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Specification tests for partially identified models defined by moment inequalities

  • Federico Bugni

    (Institute for Fiscal Studies and Duke University)

  • Ivan Canay

    (Institute for Fiscal Studies and Northwestern University)

  • Xiaoxia Shi

    (Institute for Fiscal Studies)

This paper studies the problem of specification testing in partially identified models defined by a finite number of moment equalities and inequalities (i.e., (in)equalities). Under the null hypothesis, there is at least one parameter value that simultaneously satisfies all of the moment (in)equalities whereas under the alternative hypothesis there is no such parameter value. While this problem has not been directly addressed in the literature (except in particular cases), several papers have suggested implementing this inferential problem by checking whether confidence intervals for the parameters of interest are empty or not. We propose two hypothesis tests that use the infimum of the sample criterion function over the parameter space as the test statistic together with two different critical values. We obtain two main results. First, we show that the two tests we propose are asymptotically size correct in a uniform sense. Second we show our tests are more powerful than the test that checks whether the confidence set for the parameters of interest is empty or not.

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File URL: http://www.cemmap.ac.uk/wps/cwp011313.pdf
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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP01/13.

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Date of creation: Jan 2013
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Handle: RePEc:ifs:cemmap:01/13
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  1. Joseph P. Romano & Azeem M. Shaikh, 2010. "Inference for the Identified Set in Partially Identified Econometric Models," Econometrica, Econometric Society, vol. 78(1), pages 169-211, 01.
  2. Yuichi Kitamura & Jörg Stoye, 2013. "Nonparametric analysis of random utility models: testing," CeMMAP working papers CWP36/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  3. Maria Ponomareva & Elie Tamer, 2011. "Misspecification in moment inequality models: back to moment equalities?," Econometrics Journal, Royal Economic Society, vol. 14(2), pages 186-203, 07.
  4. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
  5. Federico A. Bugni, 2010. "Bootstrap Inference in Partially Identified Models Defined by Moment Inequalities: Coverage of the Identified Set," Econometrica, Econometric Society, vol. 78(2), pages 735-753, 03.
  6. Canay, Ivan A., 2010. "EL inference for partially identified models: Large deviations optimality and bootstrap validity," Journal of Econometrics, Elsevier, vol. 156(2), pages 408-425, June.
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