We construct, and then estimate by maximum likelihood, a tractable dynamic stochastic general equilibrium model with incomplete insurance and heterogenous agents. The key feature of our framework is that cross-sectional heterogeneity remains finite dimensional. The solution to the model thus admits a state- space representation that can be used to recover the distribution of the model's parameters. Household heterogeneity expands the set of observables to cross- sectional moments available at the business-cycle frequency (in addition to theusual macro and monetary time series). Incomplete insurance gives rise to a precautionary motive for holding wealth that propagates aggregate shocks via (i) a stabilizing aggregate supply effect, working through the supply of capital, and (ii) a destabilizing aggregate demand effect coming from the feedback loop between unemployment risk and precautionary saving. Using the estimated model to measure the contribution of precautionary savings to the propagation of recent recessions, we find strong aggregate demand effects during the Great Recession and, to a lesser extent, during the 1990-1991 recession. In contrast, the supply effect at least offsets the demand effect during the 2001 recession.