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Approximate Maximum Likelihood for Complex Structural Models

Author

Listed:
  • Czellar, Veronika

    (Department of Data Science, Economics and Finance, EDHEC Business School)

  • Frazier, David T.

    (Department of Econometrics and Business Statistics, Monash University)

  • Renault, Eric

    (Department of Economics, University of Warwick and Department of Econometrics and Business Statistics, Monash University.)

Abstract
Indirect Inference (I-I) is a popular technique for estimating complex parametric models whose likelihood function is intractable, however, the statistical efficiency of I-I estimation is questionable. While the efficient method of moments, Gallant and Tauchen (1996), promises e ciency, the price to pay for this efficiency is a loss of parsimony and thereby a potential lack of robustness to model misspecification. This stands in contrast to simpler I-I estimation strategies, which are known to display less sensitivity to model misspecification due in large part to their focus on specific elements of the underlying structural model. In this research, we propose a new simulation-based approach that maintains the parsimony of I-I estimation, which is often critical in empirical applications, but can also deliver estimators that are nearly as efficient as maximum likelihood. This new approach is based on using a constrained approximation to the structural model, which ensures identification and can deliver estimators that are consistent and nearly efficient. We demonstrate this approach through several examples, and show that this approach can deliver estimators that are nearly as efficient as maximum likelihood, when feasible, but can be employed in many situations where maximum likelihood is infeasible.

Suggested Citation

  • Czellar, Veronika & Frazier, David T. & Renault, Eric, 2021. "Approximate Maximum Likelihood for Complex Structural Models," The Warwick Economics Research Paper Series (TWERPS) 1337, University of Warwick, Department of Economics.
    • Handle: RePEc:wrk:warwec:1337
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    File URL: https://warwick.ac.uk/fac/soc/economics/research/workingpapers/2021/twerp_1337_-_renault.pdf
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    References listed on IDEAS

    as
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