Regression Discontinuity Design (RDD) Skill

Regression Discontinuity Design (RDD) Skill

This skill covers sharp and fuzzy RDD: identification assumptions, bandwidth selection, local polynomial estimation, validity tests, and reporting standards for academic papers.

Core Logic

RDD exploits a known threshold in a continuous "running variable" (X) that determines treatment assignment. Units just above and below the cutoff (c) are comparable on all dimensions except treatment.

Sharp RDD: Treatment perfectly determined by crossing cutoff

• T_i = 1 if X_i ≥ c, T_i = 0 if X_i < c
• Estimand: Average treatment effect at the cutoff (τ_SRD)

Fuzzy RDD: Crossing cutoff increases probability of treatment (like an instrument)

• Use when there's non-compliance around the cutoff
• Estimand: LATE at the cutoff (τ_FRD = reduced form / first stage)

RDD Assumptions

1. Continuity of conditional expectation: E[Y(0)|X] and E[Y(1)|X] are continuous at X = c
   • Means: units cannot precisely manipulate running variable to select into treatment
2. No other discontinuities: Nothing else changes discontinuously at the cutoff
3. Bandwidth continuity: Observations near cutoff are locally valid comparisons

Complete RDD Workflow

Step 1: Visualize the Discontinuity

Always plot the raw data with binned means before any regression.

# Python
import matplotlib.pyplot as plt
import numpy as np

# Bin the running variable
df['bin'] = pd.cut(df['running_var'], bins=50)
bin_means = df.groupby('bin')[['running_var', 'y']].mean().reset_index()

plt.figure(figsize=(10, 6))
plt.scatter(bin_means['running_var'], bin_means['y'], s=30, color='steelblue')