We develop a methodology to derive formulas that facilitate interpretation of the forces determining optimal labor and savings distortions in dynamic settings. The formulas for the labor wedges extend the static optimal taxation analysis of Diamond (1998) and Saez (2001) to dynamic settings. Compared to the static analysis, the dynamic nature of the problem offers three novel insights. First, the opportunity to provide incentives dynamically adds a force lowering labor distortions. Second, labor distortions in dynamic settings may differ significantly from those in static settings because a key determinant of the wedge in the dynamic setting is the conditional rather than the unconditional distribution of skill shocks. The conditional distribution of shocks differs significantly from the unconditional one. Third, the persistence of shocks manifests itself as an increase in the redistributive motive of the planner. We also derive a novel formula to analyze the determinants of the savings distortions.

Our second set of results is to show that the labor wedge tends to zero for sufficiently high skills in both the i.i.d. case and, under certain conditions, in the case of persistent shocks. This is in sharp contrast to the static case with Pareto tail of the skill distribution in Diamond (1998) and Saez (2001), who show that taxes on the high skill agents are increasing and tend to potentially high levels depending on the parameters of the tail.

Our third contribution is to numerically simulate the optimal labor and savings distortions. The analysis is conducted for a realistically calibrated economy based on empirical income distributions. The computed optimal dynamic distortions differ significantly from the optimal static distortions, high-lighting the importance of the forces in the theoretical analysis. The welfare gains compared to optimal linear taxes are non-trivial in the case of the utilitarian social planner and are significant (close to 5% of consumption) for a more redistributive Rawlsian criterion.