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Doubly Robust GMM Inference and Differentiated Products Demand Models

Author

Listed:
  • Stépahne Auray

    (CREST; ENSAI; ULCO)

  • Nicolas Lepage-Saucier

    (CREST; ENSAI)

  • Purevdorj Tuvaandor

    (CREST; ENSAI)

Abstract

This paper develops robust inference methods for moment condition models implemented with a n1=2-consistent auxiliary estimator of the nuisance parameters. When applied to models subject to weak identification and boundary parameter problems; they simultaneously overcome both irregularities and are asymptotically pivotal with minimal assumptions on the parameter space. If these problems are not present in the data; they are asymptotically equivalent to standard statistics for nonlinear models. They also have similar computational requirements. We apply our tests to the differentiated products demand model; which may suffer from both problems: the variance of the random coefecients is often close to zero; causing the boundary parameter problem; and the strength of the available instruments is often put in doubt; which may cause weak identification. We evaluate the performance of the proposed tests by simulations.

Suggested Citation

  • Stépahne Auray & Nicolas Lepage-Saucier & Purevdorj Tuvaandor, 2018. "Doubly Robust GMM Inference and Differentiated Products Demand Models," Working Papers 2018-13, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2018-13
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    References listed on IDEAS

    as
    1. Jean‐Pierre Dubé & Jeremy T. Fox & Che‐Lin Su, 2012. "Improving the Numerical Performance of Static and Dynamic Aggregate Discrete Choice Random Coefficients Demand Estimation," Econometrica, Econometric Society, vol. 80(5), pages 2231-2267, September.
    2. Reynaert, Mathias & Verboven, Frank, 2014. "Improving the performance of random coefficients demand models: The role of optimal instruments," Journal of Econometrics, Elsevier, vol. 179(1), pages 83-98.
    3. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    4. Laura Nurski & Frank Verboven, 2016. "Exclusive Dealing as a Barrier to Entry? Evidence from Automobiles," Review of Economic Studies, Oxford University Press, vol. 83(3), pages 1156-1188.
    5. Donald W. K. Andrews & Marcelo J. Moreira & James H. Stock, 2006. "Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression," Econometrica, Econometric Society, vol. 74(3), pages 715-752, May.
    6. Andrews, Donald W.K. & Guggenberger, Patrik, 2017. "Asymptotic Size Of Kleibergen’S Lm And Conditional Lr Tests For Moment Condition Models," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1046-1080, October.
    7. Chaudhuri, Saraswata & Zivot, Eric, 2011. "A new method of projection-based inference in GMM with weakly identified nuisance parameters," Journal of Econometrics, Elsevier, vol. 164(2), pages 239-251, October.
    8. Alon Eizenberg, 2014. "Upstream Innovation and Product Variety in the U.S. Home PC Market," Review of Economic Studies, Oxford University Press, vol. 81(3), pages 1003-1045.
    9. Kenneth L. Judd & Ben Skrainka, 2011. "High performance quadrature rules: how numerical integration affects a popular model of product differentiation," CeMMAP working papers CWP03/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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    More about this item

    Keywords

    Boundary parameter; heterogeneity; pivotal statistic; random utility; robust inference; weak identification.;
    All these keywords.

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