In non-experimental settings, the Regression Discontinuity (RD) design is one of the most credible identification strategies for program evaluation and causal inference. However, RD treatment effect estimands are necessarily local, making statistical methods for the extrapolation of these effects a key area for development. We introduce a new method for extrapolation of RD effects that relies on the presence of multiple cutoffs, and is therefore design-based. Our approach employs an easy-to-interpret identifying assumption that mimics the idea of "common trends" in difference-in-differences designs. We illustrate our methods with data on a subsidized loan program on post-education attendance in Colombia, and offer new evidence on program effects for students with test scores away from the cutoff that determined program eligibility.
Numerous empirical studies employ regression discontinuity designs with multiple cutoffs and heterogeneous treatments. A common practice is to normalize all the cutoffs to zero and estimate one effect. This procedure identifies the average treatment effect (ATE) on the observed distribution of individuals local to existing cutoffs. However, researchers often want to make inferences on more meaningful ATEs, computed over general counterfactual distributions of individuals, rather than simply the observed distribution of individuals local to existing cutoffs. This paper proposes a consistent and…
We introduce the \texttt{Stata} (and \texttt{R}) package \texttt{rdmulti}, which includes three commands (\texttt{rdmc}, \texttt{rdmcplot}, \texttt{rdms}) for analyzing Regression Discontinuity (RD) designs with multiple cutoffs or multiple scores. The command \texttt{rdmc} applies to non-cumulative and cumulative multi-cutoff RD settings. It calculates pooled and cutoff-specific RD treatment effects, and provides robust bias-corrected inference procedures. Post estimation and inference is allowed. The command \texttt{rdmcplot} offers RD plots for multi-cutoff settings. Finally, the command \t…
Regression discontinuity designs are extensively used for causal inference in observational studies. However, they are usually confined to settings with simple treatment rules, determined by a single running variable, with a single cutoff. Motivated by the problem of estimating the impact of grade retention on educational and juvenile crime outcomes in Chile, we propose a framework and methods for complex discontinuity designs that encompasses multiple treatment rules. In this framework, the observed covariates play a central role for identification, estimation, and generalization of causal ef…
Regression discontinuity designs (RDDs) are a common quasi-experiment in economics and statistics. The most popular methodologies for analyzing RDDs utilize continuity-based assumptions and local polynomial regression, but recent works have developed alternative assumptions based on local randomization. The local randomization framework avoids modeling assumptions by instead placing assumptions on the assignment mechanism near the cutoff. However, most works have focused on completely randomized assignment mechanisms, which posit that propensity scores are equal for all units near the cutoff. …
In this Element and its accompanying Element, Matias D. Cattaneo, Nicolas Idrobo, and Rocio Titiunik provide an accessible and practical guide for the analysis and interpretation of Regression Discontinuity (RD) designs that encourages the use of a common set of practices and facilitates the accumulation of RD-based empirical evidence. In this Element, the authors discuss the foundations of the canonical Sharp RD design, which has the following features: (i) the score is continuously distributed and has only one dimension, (ii) there is only one cutoff, and (iii) compliance with the treatment …
The regression discontinuity (RD) design is a popular approach to causal inference in non-randomized studies. This is because it can be used to identify and estimate causal effects under mild conditions. Specifically, for each subject, the RD design assigns a treatment or non-treatment, depending on whether or not an observed value of an assignment variable exceeds a fixed and known cutoff value. In this paper, we propose a Bayesian nonparametric regression modeling approach to RD designs, which exploits a local randomization feature. In this approach, the assignment variable is treated as a c…
Many empirical examples of regression discontinuity (RD) designs concern a continuous treatment variable, but the theoretical aspects of such models are less studied. This study examines the identification and estimation of the structural function in fuzzy RD designs with a continuous treatment variable. The structural function fully describes the causal impact of the treatment on the outcome. We show that the nonlinear and nonseparable structural function can be nonparametrically identified at the RD cutoff under shape restrictions, including monotonicity and smoothness conditions. Based on t…
Evaluating Threshold Policies in Randomized Threshold Designs: A Cautionary Tale for Regression Discontinuity Designs
Graduate School of Economics, Kyoto University（京都大学经济学研究科）；Graduate School of Economics, The University of Tokyo（东京大学经济学研究科）；Graduate School of Economics, Hitotsubashi University（一桥大学经济学研究科）
This paper explores the use of a fuzzy regression discontinuity design where multiple treatments are applied at the threshold. The identification results show that, under the very strong assumption that the change in the probability of treatment at the cutoff is equal across treatments, a difference-in-discontinuities estimator identifies the treatment effect of interest. The point estimates of the treatment effect using a simple fuzzy difference-in-discontinuities design are biased if the change in the probability of a treatment applying at the cutoff differs across treatments. Modifications …
