The Optimum Quantity of Capital and Debt

Abstract

This paper solves a 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. We theoretically characterize the optimal policy in the long-run steady state and along the full transition path. We 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 the labor tax rate increases from an initial low value to a high steady-state value, the capital income tax rate falls from a very high to a quite low level and government debt converges to its high steady-state level.

Keywords: Optimal Government Debt, Incomplete Markets, Capital Taxation, Dynamically Optimal Taxation

JEL Classification: E62, H20, H60