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Inference Based on Many Conditional Moment Inequalities




In this paper, we construct confidence sets for models defined by many conditional moment inequalities/equalities. The conditional moment restrictions in the models can be finite, countably infinite, or uncountably infinite. To deal with the complication brought about by the vast number of moment restrictions, we exploit the manageability (Pollard (1990)) of the class of moment functions. We verify the manageability condition in five examples from the recent partial identification literature. The proposed confidence sets are shown to have correct asymptotic size in a uniform sense and to exclude parameter values outside the identified set with probability approaching one. Monte Carlo experiments for a conditional stochastic dominance example and a random-coefficients binary-outcome example support the theoretical results.

Suggested Citation

  • Donald W.K. Andrews & Xiaoxia Shi, 2015. "Inference Based on Many Conditional Moment Inequalities," Cowles Foundation Discussion Papers 2010, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:2010

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    References listed on IDEAS

    1. Donald W. K. Andrews & Xiaoxia Shi, 2013. "Inference Based on Conditional Moment Inequalities," Econometrica, Econometric Society, vol. 81(2), pages 609-666, March.
    2. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2013. "Testing Many Moment Inequalities," CeMMAP working papers CWP65/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Andrews, Donald W.K. & Shi, Xiaoxia, 2014. "Nonparametric inference based on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 179(1), pages 31-45.
    4. repec:cwl:cwldpp:1840rr is not listed on IDEAS
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    More about this item


    Asymptotic size; Conditional moment inequalities; Confidence set; Many moments; Multiple equilibria; Partial identification; Random coefficients; Stochastic dominance; Test;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables

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