We provide a theory of truncation for incomplete insurance-market economies with aggregate shocks, which is shown to be a consistent representation of standard incomplete-market economies. This representation allows deriving optimal policies with capital and aggregate shock. We apply this framework to an economy where the government can use capital and labor taxes, positive transfers and public debt to smooth aggregate shocks. The average capital tax is shown to be positive if and only if credit constraints are binding for some households. In a quantitative exercise, the capital tax appears to be more volatile than the labor tax and public debt is countercyclical and mean-reverting.