Optimal Dynamic Income Taxation under Quasi-Hyperbolic Discounting and Idiosyncratic Productivity Shocks

In the context of a dynamic (three-period) general equilibrium model, this paper examines the optimal tax rates on capital savings and labor income under quasi-hyperbolic discounting and idiosyncratic productivity shocks. In the absence of skill-type uncertainty, we analytically show that the marginal capital tax wedges on agents' first-period savings are negative for correcting inherent preference internalities, and that these tax rates will be higher when productivity disturbances are incorporated. In the stochastic two-type setting with exogenously-given factor input prices, our calibrated numerical experiments find that the marginal capital wedges for both types on their period-1 savings are positive, indicating the government's motive to relax individuals' incentive-compatibility constraints. We also quantitatively find that the optimal tax rates for both types on their first- and second-period capital savings, as well as the economy's social welfare, are ceteris paribus decreasing in the degree of quasi-hyperbolic discounting because of a stronger need to rectify negative utility internalities.