The welfare effects of tax progressivity in a frictional labor market

A progressive tax schedule is usually justified in terms of redistribution and insurance. When the labor market is frictional and there is no intensive margin of labor supply, progressive taxation has been shown to reduce unemployment by lowering wages. However, a more progressive tax schedule discourages the individual's supply of labor and (precautionary) savings, thus potentially reducing capital accumulation and total production. I examine the different effects of a progressive tax and transfer schedule on unemployment, labor income, an individual's labor supply, and savings. My modeling strategy follows Setty and Yedid-Levi (2020), who build on the workhorse model of Krusell et al. (2010), to which I add individual labor supply. I allow for ex ante heterogeneity in productivity, as well as in preferences, while the only idiosyncratic risk is the endogenous risk of unemployment. I compare my baseline model with a frictional labor market to one with a Walrasian labor market where the unemployment risk is exogenous. Steady state comparisons, based on a utilitarian welfare criterion, show that a tax and transfer schedule with a positive degree of progressivity is optimal in both frameworks, and that the presence of labor market friction implies that the optimal level of progressivity is (slightly) higher.