Corruption, inequality, and fairness $

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1 ARTICLE IN PRESS Journal of Monetary Economics 52 (2005) Corruption, inequality, an fairness $ Alberto Alesina a,b,c, George-Marios Angeletos,e, a Harvar University, USA b NBER, USA c CEPR, UK NBER, USA e Department of Economics, MIT, 50 Memorial Drive, E52-251, Cambrige, MA 02142, USA Receive 26 February 2005; accepte 25 May 2005 Available online 6 October 2005 Abstract Bigger governments raise the possibilities for corruption; more corruption may in turn raise the support for reistributive policies that inten to correct the inequality an injustice generate by corruption. We formalize these insights in a simple ynamic moel. Apositive feeback from past to current levels of taxation an corruption arises either when wealth originating in corruption an rent seeking is consiere unfair, or when the ability to engage in corruption is unevenly istribute in the population. This feeback introuces persistence in the size of the government an the levels of corruption an inequality. Multiple steay states exist in some cases. r 2005 Elsevier B.V. All rights reserve. JEL classification: D31; E62; H2; P16 Keywors: Corruption; Rent seeking; Inequality; Fairness; Reistribution; Political economy 1. Introuction Market economies generate large ifferences in income an wealth. The poor are always likely to eman reistributive policies, but have a much stronger moral justification for $ We are grateful to Robert King (the eitor), an anonymous referee, Marco Bassetto an Rafael Di Tella for etaile comments an feeback. We also thank Vasia Panousi an Janina Matzuseski for excellent research assistance an Emily Gallagher for excellent eitorial assistance. Corresponing author. Department of Economics, MIT, 50 Memorial Drive, E52-251, Cambrige, MA 02142, USA. Tel.: aress: angelet@mit.eu (G.-M. Angeletos) /$ - see front matter r 2005 Elsevier B.V. All rights reserve. oi: /j.jmoneco

2 1228 ARTICLE IN PRESS A. Alesina, G.-M. Angeletos / Journal of Monetary Economics 52 (2005) oing so when inequality stems from corruption an rent seeking. Yet, often these same measures that are intene to correct the effect of unfair inequality such as progressive income taxation, extensive regulation, an large public projects create more scope for corruption an rent seeking. Think, for example, of tax loopholes, corruption in the allocation of public projects, or regulations justifie on the basis of the greater goo but tailore to the interest of particular lobbies. What is more, those who benefit from corruption may prefer higher taxation an more regulation, not for the sake of the poor, but because bigger governments increase the rents they can extract. As a result, high levels of government intervention, corruption, an rent seeking may be self-sustaining. We formalize these insights in a simple ynamic moel base on three key ieas. The first is that bigger governments increase the private gains from corruption, lobbying, an other forms of rent seeking. The secon is that the istribution of these gains is uneven in the population. The thir is that societies consier inequality originating in corruption an rent seeking more unfair than inequality originating from prouctive effort an market competition. Our main result is that the combination of the first ingreient with either of the other two ingreients introuces a complementarity between current an past politico-economic outcomes there can exist multiple steay states in the level of inequality, reistribution, an corruption. The first builing block of our moel is that the larger the resources controlle by the government, or the more extensive the regulation of the market, the larger the scope for corruption an rent seeking. While we moel corruption strictly as private appropriation of tax revenues outsie the law (i.e., outsie of sanctione reistributive schemes), we inten to capture a broaer set of activities that favor various groups of privilege insiers, these woul inclue inustrialists receiving favorable regulations, public employees receiving high salaries, job security an perks, certain localities being favore by political entrepreneurs, an so on. 1 The secon ingreient is also quite plausible: not all iniviuals have the same political connections, access to the bureaucracy, or moral hesitation in becoming corrupt. More novel is the thir element, the concern for fairness. In our moel, iniviual income originates from two sources: a stanar prouctive activity, an a non-market, rent-seeking activity. Inequality generate by the prouctive activity is consiere fair; inequality generate by the rent-seeking activity is unfair. Ceteris paribus, the optimal level of reistribution increases with the ratio of unfair to fair inequality. 2 This concept of fairness, which we introuce in Alesina an Angeletos (2005), is supporte by a variety of experimental an empirical evience that shows that people are more willing to accept inequality of outcomes generate by what is perceive as effort or ability than luck or connections. 3 Using the Worl Values Survey, Alesina et al. (2001b) an Alesina an Angeletos (2005) fin that countries or iniviuals who believe that wealth an success are mostly the outcome of luck an connections rather than of har 1 For a iscussion of the use of public employment for patronage an reistribution, see Alesina et al. (2000) for US cities, an Alesina et al. (2001a) for Italian regions. 2 Along with this altruistic motive for reistribution, there is a stanar selfish motive as in Meltzer an Richar (1981). 3 For a review of relevant experimental evience on fairness, see Fehr an Schmit (2001); see also Alesina an Angeletos (2005, Section 2).

3 ARTICLE IN PRESS A. Alesina, G.-M. Angeletos / Journal of Monetary Economics 52 (2005) work an effort ten to prefer more leftist policies. Alesina an La Ferrara (2005) fin a similar pattern using the General Social Survey for the Unite States. In the presence of such a fairness concern, a history of big governments an extensive corruption means that wealth istribution is rather unfair in the present, which in turn implies stronger support for reistribution for any given level of inequality. But even when there is no fairness concern, if the gains from corruption are unevenly istribute in the population, a history of bigger governments an higher levels of corruption in the past implies a higher overall level of inequality in the present, which in turn may raise the support for reistribution. In either case, multiplicity relies on the enogeneity of corruption: if the size of the government i not affect the scope for corruption, the steay state woul have been unique. The two steay states can easily be ranke in terms of aggregate income, which is higher in the low-tax steay state, but cannot be Pareto ranke. First, iniviuals who have a sufficiently high avantage in rent seeking prefer the regime with the bigger government. Secon, the poor benefit from reistribution an may therefore prefer the high-tax steay state even at the cost of more government resources issipate by corruption. This effect may unerlay the political economy of various populist regimes in Latin America, which are supporte by a prima-facie paraoxical coalition between the poor, who benefit from reistribution, an rich insiers, who benefit from corruption. 4 These points are consistent with Glaeser an Shleifer (2003), who view the rise of the regulatory state in the Unite States as a response to the wil capitalism an the robber barons of the late nineteenth century (Josephson, 1934). For some the American regulatory state ha gone too far, becoming a source of favoritisms an capture (Stigler, 1971). Focusing on eveloping countries, Di Tella an Mc Culloch (2003) argue that people who perceive corruption as a major problem vote for left-wing parties which favor policies that inten to tax the corrupt capitalists. Djaonkv et al. (2002) similarly fin that regulation of entry is more intrusive in countries where corruption is higher. Finally, using a variety of historical an current examples, Rajan an Zingales (2002) show how a perception that capitalism is corrupt unermines market reform an supports heavy interventionism. Our interpretation of these facts is that government intervention is often invoke in an attempt to fight social injustices, but also that government intervention fosters corruption an injustice. Welfare programs in eveloping countries often o not reach the poor an instea create a vast array of favore groups. The iea that corruption is a by-prouct of government activities that are motivate by benevolent goals in our case reucing income inequality is best formalize in Banerjee (1997), who explicitly moels bureaucracy an corruption. We instea take the usual shortcut of moeling corruption as a simple rent-seeking activity. 5 Multiple equilibria (or steay states) in the level of reistribution appear also in Piketty (1995) an Benabou an Tirole (2005). The multiplicity there is ue to istortions in beliefs about the sources of inequality, whereas in our moel beliefs perfectly reflect the truth; moreover, neither of these papers examines the role of corruption. Anvig an Moene (1991) an Johnson et al. (1997) obtain multiple equilibria in the level of corruption or tax evasion, but the source of multiplicity is again very ifferent. In Anvig an Moene (1991), the complementarity originates in the interaction between the profitability of corruption 4 For a relate iscussion of populism in Latin America, see Dornbusch an Ewars (1991). 5 See, for example, Baumol (1990), Murphy et al. (1993), an Angeletos an Kollintzas (1999).

4 1230 ARTICLE IN PRESS A. Alesina, G.-M. Angeletos / Journal of Monetary Economics 52 (2005) an the number of corrupt officials; in Johnson et al. (1997), multiplicity emerges because the larger the unofficial sector, the smaller the tax base, the lower the amount of public goos provie by the government to the official sector, an hence the lower the incentive of firms to operate in the official sector. The rest of the paper is organize as follows. Section 2 introuces the moel. Section 3 examines the interaction between past an current politico-economic outcomes. Section 4 characterizes the equilibrium policy for a given history. Section 5 analyzes the steay state(s). Section 6 further iscusses the implications of our results an Section 7 conclues. All proofs are in the Appenix. 2. The moel We consier a non-overlapping-generations moel. Each generation consists of a large number of agents (a measure-one mass, inexe by i an istribute uniformly over ½0; 1ŠÞ. Agents live only for one perio an are connecte to past an future generations via intergenerational wealth transfers an parental investment (bequests, eucation, status, etc.). During their lives, agents engage in two types of economic activity: a prouctive activity (work, invest, etc.) an a rent-seeking one (corruption, lobbying etc.). Preferences for reistribution originate from two sources: a selfish motive an an altruistic eman for fairness. Prouction an corruption. Wealth net of taxes, transfers, an rent seeking is the prouct of innate ability, effort, an parental investment. For agent i in generation t, this is given by w it ¼ A it e it þ k it 1, (1) where A it enotes the agent s innate ability, e it enotes his effort, an k it 1 his parents investment or bequest. We let reistribution be the only reason for the existence of a government. Following Romer (1975) an Meltzer an Richar (1981), we assume that the government imposes a flat tax on iniviual wealth in orer to finance a lump-sum transfer across all agents (or some sort of reistributive public goo). Unlike earlier work, however, we introuce corruption by letting a fraction of government resources be up for grabs. In particular, enoting with G t the size of the government in perio t; R t the resources that are up for grabs, an T t the resources that remain for lump-sum reistribution, we let T t ¼ð1 fþg t an R t ¼ fg t, (2) where f 2½0; 1Š parametrizes the extent of corruption. 6 R t in turn is split among the agents on the basis of their rent-seeking activity: agent i receives a portion z it =Z t of the total pie, r it ¼ z it R t, (3) Z t where Z t is the aggregate, an z it is his own, level of rent seeking. The latter is given by z it ¼ B it x it, where x it is the effort agent i allocates to rent seeking an B it is his efficiency in corruption (the extent of his political connections, his negotiation power vis-a` -vis 6 Olken (2003) collecte ata on a reistributive program for rice in Inonesian villages an foun that between 20% an 40% of the rice collecte for reistribution isappeare in the process, obviously stolen by various village aministrators an their friens.

5 ARTICLE IN PRESS A. Alesina, G.-M. Angeletos / Journal of Monetary Economics 52 (2005) bureaucrats, or his inifference towars the ethics of his business life). Note that rent seeking is a zero-sum game: it affects only the istribution of the pie that is up for grabs, not its size. Disposable wealth is then given by the sum of after-tax wealth, lump-sum transfers from the government, an procees from rent seeking: y it ¼ð1 t t Þw it þ T t þ r it. (4) This is spent on private consumption, which we enote with c it, an parental investment, k it. The agent s buget is thus c it þ k it ¼ y it. (5) The government buget, on the other han, is given by G t ¼ lt t W t þð1 lþt t 1 W t 1, (6) where W t is aggregate wealth in perio t, t t is the tax rate in that perio, an l 2½0; 1Š. We allow lo1 for various reasons. First, this captures the iea that the size of the government an the pie that is up for grabs in one perio is not a function of contemporaneous tax revenues alone. 7 Secon, we coul interpret lo1 as a time-to-buil assumption: welfare programs an other reistributive schemes set in place by one generation partly exten to future generations. Finally, an most importantly, l parametrizes the extent to which generation t internalizes the effect that bigger governments lea to more corruption: the higher l, the higher the same-perio increase in corruption that results from a given increase in tax revenues. Iniviual preferences. Agents preferences are given by U it ¼ u it g it O t, (7) where u it measures the private utility from own consumption, bequests, an effort choices, an O t represents a common isutility generate by unfair social outcomes (to be efine below). The parameter g it measures the strength of the eman for fairness an is allowe to iffer across iniviuals. 8 For tractability, we assume quaratic effort costs an a Cobb Douglas aggregator over consumption an bequests: 1 u it ¼ uðc it ; k it ; e it ; x it Þ¼ ð1 Þ 1 ðc itþ 1 ðk it Þ 1 2 ½ðe itþ 2 þðx it Þ 2 Š, (8) where 2ð0; 1Þ. The first term represents the utility from own consumption an bequests, the secon the isutility of effort. The Cobb Douglas specification implies that optimal consumption an parental investment satisfy c it ¼ð1 Þy it an k it ¼ y it, (9) so that represents the fraction of wealth allocate to parental investment (equivalently, the strength of intergenerational linkages). 7 Note that, as long as we focus on steay states, (6) is equivalent to the more general specification G t ¼ P 1 j¼0 l jt tþj W tþj, with l 0 ¼ l an P 1 j¼1 l j ¼ 1 l. 8 An interesting possibility is that g it is inversely relate to B it, in which case iniviuals who are most proficient at being corrupt are also those least offene by it.

6 1232 ARTICLE IN PRESS A. Alesina, G.-M. Angeletos / Journal of Monetary Economics 52 (2005) Fairness. The concept of fairness we aopt is base upon the istinction between two types of inequality: justifiable inequality inuce by variation in talent an effort, an unjustifiable inequality inuce by variation in corruption an rent seeking. Since wealth is transmitte from one generation to another through parental investment, we nee to keep track of this istinction along each agent s entire family tree. We assume that parental investment is consiere fair only to the extent that it reflects income from effort an talent not income from corruption an rent seeking. We thus efine the fair levels of consumption, bequests, an wealth as ^c it ¼ð1 Þ^y it ; ^kit ¼ ^y it an ^y it ¼ ^w it ¼ A it e it þ ^k it 1. (10) (Throughout, fair levels are inicate by a hat.) Our measure of social injustice is then the average istance between actual an fair utilities: Z O t ¼ ðu it ^u it Þ 2, (11) i where u it ¼ uðc it ; k it ; e i ; x i Þ an ^u it ¼ uð^c it ; ^k it ; e i ; x i Þ. 9 By conitions (8) an (9), utility is quasi-linear in isposable wealth, implying that u it ^u it ¼ y it ^y it for all i an therefore O t ¼ R i ðy it ^y it Þ 2. As we will see later in more etail, ^y it reflects the cumulative contribution of talent an effort throughout the iniviual s family history, while y it also inclues the cumulative contribution of corruption an rent seeking. O t thus takes into account the intergenerational propagation of unjustifiable income. The political process. We assume an unstructure moel of political choice which is represente by the maximization of the following social welfare function: Z U t ¼ U it p i. (12) p : ½0; 1Š!½0; 1Š is a probability measure capturing the istribution of political power. When p i assigns measure one to the meian of the population, this specification essentially nests the meian-voter paraigm. When instea p i is the ientity function, the policy maximizes utility behin the veil of ignorance. Alternatively, p i may assign more weight to the rich or the agents with political connections (i.e., agents with relatively high B it Þ. Equilibrium. Let a it A 2 it an b it B 2 it. To simplify, we assume that ða it; b it Þ are inepenent of each other an that ða it ; b it ; g it Þ are i.i.. across agents but fully persistent over time. A ynasty is thus ientifie with a particular raw ða i ; b i ; g i Þ. Finally, for any parameter y 2fa; b; gg, we let ȳ ¼ R y i i an y ~ ¼ R y i p i enote the simple an politically weighte population averages, D y ¼ y y ~ the istance between the two, an s 2 y ¼ Varðy iþ the variance in the cross-section of the population. We will see that a sufficient statistic for the characteristics of the economy turns out to be the parameter vector E ¼ðf; ~g; D a ; D b ; s a ; s b ; ā; b; ~a; b; ~ Þ. D a an D b play a role similar to the gap between the meian an the mean of the wealth istribution in Meltzer an Richar (1981). s a an s b, on the other han, parametrize the exogenous variation in the fair an unfair sources of wealth, respectively, an affect outcomes only when there is a eman for fairness (~g40þ. We finally efine 9 An alternative efinition of fair utility that gives similar results is ^u it ¼ uð^c it ; ^k it ; e i ; 0Þ.

7 ARTICLE IN PRESS A. Alesina, G.-M. Angeletos / Journal of Monetary Economics 52 (2005) Definition. An equilibrium for economy E is a sequence of policies ft t ; G t g 1 t¼0 allocations fðe it ; x it ; c it ; k it Þ i2½0;1š g 1 t¼0 such that: an (i) Given policy ðt t ; G t Þ an enowment k it 1, the bunle ðe it ; x it ; c it ; k it ; y it Þ maximizes U it subject to (1) an (4) (5), for all i an t. (ii) Given history of policies an allocations ft s ; G s ; ðe is ; x is ; c is ; k is Þ i2½0;1š g t 1 s¼0, the policy ðt t ; G t Þ in perio t maximizes (12), for all t. 3. The interaction of corruption, inequality, an fairness We start by analyzing how inequality, fairness, an corruption affect optimal policy choices an how policies in turn affect the equilibrium levels of inequality, fairness, an corruption. Using Eqs. (4) an (10), the gap between actual an fair income can be ecompose into four terms: y it ^y it ¼ð1 t t Þðw it ^w it Þ t t ^w it þ G t þðr it R t Þ. (13) The first term implies that a higher tax rate corrects more for the unfairness generate by unjustifiable inherite wealth, whereas the secon term implies that a higher tax rate also eprives the iniviual of some of her fair wealth. Therefore, to the extent that w it 1 a ^w it 1 for a positive measure of agents, society faces a trae-off in choosing the size of the government that is optimal from a fairness perspective. The last term, on the other han, captures the net gain or loss of the agent from his participation in the zero-sum game of corruption, which also epens on the size of the government. The trae-off introuce by fairness becomes clear once we use (13) to express O t as a weighte average of the variance ecomposition of wealth inequality: O t ¼ t 2 t Varð ^w itþþð1 t t Þ 2 Varðw it ^w it ÞþVarðr it Þþcov s t, (14) where Varð:Þ enotes variance in the cross-section of agents an cov s t inclues constants an covariance terms (see Appenix for the erivation an the exact formula). When ðt t ; G t Þ¼0, the above reuces to O t ¼ Varðw it ^w it Þ, thus measuring how unfair the wealth istribution woul be in the absence of government intervention; when instea ðt t ; G t Þ40, the above incorporates the effect of reistribution an corruption. To gain further intuition, ignore for a moment the covariance terms in Eq. (14) an suppose that minimizing O t is the only policy goal, taxation is not istortionary, an the wealth istribution is exogenous. The optimal tax rate is then given by 1 t t ¼ Varð ^w itþ Varðw it ^w it Þ. (15) The right-han sie represents the signal-to-noise ratio in the wealth istribution: the signal is the fair component of wealth, the cumulative effect of talent an effort; the noise is the unfair component, the cumulative effect of corruption an rent seeking. The optimal tax rate is ecreasing in this signal-to-noise ratio, reflecting the esire to correct for the inequality generate by corruption. The wealth istribution, however, is enogenous in equilibrium; as we show next, the signal-to-noise ratio itself epens on current an past tax policies.

8 1234 ARTICLE IN PRESS A. Alesina, G.-M. Angeletos / Journal of Monetary Economics 52 (2005) Consier the equilibrium allocations for a given policy. Househol i in generation t is born with a given k it 1 an chooses ðc i t ; ki t ; ei t ; xi tþ so as to maximize his utility subject to his buget constraint, taking ðt t ; G t Þ an O t as given. The optimal levels of consumption an parental investment are given by conition (9). Utility then reuces to u it ¼ y it e 2 it =2 x 2 it =2, implying that the optimal levels of effort evote to prouction an rent seeking are, respectively, e it ¼ð1 t t ÞA it an x it ¼ B it fg t =Z t. (16) The equilibrium level of corruption is thus increasing in the fraction of government resources up for grabs: qffiffiffiffiffiffiffiffiffiffiffi Z t ¼ bfg t. (17) Combining (16) an (17), we infer that A it e it ¼ð1 t t Þa it an r it ¼ðb it = bþfg t. (18) To simplify the notation, we henceforth normalize b ¼ 1. Let t t s 1 Q t j¼s ð1 t jþ enote the cumulative rate of taxation between perios s an t, with the convention t t s ¼ 0 when s4t. As we show in the Appenix, iterating on (1), (4), an (9) implies that, in equilibrium, actual wealth is w it ¼ A it e it þ k it 1, with k it 1 ¼ X t s ð1 t t 1 sþ1 Þ½ð1 t sþa is e is þ G s þðr is R s ÞŠ. (19) spt 1 In contrast, fair wealth is ^w it ¼ A it e it þ ^k it 1, with ^k it 1 ¼ X t s A it e it. (20) spt 1 Combining the above with (18), we infer that heterogeneity in A it generates variation in the fair level of wealth (the signal ^w it Þ, whereas heterogeneity in B it generates variation in the unfair component of wealth (the noise w it ^w it Þ. The relative contribution of the two types of inequality epens on past policies: the perio-t equilibrium signal-to-noise ratio reuces to P Varð ^w it Þ Varðw it ^w it Þ ¼ ½ spt t s ð1 t s ÞŠ 2 s 2 a ½ P spt 1 t s t t 1 s ð1 t s ÞŠ 2 s 2 a þ½p spt 1 t s ð1 t t 1 sþ1 ÞðfG sþš 2, s 2 b (21) where s 2 a ¼ Varða iþ, s 2 b ¼ Varðb iþ, an ða i ; b i ÞðA 2 i ; B2 i Þ. This ratio tens to ecrease with G s for every spt 1, because a history of big governments means that corruption has playe a major role in shaping the wealth istribution. The impact of t s, on the other han, is generally non-monotonic. When there has been no corruption in the past, a higher tax in the past means a less fair wealth istribution toay; but when there has been corruption in the istant past, a higher tax in the more recent past may have alreay correcte for the unfairness of the earlier corruption. Notwithstaning the latter effect, a society that has a history of high-tax istortions, big governments, an pervasive corruption will ten to inherit an unfair wealth istribution, which in turn may raise the altruistic eman for reistribution in the present.

9 ARTICLE IN PRESS A. Alesina, G.-M. Angeletos / Journal of Monetary Economics 52 (2005) Moreover, if the variation in rent-seeking abilities across the population ðs b Þ is high, an economy with a history of high taxation an high corruption may also inherit a high overall level of inequality. This may raise the selfish eman for reistribution. We conclue that the interaction of corruption with either the fairness concern or the selfish motive introuces a complementarity between past an current political choices: the equilibrium tax toay may be an increasing function of the tax yesteray. 4. Equilibrium policy In this section we characterize the equilibrium policy t t for a given history ft s g spt 1.We focus on stationary histories an begin by examining how a particular iniviual ranks ifferent policy alternatives in equilibrium. Proposition 1. Suppose t s ¼ t 2½0; 1Š for all sot. The utility of agent i in perio t is U it ¼ Vðt t ; t; a i ; b i Þ g i Oðt t ; tþ, (22) where Vðt t ; t; a; bþ 1 2 at2 t þ 1 2 bfg tðt t ; tþþ 1 l Gðt t ; tþ þ t t ð1 t t Þðā aþ l þ t t 1 ð1 tþ ½ð1 tþ2 ðā aþþfgðt; tþð1 bþš þ fgðt t ; tþðb i 1Þ, ð23þ ð1 tþ 2 2 ð1 tþ Oðt t ; tþ t t ð1 t t Þþð1 t t Þ s 2 a 1 ð1 tþ 1 2 þ Gðt t ; tþþð1 t t Þ Gðt; tþ 1 ð1 tþ f 2 s 2 b þ 1 l 2 ð1 Þl ðgðt t; tþ Gðt; tþþ, ð24þ Gðt t ; tþ 1 1 ½lt tð1 ð1 Þt t tþþð1 lþtð1 tþšā. (25) This efines i s preferences over t t ; the expressions in Eqs. (22) (25) are complicate, but their interpretation is simple. Conition (24) gives the equilibrium level of social injustice. The first term represents the injustice generate when a positive tax reallocates income from more worthy (i.e., more talente, har-working) to less worthy agents. This term is positive only if s a 40, that is, only if there is justifiable inequality. The secon term represents the injustice generate by corruption an rent seeking. This term is positive only if f40 an s b 40, that is, only if there is corruption an unjustifiable inequality. Moreover, this term is non-monotonic in t t : a bigger government corrects more for the corruption in the past but also opens the oor to more corruption toay. Both terms epen on the past level of t, as the size of the government in the past has etermine the istribution of k it 1 inherite toay The last term in Eq. (24) measures Y ^Y (see the Appenix).

10 1236 ARTICLE IN PRESS A. Alesina, G.-M. Angeletos / Journal of Monetary Economics 52 (2005) Conition (23), on the other han, gives the private utility an agent enjoys from his effort choices an wealth. The first term represents the istortionary costs of taxation an corruption; the secon an thir terms capture the reistribution of contemporaneous income an inherite bequests; the last term is the net transfer enjoye from rent-seeking activity. Finally, conition (25) gives the equilibrium size of the government. When ¼ 0 an l ¼ 1, in which case the moel reuces to a static economy, (25) reuces to G t ¼ t t ð1 t t Þ. More generally, (25) exhibits the usual Laffer-curve effect: at very high levels of taxation, a further increase in t t istorts incentives an reuces income so much that tax revenues fall. At the same time, G t is a ecreasing function of t, for higher tax istortions in the past imply less aggregate income in the past an therefore a lower tax base in the present. Consier now how t t is chosen in equilibrium. By (22), iniviual utilities are linear in iniviual characteristics ða i ; b i ; g i Þ. The policy objective thus reuces to Z U t ¼ u i p i ¼ Vðt t ; t; ~a; bþ ~goðt ~ t ; tþ; an since t t maximizes U t, we have the following result. 11 Proposition 2. Suppose t s ¼ t for all sot. The equilibrium policy in perio t is t t ¼ Fðt; EÞ, where F ðt; EÞ arg max t 0 2½0;1Š fvðt0 ; t; ~a; ~ bþ ~goðt 0 ; tþg. (26) 5. Multiple steay states The mapping F in (26) represents the best response of generation t to a stationary history. Asteay state is any fixe point of this mapping, that is, any t such that t ¼ Fðt ; EÞ. In orer to gain intuition into the steay-state properties of the moel, consier first f ¼ ~g ¼ 0, that is, isregar both corruption an fairness. To simplify, let also l ¼ 1. The mapping F then reuces to t t ¼ FðtÞ ¼ D a þ ð1 tþ 2 =ð1 ð1 tþþd a, (27) ā þ D a where, recall, D a ā ~a. When ¼ 0, meaning that there are no intergenerational links, the above gives t t ¼ D a =ðā þ D a Þ. This result is ientical to that in Meltzer an Richar (1981): the optimal tax rate is increasing in D a, which can be interprete as the istance between the mean an the meian of the population. When 40, the aitional term ½ð1 tþ 2 =1 ð1 tþšd a reflects the gain from reistributing inheritances: the higher the istance between the mean an the meian inheritance, the higher the gain from reistribution for the meian agent. In the absence of corruption, a higher level of reistribution in the past implies less inequality in inheritances an therefore a lower gain from reistribution toay. The 11 Note that policy preferences in any given perio epen only on realize past policies, not expectations about future policies. This is ue to the warm-glow specification of intergenerational altruism an rules out any form of strategic interaction across generations.

11 ARTICLE IN PRESS A. Alesina, G.-M. Angeletos / Journal of Monetary Economics 52 (2005) current tax τ t = F (τ) historical tax τ Fig. 1. The stanar Meltzer Richar effect unique steay state in the absence of corruption. optimal t t in (27) ecreases with t an F intersects the 45-egree line only once, as illustrate by the soli line in Fig This ensures that the steay state is unique. If we allow for a fairness concern ð~g40þ but continue to assume no corruption ðf ¼ 0Þ, the optimal level of reistribution is zero from a fairness perspective. The Meltzer Richar effect, however, kicks in as long as D a 40. All that fairness then oes is to increase the cost of taxation, as a higher tax increases the gap between fair an actual outcomes. The F curve thus shifts own, an the optimal tax is lower than when ~g ¼ 0, as illustrate by the otte line in Fig. 1. Nevertheless, the steay state remains unique. Consier next the impact of corruption ðf40þ in the absence of a fairness concern ð~g ¼ 0Þ. Also let D a ¼ 0 an D b 40, that is, isregar the usual Meltzer Richar effect but allow for skewness in the istribution of rent-seeking abilities. This introuces a novel motive for reistribution. If the size of the government in the past is large, then the income from corruption an rent seeking in the past is also high. With D b 40 ¼ D a, this implies that the meian of the income istribution in the present is poorer than the mean, not because his parents have been less prouctive, but because his parents have been less effective in rent seeking. Hence, inequality originating in corruption in the past creates support for reistribution in the present. But as the optimal size of the government toay is positive, the level of corruption toay is also positive, which tens to make high levels of government an corruption self-sustaining. On the other han, if a society starts with a history of no (or small) government an no (low) corruption, there is no corruption-born inequality in the present, which together with the fact that there is no (low) stanar Meltzer Richar effect implies that the optimal size of government in the present is zero (small). We conclue that multiple levels of corruption an reistribution can be self-sustaine even in the absence of any concern for fairness. Such a situation is illustrate by the soli line in Fig. 2: there are two stable steay states, one with t ¼ 0 an another with t40, as well as an intermeiate unstable one, which we isregar. 12 All numerical examples are only illustrative.

12 1238 ARTICLE IN PRESS A. Alesina, G.-M. Angeletos / Journal of Monetary Economics 52 (2005) current tax τ t = F (τ) historical tax τ Fig. 2. Self-sustaine corruption multiple steay states in the absence of both the stanar Meltzer Richar effect an the concern for fairness. The coefficient l now plays an important role. The otte line in Fig. 2 illustrates the impact of an increase in l: once l is sufficiently high, the multiplicity of steay states may isappear. This is because the attempt to reistribute from the high-b iniviuals to the low-b ones becomes self-efeating when l is very high, as then a large fraction of the tax revenue is up for grabs by the very same high-b iniviuals whom taxation is suppose to target. In other wors, the higher l is, the more the current generation internalizes the effect that an increase in taxation an reistribution leas to an increase in corruption. Finally, consier the interaction of corruption an fairness (f40 an ~g40). To make the argument sharper, let D a ¼ D b ¼ 0. If ~g were zero, taxation woul have only costs an no benefits, so that t t ¼ 0 woul be both the unique equilibrium an the unique steay state. When ~g40, Fð0Þ ¼0 an t ¼ 0 remains a steay state: a history of no taxation an no government means also a history of no corruption, so that the wealth istribution is fair an there is no nee to reistribute for fairness reasons. If, however, the economy inherits a history of high taxes an big governments, this means also a history in which corruption has playe some role in etermining the wealth istribution, in which case there is necessarily a esire to reistribute. It is then possible that, together with t ¼ 0, there also exists a steay state in which t40. Such a possibility is illustrate by the soli line in Fig. 3. The two extreme intersection points of F with the 45- egree line ientify the two locally stable steay states. The lower one correspons to t ¼ 0, Z ¼ 0, an O ¼ 0 (low taxation, low corruption, an fair outcomes), the higher one to t40; Z40, an O40 (high taxation, high corruption, an unfair outcomes). The impact of l is similar as in the earlier case of self-sustaine corruption. As illustrate by the otte line in Fig. 3, an increase in l reuces the incentive to reistribute an limits the possibility of multiple steay states. The only ifference is that taxation now becomes self-efeating, not because it increases the resources that are up for grabs by high-b iniviuals, but rather because it increases the inequality inuce by corruption. In the examples epicte in Figs. 2 an 3, the lower steay state has a zero tax rate: if there has been no taxation an no corruption in the past, no taxation is optimal toay as

13 ARTICLE IN PRESS A. Alesina, G.-M. Angeletos / Journal of Monetary Economics 52 (2005) current tax τ t = F (τ) historical tax τ Fig. 3. The effect of fairness multiple steay states in the absence of any self-motivate reistribution current tax τ t = F (τ) historical tax τ Fig. 4. The effect of fairness combine with the Meltzer Richar effect multiple steay states. well. This is an artifact, however, of the absence of any other motive for taxation. If instea there were some exogenous amount of government spening to be finance, the lower steay state coul have a positive tax rate. The same is true if fairness interacts with selfmotivate reistribution (that is, if we combine ~g; s a ; s b 40 with D a 40Þ. This case is illustrate by Fig. 4. Summarizing the above analysis, we have the main result of the paper. Proposition 3. A steay state for economy E is any fixe point t ¼ Fðt ; EÞ. If there is no room for corruption ðf ¼ 0Þ, there exists a unique steay state. If instea there is room for corruption ðf40þ couple with either skewness in rent-seeking abilities ðd b 40Þ or a eman for fairness ð~g40þ, there robustly exist multiple steay states.

14 1240 ARTICLE IN PRESS A. Alesina, G.-M. Angeletos / Journal of Monetary Economics 52 (2005) Discussion i. When there is no corruption, the steay state is unique, as in Meltzer an Richar (1981). In this case, a eman for fairness affects the level but not the eterminacy of the steay state it merely introuces a trae-off between the private goo of reistribution from the rich to the poor an the public goo of fairness. ii. When there is corruption, we may have a complementarity between past an current policies for two reasons: either because more corruption in the past means more inequality in the present, or because more corruption in the past means more unfairness in the present. Either one may lea to multiple steay states or, more generally, to persistence in politico-economic outcomes. iii. We coul easily recast our main result in a static (one-generation) economy as multiple self-fulfilling equilibria. We chose to focus on the ynamic version merely to emphasize the role of history. Different regimes are explaine by ifferent historical experiences, not ifferent self-fulfilling expectations. iv. Atheoretical preiction share by many moels of reistribution is that more inequality leas to more reistribution. There is plenty of evience, however, that this preiction is rejecte by the ata. 13 Our moel may help explain this puzzle in two ways. First, an economy with less inequality may have more reistribution because more of that inequality is ue to corruption an is thus consiere unfair, or because there is a stronger eman for fairness; in this case, the missing variable is the level of corruption or the strength of concerns for fairness. Secon, an economy with less inequality may have more reistribution because it rests in a higher steay state; in this case, the missing variable is history. v. Astrong correlation isplaye by the ata is that corruption ecreases with income per capita (e.g., Mauro, 1995; Knack an Keefer, 1995). One coul interpret these ata in the context of our moel as suggesting that f is higher in poorer countries. An alternative interpretation is that poverty an corruption are both enogenous. In this case, certain countries may be stuck in a corruption-inuce poverty trap. Note that poorer countries ten to have smaller governments as measure by the ratio of government spening over GDP; yet, government intrusiveness in the economy rely also on regulations an other various sources of intervention that go beyon the share of spening over GDP an that ten to be higher in poorer economies. 14 vi. When there are multiple steay states, the one with bigger government (higher tþ is inferior in the sense that fewer resources are evote to prouctive activities, while more resources are waste in the zero-sum game of rent seeking. However, in general, the two steay states cannot be Pareto ranke for two reasons. First, those who are especially prouctive in rent seeking may prefer the high corruption regime. Secon, the poor may prefer a high level of reistribution even at the cost of high corruption. An interesting possibility is then that a large corrupt government may raw support from an unlikely coalition of the very poor an the rich insiers. This is a coalition of those who benefit 13 See for example Perotti (1996). Alesina an Glaeser (2004) ocument in etail that there are both more pretax inequality an less reistribution in the Unite States than in continental Europe. Di Tella an Mc Culloch (2003) similarly fin that more inequality often leas to the election of right-wing governments. 14 Neeless to say, there are many reasons unrelate to the story highlighte in this paper that explain the growth of government as a function of per capita income. For a survey of the literature of the size of the government, see Mueller (2003).

15 ARTICLE IN PRESS A. Alesina, G.-M. Angeletos / Journal of Monetary Economics 52 (2005) from high reistribution per se an those who are hurt by taxation per se but are close to the levers of power. This seems a pretty accurate escription of several populist governments in Latin America, as emphasize for instance by Dornbusch an Ewars (1991). vii. Fairness can be lower in the steay state with bigger government, for a larger proportion on wealth can then be ue to corruption. So, paraoxically, the attempt to correct the impact of corruption an increase fairness may sustain a steay state which is less fair. This is the sort of paraox emphasize by Di Tella an Mc Culloch (2003) when they ask, why oesn t capitalism flow to poor countries? The answer that our paper proposes is that the perception that capitalism is corrupt an that government intervention is necessary can be self-sustaining; quite unfortunately, attempts to reuce unfairness often result, not only in higher efficiency losses, but also in more corruption an less fair outcomes. 7. Concluing remarks The main message of our analysis is that reistributive an regulatory policies intene to reuce inequality or improve the fairness of economic outcomes may bring about even more opportunities for corruption. This creates a policy ilemma: a small government oes not correct enough for market inequalities an injustices; a large government increases corruption an rent-seeking. Many policy-makers an observers appear to be aware of this trae-off. Especially in eveloping countries, public spening towar the poor is often mis-targete an creates pockets of corruption an favoritism; an often certain lobbies come out as big winners at the expense of the truly neey. Nevertheless, even well-intene policy-makers woul resist calls for cutting these programs because they perceive the cost of corruption as worth paying this is often the only way to at least partially improve the conition of the poor. What is perhaps less unerstoo is that the willingness to accommoate some corruption in the present may lea to a vicious cycle where high levels of government intervention, market inefficiency, an corruption are self-sustaine in perpetuity. The failure to internalize this intergenerational externality can jeoparize the long-run effectiveness of well-intene policies. Appenix Proof of Conition (14). From the familiar result that EðX 2 Þ¼ðEXÞ 2 þ VarðXÞ, we have O t ¼ R i ðy it ^y it Þ 2 ¼ðY ^YÞ 2 þ Varðy it ^y it Þ, where Y ^Y ¼ R i ðy it ^y it Þ. By the assumption that a it an b it are inepenent, Covð ^w it ; r it Þ¼0. (13) thus implies Varðy it ^y it Þ¼ð1 t t Þ 2 Varðw it ^w it Þþt 2 t Varð ^w itþþvarðr it Þ þ 2ð1 t t Þt t Covð ^w it ; w it ^w it Þþ2ð1 t t Þ Covðr it ; w it ^w it Þ. Combining the above an letting cov s t ¼ðY ^YÞ 2 þ 2ð1 t t Þt t Covð ^w it ; w it ^w it Þþ2ð1 t t Þ Covðr it ; w it ^w it Þ proves (14). &

16 1242 ARTICLE IN PRESS A. Alesina, G.-M. Angeletos / Journal of Monetary Economics 52 (2005) Proof of Conitions (19), (18), an (21). To simplify notation, let q t ð1 t t Þ, Q t t ¼ 1; Q t s Q t j¼sþ1 q j for spt 1, p t ½ð1 t t ÞA t e t þ T t þ r t Š, an rop the inex i. Note that q t 2ð0; 1Þ an therefore Q t s 2ð0; 1Þ as well. We can then write k t ¼ y t ¼ q t k t 1 þ p t an therefore k t ¼ P spt Qt s p s. Combining the latter with Q t s ¼ t s ð1 t t sþ1 Þ an p s ¼ ½ð1 t s ÞA s e s þ T s þ r s Š, using T s ¼ G s R t, an expressing the result for t 1 instea of t, gives (19). Next, by (16), z it ¼ B it x it ¼ðB 2 it =Z tþr t ¼ðB 2 it =Z tþfg t. By implication, the equilibrium level of corruption satisfies Z t ¼ R i z it ¼ R i B itx it ¼ R i B2 it fg t=z t. Solving for Z t gives (17) an combining this with (16) gives the secon part of (18). Finally, from (19), (20), an (18), the assumption that a it ¼ a i an b it ¼ b i for all t, an the normalization b ¼ 1, we have w it ^w it ¼ X t s f t t 1 s ð1 t s Þa i þð1 t t 1 sþ1 ÞðG s þðb i 1ÞfG s Þg, spt 1 ^w it ¼ X t s ð1 t s Þa i. spt Calculating the variances gives (21). & Proof of Proposition 1. Consier a stationary history, t s ¼ t for all spt 1, in which case we also have t t s ¼ 1 ð1 tþt sþ1 an G s ¼ G; W s ¼ W, Y s ¼ Y, K s ¼ K, for all spt 1. To compute the stationary levels G; W; Y, an K, note that Y ¼ R i y i ¼ð1 tþw þ G, which together with G ¼ ltw þð1 lþtw ¼ tw gives Y ¼ W, an therefore K ¼ R k i ¼ Y ¼ W. Combining this with W ¼ R i ða ise is þ k is 1 Þ¼ð1 tþāþk gives W ¼ 1=ð1 Þð1 tþā, an therefore G ¼ 1=ð1 Þtð1 tþā an K ¼ s=ð1 Þð1 tþā. Now consier equilibrium outcomes in perio t. Using K t 1 ¼ K, we now have W t ¼ð1 t t Þā þ K t 1 ¼ 1 1 ð1 ð1 Þt t tþā (28) which together with G t ¼ lt t W t þð1 lþtw gives (25). When t s ¼ t for all spt 1, P spt 1 t s ð1 t sþ1 t 1 Þ¼=ð1 ð1 tþþ an therefore w it ¼ð1 t t Þa i þ 1 ð1 tþ fð1 tþ2 a i þðg þðb i 1ÞfGÞg, (29) whereas ^w it ¼ð1 t t Þa i þ 1 ð1 tþa i. It follows that y it ^y it ¼ð1 t t Þw it þ G t þðr it R t Þ ^w it ¼ t t ð1 t t Þþ 1 ð1 tþ ð1 t tþð1 tþ 2 ð1 tþ 1 þ G t þð1 t t Þ 1 ð1 tþ G ð1 þ fðb i 1ÞÞ. Next, using (13) an w it ^w it ¼ k it 1 ^k it 1, we get Y ^Y ¼ðK t 1 ^K t 1 Þ þðg t t t W t Þ. By the expressions for G t an G; G t t t W t ¼ ð 1 l l ÞðG t GÞ, while a i

17 ARTICLE IN PRESS A. Alesina, G.-M. Angeletos / Journal of Monetary Economics 52 (2005) K ^K ¼ ðw ^WÞ ¼ðY ^YÞ. It follows that Y ^Y ¼ 1 l ð1 Þl ðg t GÞ an therefore O t ¼ Varðy it ^y it ÞþðY ^YÞ 2 ¼ t t ð1 t t Þþ 1 ð1 tþ ð1 t tþð1 tþ 2 2 ð1 tþ 1 s 2 a 2 þ G t þ 1 ð1 tþ ð1 t tþg f 2 s 2 b þ 1 l 2 ð1 Þl ðg t GÞ. Substituting G ¼ Gðt; tþ an G t ¼ Gðt t ; tþ an rearranging gives (24). Finally, consier the private utility of agent i in perio t. Since the history is stationary an iniviual characteristics are fully persistent, we have that k is ¼ k i (an similarly y is ¼ y i, r is ¼ w i, r is ¼ w i Þ for all spt 1. From (8) an (16), u it ¼ 1 2 ð1 t tþ 2 a i þð1 t t Þk i þ G t þð 1 2 b i 1ÞfG t. (30) Using the fact that G t t t W t ¼ ð1 lþ=lðg t GÞ an t t W t ¼ t t ðð1 t t Þā þ KÞ, an rearranging, we get u it ¼ 1 2 a i þ k i þ 1 l G 1 l 2 a it 2 t þ 1 2 b ifg t þ 1 l G t l þ t t ð1 t t Þðā a i Þþt t ðk k i Þþðb i 1ÞfG t. Next, as in (29), k i ¼ 1 ð1 tþ ½ð1 tþ2 a i þ G þðb i 1ÞfGŠ, an therefore K k i ¼ 1 ð1 tþ ½ð1 tþ2 ðā a i Þþð1 b i ÞfGŠ. (32) That is, agent i has inherite more wealth than the mean if his a i an/or b i is sufficiently high. Combining the above with (31), an ignoring the term 1 2 a i þ k i þðð1 lþ=lþg which oes not epen on t t, we get u it ¼ 1 2 a it 2 t þ 1 2 b ifg t þ 1 l l G t þ t t ð1 t t Þðā a i Þ þ t t 1 ð1 tþ fð1 tþ2 ðā a i Þþð1 b i ÞfGgþðb i 1ÞfG t. Substituting G ¼ Gðt; tþ an G t ¼ Gðt t ; tþ into the above gives (23) an conclues the proof. & Proof of Propositions 2 an 3. It follows from the analysis in the main text. & ð31þ References Alesina, A., Angeletos, G.M., Fairness an reistribution. American Economic Review 95, Alesina, A., Glaeser, E., Fighting Poverty in the US an Europe: A Worl of Difference. Oxfor University Press, Oxfor, UK.

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