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Multiscale Adaptive Inference on Conditional Moment Inequalities

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    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.

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    File URL: http://cowles.econ.yale.edu/P/cd/d18b/d1885.pdf
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    Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1885.

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    Length: 47 pages
    Date of creation: Jan 2013
    Date of revision:
    Handle: RePEc:cwl:cwldpp:1885
    Contact details of provider: Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
    Phone: (203) 432-3702
    Fax: (203) 432-6167
    Web page: http://cowles.econ.yale.edu/

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    Order Information: Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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    1. Beresteanu, Arie & Molinari, Francesca, 2006. "Asymptotic Properties for a Class of Partially Identified Models," Working Papers 06-04, Duke University, Department of Economics.
    2. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, 03.
    3. Ciliberto, Federico & Tamer, Elie, 2009. "Market structure and multiple equilibria in airline markets," MPRA Paper 38635, University Library of Munich, Germany.
    4. Jorg Stoye, 2009. "More on Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 77(4), pages 1299-1315, 07.
    5. Horowitz, Joel L & Spokoiny, Vladimir G, 2001. "An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model against a Nonparametric Alternative," Econometrica, Econometric Society, vol. 69(3), pages 599-631, May.
    6. 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.
    7. Sokbae 'Simon' Lee & Kyungchul Song & Yoon-Jae Whang, 2011. "Testing functional inequalities," CeMMAP working papers CWP12/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Khan, Shakeeb & Tamer, Elie, 2009. "Inference on endogenously censored regression models using conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 152(2), pages 104-119, October.
    9. 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.
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