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Title: Identification-robust tests for probit models with endogenous regressors Authors:  Jean-Marie Dufour - McGill University (Canada)
Tianyu He - McGill University (Canada) [presenting]
Abstract: Weak identification is a well-known issue in the context of linear structural models but is less studied in binary outcome models. We focus on weak identification in probit models with endogenous regressors and propose the asymptotic maximized Monte Carlo test, which is identification-robust. We compare our tests in simulation experiments to generalized minimum distance (MD) robust tests and common asymptotic tests including Wald, Lagrangian multiplier and likelihood ratio (LR) tests based on generalized method of moments (GMM), and likelihood ratio tests based on maximum likelihood estimators (MLE). We find that LR test based on MLE can have large level distortions in the presence of weak identification which is rarely documented in the literature. Meanwhile, our proposed tests control the level regardless of whether the structural parameters are identified. As for the power of tests, the simulation evidence suggests that the proposed tests exhibit reasonable power compared with MD type tests and asymptotic tests based on GMM and MLE whose critical values are locally corrected. We finally apply our method to analyze labor force participation of married female.