This paper analyzes the theoretical and quantitative implications of optimal capital taxation in the neoclassical growth model with aggregate shocks and incomplete markets. The model features a representative-agent economy with proportional taxes on labor and capital. I first consider the case that the only asset the government can trade is a real risk-free bond. Taxes on capital are set one period in advance, reflecting inertia in tax codes and ruling out replication of the complete markets allocation. Because capital income varies with the state of the economy, capital taxation provides a state contingent source of revenues. I thus identify a novel potential role for capital taxation as a risk sharing instrument between the government and private agents. However, this benefit must be weighted again the distortionary cost of capital taxation. For a baseline case, the optimal policy features a zero tax on capital. Moreover, numerical simulations show that the baseline case provides an excellent benchmark. I next allow the government to hold a non trivial position in capital. Capital ownership provides the same benefit or risk sharing but without the cost of tax distortions. In a variety of quantitative exercises, I show that capital ownership allows the government to realize about 90% of the welfare gains from moving to complete markets. Large positions are typically required for optimality. But smaller positions achieve substantial benefits. In a business-cycle simulation, I show that a 15% short equity position achieves over 40% of the welfare gains from completing markets.
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