This paper examines a dynamic stochastic economy with a benevolent government that cannot commit to its future policies. I consider equilibria that are time-consistent and allow for history-dependent strategies. A new numerical algorithm is developed to solve for the set of equilibrium payoffs. For a baseline economy calibrated to the U.S. economy, the capital income tax with the highest social welfare is slightly procyclical, while the labor income tax is countercyclical. Compared with the data, this equilibrium provides a better account of the cyclical properties of U.S. tax policy than other solutions that abstract from history dependence. The welfare cost of no commitment is about 0.22% of aggregate consumption as compared to the Ramsey allocation with full commitment.
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