Intent-to-Treat (ITT) Reduced-Form Effect Estimation

In Simple Words

If a doctor assigns patients to a specific health routine but some patients do not follow it, checking how much healthier the whole assigned group became measures the effectiveness of giving out the advice, rather than the physical impact of doing the routine itself.

Research question

Estimating the impact of an assigned intervention without adjusting for non-compliance measures the policy impact of initial assignment rather than the direct effect of receiving the actual treatment.

Participants

N = 27,255 randomized students in grades 4–8 across 6 urban school districts.

Study Design

Ordinary Least Squares regression of student end-of-year achievement directly on the predicted effectiveness of the randomly assigned teacher ($\hat{\tau}_{jAssigned}^{S}$).

Results

The intent-to-treat reduced-form estimate yielded a coefficient of ~0.280 to 0.326, which reflected the true treatment impact (~0.955) diluted by an overall compliance rate of approximately 29.3%.

Takeaway

Calculate the intent-to-treat reduced-form regression of outcomes on assigned treatment variables to establish the baseline causal impact of program assignment prior to instrumental variable adjustments.

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