The Impact of Retention on School Attainment: Local Average Treatment Effect(s) with a Multivalued Instrument
We investigate the identification and estimation of different local average treatment effect (LATE) parameters that are defined in terms of a multivalued instrument. We extend the existing literature on conditionally valid multivalued instruments by explicitly defining two types of LATE and proposing (i) a weighted regression method and (ii) a normalized weighting estimator for both. Subsequently, we apply our proposed methods to estimate the causal effects on school attainment of retention at the end of 10th grade in Germany. We exploit the discontinuity induced by the rules for retention to construct our multivalued instrument. Our estimation indicates substantial treatment heterogeneity.