On the Optimal Progressivity of the Income Tax Code

Economists throughout recent history have created models in search of answering the following question: what is the optimal income tax structure? Optimal is generally defined by some social welfare function. While liberals generally favor progressive taxes over proportional or regressive taxes for ideological reasons, this paper makes an argument for progressive taxes by employing economic theory. Although they may distort labor supply decisions for individuals at the high end of the income spectrum, progressive taxes not only increase equality in society but also act as a from of insurance from idiosyncratic wage shocks.

The authors overlapping generations (OLG) model has individuals with two types of ability levels (αL, αH). Each year the individual receives an idiosyncratic, serially correlated shock to their wage (ηt). Thus, individual’s wage depends on their 1) age (εj), 2) ability level, 3) the idiosyncratic shock, and 4) overall wage rate in the economy. The individual can save money in a risk free asset, but is not allowed to borrow; thus, having a progressive tax code will act as insurance policy for their after tax income. The authors assume that sales taxes are determined exogenously and Social Security taxes are set at a balance budget level each year. The utility function is assumed to be time separable and each individual has significant levels of risk aversion.

The authors find that a tax structure with a constant marginal tax rate of 17.2% with a fixed $9,400 deduction would be optimal. The taxes implied under this system would be as follows:

Pre-tax Income Tax Owed Average Tax Rate
$5,000 $0 0.0%
$10,000 $103 1.0%
$20,000 $1,823 9.1%
$30,000 $3,543 11.8%
$40,000 $5,263 13.2%
$50,000 $6,983 14.0%
$60,000 $8,703 14.5%
$80,000 $12,143 15.2%
$100,000 $15,583 15.6%
$150,000 $24,183 16.1%
$200,000 $32,783 16.4%
$500,000 $84,383 16.9%

The authors claim that compared to the current U.S. system, their optimal system would have both the poor and the rich paying less taxes with the middle class paying more. An ex-ante expected utility calculation finds that 62% of individuals will have increased utility from this plan over their lifetime.

This paper, however, does have some serious shortcomings. First, sales taxes and Social Security taxes are taken to be exogenous. Second, government spending is taken to be completely exogenous as well. Third, the paper does not allow poor individuals with no income to receive a grant from the government (i.e..: EITC). Also, transfer payments, such as welfare (a.k.a. TANF) are a de facto tax which redistributes income from rich to poor, but these calculations are not taken into account in the paper. Finally, many poor people with incomes near the Medicaid eligibility limit face implicit tax rates of over 100%; the paper ignores government considerations regarding these in-kind transfer programs.

I think this paper is only really important in that it shows that a simplified tax structure is superior to a complicated one, and that some progressivity is desirable even for those with no altruistic leanings in that it acts as insurance against adverse income shocks.