Weak identification in probit models with endogenous covariates

Weak identification is a well known topic for linear multiple equation models. However, little is known whether this problem also matters for probit models with endogenous covariates. Therefore, the behaviour of the usual z-statistic in case of weak identification is analysed in a simulation study. It shows large size distortions. However, a new puzzle is found: The magnitude of the size distortion depends heavily on the parameter value that is tested. Alternatively the LR-statistic was calculated which is known to be more robust against weak identification in case of linear multiple equation models. The same seems to be true for probit equations. No size distortions are found. However, medium undersizing is observed.