Regression Discontinuity Designs with Sample Selection

This paper extends the standard regression discontinuity (RD) design to allow for sample selection or missing outcomes. We deal with both treatment endogeneity and sample selection. Identification in this paper does not require any exclusion restrictions in the selection equation, nor does it require specifying any selection mechanism. The results can therefore be applied broadly, regardless of how sample selection is incurred. Identification instead relies on smoothness conditions. Smoothness conditions are empirically plausible, have readily testable implications, and are typically assumed even in the standard RD design. We first provide identification of the ‘extensive margin’ and ‘intensive margin’ effects. Then based on these identification results and principle stratification, sharp bounds are constructed for the treatment effects among the group of individuals that may be of particular policy interest, i.e., those always participating compliers. These results are applied to evaluate the impacts of academic probation on college completion and final GPAs. Our analysis reveals striking gender differences at the extensive versus the intensive margin in response to this negative signal on performance.