The Confidence Interval Method for Selecting Valid Instrumental Variables

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