Deep Learning in the Sequence Space

Abstract

We develop a deep learning algorithm for constructing globally accurate approximations to functional rational expectations equilibria of dynamic stochastic economies in the sequence space. We use deep neural networks to parameterize key equilibrium objects, such as policies or prices, as functions of truncated histories of exogenous shocks. We train the neural networks to satisfy equilibrium conditions along simulated paths of the economy. We illustrate the performance of our method in three environments: (i) a high-dimensional overlapping generations economy with multiple sources of aggregate risk; (ii) an economy with heterogeneous households and firms facing uninsurable idiosyncratic risk and large shocks to idiosyncratic and aggregate volatility; and (iii) a stochastic life-cycle economy with a continuous asset choice and a discrete early-retirement choice that induces local convexities in the continuation values of working-age cohorts. We also propose practical neural policy architectures that guarantee monotonicity of predicted policies, enabling the endogenous grid method to simplify parts of the algorithm. We achieve high precision throughout, with the mean error in equilibrium conditions below $0.2\%$.