Obtaining Analytic Derivatives for a Class of Discrete-Choice Dynamic Programming Models

This paper shows how to recursively calculate analytic first and second derivatives of the likelihood function generated by a popular version of a discrete-choice, dynamic programming model, allowing for a dramatic decrease in computing time used by derivative-based estimation algorithms. The derivatives also are very useful for finding the exact maximum of the likelihood function, for de-bugging complicated program code, and for estimating standard errors. JEL classification: C4, C5, C6 ∗John Ham would like to thank the NSF for financial support. The authors would like to thank Donghoon Lee, Holger Sieg and Kenneth Wolpin for helpful comments. All mistakes are ours and the opinions expressed here in no way reflect those of the NSF. †Center for Human Resource Research, Ohio State University, 921 Chatham Lane, Suite 100, Columbus, OH 43221, E-mail: [email protected] ‡Professor, Department of Economics, University of Southern California, E-mail: [email protected]