Quantitative Methods

Regression Discontinuity and the Local Average Treatment Effect

Turn a cutoff you already wrote — a score, a spend threshold, a tier boundary — into something close to a randomized experiment, and learn why the answer describes only the customers standing right on the line.

  • Expert
  • 15 min total
  • 14 chapters

What decision this helps you make: Whether to move a threshold in one of your own business rules: the credit score that auto-approves, the basket value that earns free shipping, the spend that unlocks a tier. The answer turns on the marginal customer at the line, not the average customer inside it.

What this topic is

A regression discontinuity design exploits a rule that assigns treatment based on whether some measured quantity crosses a threshold. Customers just below and just above the line are, in every respect that matters, the same people — the difference between a score of 639 and 641 is noise — but one group gets treated and the other does not. Comparing outcomes in a narrow window either side of the cutoff isolates the effect of the treatment on customers at that point on the scale, and at that point only.

Why it matters

Businesses are full of thresholds, and almost all of them were set by somebody's judgement years ago and never revisited. Free shipping over $50. Auto-approval above 640. Gold tier at 5,000 points. Dedicated account manager above $30,000 of annual spend. Every one of those lines is a natural experiment running continuously in your own data, and moving one is a decision worth millions. The design tells you what the marginal customer at the line is worth — which is the only number that matters when the question is where to put the line.

Who should learn it

Credit and risk teams setting approval cutoffs, commerce and pricing teams setting shipping and discount thresholds, loyalty and customer success teams setting tier boundaries, and anyone who has been asked to justify a threshold that predates them.

What you will understand

  • Why customers either side of a cutoff are comparable, and what continuity assumption that rests on
  • How to compute the estimate, choose a bandwidth, and read the bias-variance trade-off in the interval
  • Why the answer is local to the cutoff and what goes wrong when it is extrapolated to a different threshold
  • How manipulation of the running variable destroys the design, and how to detect it

Prerequisites

Common misconception

"Approved accounts earn $120 of contribution, so lowering the cutoff will bring in more accounts earning something like $120." The average approved account and the marginal approved account are different animals, and the whole point of the design is that it estimates the second one. In the worked example the average approved account contributes $120 while the account sitting exactly at the cutoff contributes $54 — less than half — against a $60 cost to originate and service it. The rule is not marginally profitable even though the portfolio is comfortably profitable. Extending the rule downward on the strength of the portfolio average is how a profitable lending book acquires an unprofitable tail.