Debiased Continuous Updating GMM with Many Weak Instruments

Many weak instrumental variables (IVs) are routinely used in the health and social sciences to improve identification and inference, but can lead to bias in the usual two-step generalized method of moments methods. We propose a new debiased continuous updating estimator (CUE) which simultaneously address the biases from the diverging number of weak IVs, and concomitant first-step nonparametric or high-dimensional estimation of regression functions in the measured covariates. We establish mean-square rate requirements on the first-step estimators so that debiased CUE remains consistent and asymptotically normal under a many weak IVs asymptotic regime, in which the number of IVs diverges with sample size while identification shrinks. We evaluate the proposed method via extensive Monte Carlo studies and an empirical application to estimate the returns to education.