Constrained Optimization Approaches to Estimation of Structural Models


  • Che-Lin Su,

    1. University of Chicago, Booth School of Business, Chicago, IL 60637, U.S.A.;
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  • Kenneth L. Judd

    1. Hoover Institution, Stanford, CA 94305, U.S.A. and NBER;
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    • We have greatly benefited from the comments and suggestions of a co-editor and four anonymous referees. We are grateful to Richard W. Cottle and Harry J. Paarsch for their careful reading of this paper and detailed suggestions. We thank Steven Berry, John R. Birge, Jean-Pierre Dubé, Jeremy T. Fox, A. Ronald Gallant, Philip A. Haile, Lars P. Hansen, James J. Heckman, Günter Hitsch, Panle Jia, Sven Leyffer, Todd Munson, Jorge Nocedal, Ariel Pakes, Peter E. Rossi, John Rust, and seminar participants at various universities and conferences for helpful discussions and comments. We acknowledge financial support from the NSF under Grant SES-0631622. Su is grateful for financial support from the IBM Corporation Faculty Research Fund at the University of Chicago Booth School of Business. The AMPL and MATLAB code used in this paper are available at:


Estimating structural models is often viewed as computationally difficult, an impression partly due to a focus on the nested fixed-point (NFXP) approach. We propose a new constrained optimization approach for structural estimation. We show that our approach and the NFXP algorithm solve the same estimation problem, and yield the same estimates. Computationally, our approach can have speed advantages because we do not repeatedly solve the structural equation at each guess of structural parameters. Monte Carlo experiments on the canonical Zurcher bus-repair model demonstrate that the constrained optimization approach can be significantly faster.