Finding the Strength in a Weak Instrument in a Study of Cognitive Outcomes Produced by Catholic High Schools

• Activity Number: 337 - SPEED: Methodological Developments in Social Statistics, Part 1
• Type: Contributed
• Date/Time: Tuesday, July 30, 2019 : 10:30 AM to 12:20 PM
• Sponsor: Social Statistics Section
• Author(s): Siyu Heng* and Dylan Small and Paul Rosenbaum
• Companies: University of Pennsylvania and University of Pennsylvania and University of Pennsylvania
• Keywords: Bahadur efficiency; Causal effects; Design sensitivity; Instrumental variables; Observational studies; Sensitivity analysis

Abstract

The strength of an instrument is incompletely characterized by the proportion of compliers. For a fixed small proportion of compliers, the presence of an equal number of always-takers and never-takers weakens an instrument, whereas the absence of always-takers or, equivalently, the absence of never-takers, strengthens an instrument. Here, the strength of an instrument refers to its ability to recognize and reject a false hypothesis about a structural parameter. This ability is measured by the Bahadur efficiency of a sensitivity analysis that assumes the instrument may be somewhat biased. Viewed in this way, the choice of test statistic strongly affects power, efficiency and sensitivity to unmeasured bias. Studies of the effects of Catholic high schools on academic test performance have used being Catholic as an instrument for attending a Catholic high school, and the application concerns such a comparison using the US National Educational Longitudinal Study. Most Catholics do not attend Catholic school, so there are few compliers, but it is quite rare for non-Catholics to attend Catholic school, so there are very few always-takers.