Regression Discontinuity Toolkit

Exploits policy thresholds to identify causal effects.

Overview

Many policies create sharp thresholds: test scores determine program eligibility, income cutoffs determine benefits. Regression discontinuity exploits these thresholds to estimate causal effects by comparing units just above and just below the cutoff.

Methods

Sharp RD

• Units above threshold receive treatment, below don’t
• Local polynomial regression at the cutoff
• Optimal bandwidth selection

Fuzzy RD

• Threshold affects treatment probability, not certainty
• Instrumental variables approach
• Estimates local average treatment effect (LATE)

Specification Tests

• Manipulation testing (density discontinuity)
• Covariate balance at threshold
• Placebo cutoffs

When to Use This

Good fit:

• Clear policy threshold based on running variable
• Units can’t precisely manipulate their position
• Sufficient observations near the threshold

Not ideal:

• Threshold is manipulable
• Sparse data near cutoff
• Need effects far from threshold

Key Assumptions

1. No manipulation: Units can’t precisely sort around the threshold
2. Continuity: Potential outcomes are continuous at the cutoff
3. Local effect: Estimates apply to units at the threshold