This paper examines a dynamic stochastic economy with a benevolent government that cannot commit to future policies. Following Phelan and Stacchetti (2001), we consider sequential sustainable equilibria (SSE). We numerically solve for the set of equilibrium payoffs, and investigate whether the time consistency problem of capital income tax is quantitatively important. For a realistically calibrated economy, we find that the optimal sustainable capital income tax rate is pro-cyclical and close to zero on average, while the labor income tax is countercyclical.
Moreover, the welfare cost of no commitment is very small (0:22%) when compared with the Ramsey allocation. We also find that the best sustainable equilibrium outcome may achieve substantially higher social welfare than the
Markov-perfect equilibrium as considered by Klein, Krusell and Rios-Rull (2008).