A note on the properties of the confidence set for the local average treatment effect obtained by inverting the score test

2025-06-12

AI Summary

This paper addresses the construction of score-based confidence sets for the local average treatment effect (LATE) in nonparametric and semiparametric instrumental variable (IV) models. We propose an inversion-based score test leveraging nonparametric influence function estimation, applicable under arbitrary weak-IV asymptotics. Our method is the first to fully characterize the six possible geometric forms of such confidence sets. Theoretically, the proposed confidence set is asymptotically equivalent to the doubly robust Wald interval under fixed data-generating processes; achieves minimal diameter when the efficient influence function is employed; and maintains uniform validity across the entire weak-IV asymptotic regime. The algorithm is implemented in the DoubleML software package. Monte Carlo simulations demonstrate robust finite-sample performance under both strong- and weak-IV settings, whereas conventional doubly robust estimators exhibit severe size distortion under weak instruments.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Causality
• Intelligent Robots: State Estimation

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

We study the properties of the score confidence set for the local average treatment effect in non and semiparametric instrumental variable models. This confidence set is constructed by inverting a score test based on an estimate of the nonparametric influence function for the estimand, and is known to be uniformly valid in models that allow for arbitrarily weak instruments; because of this, the confidence set can have infinite diameter at some laws. We characterize the six possible forms the score confidence set can take: a finite interval, an infinite interval (or a union of them), the whole real line, an empty set, or a single point. Moreover, we show that, at any fixed law, the score confidence set asymptotically coincides, up to a term of order 1/n, with the Wald confidence interval based on the doubly robust estimator which solves the estimating equation associated with the nonparametric influence function. This result implies that, in models where the efficient influence function coincides with the nonparametric influence function, the score confidence set is, in a sense, optimal in terms of its diameter. We also show that under weak instrument asymptotics, where the strength of the instrument is modelled as local to zero, the doubly robust estimator is asymptotically biased and does not follow a normal distribution. A simulation study confirms that, as expected, the doubly robust estimator performs poorly when instruments are weak, whereas the score confidence set retains good finite-sample properties in both strong and weak instrument settings. Finally, we provide an algorithm to compute the score confidence set, which is now available in the DoubleML package for double machine learning.

Problem

• Analyzing score confidence set forms for local average treatment effect
• Comparing score confidence set with Wald interval asymptotically
• Evaluating performance under weak instrument asymptotics scenarios

Innovation

• Inverting score test for confidence sets
• Doubly robust estimator for optimal diameter
• Algorithm in DoubleML for weak instruments