[Paper Review] A Practical Introduction to Regression Discontinuity Designs: Foundations

Matias D. Cattaneo, Nicolás Idrobo+1 more|RePEc: Research Papers in Economics|Nov 21, 2019

Statistical Methods and Inference56 references60 citations

TL;DR

A practical guide detailing Sharp Regression Discontinuity designs, focusing on the continuity-based framework, RD plots, validation techniques, and practitioner-friendly replication in R and Stata.

ABSTRACT

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 assignment is perfect. In the accompanying Element, the authors discuss practical and conceptual extensions to the basic RD setup.

Motivation & Objective

• Identify when Regression Discontinuity (RD) designs are applicable by defining score, cutoff, and treatment.
• Explain the Sharp RD setup and its local, causal interpretation.
• Present continuity-based inference and graphical tools for RD analysis.
• Provide practical guidance, validation tests, and replication codes to standardize RD analysis.

Proposed method

• Define the canonical Sharp RD design with a continuous running variable, a single cutoff, and perfect compliance.
• Adopt the potential outcomes framework to formalize causal effects at the cutoff.
• Describe continuity-based identification: E[Yi(1)|Xi=c] − E[Yi(0)|Xi=c] = lim x↓c E[Yi|Xi=x] − lim x↑c E[Yi|Xi=x].
• Outline local polynomial estimation and bandwidth selection in RD analysis.
• Introduce RD plots and graphical diagnostics to assess validity and plausibility of assumptions.
• Provide R and Stata replication codes and reference software packages (rdrobust, rddensity, etc.).

Experimental results

Research questions

• RQ1 What is the local average treatment effect at the RD cutoff under continuity assumptions?
• RQ2 How can continuity-based methods be used to estimate RD treatment effects near the cutoff?
• RQ3 What graphical and falsification tools are effective for validating an RD design?
• RQ4 How can researchers implement RD analysis in common software (R/Stata) with replication code?
• RQ5 What are the key distinctions between Sharp RD and extensions like Fuzzy RD (discussed in the companion Element)?

Key findings

• RD designs identify local causal effects at the cutoff via a discontinuous probability of treatment.
• Continuity of regression functions near the cutoff justifies using observations near c to estimate treatment effects.
• The Sharp RD effect is local to the cutoff and interpretable as a local average treatment effect on the treated at Xi = c.
• The framework emphasizes validation through plots and falsification tests to support design plausibility.
• Practical implementation is facilitated by open-source software and replication material (rdrobust, rdplot, rddensity).