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st: interaction with non-random treatment
Here's a question that's giving me a headache. I am estimating a model of firm value V,
V= beta1 * X + beta2*T + beta3*T * Y + u
where X are firm-level exogenous variables, T is a some treatment the firm is subjected to and Y is a continuous exogenous industry-level variable and u is the error term. Firms that receive treatment T are not a random sample of firms - factors that lead to a firm being given a treatment are correlated with firm value. In the absence of an interaction term of T withY, I would use the treatreg command in Stata to deal with the potential correlation between T and u. But how do I get consistent estimates of beta2 and beta3?
Thank for helping.