Coefficients Interpretation of a xtpoisson fe model

[Maria Pereira]

Dear all,

I'm estimating a xtpoisson model with fixed effects in which my dependent variable (units sold) is in level and my independent variables are in logs except a dummy (campaign: 1 if the product is in a campaign during that month, 0 otherwise). I have panel data, meaning monthly observations for each firm (individual).
My question is how can I interpret the following coefficients:

-> log_discount = 0.6228653; is this a semi-elasticity?
-> dummy_campaign = 0.0108165

Many thanks in advance!
Maria

[Clyde Schechter]

log_discount = 0.6228653; is this a semi-elasticity?

It depends on what you are thinking about. It is, indeed, a semi-elasticity of log_discount. But if you are thinking about what it says about differences in discount itself, it is an elasticity, not semi-.

dummy_campaign = 0.0108165

You know, instead of trying to remember what is an elasticity and what is a semielasticity and what is something else, it is probably simpler to just work it out from first principles instead. Poisson regression is log linked, which means that the linear combination of the variables with the coefficients expresses the log of the expected value of the dependent variable. So your model is

log(expected # units sold)  = ... + 0.0108165*dummy_campaign + ...

So if we have dummy_campaign = 0 at one time and dummy_campaign = 1 at another time, and all else remains the same, then the log of the expected value of units sold increases by 0.0108165. (For simplicity I'm just going to call this 0.011 for the rest of this post.) That corresponds to a multiplicative increase by a factor of exp(0.011) = 1.011, or, if you want to put it in percentages, a 1.1% increase. (Which satisfies the definition of a semi-elasticity.)