An Alternative Solution Method for Continuous-Time Heterogeneous Agent Models with Aggregate Shocks

The increasing availability of micro data has led researchers to develop increasingly rich heterogeneous agent models. Solving these models involves nontrivial computational costs. The continuous-time solution method proposed by Ahn, Kaplan, Moll, Winberry, and Wolf (NBER Macroeconomics Annual 2017, volume 32) is dramatically fast, making feasible the solution of heterogeneous agent models with aggregate shocks by applying local perturbation and dimension reduction. While this computational innovation contributes enormously to expanding the research frontier, the essential reliance on the local linearization limits a class of problems researchers can investigate to the one where certainty equivalence with respect to aggregate shocks holds. This implies that it may be unsuitable for analyzing models where large aggregate shocks exist or nonlinearity matters. To resolve this issue, I propose an alternative solution method for continuous-time heterogeneous agent models with aggregate shocks by extending the Backward Induction method originally developed for discrete time models by Reiter (2010). The proposed method is nonlinear and global with respect to both idiosyncratic and aggregate shocks. I apply this method to solve a Krusell and Smith (1998) economy and evaluate its performance along two dimensions: accuracy and computation speed. I find that the proposed method is accurate even with large aggregate shocks and high curvature without surrendering computation speed (the baseline economy is solved within a few seconds). This new method is also applied to a model with recursive utility and an Overlapping Generations (OLG) model, and it is able to solve both models quickly and accurately.