Preference responsibility versus poverty reduction in the taxation of labor incomes

https://doi.org/10.1016/j.jpubeco.2021.104386Get rights and content

Highlights

  • We use fairness axioms to build a social welfare function.

  • Our axioms are: Pareto efficiency, preference responsibility and poverty reduction.

  • Tax rates jump at the earning level of a minimum wage household working full-time.

  • Our optimal tax scheme is similar to the current income tax in the United States.

  • A fairness-based approach can close the gap between policy and optimal tax theory.

Abstract

We study the tax schemes that maximize social welfare functions built on axioms of responsibility for one’s preferences (the requirement that the social welfare function should treat identically agents with the same wage, independently of their preferences) and poverty reduction. We find zero and negative marginal tax rates on low incomes at the optimum and bunching at the income level of the most hardworking minimum wage households. When preferences are iso-elastic, we derive the optimal tax formula, which we calibrate to the US economy. Our formula approximates the shape of the current US tax function for households with at least one child. This result suggests that a fairness-based approach, and these axioms in particular, can help close the gap between the recommendations of optimal tax theory and actual policies.

Introduction

Income taxation in general, and labor income taxation in particular, is the ultimate policy instrument to reduce income inequality. Since Mirrlees (1971)’s seminal contribution, most of the literature has embraced the view that full income equality is not a legitimate objective. The literature on optimal taxation is mainly welfarist: the utilitarian objective, especially when individual utility functions are concave, has long been seen appropriate to reduce inequality without eliminating it. Several authors, however, have recently expressed dissatisfaction with the utilitarian objective, in particular when preference heterogeneity is taken into account (see, for instance, Boadway, 2012, or Piketty and Saez, 2013). In addition, as reflected in the above quotation of President Bill Clinton, public tax policy discussions rarely revolve around utilitarian principles and often invoke some notion of “fairness” or other non-welfarist considerations. Finally, Weinzierl (2014) also finds survey-based evidence that most Americans reject important implications of utilitarianism.

An alternative approach to utilitarianism has been recently proposed, after the introduction of the ethics of responsibility into normative debates (see detailed accounts in Roemer, 1998, and Fleurbaey, 2008). This ethics recently emerged in political philosophy and yielded theories of equality of resources and equality of opportunities, to list just two main examples (see Roemer, 1998, and Fleurbaey, 2008 for discussions and references). In a nutshell, the ethics of responsibility is grounded on the assumption that not all inequalities are unjust. As a consequence, the social objective should be to identify and eliminate the unjust inequalities and to remain neutral towards the other inequalities. Several authors have studied the consequences on income taxation of considering that income inequalities due to differences in labor time are not unjust (see Fleurbaey and Maniquet, 2006, Fleurbaey and Maniquet, 2007 and Lockwood and Weinzierl, 2015). To put it differently, under the latter view, agents with the same wage rate should be free to choose their labor time and redistributing incomes among them is not legitimate. In addition to existing references to this view by politicians (see, for instance, the quotation of President Bill Clinton above), it seems to reflect views of citizens. Using questionnaire-based experiments, Konow (2001) presents hypothetical redistribution situations to American subjects. Redistributing production among equally skilled individuals having exerted different levels of efforts is largely viewed as unfair, whereas redistributing from high-skill to low-skill individuals is viewed as fair.1

One may argue, however, that freeness to choose may lead to freeness to lose, if there is not enough redistribution to lift agents out of poverty. Also using questionnaire experiments, Weinzierl (2014) investigates the popular support to redistributing towards the poor. Subjects have to express their opinion over actual and counterfactual tax-transfer schemes in the US. Weinzierl observes that a majority of subjects agree to subsidize the poor but less than what utilitarian or maximin welfarist preferences would recommend. That raises the question of the compatibility between the fairness principles of responsibility and poverty reduction.

In this paper, we derive the formula of the optimal labor income tax scheme consistent with the fairness principles of responsibility and poverty reduction and we calibrate the formula to the US economy. More specifically, we first build a family of social welfare functions that combine neutrality towards inequalities caused by different labor time choices with the goal of reducing poverty. Second, we derive an optimal tax formula from the maximization of these unconventional social welfare functions under incentive and budget constraints.2 Third, using Current Population Survey (CPS) data, in combination with an estimate of the labor supply elasticity from Chetty (2012), we calibrate the formula to the US economy. Finally, we compare the resulting calibrations with the current system.

There are three main lessons to draw from our paper. First, it is possible to define a social objective combining the three goals of poverty alleviation, responsibility and efficiency and to derive the resulting optimal tax. Surprisingly enough, the most basic tension among these three goals is the conflict between poverty reduction and Pareto efficiency. If being poor means consuming a bundle of goods below some poverty line, the main issue comes from the fact that agents may prefer bundles below the poverty line to bundles above it if the labor time associated to the latter is too large. This issue echoes analyses of optimal labor income tax that reduces poverty when poverty is merely defined in terms of income (see, for instance, Kanbur et al., 1994a, Kanbur et al., 1994b, Wane, 2001), and the resulting optimal tax schemes are Pareto inefficient. We propose a definition of “being poor” that is consistent with Pareto efficiency. Somewhat surprisingly, it can easily be further adjusted to also be compatible with the requirement of responsibility (that is the requirement that the social welfare function should be such that, absent any informational constraint, no redistribution take place among agents with the same wage). Being poor, under this definition, means consuming a bundle on an indifference curve that lies everywhere below the poverty line.

The second main lesson of our paper is that it is possible to fully characterize the optimal income tax derived from an unconventional social objective that embodies notions of fairness. Indeed, on the one hand, the literature on optimal taxation has successfully obtained and calibrated expressions detailing the optimal tax as a function of behavioral responses, distribution of income (or types) and a set of weights capturing the normative preferences of society. It has provided very little guidance, however, on how to choose those weights.3 When the objective is utilitarian, for instance, weights depend on an arbitrary cardinalization of the utility function used to describe behavioral responses.

On the other hand, a long tradition in the social choice literature has highlighted how different fairness principles can be called for to characterize social welfare functions (see, among many others, the surveys of Roemer, 1998, Fleurbaey and Maniquet, 2011). Though some criteria for the taxation of labor income have been previously derived from these social welfare functions, this literature has not derived the precise formula of the tax function, leading to somewhat of a disconnect with the optimal tax literature (in addition to not allowing for precise calibrations). As a result, we view this study as an example of how to bridge the divide between the (essentially axiomatic) fairness approach to optimal tax and a classical social welfare function based approach.

The third main lesson of our paper is that the optimal tax function that is consistent with our fairness principles shares some salient features of the current income tax schedule in the US. As can be seen on Fig. 1, the optimal tax corresponding to the combination of Pareto efficiency, responsibility and poverty reduction exhibits zero and negative marginal tax rates on low-incomes as well as a discrete jump to positive marginal tax rates around $16,000. These features are somewhat unconventional in the optimal taxation literature and yet approximate some important characteristics of the current US income tax. The jump mimics the phaseout of the Earned Income Tax Credit (EITC) and of various welfare programs. The existence of non-positive marginal tax rates on low incomes and the steep jump towards positive rates is a very robust result under our normative objective and does not depend on the specific parameterizations of the poverty line, the agents’ preferences or the distribution of types. Finally, depending on the specific parametrization of the poverty line, optimal marginal tax rates on high-incomes may be lower than would be implied by setting the marginal welfare weights to zero in the upper tail (a common normative assumption in the optimal tax literature under utilitarianism).4 We discuss more precisely the similarities and differences between our calibrations and the current US tax schedule in Section 5.

To be precise, we don’t claim that the current US tax schedule is the outcome of maximizing a normative objective similar to ours. Of course a tax schedule is the outcome of a series of reforms inspired by different normative and electoral objectives. What we do claim is that the tax schedule that emerges as optimal in our study is reasonable, given its similarity with an existing one. In addition, we believe that our analysis shows that switching from the traditional utilitarian normative assumption to a fairness-based approach can help close the gap between the recommendations of optimal tax models and the reality of policy.

The rest of the paper is organized as follows. In Section 2, we define the model and the basic properties. In Section 3, we introduce a definition of poverty reduction that is compatible, as a normative goal, with Pareto efficiency and responsibility for agents’ preferences and we define a prominent family of social welfare functions combining the three goals we are interested in as well as a fourth, auxiliary, property. In Section 4, assuming that preferences are quasi-linear and iso-elastic (customary assumptions in the literature), we derive the formula of the second-best tax schemes that maximize our social objective. In Section 5, we estimate the distribution of types using Current Population Survey (CPS) microdata and calibrate the tax formula to the U.S. economy. We also use the CPS data and NBER’s TAXSIM to obtain a description of the current tax system and put our results into perspective.5 Finally, in Section 6, we compare the ability of our results to mimic the U.S. system with that of other optimal tax results in the literature. In Section 7, we give some concluding comments.

Section snippets

The model and the basic axioms

There are two goods, labor time, denoted , and consumption, denoted c. A bundle (of goods) is a pair z=(,c)X=R+2. There is a finite set N of agents. Each agent iN is characterized by their wage, wi[w̲,), and their preferences RiR over bundles. Wages are assumed to be bounded from below. Preferences are assumed to be continuous, increasing in consumption, decreasing in labor time, convex, and such that a best bundle exists in each budget.6

Poverty reduction

Studying poverty reduction first requires introducing a poverty line in the model. We indeed assume that there is a thin, connected and strictly increasing set of bundles in the consumption set that captures the desire by society to let all agents live a materially decent life. Let PLX satisfy the following properties:

  • for all z=(,c),z=(,c)PL, either z=z or <c<c,

  • for all R, there exists cR such that (,c)PL,

  • the set of bundles above PL is convex.

One comment is in order. Our

Optimal tax functions

In the remaining of the paper, we study the properties of the tax schemes that maximize the SWFs we have justified in the previous sections. We adopt the classical Mirrlees setting. The planner does not observe the characteristics of the agents. She only observes their income. She has to design a redistributive tax scheme τ:R+R. As a result, an agent with wage w[w̲,) and a labor time of earns income y=w, pays income tax τ(y) and consumes c=y-τ(y).

Given the complexity of the problem, we

Calibration to the US economy

The optimal tax formula that we obtained in the previous section leaves us with a number of questions that cannot be answered theoretically and that require some calibrations. In general, we are interested in the magnitudes implied by our optimal formula as well as the differences between the three polar choices of R~. More specifically, we focus on four questions - introduced below - that calibrations help us answer. Before proceeding to the analysis, let us briefly describe the data sources

Relationship to the literature

In this section, we compare the shape of our optimal tax scheme with optimal tax schemes derived from other SWFs.

First, when agents are assumed to have identical preferences, in which case the SWF is often written as utilitarian, marginal tax rates are typically large on low incomes and decreasing after, contrary to what we obtain (see Diamond, 1998, for a survey of the consequences of the utilitarian objective). This is the case under the maximin objective in incomes as well. This maximin

Conclusion

This paper starts an analysis of optimal taxation at the level of axioms that the social welfare function should satisfy and it completes the analysis at the level of the full characterization of the optimal tax formula, a formula that is then calibrated to the US economy.

The axioms that we started with embed fairness principles. For this reason, this paper follows a current trend of the literature in which the emphasis shifts from the classical utilitarian objective, in which the social

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

We thank two anonymous referees, the editor, Marianne Bertrand, Stéphane Bonhomme, Richard Blundell, Nathaniel Hendren, Hilary Hoynes, Guy Laroque, Casey Mulligan, Doron Ravid, Raaj Sah, Johannes Spinnewyn, Matthew Weinzierl, Glen Weyl and John Weymark as well as seminar participants at the LSE, IFS, LISER, the Universities of Chicago, Cologne, Manchester, Oslo, the Delhi School of Economics and conference attendees at the 2016 and 2018 Social Choice and Welfare meetings at Lund and Seoul, 2017

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  • Cited by (1)

    François Maniquet’s work was supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ ERC n° 269831. This research advanced while Maniquet was visiting the department of economics of University College London. Generous support from the Leverhulme Foundation is gratefully acknowledged. Declarations of interest: none.

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