Beyond F-statistic - A General Approach for Assessing Weak Identification

We propose a new method to detect weak identification in instrumental variable (IV) models. This method is based on the asymptotic normality of the distributions of the estimated endogenous variable structural equation coefficients in the presence of strong identification. Therefore, our method resulting in a specific test is more flexible than previous tests as it does not depend on a specific class of models, but is applicable for a variety of both linear and non-linear IV models or mixtures of them, which can be estimated by generalized method of moments (GMM). Moreover, our proposed test does not rely on assumptions of homoscedasticity or the absence of autocorrelation. For linear models estimated by two-stage- least-squares (2SLS), our novel test yields the same qualitative conclusions as the usually applied test on excluded instruments at the reduced form. By adopting weak identication definitions of Stock and Yogo (2005), we provide critical values for our test by means of a comprehensive Monte Carlo simulation. This enables applied econometricians to make case- by-case decisions regarding weak identification in non-homoscedastic linear models by using pair bootstrapping procedures. Moreover, we show how our insights can be applied to assess weak identication in a specific non-linear IV model.