st: xtabond2 nolevel vs ivreg2 gmm

[Kit Baum <baum@bc.edu>]

Mariarosaria said

I estimated a dynamic equation:
yt= a +b*y(t-1)+c*xt+et
 using xtabond2  (with the nolevel option) and ivreg2 (with the gmm  
option). I
have used the same number of IVs for the endogenous variables (x is a  
vector
of endogenous and exogenous variables).
I am aware that the first command implies the adoption of an  
Arellano- Bond
(difference GMM) estimator, while the other the use of a two-step  
feasible GMM
estimator. However, I don't understand why I get an estimation sample  
rather
different for the two commands: the ivreg2 sample is half that of the  
xtabond2
(4108 vs 8467 obs).

First of all the equivalent model to Arellano-Bond difference GMM  
would be D.y on LD.y and D.x if you did it "by hand" in ivreg2. If  
you used xtivreg2, fd, it would do the differencing for you.

ivreg2 (and any straightforward iv technique, such as xtivreg2, fd)  
will drop one observation on every panel for each lag mentioned in  
the model or instrument specification. So if your instruments  
included, e.g., L2D.y, L3D.y, L4D.y, you would lose five observations  
per panel (one for the difference and four for the lags). The cunning  
strategy of the Arellano-Bond estimator (see Roodman's "How to do  
xtabond2" in RePEc, http://ideas.repec.org) avoids the loss of these  
additional observations for the instrumenting (or rather loses only  
one for the lags used in instrumenting; System GMM does not even lose  
that). So it is perfectly understandable that a traditional IV  
estimator (such as Anderson-Hsiao implemented by xtivreg2, fd) will  
work with a much smaller sample than will Arellano-Bond or Blundell- 
Bond.

Kit

Kit Baum, Boston College Economics
http://ideas.repec.org/e/pba1.html
An Introduction to Modern Econometrics Using Stata:
http://www.stata-press.com/books/imeus.html


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