Economic Inequality, Political Inequality, And Redistribution

Economic Inequality, PoliticalInequality, and RedistributionAdam PrzeworskiAbstractCitizens are not politically equal in economically unequal societies. When political in‡uence of individuals increases in theirincome and political decisions are made by coalitions with greaterpolitical in‡uence, the decisive agent has income higher than themedian. Policy consequences are far reaching. In particular, theextent of redistribution of income through taxes and transfers isnot only always lower than the rate desired by the citizen with themedian income but when political in‡uence is su ciently sensitiveto income, the rate of redistribution falls when income inequalityincreases. The mechanism that generates this pattern is competition among interest groups for political in‡uence. The endresult is that representative institutions do not mitigate economicinequality, as they would in politically egalitarian systems. Yetsome extent of political inequality is inexorable in economicallyunequal societies.1

"The state abolishes, in its own way, distinctions of birth, social rank, education, occupation, when it declares that birth,social rank, education, occupation, are non-political distinctions, when it proclaims, without regard to these distinctions,that every member of the nation is an equal participant innational sovereignty. Nevertheless the state allows privateproperty, education, occupation to act in their way –i.e., asprivate property, as education, as occupation, and to exertthe in‡uence of their special nature." (Marx 1844)1IntroductionCitizens are not politically equal in economically unequal societies. Whilepolitical equality is an attractive normative principle, pace Downs (1957:32-33), the assumption that "the preferences of no one citizen are weightedmore heavily than the preferences of any other citizen" (Dahl and Lindblom 1953: 41) cannot serve as a point of departure for positive analysis.Yet, ever since Black (1948), political economists have relied almost exclusively on a model that assumes political equality of all citizens andimplies that the decisive actor is the one with the median preference,a model extended in the context of income by Romer (1975), Roberts(1977), and Meltzer and Richards (1981) to identify this actor as the onewith median income.1 This entire construction is a house of cards: theassumption of political equality ‡ies in the face of everyday experiencewhile empirical tests of such models fail miserably.Explanations of why the median voter theorem fails come in droves(For overviews, see Putterman (1996), Harms and Zink (2003), Lind(2005), Ansell and Samuels (2010)). Roemer (1998) shows that the rateof redistribution that emerges from electoral competition is lower thanthe one desired by the median voter when the competition entails adimension other than economic. Huber and Staning (2003), Goskens,Golder, and Siegel (2005), as well as Stemueller (2013) single out religion as the second dimension, while Dion (2010) invokes not speci c religions but religious or ethnic fragmentation. Piketty (1995), Fong (2001),and Alesina and Angeletos (2005) argue that people vote according totheir norms of fairness, applying beliefs about whether incomes are generated by e ort or luck. Bénabou and Ok (2001) believe that peoplevote according to their expectations of upward social mobility. Corneo1Bertola (1993) extended this model to the growth framework. Acemoglu andRobinson (2000) used it explain franchise extensions. Rosendorf (2001) applied it toregime transitions. These are just a few examples: applications of this model mustrun in hundreds, if not thousands.2

and Gruner (2000) maintain that the median voter is concerned abouther social status and wants to preserve their distinction from the poor.Przeworski, Rivero, and Xi (2015) assume that feasible redistributionsare constrained by the threat of violent con‡icts. Finally, Bartels (2005)provides evidence that voters who hold egalitarian views often do notunderstand which policies would implement them. My claim is that allthese are second-order reasons: the basic assumption that is wrong withthe median voter model is that citizens are politically equal. Hence, Ijoin Bassett, Burkett, and Putterman (1999), Bénabou (2000), Bernagen and Bräuninger (2005), and Kelly and Enns (2010) in examining thee ects of political inequality.I show that when political in‡uence of individuals increases in theirincomes and political decisions are made by coalitions with greater political in‡uence, the decisive agent has income higher than the median.Policy consequences are far reaching. In particular, the extent of redistribution of income through taxes and transfers ("the sc") is notonly always lower than the rate desired by the citizen with the medianincome but, when political in‡uence is su ciently sensitive to income,the rate of redistribution falls, rather than increase, when income inequality increases. The mechanism that generates this pattern is competition among interest groups for political in‡uence. The end result isthat representative institutions do not mitigate economic inequality, asthey would in politically egalitarian systems. Some extent of politicalinequality, however, is inexorable in economically unequal societies.In what follows, I work backwards. First, I analyze the functioning ofrepresentative institutions just assuming that people with higher incomesexert greater political in‡uence. Only then, I study some mechanisms bywhich economic inequality results in political inequality: lower rates ofpolitical participation among people with lower incomes and competitionfor political in‡uence. The concluding section is a call to rethink otherpolicies through the prism of political inequality.2Political InequalityThis section proves and illustrates the claim that when agents withhigher incomes have more political in‡uence and collective decisions aremade by the coalition majoritarian in political in‡uence, the decisiveagent has income higher than the median and her location in incomedistribution increases as the e ect of income on political in‡uence becomes larger.In what follows, y i stands for income of i 2 [0; 1] and F (y) is somecontinuos, unimodal, right-skewed distribution of income.3

Proposition 1 Assume that income is distributed according to p F (y), where p stands for the location of an individual in the distribution. When all agents have equal political in‡uence, the decisive agent isthe agent with the median income, p 0:5. Given any "political in‡uence function" w(y) y ; with constant elasticity ; the decisive agenti D has pD 0:5 for any 0. Moreover, the higher the ; thehigher the pD of the decisive agent.Proof. Consider any distribution of income FY (y) and a monotonically increasing function of income, w(y); where w stands for "politicalweight." Then the random variable w(y) FW with FW : FY w 1 ;FW (k) p(fw : w 6 kg) p(fy : w(y) 6 kg) p(fy : y 6 w 1 (k)g) FY (w 1 (k)) FY w 1 (k):Assume that collective decisions are made by a coalition majoritarian inpolitical in‡uence and consider a value of w wD ; where D stands forR F (wD )R1"decisive," such that 0 Winf(FW ) 1 (t)dt FW (wD ) inf(FW ) 1 (t)dt:By de nition of Lorenz curve, L(FW (wD )) 0:5. Let w y : Thedistribution of political in‡uence is then FW (w) FY (y ) and F ( 0) 2 F ( 0), where 2 stands for second-order stochastic dominance.Use now the result of Thistle (1989, Proposition 4) that if distributionF1 second-order stochastically dominates F2 , then F1 Lorenz dominatesF2 , i.e. L1 (p) L2 (p) 8p 2 [0; 1]. Hence, L( 0) L( 0), so thatpD ( 0) pD ( 0): It is obvious that when w(y) 1; 8y; L(pD ) 0:5 when p(y D ) 0:5. Because pD ( 0) 0:5, pD ( 0) 0:5:The intuition is embarrassingly simple. The winning coalition is theone for which the sum of political weights is greater. Hence, the decisiveagent is the one whose inclusion determines which coalition –of agentswith incomes lower or higher than she –has larger in‡uence. Take veagents with weights w f1; 2; 3; 4; 5g. The possible coalitions majoritarian in political in‡uence are then f1; 2; 3; 4g; f4:5g and because theagent with w 4 must be included in any majority coalition, this agentis decisive.2 Now, hold the distribution of income constant and compare distributions of political in‡uence di ering in the elasticity of thein‡uence function. The Lorenz curve for higher elasticity lies below withlower elasticity. Hence, the pD for which L(p) 0:5 must be higher forthe more unequal distribution of political in‡uence. Figure 1 shows the2Because w increases monotonically in y and because preferences over r dependonly on income, the order restriction of Rothstein (1991) holds, which implies in turnthat any coalition can contain only individuals with adjacent incomes.4

e ect of political inequality holding income distribution 00.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0pFigure 1: Percentile locations of the decisive agent as a function ofinequality of political in‡uence, given income distribution.Thus, for any distribution of income, political inequality places thedecisive political in‡uence in the hands of an agent with income higherthan the median.3Political Inequality and RedistributionThe main implication of the median voter model is that the rate ofredistribution through the sc increases in income inequality. Supposeeach agent i 2 [0; 1]; with pre- sc income y i ; solves the problemarg maxf(1rr)y i r(1r)yg;(1)where r is the rate of redistribution,4 represents static deadweightloss, due to labor supply, administrative costs, waste, corruption, etc.,and y is the average income. The solution to this problem is0 ifyi yiri y2 yy if 0 1 y i y 21 if1 y i y 23(2)Obviously, the same is true if political elasticity is constant but income inequalityis higher.4I deliberately write the rate of redistribution as r, rather than , because taxrevenues are used for many purposes other than redistribution.5

Now, under the egalitarian mechanism the decisive agent is the agentwith the median income, to be denoted as i M . Hence, in the interior,MrM 1 y2 y and the rate of redistribution moves in the same directionas income inequality, indicated by ; whether 1 y M y or the Ginicoe cient.Consider now inegalitarian mechanisms, for which political in‡uenceis given by w y ; 0; and collective decisions are made by thecoalition majoritarian in in‡uence, The decision about redistribution isnow made by the agent for whom L(FW (w)) 0:5; with income y D :This agent chooses (in the interior)rD ( ; ) 1(12yD ( ; )):y(3)The following result can be proved for the two distributions commonly used to characterize distributions of income: lognormal and Pareto.Proposition 2 If the distribution of income is lognormal, there existsa value 2 1 2 0:71 such that if , the rate of redistributionincreases and if it decreases in income inequality. If incomedistribution is Pareto, the rate of redistribution increases monotonicallyin income inequality if 0:78 and it has an internal maximumif . Moreover, the maximum occurs at a lower level of inequality,so that the rate of redistribution decreases in a broader range of incomeinequality when is larger.Proof. In the Appendix.The intuition behind this result is that as income inequality increases,the ratio of median to mean income decreases but the location of thedecisive agent in income distribution increases. When is su cientlyhigh, the second e ect dominates the rst, so that the ratio y D y increases and rD decreases. These two e ects are portrayed in Figure 2for a Pareto distribution and 0:8:55The range of Gini coe cients of gross income given by SWIID (2011) is from0:17 in Bulgaria in 1968 to 0:79 in the Maldives in 1998. I present most results inthis range.6