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Asymptotic Efficiency in Parametric Structural Models with Parameter-Dependent Support

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  • Keisuke Hirano
  • Jack R. Porter

Abstract

In certain auction, search, and related models, the boundary of the support of the observed data depends on some of the parameters of interest. For such nonregular models, standard asymptotic distribution theory does not apply. Previous work has focused on characterizing the nonstandard limiting distributions of particular estimators in these models. In contrast, we study the problem of constructing efficient point estimators. We show that the maximum likelihood estimator is generally inefficient, but that the Bayes estimator is efficient according to the local asymptotic minmax criterion for conventional loss functions. We provide intuition for this result using Le Cam's limits of experiments framework. Copyright The Econometric Society 2003.

Suggested Citation

  • Keisuke Hirano & Jack R. Porter, 2003. "Asymptotic Efficiency in Parametric Structural Models with Parameter-Dependent Support," Econometrica, Econometric Society, vol. 71(5), pages 1307-1338, September.
  • Handle: RePEc:ecm:emetrp:v:71:y:2003:i:5:p:1307-1338
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    Cited by:

    1. Xiaohong Chen & Timothy Christensen & Keith O'Hara & Elie Tamer, 2016. "MCMC Confidence sets for Identified Sets," Cowles Foundation Discussion Papers 2037R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2016.
    2. Xiaohong Chen & Timothy M. Christensen & Elie Tamer, 2017. "Monte Carlo confidence sets for identified sets," CeMMAP working papers CWP43/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Xiaohong Chen & Timothy M. Christensen & Keith O'Hara & Elie Tamer, 2016. "MCMC confidence sets for identified sets," CeMMAP working papers CWP28/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Tong Li & Xiaoyong Zheng, 2009. "Entry and Competition Effects in First-Price Auctions: Theory and Evidence from Procurement Auctions," Review of Economic Studies, Oxford University Press, vol. 76(4), pages 1397-1429.
    5. Vukina, Tomislav & Zheng, Xiaoyong & Marra, Michele & Levy, Armando, 2008. "Do farmers value the environment? Evidence from a conservation reserve program auction," International Journal of Industrial Organization, Elsevier, vol. 26(6), pages 1323-1332, November.
    6. Li, Tong & Zheng, Xiaoyong, 2012. "Information acquisition and/or bid preparation: A structural analysis of entry and bidding in timber sale auctions," Journal of Econometrics, Elsevier, vol. 168(1), pages 29-46.
    7. Xiaohong Chen & Timothy Christensen & Elie Tamer, 2016. "MCMC Confidence sets for Identified Sets," Cowles Foundation Discussion Papers 2037, Cowles Foundation for Research in Economics, Yale University.
    8. Michael Jansson, 2008. "Semiparametric Power Envelopes for Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 76(5), pages 1103-1142, September.
    9. Gaurab Aryal & Dong-Hyuk Kim, 2013. "Emprical Relevance of Ambiguity in First Price Auction Models," ANU Working Papers in Economics and Econometrics 2013-607, Australian National University, College of Business and Economics, School of Economics.
    10. Xiaohong Chen & Timothy Christensen & Elie Tamer, 2016. "Monte Carlo Confidence sets for Identified Sets," Cowles Foundation Discussion Papers 2037R2, Cowles Foundation for Research in Economics, Yale University, revised Sep 2017.
    11. Joris Pinkse & Margaret Slade, 2007. "Semi-structural models of advertising competition," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(7), pages 1227-1246.
    12. Loertscher, Simon & Niedermayer, Andras, 2012. "Assessing the Performance of Simple Contracts Empirically: The Case of Percentage Fees," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 435, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    13. Yu, Ping, 2012. "Likelihood estimation and inference in threshold regression," Journal of Econometrics, Elsevier, vol. 167(1), pages 274-294.
    14. Li, Tong, 2010. "Indirect inference in structural econometric models," Journal of Econometrics, Elsevier, vol. 157(1), pages 120-128, July.
    15. Li, Tong, 2009. "Simulation based selection of competing structural econometric models," Journal of Econometrics, Elsevier, vol. 148(2), pages 114-123, February.
    16. Hickman Brent R. & Hubbard Timothy P. & Sağlam Yiğit, 2012. "Structural Econometric Methods in Auctions: A Guide to the Literature," Journal of Econometric Methods, De Gruyter, vol. 1(1), pages 67-106, August.
    17. Ploberger, Werner & Phillips, Peter C.B., 2012. "Optimal estimation under nonstandard conditions," Journal of Econometrics, Elsevier, vol. 169(2), pages 258-265.
    18. Drost, F.C. & van den Akker, R. & Werker, B.J.M., 2009. "The asymptotic structure of nearly unstable non negative integer-valued AR(1) models," Other publications TiSEM ac0494ae-7a32-43ca-b5b4-d, Tilburg University, School of Economics and Management.
    19. Gourieroux, C. & Jasiak, J., 2008. "Dynamic quantile models," Journal of Econometrics, Elsevier, vol. 147(1), pages 198-205, November.
    20. Yu, Ping, 2015. "Adaptive estimation of the threshold point in threshold regression," Journal of Econometrics, Elsevier, vol. 189(1), pages 83-100.
    21. Wang, Haiying & Sun, Dongchu, 2012. "Objective Bayesian analysis for a truncated model," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2125-2135.
    22. Xiaohong Chen & Timothy Christensen & Elie Tamer, 2016. "Monte Carlo Confidence Sets for Identified Sets," Papers 1605.00499, arXiv.org, revised Sep 2017.
    23. Patrick Bayer & Shakeeb Khan & Christopher Timmins, 2008. "Nonparametric Identification and Estimation in a Generalized Roy Model," NBER Working Papers 13949, National Bureau of Economic Research, Inc.

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