Estimating nonlinear heterogeneous agent models with neural networks

Summary

Focus

Modern macroeconomic models are often challenging to solve, forcing economists to study tractable approximations of these models and limiting their empirical analysis. These simplifications often result in the loss of interesting features of the model, such as non-linear dynamics. However, accounting for these non-linear dynamics is essential to understanding macroeconomic events such as recurring and prolonged periods at the zero lower bound (ZLB), deep recessions and the recent rise in inflation. This raises a critical question: how can we solve and estimate these complex models?

Contribution

We use recent advances in artificial intelligence to develop a neural-network-based method for solving and estimating these non-linear macroeconomic models. Our approach can handle non-linear heterogeneous agent New Keynesian (HANK) models. Therefore, we can now integrate both idiosyncratic and aggregate shocks, along with non-linearities like household borrowing limits and a ZLB constraint. Using simulated data, we show that our method accurately solves and estimates these models.

Findings

We apply our methodology to estimate a HANK model with a ZLB constraint using US data. We show that the interaction between the ZLB constraint and idiosyncratic income risks emerges as a key source of output volatility. Furthermore, the estimated model closely matches a set of key moments in the data, despite its stylised nature.

Abstract

We leverage recent advancements in machine learning to develop an integrated method to solve globally and estimate models featuring agent heterogeneity, nonlinear constraints, and aggregate uncertainty. Using simulated data, we show that the proposed method accurately estimates the parameters of a nonlinear Heterogeneous Agent New Keynesian (HANK) model with a zero lower bound (ZLB) constraint. We further apply our method to estimate this HANK model using U.S. data. In the estimated model, the interaction between the ZLB constraint and idiosyncratic income risks emerges as a key source of aggregate output volatility.

JEL classification: C11, C45, D31, E32, E52

Keywords: neural networks, likelihood, global solution, heterogeneous agents, nonlinearity, aggregate uncertainty, HANK, zero lower bound