Journal
ECONOMETRICA
Volume 81, Issue 2, Pages 609-666Publisher
WILEY-BLACKWELL
DOI: 10.3982/ECTA9370
Keywords
Asymptotic size; asymptotic power; conditional moment inequalities; confidence set; Cramervon Mises; generalized moment selection; KolmogorovSmirnov; moment inequalities
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Funding
- National Science Foundation [SES-0751517, SES-1058376]
- Direct For Social, Behav & Economic Scie
- Divn Of Social and Economic Sciences [1058376] Funding Source: National Science Foundation
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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 Cramervon Mises-type or KolmogorovSmirnov-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 n1/2-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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