Boosting GMM with Many Instruments When Some Are Invalid 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. Monte Carlo compares GMM using DB with other methods such as GMM using Lasso and shows DB-GMM gives lower bias and RMSE. In the empirical application to automobile demand, the DB-GMM estimator is suggesting a more elastic estimate of the price elasticity of demand than the standard 2SLS estimator.