st: ivreg2: Sample split finds bigger effect in period 1, interaction in period 2-- which one is right?

[Jen Zhen <jenzhen99@gmail.com>]

I have estimated a standard -ivreg2- regression of the following form:
ivreg2 y controls (x = z)
where controls includes year and month fixed effects as well as a
bunch of other variables.

Now I'd like to know whether the IV effect of x thus estimated differs
between the first  2 and the last 3 years of my sample.

I first tried this by splitting the sample and running
ivreg2 y controls (x = z) if inrange(year,1,2)
ivreg2 y controls (x = z) if inrange(year,3,5)
This gave the result that the effect of x was smaller in the last 3 years.

Since I wasn't entirely sure how to formally test whether the
difference was significant, I then pooled the two periods again and
re-ran my first regression with an interaction as follows:
gen late = year>=3
gen x_late = x*late
gen z_late = z*late
ivreg2 y controls (x x_late = z z_late)
This does pretty much follow suggestions made in earlier posts by Kit
Baum and Mark Schaffer.

The thing I do not understand though is that now I find x_late to be
significantly positive and hence to have the same sign as x itself,
implying the the effect is larger in the second period. This stands in
contrast to the results obtained earlier by means of the sample split.

Would anyone happen to see where I'm getting this wrong?

Thank you so much and kind regards,
JZ
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