The Confidence Interval Method for Selecting Valid Instrumental Variables

Frank Windmeijer,Xiaoran Liang,Fernando P Hartwig,Jack Bowden

doi:10.1111/rssb.12449

Abstract

AbstractWe propose a new method, the confidence interval (CI) method, to select valid instruments from a larger set of potential instruments for instrumental variable (IV) estimation of the causal effect of an exposure on an outcome. Invalid instruments are such that they fail the exclusion conditions and enter the model as explanatory variables. The CI method is based on the CIs of the per instrument causal effects estimates and selects the largest group with all CIs overlapping with each other as the set of valid instruments. Under a plurality rule, we show that the resulting standard IV, or two-stage least squares (2SLS) estimator has oracle properties. This result is the same as for the hard thresholding with voting (HT) method of Guo et al. (Journal of the Royal Statistical Society : Series B, 2018, 80, 793–815). Unlike the HT method, the number of instruments selected as valid by the CI method is guaranteed to be monotonically decreasing for decreasing values of the tuning parameter. For the CI method, we can therefore use a downward testing procedure based on the Sargan (Econometrica, 1958, 26, 393–415) test for overidentifying restrictions and a main advantage of the CI downward testing method is that it selects the model with the largest number of instruments selected as valid that passes the Sargan test.

Highlights

Instrumental variables (IV) estimation is a well-established method for determining causal effects of an exposure on an outcome, when this relationship is potentially affected by unobserved confounding
Use of invalid instruments in an IV analysis leads to inconsistent estimates of the causal effect and it is important to select the set of valid instruments from the set of putative IVs that may include invalid ones
We have shown that the confidence interval (CI) method for selecting the set of valid instruments from a putative set of instruments that may include invalid ones for an instrumental variables analysis is a viable alternative to the hard thresholding method and the adaptive Lasso method when the plurality rule holds

Summary

Introduction

Instrumental variables (IV) estimation is a well-established method for determining causal effects of an exposure on an outcome, when this relationship is potentially affected by unobserved confounding. (2018) proposed a two-stage hard thresholding with voting (HT) method that results in consistent selection of the valid instruments and oracle properties of the 2SLS estimator when the weaker plurality rule holds. We find that the HT method selects too few instruments as invalid, resulting in models that are rejected by the Sargan test.

Results

Conclusion