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Local Average Treatment Effect (LATE / CACE)

Also known as: LATE, CACE, complier average causal effect, Yerel Ortalama Tedavi Etkisi (LATE / CACE)

OriginatorImbens & Angrist (1994); Angrist, Imbens & Rubin (1996)Year1994Sources2Related methods18

The Local Average Treatment Effect is an instrumental-variable estimand, introduced by Imbens and Angrist (1994) and formalised with Rubin (1996), that recovers the average treatment effect for the subpopulation of compliers — units whose treatment status is actually moved by the instrument. It is closely tied to compliance analysis.

Key highlights

  • Delivers a credible causal effect even when treatment take-up is imperfect, as in encouragement designs and randomised offers.
  • Has a transparent interpretation: it is the intent-to-treat effect rescaled by the compliance rate.
  • Relies only on instrument validity and monotonicity rather than on selection-on-observables, making it robust to unobserved confounding.

Intuition

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How it works

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When to use it

Use LATE when treatment is not fully under the analyst's control but a valid instrument shifts take-up, and you need a credible causal effect from observational or imperfect-compliance data. It requires a valid instrument (relevant, exogenous, exclusion restriction), monotonicity (the instrument moves treatment in one direction, with no defiers), and a reasonable sample (at least about 100 observations so the complier subgroup is well populated). The estimate is local: it applies only to compliers, not to always-takers or never-takers.

Strengths & limitations

Strengths
  • Delivers a credible causal effect even when treatment take-up is imperfect, as in encouragement designs and randomised offers.
  • Has a transparent interpretation: it is the intent-to-treat effect rescaled by the compliance rate.
  • Relies only on instrument validity and monotonicity rather than on selection-on-observables, making it robust to unobserved confounding.
Limitations
  • The effect is local to the complier subpopulation and does not generalise to always-takers, never-takers, or the full population.
  • In small samples (n < 100) the complier subgroup is thin, so the LATE estimate has very wide confidence intervals.
  • A violation of monotonicity mixes compliers and defiers, after which the estimand can no longer be interpreted cleanly.

Common pitfalls

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Applications

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Frequently asked

What exactly is a complier?

A complier is a unit that takes the treatment when the instrument pushes toward it and does not take it when the instrument pushes away. LATE measures the average effect for this group only, in contrast to always-takers and never-takers whose behaviour the instrument does not change.

How does LATE relate to the intent-to-treat (ITT) effect?

LATE equals the ITT effect — the instrument's effect on the outcome — divided by the compliance rate, which is the instrument's effect on treatment take-up. Rescaling the ITT by the share of compliers converts the effect of being offered treatment into the effect of actually receiving it.

Why is the monotonicity assumption so important?

Monotonicity says the instrument moves everyone's treatment in the same direction, ruling out defiers. Without it, compliers and defiers mix and the instrumental-variable estimate no longer corresponds to a clean average effect for any single, interpretable group.

When should I prefer matching or plain 2SLS instead?

If your instrument is too weak or monotonicity fails, propensity score matching under selection-on-observables may be more defensible. In small samples where the complier subgroup is sparse, a standard 2SLS instrumental-variable estimate is the natural fallback.

Sources

  1. 1.
    Imbens, G. W., & Angrist, J. D. (1994). Identification and Estimation of Local Average Treatment Effects. Econometrica, 62(2), 467-475.
    DOI 10.2307/2951620
  2. 2.
    Angrist, J. D., Imbens, G. W., & Rubin, D. B. (1996). Identification of Causal Effects Using Instrumental Variables. Journal of the American Statistical Association, 91(434), 444-455.
    DOI 10.1080/01621459.1996.10476902

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ScholarGate. (2026, June 1). Local Average Treatment Effect. ScholarGate. https://scholargate.app/causal-inference/local-average-treatment-effect

Local Average Treatment Effect (LATE / CACE) | ScholarGate