I've estimated a diff-in-diff using Stata - very simple situation:
y = b0 + b1 T + b2 P + b3 TxP + e
T = 1 means treatment, 0 is control. P = 1 means post treatment, 0 is pre-treatment.
Problem: The coefficient on the constant term in my diff-in-diff regression (using Stata 14) is very high. As a sensibility check on my estimates, my sense was that if I want to, say, back out what the value of outcome y is for my control group post-treatment, I add the constant (b0) and the coefficient on post-treatment (b1). However, my constant is incredibly high and yields a number that is an order of magnitude larger than what the mean for control post-treatment is and is no where near the value.
The coefficient on my interaction, b3 (see fig. 1), is the exact same as a manual calculation of diff-in-diff using means by treatment-time (see fig. 2). That seems reassuring but the constant being so high as to be nonsensical is worrying.
Should I be worried? What, if anything, is going wrong here?
(1) We've got clean data, no issues of treatment assignment or time.
(2) Out total sample is 800 people across 30 sub-districts.
(3) We cluster errors at the sub-district level.
(4) Treatment assignment was not random - people selected into the program.
(5) Moreover, we have people who are in control and people who are in treatment from within each sub district i.e. each sub-district has roughly the same number of control people and treatment people.