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Inference Based on Conditional Moment Inequalities

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.

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File URL: http://cowles.econ.yale.edu/P/cd/d17b/d1761-rra.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 1761RR.

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Length: 170 pages
Date of creation: Jun 2010
Date of revision: May 2012
Publication status: Published in Econometrica (March 2013), 81(2): 609-666
Handle: RePEc:cwl:cwldpp:1761rr
Note: Includes supplement. CFP 1377 and CFP 1377s.
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Web page: http://cowles.econ.yale.edu/

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