On the application of automatic differentiation to the likelihood function for dynamic general equilibrium models

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.