Estimation in an Instrumental Variables Model With Treatment Effect Heterogeneity

This paper analyzes estimators based on the classic linear instrumental variables model when the treatment effects are in fact heterogeneous, as in Imbens and Angrist (1994). I show that if the local average treatment effects vary, two-step instrumental variables estimators (tsiv), such as the two-stage least squares estimator (tsls) typically all estimate the same convex combination of them. In contrast, estimands of minimum distance estimators, such as the limited information maximum likelihood (liml) estimator, may be outside of the convex hull of the local average treatment effects, and may therefore not correspond to a causal effect. This result questions the standard recommendation to use liml when the number of instruments is large as a way of addressing the bias exhibited by tsls in these settings. Instead, I propose a new tsiv estimator, a version of the jackknife instrumental variables estimator (ujive). Unlike tsls or liml, ujive is consistent for a convex combination of local average treatment effects under many instrument asymptotics that also allow for many covariates and heteroscedasticity.