Abstract
In this paper, we determine treatment effects when the treatment assignment is based on two or more cut-off points of covariates rather than on one cut-off point of one assignment variable. using methods that are referred to as multivariate regression discontinuity designs (MRDD). One major finding of this paper is the discovery of new evidence that both matric points and household income have a huge impact on the probability of eligibility for funding from the National Student Financial Aid Scheme (NSFAS) to study for a bachelor’s degree program at universities in South Africa. This evidence will inform policymakers and educational practitioners on the effects of matric points and household income on the eligibility for NSFAS funding. The availability of the NSFAS grant impacts greatly students’ decisions to attend university or seek other opportunities elsewhere. Using the frontier MRDD analytical results, barely scoring matric points greater than or equal to 25 points compared to scoring matric points less than 25 for students whose household income is less than R350,000 (≈US$2500) increases the probability of eligibility for NSFAS funding by a significant 3.75 ( p-value = 0.0001 < 0.05) percentage points. Therefore, we have shown that the frontier MRDD can be employed to determine the causal effects of barely meeting the requirements of one assignment variable, among the subjects that either meet or fail to meet the requirements of the other assignment variable.
Highlights
Multivariate regression discontinuity designs (MRDD) raise challenges that are distinct from those identified in traditional RDD [1]
Using the frontier multivariate regression discontinuity designs (MRDD) analytical results, barely scoring matric points greater than or equal to 25 points compared to scoring matric points less than 25 for students whose household income is less than R350,000 (≈US$2500) increases the probability of eligibility for National Student Financial Aid Scheme (NSFAS) funding by a significant 3.75 ( p-value = 0.0001 < 0.05) percentage points
We focus on estimating the impact that matric points and household income have on the chance that a student qualifies for the NSFAS grant to support his or her bachelor’s degree studies using simulated data for household income (INC) and matric points (MP)
Summary
Multivariate regression discontinuity designs (MRDD) raise challenges that are distinct from those identified in traditional RDD [1]. Traditional RDD studies focus on units that are assigned to a treatment based on a single cut-off point and a single continuous assignment variable [2]. Treatment effects may be estimated across a multi-dimensional cut-off frontier, as opposed to a single point on the assignment variable, using methods referred to as multivariate regression discontinuity designs (MRDD) [1,3,4]. The term frontier means that the average treatment effect estimates for MRDD are only for sub-populations of units located at the cut-off frontier as opposed to the average treatment effect for the overall population under study.
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