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On the application of automatic differentiation to the likelihood function for dynamic general equilibrium models. (English) Zbl 1151.91605
Bischof, Christian H. (ed.) et al., Advances in automatic differentiation. Selected papers based on the presentations at the 5th international conference on automatic differentiation, Bonn, Germany, August 11–15, 2008. Berlin: Springer (ISBN 978-3-540-68935-5/pbk). Lecture Notes in Computational Science and Engineering 64, 303-313 (2008).
Summary: 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.
For the entire collection see [Zbl 1143.65003].

91B50 General equilibrium theory
91B82 Statistical methods; economic indices and measures
91B62 Economic growth models