Regression discontinuity design

Regression Discontinuity Design

The Regression Discontinuity Design (RDD) is a quasi-experimental pretest-posttest design that is used to identify causal effects of interventions by assigning a cutoff or threshold above or below which an intervention is assigned. This design is particularly useful in situations where random assignment is not feasible.

Overview

Regression Discontinuity Design is a method used in econometrics and statistics to estimate the causal effect of an intervention. The key feature of RDD is the assignment of a treatment based on whether an observed covariate, known as the running variable, is above or below a certain threshold. This creates a discontinuity at the cutoff point, which can be exploited to estimate the treatment effect.

Methodology

In RDD, individuals are assigned to a treatment or control group based on whether their value of the running variable is above or below a predetermined cutoff. The basic idea is that individuals just above and just below the cutoff are similar in all respects except for the treatment assignment. This allows for a comparison that mimics a randomized experiment.

Types of RDD

There are two main types of Regression Discontinuity Designs:

• Sharp RDD: In a sharp RDD, the treatment assignment is a deterministic function of the running variable. That is, all units above the cutoff receive the treatment, and all units below do not.

• Fuzzy RDD: In a fuzzy RDD, the probability of receiving the treatment changes discontinuously at the cutoff, but not all units comply perfectly with the treatment assignment.

Assumptions

For RDD to provide valid causal estimates, several assumptions must be met:

• Continuity Assumption: The potential outcomes must be continuous at the cutoff.
• No Manipulation: The running variable should not be manipulable by the subjects.
• Local Randomization: Units near the cutoff are assumed to be randomly assigned to treatment and control groups.

Applications

Regression Discontinuity Design is widely used in various fields such as economics, political science, and education. It is particularly useful in evaluating the impact of policies where eligibility is determined by a cutoff score, such as test scores for educational programs or income thresholds for welfare programs.

Advantages and Limitations

Advantages

• Causal Inference: RDD provides a robust method for causal inference in non-experimental settings.
• Clear Identification: The cutoff provides a clear point of identification for the treatment effect.

Limitations

• Local Validity: The estimated treatment effect is only valid for individuals near the cutoff.
• Data Requirements: RDD requires a large amount of data around the cutoff to provide precise estimates.

Related Pages

• Quasi-experiment
• Causal inference
• Econometrics
• Experimental design