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Title: Exogeneity tests, weak identification, incomplete models and instrumental variables: Identification-robust inference Authors:  Jean-Marie Dufour - McGill University (Canada) [presenting]
Abstract: Recent work is reviewed on exogeneity tests in the presence of possibly weak identification, incomplete models, and non-Gaussain errors. After reviewing the finite-sample theory, we study the asymptotic distribution of Durbin-Wu-Hausman (DWH) and Revankar-Hartley (RH) tets for exogeneity, and the properties of pretest estimators where ordinary least squares (OLS) or two-stage least squares (2SLS) estimator is selected depending on the outcome of a DWH- or RH-type test. We consider linear structural models where structural parameters may not be identified and we provide a large-sample analysis of the distribution of the DWH and RH statistics under both the null (exogeneity) and the alternative (endogeneity) hypotheses. Under exogeneity, the usual asymptotic $\chi^2$ critical values are applicable, with or without weak instruments. So, DWH and RH tests are asymptotically identification-robust. A necessary and sufficient condition is given under which all tests are consistent under endogeneity. The condition holds when the usual rank condition for identification in this type of models is satisfied. The consistency condition also holds in a wide range of cases where model identification fails. This is the case when at least one structural parameter is identified. An analysis of the bias and mean squares errors is presented for the pretest estimators. Conditions under which OLS may be preferred to an alternative 2SLS estimator are provided. Empirical results are discussed.