In the lecture, the average treatment eect was introduced under a binary treatment status, but we often encounter randomized control trials with multiple treatments. Consider the case of three treatment status, where we have no treatment, treatment 1 and treatment 2. Let d1 be a dummy variable taking 1 for treatment 1 and 0 otherwise, and d2 be a dummy variable taking 1 for treatment 2 and 0 otherwise.

1. We consider the following regression

y = + d1 + d2 + error,

where , and are parameters and error is the error with E[error] = 0. Using and in this regression, explain what you can estimate First, express only the nal outcomes mathematically (no derivations) and second, explain each.

2. Suppose that we want to estimate the dierence of treatment eects between treatment 1 and 2 on average. To this end, consider and expression a specication of a regression when only y, d1 and d2 are available, and denote the key parameter by . Express mathematically what measures.