Perfectly balanced? - On the optimal tax progressivity for couples and singles

Abstract

In this work I want to find the welfare-optimizing degree of tax progressivity for labor income. To reach this ambitious goal I develop a general equilibrium model in the context of an overlapping generations life-cycle economy with heterogeneity. The economy consists of three different household types, namely married couples, single males and single females. The income is determined by an age- and gender-dependent productivity and a stochastic component. Women can decide between working not at all, part-time or full-time while all men in the economy are assumed to work full-time until they retire. There are utility costs of working for women and transfers for non-working women, both depend on marital status. There are different tax functions of the same form for singles and married couples. I solve the model using Bellman equations and only look at the model in stationary equilibrium. I calibrate the model to US data from PSID to match labor market decisions of single and married women. Then tax progressivity is optimized in two different settings. At first, the optimal tax progressivity for each household type is determined separately by only allowing his tax parameters to change. Couples would prefer a degressive tax system, because their income in my economy is always high enough for them to profit from this tax reform. The lower tax rate for higher incomes sets an incentive for less productive females to join the labor market. This reaction already finances the tax, because even though couple households are taxed less, there is more labor income to tax.The optimal degree of tax progressivity for female singles is larger than in the tax function of the calibrated model. They want to insure themselves better against negative income shocks and more single women are able to work part-time in their optimum opposed to the calibrated model. Labor participation of single females rises overall and their wealth shrinks a little as expected, because in more progressive tax systems the incentives to save are smaller. For single males a corner solution on a restricted range for optimal tax progressivity is found - the most progressive tax system allowed seemingly is the best option for male singles, because they have no way of reacting to changes in labor income taxes and the only goal they have is to insure themselves agains negative income shocks as good as possible.Next, I look for the optimal tax progressivity for singles in general, combining female and male singles. Here the same scenario occurs as in optimizing single males' tax progressivity - a corner solution on the high end of the restricted area of tax progressivities is found to be optimal. The intuition behind the solution is different in this scenario. Single women earn a lot less than single males in the base scenario and the very progressive tax leads to a shift of after-tax labor income from men to women and a huge increase of part-time working single females, because the progressive tax of course also applies to labor income of part-time work. Overall, labor participation is 100\% after this tax reform.\\Finally, the optimal tax progressivity for all types of households together is identified. The restriction of progressivity degree being the same for married couples and singles is imposed. The optimal tax progressivity is very close to the real one, but the difference in tax levels for singles and married couples is huge. The tax level of singles is way lower than the one of married couples, which leads to significant shifts in after-tax labor income from couples to singles. Basically all singles get transfers for working in this system - financed by married couples. As a consequence, a large share of married women switches from working part-time in the benchmark model to working full-time in the optimum. In contrast, more single women prefer to work part-time in the optimum. Because the solution presented above obviously is not Pareto improving, also a set of Pareto improving combinations of progressivity levels is visualised.