We propose and compare new global solution algorithms for continuous time heterogeneous agent economies with aggregate shocks. First, we approximate the agent distribution so that equilibrium in the economy can be characterized by a high, but finite, dimensional non-linear partial differential equation. We consider different approximations: discretizing the number of agents, discretizing the agent state variables, and projecting the distribution onto a finite set of basis functions. Second, we represent the value function using a neural network and train it to solve the differential equation using deep learning tools. We refer to the solution as an Economic Model Informed Neural Network (EMINN). The main advantage of this technique is that it allows us to find global solutions to high dimensional, non-linear problems. We demonstrate our algorithm by solving important models in the macroeconomics and spatial literatures (e.g. Krusell and Smith (1998), Khan and Thomas (2007), Bilal (2023)).

These models feature high degrees of nonlinearity originating from either agents' financial constraints or preferences, which make the linearization methods widely used in the macro literature infeasible. The literature has thus far mostly focused on highly tractable models with a small number of state variables (typically one or two). Furthermore, since solving these models numerically, such as by finite differences (Achdou et al., 2014; Brunnermeier and Sannikov, 2014), could be quite time-consuming, model parameters are often picked by calibration, which involves intensive model evaluation. Matching moments involves solving the model, simulating the model for a long period and calculating the moment value, and repeating the same procedure for a large number of parameter combinations. Although simulated methods of moment have been applied to corporate-finance models (Gomes et al., 2003; Whited and Wu, 2006; Hennessy and Whited, 2007; Matvos and Seru, 2014), dynamic equilibrium models are restricted by the curse of dimensionality. Additionally, taking expectations is typical in dynamic problems, but it incurs a significant computational burden.