1 ECONOMICS & POLITICS Volume 16 November 2004 No. 3 INEQUALITY, REDISTRIBUTION, AND RENT-SEEKING FRANCISCO RODRI GUEZ This paper presents a non-m...

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0954-1985 November 2004

No. 3

INEQUALITY, REDISTRIBUTION, AND RENT-SEEKING FRANCISCO RODRI´GUEZ

This paper presents a non-median voter model of redistribution in which greater inequality leads to lower redistribution. Bargaining between interest groups and politicians over exemptions implies that individuals with suﬃciently high income will not pay taxes in equilibrium. Therefore, voters will set tax rates low enough so as to control the incentives for rent-seeking. An increase in inequality, by putting more income in the hands of individuals that can buy exemptions, will lead to lower equilibrium redistribution. The model can be used to account for a negative relationship between inequality and growth and provides a new explanation of why the poor do not expropriate the rich in democracies.

Civil Government, so far as it is instituted for the security of property, is in reality instituted for the defence of the rich against the poor, or of those who have some property against those who have none at all. (Wealth of Nations, V.i.b.)

1. INTRODUCTION

IS

REDISTRIBUTION greater in more unequal societies? Casual observation seems to answer this question in the negative. The most unequal countries of the world, such as Brazil and South Africa, do not spring to mind when one conjures up examples of large welfare states. Even among countries that have similar levels of income, the contrast between the United States’ late development of welfare state institutions vis-a`-vis Europe suggests that more unequal societies tend to redistribute less. More careful empirical analysis has consistently conﬁrmed these casual inferences. Benabou (1996) surveys the cross-country evidence linking inequality and redistribution and lists ten studies out of which nine failed to uncover a consistently signiﬁcant relationship of any sign between these variables.1 Perotti (1996) regresses six indicators of redistribution on inequality and ﬁnds very little pattern in their relation, regardless of whether the sample is restricted to democracies or not. Rodrı´ guez (1999a) ﬁnds no Contact address: IESA POBA International No. 646, PO Box 025255, Miami, FL 331025255, USA. E-mail: [email protected] 1 The tenth study (Lindert, 1996) ﬁnds a consistently negative relationship between inequality and redistribution among OECD economies. This negative link between inequality and redistribution for OECD economies has been conﬁrmed by Rodrı´ guez (1998), who does point out that the ﬁnding is somewhat sensitive to the sample of countries used.

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evidence of a link between inequality and redistribution in cross-state regressions using higher quality US data. In fact, Pineda and Rodrı´ guez (1999) have found a strong negative association between redistribution and capital’s share of GDP.2 Despite this preponderance of evidence to the contrary, existing theories of the political economy of redistribution point in the direction of a positive association between inequality and redistribution. In traditional models, built on the assumption of well-functioning democratic systems,3 inequality creates redistributive pressures that even in non-democratic countries translate into more redistributive policies. As inequality increases and the median voter becomes poorer, her incentives to vote for redistribution also increase, leading her to choose higher levels of transfers. Our paper will attempt to bridge this disagreement between data and theory by presenting a model of politics in which there can be a negative association between inequality and redistribution. The channel we will appeal to is that of political inﬂuence. In our model increased inequality is synonymous with a transfer of economic resources from poor to rich. If such a transfer results in increased access to political power by the rich, then it will also result in a reduction in the capacity of the poor to control the political system. The end result will be a reduction in the average tax burden that the poor can impose on the rich and a more regressive tax system. The process through which this occurs is set out in the following pages, where we describe how individuals bargain over tax favors with policy-makers who use political contributions to buttress their political power. Voters are not naive, though: they perfectly understand the workings of the political process and react to it. Precisely for this reason, they will decide to keep taxes low so as to control the incentives for rent-seeking. Theoretical work on the relationship between inequality and growth has relied on the presumed existence of a positive link between inequality and redistribution (Alesina and Rodrik, 1994; Persson and Tabellini, 1994).4 In those models inequality raises redistribution; redistribution in turn generates disincentives for capital accumulation and growth. In this paper we show that our model, in which inequality is negatively associated with redistribution, can provide an alternative explanation for why inequality is harmful for growth. In our model increased inequality, which enhances the 2 As Pineda and Rodrı´ guez point out, there are good reasons to believe that capital’s share of GDP may be a superior indicator of income inequality than indicators derived from existing income distribution data. These authors argue that, whereas income inequality data are often drawn from studies of questionable comparability, the standardization of the UN System of National Accounts makes capital shares highly comparable. They do, however, warn that the correlation between Gini coeﬃcients and capital’s share of income after controlling for GDP is quite low. 3 Meltzer and Richard (1981), Alesina and Rodrik (1994), and Persson and Tabellini (1994). 4 Benabou (1996) deals with the eﬀect of alternative assumptions about the relationship between inequality and redistribution on the growth–inequality link.

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political power of the rich, also increases the amount of resources deviated from productive activities into directly unproductive rent-seeking activities. By taking away resources which otherwise could have been invested, increased rent-seeking harms capital accumulation and growth. An alternative way to pose the question of the relationship between inequality and redistribution is by asking why it is that in democratic capitalist societies, in which political rights are equally distributed but economic rewards are not, the losers from the economic process do not decide to expropriate the winners. This is a question that has puzzled economists and political thinkers for ages, and which led a number of eighteenth- and nineteenth-century political economists to consider restriction of the franchise to property owners a necessary evil without which capitalism would fall apart. In the minds of the likes of David Ricardo and Benjamin Constant, capitalism and democracy were incompatible.5 An alternative point of view can be traced back to Alexis de Tocqueville (1835), whose comments on early American political arrangements point to the relationship between the extension of the franchise and the proportion of the electorate favoring redistribution. Meltzer and Richard (1981) coupled Tocqueville’s insightful intuition with the observation that rational voters could understand how wholesale expropriation of the rich would destroy incentives for capital accumulation and thus work against voters’ interests. They formulated a formal model of voting over redistribution, in which they established that tax rates in political equilibrium would be kept well below expropriation levels and that there would be an increasing relationship between inequality and redistribution, as more unequal societies are characterized by higher incentives for the median voter to support highly redistributive policies. If the question is posed as one of why the poor do not expropriate the rich in democracies, then our explanation is that they do not do so because they cannot do so. The rich have access to political power which allows them to insulate themselves from redistributive pressures. A nominal tax rate of unity would generate such perverse incentives for policy-makers to strike deals with the wealthy that it would be against the interests of predominantly poor voters to set it so high. Voters understand this power and set tax rates low enough so as to keep the incentives for rent-seeking under control. Better low taxes that are paid than high taxes that are not. In our model, the power of the rich is not predicated on an unexplained hegemony of the ruling class nor on the absence of free-rider considerations. Rather, we study a game in which each wealthy individual cannot aﬀect the overall redistributive tax rate but rather bargains over personalized tax favors with the policy-maker. It is the uncoordinated actions of all wealthy 5 For example, Ricardo argued that suﬀrage should only be extended ‘‘to that part of them [the people] which cannot be supposed to have an interest in overturning the right to property’’ (Ricardo, 1818 [1951]).

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individuals that sum up to a whole in which the rich have the power to partially thwart the redistributive eﬀorts of the poor. In this sense, we provide microfoundations for the claim that economic power is political power that is not open to the charge of being a functional explanation.6 Our model emerges from the conﬂuence of three types of theories of redistribution. In building a model in which rational actors vote over redistributive policies we follow the contributions of Downs (1957) as applied to the positive analysis of the size of government by Meltzer and Richard (1981, 1983) and integrated into theories of economic growth by Alesina and Rodrik (1991, 1994), Persson and Tabellini (1994), and Perotti (1993). In taking into account the eﬀect on political equilibrium of interest groups we borrow from a diﬀerent and equally important literature pioneered by Peltzman (1976) and Becker (1983) and later advanced by Baron (1994), Austen-Smith (1987), Grossman and Helpman (1996) and Grossman et al. (1996). And by formalizing the claim that economic and political power are correlated, our model borrows from the political theory literature on the state initiated by Marx and Engels’s (1848) statement that under capitalism ‘‘the executive of the modern State is but a committee for managing the common aﬀairs of the whole bourgeoisie,’’ a lead that was followed by various generations of mostly, although not exclusively, Marxist and radical researchers.7 In section 2 we present our model in detail. It consists of a simple game between voters, politicians, and capitalists. We derive our basic result that greater inequality leads to less redistribution under a general functional form for the distribution of income as well as under speciﬁc empirically plausible speciﬁcations. We also provide microfoundations for our key assumption, the existence of increasing returns in political inﬂuence. Section 3 incorporates our model into a simple two-period model of capital accumulation. We show that when the eﬀects of rent-seeking on capital accumulation are taken into account, inequality can lead to lower growth via increased rent-seeking by richer capitalists eager to escape taxes. We furthermore establish that the main results of our model are maintained when we design the tax-cum-subsidy scheme to be incentive-compatible. Section 4 concludes. 2. A MODEL OF REDISTRIBUTION AND POLITICAL INFLUENCE

2.1

The Basic Model

In this section we present a model of political inﬂuence embedded within a median voter framework where redistribution is decreasing in inequality. 6 Functional explanations predicate that social mechanisms originate as a result of the need of collectives to fulﬁll needs. This type of explanation, closely associated with nineteenth-century sociology and marxism, was harshly criticized by Popper (1962). See also the discussion by Elster (1983). 7 See Milliband (1969), Poulantzas (1975), Skocpol (1979), and Baran and Sweezy (1996).

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Our model consists of a game played between voters, politicians, and inﬂuence-seekers. In this game, politicians will strive to maximize political support by mixing popular policies with campaign spending. Campaign contributions are oﬀered by individual capital owners, who in return receive tax exemptions from the government. These may (but need not) be interpreted literally as income tax exemptions; they could represent any mix of political favors that the government is in the position to give to campaign contributors. In what follows we will refer to contributors as those who give campaign contributions and taxpayers as those who pay taxes. Capitalists are assumed to be atomistic and therefore oﬀer campaign contributions purely in return for privately appropriable favors. We therefore exclude any public-good nature from the policies over which political inﬂuence is exerted. Voters are able to control the incentives under which politicians and capitalists bargain by setting the tax rate. Individuals own endowments in labor and capital. We assume that labor endowment is equally distributed while capital income is unequally distributed. Therefore the inequality in capital endowments generates the observed inequality in income distribution. Given a wide deﬁnition of capital which allows for human capital, this division accords well with the fact that empirically asset wealth is more unequally distributed than labor wealth.8 What is important for the purposes of this section, however, is simply that there are two assets, one of which is unequally distributed.9 The capital– labor distinction will become important when we turn to capital accumulation in section 3. We label as workers those individuals who have no capital income; those who do will be called capitalists. Thus there are two types of heterogeneity: that between capitalists who own capital and workers who lack it, and that among capitalists who own diﬀerent amounts of capital. We assume that the mass of workers nw is greater than nk, the mass of capitalists, so that the median voter is a worker. Since, empirically, most income inequality is generated by the upper tail of the income distribution, this assumption does not give up much descriptive power; it does in turn permit us to characterize equilibrium policies as the preferred policies of a representative worker, allowing for a tractable mathematical framework. Workers receive their wage w and a transfer from the government s. They also pay the linear income tax t. Income of workers is thus: Yl ¼ wð1 tÞ þ s:

ð1Þ

In addition to their wage income, capitalists also derive income from their capital earnings. The income of capitalist i is: 8

See Wolﬀ (1994). We could thus alternatively use the labels ‘‘insider status’’ vs. ‘‘outsider status,’’ ‘‘monopolists’’ vs. ‘‘competitive ﬁrms,’’ or any other subdivision which we believe to be at the root of income inequality. 9

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Yki ¼ ðw þ rKi Þð1 t þ ei Þ Ci C0 C0 ¼

a 0

if Ci > 0 otherwise;

ð2Þ

ð3Þ

where r is the rental rate on capital, t is the tax rate, ei t is an individualspeciﬁc tax exemption,10 Ci is the contribution that individual i gives to the politician in power, and Ki is individual i’s ownership of capital income. Thus heterogeneity among capitalists is captured by diﬀerences in their holdings of capital. No generality is lost by assuming that workers cannot make political contributions; as we shall see below, the minimum political contribution would always be inaccessible to a worker in equilibrium. Groups are assumed to be perfectly identiﬁable; we show in subsection 4.1 that none of our results is aﬀected by incentive-compatibility considerations. The contributor is assumed to pay a ﬁxed cost C0 ¼ a whenever he gives a campaign contribution. This assumption is vital to the results below, as it captures the increasing returns in political activity necessary to generate a split between the poor and the rich in terms of political organization. There are two possible ways to justify the increasing-returns assumption. On the one hand, one could think about a set of real-world characteristics of political markets which are likely to generate increasing returns, such as the existence of the signiﬁcant transactions cost of lobbying, administrative costs of approving exemptions, large ﬁxed costs of political organization, or eﬀort costs of providing political favors. An alternative, perhaps more compelling, justiﬁcation could be derived from the simple economics of collective action. A group of individuals organized in order to undertake collective action faces pervasive incentives for free-riding from each of its members. Controlling free-riding is easier the more resources you have, both because the numbers necessary to achieve a certain scale of political organization are smaller, and because you have more resources to monitor freeriders.11 In subsection 2.2 we show that a model of endogenous political mobilization that takes these considerations into account is isomorphic to the speciﬁcation in equation (3). It is important to note that, whatever the theoretical justiﬁcation, the assumption of increasing returns in political inﬂuence seems to be quite consistent with the empirical evidence. Lobbying for small-scale political favors is seldom observed, and there is substantial empirical evidence that the rich participate more in politics in developed countries, both as 10 More generally, individuals would be split into sectors and the government would decide whether to grant an exemption to each sector. If members of that sector can arrange a set of optimal internal transfers then all our results below follow. 11 These points were ﬁrst made by Olson (1965).

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contributors of time and of money.12 Statistical evidence is scantier for developing countries, but what there is conﬁrms the existence of an increasing relation between political participation and levels of income,13 and numerous studies of political elites tend to show that they arise almost exclusively from privileged groups.14 In most of what follows, we treat increasing returns in political inﬂuence as a primitive of our model and analyze its eﬀect on the relationship between inequality and redistribution. We simplify by assuming that both individuals’ utility is linear in consumption. Politicians, however, are assumed to maximize a utility function which is a weighted average of the median voter’s utility and the total of 15 campaign or political expenditures: Z Upol ¼ Yl þ lg

Ci ðei jKi Þf ðKi ÞdKi Z ¼ wð1 tÞ þ s þ lg Ci ðei jKi Þf ðKi ÞdKi ; i

ð4Þ

i

where we assume that l41.16 The ﬁrst two terms are simply the median voter’s utility, whereas the third term in (4) is the average contribution of capitalists weighed by the relative mass of capitalists to workers g ¼ nk =nw and by their political eﬀectiveness l. This type of speciﬁcation is common in the literature and is meant to capture the intuition that both popular policies and money are required to win elections. Grossman and Helpman (1996) have used a similar equation in the context of a general menu-auction political game (of which our model is a special case) with politicians jockeying for the support of both informed and uninformed voters.17 An alternative model by Austen-Smith (1987) shows when voters are risk-averse and uncertain about candidates’ stance on the issues politicians will ﬁnd it optimal to deviate from the policies preferred by the median voter in order to attract campaign contributions. In Rodrı´ guez (1998) we 12 Rosenstone and Hansen (1993) use data from 19 National Election Studies to study political mobilization in the United States. Besides conﬁrming the well-known ﬁnding that wealthy Americans are more likely than poor Americans to take part in political activities, they also ﬁnd that ‘‘the prosperous are two and a half times more likely than the poor to attempt to inﬂuence how others vote and over ten times more likely to contribute money to campaigns’’ (pp. 43–44). 13 Portes and Itzigsohn (1997) and Gaviria and Sedden (1999). 14 Bakewell (1997) points out that during the 1930s ‘‘the whole [of Chile] was controlled by families who inhabited four square blocks in central Santiago’’ (p. 424). Payne (1997) describes Jamaican politics as ‘‘both elitist and authoritarian . . . led by the educated middle class, funded by local businessmen, and only involving the masses as voters, cheerleaders or recipients of patronage’’ (pp. 2–3). Other examples are in Baloyra and Martz (1979), Bauer (1975), and Dumont (1970). 15 Ci should be viewed broadly as any uses that contributors can make of their money to aﬀect political outcomes. Even in non-democratic systems, political activity is usually costly and requires ﬁnancial support. 16 Otherwise the politicians will approve no tax exemptions in equilibrium since they care more about the workers’ income than about their own. 17 They use a weighted average of national income and political contributions, whereas we use a weighted average of the median voter’s utility and political contributions.

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provide microfoundations for (4) by showing that maximization of this term will characterize equilibrium policies in the context of a game in which politicians compete for the votes of voters who are informed but uncertain about the underlying eﬀectiveness of the candidates as policy-makers.18 Note that equation (4) embodies two possible alternative assumptions about how money matters for politics. In the ﬁrst one, politicians care about the amount of contributions received relative to the total income of workers. An alternative would be to assume that politicians care about the sum total of contributions in relation to the average income (or utility) of the median voter. The latter characterization can be obtained from (4) by using l ¼ lnw in place of l in equation (4). This renormalization has no eﬀect on any of the comparative statics results that we present in this paper. The policy-maker maximizes (4) subject to his budget constraint: Z s ¼ tw þ g ðt ei Þðw þ rKi Þf ðKi ÞdKi ; ð5Þ i

so that the transfer must be ﬁnanced from taxes on workers and on capitalists. The government always has the possibility of choosing Ci ¼ 0, ei ¼ 0. Substituting the budget constraint in the politician’s utility function: Z Upol ¼ w þ g ðt ei Þðw þ rKi Þf ðKi ÞdKi i Z þ lg Ci ðei jKi Þf ðKi ÞdKi : ð6Þ i

We now go on to describe the time structure of the game. In t ¼ 1, the median voter votes over a tax rate t[½0; 1, which is henceforth ﬁxed. In t ¼ 2, each individual enters a bargain with the policy-maker over the level of the exemption ei [½0; t set by the politician, and the contribution Ci [Rþ given by the capitalist.19 We do not restrict the nature of this bargain but only assume that the politician and the capitalist reach an eﬃcient bargain.20 Note that our model allows voters to control the nominal tax rate but not the vector of exemption levels nor the level of spending. This key assumption embodies the main feature of our model, which is that it allows for limited 18 An alternative justiﬁcation of the Politician’s Objective would take C to be pure bribes and l to represent the average politician’s preference for money as opposed to his need of maintaining some measure of political support. This may be a more adequate characterization for the political systems of some countries. 19 The standard menu auction structure in which the principals (capitalists) propose a schedule of contributions Ci ðei Þ : ½0; 1 ! Rþ and the agent (politician) then picks an exemption ei [½0; t is a special case of our model. However, a great part of the common agency problem disappears in our model since each capitalist does not care about the exemption levels gained by other capitalists. 20 That is, a bargain such that the joint utilities of the capitalist and the politician are on their utility possibilities frontier.

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power in the hands of voters, whereas traditional median voter models of redistribution assume voters have total power to set all policies.21 It is precisely by allowing voters the power to determine a subset of policies and letting politicians have leeway to set the rest that we introduce a deviation from the median voter framework. That voters are allowed control over the tax rate is predicated on the fact that it makes sense to think of the tax rate as an issue on which promises are both enforceable and veriﬁable.22 Real-world institutions typically restrict changes in taxation to the highly visible process of legislation reform. The principle of nullum tributium sine lege (no taxes without law, more commonly referred to in the United States as the principle of ‘‘no taxation without representation’’) is one of the few legal principles of universal acceptance in both common and civil law systems, and implies that taxes can only be imposed or changed by the Legislative Branch of government. This principle dates at least from the Magna Carta of 1215, and in the United States it is enshrined in Article 1, Section 8, of the Constitution, which states that the Congress shall have the right to lay and collect taxes, duties, imposts, and excises. In contrast, several factors militate to make both exemptions and the spending level less veriﬁable and enforceable than tax rates. With respect to exemptions, the power to set them can and often is delegated to the Executive Branch. This process of delegation is common in countries with a civil law system.23 Even in countries in which the determination of tax exemptions cannot be delegated to the Executive Branch, it has considerable power to alter tax obligations. In the US, the Executive is in charge of administering tax credits, and the criteria to assign those credits can be used as a policy variable.24 With respect to spending, real-world institutions often accord the Executive Branch substantial leeway in altering the level of expenditures through discretional decisions and with little oversight, especially when they 21

Given the government’s budget constraint, choice of the tax rate and exemptions determine the subsidy, so that in order for there to be limited control at least two policies must not be controlled by voters. 22 The terminology comes from recent applications of principal–agent theory to political economy. One of the key results that has emerged from this literature is that when promises are veriﬁable and enforceable, politicians will be forced to implement the preferred policies of the median voter, whereas when they are non-enforceable, politicians will pick their own preferred policies without regard to voters’ preferences (enforceable but non-veriﬁable promises lead to intermediate outcomes). See Persson and Tabellini (2000, chapter 4) for a useful survey and references. 23 See Villegas (1998, p. 195). Some countries distinguish between exemptions, which are set by the Legislative, and tax exonerations, which are set by the Executive. 24 A typical case is that of the New Markets Tax Credit (NMTC) Program, established by Congress in December 2000, which permits individual and corporate taxpayers to receive a credit against federal income taxes for making qualiﬁed equity investments in low-income areas. The NMTC Program is administered by the Department of Treasury, which is in charge of the selection of taxpayers that receive the credits. A thorough description of this program can be found in http://cdﬁfund.gov/programs/programs.asp?programID ¼ 5 r Blackwell Publishing Ltd 2004.

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imply a level of spending lower than that which is budgeted. For example, in a survey of Latin American budget institutions, Alesina et al. (1996) show that in 21 out of 25 countries the budget can be modiﬁed on the Executive’s initiative, and in 18 out of 21 countries the government can cut spending without Congressional approval after the budget is approved. Similar results are provided by von Hagen (1992) in a survey of European budget institutions. Furthermore, the fact that spending is often not under the direct control of the policy-maker due to uncertainty about the size of the tax base and the eﬃciency of tax collection and provision of public goods and services makes it costly for voters to punish politicians for deviating from promises regarding spending levels, making promises about spending considerably less enforceable than those regarding tax rates. The other key assumption in the setup is that voters move ﬁrst and politicians move second. Although this assumption is intuitively designed to capture the nature of the diﬀerence between the interventions of voters in the political landscape, which happen at discrete intervals, as opposed to those of political contributors, which happen in continuous time within the framework set by voters’ decisions, it is actually irrelevant to our results. The same results can be proven if we assume voters set the tax rate after politicians and contributors bargain on an exemption conditional on a rational expectation of the voters’ decision.25 Note that in our model the policy-maker and contributor i bargain over ei but not over t. This corresponds to an implicit assumption that free-rider problems are pervasive in bargaining over redistributive policies; therefore we should not commonly observe bargains in which money contributions are exchanged for redistributive policies that have direct eﬀects on all individuals in society. Indeed, one characteristic of modern-day redistributive policies is that political institutions do not commonly allow participation in redistributive schemes to be conditioned on participation in a political group.26 In Olson’s (1965) language, it is not possible to provide selective incentives to those that participate in political action targeted towards 25 In Rodrı´ guez (1998) we discuss an alternative formulation of the game just presented which has a truly more dynamic framework. In it we argue that the same policies we will now derive will be generated by a game in which two politicians [taking contribution schedules Ci (ei) as given] set t and e to maximize their probability of winning an election in which they use political contributions to pay for campaign spending and voters can only punish politicians in future elections conditional on the history of tax rates (and thus not conditional on the history of tax exemptions or spending levels). We show that the equilibrium tax rates we will now derive in our simpler model will be Pareto-superior to all symmetric equilibria that can be supported in the dynamic game for sensible restrictions on the form of the strategies played. Since the proof involves appealing to complex punishment strategies common in the game-theory literature on repeated games, we specialize in the more tractable static model in the rest of the paper. There we also discuss the eﬀects of introducing time inconsistency into our framework. 26 Some papers in the literature on redistributive politics (Dixit and Londregan, 1995) center precisely on selective transfers to small groups. However, our paper is concerned with redistribution understood as transfers from richer to poorer sectors of society.

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altering redistributive institutions. This fact, combined with the sheer numbers of persons among whom the gains (in terms of welfare state transfers) and costs (in terms of taxes on the rich) are spread out, imply that we should not expect to see large groups organize in order to exert pressure to favor diﬀerent redistributive policies. Rather we should expect, as in our model, small and very compact groups of individuals assemble to gain targeted tax favors, with the rest of the individuals exerting pressure through their right to vote.27 We are now ready to solve the model backwards. The ﬁrst step is to solve for the set of eﬃcient bargains that can be reached between each capitalist and the politician in t ¼ 2. This is done in the following proposition. Proposition 1. Any eﬃcient bargain between capitalist i and the politician will be characterized by exemption levels 8 al < t if w þ rKi ei ¼ ð7Þ ðl 1Þt : 0 otherwise: See the Appendix for proof. Therefore the distribution of taxes paid will be as follows. Capitalists with al ðw þ rKi Þ > t ð l 1Þ will get an exemption for the total value of their taxes, and therefore pay zero taxes. Those with al ðw þ rKi Þ < t ð l 1Þ will give no contributions, get no exemptions, and therefore pay the fraction t of their incomes speciﬁed by law as taxes.28 The reason for this is that when a capitalist’s income is lower than al=tðl 1Þ it does not pay for her to oﬀer to the politician the minimum bargain that would keep him at least 27

It could be argued that labor union federations represent precisely the type of broad-ranging associations that exert pressure in favor of universal transfers and which our model assumes away. However, labor union federations are relatively unimportant contributors to political campaigns in terms of money contributions. To the extent that their main bargaining strength is in the votes of their participants, their inﬂuence is captured by the weight which the (wageearning) median voter’s utility has in the politician’s utility. 28 The distribution of contributions is subject to the choice among eﬃcient bargains. If the capitalist is able to extract all surplus from the politician, he will pay ðw þ rKi Þt ; Ci ¼ l the minimum he needs to make the politician content to carry out the policy. If the politician captures the surplus, then the capitalist’s contribution will be a þ ðw þ rKi Þt. r Blackwell Publishing Ltd 2004.

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indiﬀerent between giving the exemption and collecting the taxes. This of course comes out of the assumption of increasing returns to scale in political activity. But when the capitalist’s income is higher than al=tðl 1Þ, there is scope for a bargain between the capitalist and the politician that leaves both at least as well oﬀ. Since the politician has a constant marginal cost of raising the level of the exemptions and the capitalist’s utility is linear in ei once the ﬁxed cost has been paid, then both individuals can gain from setting the exemption to its maximum level, t, given their decision to strike a bargain. Using this result, we solve the model in t ¼ 1. Using (7), we can write the total per capita transfer to be received by workers from the government as: Z ð al wÞ1 r tðl1Þ s¼g tðw þ rKi Þf ðKi ÞdK þ tw: ð8Þ 0

Substituting in (1), we ﬁnd that workers’ utility will be: Z ð al wÞ1 r tðl1Þ Uw ¼ w þ g tðw þ rKi Þf ðKi ÞdK:

ð9Þ

0

Voters will set t to maximize the net resource transfer from capitalists Z al tðl1Þ r¼ tyi f ðyi Þdy; ð10Þ w

where we have written the income distribution among capitalists in terms of Y ¼ w þ rKi f ðYÞ.29 Equation (10) captures the main tradeoﬀ facing the median voter in our model. Voters want to set the tax rate to maximize the net resource transfer received R al=tðl1Þfrom capitalists. If they raise the tax rate they will raise r by ð w yi f ðyi ÞdyÞdt, as all capitalist taxpayers will now have to pay a higher tax rate. But a higher tax rate raises the incentives for rent-seeking and makes the number of capitalists who give political contributions in exchange for tax favors go up. This is captured by the negative eﬀect of t on the upper limit of the integral deﬁning r, ½al=tðl 1Þ. If the possibility for evading taxes through political contributions did not exist, only the ﬁrst eﬀect would operate and therefore voters would set a tax rate of 1. But the fact that this may lead to a level of rent-seeking that would create massive tax evasion makes voters keep the tax rate limited. Thus, voters may in equilibrium set a tax rate lower than 1 even absent incentive considerations.30 29 We abuse notation by writing f(y) which is a distinct density from f(ki). The change of variable rule implies that f(yi) ¼ f(ki)/r. 30 They may but they need not. It is perfectly possible theoretically for the minimum possible ¼ al=ðl 1Þ to be so high that the gains to voters from keeping threshold level of income ymin the tax rate low are simply not enough to encite them to maintain their tax rates restricted. In this case, voters would decide to set a tax rate of unity so as to ‘‘milk’’ those capitalists who would never be able to buy into political inﬂuence. In other words, most income is in the hands

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The central contention of our paper is that in a model that takes into account how an inegalitarian distribution of income enhances the political power of the richer sectors of society, inequality will be negatively associated with redistribution. As our main indicator of redistribution we center on the eﬀective tax rate on capitalists, r0 ¼ r/mk, which measures what percentage of the income of capitalists is being taxed. This contrasts with t, the nominal tax rate on capitalists, which in traditional models is equal to r0 . In our model t and r0 will generally have diﬀerent comparative statics. Between these, r0 is obviously the variable of normative signiﬁcance as a measure of redistribution, as it measures what percentage of their income an individual capitalist is required to surrender to the state. We will also concentrate on the Tax/GDP ratio, and the Transfer/GDP ratio. To analyze the eﬀect of changes in income distribution on r0 , we will write the density function of income as f(y, s) and look for the change in r0 caused by a change in s, the parameter (or vector of parameters) that captures inequality of income distribution. By the envelope theorem: dr @r @t @r @r ¼ þ ¼ : ds @t @s @s @s

ð11Þ

Equation (11) tells us that we need only look at the partial eﬀects of the changes in income inequality on the net resource transfer when assessing perturbations to equilibria and can disregard the eﬀects that go through changes in t, as these will be of second-order magnitude. Armed with this result, we can go on to establish some comparative statics eﬀects of inequality on income distribution. Proposition 2. (i) A mean preserving transfer of income between capitalists with income below y ¼ al=tðl 1Þ and capitalists with income above y will lower r0 ; an identical transfer in the opposite direction will raise r0 . (ii) A transfer of income from workers to capitalists which leaves the distribution of income among capitalists untouched will lower r0 ; a similar transfer from capitalists to workers will raise r0 . See the Appendix for proof. Proposition 2 characterizes an important class of transfers from poor to rich individuals which will worsen redistribution. Transfers of income from suﬃciently poor individuals to suﬃciently rich individuals will unequivocally lower r0 . This result establishes a strong link between a class of inequalityraising transfers and redistribution in our model. Indeed, responsiveness of

of people who have no choice other than to pay taxes, and it would imply great sacriﬁce in terms of tax revenues to lower the tax rate to a level consistent with the really rich paying taxes. Note that even when voters set a tax rate of unity the eﬀective tax rate on capital income r0 ¼ r/mk will be less than unity. As a matter of fact, t ¼ 1 is more an expression of the powerlessness of voters to capture income accumulated at the higher ends of the scale than anything else. r Blackwell Publishing Ltd 2004.

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inequality indices to poor-to-rich transfers has long been argued for as a minimal condition for inequality indices in traditional welfare economics.31 It is not the case, however, that all poor-to-rich transfers will lower r0 . To see this, suppose that a mass of individuals with income just above y transfers its income to individuals richer than them, thus seeing their own income fall below y . In that case the deterioration in income distribution makes a group of individuals fall below the threshold which separates political contributors from taxpayers, thereby raising the amount of income that is taxable at the initial equilibrium. The possibility of such eﬀects is governed by the magnitude of the income transfer received by an individual at the threshold y .32 It is easy to prove that if individuals with threshold income y are not aﬀected, a transfer from poor-to-rich capitalists will unequivocally deteriorate redistribution. In order to get more speciﬁc results, we will need to restrict the functional form of f(K). In the following, we work through two examples of our model using the uniform and the Pareto distribution for f(K). The former is of illustrative interest, whereas the latter is of greater empirical relevance. We derive the result that, under these two cases, greater inequality will lower the equilibrium r0 .33 Example 1. Let capitalists’ income yik be distributed with uniform density over ½w; w þ rK. That is: ( 1 i f ð yik Þ ¼ rK for Yk [½w; w þ rK 0 otherwise: Then the nominal tax rate t, the net tax rate on capital r0 ¼ r=nk mk , the Tax/ GDP ratio and the Transfer/GDP ratio are all declining in the variance of income, the Gini coeﬃcient of the income distribution, the mean/median income ratios, and capital’s share of income. The uniform density is an interesting benchmark but is clearly not a realistic description of income distribution among capitalists. A realistic functional form for the distribution of income among capitalists would ideally be a good empirical description of income distribution among the richer individuals in society. This is because the distribution of income f(y) which goes into (10) is the distribution of income among capitalists, who in our model comprise less than 50 percent of the population. The empirical literature in income distribution estimation has shown that the Pareto 31 Known statements of this principle go back at least as early as the 1910s, when it was ﬁrst proposed by Pigou and Dalton. See Pigou (1912), Dalton (1920), and Sen (1973). 32 From equation (A4) in the Appendix one can see that such eﬀects are totally due to the eﬀect of the transfer on the threshold individual, a(y, s). 33 Details of derivations can be found in the working paper version of this paper (Rodrı´ guez, 1999b).

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density appears to accurately describe income distributions along their upper tail.34 We illustrate this case in the following example. Example 2. Capitalists’ income yik is distributed according to a Pareto density P(a, w): a a1 aw y for y > w f ðyÞ ¼ 0 otherwise: Then the net tax rate on capital r0 ¼ r=nk mk , the Tax/GDP ratio and the Transfer/GDP ratio are all declining in the variance of income, the Gini coeﬃcient of the income distribution, the mean/median income ratio and capital’s share of income. The nominal tax rate t has a unique interior minimum and is therefore declining in inequality at low levels and increasing at high levels of inequality. As in the uniform distribution, more inequality leads to less redistribution. Increases in inequality are equivalent to shifts of resources from the poor to the rich. If resources are shifted from people below the threshold level of income (the taxpayers) to people above the threshold level of income (the tax-exempt) then at the original tax rate total taxes collected will decrease. Of course, to understand the total eﬀect of this increase in inequality on tax revenues we should understand how voters raise or lower the tax rate in response to the increase in inequality. But the envelope theorem result in (11) shows us that we can disregard the eﬀect of voters’ reoptimization, as this will be of a second-order magnitude. We can concentrate on the ﬁrst-order eﬀects of an increase in inequality on taxes collected. We have established that this eﬀect will always be negative. Note that, unlike in the uniform case, the nominal tax rate is not monotonic in inequality. At low levels of inequality, higher inequality leads to a fall in the nominal tax rate. But as inequality becomes high enough, this eﬀect changes and deteriorations in income distribution start leading to higher nominal tax rates. This eﬀect is illustrated in Figure 2(c). This is in contrast to the uniform case [Figure 1(c)], where an increase in income inequality invariably brings about a fall in the nominal tax rate. Under the uniform distribution, a higher level of inequality leads voters to lower tax rates so as to not let the group of individuals with higher income have incentives to buy themselves tax exemptions. In the Pareto case, such an eﬀect occurs at low levels of income inequality (at which the Pareto form is closest 34 See Harrison (1977) and Lambert (1989). The Pareto density has been found to be superior to the log-normal distribution in describing the upper tail of the income distribution. The lognormal distribution is often used in theoretical work on income inequality, as in Benabou (1996), because it captures adequately the negative skewness of income distributions. That skewness is captured in our model by the fact that in our speciﬁcation at least one-half of the population receives an income equal to w, lower than that received by any capitalist.

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(b)

0.5

0.5 Effective Tax on K

Transfer/GDP Ratio

(a)

0.4 0.3 0.2 0.1 0

1

1.5

2

2.5

3

3.5

0.4 0.3 0.2 0.1 0

4

1

1.5

Mean/Median Ratio (c)

4

(d)

0.5 Tax/GDP Ratio

0.5 Nominal Tax Rate

2 2.5 3 3.5 Mean/Median Ratio

0.4 0.3 0.2 0.1 0

1

1.5 2 2.5 3 3.5 Mean/Median Ratio

0.4 0.3 0.2 0.1 0

4

1

1.5 2 2.5 3 3.5 Mean/Median Ratio

4

Figure 1. Taxes, transfers, and inequality under uniform distribution.

(a)

(b) 0.5 Effective Tax on K

Transfer/GDP Ratio

0.5 0.4 0.3 0.2 0.1 0

-4

-3.5 -3 -2.5 -2 -1.5 Inequality [-alpha]

0.3 0.2 0.1 0

-1

(c)

-4

-3.5 -3 -2.5 -2 -1.5 Inequality [-alpha]

-1

(d) 0.44

0.5

0.42

0.4

Tax/GDP Ratio

Nominal Tax Rate

0.4

0.4 0.38 0.36 -4

-3.5 -3 -2.5 -2 -1.5 Inequality [-alpha]

-1

0.3 0.2 0.1 0

-4

-3.5 -3 -2.5 -2 -1.5 Inequality [-alpha]

Figure 2. Taxes, transfers, and inequality under Pareto distribution. r Blackwell Publishing Ltd 2004.

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to the uniform distribution). But at high levels of income inequality, those in the higher-income brackets see their possibilities for escaping taxation enhanced. The cost of giving these individuals incentives to not buy themselves tax exemptions by keeping low tax rates becomes too large. Rather than reduce taxation to control their incentives for rent-seeking, voters prefer to raise the tax rate and extract more resources from those whose income is too low to give campaign contributions. Thus one could say that at low levels of income inequality voters decide to pander to capitalists so that they will not have an incentive to go into rent-seeking activities, whereas when inequality becomes very high voters would rather try to milk lower-income capitalists by raising very high tax rates on them and letting the really rich capitalists escape taxation. The indeterminacy of the sign of dt=da under the Pareto form suggests that empirical testing of hypotheses with respect to the relation between inequality and redistribution must be approached with care. To the extent that the indicators of redistribution used are measures of eﬀective redistribution, then our theory implies a negative relationship between inequality and redistribution. But to the extent that these are indicators of the nominal tax rate gross of exemptions our theory would predict that there ought to be no linear relationship between these variables. Now if the exemptions of our model take the form of favors which are paid out of the government budget (such as government contracts to favored ﬁrms or government subsidies to politically friendly ﬁrms) then government spending would be analogous to the nominal tax rate in our model. Our results suggest that we concentrate on eﬀective measures of redistribution, such as government transfers to the poor or spending on education and health, for understanding the eﬀect of inequality on redistribution. They thus also recommend caution when interpreting standard results from cross-country regressions [such as those in Perotti (1996)] that ﬁnd little eﬀect of inequality on government spending. 2.2

Endogenous Political Mobilization

In the previous subsection we assumed that political inﬂuence was characterized by increasing returns. These increasing returns were captured by a ﬁxed-cost parameter a, which made it proﬁtable to participate in political activity only for individuals with income higher than a threshold level of income al=tðl 1Þ. In what follows we show that there is a natural way to endogenize these increasing returns in political inﬂuence from a model in which interest groups set their size to balance two eﬀects of having a larger group. On the one hand, greater size means greater capacity to raise money and therefore greater bargaining power vis-a`-vis policy-makers. On the other hand, greater size implies greater costs of controlling free-riding. Groups with higher income will have higher capacity to raise money and therefore will be in a better position to cover the costs of political organization. We r Blackwell Publishing Ltd 2004.

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show in what follows that whenever the cost of political mobilization is increasing, convex and homogeneous of degree r in the proportion of participants for any r, only groups above a certain threshold level of income will obtain exemptions (and will bargain for ei ¼ t); groups below that threshold will not organize politically and will receive no exemptions. The division between contributors and non-contributors obtained from this more complex speciﬁcation is therefore identical to that obtained using a simple ﬁxed cost of political organization. Our model of political mobilization is as follows: before bargaining with policy-makers takes place, interest groups are formed. There is one interest group for each set of individuals of income yi (including workers). Each group will be composed of n0i individuals. They will bargain with the policymaker over exemptions and contributions in order to maximize the total surplus obtained for members of the group – they will not take into account the welfare of non-members of the group. However, an exemption obtained by a group will be valid for all individuals with their level of income (not just group members). The number of participants in the group will be set so as to maximize the total surplus obtained by group members (therefore there is an implicit assumption of lump-sum transfers between group members). This means that an interest group can exclude an entrant if it believes that his contribution to the group will be smaller than his capacity of generating additional surplus for existing members. To control free-riding by the members of a group of size n0i it must expend resources C(n0i). We assume C( ) is increasing and convex. We model the bargain between the policy-maker and the capitalists as a generalized Nash bargain. Thus we will look for the sets of e, t which simultaneously solve: maxfð1 ZÞlnðn0i yi ei Ci Þ þ Z lnðyi ei þ lCi Þg ei ;t

subject to 0 ei t; Ci 0: Note that this includes as polar cases the case in which capitalists capture all the surplus (Z ¼ 0) as well as when politicians capture all the surplus (Z ¼ 1). The symmetric Nash-bargaining solution corresponds to Z ¼ 12. Lemma 1 establishes the outcome of the bargaining process. Lemma 1. The Nash-bargaining solution for a group of size n0i and the policy-maker will be characterized by: ei ¼ t 1 Ci ¼ ½Zðln0i 1Þ þ 1yi t l r Blackwell Publishing Ltd 2004.

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if n0i > 1=l and ei ¼ 0 Ci ¼ 0 otherwise. Lemma 1 allows us to specify the indirect payoﬀs to interest groups of organizing: ( 1 1 VðÞ ¼ n0i yi t l½ZðlZ0i 1Þ þ 1yi t CðZ0i Þ if Z0i > l ð12Þ CðZ0i Þ otherwise: Using these payoﬀs, we can derive the conditions for there to be political organization as the conditions for the optimal n0i to be greater than 1=l as well as for (12) to be greater than zero. Proposition 3 shows that for both conditions to be satisﬁed only individuals above a certain threshold level of income will organize politically and therefore obtain exemptions. Proposition 3. Let C( ) be homogeneous of degree t. Then all groups with yi > Tð1=tÞ will organize politically. The exemption and contribution levels that they will bargain for will be: ei ¼ t ð13Þ

1 Ci ¼ ½Zðln0i 1Þ þ 1yi t: l

All groups with yi < Tð1=tÞ will decide not to organize politically and therefore their outcome will be characterized by ei ¼ 0 Ci ¼ 0 where

T¼

ð1 ZÞ l½ð1 ZÞC 0 1 ðð1 ZÞÞ CðC 0 1 ðð1 ZÞÞÞ

t1 :

See the Appendix for proof. Note that the threshold level of income is a constant multiplied by 1=t. This is precisely the same functional form as the threshold we derived above for the case of a ﬁxed cost. If we set the ﬁxed cost a¼T

l1 l

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then the model in this subsection can be seen to be identical to the model with an exogenous ﬁxed cost. Proposition 3 can therefore be seen as providing microfoundations for the increasing returns in political inﬂuence assumption. 2.3

Alternative Political Settings

How are the results above sensible to our speciﬁcation of the political setting? In our political system voters control the tax rate and politicians control the level of exemptions. This assumption has allowed us to model a setting in which voters have limited control over policies. How would the results change as we go towards the extremes in which either voters or politicians control both the tax rate and the levels of exemptions? If voters were to control both variables, then we would be back in the setting of the pure median voter model. Results would be analogous to those of the Meltzer– Richard model in the absence of incentive considerations – voters would set taxes to 1 and exemptions to 0, therefore totally expropriating the wealth of richer individuals. The Meltzer–Richard result can also be replicated via control of the subsidy by voters (even if they do not control the tax rate) so that our discussion above on imperfect enforceability and veriﬁability of promises regarding spending levels is an important element of our argument. The other extreme is perhaps more interesting. What would happen if politicians were to control both variables? In this case, they would set the tax rate to maximize (6). This introduces an additional consideration in the determination of the equilibrium tax rate. Politicians will want to set tax rates higher than is desired by voters in order to raise their bargaining power vis-a`-vis capitalists. Therefore @[email protected] 6¼ 0 and the envelope theorem cannot be applied to establish (11). How this will aﬀect the comparative statics eﬀect of inequality on equilibrium redistribution will depend on the precise form of the bargain struck between politicians and capitalists. In the working paper version of this paper (Rodrı´ guez, 1999b) we show that for the two polar cases in which either capitalists or politicians capture the entire surplus of the bargain, as well as for all contribution schedules which are linear in tyi ,35 the nominal tax rate set by policy-makers will be independent of the level of inequality. Therefore, @[email protected] ¼ 0 and (11) will continue to hold. 3. INEQUALITY, REDISTRIBUTION, AND CAPITAL ACCUMULATION

We have established above that in our model increased inequality leads to more redistribution. Some authors have argued that there is a negative link between inequality and growth present in the cross-country data.36 Can our 35 The case of contribution schedules which are linear in tyi includes as a special case all solutions to the generalized Nash-bargaining problem described in subsection 2.2. 36 See Alesina and Rodrik (1994), Persson and Tabellini (1994), and, more recently, Deininger and Olinto (2000). A number of authors have contested the existence of this relationship, generally based on panel data evidence (Barro, 1999; Banerjee and Duﬂo, 2000; Forbes, 2000).

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model be made consistent with an observed negative relationship between inequality and growth? In this section we present a simple two-period model of capital accumulation which shows that, if the resources that go into political contributions are thereby not invested in productive capital accumulation, the increase in rent-seeking associated with increased inequality may take such a large chunk of resources from capital accumulation that it can end up harming economic growth. The interaction between investment and political contributions requires a more speciﬁc description of the amount of transfers from capitalists to politicians. Proposition 1 and all the results that follow from it are independent of the form that this transfer takes, provided it is the outcome of an eﬃcient bargain. No such generality is possible in the analysis of the interaction between rent-seeking and economic growth. In this section we restrict ourselves to the study of three special cases: 1. when capitalists capture all the surplus of the bargain between them and politicians and thus Ci ¼ ½ðw þ rki Þ=l; 2. when politicians capture all the surplus and Ci ¼ ðw þ rki Þt a; 3. when the equilibrium contribution is linear in tyi , as is the result in the generalized Nash bargain developed in subsection 2.2.37 We look at a two-period setting, in which capitalists decide in period 1 whether to invest or consume an endowment yi1 of resources with which they are born. They can either consume it in period 1 or invest it. If invested, they have the choice of either investing in productive capital, which earns a return of r38 but is subject to a tax of t, or alternatively of investing it in contributions to politicians. This investment has a cost of Ci. Its return is the value of the tax exemption that the capitalists will get in period 2 in return, tyi. The waiting time between the moment in which the contribution is paid and the moment in which the exemption is given eﬀectively makes the political contribution into an investment, forcing capitalists to decide whether to dedicate their limited resources to capital accumulation (ki) or to political contributions (Ci). Note that the tax falls on endowments since in order to concentrate on the eﬀect of rent-seeking on investment we assume away disincentive eﬀects of taxation on capital accumulation. The tax falls on the 37 Note that if we follow the standard common agency setup in which capitalists oﬀer a contribution schedule conditional on exemptions and the politician decides whether to accept or reject their oﬀer then capitalists will end up capturing all the surplus and we are in case (i). For general applications of this setup, see Bernheim and Whinston (1986) and Dixit et al. (1997). Note also that our problem is diﬀerent from standard common agency problems in one relevant sense, which is that the bids are over individual-speciﬁc policies rather than policies which aﬀect everyone. Thus, the setup in which contributors move ﬁrst allows capitalists to capture all the surplus whereas in standard common agency problems it can eﬀectively lead the politician to capture all the surplus (Dixit et al., 1997, proposition 5). 38 We assume a linear technology or that the economy is open and the rate of return is therefore constant.

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capitalist’s ‘‘full income’’ yi ¼ w þ ryi1 . We assume that capitalists may go into debt, but the amount of debt is bounded above by a non-negativity restriction on each period’s consumption. Therefore, consumption in each period for capitalist i is given respectively by d1i ¼ yi1 ki Ci C0 d2i ¼ ðt þ ei Þyi þ rki þ w d1i 0; d2i 0: As long as r > 1, those who make no contributions will invest ki ¼ yi1 ¼ ðyi wÞ=r. Those who do make contributions will invest proportionately less, yi1 Ci C0 . Table 1 gives the level of contributions and capital accumulation that correspond to cases (1) to (3) described above. The change in investment when inequality rises will depend on three factors: (i) inequality puts more resources in the hands of capitalists, so that mk rises and w falls, leading to a rise in capital accumulation; (ii) as inequality rises the gap between the nominal and the eﬀective tax rates tr0 rises, which causes capital accumulation to fall; and (iii) as inequality rises the amount of ﬁxed costs expended in rent-seeking að1 FðX ÞÞ goes up,39 leading to lower capital accumulation in cases (1) and (3). Thus, even though an increase in inequality increases the proportion of income that is in capitalists’ hands and can be invested, it also raises the amount of resources devoted to rent-seeking. The total eﬀect of an increase in inequality on investment is a sum of these two eﬀects and is therefore indeterminate. We have carried out a battery of computer simulations, not reported for reasons of space, that show that a negative eﬀect of inequality on investment can commonly arise over some range of the distribution of income. It is interesting to relate our model to some of the previous literature on inequality and growth. Before the emergence of median voter models of growth and distribution, the consensus among economists was that greater inequality would foster growth by raising the savings rate.40 These classical models assumed, as we do, that capitalists were able to save and workers were not, so that a transfer of income from workers to capitalists would raise the overall savings rate of the economy. What we have established is that, within a framework in which capitalists are assumed to save more than workers, income inequality may raise the amount of resources devoted to rent-seeking activities so much that it may oﬀset the classical eﬀect and diminish classical accumulation. The above result has been proved assuming non-distortionary taxation. Although this has served to isolate our eﬀect, it is worth asking to what extent our results change when one takes into account the eﬀects that higher tax rates 39 40

See the working paper version (Rodrı´ guez, 1999b) for proofs. Kaldor (1960), Kalecki (1971), and Marglin (1984).

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Table 1 Case

Ci

(1)

yi t l

(2)

yi t a

(3)

qyi t

ki jyi > y i

1 1 w ta yi r l r 1 w 1 t yi r r 1 w 1 ta yi r r

ki jyi < y

K

yil

1 r

i

where a0 ¼ ar; l0 ¼ l=r; yi ¼

yil yil

1 mk ½1 0 ðt r0 Þ l a0 ð1 ðFðy ÞÞ w

!

1 ðm ½1 ðt r0 Þ wÞ r k 1 mk ½1 qðt r0 Þ r a0 ð1 Fðy ÞÞw

al : ðl 1Þt

may have on capital accumulation. When we introduce distortionary taxes we introduce an additional positive eﬀect of inequality on capital accumulation. The reason is that inequality puts resources into the hands of those who have the capacity to buy themselves tax exemptions and who therefore face lower marginal tax rates and invest more. This eﬀect is aggravated when governments have little capacity to commit themselves to less than optimal tax rates. In the limit, time inconsistency implies a capital levy on those who do not have the capacity to isolate themselves from taxation by buying oﬀ politicians. Investors below the threshold of resources necessary to enter into rent-seeking activities, if certain they will be subjected to a capital levy, will not invest. The only capitalists who will invest are those who are rich enough to pay oﬀ the politicians so that they will not be taxed. A shift of income into the hands of those capitalists will raise the rate of investment and growth.41 Whether inequality has a negative eﬀect on economic growth thus hinges on what is more important for capital accumulation: low tax rates or controlled rent-seeking and corruption. The empirical evidence showing a negative association between inequality and redistribution may suggest that the latter eﬀect is more important than the former one, emphasized by the previous literature. So, perhaps, do the studies on corruption and economic performance in highly unequal developing countries, which describe societies characterized by massive systems of transfers from businesses to politicians (Bates, 1981; Klitgaard, 1988; Mauro, 1995). It is our contention that these systems have their primary origin in the very unequal distribution of income of these countries. Our theory of inequality, rent-seeking, and growth may shed light on some puzzles in economic history such as the vast diﬀerences in economic performance between North and South America, which at the beginning of the nineteenth century had similar levels of GNP per capita. Especially during the nineteenth century, the US’s GDP per capita grew between four and six times while that of most Latin American countries stagnated.42 41 42

For further discussion of these results, see Rodrı´ guez (1998). Atack and Passell (1994) and Haber (1997).

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Cultural explanations that rely on the diﬀerences in economic institutions inherited from their respective metropolises fail to account for the disappointing growth performance of the former British colonies of the Caribbean and South America. Explanations based on political instability have the challenge of accounting for the Brazilian experience, during which, despite a nineteenth century without wars or internal disputes, there was an average annualized growth rate of less than 0.1 percent from 1820 to 1900. Recent research in economic history (Engerman and Sokoloﬀ, 1997) has argued that inequality was at the root of the diﬀerences in economic performance between the northern and southern halves of the Western Hemisphere. Numerous case studies have documented the power of landed elites in nineteenth-century Latin America and how it put severe limits on the ability of the political system to enact ﬁscal and economic reforms that would have created a suﬃciently high tax base and well-deﬁned property rights. Without these reforms, Latin America was unable to fund the investments in infrastructure, public goods and human capital accumulation which were key for economic growth during the nineteenth century.43 4. CONCLUDING COMMENTS

4.1

Incentive Compatibility

The tax scheme used in this paper has the drawback of not being incentivecompatible. Some poor capitalists may be enticed to throw away their capital since they are better oﬀ becoming workers. We have written the model in this way for reasons of analytical tractability, but the results are preserved when one considers a more complex incentive-compatible scheme. A simple incentive-compatible redistributive scheme would be one that taxed only capital and gave the subsidy both to workers and to capitalists. Given a tax rate of less than unity, even the poorest capitalist prefers being a capitalist to being a worker. Workers will still vote to optimize r, and capitalists will give political contributions whenever rki > al=tðl 1Þ. All our results therefore follow identically. Although the mathematics of this speciﬁcation are formally identical, one must be careful with the meaning of f(y), the distribution of income among capitalists. If capitalists pay taxes only when rki < al=tðl 1Þ, then r would equal r¼t

Z

al tðl1Þ

rki f ðki Þdk;

ð14Þ

0 43 Studies of the political power wielded by economic elites in nineteenth-century Latin America include Prado Ju´nior (1957), Perry (1978), and Graham (1990). Summerhill (1997) describes the retarded evolution of railroads in nineteenth-century Latin America, while Marichal (1997) deals with obstacles to the development of ﬁnancial markets. On the importance of these factors for nineteenth-century US economic growth see Fogel (1964) for railroads, Timberlake (1993) for the ﬁnancial system, and Goldin and Katz (1995) for education.

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the amount of capital held by people for which their capital income is lower than the threshold. Thus whatever functional form we pick for f( ) must now be an adequate representation of the distribution of capital income and not of the income of capitalists. This is particularly relevant when we discuss the Pareto speciﬁcation, as we have argued that this is a good representation of the distribution of income in the upper tail of the distribution. If we want to keep to this argument, then f(k) ought to be the distribution of capital income induced by a distribution of total (capital plus labor) income that follows the Pareto form. Although the mathematics of the Pareto speciﬁcation for this case become mathematically much more complex, it can be proven that the negative comparative statics eﬀect of inequality on redistribution is preserved.

4.2 The Meltzer–Richard Hypothesis, Revenue Leakage, and Channels of Political Pressure It may seem surprising that the eﬀect of inequality on redistribution is always negative in our model. After all, didn’t Meltzer and Richard (1981) prove that the median voter would always desire greater redistribution when inequality is greater? Shouldn’t that eﬀect at least partially oﬀset our result? The answer to the second question requires understanding the particular assumptions behind Meltzer and Richard’s results. As Rodrı´ guez (1998) has shown, the Meltzer–Richard hypothesis is largely driven by the restriction that the tax rate be linear in income or that voters are unable to target subsidies to themselves. If any of these assumptions is relaxed, as in our model, the Meltzer–Richard eﬀect can easily be reversed. Although we believe that targeted subsidies are more characteristic of the welfare-state-type redistributive programs that we want to study, our characterization was selected more than anything for reasons of expositional clarity. We could assume instead that workers are unable to target all of the subsidy to themselves. In that case they would receive only a fraction y of revenues with the rest, 1 y, captured by capitalists. For example, government redistributive policies could take the form of subsidies to consumption of essential goods which primarily beneﬁt the poor but in part also subsidize the consumption of the rich. In that case the typical worker would have income: wð1 tÞ þ twy þ ygr ¼ w þ ygr twð1 yÞ; and thus workers would vote to maximize v ¼ ygr twð1 yÞ. The envelope theorem argument would now imply dv @v @t @v @r @w ¼ þ ¼ yd ð1 yÞt : ds @t @s @s @s @s r Blackwell Publishing Ltd 2004.

ð15Þ

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Equation (15) is composed of two eﬀects. The ﬁrst one is the eﬀect that we have been studying, the partial eﬀect of income inequality on Z al tðl1Þ tyi f ð yi Þdy: w

As y ! 1, we would expect that this eﬀect becomes dominant and inequality deteriorates redistribution. The second eﬀect captures the traditional Meltzer–Richard channel through which inequality aﬀects redistribution. As w falls when income inequality deteriorates, this eﬀect is positive, and more inequality generates more redistribution. As y ! 0, the standard Meltzer– Richard eﬀect dominates and inequality increases redistribution. For intermediate values of y, we have two eﬀects, and which of them is stronger cannot be established without assumptions on the parameters of the system.44 It is straightforward although messy to extend this argument to the case of the previous subsection in which there is a pure tax on capital and the subsidy is received by all individuals; in that case we would introduce the Meltzer–Richard eﬀect by requiring workers to pay taxes on labor. In this paper we have assumed away the Meltzer–Richard channel for reasons of simplicity. But to what extent it exists is an empirical question, which can only be answered by evaluating the sign of the correlation between inequality and redistribution. The failure of most empirical studies to ﬁnd a relation between inequality and redistribution is suggestive that the eﬀect we have described in this paper and the Meltzer–Richard eﬀect may to a certain extent oﬀset each other in the existing data. In other words, more unequal societies may experience greater demand for redistribution from voters because they have less to lose from higher taxes (the Meltzer–Richard eﬀect). However, it may also become more diﬃcult for voters to enact redistributive transfers because politicians are more liable to be bought by rich individuals. 4.3

Conclusions

This paper has suggested that we should not expect more unequal societies to redistribute more. Unequal societies are characterized by a greater capacity of its richer members to aﬀect the state’s policies in their favor. Increases in inequality translate into a greater share of resources in the hands of individuals with the capacity to extract ﬁscal favors from policy-makers and thus redound is a decrease in the resources a society is able to devote to redistribution. In our model, the poor do not expropriate the rich not because they are worried about reducing the size of the pie, but because the rich have enough political power to keep a sizable portion of the pie for 44 The equilibrium threshold will now be higher (the tax rate lower) than that implied by the ﬁrst-order condition of the Pareto problem in subsection 2.1. Thus the proof that @[email protected] < 0 in that subsection does not apply to this problem. However, it can be established that for the Pareto density it is still the case that @[email protected] < 0.

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themselves. We have seen that this negative link between inequality and redistribution is preserved under a variety of functional speciﬁcations and assumptions about the tax schedule. We have shown that our model can explain the existence of a negative link between inequality and growth. This cannot happen if the main eﬀect of taxes on growth is due to disincentives to invest. But if rent-seeking has a negative eﬀect on investment, inequality may harm growth by expanding the scope for unproductive activities which pull resources away from productive investments. It is in this sense that inequality causes redistributive pressures that can hamper growth. And it is also in this sense that the basic intuition of models such as those by Alesina and Rodrik (1994) and Persson and Tabellini (1994) is preserved. Inequality generates political distortions which cause disincentives to capital accumulation. However, more unequal societies do not see a greater amount of resources devoted to helping the poor. Rather, those resources taken away from productive investments go either into the pockets of politicians or are wasted in unproductive proﬁt-seeking activities. In other words, inequality allows policy-makers to raise their bargaining power vis-a`-vis capitalists and to thus extract more resources from them, by raising the percentage of income held by those who actually have to gain from entering into a bargain with the government. This model has of course presented one explanation of what limits redistribution in contemporary capitalist societies. We do not claim that it is the only explanation, and our treatment of incentive considerations in section 3 has been geared precisely towards examining to what extent our model’s conclusions are qualiﬁed when it interacts with other factors. But our model has arisen from the realization that models that rely purely on incentive considerations tend to get the comparative statics results wrong when they are pitted against the data. We believe we have oﬀered an alternative explanation which is simple, intuitive, and consistent with the empirical evidence. APPENDIX. PROOFS OF PROPOSITIONS

Proof of Proposition 1 To characterize the Eﬃcient Bargain, it is simply necessary to note that the individual rationality constraints of the agents are: ðw þ rKi Þei Ci a 0 ðA1Þ ðw þ rKi Þei þ lCi 0: In order for them both to be satisﬁed it must be the case that: w þ rKi Ci [ ei ; ðw þ rKi Þei a : l r Blackwell Publishing Ltd 2004.

ðA2Þ

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A necessary condition for (A2) to be non-empty is w þ rKi ei ðw þ rKi Þei a; l which can be expressed as: w þ rKi

al : ðl 1Þei

It follows that, since ei t there will be no individual for which w þ rKi <

al ðl 1Þt

for which there exists a bargain that fulﬁlls the individual rationality conditions. Therefore individuals with income lower than al=ðl 1Þt will give no contributions and get no exemptions. Now when w þ rKi ½al=ðl 1Þt there will always be a set of eﬃcient bargains which (weakly) Pareto-dominate the reservation utilities, and thus we shall expect ei > 0 in these cases. It is left to establish that when w þ rKi ½al=ðl 1Þt then a full exemption ei ¼ t is granted. To see this, we write down the utility possibilities frontier as the solution to: maxfðw þ rKi Þei Ci ag subject to ðw þ rKi Þei þ lCi u ei ;Ci

ei t: Substituting the ﬁrst constraint in the objective: u ðw þ rKi Þei a subject to ei t: max ðw þ rKi Þei ei ;Ci l l As l > 1, the maximand is linear in ei, and thus ei ¼ t.

&

Proof of Proposition 2 To deal with changes in income distributions as transfers of income, let the income density at any income distribution be distributed as y0 ¼ y þ a(y, s)45 h(y0 , s) such that the percentage of people who receive incomes between y and y before the transfer is the same as the proportion of people who receive incomes between y þ að y; sÞ and y þ að y; sÞ for any y; y: Let að0; sÞ ¼ 0: Therefore: Z y Z yþað y; sÞ f ð yÞdy ¼ hð y0 Þdy0 : y

45

yþað y; sÞ

a(y, s) should not be confused with the ﬁxed cost from rent-seeking a.

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Changing variables under the integral sign gives us: Z y Z y @að y; sÞ f ð yÞdy ¼ hð y þ aðy; sÞÞ 1 þ dy 8 y; y @y y y which implies that hð y þ að y; sÞÞ ¼

f ð yÞ : @að y; sÞ 1þ @y

In other words, we write the income density h as the result of transferring aðy; sÞ units of income to a capitalist with income y from a baseline income density f(y). We can write the net resource transfer as: Z gðy ; sÞ Z y ðy0 Þhðy0 Þdy ¼ t ðy þ aðy; sÞÞf ðyi Þdy; ðA3Þ r¼t w

w

where y ¼ al=tðl 1Þ and gð y ; sÞ is deﬁned implicitly from the equation y þ að y; sÞ ¼ y : We deﬁne a transfer from a group A to a group B as a change in income distribution such that no individual in group A is better oﬀ as a result of the transfer and no individual in group B is worse oﬀ. That is, @að yi ; sÞ[email protected] < 0 only if iAA and @að yi ; sÞ[email protected] > 0 only if iAB. The envelope theorem argument from (11) applies identically to (A3), and since the mean preserving spread among capitalists implies that duk ¼ 0, we can ﬁnd the comparative statics eﬀect of a change in s on r0 only by looking at the sign of @[email protected] We can, without loss of generality, make a(y, s) ¼ 0 at the level of inequality at which we take derivatives. Taking derivatives and using the implicit function rule for @[email protected]; we ﬁnd: 9 8 @að y ; sÞ > > > > =

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and use the same reasoning to derive the eﬀect of a transfer from capitalists with income higher than y to those with income lower than or equal to y . Now consider a transfer of income from workers which leaves untouched the distribution of income among capitalists, as measured by the Lorenz curve of the income distribution. Let h( ) denote the density function for post-transfer income distribution and f( ) for the pre-transfer density. Let y0 (y) be deﬁned implicitly by H(y0 ) ¼ F(y). That is, y0 is the level of income held by the person at the same percentile of the population which held y before the transfer. Remember that the ﬁrst derivative of the Lorenz curve at percentile p is y/mk and the second derivative is 1/mk f(y), with y ¼ F1(p). Therefore if the pre-transfer and post-transfer Lorenz curves are identical, with k the ratio of post- to pre-transfer mk, it means that y0 ¼ ky and h(y0 ) ¼ f(y)/k. We can now write the eﬀective tax rate on capital as: t r r0 ¼ ¼ mk

R y 0

y0 hð y0 Þdy0 t kmk

R yk 0

kyf ð yÞdy t ¼ kmk

R yk 0

yf ð yÞdy mk

with @r0 t ¼ @k mk

( ) 2 y f ð y Þ < 0: k

&

Proof of Lemma 1 First we characterize the levels of ei which will be on the contract curve. We can write the equation for the contract curve as: U w þ rKi ei max n0i ðw þ rKi Þei : ei l l Note that the maximand is increasing (decreasing) in ei when n0i > ð<Þð1=lÞ: Therefore any optimal contract must satisfy: t if n0i > 1=l ei ¼ 0 if n0i < 1=l: The exemption level will be indeterminate for the case with n0i ¼ 1=l. As this will be an occurrence with mass zero we can ignore this knife-edge case. With ei ¼ 0 the individual rationality constraint for the capitalist dictates Ci ¼ 0. Now we can characterize the outcome of the generalized Nash bargaining for n0i > 1=l solution as: Ci ¼ arg maxfð1 ZÞlnðZ0i yi t Ci Þ þ Z lnðyi t þ lCi Þg; r Blackwell Publishing Ltd 2004.

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with ﬁrst-order condition ð1 ZÞ

1 l þZ ¼ 0; n0i yi ei Ci yi ei þ lCi

which, after some algebra, reduces to: 1 Ci ¼ ½Zðln0i 1Þ þ 1yi t: l

&

Proof of Proposition 3 Maximizing (12) with respect to n0i and manipulating the ﬁrst-order condition gives us the optimal n0i (provided a positive payoﬀ) as: ðA5Þ C 01 ðy tð1 ZÞÞ ¼ n : i

0i

We can insert (A5) in (12) to get: Vðyi tÞ ¼ C 01 ðyi tð1 ZÞÞyi t 1 ½ZðlC01 ðyi tð1 ZÞÞ 1Þ þ 1yi t CðC 01 ðyi tð1 ZÞÞÞ: l

ðA6Þ

For political organization to take place, Vðyi tÞ > 0: If C( ) is homogeneous of degree t then we know C0 is homogeneous of degree t1 and C 01 is homogeneous of degree 1/(t1). We can rewrite (A6) being greater than zero as: t

t

Vðyi tÞ ¼ C01 ðð1 ZÞÞðyi tÞt1 ZC01 ð1 ZÞðyi tÞt1 t Z 1 yi t ðyi tÞt1 CðC01 ðð1 ZÞÞÞ > 0; þ l l after some algebra, this becomes: t1 ð1 ZÞ yi t > ðyi tÞ ¼ : l½ð1 ZÞC 01 ðð1 ZÞÞ CðC 01 ðð1 ZÞÞÞ

ðA7Þ

ðA8Þ

Note that the right-hand side of the equation is a complete function of the > 1=l, as at parameters and the function C( ). Note also that at ðyi tÞ ; n0i n0i ¼ 1=l, Vðyi tÞ < 0 and (A5) speciﬁes that n0i is an increasing function of yit. Using Lemma 1 the proposition is established. &

ACKNOWLEDGMENTS

The author thanks Alberto Alesina, Roger Betancourt, Allan Drazen, Elhanan Helpman, Stephen Marglin, John McLaren, Daniel Ortega, Dani Rodrik, Jeﬀrey Sachs, Eduardo Zambrano, participants at seminars at Alicante, Universidad Carlos III, Georgia State, Harvard, IESA, Maryland, Miami, and UC-Irvine, r Blackwell Publishing Ltd 2004.

318

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and an anonymous referee for comments and suggestions. Homero Gutie´rrez provided excellent research assistance. All errors remain my responsibility. FRANCISCO RODRI´GUEZ

Instituto de Estudios Superiores de Administracio´n, Caracas

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