We show how a heterogeneous agent New Keynesian (HANK) model with incomplete markets and portfolio choice can be estimated in state space using a Bayesian approach. To render estimation feasible, the structure of the economy can be exploited and the dimensionality of the model automatically reduced based on the Bayesian priors. We apply this approach to analyze how much inequality matters for the business cycle and vice versa. Even when the model is estimated on aggregate data alone and with a set of shocks and frictions designed to match aggregate data, it broadly reproduces observed US inequality dynamics. (JEL D31, D52, E12, E32, E52, E62)

In economies with fixed exchange rates, the adjustment to government-spending shocks is asymmetric. Expansionary shocks are absorbed by the real exchange rate, contractionary shocks by output. This result emerges in a small open-economy model with downward nominal wage rigidity and is supported by new empirical evidence based on panel data from different exchange-rate regimes. The exchange-rate regime, economic slack, inflation, and how spending is financed all matter for the fiscal transmission mechanism in the way predicted by the model. Estimates that fail to distinguish between the effects of positive and negative shocks are subject to a “depreciation bias.”