This paper is a normative investigation of the theoretical and quantitative properties of optimal capital taxation in the neoclassical growth model with aggregate shocks and incomplete markets. The model features a representative-agent economy with linear taxes on labor and capital. I first allow the government to trade only a real risk-free bond. Taxes on capital are set one period in advance, reflecting inertia in tax codes and preventing replication of the completemarkets allocation. Optimal

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... policy has the following features: labor taxes fluctuate very little; capital taxes are volatile and feature a positive (negative) spike after a negative (positive) shock to the government budget; and capital taxes average to roughly zero across periods. I then consider the implications of allowing the government to trade capital. Optimality calls for a large short position.