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Multiscale Adaptive Inference on Conditional Moment Inequalities

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Abstract
This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple analytic formula. We also propose critical values based on a modified bootstrap procedure and prove their asymptotic validity. The asymptotic distribution is extreme value, and the proof uses new techniques to overcome several technical obstacles. We provide power results that show that our test detects local alternatives that approach the identified set at the best possible rate under a set of conditions that hold generically in the set identified case in a broad class of models, and that our test is adaptive to the smoothness properties of the data generating process. Our results also have implications for the use of moment selection procedures in this setting. We provide a monte carlo study and an empirical illustration to inference in a regression model with endogenously censored and missing data.

Suggested Citation

  • Timothy B. Armstrong & Hock Peng Chan, 2013. "Multiscale Adaptive Inference on Conditional Moment Inequalities," Cowles Foundation Discussion Papers 1885, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1885
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    References listed on IDEAS

    as
    1. Andrews, Donald W.K. & Guggenberger, Patrik, 2009. "Validity Of Subsampling And “Plug-In Asymptotic” Inference For Parameters Defined By Moment Inequalities," Econometric Theory, Cambridge University Press, vol. 25(3), pages 669-709, June.
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    More about this item

    Keywords

    Moment inequalities; Set inference; Adaptive inference;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models

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