Statalist:

I am running the following Probit model on pooled panel data:
\[ P(y_{it} = 1 \vert x_{it}) = \Phi(b_0 + \delta_t + b_1 \varepsilon_t \times x_{it} + b_2 x_{it}) \] The RHS includes two terms: (i) an interaction term between the individual-specific, binary variable x and a variable epsilon that is common across all observations in each time period, i.e., a macro variable; and (ii) time fixed-effects, denoted delta. Suppose I want to estimate exactly this specification, with x = 0 as base value. Then Stata correctly returns the coefficient b2 which indicates a level shift if x = 1. However, the interaction effect b1 captures the additional elasticity of y w.r.t. to x if x = 0, i.e., the wrong base level. Here is a cooked-up example:

Code:
webuse union, clear

* generate variable common across all observations in a given year
gen vareps = rnormal()
by year, sort: replace vareps = vareps[1]

drop if grade<4

* model with both level terms and interaction
probit union c.vareps##ib1.black, coeflegend

* model with level of black and interaction with vareps plus year fixed-effects
probit union ib1.black c.vareps#ib1.black i.year, coeflegend
Note that as long as I allow for the level of varepsilon to enter the model, the base categories are correct (obviously, I cannot have time fixed-effects in this case).

Any hints would be greatly appreciated!

Thanks,
Peter