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A Simple Specification Test for Models with Many Conditional Moment Inequalities

Author

Listed:
  • Mathieu Marcoux
  • Thomas Russell
  • Yuanyuan Wan

Abstract

This paper proposes a simple specification test for partially identified models with a large or possibly uncountably infinite number of conditional moment (in)equalities. The approach is valid under weak assumptions, allowing for both weak identification and non-differentiable moment conditions. Computational simplifications are obtained by reusing certain expensive-to-compute components of the test statistic when constructing the critical values. Because of the weak assumptions, the procedure faces a new set of interesting theoretical issues which we show can be addressed by an unconventional sample-splitting procedure that runs multiple tests of the same null hypothesis. The resulting specification test controls size uniformly over a large class of data generating processes, has power tending to 1 for fixed alternatives, and has power against certain local alternatives which we characterize. Finally, the testing procedure is demonstrated in three simulation exercises.

Suggested Citation

  • Mathieu Marcoux & Thomas Russell & Yuanyuan Wan, 2023. "A Simple Specification Test for Models with Many Conditional Moment Inequalities," Working Papers tecipa-764, University of Toronto, Department of Economics.
  • Handle: RePEc:tor:tecipa:tecipa-764
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    References listed on IDEAS

    as
    1. Galichon, Alfred & Henry, Marc, 2009. "A test of non-identifying restrictions and confidence regions for partially identified parameters," Journal of Econometrics, Elsevier, vol. 152(2), pages 186-196, October.
    2. 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, July.
    3. Toru Kitagawa, 2015. "A Test for Instrument Validity," Econometrica, Econometric Society, vol. 83(5), pages 2043-2063, September.
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    More about this item

    Keywords

    Misspecification; Moment Inequality; Partial identification; Specification Testing;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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