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Constrainted Optimization Approaches to Estimation of Structural Models


  • Che-Lin Su
  • Kenneth L. Judd


Maximum likelihood estimation of structural models is often viewed as computationally difficult. This impression is due to a focus on the Nested Fixed-Point approach. We present a direct optimization approach to the general problem and show that it is significantly faster than the NFXP approach when applied to the canonical Zurcher bus repair model. The NFXP approach is inappropriate for estimating games since it requires finding all Nash equilibria of a game for each parameter vector considered, a generally intractable computational problem. We formulate the problem of maximum likelihood estimation of games as a constrained optimization problem that is qualitatively no more difficult to solve than standard maximum likelihood problems. The direct optimization approach is also applicable to other structural estimation methods such as methods of moments, and also allows one to use computationally intensive bootstrap methods to calculate inference. The MPEC approach is also easily implemented on software with high-level interfaces. Furthermore, all the examples in this paper were computed using only free resources available on the web.

Suggested Citation

  • Che-Lin Su & Kenneth L. Judd, 2008. "Constrainted Optimization Approaches to Estimation of Structural Models," Discussion Papers 1460, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1460

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    References listed on IDEAS

    1. Border, Kim C, 1991. "Implementation of Reduced Form Auctions: A Geometric Approach," Econometrica, Econometric Society, vol. 59(4), pages 1175-1187, July.
    2. Alexey Malakhov & Rakesh V. Vohra, 2004. "Single and Multi-Dimensional Optimal Auctions - A Network Approach," Discussion Papers 1397, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
    4. Simon Board, 2008. "Durable-Goods Monopoly with Varying Demand," Review of Economic Studies, Oxford University Press, vol. 75(2), pages 391-413.
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    More about this item


    Constrained Optimization; Structural Estimation; Maximum Likelihood Estimation; Games with Multiple Equilibria;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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