Title: A Randomization Inference Approach to Regression Discontinuity
Advisor: Associate Professor Ben Hansen
Committee Members: Professor Kerby Shedden, Professor Walter Mebane, Associate Professor Susan Dynarski (Public Policy)
Abstract: In 1947, the United Kingdom increased the minimum age at which students could drop out of school from 14 to 15 years. Presumably, students who turned 14 right before the law went into effect and students who turned 14 right after the cutoff have approximately equal covariate distributions; if that is true, by comparing the two populations, we can estimate the effect of the extra year of compulsory education on an outcome of interest such as income. This is an example of a ”regression-discontinuity” (RD) design—an increasingly-popular causal inference strategy that exploits arbitrary cutoffs in policy to identify natural experiments and infer causal relationships. Conventionally, social scientists analyze data from RD designs by building models to fit the data, and estimating their parameters. However, a better approach may be to treat them as randomized experiments close to the cutoff. This proposal will introduce method for defining and estimating what is meant by ”close to the cutoff,” and hence identifying (approximately) randomized experiments in RD data. This method, which relies on finding a region around the cutoff in which pre-treatment covariates are balanced, also serves to test the RD assumptions. In addition, the study will suggest a randomization-inference strategy, which Rosenbaum (2001) refers to as ”displacement effects,” that accounts well for treatment-effect heterogeneity—when different subjects are affected differently by a treatment—and that possesses other technical advantages that make it well-suited to RD applications. The presentation will show, in particular, how the displacement-effects framework may help answer the question of whether men and women benefited equally from the extra year of compulsory education.