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 sameconvex combination of them. In contrast, estimands of minimum distance estimators, suchas the limited information maximum likelihood (LIML) estimator, may be outside of theconvex hull of the local average treatment effects, and may therefore not correspond to acausal effect. This result questions the standard recommendation to use LIML when thenumber of instruments is large as a way of addressing the bias exhibited by TSLS in thesesettings. Instead, I propose a new TSIV estimator, a version of the jackknife instrumentalvariables estimator (UJIVE). Unlike TSLS or LIML, UJIVE is consistent for a convex combinationof local average treatment effects under many instrument asymptotics that also allow formany covariates and heteroscedasticity.
You can download the paper for this seminar here.