By YiLi Chien and Yi Wen
We build a tractable infinite-horizon Aiyagari-type 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 Ramsey steady states and establish several strong and novel results: (i) Depending on the government’s capacity to issue debts, there can exist different types of Ramsey steady state and their existence depends critically on model parameter values. (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, 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, reminiscent of the result obtained by Aiyagari (1995). (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 self-insurance. Since taxing capital in the steady state permanently hinders individuals’ self-insurance positions, the Ramsey planner prefers (i) issuing debt rather than imposing a steady-state capital tax to correct the capital-overaccumulation problem under precautionary saving motives, and (ii) taxing capital only in the short run regardless of its debt positions. Thus, in sharp contrast to Aiyagari’s argument, 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.
The literature on optimal capital taxation seems endless with conclusions getting reversed frequently, like whether eggs are healthy or not. This is another, but important, contribution that maybe will get us closer to resolution.