The Optimum Quantity of Capital and Debt

In this paper we solve the dynamic optimal Ramsey taxation problem in a model with incomplete markets, where the government commits itself ex-ante to a time path of labor taxes, capital taxes and debt to maximize the discounted sum of agents' utility starting from today. Whereas the literature has been limited mainly to studying policies that maximize steady-state welfare only, we instead characterize the optimal policy along the full transition path. We show theoretically that in the long run the capital stock satisfies the modified golden rule. We also prove that in contrast to complete markets economies, in incomplete markets economies the long run steady-state resulting from an infinite sequence of optimal policy choices is independent of initial conditions. This result is not only of theoretical interest but moreover enables computing the long-run optimum independently from the transition path, rendering a quantitative analysis tractable. Quantitatively we find, robustly across various calibrations, that in the long run the government debt-to-GDP ratio is high, capital is taxed at a low rate and labor income at a high rate when compared to current U.S. values. Along the optimal transition to the steady state, labor taxes initially are lowered, financed through issuing more debt and taxing capital income heavily, before they are eventually increased to their steady-state level.