Notes on "Positive long run capital taxation: Chamley-Judd revisited" (Ludwig Straub and Ivan Werning)

Positive long run capital taxation: Chamley-Judd revisited

Ludwig Straub and Ivan Werning

Nov. 2014

According to the Chamley-Judd result, capital should not be taxed in the long run. In this paper, we overturn this conclusion, showing that it does not follow from the very models used to derive them. For the model in Judd (1985), we prove that the long run tax on capital is positive and significant, whenever the intertemporal elasticity of substitution is below one. For higher elasticity, the tax converges to zero but may do so at a slow rate, after countries of high tax rates. We also show that inverse elasticity rules are misleading in this content. The model in Chamley (1986) imposes an upper bound on capital taxes. We prove that these constraints may bind forever, implying positive long run taxes. When these bounds do not bind forever the steady state tax is indeed zero; however,  when preferences are recursive, but non-additive over time, the zero-capital-tax limit must be accompanied by zero private wealth (zero tax base) or by zero labor taxes (first best). Finally, we explain why the equivalent of a positive capital tax with ever increasing consumption taxes does not provide a firm rationale against capital taxation.

Elasticity: tax-rate to behavior elasticity

Judd (1985)’s and Chameley’s papers assume that endogenous multiplies associated with the planning problem converge. We have shown that this is not necessarily the case. In fact, as we argued, postulating convergence of endogenous multiplies is equivalent to postulating that the planner’s marginal rate of substitutions equals the agent’s, so that no intertamporal distortion is present. In this sense, assuming this convergence amounts to little more than assuming zero long-run taxes.

In quantitative evaluation it may well be the case that are finds a zero long-run tax on capital. In this paper we stay away from making any such claim, one way or another. We confined attention to the original theoretical results, widely perceived as delivering zero long-run taxation as an ironclad conclusion, independent of parameter value. Based on our analysis, we find little basis for such an interpretation.