Evaluating the Causal Effect of University Grants on Student Dropout: Evidence from a Regression Discontinuity Design Using Principal Stratification

TL;DR

This paper develops a Bayesian principal stratification approach within a fuzzy regression discontinuity design to evaluate the causal effect of university grants on student dropout, addressing post-assignment intermediate variables and local randomization.

Contribution

It introduces a probabilistic formulation of the RD assignment mechanism and a Bayesian method for selecting subpopulations and estimating causal effects.

Findings

University grants reduce dropout rates among low-income students.

The method effectively accounts for intermediate variables and local randomization.

Empirical evidence supports grants' effectiveness in higher education retention.

Abstract

Regression discontinuity (RD) designs are often interpreted as local randomized experiments: a RD design can be considered as a randomized experiment for units with a realized value of a so-called forcing variable falling around a pre-fixed threshold. Motivated by the evaluation of Italian university grants, we consider a fuzzy RD design where the receipt of the treatment is based on both eligibility criteria and a voluntary application status. Resting on the fact that grant application and grant receipt statuses are post-assignment (post-eligibility) intermediate variables, we use the principal stratification framework to define causal estimands within the Rubin Causal Model. We propose a probabilistic formulation of the assignment mechanism underlying RD designs, by re-formulating the Stable Unit Treatment Value Assumption (SUTVA) and making an explicit local overlap assumption for a subpopulation around the threshold. A local randomization assumption is invoked instead of more standard continuity assumptions. We also develop a model-based Bayesian approach to select the target subpopulation(s) with adjustment for multiple comparisons, and to draw inference for the target causal estimands in this framework. Applying the method to the data from two Italian universities, we find evidence that university grants are effective in preventing students from low-income families from dropping out of higher education.