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) In the absence of any redistributional effects of capital taxation or lump-sum transfers, the optimal capital tax is exclusively zero in a Ramsey steady state regardless of the modified golden rule (MGR) and government debt limits. (ii) Whether the MGR holds or not depends critically on the government's capacity to issue debt but has no bearing on the planner's long-run capital tax scheme. (iii) The optimal debt-to-GDP ratio, however, is determined by a positive wedge times the MGR saving rate: The wedge is decreasing in the strength of individuals' self-insurance positions and approaches zero when the idiosyncratic risk vanishes or markets are complete. (iv) The assumption of the existence of a Ramsey steady state commonly made in the existing literature is not innocuous: When a Ramsey steady state does not exist but is erroneously assumed to exist, the MGR always appears to “hold" and the implied “optimal" long-run capital tax is strictly positive. (v) Along the transition path toward a Ramsey steady state, the optimal capital tax depends positively on the elasticity of intertemporal substitution. The key insight behind our results is that in the absence of any redistributional effects, taxing capital in the steady state permanently hinders individuals' self-insurance positions and thus the Ramsey planner opts to issue debt rather than impose a steady-state capital tax to correct the capital-overaccumulation problem. However, if the demand for debt approaches infinity when the interest rate approaches the time discount rate, a Ramsey steady state may not exist; thus, the MGR can fail to hold in a Ramsey equilibrium whenever the government encounters a binding 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