Econometrica: Jul 2016, Volume 84, Issue 4

Conditional Inference with a Functional Nuisance Parameter

https://doi.org/10.3982/ECTA12868
p. 1571-1612

Isaiah Andrews, Anna Mikusheva

This paper shows that the problem of testing hypotheses in moment condition models without any assumptions about identification may be considered as a problem of testing with an infinite‐dimensional nuisance parameter. We introduce a sufficient statistic for this nuisance parameter in a Gaussian problem and propose conditional tests. These conditional tests have uniformly correct asymptotic size for a large class of models and test statistics. We apply our approach to construct tests based on quasi‐likelihood ratio statistics, which we show are efficient in strongly identified models and perform well relative to existing alternatives in two examples.

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Supplemental Material

Supplement to "Conditional Inference with a Functional Nuisance Parameter"

The supplementary appendix contains additional results concerning the interpretation of our conditional critical values, the bounded completeness of our sufficient statistics, the derivation of the conditioning process hT (.) in homoscedastic linear IV, the power of tests in a simple Gaussian model, the power of the conditional QLR tests in linear IV with non-homoscedastic errors, proofs of asymptotic results stated in the paper, a theoretical analysis and additional simulation results for the quantile IV model, and additional results for Stock and Wright (2000)'s setting.

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