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Semiparametric tests of conditional moment restrictions under weak or partial identification. (English) Zbl 1431.62188
Summary: We propose two new semiparametric specification tests which test whether a vector of conditional moment conditions is satisfied for any vector of parameter values $$\theta_{0}$$. Unlike most existing tests, our tests are asymptotically valid under weak and/or partial identification and can accommodate discontinuities in the conditional moment functions. Our tests are moreover consistent provided that identification is not too weak. We do not require the availability of a consistent first step estimator. Like P. M. Robinson [Econometrica 55, 875–891 (1987; Zbl 0651.62107)] and many others in similar problems subsequently, we use $$k$$-nearest neighbor (knn) weights instead of kernel weights. The advantage of using knn weights is that local power is invariant to transformations of the instruments and that under strong point identification computation of the test statistic yields an efficient estimator of $$\theta_{0}$$ as a byproduct.

##### MSC:
 62G10 Nonparametric hypothesis testing 62P20 Applications of statistics to economics
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##### References:
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