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 the Ramsey steady state and establish several novel results within standard parameter spaces: (i) The failure of the modified golden rule (MGR) cannot by itself justify a positive steady-state capital tax—we prove that in the absence of wealth-redistribution effects the optimal capital tax is exclusively zero in the Ramsey steady state regardless of the validity of the MGR. (ii) The optimal capital tax is positive only along the transition path, and it depends positively on the elasticity of intertemporal substitution. (iii) The optimal debt-to-GDP ratio, however, is determined by a positive wedge times the MGR saving rate. The key insight behind our results is that in the absence of any wealth-redistribution effects, taxing capital in the steady state cannot eliminate the liquidity premium—the primal friction in the model—but instead permanently erodes individuals' buffer-stock savings and self-insurance position; thus, the Ramsey planner opts to issue debt rather than impose a steady-state capital tax to correct the capital-overaccumulation problem whenever the interest rate lies below the time discount rate. Also, the MGR fails to hold in a Ramsey equilibrium whenever the government encounters a binding debt limit; but even in this case the optimal long-run capital tax is zero. Therefore, if there is a reason to tax capital in the Ramsey steady state, it may have something to do with the tax's effect on wealth redistribution rather than on the failure of the MGR due to capital overaccumulation.