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Inference Based on Conditional Moment Inequalities

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Abstract

In this paper, we propose an instrumental variable approach to constructing confidence sets (CS's) for the true parameter in models defined by conditional moment inequalities/equalities. We show that by properly choosing instrument functions, one can transform conditional moment inequalities/equalities into unconditional ones without losing identification power. Based on the unconditional moment inequalities/equalities, we construct CS's by inverting Cramer-von Mises-type or Kolmogorov-Smirnov-type tests. Critical values are obtained using generalized moment selection (GMS) procedures. We show that the proposed CS's have correct uniform asymptotic coverage probabilities. New methods are required to establish these results because an infinite-dimensional nuisance parameter affects the asymptotic distributions. We show that the tests considered are consistent against all fixed alternatives and have power against some n^{-1/2}-local alternatives, though not all such alternatives. Monte Carlo simulations for three different models show that the methods perform well in finite samples.

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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1761.

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Length: 148 pages
Date of creation: Jun 2010
Date of revision:
Handle: RePEc:cwl:cwldpp:1761

Note: Includes supplement.
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Keywords: Asymptotic size; asymptotic power; conditional moment inequalities; confidence set; Cramer-von Mises; generalized moment selection; Kolmogorov-Smirnov; moment inequalities;

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Citations

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Cited by:
  1. Andrews, Donald W.K. & Shi, Xiaoxia, 2014. "Nonparametric inference based on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 179(1), pages 31-45.
  2. Jason R. Blevins, 2013. "Non-Standard Rates of Convergence of Criterion-Function-Based Set Estimators," Working Papers 13-02, Ohio State University, Department of Economics.
  3. Laffers, Lukas, 2013. "Identification in Models with Discrete Variables," Discussion Paper Series in Economics 1/2013, Department of Economics, Norwegian School of Economics.
  4. Donald, Stephen G. & Hsu, Yu-Chin, 2014. "Estimation and inference for distribution functions and quantile functions in treatment effect models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 383-397.
  5. Fan, Yanqin & Park, Sang Soo, 2014. "Nonparametric inference for counterfactual means: Bias-correction, confidence sets, and weak IV," Journal of Econometrics, Elsevier, vol. 178(P1), pages 45-56.
  6. Tsunao Okumura & Emiko Usui, 2014. "Concave‐monotone treatment response and monotone treatment selection: With an application to the returns to schooling," Quantitative Economics, Econometric Society, vol. 5, pages 175-194, 03.
  7. Federico Bugni & Ivan Canay & Xiaoxia Shi, 2014. "Specification tests for partially identified models defined by moment inequalities," CeMMAP working papers CWP19/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  8. Ying-Ying Lee, 2014. "Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models," Economics Series Working Papers 706, University of Oxford, Department of Economics.
  9. Toru Kitagawa, 2013. "A bootstrap test for instrument validity in heterogeneous treatment effect models," CeMMAP working papers CWP53/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  10. 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.
  11. Hiroaki Kaido, 2014. "Asymptotically efficient estimation of weighted average derivatives with an interval censored variable," CeMMAP working papers CWP03/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  12. Federico Bugni & Ivan Canay & Xiaoxia Shi, 2014. "Inference for functions of partially identified parameters in moment inequality models," CeMMAP working papers CWP05/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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