When Inequality Matters for Macro and Macro Matters for Inequality

We study the aggregate consumption, interest rate and output dynamics of a heterogeneous agent economy that is parameterized to match key features of the cross-sectional distribution of labor income, wealth, and marginal propensities to consume measured from household-level micro data. Households face a process for idiosyncratic income risk with leptokurtic growth rates and can self-insure in two assets with different degrees of liquidity . The equilibrium features a three-dimensional distribution that moves stochastically over time, rendering computation difficult with existing methods. We develop computational tools to efficiently solve a broad class of heterogeneous agent model with aggregate shocks that include our model as a special case. The method uses linearization to solve for the dynamics of a reduced version of the model, which is obtained from a model-free dimensionality reduction method for the endogenous distributions. We will publish an open source set of Matlab codes to implement our method in an easy-to-use and model-free way. We find that our model, which is parameterized to household level facts, is consistent with the sensitivity of aggregate consumption to predictable changes in aggregate income, and with the relative smoothness of aggregate consumption - features that are difficult to generate in representative agent model. We illustrate the usefulness of our model and methods for studying the distributional implications of shocks more generally.