Inference in an Instrumental Variables Model with Heterogeneous Treatment Effects and Many Instruments

• Activity Number: 271 - Methodological Challenges for Handling Unmeasured Confounders in Causal Inference with Social Science Data
• Type: Invited
• Date/Time: Tuesday, August 1, 2017 : 8:30 AM to 10:20 AM
• Sponsor: Social Statistics Section
• Author(s): Michal Kolesar* and Kirill Evdokimov
• Companies: Princeton University and Princeton University
• Keywords: instrumental variables ; many instruments ; treatment effect heterogeneity ; local average treatment effects ; standard errors

Abstract

We study inference in an instrumental variables model with heterogeneous treatment effects and possibly many instruments and/or exogenous covariates. In this case the two-step estimators such as two-stage least squares (TSLS) or versions of the jackknife instrumental variables (JIV) estimator estimate a particular weighted average of local average treatment effects. The weights in these estimands depend on the first-stage coefficients, and either the sample or population distribution of the the covariates and instruments, depending on whether they are treated as fixed or random. We give new asymptotic variance formulas for TSLS and JIV estimators, and derive consistent estimators of this variance. Compared to the case with homogeneous treatment effects, the variance expression contains an additional term reflecting variability of the local average treatment effects that is quantitatively important.