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Title: The confidence interval method for selecting valid instrumental variables Authors:  Frank Windmeijer - University of Bristol (United Kingdom) [presenting]
Xiaoran Liang - University of Bristol (United Kingdom)
Fernando Hartwig - University of Bristol (United Kingdom)
Jack Bowden - University of Exeter (United Kingdom)
Abstract: A new method, the confidence interval (CI) method, is proposed 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, meaning that it has the same limiting distribution as the oracle 2SLS estimator with the set of invalid instruments known. This result is the same as for the hard thresholding with voting (HT) method. 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, which determines the width of the confidence intervals. For the CI method, we can therefore use a downward testing procedure based on the Sargan test for overidentifying restrictions.