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Uniform Inference in Nonlinear Models with Mixed Identification Strength

Listed author(s):
  • Xu Cheng

    ()

    (Department of Economics, University of Pennsylvania)

Registered author(s):

The paper studies inference in nonlinear models where identification loss presents in multiple parts of the parameter space. For uniform inference, we develop a local limit theory that models mixed identification strength. Building on this non-standard asymptotic approximation, we suggest robust tests and confidence intervals in the presence of non-identified and weakly identified nuisance parameters. In particular, this covers applications where some nuisance parameters are non-identified under the null (Davies (1977, 1987)) and some nuisance parameters are subject to a full range of identification strength. The asymptotic results involve both inconsistent estimators that depend on a localization parameter and consistent estimators with different rates of convergence. A sequential argument is used to peel the criterion function based on identification strength of the parameters. The robust test is uniformly valid and non-conservative.

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File URL: http://economics.sas.upenn.edu/system/files/14-018.pdf
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Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 14-018.

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Length: 54 pages
Date of creation: 08 May 2014
Handle: RePEc:pen:papers:14-018
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  9. Adam McCloskey, 2012. "Bonferroni-Based Size-Correction for Nonstandard Testing Problems," Working Papers 2012-16, Brown University, Department of Economics.
  10. Peter C.B. Phillips, 1987. "Partially Identified Econometric Models," Cowles Foundation Discussion Papers 845R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1988.
  11. Donald W.K. Andrews & Panle Jia, 2008. "Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure," Cowles Foundation Discussion Papers 1676, Cowles Foundation for Research in Economics, Yale University.
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  15. Donald W.K. Andrews & Xu Cheng & Patrik Guggenberger, 2011. "Generic Results for Establishing the Asymptotic Size of Confidence Sets and Tests," Cowles Foundation Discussion Papers 1813, Cowles Foundation for Research in Economics, Yale University.
  16. In Choi & Peter C.B. Phillips, 1989. "Asymptotic and Finite Sample Distribution Theory for IV Estimators and Tests in Partially Identified Structural Equations," Cowles Foundation Discussion Papers 929, Cowles Foundation for Research in Economics, Yale University.
  17. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  18. Yuichi Kitamura & Peter C.B. Phillips, 1994. "Fully Modified IV, GIVE and GMM Estimation with Possibly Non-Stationary Regressions and Instruments," Cowles Foundation Discussion Papers 1082, Cowles Foundation for Research in Economics, Yale University.
  19. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-1633, November.
  20. Hahn, Jinyong & Kuersteiner, Guido, 2002. "Discontinuities of weak instrument limiting distributions," Economics Letters, Elsevier, vol. 75(3), pages 325-331, May.
  21. Saraswata Chaudhuri & Eric Zivot, 2008. "A new method of projection-based inference in GMM with weakly identified nuisance parameters," Working Papers UWEC-2008-26, University of Washington, Department of Economics.
  22. Peter C.B. Phillips & Joon Y. Park, 1986. "On the Formulation of Wald Tests of Nonlinear Restrictions," Cowles Foundation Discussion Papers 801, Cowles Foundation for Research in Economics, Yale University.
  23. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation for Research in Economics, Yale University.
  24. Patrik Guggenberger & Frank Kleibergen & Sophocles Mavroeidis & Linchun Chen, 2012. "On the Asymptotic Sizes of Subset Anderson–Rubin and Lagrange Multiplier Tests in Linear Instrumental Variables Regression," Econometrica, Econometric Society, vol. 80(6), pages 2649-2666, November.
  25. Bertille Antoine & Eric Renault, 2009. "Efficient GMM with nearly-weak instruments," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 135-171, 01.
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