Efficient GMM with nearly-weak identification

This paper is in the line of the recent literature on weak instruments, which, following the seminal approach of Staiger and Stock (1997) and Stock and Wright (2000) captures weak identification by drifting population moment conditions. In contrast with most of the existing literature, we do not specify a priori which parameters are strongly or weakly identified. We rather consider that weakness should be related specifically to instruments, or more generally to the moment conditions. As a consequence, we consider that the relevant partition between the strongly and weakly identified structural parameters can only be achieved after a wellsuited rotation in the parameter space. In addition, we focus here on the case dubbed nearlyweak identification where the drifting DGP introduces a limit rank deficiency reached at a rate slower than root-T . This framework ensures that GMM estimators of all parameters are consistent but at rates possibly slower than usual. This allows us to characterize the validity of the standard testing approaches like Wald and GMM-LM tests. Moreover, we are able to identify and estimate directions in the parameter space where root-T convergence is maintained. These results are all directly relevant for practical applications without requiring the knowledge or the estimation of the slower rates of convergence. JEL Classification: C13; C14; C32.