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

Matias D. Cattaneo, Nicolás Idrobo+1 more|arXiv (Cornell University)|Jan 21, 2023

Advanced Statistical Methods and Models51 citations

TL;DR

This monograph extends RD methodology with a local randomization framework, fuzzy RD, discrete running variables, and multi-dimensional designs, plus empirical applications and replication code.

ABSTRACT

This monograph, together with its accompanying first part Cattaneo, Idrobo and Titiunik (2020), collects and expands the instructional materials we prepared for more than $50$ short courses and workshops on Regression Discontinuity (RD) methodology that we taught between 2014 and 2023. In this second monograph, we discuss several topics in RD methodology that build on and extend the analysis of RD designs introduced in Cattaneo, Idrobo and Titiunik (2020). Our first goal is to present an alternative RD conceptual framework based on local randomization ideas. This methodological approach can be useful in RD designs with discretely-valued scores, and can also be used more broadly as a complement to the continuity-based approach in other settings. Then, employing both continuity-based and local randomization approaches, we extend the canonical Sharp RD design in multiple directions: fuzzy RD designs, RD designs with discrete scores, and multi-dimensional RD designs. The goal of our two-part monograph is purposely practical and hence we focus on the empirical analysis of RD designs.

Motivation & Objective

• Present an accessible continuation of RD methodology focusing on extensions beyond the canonical sharp RD design.
• Introduce and formalize the local randomization approach as an alternative robustness check to continuity-based RD.
• Discuss fuzzy RD, discrete running variables, and multi-dimensional RD designs and their estimation and inference.
• Provide empirical illustrations and replication materials to facilitate applied use of RD extensions.

Proposed method

• Explain the local randomization framework with window W around the cutoff and two LR conditions (LR1, LR2).
• Compare the local randomization approach with the continuity-based RD framework and randomized experiments in terms of assumptions and inference.
• Develop and discuss estimation/inference methods for fuzzy RD within both continuity-based and local randomization frameworks.
• Describe RD designs with discrete running variables and multi-dimensional RD designs, including multi-cutoff and multi-score RD settings.
• Provide empirical illustrations using real datasets and replication codes.
• Reference and integrate software tools such as rdrobust, rddensity, rdwinselect, rdmc, and others for implementation.

Experimental results

Research questions

• RQ1 How can the local randomization framework be used to analyze RD designs near the cutoff?
• RQ2 How do fuzzy RD designs alter identification and estimation under noncompliance?
• RQ3 What are the appropriate methods for RD designs with discrete running variables and mass points?
• RQ4 How can multi-cutoff and multi-score RD designs be validly implemented and inferred from data?
• RQ5 What empirical insights do the extensions yield in the provided applications?

Key findings

• The local randomization approach provides a complement to continuity-based RD analysis and enables finite-sample inference within a chosen window.
• Fuzzy RD and noncompliance require new parameters and estimation strategies within both continuity-based and local randomization frameworks.
• Discrete running variables necessitate alternative methods since standard continuity-based RD is inadequate in the presence of mass points.
• Multi-cutoff and multi-score RD designs extend RD applicability to more complex assignment rules and geographic or multi-dimensional contexts.
• Empirical illustrations demonstrate the practicality of the extensions and are accompanied by complete replication code in Python, R, and Stata.