Instrumental Variable Estimation in Demographic Studies: The LATE interpretation of the IV estimator with heterogenous effects

Heterogeneous effects of treatment on an outcome is a plausible assumption to make about the vast majority of causal relationships studied in the social sciences. In these circumstances the IV estimator is often interpreted as yielding an estimate of a Local Average Treatment Effect (LATE): a marginal change in the outcome for those whose treatment is changed by the variation of the particular instrument in the study. Our aim is to explain the relationship between the LATE parameter and its IV estimator by using a simple model which is easily accessible to applied researchers, and by relating the model to examples from the demographic literature. A focus of the paper is how additional heterogeneity in the instrument – treatment relationship affects the properties and interpretation of the IV estimator. We show that if the two kinds of heterogeneity are correlated, then the LATE parameter combines both the underlying treatment effects and the parameters from the instrument – treatment relationship. It is then a more complicated concept than many researchers realise.