Asymptotic F Tests under Possibly Weak Identification

This paper develops asymptotic F tests robust to weak identification and temporal dependence. The test statistics are modified versions of the S statistic of Stock and Wright (2000) and the K statistic of Kleibergen (2005), both of which are based on the continuous updating generalized method of moments. In the former case, the modification involves only a multiplicative degree-of-freedom adjustment. In the latter case, the modification involves an additional multiplicative adjustment that uses a J statistic for testing overidentification. By adopting fixed-smoothing asymptotics, we show that both the modified S statistic and the modified K statistic are asymptotically F-distributed. The asymptotic F theory accounts for the estimation errors in the underlying heteroskedasticity and autocorrelation robust variance estimators, which the asymptotic chi-squared theory ignores. Monte Carlo simulations show that the F approximations are much more accurate than the corresponding chi-squared approximations in finite samples.