Income inequality, size of government, and tax progressivity: A positive theory

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Abstract

I investigate the relationship between income inequality and the composition of public spending in redistributive policies. I extend the Meltzer–Richard model of voting over redistribution allowing voters to choose not only the amount of a uniform lump-sum transfer, but also the level of provision of a public good. The governmental budget is balanced; thus these two choices determine the tax rate on labor income. The multidimensionality of the policy space implies that there is no Condorcet winner. I adopt a citizen-candidate model of electoral competition to tackle this problem. I show that the progressivity of the tax system is increasing in the mean-to-median income ratio while the size of the government need not be. This means that higher income inequality implies a more progressive tax system but, in contrast with the traditional analysis, it may also result in a smaller size of government. Such results are consistent with the most recent findings in the empirical literature.

Introduction

Does the degree of income inequality affect the (i) size and/or the (ii) composition of public spending in redistribution within democratic countries? If so, how? Question (i) has been at the very core of the political economy literature for decades. Conversely, question (ii) has been mostly overlooked.

The seminal theoretical paper by Meltzer and Richard (1981) investigates the relationship between a society’s income distribution and the extent of redistributive policies in the presence of majoritarian institutions. A well-known implication of their analysis is that the size of the governmental sector should be positively related to the degree of income inequality (or more precisely, to the skewness of the income distribution). Such prediction seems to be in sharp contrast with most anecdotal evidence, several examples of which are provided in Bénabou (2000). The author emphasizes that among industrial economies the more unequal ones tend to redistribute less, not more. For instance, one can notice the differences in the extent of redistribution between Europe and the U.S.A., or within Europe as with the case of Scandinavian countries, which are not strongly unequal but have adopted highly redistributive policies. Moreover, Bénabou observes that the cuts in welfare spending experienced by most industrial democracies during the previous two decades occurred at the same time as an unprecedented rise in income inequality.

Such anecdotal evidence is reinforced by several findings in the empirical literature. The predictions of Meltzer and Richard’s model have been tested in several empirical studies (which I survey in the next section), finding very little support. In particular, there is limited evidence of a causal link between the degree of inequality or skewness of the income distribution and the size of public intervention in redistributive policies. Moreover, if any statistically significant relationship is found at all in such studies, it often exhibits the opposite direction relative to the one implied by Meltzer and Richard’s paper. Conversely, there is some evidence that higher income inequality is associated with higher in-cash redistribution, typically in the form of a more progressive tax system.

There are several channels that could explain either part of this puzzle and some, which I briefly mention in the next section, have been investigated extensively in the theoretical literature. This paper provides a mechanism that can explain the puzzle. A number of theoretical and empirical arguments, which I illustrate in the next section, suggest that it may be a key mechanism.1

In light of the empirical regularities, in this paper I claim that the progressivity of the tax system is increasing in income inequality while the size of the government need not be. I focus on one, specific theoretical channel: the role that the interaction among different kinds of policies with redistributive effects (i.e. the composition of public spending) plays in shaping the relationship of interest. The literature has largely overlooked the consequences of such interaction mostly as a result of technical obstacles. Namely, analyzing voters’ choice over various types of redistributive policy requires the use of a multidimensional policy space. Unfortunately, the simple theoretical results that the traditional literature exploits in order to form predictions about equilibrium policy outcome (e.g. the median voter theorem) generally do not hold in a multidimensional policy space. The reason is that in such case a Condorcet winner, i.e. a policy platform that is preferred by the majority of voters to any alternative in the policy space, does not usually exist (Plott, 1967, Grandmont, 1978). Thus, most papers in this literature2 usually focus on studying a single endogenous redistributive policy. As a result, such papers cannot formulate distinct predictions for the size of government and the progressivity of the tax system.

In keeping with recent literature (Calabrese, 2007, Epple, Romano, 2014, Epple, Romano, Sarpça, 2018) I adopt a citizen-candidate model (Osborne, Slivinski, 1996, Besley, Coate, 1997) to tackle the problem of multidimensionality of the policy space. In particular, I build on the model of elections proposed by Dotti (2019b).

Departing from this literature, however, I do not find the equilibrium and the sign of the comparative statics computationally. Instead, I derive sufficient theoretical conditions for existence of a unique single-candidate equilibrium of the citizen-candidate model. I show that these conditions are weaker and easier to verify relative to those required by alternative approaches in the literature, and I derive a sharp characterization of the policy outcome without further restrictions.3

Specifically, I prove that a multidimensional median voter theorem holds, meaning that the median citizen always obtains his/her most preferred policy. Moreover, I show that the equilibrium policy outcome possesses monotone comparative statics properties. These results are rather general, and could prove useful to tackle several other questions in political economy.

I apply these methodological results to study a labor economy in which redistribution can be achieved through two different channels: the tax system vs. the provision of a public good.4 In particular, I assume a tax schedule characterized by two variables: a linear tax on labor income and a uniform lump-sum transfer. Both are assumed to be endogenous outcomes of the political process.

Theorems 1 and 2 deliver the main results of this paper, which are the following. Firstly, I show that Meltzer and Richard (1981) prediction does not generally hold in the augmented model. In particular, if income inequality is sufficiently low in the neighborhood of the equilibrium, then the opposite prediction prevails, i.e. the size of the government is decreasing in the mean-to median income ratio. Secondly, I show that in the augmented model the progressivity of the tax system (and not the overall size of the government sector) is weakly increasing in the mean-to-median income ratio.5

The intuition that underpins this result is simple. The higher the mean-to-median income ratio, the lower the relative income of the pivotal voter. A relatively low income implies not only a stronger support for in-cash redistribution as in the model by Meltzer and Richard (1981), but also a lower preferred level of public good provision (as long as the public good is a normal good). Thus, the progressivity of the tax system is positively related to the skewness of the income distribution while the total size of tax revenues (and in turn total public spending) need not be. These predictions are consistent with the most recent findings in the empirical literature.

The paper is organized as follows. In Section 2, I illustrate the contrast between theoretical prediction of standard models and empirical findings in the literature. In Section 3, I present the model and the equilibrium concept. Section 4 incorporates all results. Section 5 concludes.

Section snippets

Empirical puzzle

In their seminal 1981 paper, Meltzer and Richard analyze the relationship between the mean-to-median income ratio and the size of redistribution policy using a simple general equilibrium labor economy model. They adopt the Downsian framework of electoral competition and assume a unidimensional policy space, in which the collective choice only concerns the amount of a uniform lump-sum transfer financed through a linear tax on labor income. They prove the famous result that

[... ] An increase in

The model

The setup is similar to the one proposed by Meltzer and Richard (1981). The main difference is that the budget of the government is spent not only in-cash redistribution, but also in the provision of a pure public good.

Specifically, the citizens’ population P is a continuum with Lebesgue measure equal to 1. This assumption is meant to represent an economy with a large number of voters. Individuals differ only in their productivity ω, which possesses a continuous distribution over [ω̲,ω¯]. I

Results

Define ω˜γ/u(E[u1(γ/ω)])μ.31 The main results of the paper are stated in the following two theorems.

Theorem 1

There exists a threshold ωˇ[ω̲,ω˜] such that, if ωmωˇ, then the size of the government is weakly decreasing in the mean-to-median income ratio.

Theorem 2

The degree of progressivity of the tax system is weakly increasing in the

Concluding remarks

In this paper I study the effects of a marginal increase in the skewness of the income distribution on the size of the government and on the progressivity of the tax system using a citizen-candidate model of elections. The main novelty of this analysis is that I derive sufficient theoretical condition for the existence of a single-candidate equilibrium and for monotone comparative statics of the policy outcome. These are general results that can prove useful for several applications in

Declarations of Competing Interests

None.

Acknowledgments

I am thankful to Antonio Cabrales, Aureo de Paula, Ian Preston and John Roemer for their invaluable advice and to V. Bhaskar, Marcus Berliant, Randall Calvert, Johannes Hörner, Guy Laroque, Nikita Roketskiy and Larry Samuelson for their helpful comments. I thank the Editor of the European Economic Review Peter Rupert, the Associate Editor, and the anonymous referee for contributing to improve the quality of this manuscript by providing extremely careful and detailed reviews. I also thank

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