Under which conditions should we expect the difference-in-difference estimate to be equal to the equivalent panel data model?
Strictly speaking, whenever we have a experiment that offers a well defined treated and control groups in two periods of time, for using difference-in-difference methods, people recommend running OLS of models such as:
Stata: reg y post treatment postXtreatment and the coefficient on "postXtreatment" would represent the treatment effect At the same time, in case we have panel data for two periods we can run: xi: xtreg y i.year postXtreatment, fe
When exactly should we expect equivalence? Does it have anything to do with the panel being balanced?
Just one more question, in case we have more years available is the fixed effect model in the fashion the described above a good way to infer the treatment effect?