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A randomized trial assigns 1,000 eligible workers to a job training program (treatment, n=500) or control (n=500). However:
- Compliers (500 assigned to treatment): 400 actually complete the program, 100 don't
- Non-compliers (500 assigned to treatment): 80 refuse assignment, 20 sneak into treatment anyway
- Control group (500): all honor non-participation
(Assume monotonicity: no one is a "defier" who would participate if NOT assigned but refuse if assigned.)
Intent-to-Treat effect: Average earnings increase of $1,200 (all 500 treated vs. all 500 control).
Compliance rate (fraction with treatment if assigned): 500/500 = 1.0 (all units have potential to comply or not comply).
Actual receipt rate among those assigned: (400 + 20)/500 = 0.84.
Using the Instrumental Variables / LATE formula:
If effect of assignment on receipt = 0.84, the Local Average Treatment Effect (LATE) for compliers is approximately:
A randomized trial assigns 1,000 eligible workers to a job training program (treatment, n=500) or control (n=500). However:
- Compliers (500 assigned to treatment): 400 actually complete the program, 100 don't
- Non-compliers (500 assigned to treatment): 80 refuse assignment, 20 sneak into treatment anyway
- Control group (500): all honor non-participation
(Assume monotonicity: no one is a "defier" who would participate if NOT assigned but refuse if assigned.)
Intent-to-Treat effect: Average earnings increase of $1,200 (all 500 treated vs. all 500 control).
Compliance rate (fraction with treatment if assigned): 500/500 = 1.0 (all units have potential to comply or not comply).
Actual receipt rate among those assigned: (400 + 20)/500 = 0.84.
Using the Instrumental Variables / LATE formula:
If effect of assignment on receipt = 0.84, the Local Average Treatment Effect (LATE) for compliers is approximately: