A simple and robust confidence interval for causal effects with possibly invalid instruments

TL;DR

This paper introduces a simple, robust confidence interval method for causal effect estimation using instrumental variables that may be invalid, providing theoretical guarantees and improved performance over traditional methods.

Contribution

It proposes a novel, general approach to construct confidence intervals that remain valid even with invalid instruments, enhancing causal inference robustness.

Findings

The robust confidence interval maintains correct coverage with invalid instruments.

It outperforms traditional IV confidence intervals in simulations.

Applied to a developmental economics study, it provided reliable causal estimates.

Abstract

Instrumental variables have been widely used to estimate the causal effect of a treatment on an outcome. Existing confidence intervals for causal effects based on instrumental variables assume that all of the putative instrumental variables are valid; a valid instrumental variable is a variable that affects the outcome only by affecting the treatment and is not related to unmeasured confounders. However, in practice, some of the putative instrumental variables are likely to be invalid. This paper presents a simple and general approach to construct a confidence interval that is robust to possibly invalid instruments. The robust confidence interval has theoretical guarantees on having the correct coverage and can also be used to assess the sensitivity of inference when instrumental variables assumptions are violated. The paper also shows that the robust confidence interval outperforms traditional confidence intervals popular in instrumental variables literature when invalid instruments are present. The new approach is applied to a developmental economics study of the causal effect of income on food expenditures.