Representativeness and Efficiency in Overidentified IV
Chun Pang Chow, Hiroyuki Kasahara
TLDR
This paper introduces the Representative Targeting (RT) estimator to address efficiency and interpretability issues in GMM for overidentified IV models.
Key contributions
- Identifies that efficient GMM in overidentified IV often uses negative weights, undermining causal interpretation.
- Shows GMM cannot simultaneously achieve efficiency and accommodate researcher-specified weights.
- Introduces the Representative Targeting (RT) estimator to resolve the efficiency-representativeness trade-off.
- RT ensures non-negative weights and achieves semiparametric efficiency for its targeted estimand.
Why it matters
Existing GMM methods for overidentified IV struggle with causal interpretation due to negative weights and cannot balance efficiency with researcher-specified estimands. The RT estimator provides a robust solution, ensuring interpretable, non-negative weights while maintaining statistical efficiency.
Original 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.
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