An Alternative Assumption to Identify LATE in Regression Discontinuity Designs

One of the key identifying assumptions for regression discontinuity (RD) designs is the local independence assumption (LIA). This paper shows that LIA puts a restriction on treatment effect heterogeneity and hence may not hold in many empirical applications. This paper then shows that LATE in both sharp and fuzzy designs can be identified under alternative smoothness conditions, and that the required smoothness can be satisfied given a weak and empirically plausibly behavioral assumption, in the spirit of Lee (2008). A sufficient (but stronger than necessary condition) is smoothness of the conditional density of the running variable, which provides formal justification for McCrary’s (2008) density test in fuzzy RD designs. Theoretical and empirical relevance of the discussion is illustrated in two empirical applications. JEL codes: C21, C25