We construct, and estimate by maximum likelihood, a tractable DSGE model with incomplete insurance and heterogenous agents. Household heterogeneity expands the set of potiental observables to cross-sectional moments available at the business-cycle frequency, in addition to the usual macro and monetary time-series. 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 underlying parameters. In our model incomplete insurance gives rise to a precautionary motive for holding wealth that propagates structural shocks via i. a stabilizing aggregate supply effect, working through the supply of capital; and ii. a destabilizing aggregate demand effect, generated by a feedback loop between unemployment risk,
precautionary saving and aggregate demand. 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 has at least offset the demand effect during the 2001 recession. Joint with Julien Matheron, Xavier Ragot, and Juan F. Rubio-Ramirez.