How does regression discontinuity identify causal effects?

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AcadiFi · Accepted Answer

Regression discontinuity design (RDD) exploits a sharp treatment assignment rule based on a continuous running variable crossing a threshold. Below the cutoff c, units are untreated; above c, treated. Treatment effect at the threshold: tau = lim_{x→c+} E[Y|X=x] - lim_{x→c-} E[Y|X=x]. Because units just above and just below are essentially identical, any jump in Y at c is attributable to treatment. For Talon's study: FICO cutoff 620 for loan approval. Borrowers with FICO 621 vs 619 are essentially identical except for approval status. Compare outcomes (default, business growth) just above vs just below. If 5-year default rates are 15% at FICO 621 and 18% at FICO 619 among those who eventually obtained credit, the RDD estimate of getting loans at marginal scores is meaningful. ```mermaid flowchart LR X[Running
variable] --> C{Above
cutoff?} C -->|Yes| T[Treatment] C -->|No| U[Control] T --> J[Jump at
boundary] ``` Implementation: fit local linear regressions on each side of c using observations within a bandwidth h. Optimal bandwidth (Imbens-Kalyanaraman, Calonico-Cattaneo-Titiunik) balances bias (wider h) vs variance (narrower h). Assumptions: (1) running variable cannot be precisely manipulated—check McCrary density test for bunching at cutoff; (2) no confounders that also jump at cutoff. Validity checks: placebo tests at non-cutoff points, balance tests of covariates at c, sensitivity to bandwidth. RDD is considered one of the cleanest quasi-experimental designs. Applications include returns to education (SAT cutoffs for scholarships), credit effects, electoral incumbency, and clinical thresholds. Fuzzy RDD handles imperfect compliance (crossing the threshold changes probability of treatment, not determinism).

How does regression discontinuity identify causal effects?

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