According to my understanding about the difference-in-differences (DID) model with fixed effects, there are two specifications
- y=a0 + a1*TREAT + a2*POST + a3*TREAT_POST + e
- y=a0 + a1*TREAT_POST + timeFE + individualFE + e
Here, the dependent variable is a count variable and
TREAT is an indicator variable that represents multiple groups of individuals affected by an event/treatment. The treatment affects groups of individuals at different calendar years, so
yrsfromtreatment is a dummy variable for year pre- and post-treatment.
TREAT represent 1 for treated individuals (regardless of group) and 0 for matched control individuals.
POST represent 1 for all years after the treatment is introduced.
TREAT_POST=1 for the treated individuals in the post-treatment period.
So, Model 2 is better if there are possible omitted time-invariant and time-specific variables. And
POST indicator variables should usually be dropped in Model 2.
However, I find that I can actually run a fixed-effect negative binomial regression with calendar year (
i.year) and treatment year (
i.yrsfromtreatment) dummies in Stata:
xtset panelid yrsfromtreatment
xtnbreg y i.TREAT##i.POST i.yrsfromtreatment i.year, fe robust
Stata reports positive signs and significance in
How do I explain the coefficients on
POST when fixed effects are included? Is this model incorrect?