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.

We argue that consumer credit spreads matter for household choices and that time-varying spreads have important distributional consequences. Studying Danish household data, we show that consumer credit spreads have heterogeneous impact on asset dynamics and consumption choices across the wealth distribution and that time-varying spreads induce a countercyclical marginal propensity to consume. We study a HANK model where banks provide consumer credit and corporate loans. Through countercyclical credit spreads, frictional finance amplifies aggregate shocks and induces consumption inequality. Economies with less leveraged banks experience reduced aggregate volatility but may face higher volatility and lower welfare at the household level.