Dear all,

I'm running the following regressions:

reg Y X i.id i.year if C==1 (1)
reg Y X i.id i.year if C==0 (2)
reg Y c.X##C i.id i.year (3)

where, X is a continuous variable, C is a dummy variable (categorical) and "id" and "year" are used for fixed effects.

The results I find are such that:
  • in (1), the coefficient of X is negative (insignificant)
  • in (2), the coefficient of X is positive (significant)
  • in (3), the coefficient of X alone is positive significant (and similar to (2)), the coefficient of C#X is positive significant, the coefficient of C alone is negative (significant).
This is puzzling to me. From (1) and (2), I infer that X has no effect on Y when C==1 and has a positive effect on Y when C==0. But from (3), my interpretation is that the effect of X on Y is positive and even stronger when C==1 (as compared to C==0), which comes to contradict results from (1) and (2).

Am I missing something? I cannot just wrap my head around this.

Thanks much for your help.
Greg