Entropy Based Moment Selection in Generalized Method of Moments

Abstract

GMM provides a computationally convenient estimation method and the resulting estimator can be shown to be consistent and asymptotically normal under the fairly moderate regularity conditions. It is widely known that the information content in the population moment condition has impacts on the quality of the asymptotic approximation to finite sample behavior. This dissertation focuses on a moment selection procedure that leads us to choose relevant (asymptotically efficient and non-redundant) moment conditions in the presence of weak identification. The contributions of this dissertation can be characterized as follows: in the framework of linear model, (i) the concept of nearly redundant moment conditions is introduced and the connection between near redundancy and weak identification is explored; (ii) performance of RMSC(c) is evaluated when weak identification is a possibility but the parameter vector to be estimated is not weakly identified by the candidate set of moment conditions; (iii) performance of RMSC(c) is also evaluated when the parameter vector is weakly identified by the candidate set; (iv) a combined strategy of Stock and Yogo's (2002) test for weak identification and RMSC(c) is introduced and evaluated; (v) (i) and (ii) are extended to allow for nonlinear dynamic models. The subsequent simulation results support the analytical findings: when only a part of instruments in the set of possible candidates for instruments are relevant and the others are redundant given all or some of the relevant ones, RMSC(c) chooses all the relevant instruments with high probabilities and improves the quality of the post-selection inferences; when the candidates are in order of their importance, a combined strategy of Stock and Yogo's (2002) pretest and RMSC(c) improves the post-selection inferences, however it tends to select parsimonious models; when all the possible candidates are equally important, it seems that RMSC(c) does not provide any merits. However, in the last case, asymptotic efficiency and non-redundancy can be achieved by basing the estimation and inference on all the possible candidates.