Exploiting Symmetry in High-Dimensional Dynamic Programming / Mahdi Ebrahimi Kahou, Jesús Fernández-Villaverde, Jesse Perla, Arnav Sood.

Format:

Book

Author/Creator:

Ebrahimi Kahou, Mahdi.

Contributor:

National Bureau of Economic Research.

Fernández-Villaverde, Jesús.

Perla, Jesse.

Sood, Arnav.

Series:

Working Paper Series (National Bureau of Economic Research) no. w28981.

NBER working paper series no. w28981

Language:

English

Physical Description:

1 online resource: illustrations (black and white);

Place of Publication:

Cambridge, Mass. National Bureau of Economic Research 2021.

Summary:

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. We avoid the curse of dimensionality thanks to three 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; and (3) designing and training deep learning architectures that exploit symmetry and concentration of measure. As an application, we find 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 the nonlinear version where no accurate or closed-form solution exists. Finally, we describe how our approach applies to a large class of models in economics.

Notes:

Print version record

July 2021.