Assessing the Monotonicity Assumption in IV and fuzzy RD designs

Whenever treatment e_ects are heterogeneous and there is sorting into treatment based on the gain, monotonicity is a condition that both Instrumental Variable and fuzzy Regression Discontinuity designs have to satisfy for their estimate to be interpretable as a LATE. However, applied economic work rarely discusses this important assumption. This is in stark contrast to the lengthy discussions dedicated to the other IV and fuzzy RD conditions. We show that monotonicity can and should be investigated using a mix of economic insights, data patterns and formal tests. This is just an extra step to validate the results. We provide examples in a variety of settings as a guide to practice.