Debiased Continuous Updating GMM with Many Weak Instruments

2025-04-25

AI Summary

This paper addresses the pervasive “many weak instruments” problem in health and social sciences—where a large number of weak instrumental variables (IVs), coupled with high-dimensional or nonparametric first-stage estimation, induces severe bias in conventional two-stage generalized method of moments (GMM). To tackle this, we propose a debiased continuous-updating GMM estimator that jointly corrects for the dual bias arising from both the growing number of weak instruments and the first-stage nonparametric/high-dimensional estimation—a novel contribution. Under a weak-identification asymptotic framework, we rigorously establish the estimator’s consistency and asymptotic normality. Monte Carlo simulations demonstrate its robust finite-sample performance. An empirical application to returns to education yields substantially improved estimation accuracy and inference reliability.

Technology Category

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Application Category

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Abstract

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.

Problem

• Address bias from many weak instrumental variables
• Debias first-step nonparametric or high-dimensional estimation
• Ensure consistency under diverging IVs and shrinking identification

Innovation

• Debiased continuous updating estimator (CUE)
• Addresses biases from many weak IVs
• Ensures consistency and asymptotic normality