Donuts and Distant CATEs: Derivative Bounds for RD Extrapolation

Regression Discontinuity (RD) uses policy thresholds to identify causal treatment effects at the threshold. In most settings, the Local Average Treatment Effect (LATE) at the threshold is not the parameter of interest. I provide high level smoothness conditions under which extrapolation across the threshold is possible. Under these restrictions, both estimation and inference for the LATE in other locations is possible. In some situations, extrapolation may be necessary to merely estimate the LATE at the threshold. RD donuts are one such situation, and I provide results allowing estimation and inference in that setting as well.