Moment and IV Selection Approaches: A Comparative Simulation Study

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), recently extended by Liao (2013) 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). The third one is using a Continuous Updating Objective (CUE) function. This last approach is based on Hong et al. (2003), 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) provides generally better moment selection results than the empirical likelihood and exponential tilting as can be seen in Hong et al. (2003). 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) 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.