Boosting GMM With Many Instruments When Some Are Invalid And/Or Irrelevant

When the endogenous variable is an unknown function of observable instruments, its conditional mean can be approximated using the sieve functions of observable instruments. We propose a novel instrument selection method, double-criteria boosting (DB), that consistently selects only valid and relevant instruments from a large set of candidate instruments. In the Monte Carlo simulation, we compare generalized method of moments (GMM) using DB (DB-GMM) with other estimation methods and demonstrate that DB-GMM gives lower bias and root mean squared error. In the empirical application to the automobile demand, the DB-GMM estimator is suggesting a more elastic estimate of the price elasticity of demand than the standard two-stage least square estimator.