Boundary estimation in the regression-discontinuity design: Evidence for a merit- and need-based financial aid program

In the conventional regression-discontinuity (RD) design, the probability that units receive a treatment changes discontinuously as a function of one covariate exceeding a threshold or cutoff point. This paper studies an extended RD design where assignment rules simultaneously involve two or more continuous covariates. We show that assignment rules with more than one variable allow the estimation of a more comprehensive set of treatment effects, relaxing in a research-driven style the local and sometimes limiting nature of univariate RD designs. We then propose a flexible nonparametric approach to estimate the multidimensional discontinuity by univariate local linear regression and compare its performance to existing methods. We present an empirical application to a large-scale and countrywide financial aid program for low-income students in Colombia. The program uses a merit-based (academic achievement) and need-based (wealth index) assignment rule to select students for the program. We show that our estimation strategy fully exploits the multidimensional assignment rule and reveals heterogeneous effects along the treatment boundaries.