# st: RE: xtabond2: gmm in levels only meaningful?

 From "Salvati, Jean" To Subject st: RE: xtabond2: gmm in levels only meaningful? Date Thu, 5 Jan 2006 11:03:47 -0500

```There are two potential problems in a model with an individual effect:

1) Correlation between some regressors and the individual effect;
2) Correlation between some regressors and the idiosyncratic
disturbance;

First-differencing solves problem 1). IV estimation (2SLS or, more
generally, GMM) solves problem 2).

When the first lag of the dependent variable is used as a regressor,
then first-differencing solves problem 1) but generates problem 2). In
this case, using instrumental variables is required for consistency.
This is the foundation of the Anderson-Hsiao IV/2SLS estimator and of
the Arellano-Bond GMM estimator.

When 1) is not an issue for any of the regressors (that is, when all the
regressors are orthogonal to the individual effect), then you can
estimate the levels equation directly (without first-differencing). This
is the so-called "random effect" estimator. There are GLS and 2SLS/IV
versions of this estimator. If you only want to use the levels equation,
then you should consider the random-effect estimator and ask yourself
whether your regressors are all orthogonal to the individual effect. If
you really want to use GMM, then just remember that 2SLS can be seen as
a special case of GMM.

When some (but not all) of the regressors are orthogonal to the
individual effect, you can use the levels equation to establish
orthogonality conditions that can be combined with the orthogonality
conditions for the first-difference equation. This leads to the
Arellano-Bover/Blundell-Bond GMM estimator implemented in xtabond2.

To summarize, if 1) is not an issue in your model, then you don't need
first-differencing, and you don't need the kind of GMM implemented in
xtabond and xtabond2. In this case, you should look at the
"random-effect" estimators implemented in xtreg, xtivreg, and
xtivreg2/ivreg2.

If 1) is an issue, then you can only use the regressors that are
orthogonal to the individual effect to derive orthogonality conditions
from the levels equation.

Jean Salvati

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Niko Wrede
> Sent: Thursday, January 05, 2006 10:32 AM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: xtabond2: gmm in levels only meaningful?
>
> Dear all,
> the System-GMM estimator exploits moment conditions for
> equation in differences AND for equation in levels.
>
> However, using xtabond2
> ..., gmm(depvar, lag(2 .) equ(BOTH)) ...
> I do not get plausibel results (in almost all cases the
> Hansen J Test indicates overidentifying restrictions).
>
> But when using xtabond2
> ..., gmm(d.depvar, lag(2 .) equ(LEVEL)) ...
> [WITHOUT an additional gmm(depvar, lag(2 .) equ(diff)
> command] the results are economically plausibel and the
> Hansen J Test is ok.
>
> My understanding of GMM is, that one has to use the equation
> in differences to get rid of the individual effects. In
> addition, one can exploit the equation in levels and use
> differences of the depvar as instruments for those.
>
> But I have not seen GMM estimators, that use ONLY the
> equation in levels.
> However, maybe anybody knows of such cases and is able to
> give some references.
> I would greatly appreciate any help since I already spent a
> lot of time searching for valuable information on this topic.
>
> Niko
>
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```