An endogenous gridpoint method for distributional dynamics

Modeling continuous choices in heterogeneous agent models as “lotteries” over a discretized state space is standard practice (Young, 2010), but renders the distributional dynamics linear in optimal policies. We present a novel, simple method that captures nonlinearities and solves the distributional dynamics with interpolation instead of integration using the idea of an endogenous grid. Our approach solves for a stationary equilibrium as quickly as the lottery method for a given precision, outperforms it for linear dynamics, and accommodates nonlinear dynamics and aggregate risk. We demonstrate its efficacy by studying a model with aggregate investment risk with a third-order perturbation solution. • We develop a novel endogenous gridpoint method (DEGM) to solve distributional dynamics in heterogeneous agent models. DEGM is a fast and accurate interpolation scheme that captures nonlinearities without requiring integration. • Compared to the standard lottery method, DEGM converges faster and achieves higher accuracy with fewer gridpoints. This improves the computational tractability of solving models with rich heterogeneity. • We show that DEGM is compatible with third-order perturbation methods and captures nonlinear distributional effects that the lottery method misses. • Applying our method to a model with capital depreciation shocks, we find that aggregate investment risk increases wealth inequality. The effect arises from nonlinear distributional dynamics that DEGM captures and standard methods miss.