Don’t Tax Capital — Optimal Ramsey Taxation in Heterogeneous Agent Economies with Quasi-Linear Preferences

Chien, YiLi; Wen, Yi

doi:10.20955/wp.2019.007

Working Paper

Don’t Tax Capital — Optimal Ramsey Taxation in Heterogeneous Agent Economies with Quasi-Linear Preferences

Abstract: We build a tractable heterogeneous-agent incomplete-markets model with quasi-linear preferences to address a set of long-standing issues in the optimal Ramsey taxation literature. The tractability of our model enables us to analytically prove the existence of a Ramsey steady state and establish several novel results (i) Depending on the government's capacity to issue debt, there can exist different types of Ramsey steady states but they have the same implications for optimal long-run tax policies. (ii) The optimal capital tax is exclusively zero in a Ramsey steady state regardless of the modified golden rule and government debt limits. (iii) Along the transition path toward a Ramsey steady state, the optimal capital tax depends positively on the elasticity of intertemporal substitution. (iv) When a Ramsey steady state (featuring a non-binding government debt limit) does not exist but is erroneously assumed to exist, the modified golden rule always \"holds\" and the implied \"optimal\" long-run capital tax is strictly positive. (v) Whether the modified golden rule holds depends critically on the government's capacity to issue debts, but has no bearing on the planner's long-run capital tax scheme. (vi) The optimal debt-to-GDP ratio in the absence of a binding debt limit, however, is determined by a positive wedge times the modified-golden-rule saving rate: The wedge is decreasing in the strength of the individual self-insurance position and approaches zero when the idiosyncratic risk vanishes or markets are complete. The key insight behind our results is the Ramsey planner's ultimate concern for individuals' self-insurance positions. Since taxing capital in the steady state permanently hinders individuals' self-insurance position, the Ramsey planner prefers (i) issuing debt rather than imposing a steady-state capital tax to correct the capital-overaccumulation problem even if the government's debt-limit constraint binds, and (ii) taxing capital only in the short run regardless of the government's debt position. Thus, permanent capital taxation is not the optimal tool to achieve aggregate allocative efficiency despite overaccumulation of capital, and the modified golden rule can fail to hold in a Ramsey equilibrium whenever the government encounters a debt limit.

Keywords: Optimal Capital Taxation; Ramsey Problem; Incomplete Markets;

JEL Classification: E13; E62; H21; H30;

https://doi.org/10.20955/wp.2019.007

Status: Published in Review of Economic Dynamics