I would like to run the regression in the classical difference-in-difference framework, i.e.:
$Y_{i,t}$ = $\psi + \beta\text{Post}\times\text{Treat} + \delta\text{Post} +\gamma\text{Treat} + \epsilon_{i,t}$
Say my outcome variable is binary, or a count, or some other scenario for which I would like to run a logit or a Poisson or another GLM. Is there still a difference-in-difference interpretation for the $\beta$ term, just in terms of the link function (i.e. replacing $E[Y|x]$ with $g(x)$ -- the relevant link term?)
So for logit, it is a difference-in-difference in log odds, or for Poisson with a log link function, the same interpretation as a diff in diff with $\log(y)$ as a dependent variable with OLS?
