Regression Discontinuity Design (RDD)
Regression Discontinuity Design (RDD) is a quasi-experimental research design that leverages a cutoff or threshold in an assignment variable to estimate the causal effect of a treatment or intervention. It's particularly powerful in social science research when random assignment is not feasible.
The Core Idea of RDD
RDD estimates causal effects by comparing outcomes for units just above and just below a sharp cutoff.
Imagine a scholarship awarded to students scoring above a certain test score. RDD compares the outcomes (e.g., future earnings) of students who scored just above the cutoff to those who scored just below it, assuming these groups are otherwise similar.
The fundamental assumption of RDD is that individuals or units are assigned to a treatment (or intervention) based on whether they fall above or below a specific threshold on a continuous assignment variable. By examining the relationship between the assignment variable and the outcome variable, we can observe a 'discontinuity' or jump at the cutoff point. This jump is interpreted as the causal effect of the treatment, as individuals on either side of the cutoff are assumed to be very similar in all other relevant characteristics, except for their exposure to the treatment.
Types of RDD
| Feature | Sharp RDD | Fuzzy RDD |
|---|---|---|
| Treatment Assignment | Deterministic (100% if above cutoff, 0% if below) | Probabilistic (probability of treatment changes at cutoff) |
| Estimation Method | Simple regression discontinuity estimation | Instrumental variables (IV) or other methods to account for partial compliance |
| Data Requirement | Clear cutoff and assignment variable | Clear cutoff, assignment variable, and measure of treatment received |
Key Assumptions and Considerations
For RDD to yield valid causal estimates, several assumptions must hold:
- Continuity of Potential Outcomes: The potential outcomes (what would have happened with or without the treatment) are continuous at the cutoff. This means that individuals just above and below the cutoff would have had similar outcomes if they had received the same treatment.
- No Manipulation of the Assignment Variable: Individuals cannot precisely manipulate their score on the assignment variable to fall on one side of the cutoff or the other. If manipulation is possible, it can bias the results.
- Correct Functional Form: The relationship between the assignment variable and the outcome variable should be correctly modeled (e.g., linear, quadratic) on either side of the cutoff. The choice of bandwidth (the range around the cutoff used for estimation) is also crucial.
The causal effect estimated by RDD is local – it applies only to individuals at the cutoff point.
Visualizing the Discontinuity
A scatter plot of the outcome variable against the assignment variable is essential for visualizing RDD. The plot should show data points on both sides of the cutoff. A regression line is fitted to the data on each side of the cutoff. The vertical difference between these two lines at the cutoff point represents the estimated treatment effect. The density of observations should ideally be similar on both sides of the cutoff, and there should be no observable jumps in other covariates at the cutoff, which would suggest manipulation or confounding.
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Practical Application in Social Science
RDD is widely used in social sciences to evaluate policies and programs. Examples include:
- Estimating the effect of attending a selective school based on admission test scores.
- Assessing the impact of financial aid programs awarded based on income thresholds.
- Evaluating the effect of policy changes implemented at specific demographic or geographic cutoffs.
The primary assumption is that individuals just above and just below the cutoff are similar in all relevant characteristics except for their treatment status.
It refers to the causal effect estimated specifically for individuals at the cutoff point of the assignment variable.
Learning Resources
A foundational paper providing a clear and accessible introduction to RDD, its assumptions, and applications.
A video tutorial that visually explains the concept of RDD, including sharp and fuzzy designs, and how to interpret results.
An overview of RDD, its strengths, weaknesses, and common applications in policy evaluation.
A chapter from a popular online book on causal inference, offering a conceptual and practical guide to RDD.
Documentation from Stata on implementing RDD analysis, including commands and examples.
A comprehensive Wikipedia entry covering the history, methodology, assumptions, and variations of RDD.
Another excellent video explanation of RDD, focusing on the intuition behind the design and its validity conditions.
A practical tutorial demonstrating how to implement RDD using R, with code examples and explanations.
A review article discussing the development and application of RDD in economics and other fields.
A clear and concise explanation of RDD, suitable for those new to causal inference methods.