Sensitivity Analysis for Golosov , Hassler , Krusell , and Tsyvinski ( 2014 ) : “ Optimal Taxes on Fossil Fuel in General Equilibrium ”

THIS DOCUMENT STUDIES the sensitivity of the optimal carbon tax formulation derived by Golosov, Hassler, Krusell, and Tsyvinski (2014) (“GHKT”). GHKT showed 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 modified 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 nonzero long-run productivity growth. The remainder of this note is structured as follows. Section 2 reviews the planner’s problem as presented in GHKT (2014), and then describes our numerical implementation. Section 3 outlines the sensitivity analyses considered, and presents the main quantitative results. Section 4 proposes a modification 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 A compares the numerical model’s benchmark case results with those from the true, infinite-horizon problem as presented in GHTK (2014).