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st: xtabond2 and postdetermined regressors


From   James Shaw <shawjw@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: xtabond2 and postdetermined regressors
Date   Fri, 21 Jan 2011 17:22:15 -0600

I have two questions regarding GMM estimation as implemented by xtabond2.

Is it valid to use the forward orthogonal deviations (FOD)
transformation when one or more regressors is postdetermined?  I have
seen no specific discussion of this topic in the literature.  Arellano
and Bover refer specifically to the case where the instrumented
variables are predetermined.  For models that include predetermined
variables only, the FOD transformation can be applied to all save the
last time period.  However, if a model includes a postdetermined
variable, such as

(1)	Y_it = Y_i(t+1) + e_it (t = 1,…, T),

then I believe an additional time period should be lost since the FOD
transform of the postdetermined variable cannot be generated in either
the Tth or (T-1) period.  Curiously, this does not appear to be the
case when using xtabond2.  I suspect that the program is substituting
a zero value in cases where the FOD transformed observation cannot be
generated.

Additionally, when using xtabond2 to fit a model that includes a
forward lag of an endogenous variable, can leads of the forward lagged
endogenous variable be used as GMM instruments?  For instance, given
the model presented in (1) above, would the following be valid:

xi: xtabond2 Y f.Y , gmm( Y , lag(-2  -2) ) gmm( Y, lag(2  2) ) robust
small twostep?

I do not believe leads could be used as instruments in conjunction
with the FOD transform, though I would think that leads of length 2 or
greater could be used if the standard difference transform is applied.
 Even in the latter case, I question whether they would be weak
instruments.

--
Jim


James W. Shaw, Ph.D., Pharm.D., M.P.H.
Assistant Professor
Department of Pharmacy Administration
College of Pharmacy
University of Illinois at Chicago
833 South Wood Street, M/C 871, Room 266
Chicago, IL 60612
Tel.: 312-355-5666
Fax: 312-996-0868
Mobile Tel.: 215-852-3045

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