Moment and IV Selection Approaches: A Comparative Simulation Study
通过模拟比较三种矩选择方法（ALASSO、J检验、连续更新目标函数）在广义矩估计中的表现，发现ALASSO结合无惩罚GMM或矩平均法能最小化结构参数估计的均方根误差。
We compare three moment selection approaches, followed by post-selection estimation strategies. The first is adaptive least absolute shrinkage and selection operator (ALASSO) of Zou (2006 Zou, H. (2006). The adaptive lasso and its oracle properties. Journal of the American Statistical Association 101:1418–1429.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), recently extended by Liao (2013 Liao, Z. (2013). Adaptive GMM shrinkage estimation with consistent moment selection. Econometric Theory FirstView:1–48. [Google Scholar]) to possibly invalid moments in GMM. In this method, we select the valid instruments with ALASSO. The second method is based on the J test, as in Andrews and Lu (2001 Andrews, D. W. K., Lu, B. (2001). Consistent model and moment selection procedures for GMM estimation with application to dynamic panel data models. Journal of Econometrics 101(1):123–164.[Crossref], [Web of Science ®] , [Google Scholar]). The third one is using a Continuous Updating Objective (CUE) function. This last approach is based on Hong et al. (2003 Hong, H., Preston, B., Shum, M. (2003). Generalized empirical likelihood based model selection criteria for moment condition models. Econometric Theory 19(06):923–943. [Google Scholar]), who propose a penalized generalized empirical likelihood-based function to pick up valid moments. They use empirical likelihood, and exponential tilting in their simulations. However, the J-test-based approach of Andrews and Lu (2001 Andrews, D. W. K., Lu, B. (2001). Consistent model and moment selection procedures for GMM estimation with application to dynamic panel data models. Journal of Econometrics 101(1):123–164.[Crossref], [Web of Science ®] , [Google Scholar]) provides generally better moment selection results than the empirical likelihood and exponential tilting as can be seen in Hong et al. (2003 Hong, H., Preston, B., Shum, M. (2003). Generalized empirical likelihood based model selection criteria for moment condition models. Econometric Theory 19(06):923–943. [Google Scholar]). In this article, we examine penalized CUE as a third way of selecting valid moments.Following a determination of valid moments, we run unpenalized generalized method of moments (GMM) and CUE and model averaging technique of Okui (2011 Okui, R. (2011). Instrumental variable estimation in the presence of many moment conditions. Journal of Econometrics 165(1):70–86.[Crossref], [Web of Science ®] , [Google Scholar]) to see which one has better postselection estimator performance for structural parameters. The simulations are aimed at the following questions: Which moment selection criterion can better select the valid ones and eliminate the invalid ones? Given the chosen instruments in the first stage, which strategy delivers the best finite sample performance?We find that the ALASSO in the model selection stage, coupled with either unpenalized GMM or moment averaging of Okui delivers generally the smallest root mean square error (RMSE) for the second stage coefficient estimators.