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

Hao Hao and Tae‐Hwy Lee

Oxford Bulletin of Economics and Statistics, 2025, vol. 87, issue 5, 899-912

Abstract: 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.

Date: 2025
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