Working Paper: CEPR ID: DP16285
Authors: Mahdi Ebrahimi Kahou; Jess Fernández-Villaverde; Jesse Perla; Arnav Sood
Abstract: We propose a new method for solving high-dimensional dynamic programming problems and recursive competitive equilibria with a large (but finite) number of heterogeneous agents using deep learning. The ``curse of dimensionality'' is avoided due to four complementary techniques: (1) exploiting symmetry in the approximate law of motion and the value function; (2) constructing a concentration of measure to calculate high-dimensional expectations using a single Monte Carlo draw from the distribution of idiosyncratic shocks; (3) sampling methods to ensure the model fits along manifolds of interest; and (4) selecting the most generalizable over-parameterized deep learning approximation without calculating the stationary distribution or applying a transversality condition. As an application, we solve a global solution of a multi-firm version of the classic Lucas and Prescott (1971) model of ``investment under uncertainty.'' First, we compare the solution against a linear-quadratic Gaussian version for validation and benchmarking. Next, we solve nonlinear versions with aggregate shocks. Finally, we describe how our approach applies to a large class of models in economics.
Keywords: Machine Learning; Dynamic Programming
JEL Codes: C45; C60; C63
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| exploiting symmetry in the approximate law of motion and the value function (C61) | avoid the curse of dimensionality in high-dimensional dynamic programming problems (C61) |
| constructing a concentration of measure (D30) | enables the calculation of high-dimensional expectations using a single Monte Carlo draw (C15) |
| sampling methods (C83) | ensure the model fits along manifolds of interest (C52) |
| method applied to a multifirm version of the Lucas and Prescott model (E19) | yields results that can be benchmarked against a linear-quadratic Gaussian version (C51) |
| method can be generalized to a large class of models in economics (C51) | broader applicability of findings (C90) |