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

["Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>]

JZ,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
> statalist@hsphsun2.harvard.edu] On Behalf Of Jen Zhen
> Sent: 13 August 2013 11:56
> To: statalist@hsphsun2.harvard.edu
> Subject: st: ivreg2: Sample split finds bigger effect in period 1, interaction in
> period 2-- which one is right?
> 
> 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?

In your pooled regression

> gen late = year>=3
> gen x_late = x*late
> gen z_late = z*late
> ivreg2 y controls (x x_late = z z_late)

you're interacting "late" with the endogenous regressors x and the instruments z, but not with the "controls".  This means you're imposing the same coefficients on "controls" in the two regressions but allowing the coeffs and instrumenting to be different.  You probably also want to interact "controls" with "late".

HTH,
Mark

> 
> Thank you so much and kind regards,
> JZ
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