Deep Equilibrium Nets

We introduce deep equilibrium nets—a deep learning-based method to compute approximate recursive equilibria of economic models featuring a substantial amount of heterogeneity, significant uncertainty, and occasionally binding constraints. Deep equilibrium nets are neural networks that directly approximate all equilibrium functions and that are trained in an unsupervised fashion to satisfy all equilibrium conditions along simulated paths of the economy. Since the neural network approximates the equilibrium functions directly, simulating the economy is computationally cheap, and training data can be generated at virtually zero cost. We apply our method to solve two distinct annually calibrated overlapping generations models with high-dimensional state-spaces, aggregate uncertainty, illiquid capital, a one-period bond, occasionally binding constraints, and idiosyncratic risk, demonstrating that deep equilibrium nets can solve rich and economically relevant models accurately