The Confidence Interval Method for Selecting Valid Instrumental Variables

• Activity Number: 299 - Machine Learning in Causal Inference with Applications in Complicated Settings
• Type: Topic Contributed
• Date/Time: Wednesday, August 5, 2020 : 10:00 AM to 11:50 AM
• Sponsor: Biometrics Section
• Author(s): Frank Windmeijer*
• Companies: University of Oxford
• Keywords: Causal inference; Instrumental variables; Invalid instruments

Abstract

We propose a new method, the confidence interval (CI) method, to select valid instruments from a set of potential instruments that may contain invalid ones, for instrumental variables estimation of the causal effect of an exposure on an outcome. Invalid instruments are such that they fail the exclusion restriction and enter the model as explanatory variables. The CI method is based on the confidence intervals of the per instrument causal effects estimates. Each instrument specific causal effect estimate is obtained whilst treating all other instruments as invalid. The CI method selects the largest group with all confidence intervals overlapping with each other as the set of valid instruments. Under a plurality rule, we show that the resulting 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. (2018), but 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 of the tuning parameter.