Semiparametric Tests of Conditional Moment Restrictions under Weak or Partial Identification∗

We propose two new semiparametric specification tests which test whether a vector of conditional moment conditions is satisfied for any vector of parameter values θ0. Unlike most existing tests, our tests are asymptotically valid under weak and/or partial identification and can accomodate 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 Robinson (1987) 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 θ0 as a byproduct. ∗We thank the co–editor and two anonymous referees for their comments and suggestions. We thank the Human Capital Foundation for their support. †(corresponding author) Department of Economics, The Pennsylvania State University, 608 Kern Graduate Building, University Park PA 16802, [email protected] ‡[email protected]; Joris Pinkse is an extramural fellow at Tilburg University