The Tradeoff Between Inequality and Growth


 Gillian Dean
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1 ANNALS OF ECONOMICS AND FINANCE 4, The Trdeoff Between Inequlity nd Growth Jess Benhbib Deprtment of Economics, New York University 269 Mercer Street, 7th floor, New York, NY 10003, USA. Emil: c 2003 Peking University Press Key Words: JEL Clssifiction Numbers: 1. INTRODUCTION Is there trdeoff between inequlity nd economic growth? The theory nd the evidence re inconclusive. In the 1950es nd 60es prevlent view ws tht inequlity leds to higher svings becuse the rich sve proportiontely more thn the poor, nd tht this leds to increses the rte of investment nd growth see Kldor 1957, Kuznets More recently, it hs been rgued tht inequlity hurts growth becuse it leds to redistributive pressures, either through the medin voter who encts redistributive txes Tbellini nd Persson1993, or through generting socil conflict, exproprition, nd rent seeking behvior see Alesin nd Rodrik 1994, Alesin 1994, Benhbib nd Rustichini 1996, Benbou 1996, Perotti 1996, Acemoglu nd Robinson All such ctivities dilute the return on investment nd reduce the rte of growth 1. Another view is tht inequlity coupled with borrowing constrints nd finncil mrket imperfections prevents the tlented poor to undertke profitble investments in physicl nd humn cpitl, thereby limiting the full potentil for the growth of the economy Glor nd Zeir 1993, Bnerjee nd Newmn By contrst, there is lso recent literture which views inequlity 1 But see St. Pul nd Verdier1993, who rgue tht redistributive txes cn enhnce growth if they re chnneled to puiblic goods or eduction tht mkes the economy more productive /2002 Copyright c 2003 by Peking University Press All rights of reproduction in ny form reserved.
2 330 JESS BENHABIB s the result of growth spurts tht re ssocited with skillbised technicl chnge Aghion On the empiricl side, the evidence on the trdeoff between inequlity nd growth, despite lrge number of recent studies, remins inconclusive. In recent pper Deininger nd Squire 1996 document the frgility nd the nonrobustness of the results obtined by using crosscountry regressions see lso Levine nd Renelt 1992, Benhbib nd Spiegel 1994, Islm 1995 nd Esterly In ddition, nd to complicte mtters further, Forbes 2000 now finds significnt positive ssocition between inequlity nd growth in the short nd medium run. Redistributive pressures, insecure property rights nd socil conflict tht stem from significnt inequlity my well discourge investment nd hinder growth. On the other hnd, excessive interference with economic inequlity tht follows from differences in effort, productivity, enterprise nd inititive is lso likely to reduce growth nd investment. In this pper we present theoreticl politicl economy model of inequlity nd growth. We wnt to demonstrte tht while excessive inequlity cn disrupt the economy by inviting politicl interference through rentseeking behvior nd pproprition, policies which support some modest inequlity to tke dvntge of productivity differences will led to the best growth rtes. Thus we show tht the reltion between inequlity nd growth my be mildly humpshped: growth my rise modestly t first, s we move wy from complete equlity, nd then drop gin s inequlity increses further. 2. THE SOCIAL PLANNER AND COOPERATIVE SOLUTIONS We strt by considering the policies of socil plnner, or government, in n economy with two clsses of gents. For simplicity, the utilities of the two sets of gents re logrithmic, they re incresing in consumption, nd they re qudrtic nd decresing in lbor. Output is produced with CobbDougls production function, Ak α l 1 l 2 σ, using cpitl k, nd there re two types of lbor, l 1 nd l 2, with different productivity levels. We will not necessrily restrict the production function to constnt returns to scle in order to llow the possibility of endogenous growth with α = 1. Given the logrithmic utility of consumption nd the qudrtic disutility of work, the problem is welldefined, with the cse of constnt returns, α + + σ = 1, s specil cse. Let us first ssume tht the government ssigns weights nd 1, to the two gents nd cn choose their consumptions nd lbor supplies to mximize the discounted utilities of the gents. If we denote the vlue function by V k, the problem is given
3 THE TRADEOFF BETWEEN INEQUALITY AND GROWTH 331 by: V k = mx c 1,c 2,l 1,l 2 { ln c ln c 2 0.5B l l 2 2 +βv Ak α l 1 l 2 σ c 1 c 2 where we will set B = 1. 2 To solve the problem let y = Ak α l 1 l 2 σ. The first order conditions for consumption re: } c 1 1 = 1 c 2 1 = βv Ak α l 1 l 2 σ c 1 c 2 c i 1 = βα c i 1 y i = 1, 2 k where primes re next period vlues. Let c i = λ i y. Then, the solution for the consumption of the first gent must stisfy: λ 1 y 1 = βα λ 1 y 1 1 λ 1 λ 2 = βα y 1 λ 1 λ 2 y λ 1 = 1 βα, λ 2 = 1 1 βα We cn now solve for the optiml lbor supplies l i tht mximize the utility function 3 : l 1 = βv Ak α l 1 1 l 2 σ 1 = c 1 1 Ak α l 1 1 l 2 σ 2 l 1 = 1 βα 1 y 1 y l 1 1 l 1 2 = 1 βα 1 l 1 2 = 1 βα ; l 2 2 σ = 1 1 βα 2 In such cses where we require lbor supply to be inelstic we cn tke B = 0, nd l 1 = l 2 = 1. 3 Eqution 2 is simply the the stndrd lbor mrket condition which requires the mrginl disutility of lbor to equl the mrginl product of cpitl times the mrinl utility of consumption.
4 332 JESS BENHABIB We re now in position to obtin the vlue function for the government: V k = s ln k + I = ln [ 1 βα Ak α l 1 l 2 σ ] +1 ln [1 1 βα Ak α l 1 l 2 σ ] σ 1 1 βα = α ln k + α1 ln k + αβs ln k 1 βα + βs ln [βα Ak α l 1 l 2 σ ] + βi + ln 1 βα A l 1 l 2 σ + 1 ln 1 1 βα A l 1 l 2 σ +βs ln βα A l 1 l 2 σ βα 1 + σ + βi 1 Note tht the vlue function is concve in k. We cn now solve for s nd I by equting coefficients of ln k nd of the constnt terms s = 1 βα 1 α I = 1 β 1 [ ln + 1 ln 1 ] [ ln 1 βα A l + 1 β 1 1 l 2 σ ] +βs ln βα A l 1 l 2 σ βα 1 + σ 1 We note tht this lloction of consumptions nd lbor supplies cn be chieved in decentrlized setting by the socil plnner through simple redistribution of the initil cpitl stocks, so tht k 1 0 = k 0, k 2 0 = 1 k 0, provided we hve constnt returns to scle in production. For exmple, if lbor supply is inelstic B = 0, l 1 l 2 σ = 1 nd we set α = 1 to chieve blnced growth, the decentrlized setting described bove would implement the plnner s solution fter the initil cpitl ws llocted ccording to the specified weights to the two gents. 4 Then if ech gent consumed nd sved optimlly, expecting return on cpitl given by the mrginl product of cpitl, the first order conditions of ech gent with respect to c i tht is their Euler equtions, would be equivlent to the first order conditions of the socil plnner. In this cse ech gent s cpitl would grow t the rte βa 1. With incresing returns to scle, 4 For, σ 0, α 1, we pproch the stndrd endogenouis growth model. The Hessin of the utility function lnak t l 1 l 2 σ k t l l 2 2 will hve root pproching zero, ssocited with the blnced growth pth, with the other roots negtive, s the utilty of leisure is strictly concve.this cn be checked by computtion or deduced from the continuity of roots in prmeters.
5 THE TRADEOFF BETWEEN INEQUALITY AND GROWTH 333 s is wellknown, the plnner s lloction in the context of decentrlized frmework would require system of txes nd subsidies. It my not be possible to design txes nd subsidies to identify or differentilly trget the segments of the popultion with different productivity levels however. Note tht if we bndon blnced growth by hving α < 1, nd focus on stedy stte levels of income nd consumption, we could reintroduce differentil lbor productivities nd still mintin constnt returns to scle. This structure would preserve the incentive issues ssocited with lbor supply in context where fully decentrlized implementtion of the socil plnner s solution is fesible by simple rellocting initil stocks. We cn now lso compute, for future use, the vlue function for the gent consuming shre λ 1 = 1 βα of the output: V 1 k = s ln k + I = ln 1 βα Ak α l 1 l 2 σ βs ln βα 1 Ak α l 1 l 2 σ + βi1 1 βα = α ln k + αβs ln k βα +ln 1 βα A l 1 l 2 σ + βs ln βα A l 1 l 2 σ + βi 1 s = α 1 βα 1 I1 = 1 β 1 ln 1 βα A l 1 l 2 σ βα 1 + βs ln βα A l 1 l 2 σ 3. THE NONCOOPERATIVE SOLUTION: MARKOV STRATEGIES We now consider sitution where ech gent cn choose to pproprite some consumption from the output, with the residul output, if ny, becoming the cpitl stock for the next period. This reflects sitution where property rights, nd in prticulr the returns to investment, re insecure, illdefined or mnipulble. We envisge politicl system where pressure groups hve power to implement redistributive policies. Such policies cn rnge from outright exproprition to redistributive txtion, infltionry finnce tht sustins powerful groups, exchnge rte policies tht fvor certin constituencies over others, the provision of government employment trgeted to specific sections of the popultion, price controls, monopolistic mrketing bords creted to dvntge prticulr clsses, or other legisltive mesures tht cn ffect nd lter the brgining power of lbor nd/or
6 334 JESS BENHABIB cpitl. It is importnt to note tht while policies fvoring mny diverse groups cn coexist, they my no mens wsh out, or cncel ech other out. Ech one represents dilution of returns to investment tht tends to diminish nd discourge growth. These redistributive policies however my be the unvoidble result of the politicl process, nd it must be the job of good government nd purpose of effectively designed institutions to chieve the lest costly implementtion of the politicl consensus. Sustining productive politicl consensus will require specifiction of the equilibrium for the cse where the consensus breks down. We will model this s noncoopertive MrkovNsh equilibrium where ech group pproprites consumption s best response to the competing group s pproprition. For simplicity we model the politicl power of the two groups s symmetric, without specifying limits to pproprition. The model could esily be modified to reflect unequl politicl power, nd upper different bounds on the ppropribility of output 5. The vlue function of the first gent is given by: } V s k = Mx c1 {ln c l1 s 2 + βv 1 λ 2 Ak α l1 s l2 s σ c 1 where the superscript s in li s, i = 1, 2, is used to indicte the lbor supplies chosen in the noncoopertive cse, nd which re different thn the lbor supplies l i, i = 1, 2, chosen in the coopertive cse. The first order conditions re given by: c 1 1 = βα c 1 1 y Let c i = λ i y. Then the bove simplifies to: k 1 λ 2 1 λ 1 λ 2 = βα 1 λ 2, A symmetric equilibrium then implies consumption shres, identicl for the two gents, of: λ = 1 βα 2 βα 5 To fully define the gme, outcomes must be explicitly specified for situtions where the gents ttempt to pproprite mounts tht sum to more thn the totl output vilble. We will overlook such considertions here, but for n explicit tretment of such issues see Benhbib nd Rustichini 1996.
7 THE TRADEOFF BETWEEN INEQUALITY AND GROWTH 335 We cn lso solve for the lbor supplies of the first nd second gents using their first order conditions for lbor supply: y l1 s = βv c 1 l s 1 = l s 1 1 βα 2 βα 1 λ 2 = c 1 1 y l1 s y yl s 1 = l s 1 1 λ 2 = 1 λ 2 y l s 1 2 βα 1 Solving the bove, the lbor supplies for the two gents re given by: l s 1 2 = 1 βα 1 = l 1 2 l s 2 2 = σ 1 βα 1 = 1 l 2 2 Given consumption shres nd lbor supplies we cn evlute the vlue functions ssocited with this noncoopertive equilibrium: V s k = s s ln k + I s = ln λak α l1 s l2 s σ βα 1 + βs s ln 1 2λ Ak α l1 s l2 s σ + βi s where nd I s = s s = α 1 αβ 1 = s ln λa l1 s l2 s σ + βs s ln βα A l1 s l2 s σ βα 1 1 β The cpitl ccumultion eqution for the socil plnner s solution is: k t+1 = αβ Ak α t σ σ σ 1 βα 1 βα while for the noncoopertive solution it is: αβ k t+1 = A k t α l 1 l 2 σ σ 2 αβ Note tht these ccumultion equtions led to stedy sttes if α < 1. They led to sustined blnced growth pths only if α = 1, ssuming tht prmeter configurtions under logrithmic preferences lso stisfy the sufficiency conditions.
8 336 JESS BENHABIB 4. SUSTAINABLE EQUILIBRIA Sustinble equilibri re consumption nd lbor pths tht yield higher utilities to the gents thn they could chieve unilterlly by breking the greement nd reverting to the noncoopertive equilibrium. One simple wy to model this is to ssume tht defection does not yield n initil period dvntge to the defector during which his opponent continues to consume nd supply lbor ccording to the greed upon coopertive pth. We my ssume tht the defection is instntly detected, so tht reversion to the noncoopertive equilibrium is immedite. By construction, symmetric lloction tht trets both gents identiclly will dominte the symmetric noncoopertive equilibrium, but given the dispersion in productivities, pertinent question is the degree of inequlity, prmetrized by, tht cn be sustined by the socil plnner, nd whether there is n optiml degree of inequlity tht ttins the highest level of growth. Before trying to nswer this question, let us note tht n lterntive specifiction of the model, discussed in the ppendix, would llow the defector one period dvntge before both gents revert to the noncoopertive equilibrium, nd mke defection more ttrctive. In such cse the degree of enforceble inequlity my in fct shrink. Under such circumstnces, the socil plnner s preferred solution, even under complete equlity, my not be enforceble nd other secondbest solutions must be found Benhbib nd Rustichini However, the noncoopertive equilibrium described bove my not be the worst equilibrium to which the plyers cn defect: the thret or fer of reverting to n even worse equilibrium nrchy? my be ble to sustin more coopertion, even if it entils more inequlity. To evlute the degree of sustinble inequlity, we must compre the vlues of the coopertive nd the noncoopertive lloctions. Since s s = s, the comprison of the discounted sum of utilities hinge on I nd I s. We hve, since 0.5 l 1 = l s 1 nd l 2 = l s 2: I s = I 1 = ln +βs s ln 1 βα βα A 0.5 l l 2 σ A 0.5 l l 2 σ βα 1 β ln 1 βα A l 1 l 2 σ +βs ln βα A l 1 l 2 σ βα 1 1 β
9 THE TRADEOFF BETWEEN INEQUALITY AND GROWTH 337 Then the comprison of discounted utilities between the coopertive nd noncoopertive regimes for the first gent reduces to: ln 1 βα + βs ln βα βα 1 1 βα βα ln + βs s ln 2 βα 2 βα βs ln σ βα 1 or, ln βα βα 1 ln σ ln 2 βα Similrly for second gent, we obtin: ln βα 1 σ 1 1 βα 1 ln σ ln 2 βα Figure 1 illustrtes the growth rtes when α = 1, s well s the growth rtes s function of, for prmeter vlues βα = 0.98, = 0.15, σ = However, the sustinble growth rtes re those corresponding to vlues of for which both lines, representing the difference between the vlues of coopertion nd noncoopertion of ech gent, re nonnegtive. Note tht this sustinble intervl in Figure 1 is skewed to the left becuse σ >, nd is the productivity of the gent ssigned weight. The gent with the higher productivity is less willing to cooperte if he is given low utility weight, becuse he cn do better in the noncoopertive sitution. However, note tht the growth rte is mximized if the productive gent is given low weight in fct zero weight, the lowest possible vlue for 1. The figure is provided only for [0.3, 0.7] for better visibility. This is becuse the optiml lbor ssignments of the gents re decresing 6 Of course these growth rtes would be trnsitory if α < 1. The level of the ttinble stedy stte when α < 1 would be positively relted to the vlue of the function ttined in the lower figures depicting the growth rte. Prlell results hold if we ssume tht the government ims t mximizing the stedy stte level of output insted of the growth rte: the government would then implement moderte level of inequlity t the boundries of the sustinble intervl. None of the qulittive fetures of the Figures chnge if we pick, ssuming constnt returns, βα = β 1 σ. This would imply, for + σ = 0.55, vlue of βα round 0.5. See Figure 3.
10 338 JESS BENHABIB in their utility weight. To mximize growth, it is best to ssign low utility weight to productive gents tht leves them with low initil stocks of cpitl so s to get more work out of them. If the only mechnism vilble to the socil plnner to elicit work, or more ppropritely, to elicit effective effort is decentrlized system of txes nd subsidies, then the welthier gents who receive higher utility nd higher consumption will lso supply less effort. This is n rtifct of the preference specifiction where leisure nd consumption re complements, so tht higher consumption is ccompnied by lower lbor supply. Of course pproprite nonwge subsides or the prestige ssocited with higher position my reverse this feture of the model. Alterntively, if ech gent were operting his or her own stock of cpitl in combintion with his or her lbor rther thn with one ggregte cpitl nd single production function, then there would be n dditionl tendency to llocte the cpitl towrds the group tht hd the more productive lbor. This would tend to prtilly offset the lbor supply effect of welth nd consumption, nd my led to n optiml lloction of cpitl, in the sense of mximizing the growth of output, tht would fvor the more productive groups. 10 Difference between the vlue of coopertion nd non coopertion s function of V Vs, V1 Vs Growth Rte s function of 1.24 Growth Rte FIG. 1. Figure 2 illustrtes the cse = 0.3, σ = In this cse the sustinble intervl is skewed to the right since the first gent is the more productive one, nd the growth is higher s becomes lower. These results
11 THE TRADEOFF BETWEEN INEQUALITY AND GROWTH 339 re not sensitive to the choices of α nd β. Under n lterntive specifiction where βα = 0.5 nd for = 0.3, σ = 0.15, very similr results obtin, s is cler from the Figure Difference in the vlue of coopertion nd non coopertion s function of V Vs, V1 Vs Growth rte s function of 1.24 Growth Rte FIG THE TRADEOFF BETWEEN GROWTH AND INEQUALITY The min point of this nlysis is to study the optiml redistribution of welth tht mximizes the growth rte. Redistribution in terms of utility cn be implemented s relloction of the productive initil cpitl stock. As we see from the figures presented bove, when gents cnnot interfere with the politicl distribution mechnism, the growth mximizing lloction is to impoverish the most productive gents, thereby forcing them to supply more effort. However, such policy will not work becuse of politicl constrints: gents cn withhold effort, nd they cn resort to politicl rentseeking ctivities to obtin higher consumption if the distribution of welth nd income is too unfvorble to them. We see tht outside the sustinble intervl for the prmeter, the economy will revert to noncoopertive equilibrium with low growth rte ssuming α = 1 given
12 340 JESS BENHABIB 1 Difference in the vlue of coopertion nd non coopertion s function of V Vs, V1 Vs Growth rte s function of 1.24 Growth Rte FIG. 3. by g s = αβ A 1 βα σ 1 βα 1 0.5σ. 2 αβ Note tht this growth rte is independent of. The vlue of tht mximizes stedy stte level of output or the growth rte of the economy must be chosen to mximize σ g = αβ Akt α σ σ 1 βα 1 βα nd must be t the boundry of the sustinble intervl in the figures bove. Whether the optiml is the upper or lower boundry depends on the reltive productivities of the two gents. If > σ, then we choose the lower bound for, nd if < σ, we choose the higher bound unless of course productive gents cn be offered nonwge compenstion outside the mrket tht gives them dditionl utility ssocited with their jobs, working conditions, nd the prestige of their positions. We should note tht our logrithmic specifiction for the preferences ssures tht gents sve constnt frction of their income. The totl svings rte remins constnt s we vry. In decentrlized economy,
13 THE TRADEOFF BETWEEN INEQUALITY AND GROWTH 341 the supply of lbor or effort then becomes the primry mechnism through which incentives ffect stedy stte output levels. If we plot growth s function of inequlity, we will observe growth rtes tht re low nd constnt for high degrees of inequlity, corresponding to noncoopertive outcomes. As inequlity decreses we my observe jump in the growth rte s we enter the rnge of sustinble coopertion. Therefter, growth rtes will decline s we move towrds perfect equlity, nd s we diminish the incentives for the more productive gents to supply effort. see Figure 4. We my conclude therefore tht the reltion between growth nd inequlity is humpshped, nd tht growth mximizing socil plnner should im t moderte level of inequlity designed to elicit effort from the most productive gents in the economy Sustinble growth rtes Growth Rte FIG. 4. It my be possible for the government to improve the growth rte of the economy by enlrging the rnge of sustinble coopertive outcomes. This cn be chieve by mking devition to the noncoopertive equilibri more costly for the gents. If punitive costs for deviting from the coopertive outcome could be imposed, greter degree of inequlity could be sustined. In Figure 1 for exmple, incresing the costs of devition could rise the two curves representing the difference between the vlue of coopertion nd the vlue of devition, enlrging the rnge of for which the coopertive equilibrium is sustinble. In the cse depicted in Figure
14 342 JESS BENHABIB 1, this would permit the choice of higher vlue of, nd therefore of higher growth rte for the economy. Imposing such costs on devition in order to improve the growth rte however, my not lwys be politiclly fesible or desirble. APPENDIX: SUSTAINABLE EQUILIBRIA WITH A ONE PERIOD ADVANTAGE OF DEVIATION In this cse, the defecting gent the first gent in this cse considers his optiml consumption nd lbor supply ginst the cooperting gent the second gent consuming frction λ = 1 1 βα of the output nd supplying lbor l 2 = σ 1 1 βα, with the understnding tht both gents will revert to noncoopertive behvior from the next period on 1. The mximiztion problem for this gent is given s: mx c lnc d 1 0.5l1 d 2 + βα1 αβ 1 lnak α l1 d l 2 σ βα c d 1 ln 1 βα A 0.5 l + β1 β σ l 2 +βs s ln βα A 0.5 l σ l βα The first order conditions re: c d = βα 1 αβ Ak α l1 d 1 l2 σ βα c1 d nd they cn be reduced to: c d 1 = [1 1 1 βα 1 βα] Ak α l1 d l2 σ λ 1 dak α l1 d l2 σ It is lso strightforwrd to compute the optiml defection consumption of the second gent. It is given by: c d 2 = [1 1 βα 1 βα] Ak α l2 d l1 σ λ 2 dak α l2 d l1 σ Similrly, lbor supply of the defecting first gent is the solution to the first order conditions: l1 d = βα 1 αβ 1 Ak α l1 d 1 l s 2 σ βα c Ak α l d 1 1 l s 2 σ βα = c 1 Ak α l d 1 1 l2 σ βα 1 See lso Kitl nd Pohjol 1990, nd Benhbib nd Rustichini 1996.
15 THE TRADEOFF BETWEEN INEQUALITY AND GROWTH 343 They cn be simplified to: l d 1 2 = [1 1 1 βα 1 βα] βα = βα βα 1 βα = 1 βα 1 The optiml lbor supply of the defecting second gent ginst the first is, by symmetry, l s 2 2 = 1 βα 1 σ We cn lso compute the vlue function for the defection of the first gent: V D 1 = s D ln k + I1 D = ln [1 1 1 βα 1 βα] A l1 d l2 σ k α 0.5 l1 d 2 + βα 1 αβ 1 ln Ak α l1 d l2 σ {1 1 1 βα 1 βα} + β 1 β 1 ln 1 βα A l1 s l2 s σ +βs s ln A l1 s l2 s σ 0.5 βα 1 βα where s D = α 1 + βα 1 αβ 1 = α 1 αβ 1 = s s = s nd I D 1 = ln [1 1 1 βα 1 βα] A l1 d l2 σ l1 d A l d 1 l2 σ ln {1 1 1 βα [1 1 1 βα 1 βα]} + βα 1 αβ ln 1 βα A l s + β 1 β 1 1 l2 s σ +βs s ln A l1 s l2 s σ 0.5 βα 1 βα
16 344 JESS BENHABIB For the second gent, the vlue of defection is given by V1 D = s D k + I2 D, where σ 2 I2 D = ln [1 1 βα 1 βα] A l 1 l2 d 0.5 l2 d + βα 1 αβ 1 A l 1 l2 d σ ln {1 1 βα [1 1 βα 1 βα]} ln 1 βα A l s + β 1 β 1 1 l2 s σ +βs s ln A l1 s l2 s σ 0.5 βα 1 βα We cn, t this point, inquire whether coopertion cn be sustined for some specil cses. When β 0, we get: V D 1 V 1 = ln = 0.5 l d 1 l ln This quntity is positive if > e 1. This will be the cse for 0, 1. 2 Thus there cn be no coopertion s β 0. Furthermore one could show tht when = 0.5 nd = σ, then it is lwys better to cooperte s β 1. REFERENCES Acemoglu, Dron nd Robinson, Jmes A., 2002, Why did the west extend the frnchise? Democrcy, inequlity, nd growth in historicl perspective. Qurtely Journl of Economics 1154, Alesin, Alberto, 1994, Politicl models of mcroeconomic policy nd fiscl reforms. In: Stephn Hggrd nd Steven Webb, Voting Reform: Democrcy, Politicl Liberliztion, nd Economic Adjustment. Oxford University Press, New York, New York. Aghion, Philippe, 2000, Schumpeterin growth theory nd the dynmics of income inequlity. Econometric 703, Alesin, Alberto nd Rodrik, Dni, 1994, Distributive politics nd economic growth. Qurterly Journl of Economics 1092, Bnerjee, A. nd A. Newmn, 1993, Occuptionl choice nd the process of development. Journl of Politicl Economy 101, Benbou, Rolnd, 1996, Inequlity nd growth. In: Ben S. Bernnke nd Julio Rotemberg. NBER Mcroeconomics Annul Cmbridge, MA: MIT Press, Benhbib, Jess nd Spiegel, Mrk, 1994, The role of humn cpitl nd politicl instbility in economic development. Journl of Monetry Economics 34, Agin by symmetry, V2 D V 2 is negtive for the second gent if 1 > e 1.
17 THE TRADEOFF BETWEEN INEQUALITY AND GROWTH 345 Benhbib, Jess nd Rustichini, Aldo, 1996, Socil conflict nd growth. Journl of Economic Growth 1, Deininger, Klus nd Squire, Lyn, 1996, A new dt set mesuring inequlity. World Bnk Economic Review 103, Esterly, Willim, The middle clss consensus nd economic development. Journl of Economic Growth 6, Forbes, K., 2000, A ressessment of the reltionship between inequlity nd growth. Americn Economic Review 904, Glor, O. nd J. Zeir, 1993, Income distribution nd mcroeconomics. Review of Economic Studies 60, Islm, Nzrul, 1995, Growth empirics: A pnel dt pproch. Qurterly Journl of Economics 1104, Kitl, Veijo nd Pohjol, Mtti, 1990, Economic development nd greeble redistribution in cpitlism: Efficient gme equilibri in twoclss neoclssicl growth model. Interntionl Economic Review 31, No.2, Kldor, N., 1957, A model of economic growth. Economic Journl 67, Kuznets, S., 1955, Economic growth nd income inequlity. Review 451, Americn Economic Levine, Ross E. nd Renelt, Dvid, 1992, A sensitivity nlysis of cross country regressions. Americn Economic Review 824, Perotti, R., 1996, Growth, income distribution, nd democrcy. Journl of Economic Growth 1, Persson, Torsten nd Tbellini, Guido, 1994, Is inequlity hrmful for growth. Americn Economic Review 843, St. Pul, Gilles nd Verdier, Thierry, 1993, Eduction, democrcy, nd growth. Journl of Development Economics 422,
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