Published 30 March 2026

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This paper develops estimation and inference methods for two-sample instrumental variables (TSIV) regression when the number of instruments k grows proportionally with sample size n. Under this asymptotic setting, we show that the conventional two-sample two-stage least squares (TS2SLS) estimator is generally inconsistent because it suffers from an asymptotic bias of order k/n. To address this issue, we propose a bias-corrected TS2SLS estimator and establish its consistency and asymptotic normality. We further derive heteroskedasticity-robust variance estimators and provide valid Wald and Lagrange multiplier tests for structural parameters. An empirical application to Angrist and Krueger’s (1992) study shows that the conventional estimator substantially understates the effect of school-entry age on educational attainment—by more than 20%when many instruments are used. A simulation study confirms that our bias-corrected estimator exhibits negligible bias and accurate coverage, while the conventional TS2SLS estimator suffers fromsevere attenuation bias and size distortions. These results underscore the importance of addressing many-instrument bias in empirical TSIV applications.