In multi-cutoff regression discontinuity designs, constant-bias extrapolation is unreliable when the running variable is manipulable, and under monotonicity plus dominance the extrapolated treatment effect is sharply bounded by two estimable regression functions.
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On Extrapolation of Treatment Effects in Multiple-Cutoff Regression Discontinuity Designs
In multi-cutoff regression discontinuity designs, constant-bias extrapolation is unreliable when the running variable is manipulable, and under monotonicity plus dominance the extrapolated treatment effect is sharply bounded by two estimable regression functions.