@article{hall_inoue_shin_2008, title={Entropy-based moment selection in the presence of weak identification}, volume={27}, ISSN={["0747-4938"]}, DOI={10.1080/07474930801960261}, abstractNote={Hall et al. (2007) propose a method for moment selection based on an information criterion that is a function of the entropy of the limiting distribution of the Generalized Method of Moments (GMM) estimator. They establish the consistency of the method subject to certain conditions that include the identification of the parameter vector by at least one of the moment conditions being considered. In this article, we examine the limiting behavior of this moment selection method when the parameter vector is weakly identified by all the moment conditions being considered. It is shown that the selected moment condition is random and hence not consistent in any meaningful sense. As a result, we propose a two-step procedure for moment selection in which identification is first tested using a statistic proposed by Stock and Yogo (2003) and then only if this statistic indicates identification does the researcher proceed to the second step in which the aforementioned information criterion is used to select moments. The properties of this two-step procedure are contrasted with those of strategies based on either using all available moments or using the information criterion without the identification pre-test. The performances of these strategies are compared via an evaluation of the finite sample behavior of various methods for inference about the parameter vector. The inference methods considered are based on the Wald statistic, Anderson and Rubin's (1949) statistic, Kleibergen (2002) K statistic, and combinations thereof in which the choice is based on the outcome of the test for weak identification.}, number={4-6}, journal={ECONOMETRIC REVIEWS}, author={Hall, Alastair R. and Inoue, Atsushi and Shin, Changmock}, year={2008}, pages={398–427} }
 @article{hall_inoue_jana_shin_2007, title={Information in generalized method of moments estimation and entropy-based moment selection}, volume={138}, ISSN={["0304-4076"]}, DOI={10.1016/j.jeconom.2006.05.006}, abstractNote={In this paper, we make five contributions to the literature on information and entropy in generalized method of moments (GMM) estimation. First, we introduce the concept of the long run canonical correlations (LRCCs) between the true score vector and the moment function f(vt,θ0) and show that they provide a metric for the information contained in the population moment condition E[f(vt,θ0)]=0. Second, we show that the entropy of the limiting distribution of the GMM estimator can be written in terms of these LRCCs. Third, motivated by the above results, we introduce an information criterion based on this entropy that can be used as a basis for moment selection. Fourth, we introduce the concept of nearly redundant moment conditions and use it to explore the connection between redundancy and weak identification. Fifth, we analyse the behaviour of the aforementioned entropy-based moment selection method in two scenarios of interest; these scenarios are: (i) nonlinear dynamic models where the parameter vector is identified by all the combinations of moment conditions considered; (ii) linear static models where the parameter vector may be weakly identified for some of the combinations considered. The first of these contributions rests on a generalized information equality that is proved in the paper, and may be of interest in its own right.}, number={2}, journal={JOURNAL OF ECONOMETRICS}, author={Hall, Alastair R. and Inoue, Atsushi and Jana, Kalidas and Shin, Changmock}, year={2007}, month={Jun}, pages={488–512} }