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st: lags of the x's in xtabond


From   TEWODAJ MOGUES <tmogues@students.wisc.edu>
To   giovanni.bruno@unibocconi.it, Stata _ <statalist@hsphsun2.harvard.edu>
Subject   st: lags of the x's in xtabond
Date   Wed, 05 May 2004 12:05:10 -0500

Giovanni,
You have a good point, that's probably what's going on. 
Thanks.
Tewodaj

   Date: Tue,  4 May 2004 12:32:06 +0200
   From: Giovanni Bruno <giovanni.bruno@unibocconi.it>
Subject: Re: st: lags of the x's in xtabond

Tewodaj,

It seems to me that

1.  xtabond   y ,  lags(1)  pre(x, lag(1,1) )
2.  xtabond   y ,  lags(1)  pre(x lag_x, lag(0,1) )

actually provide different estimators for the same model:

y(it) =   y(i t-1)   +   x(it)  +   x(i t-1)  +   e(it).

While method 1 includes L1.x (but not further lags) as instruments, method 2
includes both L1.x and L1.lag_x, which is L2.x, as instruments. This also
explains why method 2. is equivalent to

3. xtabond   y ,  lags(1)  pre(x, lag(1,2) )

which still considers the same model but includes L1.x and L2.x as
instruments, exactly as method 2.

Giovanni

~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~.~
Tewodaj Mogues
Dept. of Agricultural and Applied Economics
University of Wisconsin - Madison
427 Lorch St. #317, Taylor Hall
Madison, WI 53706

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