Sensitivity Analysis for Golosov , Hassler , Krusell

1 Overview This document studies the sensitivity of the optimal carbon tax formulation derived by Golosov, Hassler, Krusell, and Tsyvinski (2013) ("GHKT"). GHKT show that, under certain assumptions, the optimal carbon tax-GDP ratio can be solved for in closed form, and does not depend on the paths of future output, consumption, and technological change. These assumptions include logarithmic preferences and full depreciation of capital over the course of a decade. This document relaxes these assumptions and explores the numerical sensitivity of the optimal carbon tax-GDP ratio to the structure of preferences, depreciation, and technological progress. It further proposes a slightly modi…ed version of GHKT's central optimal carbon tax formulation that approximates the optimal carbon tax in the case of non-logarithmic constant elasticity utility and non-zero long-run productivity growth. The remainder of this note is structured as follows. Section 2 reviews the planner's problem as presented in GHKT (2013), and then describes our numerical implementation. Section 3 outlines the sensitivity analyses considered, and presents the main quantitative results. Section 4 proposes a modi…cation of GHTK's formula that approximates the optimal carbon tax in the case that preferences are not logarithmic and productivity growth is positive. Finally, Appendix Section 5 compares the numerical model's benchmark case results with those from the true, in…nite-horizon problem as presented in GHTK (2013).