On the Application of Automatic Differentiation to the Likelihood Function for Dynamic General Equilibrium Models

Author
Houtan Bastani, Luca Guerrieri
Content Type
Working Paper
Institution
Board of Governors of the Federal Reserve System
Abstract
A key application of automatic differentiation (AD) is to facilitate numerical optimization problems. Such problems are at the core of many estimation techniques, including maximum likelihood. As one of the first applications of AD in the field of economics, we used Tapenade to construct derivatives for the likelihood function of any linear or linearized general equilibrium model solved under the assumption of rational expectations. We view our main contribution as providing an important check on finite-difference (FD) numerical derivatives. We also construct Monte Carlo experiments to compare maximum-likelihood estimates obtained with and without the aid of automatic derivatives. We find that the convergence rate of our optimization algorithm can increase substantially when we use AD derivatives.
Topic
Economics, Markets
Political Geography
United States