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Growth_ Inequality_ and Globalization

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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).