How strong is strong enough? Strengthening instruments through matching and weak instrument tests

Abstract

In a natural experiment, treatment assignments are made through a haphazard process that is thought to be as-if random. In one form of the natural experiment, encouragement to accept treatment rather than treatments themselves are assigned in this haphazard process. This encouragement to accept treatment is often referred to as an instrument. Instruments can be characterized by different levels of strength depending on the amount of encouragement. Weak instruments that provide little encouragement may produce biased inferences, particularly when assignment of the instrument is not strictly randomized. A specialized matching algorithm can be used to strengthen instruments by selecting a subset of matched pairs where encouragement is strongest. We demonstrate how weak instrument tests can guide the matching process to ensure that the instrument has been sufficiently strengthened. Specifically, we combine a matching algorithm for strengthening instruments and weak instrument tests in the context of a study of whether turnout influences party vote share in US elections. It is thought that when turnout is higher, Democratic candidates will receive a higher vote share. Using excess rainfall as an instrument, we hope to observe an instance where unusually wet weather produces lower turnout in an as-if random fashion. Consistent with statistical theory, we find that strengthening the instrument reduces sensitivity to bias from an unobserved confounder.