  In non-experimental settings, the Regression Discontinuity (RD) design is one
of the most credible identification strategies for program evaluation and
causal inference. However, RD treatment effect estimands are necessarily local,
making statistical methods for the extrapolation of these effects a key area
for development. We introduce a new method for extrapolation of RD effects that
relies on the presence of multiple cutoffs, and is therefore design-based. Our
approach employs an easy-to-interpret identifying assumption that mimics the
idea of "common trends" in difference-in-differences designs. We illustrate our
methods with data on a subsidized loan program on post-education attendance in
Colombia, and offer new evidence on program effects for students with test
scores away from the cutoff that determined program eligibility.
