Asymptotic F tests under possibly weak identification

This paper develops asymptotic F tests robust to weak identification and temporal dependence. The test statistics we focus on are modified versions of the S statistic of Stock and Wright (2000) and the K statistic of Kleibergen (2005). In the former case, the modification involves only a multiplicative degree-of-freedom adjustment, and the modified S statistic is asymptotically F distributed under fixed-smoothing asymptotics regardless of the strength of the model identification. In the latter case, the modification involves an additional multiplicative adjustment that uses a J statistic for testing overidentification. We show that the modified K statistic is asymptotically F-distributed when the model parameters are completely unidentified or nearly-weakly identified. When the model parameters are weakly identified, the F approximation for the K statistic can be justified under the conventional asymptotics. The F approximations account for the estimation errors in the underlying heteroskedasticity and autocorrelation robust variance estimators, which the chi-squared approximations ignore. Monte Carlo simulations show that the F approximations are much more accurate than the corresponding chi-squared approximations in finite samples.