Inference Based on Conditional Moment Inequalities

Donald Andrews () and Xiaoxia Shi
Additional contact information
Xiaoxia Shi: Department of Economics, Yale University, https://economics.yale.edu/

No 1761R2, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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 typically have power against n^{-1/2}-local alternatives to some, but not all, sequences of distributions in the null hypothesis. Monte Carlo simulations for five different models show that the methods perform well in finite samples.

Keywords: Asymptotic size; Asymptotic power; Conditional moment inequalities; Confidence set; Cramer-von Mises; Generalized moment selection; Kolmogorov-Smirnov; Moment inequalities (search for similar items in EconPapers)
JEL-codes: C12 C15 (search for similar items in EconPapers)
Pages: 170 pages
Date: 2010-06, Revised 2012-05
Note: Includes supplement. CFP 1377 and CFP 1377s.
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in Econometrica (March 2013), 81(2): 609-666

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Related works:
Journal Article: Inference Based on Conditional Moment Inequalities (2013)
Working Paper: Inference Based on Conditional Moment Inequalities (2011)
Working Paper: Inference Based on Conditional Moment Inequalities (2010)
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