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 Revision

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 (MGR) 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, MGR always appears to "hold" and the implied "optimal" long-run capital tax is strictly positive. (v) Whether MGR holds or not 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 MGR 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 that under incomplete markets the MGR has two margins---an intertemporal margin and an intratemporal margin. Since taxing capital in the steady state permanently hinders individuals' self-insurance positions and thus worsening the intertemporal margin, 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, the modified golden rule can fail to hold in a Ramsey equilibrium whenever the government encounters a debt limit.

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

JEL Classification: E13; E62; H21; H30;

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

Status: Published in Review of Economic Dynamics