Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/236703 
Year of Publication: 
2021
Series/Report no.: 
CESifo Working Paper No. 9161
Publisher: 
Center for Economic Studies and Ifo Institute (CESifo), Munich
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.
Subjects: 
dynamic programming
deep learning
breaking the curse of dimensionality
JEL: 
C45
C60
C63
Document Type: 
Working Paper
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