Representativeness and Efficiency in Overidentified IV

TL;DR

This paper introduces the Representative Targeting (RT) estimator for overidentified IV models, balancing efficiency and interpretability by ensuring non-negative weights under heterogeneity.

Contribution

It develops the RT estimator that achieves efficiency while maintaining positive weights, addressing limitations of traditional GMM in heterogeneous settings.

Findings

GMM often assigns negative weights, undermining causal interpretation.

RT estimator achieves the semiparametric efficiency bound with positive weights.

Empirical applications demonstrate RT's effectiveness in real-world scenarios.

Abstract

Under heterogeneous treatment effects, the GMM weighting matrix in overidentified IV models dictates the estimand. We show that efficient GMM downeights high-variance instruments and frequently assigning negative weights that undermine causal interpretation. Moreover, GMM cannot simultaneously achieve efficiency and accommodate researcher-specified weights. We resolve this trade-off by developing the Representative Targeting (RT) estimator. By averaging instrument-specific Wald estimators under Positive Regression Dependence, RT ensures non-negative weights while achieving the semiparametric efficiency bound for its targeted estimand. We demonstrate the heterogeneity penalty empirically in a class-size experiment and apply RT to recover the Policy-Relevant Treatment Effect within a patent leniency design.