In the lecture, the average treatment effect 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.

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