Deep Learning in the Sequence Space

We develop a deep learning algorithm for approximating functional rational expectations equilibria of dynamic stochastic economies in the sequence space. We use deep neural networks to parameterize equilibrium objects of the economy as a function of truncated histories of exogenous shocks. We train the neural networks to fulfill all equilibrium conditions along simulated paths of the economy. To illustrate the performance of our method, we solve three economies of increasing complexity: the stochastic growth model, a high-dimensional overlapping generations economy with multiple sources of aggregate risk, and finally an economy where households and firms face uninsurable idiosyncratic risk, shocks to aggregate productivity, and shocks to idiosyncratic and aggregate volatility. Furthermore, we show how to design practical neural policy function architectures that guarantee monotonicity of the predicted policies, facilitating the use of the endogenous grid method to simplify parts of our algorithm.