Discussion On A New Test Of Conventional Asymptotics In GMM

Under the conventional asymptotic theory in the GMM (Hansen,1982) model, a key assumption is identification; i.e. the moment condition have a unique zero at the true value of parameter and have a full rank gradient. However, when this assumption does not hold (or nearly non-established), to the actual sampleing distribution of estimators, conventional normal asymptotic theory can give a very poor approximation. Recently, much progress has been made that on developing method in GMM with a weak identification, and a few test statistics with good statistic property have been well established. In this paper, a new test statistics L will be introduced which is proposed by Wright in 2010. In order to better discuss this statistic, the paper is divided into three parts. the first part of the GMM model and elaborated on some of the relevant background knowledge, introduction to statistics L in the second part, In the final I give the simulation and discussion of L.