The Confidence Interval Method for Selecting Valid Instrumental Variables

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

Bristol Economics Discussion Papers from School of Economics, University of Bristol, UK

Abstract: We propose a new method, the conÂ…dence 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 conÂ…dence intervals of the per instrument causal effects estimates. Each instrument speciÂ…fic causal effect estimate is obtained whilst treating all other instruments as invalid. The CI method selects the largest group with all conÂ…dence 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 of Guo et al. (2018). 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 conÂ…dence intervals. For the CI method, we can therefore use a downward testing procedure based on the Sargan test for overidentifying restrictions. We Â…find in a simulation design similar to that of Guo et al. (2018) better properties for the CI method based estimation and inference than for the HT method and in an application of the effect of BMI on blood pressure that the CI method is better able to detect invalid instruments.

Keywords: Causal inference; Instrumental variables; Invalid instruments (search for similar items in EconPapers)
Date: 2019-06-17
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (2)

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Journal Article: The confidence interval method for selecting valid instrumental variables (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:bri:uobdis:19/715

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