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- Title
INFERENCE BASED ON CONDITIONAL MOMENT INEQUALITIES.
- Authors
ANDREWS, DONALD W. K.; XIAOXIA SHI
- 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~l/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.
- Subjects
INFERENTIAL statistics; INSTRUMENTAL variables (Statistics); MATHEMATICAL inequalities; GENERALIZED method of moments; ASYMPTOTIC distribution; NULL hypothesis; MONTE Carlo method
- Publication
Econometrica, 2013, Vol 81, Issue 2, p609
- ISSN
0012-9682
- Publication type
Article
- DOI
10.3982/ECTA9370