Positive Long Run Capital Taxation: Chamley-Judd Revisited

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 elasticities, the tax converges to zero but may do so at a slow rate, after centuries of high capital taxation. The model in Chamley (1986) imposes an upper bound on capital taxation and we prove that the tax rate may end up at this bound indefinitely. When, instead, the bounds do not bind forever, the long run tax is indeed zero; however, when preferences are recursive but non-additive across time, the zero-capital-tax limit comes accompanied by zero private wealth (zero tax base) or by zero labor taxes (first best). Finally, we explain why the equivalence of a positive capital tax with ever rising consumption taxes does not provide a firm rationale against capital taxation.