DeepHAM: A Global Solution Method for Heterogeneous Agent Models with Aggregate Shocks

We propose an efficient, reliable, and interpretable global solution method, the Deep learning-based algorithm for Heterogeneous Agent Models (DeepHAM), for solving high dimensional heterogeneous agent models with aggregate shocks. The state distribution is approximately represented by a set of optimal generalized moments. Deep neural networks are used to approximate the value and policy functions, and the objective is optimized over directly simulated paths. In addition to being an accurate global solver, this method has three additional features. First, it is computationally efficient in solving complex heterogeneous agent models, and it does not suffer from the curse of dimensionality. Second, it provides a general and interpretable representation of the distribution over individual states, which is crucial in addressing the classical question of whether and how heterogeneity matters in macroeconomics. Third, it solves the constrained efficiency problem as easily as it solves the competitive equilibrium, which opens up new possibilities for normative studies. As a new application, we study constrained efficiency in heterogeneous agent models with aggregate shocks. We find that in the presence of aggregate risk, a utilitarian planner would raise aggregate capital for redistribution less than in absence of it because poor households do more precautionary savings and thus rely less on labor income.