# Instrumental Variable : the sense of “Local” in the LATE [closed]

What intuitive sense can be given to the word "Local" in the LATE?

"Local" compared to what ?

## closed as unclear what you're asking by Michael Chernick, kjetil b halvorsen, Peter Flom♦Mar 10 '18 at 13:58

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• Intuition: running a randomized controlled trial with stage IV cancer patients won't estimate the treatment effect on stage 1 tumors. If you have an instrument for treatment, you're only estimating the treatment effect for the subset of your population where the instrument generates exogenous variation. @Andreas's answer gives a great, more formal definition. – Matthew Gunn Mar 8 '18 at 16:44
• What does LATE stand for? – Peter Flom Mar 10 '18 at 13:58

The LATE framework assumes that there is a continuum of types, say $U \sim [0, 1]$, that may all react differently to the treatment.
Only a subset of all types reacts to the instrument by changing their treatment status. Under the monotonicity assumption this will always be an interval, say $[a, b]$ with $0 < a <b < 1$.
The LATE gives you the average treatment effect averaged over types $[a, b]$, whereas the ATE will give you the average treatment effect averaged over all types $[0, 1]$.