Deep Learning: Solving HANC and HANK Models in the Absence of Krusell-Smith Aggregation

Abstract

Heterogeneous-agent neoclassical model (HANC) studied by Krusell and Smith (1998) has savings through capital. This model has a remarkable feature of approximate aggregation: the mean of wealth distribution can be accurately predicted with the mean of past wealth distribution. However, if savings are done through bonds, the HANC model does not have this feature (because the mean of bond holding is zero). We solve such model using deep learning solution method in which the decision function and price functions are approximated in terms of true state space of individual and aggregate state variables. The problem has high dimensionlaity (hundreds of state variables) and ill-conditioning but neural network reduces dimensionality and restore numerical stability. Our deep learning method delivers accurate and reliable solutions. We also show how to solve a heterogeneous-agent new Keynesian (HANK) model with savings through bonds and a zero lower bound on the nominal interest rate in the absence of Krusell and Smith (1998) aggregation.