Inference Based on Conditional Moment Inequalities

148 Pages Posted: 17 Jun 2010

See all articles by Donald W. K. Andrews

Donald W. K. Andrews

Yale University - Cowles Foundation

Xiaoxia Shi

University of Wisconsin - Madison; Yale University

Multiple version iconThere are 3 versions of this paper

Date Written: June 16, 2010

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

JEL Classification: C12, C15

Suggested Citation

Andrews, Donald W. K. and Shi, Xiaoxia, Inference Based on Conditional Moment Inequalities (June 16, 2010). Cowles Foundation Discussion Paper No. 1761, Available at SSRN: https://ssrn.com/abstract=1625890 or http://dx.doi.org/10.2139/ssrn.1625890

Donald W. K. Andrews (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
203-432-3698 (Phone)
203-432-6167 (Fax)

Xiaoxia Shi

University of Wisconsin - Madison ( email )

1180 Observatory Drive
Madison, WI 53706
United States

Yale University

28 Hillhouse Ave
New Haven, CT 06520-8268
United States

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