This question came up as part of the practice problems in the Econometrics course I am taking. Its is the following. In the potential outcomes framework with heterogeneous (non-constant) treatment effect, write the error as:
$$u_i = (1-x_i)u_i(0)+x_iu_i(1)$$.
$$\sigma_0^2 = Var[u_i(0)] \;\text{ and }\; \sigma_1^2 = Var[u_i(1)].$$ Assume Random Assignment.
- Find $Var[u_i|x_i]$
- When is this value constant?
My attempt at the problem was to take the conditional variance of $u_i$ as defined above. Where Im having troubles is how do I breakup the variance to further simplify...
Any help or hints would be greatly appreciated.
Cheers, Groot99