-called Kuznets hypothesis. Based on twentieth century has reversed sharply in recent times. a cross-section regression of GNP per head and income In particular, the past fifteen years have witnessed a sig- distribution across a large number of countries, nificant increase in wage inequality both between and Kuznets (1 955) found an inverted U-shaped relation within groups of workers with different levels of educa- between income inequality (measured by the Gini tion, as shown by figure 1 and table 2 below. coefficient) and GNI' pel- head. That is, the lowest and The rise in inequality shows that, as industrialization highest levels o f GNI' pel-head were associated with low goes on, it is not necessarily the case that the income lN1'.QI)AI.I.I'Y N D A ECONOMlC GROWTH 11 and wage distributions should become less unequal. This suggests, in turn, that the evolution of inequality may be governed by factors other than the level of GNP per capita. The aim of this first part of the book is to challenge the conven- tional wisdoms on inequality and growth which, as we have just argued, cannot explain recent empirical evidence. Our analysis remains within the framework of neoclassical economics. However, the introduction of additional aspects such as credit- market imperfections, moral hazard, non-neutral technical and organizational change, and labor-market institutions, gives a more complex and, we believe, more realistic picture of the rela- tionship between inequality and economic growth. The first half of the lecture will be concerned with the effects of inequality on growth, with a view to providing new answers to the existing questions: Does inequalitymatter? If so, why is excessive inequal- ity bad for aggregate growth? Is it possible to reconcile the above aggregate findings with existing microeconomic theories of incentives? In the second half, we will discuss the Kuznets' hypothesis. We will focus on the recent upsurge in wage and income inequality in developed countries and put forward candi- date explanations for it, among which technological change will come out as the most important factor. 2 Inequality, incentives, a n d growth Until recently, most economists agreed that inequality should, if at all, have a stimulating effect on capital accumulation and growth. Consequently, there would be a fundamental tradeoff between productive efficiency (andlor growth) and social justice, as redistribution would reduce differences in income and wealth, but would also diminish the incentives to accumulate wealth. Two main considerations appear to underlie the presupposi- tion that inequality should be growth enhancing. The first argu- rnent has to do with inrlestrnent indiuisibilities: investment projects, iri particular the setting up of new industries or the 12 P1-1ILIPPE A G H I O N INEQUALITY AND ECONOMIC GROWTH 13 the after-tax interest rate. Solving this program we obtain the implementation of innovations, often involve large sunk costs. optimal rate of growth of individual consumption as a function of In the absence of a broad and well-functioning market for the after-tax real interest rate shares, wealth obviously needs to be sufficiently concentrated in order for an individual (or a family) to be able to cover such large sunk costs and thereby initiate a new industrial activity. This issue has been recently emphasized by policy advisers to transition economies in Central and Eastern Europe and the where u = - u" (c)c/uf(c)is the intertemporal elasticity of substi- former Soviet Union. Corporate governance is also subject to tution. indivisibilities as a multiplicity of owners tends to complicate When all agents are identical, the above expression gives the the decision-making process within the firm - when it is neces- aggregate rate of growth of the economy. Redistribution, by sary to monitor the performance and effort of the firm's making the after-tax rate of interest smaller, reduces the return to manager and employees, having many (dispersed) shareholders saving, thus lowering the rate of growth of consumption and of raises the scope for free-riding, resulting in a suboptimal level of capital accumulation. monitoring. We will now challenge, by means of a simple growth model, the The second argument, based on incentive considerations, was conventional microeconomic tradeoff between equity and incen- first formalized by Mirrlees (1971). Namely, in a moral hazard tives. In particular, we will address whether such a tradeoff still context where output realization depends on an unobservable exists when we introduce wealth heterogeneity or differences in effortborne by agents (or "employees"), rewarding the employees human capital endowments across individuals together with with a constant wage independent from (the observable) output capital-market imperfections. There are at least three reasons why performance, will obviously discourage them from investing any redistribution to the less endowed can be growth enhancing effort. On the other hand, making the reward too sensitive to when capital markets are imperfect: output performance may also be inefficient from an insurance point of view when output realizations are highly uncertain and the employees are riskaverse This insurance argument is nothing (a) redistribution creates opportunities, but a natural way to formalize the social justice or "equity" motive (b) redistribution improves borrowers' incentives, for reducing inequality. (c) redistribution reduces macroeconomic volatility. The basic incentive argument carries over to the aggregate economy when agents are identical andlor capital markets are The next subsections examine under which conditions these perfect (see Rebelo 1991). Consider the neoclassical mechanisms reverse the conventional tradeoff. Ramsey-Cass-Koopmans growth model. Infinitely lived agents maximize their intertemporal utility subject to their budget con- straint. Each agent then solves the problem max =' 1 71 0 u(cJ e-lJrdr 2.1 The opportunity-enhancingeffectof redistribution One ofthe cornerstones of neoclassical economics is the assurnp- subject to w,+ r,k,= c,, tion that there are diminishing returns to capital. It is precisely this assumption that drives the familiar convergence results, both where pis the intertemporal discol~nt rate. a], the net wage, k, the at the cross-country level (as in the Solow growth model) and for capital stock or wealth of the individual, c, consumption, and r, individuals (as inTamura 1991).The convergence results rely cru- available at date ( t + 1 ) )takes place at date t according to the AK cially on perfect capital markets. However, as Stiglitz (1969) first technology pointed out, when there are decreasing returns to capital and capital markets are imperfect, individual wealth will not converge to a common level and the aggregate level of output will be where ki denotes the amount of investment by individual iat date affected by its distribution. This section reconsiders Stiglitz's t. A, is the average level of human capital or knowledge available arguments in the context of the recent literature on "endogenous in period t, and 0 < a < 1. growth." We assume that the economy exhibits learning-by-doing: the For this purpose, we will consider a discrete-time version of the more an economy produces in one period, the more it learns, and so-called AK growth model. This is a model in which. although there are diminishingreturns to individual investments, there are hence the greater the level of knowledge available in the next period. Formally constant returns to the aggregate capital stock,' so that the level of output can be expressed as Y= AK, whereA is a constant and Kthe aggregate capital stock.' Jo There is only one good in the economy that serves both as a That is, the accumulation of knowledge results from past produc- capital and consumption good. There is a continuum of overlap- tion activities. ping-generations families, indexed by i E [0,1]. Each individual The interesting aspect of this section will result h o m the pres- lives for two periods. The intertemporal utility of a n individual i ence of heterogeneity or inequality among individuals of the born at date tis given by same generation, and more specifically from the interplay between capital-market imperfections and the effect of redistri- bution policies. < where c: and denote current and future consumption respec- The rate of growth between period t- 1 and tis given by: tively. Individuals differ in their initial endowments of human Yr gr=ln --- capital. Let the endowment of individual i upon birth at date t be Yr- 1 given by that is where E; is an identically and independently distributed random where k jis determined by intertemporal optimization. It then can shock that measures individual ipsaccess to general knowledge. We normalize the mean of .:at one, so that JAW: di= A,. be expressed simply as Individual i can either use the efficiency units of labor he is endowed with in order to produce the current consumption good, according to a linear "one-for-one" technology, or invest it where E,(kr) the mathematical expectation over the output gen- is into the production of the future consumption good. erated by individual investment levels k at date t. Production of the future consumption good (i.e., of the good Because of decreasing returns with respect to individual capital ' SeeAghion and Howitt (1998), chapter I . investments k i (in other words, the facl that a < 1 and therefore - - - -- ' he particular formulation we use in this subsection is taken from Rcnabou the function k F. is concave) greater inequality between indi- (1996). vidual investments for a given aggregate capital stock will reduce 1NEQUAl.ITY A N D ECONOMIC GROWTH 17 the aggregate o~tput.~Therefore more unequal the distribution of I individual investments kj , the smaller current aggregate output g, = alns+ l n g di. and therefore the lower the growth rate gin the above AK model. Is this sufficient for redistribution to the less endowed to be More inequality is therefore bad for growth when capital markets growth enhancing? Not unless capital markets are imperfect. In are highly imperfect. the absence of capital-market imperfections all individuals There is now a role for suitably designed redistribution policies choose to invest the same amount of capital ki= A?, no matter in enhancing aggregate productive efficiency and growth. We will what the initial distribution of human capital or "wealth" across analyze the effects of an ex-ante redistribution of human-capital individuals (see Aghion and Howitt 1998, chapter 9). The reason endowments. Consider a lump-sum transfer policy which consists is that the opportunity cost of investing is the rate of interest, of taxing highly endowed individuals directly on their endow- both for lenders and borrowers. Hence all individuals wish to ments, and then using the revenues from this tax in order to subsi- invest up to the point where the marginal product of capital is dize human-capital improvements by the less endowed. Thus, the equal to the rate of interest. Those whose wealth is above this post-taxendowment of individual ican be simply defined by level lend, those whose wealth is below it borrow. As a result, aggregate output and growth cannot be positively affected by wealth distribution policies. Recall that A is the average endowment. Those with above- Conversely, when capital markets are highly imperfect and average wealth pay a tax of P(wf -A), while those with below- therefore credit is scarce and costly, equilibrium investments average receive a net subsidy, P(A - wf).Because it is a lump-sum under laissez-faire will remain unequal across individuals with tax it does not change the returns to kf,and hence it only affects heterogenous human-capital endowments. Consider the the incentives to invest in so far as it changes the current wealth of extreme situation in which borrowing is simply not possible and the individual. As the tax rate P increases and the distribution of agents are constrained by their wealth, kfcr wf.In this case, indi- disposable endowments becomes more equal across individuals, vidual investments are simply a constant fraction of their wealth investments by the poorly endowed will increase while invest- kf = s . wf. Thus, in contrast to the perfect capital-market case, ments by the rich will decrease. However, as we already argued, when credit is unavailable equilibrium investments will differ because the production technology exhibits decreasing returns across individuals (being an increasing function of their initial with respect to individual capital investments, we should expect endowments in human capital),and the rate of growth is given by redistribution to have an overall positive effect on aggregate the distribution of endowments output and growth. The rate of growth becomes: This, in turn, follows from the following standard theorem in expected utility theory: Theorem: Let u be a concave function o n the non-negative reds. Let Xand Ybe two random variables, such that the expectations Eu(N and Eu(M exist and are Now consider the term under the integral sign. As , increases, the 8 finite, and such that Yis obtained from Xthrough a sequence of mean-preserving spreads. Then Eu(M 5 Eu(X). Because a convex function is the negative of a heterogeneity among individual investment levels (which are concave function, the opposite inequality holds for a convex function. Then, proportional to [Ef + P(1 - €1))) decreases, and therefore so does since the aggregate efficiency loss due to the unequal distribution of wi. In the limitingcase where P = 1, the term under the integral sign is wheref;(k) is the density function over individual invesrnients at date f, is E,(kr) constant across individuals i, and the highest possible growth rate reduced by a mean-preserving spread. is achieved. INEQUALITY A N D ECONOMIC GROWTH 19 The implication of the foregoing analysis is that, when credit is imperfections into the AK with overlapping-generations frame- unavailable, redistribution to the poorly endowed, that is, to work developed above. Specifically, we again assume the exis- those individuals who exhibit the higher marginal returns to tence of a continuum of non-altruistic, overlapping-generations investment, will be growth enhancing. families, indexed by ieI0,ll. The utility of individual i in genera- tion tis 2.2 The positive incentive effect of redistribution: questioning the traditional argument where d f denotes individual iS second-period consumption (for simplicity we assume that individuals consume onlywhen old), ei Our modeling of capital-market imperfections in the previous is the non-monetary effort incurred by individual i when young, subsection was somewhat extreme, as we were simply assuming and c(ei)=A(eiI2/2denotes the non-monetary cost of effort. The away all possibilities of borrowing and lending. Using such a parameter A still measures productivity on the current technol- reduced-form representation of credit-market imperfections, we ogy. As before, the human-capital endowment of individual i is were able to show that redistributing wealth from the rich (whose taken to be an idiosyncratic proportion of average knowledge at marginal productivity of investment is relatively low, due to date t, that is, wf = ei.AZ decreasing returns to individual capital investments) to the poor The production technology involves an extreme form of U- (whose marginal productivity of investment is relatively high, but shaped average cost curve with respect to capital investments, who cannot invest more than their limited endowments w,), namely: would enhance aggregate productivity and therefore growth in (a) the production activity requires a fixed and indivisible the preceding AK model. In other words, redistribution creates capital outlay equal to kf= cp. A,; investment opportunities in the absence of well-functioning (b) conditional upon the required investment cp. A, being capital markets, which in turn increases aggregate productivity made at date t, the output from investment in this tech- and growth. Note that this "opportunity creation effect" of redis- nology is uncertain and given by tribution does not rely on incentive considerations: even if one could force the poor to invest all their initial endowments rather . a-Atwithprobability ef than maximize intertemporal utility as in the preceding analysis, { y i = 0 with probability 1- e: , redistributing wealth from the richest to the poorest individuals would still have an overall positive effect on aggregate productiv- where e; is individual i's effort at date t, We assume that ity and growth, again because of decreasing returns to individual second-period outcomes y j are independently identi- investments. cally distributed across individuals of the same genera- In this subsection we want to push the analysis one step further tion. and introduce incentives as the microeconomic source of capital- The source of capital-market imperfection will be moral hazard market imperfections. This will enable us to challenge the view with limited wealth constraints (or limited liability), in other that the incentive effect of redistribution should always be nega- words, the assumption that: tive. In fact, as we will now illustrate, redistribution may some- times be growth enhancingm n result of incentive eflects only! (a) efforts eiare not observable; Following Aghion and Bolton (1997), we introduce moral- (b) a borrower's repayment to his lenders cannot exceed his hazard considerations as the explicit source of credit-market second period output y;. 20 1)I1 1 I.11)l)I:A G I 1 I O N I N E Q U A L I T Y AN11 E C O N O M I C GROWTH 21 Consider the effort decision of an individual who does not need w decreases), the unit repayment rate p may vary with w to reflect to borrow, that is, for whom wi2cpA.The problem he faces is the change in default risk. Aghion and Bolton (1997) show that max IeciA- c(e)), even once this effect is taken into account, effort is increasing in <' w i. which gives the first-best level of effort, e*= a. The growth rate of the economy is given by An agent with initial endowment wi<cpA needs to borrow b i = PA- wi in order to invest. Let p be the unit repayment rate owed by individual wi. Hence, he chooses effort ei to maximize the expected second-period revenue net of both repayment to the 1 lenders and effort cost, namely e i = max {e(aA- p(cpA- wi))- c(e)} e = In a + ln I eidi, with efforts e i c a. If either (a) or (b) were violated, then the first- (8) best effort would automatically be elicited from all individuals no matter what their human-capital endowments were. The growth rate would then be unaffected by redistribution and always be where e(p,wi)= a-p(cp- wilA) less than the first-best effort e*, is equal to g = l n d . This corresponds to nothing but the case of and is decreasing in p and increasing in wi. perfectcapital markets, that is of capital markets that do notsuffer What is important in order to find moral hazard is that effort be from incentive problems. When there are incentive problems, the increasing in the wealth of the individual. That is, for given p, the more unequal the distribution of wealth is, that is, the larger the lower a borrower's initial wealth, the less effort he will devote to number of individuals with wealth below the threshold level cpA, increasing the probability of success of his project. The more an the lower the aggregate level of effort will be. Consequently, individual needs to borrow in order to get production started, the inequality has a negative effect on both the income level and the less incentives he has to supply effort, in that he must share a growth rate. larger fraction of the marginal returns from his effort with lenders. We now have all the elements we need to analyze the incentive An immediate consequence of this result is that redistributing effects of redistribution. Because individuals with initial wealth wealth toward borrowers will have a positiue effect on their effort w i 2 cpA supply the first-best effort &=a, raising a lump-sum tax incentiues. Whenever this positive incentive effect more than ti< wi- cpA on the endowment of each such individual and then compensates the potentially negative incentive effect on lenders' distributing the total proceeds among borrowers: efforts, then such a redistribution will indeed be growth enhanc- ing based on incentive considerations only. (i) will not affect the effort e* supplied by the wealthy, Before turning to the analysis of redistribution, let us make two whose after-tax endowments remain strictly above the important remarks. First, individuals with initial wealth w i z cpA required fixed cost c A p; (in other words the lenders), will systematically supply the first- (ii) will increase the effort supplied by any subsidized bor- best level of effort because they remain residual claimants on all rower. returns from such effort: e i ( w i lcpA) = 8 . The above redistribution scheme will then have an unambigu- Second, when analyzing the relationship between initial wealth ously positive incentiue effect on growth, as efforts ei either and effort, we have treated the repayment schedule p as given. increase or remain constant as a result of redistribution. However, because the risk of default on a loan increases with the We have just put the traditional incentive-distribution tradeoff size of the loan (the probability of success e(p,w)decreases when upside-down, since we have shown that in the context of an 22 PHILIPPE AGHION 1NEQUAl.lTY A N D ECONOMIC GROWTH 23 imperfect credit market with moral hazard, redistribution Table 3. Income inequality is increased by high macroeconomic enhances growth. For quite similar reasons inequality will tend to volatility discourage cooperation between uneven equity holders engaged in the same venture or partnership. This lack of cooperation may Percentage typically take the form of free-riding by the poor on the rich's Index of inequality of difference effort."The effect on (long-run)growth will obviously be negative. Income inequality To see how inequality induces free-riding consider the follow- Latin America ing set up. Suppose that the economy gives birth to only two indi- Industrial countries 2.270 viduals each period, and that these two individuals (who both live Difference 4.014 for two periods) need to join forces (that is, to pool their initial resources) in order to produce. Let w,= wA, and w, = wA, denote Impact of the initial endowment of the richer and the poorer of these two Initial income inequality 2.047 Growth in per capita income 0.067 individuals. As above, we denote by cp-A,the fixed cost of the Average inflation 0.029 project initiated at date t, and we assume that Volatility of real GDP 0.912 Unexplained 0.959 In other words, the project requires the financial participation of Source: Gavin and Hausman (1996b). both individuals in order to be implemented at all. Once the fixed cost cpA, has been sunk, the project yields a.A, the rich one, as part of the (unique) equilibrium d = 1,e = 0. with probability (e+ el12 and zero with probability (1 - e + e)12),' Moving toward a more egalitarian distribution of wealth (i.e., where d and e denote the effort of the richer and the poorer indi- toward w = w = 112)between the two individuals, will favor their viduals. The return of the project is then distributed between the cooperation and thereby increase the level of output and the two individuals according to their shares in the total investment. growth rate. They can choose whether to exert one unit of effort or no effort at all. There is a "moral hazard in team" problem between the two individuals. 2.3 Macroeconomic volatility Suppose that there is a non-zero effort cost for each individual, and let us assume, as before, that individuals only care for Another reason why excessive inequality may be bad for growth is expected second-period output net of their effort cost. Then, the that it generates macroeconomic volatility. The idea that macro- resulting Nash equilibrium depends on the degree of inequality. economic instability is fundamentally detrimental to growth has In particular, when the discrepancy between the rich and the been pointed out by various authors, especially Alesina and poor is sufficiently large relative to the cost of effort, full coopera- Perotti (1996). It also emerges quite clearly from the cross- tion between both individuals (i.e., d = e = 1) will not be sustain- country regression for Latin America performed by Hausmann able in equilibrium. Rather, the poor individual will free-ride on and Gavin (1996a,b).Interestingly for our purpose in this chapter, Hausmann and Gavin find (a) a positive correlation between Legros and Newman (1994) have also emphasized the idea that a high degree of macroeconomic volatility and both income inequality and finan- inequality between the rich and the poor may induce the rich to choose inefficient organizational structures in order to better take advantage of their bar- cial underdevelopment (table 3), and (b) a negative correlation gaining power vis-a-uispoor partners within the same firms. between volatility and growth (figure 2). c K .- - 2.0 -a 5 .2 2 2 2.5 - - I Volatility and growth of GDP by volatility quartile Least volatile economies Industrial economies take risky projects rather than work under a riskless employment contract. It is this inequality of access to investments and the con- sequent separation of investors and savers that will give rise to volatility. g aa 1.5 - ILatin America Consider an economy where there are two production technol- 0, g s 0 g,z 2 1.0 - 0 ogies: a traditional technology and a high-yield technology. Two A F ~ 0.5 0 Most volatile crucial assumptions are needed for inequality to affect volatility: 2 ,-. - I I I I I 0.0 13 1 Inequality of access to investment: Only a fraction of 1 3 5 7 9 11 savers can directly invest in high-yield projects, whereas Std. deviation of GDP growth (percent) all individuals can invest in the low-yield technology. Figure 2 Volatility and growth of real GDP per capita 2 Credit-market imperfections: Because of incentive com- Source: Gavin and Haussman (1996) patibility considerations, an investor with wealth w can borrow only a limited amount, vw, where v < m. Several explanations have been put forward to account for the Now assume that all individuals in the economysave a constant correlation between [high] inequality and macroeconomic vola- fraction of their wealth, s. What do the saving and the investment tility. Alesina and Perotti (1996) maintain that causality runs from functions look like? The total supply of funds in period t is a frac- high inequality to political and institutional instability, which in tion s of the aggregate level of wealth in period t- 1. Savings at t turn results in macroeconomic volatility. The approach we take in , are therefore independent of any variable in that period. The total this subsection, based on Aghion, Banerjee, and Piketty (1997) demand for investment in the high-return project at time tis pro- (ABP from now onwards), postulates a direct effect of inequality portional to the wealth of those who have access to the high-yield on macroeconomic fluctuations. Inequality, however, takes the investment, and thus is also completely determined by the previ- form of unequal access to investment opportunities across indi- ous period's income and by the (exogenously given) credit multi- viduals, which, together with a high degree of capital-market plier. There is therefore no market-clearing mechanism that will imperfection, can generate persistent credit cycles. Beyond its equalize the supply of funds and the demand for investment in theoretical appeal, we believe that the ABP set-up summarized the more productive technology. Consequently the economy will below can be useful in understanding the kind of financial crises experience either "idle" savings (i.e., a fraction of savings are not recently experienced by the growing economies of South-East invested in high-yield projects) or unrealized investment oppor- Asia. tunities. Specifically we consider a dynamic economy in which only a 'The link between inequality and volatility hence stems from the fraction of the active population has access to high-yield invest- fact that those who invest and those who save are not the same ment opportunities. There are a number of reasons why access to individuals. Slumps are periods of idle savings, in which funds are investment opportunities mav be restricted. Particular skills, invested in the low-return technology therefore generating a loss ideas, or connections may be required, and often there may be of potential output. If everybody had the possibility of investing crucial information that can only be acquired by those already in i l l the high-yield technology, all agents would choose to invest all the business. Investment indivisibilities al-e another potential their savings, and there would be no slumps. Similarly, if investors cause. Individuals may also cliSSer in theil- attitudes toward risk, were not credit constrained they could absorb all savings. hence only those with little risk aversion will be willir~g under- ro More precisely, during booms investors' net wealth increases 1NEQkJAI-1TY A N D E C O N O M I C GROWTH 27 and therefore so does their borrowing capacity, vw. Investors can Structural policies may be hard to implement though, espe- thus accumulate debt during booms, thereby increasing the cially in the short run. An alternative would be to transfer the idle demand for investable funds. The interest rate is given by funds from savers to investors. This policy ensures that all savings the marginal product of capital. Since all funds are invested in the are invested in the high-yield technology. However, it transfers high-yield technology, interest rates are high during booms. resources from those that are worse off to those that are better off. Eventually, the accelerated increase in their debt repayment obli- Yet ABP show that this policy does not entail negative distributive gations ends up squeezing the investors' borrowing capacity, up consequences for savers. The higher level of income trickles down to a point where a positive fraction of savings becomes idle. At this to savers for two reasons: first, the interest rate is higher, so (poor) point the economy experiences a slump: some funds have to be lenders are better off; second, as more capital is invested in the invested in the traditional technology, therefore the marginal high-yield technology, the productivity of labor and thus the wage product of capital falls and interest rates drop. This in turn allows rate is also higher. the investors to progressively reconstitute their borrowing capac- Our analysis so far has concentrated on the case of a closed ity, and so eventually the economy will re-enter a boom. If the economy and much of the output cycle appeared to be driven by fraction of the population with high-yield investment possibil- movements in the real interest rate. However, in more recent ities is small enough and/or the credit multiplier low enough, work with l? Bacchetta and A. Banerjee, we are considering a there will be continuous oscillations of the investment level. Such small open economy extension of the same framework, where volatility of investment in turn implies that there are unexploited real interest rates remain fixed at the international market-clear- production possibilities and hence the long-run growth rate is ing level and the transmission variable becomes the price of lower than it could be. non-tradeable goods in terms of the tradeable good. More pre- The government has two structural policy options to try to cisely, high-yield investments in the domestic economy require move the economyout of the above cyclical equilibrium into a sit- the use of non-tradeable goods (such as real estate) as inputs to uation in which all savings are invested in the high-return pro- produce tradeable goods. Then, the story goes as follows: during duction technology. One is to reduce the borrowing constraints, a boom the domestic demand for non-tradeable goods keeps thus increasing the credit multiplier and ensuring that there is going up as high-yield investments build up, and thus so does sufficient demand for funds. This is, however, a hard policy to the price of non-tradeables relative to that of tradeables. This, implement unless the government is willing to lend to individuals together with the accumulation of debt that still goes on during itself. Moreover, if the credit constraint is the result of a moral booms, will eventually squeeze investors' borrowing capacity hazard problem, such as that examined in subsection 2.2, it and therefore the demand for non-tradeable goods. At this would not be possible to increase the credit multiplier without point, the economy experiences a slump and two things occur: generating adverse incentive effects. A second structural policy the price of non-tradeables collapses to the level where it is consists in reducing the degree of inequality of access to invest- equal to the real rate of return of the asset (i.e.,it falls relative to ment. By increasing the fraction of savers that can directly invest that of tradeables), while a fraction of the assets on offer is not in high-yield projects, the economy can move to a permanent- purchased as there are not enough investment funds. This boom situation and thus increase its growth rate. Structural second effect has real consequences, as those individuals who reforms such as investing in infrastructure or in human capital, or cannot undertake tradeable production have to move into the reducing the bureaucratic obstacles faced by entrepreneurs that backyard technology. The collapse in the price of non-trade- wish to set up a firm, would reduce entry barriers and promote ables thus results in a contraction of the tradeable-goods sector growth. and of the level of real output. Unlike in Krugman (1998),the argument that we have just pre- as Alesina and Rodrik (19941, Persson and Tabellini (1994), and sented does not rely on any regime or policy change."nvestors Benabou (19961, maintain that inequality affects taxation are constrained in their borrowing at any point in time. The through the political process when individuals are allowed to vote increase in the price of non-tradeable goods relative to tradeables in order to choose the tax rate (or, equivalently, vote to elect a and the accumulation of debt, make the credit-market constraint government whose program includes a certain redistributive bind at a certain moment in time, and bring about the collapse in policy). In general, we would expect that in very unequal soci- the price of non-tradeables. The effect of credit-market imperfec- eties, a majority of voters prefer high redistribution than in more tions would, clearly, be worsened if production were risky and if equal societies. If redistribution is harmful for growth, then more there were moral hazard on the part of investors. What is new unequal societies would grow faster. about this approach is that the financial slump is the conse- To illustrate this argument suppose that individuals are, as quence of rapid growth. Growth is financed by the accumulation before, endowed with different amounts of human capital, given of debt. The debt build up and the consequent increase in the by wf= ~f .A,, and that production of the future consumption price of non-tradeables is what causes the crisis. This raises the good takes place according to the AK-technology. The govern- question of what is sustainable growth. If periods of fast growth ment now introduces redistributive taxation that takes the follow- are followed by slumps due to excessive debt build-up, it maybe a ing form: there is a proportional tax on individual investments better long-run strategy to allow the economy to develop at a and the revenue is used to distribute a lump-sum subsidy which is slower but steady pace. proportional to the average investment. This is, an individual i with pre-tax investment kiends up with the post-tax investment 2.4 Political economy where k is the average investment. Clearly, those with above- Economic conflicts surface through the political process, espe- average investments pay a net tax, while those with below- cially when the society as a whole must decide about redistribu- average ki receive a net subsidy. tion or public-good investments such as education or health. By When capital markets are perfect so that all agents can borrow affecting the outcome of the political game, inequality will at the risk-free interest rate, all individuals choose to invest the directly influence the extent of redistribution and thereby the rate same amount ki = s(r).w, where s(r) is the saving rate. of growth. Interestingly, the direction in which inequality affects Individual investments depend on the average endowment and growth through the political process turns out to depend heavily on the saving rate. In the absence of moral hazard, the saving rate on the importance of credit constraints, as we will now illustrate. is the same for all individuals and is decreasing in the tax rate due As has been argued in the previous subsections, redistribution to the standard negative incentive effect (see appendix 2). affects the rate of growth in an AK-model. If inequality deter- Moreover, in the AK-model, the growth rate is a function of the mines the extent of redistribution, it will then have an indirect saving rate, g,= cwlns(r). The standard incentive argument then effect on the rate of growth of the economy. Several authors, such implies that a high tax rate, by reducing the net return to invest- ment, reduces the fraction of wealth that is invested and the growth rate. "rugman (1998) argues that the Asian crisis has been caused by moral hazard on the part of financial intermediaries whose liabilities were guaranteed by the The tax rate affects individuals differently depending on their government. The resulting overinvestn~entand excessive risk-taking made asset initial income, as it has two distinct effects: on the one hand, it are prices rise. Eventually, a "change in regime" has implied that lial~ilities no longer gu;irarlteed and asset ~ ~ r i chave collal~sed. cs affects an agent's current income through the net taxlsubsidy; on Assume now that the tax rate is endogenously determined each income through the changes in the other hand, it affects his fi~tul-e period through majorityvoting. Given that the intertemporal util- the growth rate. In fact, we can express the indirect utilitpfunction ities V(T)are single-peaked for wl< w, the equilibrium tax rate T of individual i as a function of his relative wealth and the tax rate will be that chosen by the median voter. lnequality therefore affects the degree of redistribution: the higher the degree of wealth equality, as measured by the ratio of the median voter's The term V(r) captures the incentiveeffect of redistribution and is wealth to average wealth, the higher the tax rate rwill be. Hence in the same for all agents: redistribution affects the growth rate and the absence of credit- market imperfections, more inequality (in the hence utility. In our particular example, V(T) is decreasing in T as a sense of a lower ratio of median to average wealth) will lead to result of the negative incentive effect. G(wilw , ~is an individual- ) more redistribution and therefore to lowergrowth. specific term that reflects the redistribution effect of the tax. As we noted above, appreciating the effect of capital-market Those agents with wealth above w pay a net tax, as they are taxed imperfections is crucial to understanding the relationship more than they receive in subsidies. Hence for them the term between inequality and growth. Is the result that greater inequal- G(wilw,r) is negative. For those agents with wi< w, this term is ity is harmful for growth robust to the introduction of capital- positive as they receive a net subsidy. The net investment of the market imperfections?To address this question we should couple individual with average wealth, wi= w, is unaffected by the tax, the political economy arguments just presented with the models i.e., G(1,r)is zero. Moreover, the impact of an increase in the tax developed in previous subsections. Consider, in particular, the rate on G(wilw,r) depends on the relative income position of the opportunity-creation effect. Suppose that a lump-sum tax p is individual: a higher tax reduces the utility of agents with above- introduced, and that the tax rate is chosen by majority voting. As average wealth through the redistribution effect, and increases we already argued in subsection 2.1, this tax has no incentive that of agents with below-average wi .We have effect. It, however, affects the individual's utility in two ways. dG(W'1W,T) I < 0 for wi>w = O for w i = w o for wi< w. There is aredistribution effect, that implies that thosewith wealth below average benefit from redistribution, those with average wealth are unaffected, while individuals for whom w'> w experi- ence a reduction in their net wealth. There is a second effect that An individual will prefer the tax rate at which the marginal reflects the aggregate loss from investment inequality, which increase in utility of redistribution equals the marginal loss due to arises in the no credit-market case. This loss is itself a conse- the incentive effect. The preferred tax rate of individual i is given quence of the assumption of decreasing returns to individual by the first-order condition d Ui(r)/dr= 0 capital investments; to the extent that it affects aggregate knowl- edge A at any point in time, this cost of inequality is to be borne by all individuals, the poor and the rich, in the economy. In terms of the indirect utility function, U1(r) V(T) + G(wlIw,T), this means = Individuals with initial wealth equal to w or greater will prefer a that now V(T) is increasing in the tax rate. In particular, the indi- zero tax rate, as a higher tax reduces their utility through both the vidual with average wealth wwill now vote for a positive tax rate incentive effect and the redistribution effect. Individuals with because ( I ) the redistribution effect leaves his wealth unchanged, ). initial wealth wi< wwill prefer apositive tax rate ~ ( w ' The result- and (2) redistribution creates investment opportunities, increas- ) ing preferred tax rate ~ ( w 'is decreasing in wi. Not surprisingly, ing aggregate knowledge and therefore his income. The larger the poorer individuals will prefer a higher tax rate T I , as the redistribu- degree of inequality, the more the median voter will benefit from tion effect is stronger the lower lui. the direct redistribution elfect, and the higher his preferred tax hold: educat~o~l." in Investn~ents hllman capital are characterized rate will be.-fheoverall impact of greater inequality on the growth by strong diminishing returns. Moreovel-, borrowing in order to rate is now ambiguous: on the one hand, it I-educesgrowth, as make such an intangible investment is usually expensive (if not seen in subsection 2.1, on the other, it results in a greater degree of impossible) and hence family wealth becomes a major determi- redistribution and therefore faster growth. nant of the size of the investment. If we view k;as an investment A similar point is made by Saint-Paul and Verdier (1993), in education and g a s the rate of growth of human capital (which Glomm and Ravikumar (1992),and Perotti (1993) who analyze the in turn determines the rate of output growth, as argued by Lucas voting process over public education spending aimed at circum- (198811, then our analysis predicts a negative relationship venting wealth constraints on private education investments. In between wealth inequality and the rate of growth. these papers redistribution takes the form of public education or The importance of moral hazard in determining individual education subsidies, while revenue is raised through a tax on the actions is well-known, and subsection 2.2 has examined its con- returns to investment. Consequently, redistribution has both a sequences for the aggregate level of investment. We saw how a negative incentive effect and a positive opportunity creation lump-sum tax and transfer system results in faster growth. effect.The rate of growth, and hence the term V(r)in the indirect Consider now a transfer system in which revenue is raised utility function, are a nonmonotonic function of the tax rate. through distortionary (ex-post)taxation. In this case there are two When inequality is great, so that a large fraction of the population incentive effects: the standard effect whereby taxation reduces is constrained in their investments, the opportunity creation net returns and hence lenders' incentive to invest, and moral effect dominates; for more equal distributions, public education hazard with wealth constraints which decreases the effort exerted only slightly increases the number of agents that have access to by entrepreneurs whose projects are largely financed by borrow- education while it reduces the investment of a large part of the ing. Whether redistribution increases or decreases the rate of population through the incentive effect, resulting in a reduction growth then depends on whether the standard effect of taxes on in the growth rate. Since the tax rate is strictly increasing in the those with high wealth is smaller or greater than the positive degree of inequality, the resulting relationship between wealth impact o n the effort of those with low wealth levels. distribution and growth is U-shaped. The third aspect we have dealt with introduces a different, and much neglected, concept of inequality. It is not the distribution of wealth that we look at, but rather the social and institutional envi- 2.5 Discussion ronment that affects access to investment projects. As we have seen, this institutional source of inequality will affect both the The main conclusion we can draw from this section is that when distribution ofwealth and the rate of growth ofthe economy. we allow for heterogeneity among agents along with capital- Overall, inequality actually proves bad for growth in several market imperfections, the traditional argument that inequality circumstances. Redistribution is then growth enhancing has a positive impact on growth is strongly challenged. Consider, because it creates opportunities, in~proves borrowers' incentives for example, the opportunity-enhancing effect. Our argument and/or because it reduces macroeconon~icvolatility. In such relies on three assumptions: first, that agents are heterogenous; instances, there is no longer a tradeoff between equity and second, that capital markets are highly imperfect; third, that the efficiency goals, and policies designed to tackle one then have a production technology exhibits diminishing returns to capital. A growing literaturr addresses how inequality affects growth through the pos- These may look quite strong. However, there is, at least, one par- s sibilities ol'agcnts ro i ~ ~ \ , einreducation. See Saint-I'aul andVel-dier (1993), Galor ticular type of investnlent for which these assumptions clearly :~nd %ei~;i (19931, I'c3rorr~(1993), and Garcia-l'eiialosa (1995).

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Philippe Aghion, Jeffrey G. Williamson, income inequality, Cambridge University Press, Mattioli Lectures, Raffaele Mattioli, Economic theory, World Bank, Economic History, theory & philosophy

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posted: | 3/8/2010 |

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