Inference Based on Conditional Moment Inequalities

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

No 1761, 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 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.

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: 148 pages
Date: 2010-06
New Economics Papers: this item is included in nep-ecm and nep-ore
Note: Includes supplement.
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (14)

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Related works:
Journal Article: Inference Based on Conditional Moment Inequalities (2013)
Working Paper: Inference Based on Conditional Moment Inequalities (2012)
Working Paper: Inference Based on Conditional Moment Inequalities (2011)
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