Asymptotic efficiency in an instrumental variable model - Chaves, Leonardo Salim Saker (2015)
This work studies the hypothesis testing based on generalized method of moments (GMM) estimation given by instruments condition. The importance for the development of Economics lies on the fact that when identi cation is weak, the standard test can be misleading. Therefore, it is made a review of proposed tests to overcome this problem and also present two useful frameworks of study; from Moreira (2002), Moreira and Moreira (2013) and Kleibergen (2005). So, this work conciliate the previous frameworks a way to write the score proposed initially in Kleibergen (2005) using Moreira and Moreira (2013) statistics and presents the optimal score test based on asymptotic theory from Newey and McFadden (1984). Moreover, the study shows the equivalence between the GMM and maximum likelihood estimation to deal with the weak instruments problem.