Primary Submission Category: Regression Discontinuity Designs
Bayesian Inference in Longitudinal Regression Discontinuity Designs
Authors: Alessandra Mattei, Laura Forastiere, Fabrizia Mealli,
Presenting Author: Laura Forastiere*
We study longitudinal regression discontinuity (RD) designs in which treatment is dynamically assigned over time through a sequence of cutoff rules. We focus on a two-period setting,allowing the forcing variable in the first period to affect the forcing variable in the second period. Within the potential outcomes framework, we formally characterize longitudinal RD designs as local sequentially latent regular designs. We define causal estimands that capture the effects of treatment sequences for well-defined, though generally unobserved, subpopulations where local overlap conditions and local versions of SUTVA hold. Inference relies on local longitudinal unconfoundedness, imposing conditional independence between potential outcomes for the main outcome and (a) the first-period forcing variable, and (b) the potential outcomes of the second-period forcing variable. To identify the subpopulations for which valid causal inference is possible, we extend the Bayesian model-based finite mixture approach proposed by Forastiere et al. (AOAS, 2025) to the longitudinal setting, probabilistically clustering observations into subpopulations in which the required assumptions are more or less likely to hold, based on their observable implications. We then derive posterior distributions of the target causal effects by marginalizing over uncertainty in subpopulation membership. We apply the proposed methodology to the evaluation of Italian university student-aid policies on academic outcome.