The Annals of Applied Statistics

Evaluating the causal effect of university grants on student dropout: Evidence from a regression discontinuity design using principal stratification

Fan Li, Alessandra Mattei, and Fabrizia Mealli

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Regression discontinuity (RD) designs are often interpreted as locally randomized experiments for units with a realized value of a pretreatment variable falling around a threshold. Motivated by the evaluation of Italian university grants, we consider a fuzzy RD design where the treatment status 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 reformulating the Stable Unit Treatment Value Assumption (SUTVA) and making an explicit local overlap assumption for a subpopulation around the threshold. We invoke a local randomization assumption instead of the more standard continuity assumptions. We also develop a Bayesian approach to select the target subpopulation(s) with adjustment for multiple comparisons, and to draw inference for the target causal estimands within 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.

Article information

Ann. Appl. Stat., Volume 9, Number 4 (2015), 1906-1931.

Received: December 2014
Revised: September 2015
First available in Project Euclid: 28 January 2016

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Bayesian causal effects intermediate variables principal stratification randomization regression discontinuity university grants


Li, Fan; Mattei, Alessandra; Mealli, Fabrizia. Evaluating the causal effect of university grants on student dropout: Evidence from a regression discontinuity design using principal stratification. Ann. Appl. Stat. 9 (2015), no. 4, 1906--1931. doi:10.1214/15-AOAS881.

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Supplemental materials

  • Supplement to “Evaluating the causal effect of university grants on student dropout: Evidence from a regression discontinuity design using principal stratification”. We describe in detail the Bayesian approach we used to select the subpopulations, the Markov Chain Monte Carlo (MCMC) methods used to simulate the posterior distributions of the parameters of the models, the posterior predictive checks, and the sensitivity analysis regarding local randomization described in Section 6.