External Validity in Fuzzy Regression Discontinuity Designs
Many empirical studies use Fuzzy Regression Discontinuity (FRD) designs to identify treatment effects when the receipt of treatment is potentially correlated to outcomes. Existing FRD methods identify the local average treatment effect (LATE) on the subpopulation of compliers with values of the forcing variable that are equal to the threshold. We develop methods that assess the plausibility of generalizing LATE to subpopulations other than compliers, and to subpopulations other than those with forcing variable equal to the threshold. Specifically, we focus on testing the equality of the distributions of potential outcomes for treated compliers and always-takers, and for non-treated compliers and never-takers. We show that equality of these pairs of distributions implies that the expected outcome conditional on the forcing variable and the treatment status is continuous in the forcing variable at the threshold, for each of the two treatment regimes. As a matter of routine, we recommend that researchers present graphs with estimates of these two conditional expectations in addition to graphs with estimates of the expected outcome conditional on the forcing variable alone. We illustrate our methods using data on the academic performance of students attending the summer school program in two large school districts in the US.
We are grateful for comments by Joshua Angrist, Brigham Frandsen and Arthur Lewbel on an earlier version of this paper. We are are also grateful to Brian Jacob, Lars Lefgren, and Jordan Matsudaira for making available the data used in this paper. Bertanha gratefully acknowledges the financial support received as a B.F. Haley and E.S. Shaw Fellow from the Stanford Institute for Economic Policy Research. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.
Guido W. Imbens
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Marinho Bertanha & Guido W. Imbens, 2020. "External Validity in Fuzzy Regression Discontinuity Designs," Journal of Business & Economic Statistics, vol 38(3), pages 593-612. citation courtesy of