Local average treatment effect
Also known as: Complier average causal effect
The causal effect estimated only for those whose behavior responds to the nudge or instrument.
What it means
The local average treatment effect is the causal effect of a treatment estimated specifically for the subgroup of people whose treatment status is actually changed by an instrument or encouragement—the 'compliers'—rather than for everyone in the study. It arises in instrumental-variable and encouragement designs, where some assigned-to-treatment people would not take it and some assigned-to-control would get it anyway, so randomization affects only those on the margin who do what their assignment tells them. Under assumptions including a valid instrument and 'monotonicity' (no one does the opposite of their assignment), the instrumental-variable estimate recovers the average effect for these compliers, not the population-wide average treatment effect. The crucial nuance is interpretive: the LATE may differ from the effect on always-takers, never-takers, or the whole population, and the complier group is defined by the particular instrument, so a different instrument can yield a different LATE. This limits generalizability even as it secures internal validity. It matters because much credible causal evidence from natural experiments and imperfect-compliance trials estimates a LATE, and mistaking it for the overall effect can mislead policy.
Examples
If a mailed voucher induces only some families to enroll their children in a program, the instrument identifies the program's effect on those induced families—the compliers—not on families who would never or always have enrolled.
A text nudging patients to book a screening measures the screening's effect only on those who booked because of the text, not on people who would have gone regardless.
Randomly offering a free coding course estimates its effect on people who enrol only when offered; the keen who would have paid and the uninterested who never enrol stay unmeasured.
First described in Guido Imbens & Joshua Angrist (1994).