Robust Confidence Intervals with Invalid Instruments

• Activity Number: 33
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Hyunseung Kang* and Tony Cai and Dylan Small
• Companies: The Wharton School and University of Pennsylvania and University of Pennsylvania
• Keywords: Instrumental Variables ; Anderson and Rubin ; Econometrics ; Causal Inference ; Invalid Instruments

Abstract

Instrumental variables have been widely used to estimate the causal effect of a treatment on an outcome in the presence of unmeasured confounding. Existing confidence intervals for causal effects based on instrumental variables assumes that all of the putative instrumental variables are valid; a valid instrumental variable is a variable that affects the outcome only by affecting the treatment and is not related to unmeasured confounders. However, in practice, some of the putative instrumental variables are likely to be invalid. The paper presents a simple and general approach to construct a robust confidence interval that is robust to possibly invalid instruments. The robust confidence interval has theoretical guarantees on having the correct coverage. The paper also shows that the robust confidence interval outperforms traditional confidence intervals popular in instrumental variables literature when invalid instruments are present. The new approach is applied to a study of the causal effect of income on food expenditures.