EasyEcon

Intermediate causal inference

Regression Discontinuity and the Cutoff Jump

When treatment switches on at a threshold of a running variable, units just below the cutoff are a credible counterfactual for units just above. The jump in the outcome at the cutoff estimates the treatment effect.

Econometrics Causal inference Intermediate Native JS Regression, identification, and simulated evidence
Focus

The cutoff, the local-linear fits, and the jump that estimates the treatment effect

See how a discontinuity identifies a causal effect: fit a line each side of the cutoff and read the vertical jump between them, then watch the bandwidth trade bias against noise.

Interactive diagram

Regression Discontinuity — explore it instantly

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Regression discontinuity: the jump at the cutoff estimates the treatment effect Treatment switches on at a threshold of the running variable. Fitting a line to the points within a bandwidth on each side of the cutoff, the vertical gap between the two fitted values at the cutoff estimates the treatment effect. 0 20 40 60 80 100 11 26 41 56 71 87 Running variable Outcome
Below cutoff (control) At/above cutoff (treated) Local-linear fit Estimated jump

How to read this

Each dot is a unit with a running variable on the x-axis (a test score, an income threshold, a vote share). Treatment switches on for everyone at or above the cutoff — so units just below are a natural comparison group for units just above.

Fit a straight line to the points inside the bandwidth on each side. The vertical gap between the two fitted values at the cutoff is the estimated treatment effect (τ̂). With no noise it lands exactly on the true jump; add noise and it wobbles around it.

Drag the bandwidth: a narrow window uses only points near the cutoff (less bias, but few points, so noisier); a wide window borrows more data but leans harder on the straight-line assumption far from the cutoff. That tension is the core practical choice in regression discontinuity.

What to explore

Change parameters and watch the model adjust.

  • Cutoff, the true jump, and the common trend slope
  • Noise and the estimation bandwidth around the cutoff

Core ideas

Interpret the mechanics before you chase the graphs.

  • Treatment switches on at a threshold, so units just either side of the cutoff differ only in treatment.
  • A line fitted within a bandwidth on each side estimates the outcome at the cutoff; their difference is the effect.
  • A narrow bandwidth is less biased but noisier; a wide one uses more data but leans on the linear trend.

Learning goals

What this model should help students internalize.

  • Explain why the outcome jump at a sharp cutoff identifies the treatment effect.
  • Estimate the effect with a local-linear fit on each side of the cutoff.
  • Describe how the bandwidth trades bias against variance.

Prerequisites

Concepts to review before diving in.

  • Ordinary least squares and the slope/intercept of a fitted line
  • The idea of a counterfactual / comparison group

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