st: Interaction variables in a panel model

[Mario Jose <mariojose276@gmail.com>]

Dear Statalisters,

I have ran a panel model with fixed effects (xtreg, fe) to a sample
with about 80.000 firms, firstly using only one interaction between a
continuous (x1) and a binary variable (d). The model is like this:
xtreg y x1 d x1*d control i.year, i(id)  fe

The output obtained is as follows (standard erros in parenthesis):

Y = -1.171*x1+0.457*d+0.413*x1*d+control var+years dummies
        (0.227)     (0.057)     (0.202)              ...

As expected, the combined effect of x1 on y is lower for group taking
d=1. (at this stage I was very happy)

I ran again my model including another dummy - b - taking 0 for the
first years of the sample period (3 years) and 1 for the last years (5
years). I have interacted x1 ## d ## b. The rationale was to test
whether the x1*d change significantly from the beginning of the period
to end.

I obtained the following estimates:

Y = -1.895*x1 + 0.468*d + 0.201*x1*d + -0.417*b + 0.131*x1*b
         (0.418)        (0.133)      (0.420)           (0.116)
(0.332)

- 0. 198 * x1 * b + 1.014 *x1 * d * b + control + year dummies
  (0.124)                (0.389)                      ...

Now the interaction between x1*d  is no longer significant and the x1
* d * b is significant at any level.
Under this results, one would say that the different effect of x1
found in the 1st equation between the subsamples is due to what
happened in the second part of my sample period. However, what made me
split the sample cross-sectionally (d), was the literature and
thinking that the subsamples would 'behave' differently independently
of the period taken.

When I replace the Y by another proxy, I find the results changing
significantly, in the sense that the signs obtained for dummies are
opposite to what is expected..
Is there anyone who can say whether this strategy is reasonable? and
whether it is normal obtaining such instability in models with
interaction variables?
Any help on my questions would be greatly appreciated.

Thank you,
MJ
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