Taxes and Transfers with Nonlinear Wage Dynamics

We study how the specification of wage risk in quantitative life-cycle models changes the welfare evaluation of taxes and transfers. We estimate four wage processes: a canonical linear process; a flexible nonlinear process with age dependence, non-normality, and state-dependent persistence; and two intermediate processes. Comparisons across the four isolate the role of each feature: age dependence, non-normality, and nonlinear persistence. The estimated processes imply different allocations of wage risk across permanent, persistent, and transitory components: the richer processes assign less risk to short-lived transitory shocks and more to long-lived permanent and persistent components. We embed each process in the same incomplete-markets life-cycle economy with endogenous labor supply. Removing federal tax progressivity and means-tested transfers raises mean welfare by $0.72%$ of lifetime consumption under the nonlinear process but lowers it by $0.47%$ under the non-normal process. These welfare differences reflect both the total amount of wage risk and its allocation across permanent heterogeneity, persistent shocks, and transitory shocks. Holding this amount and allocation fixed, non-normal shocks create rare but severe low-income states that increase the value of public insurance, while the state-dependent mean reversion that characterizes the nonlinear specification works in the opposite direction: unusually bad persistent states tend to be undone by subsequent favorable shocks, so the wage process partly insures itself, and that lowers the value of public insurance.