An empirically based just linear income tax system

ABSTRACT

This paper develops and illustrates a method for empirically designing an income tax system that people will regard as fair. The paper begins with the classical Principles of Tax Justice, viz., as pretax income increases, three quantities should also increase – posttax income, tax amount, and tax rate. GSOEP data on residents’ pretax income and the posttax income they regard as fair are used to estimate a just linear income tax system. Analytic results include a signature standard form of the tax system showing the intertwined fates of poor and rich and the conditions which threaten fairness. Empirical results show that the estimated tax system lowers taxes for a majority of respondents, especially the relatively poorer, and substantially reduces inequality.

KEYWORDS:

• Principles of tax justice
• just linear income tax system
• inequality

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Acknowledgments

Earlier versions of portions of this paper were presented at the annual meeting of the Econometric Society, San Francisco, CA, December 1983; the annual Group Processes Conference, Las Vegas, NV, August 2011; the Fifth Joint Japan-North America Mathematical Sociology Conference, Denver, CO, August 2012; the annual meeting of the American Sociological Association, Denver, CO, August 2012; the 14^th Biennial Conference of the International Society for Justice Research (ISJR), Rishon LeZion, Israel, September 2012; at the Conference of the Research Committee 28 on Social Stratification of the International Sociological Association (ISA-RC28), Trento, Italy, May 2013; at the Joint Statistical Meetings, Montreal, Canada, August 2013; and at the annual meeting of the American Sociological Association (ASA), New York, NY, August 2013. We thank participants at those conferences and especially Leslie McCall, Maria Metzing, James M. Poterba, Yoshimichi Sato, Simone Schneider, Christian Seidl, Kenneth D. Simonson, anonymous referees, and the Editor for valuable comments and suggestions. We also gratefully acknowledge the intellectual and financial support of Humboldt University and New York University.

Notes

¹ The three Principles have a rich history, which is beyond the scope of this paper. Suffice it to note that the Third Principle is still debated. Adam Smith, [1776] 1976) famously advocates both proportional taxation (Volume Two, Book V, Chapter II, Part II) and, a few pages later, progressive taxation (Volume Two, Book V, Chapter II, Part II, Article I). In the religious world, proportional taxation appears as the Biblical tithe (Deuteronomy 14:28), while progressive taxation appears in the Islamic Zakat. Interestingly, and foreshadowing the analysis below, both the tithe and the Zakat require a fixed proportion; they differ in that the Zakat shelters a need amount (the Nisab), thus transforming Zakat into a progressive tax.

² A few notes on terms: First, the term “tax” encompasses both taxes and transfers. Second, pretax and posttax income are also called initial and final income, respectively. Third, the words “justice” and “fairness” and their cognates are used interchangeably, as is common in the social sciences. Fourth, in discussing the linear tax system, the terms “intercept” and “slope” refer to the intercept and slope in the final income equation (viz., the equation that converts pretax income into posttax income).

³ A person may both “pay a tax” and “receive a subsidy,” in which case the tax t in this paper is the net amount paid. For example, if a person pays $10,000 in taxes and receives transfer payments of $12,000, the tax t is -$2,000 (a net subsidy).

⁴ The tax rate r (the tax paid as a proportion of pretax income) is often called the “effective tax rate” or “average tax rate” to distinguish it from the “marginal tax rate,” which is the tax rate that would apply on an additional dollar of income (Landler, 2012; Sullivan, 2012).

⁵ The contrary phenomena, such as rank reversals, trading places, “the last shall be first” maxims, and so on, are generally considered to lie beyond the ordinary concerns of tax analysis. Of course, understanding tax systems which satisfy the First Principle sheds light on redistributive schemes which do not.

⁶ Sometimes a fourth Principle is proposed, namely, that the marginal tax rate also increase as pretax income increases (or, equivalently, that as pretax income increases, the tax amount increase at an increasing rate). In the linear tax system, the marginal tax rate is constant (the tax amount increases at a constant rate), as will be seen below, and thus we leave to future research the analysis of tax systems which satisfy not only the three Principles highlighted in the classical literature and in this paper but also the fourth Principle on marginal tax rates.

⁷ The positive intercept a also ensures that the tax rate [(x-y)/x] is always less than the marginal tax rate (1-b). If a were zero, the tax rate would equal the marginal tax rate.

⁸ Stuart and Ord (1987, p. 1) opened the classic Kendall’s Advanced Theory of Statistics with a line that slightly modified could serve as the introduction to this Section: “The fundamental notion in statistical theory is that of the group or aggregate, a concept for which statisticians use a special word – ‘population’.” And they started the second paragraph with a line that slightly altered could summarize the work of this Section: “The science of Statistics deals with the properties of populations.” Put differently, Sections 2 and 3 were in the world of mathematics; Section 4 enters the world of statistics.

⁹ People’s ideas of the just k may also depend on the particular source of funds in the injection scenario or the particular expenditures envisioned. Incorporating a family of just k is an important next step for future research.

¹⁰ Consistent with the understanding of pretax income in the German context, actual pretax income includes the worker’s share of mandatory social insurance (roughly half, the other half paid by the employer, of health insurance, nursing care insurance, old age pension insurance, and unemployment insurance). Thus, posttax income equals pretax income minus taxes paid minus mandatory social insurance.

¹¹ The marginal tax rates under discussion in the United States range from 15 to 30%, an interval whose midpoint matches the estimated just marginal tax rate of .225 for Germany.