st: Standard errors on interaction, when fully interacting ivreg2

[Jen Zhen <jenzhen99@gmail.com>]

I first ran
-ivreg2 outcome covar1 covar2 (endogreg= inst), robust-
separately on two subsamples of roughly equal size, defined by the
indicator gamma.

The estimated effect of endogreg on outcome was different and the
difference was a bit larger than twice the average of the standard
errors of that coeffient in the two samples. I hence guessed that it
would also be larger than twice the pooled standard error and hence
that the difference would be statistically significant.

I then wanted to test this formally by interaction, so I said:

gen g_endogreg = gamma*endogreg
gen g_inst           = gamma*inst
gen g_covar1      = gamma*covar1
gen g_covar2      = gamma*covar2
ivreg2 outcome covar1 covar2 g_covar1 g_covar2 (endogreg g_endogreg =
inst g_inst), robust-

The resulting point estimates correspond to those obtained in my
sample split. However, most (robust) standard errors are now about 50%
larger than both of the previous standard errors, so that the
difference is not statistically significant at conventional levels.

Now I'm wondering: Are these standard errors correct?

Thank you so much, JZ
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