Causal Inference with Invalid Instruments: Post-selection Problems and A Solution Using Searching and Sampling

TL;DR

This paper develops a robust method for causal inference with potentially invalid instruments, providing uniformly valid confidence intervals through searching and sampling techniques, applicable in observational studies like education and earnings.

Contribution

It introduces a novel searching and sampling approach to construct confidence intervals that are robust to invalid instruments in causal inference.

Findings

Confidence intervals are uniformly valid under finite-sample majority and plurality rules.

The method achieves parametric length, improving precision over existing approaches.

Application to education and earnings demonstrates practical utility.

Abstract

Instrumental variable methods are among the most commonly used causal inference approaches to deal with unmeasured confounders in observational studies. The presence of invalid instruments is the primary concern for practical applications, and a fast-growing area of research is inference for the causal effect with possibly invalid instruments. This paper illustrates that the existing confidence intervals may undercover when the valid and invalid instruments are hard to separate in a data-dependent way. To address this, we construct uniformly valid confidence intervals that are robust to the mistakes in separating valid and invalid instruments. We propose to search for a range of treatment effect values that lead to sufficiently many valid instruments. We further devise a novel sampling method, which, together with searching, leads to a more precise confidence interval. Our proposed searching and sampling confidence intervals are uniformly valid and achieve the parametric length under the finite-sample majority and plurality rules. We apply our proposal to examine the effect of education on earnings. The proposed method is implemented in the R package RobustIV available from CRAN.