Hi Michele,
> I estimated a dynamic panel data model with xtabond2 to
> obtain the results in level equations and not in differences
> as xtabond does.
Unless the noleveleq option is specifief, xtabond2 uses the
first-difference equation as well as the levels equation to estimate the
model.
> But: How does
> xtabond2 remove the unobserved individual effect? xtabond
> removes it by taking first difference and so it quites, but
> how does xtabond2 do this?
As I said above, by default xtabond2 uses not only the levels equation,
but also the first-difference equation, in which the individual effect
does not appear. The unobserved individual effect is not removed from
the levels equation.
By default, if you use a regressor x to establish orthogonality
conditions, x is used as an instrument for both equations, and therefore
you implicitly assume that x is orthogonal to the individual effect.
However, you can use the equation() sub-option of ivstyle() and
gmmstyle() to prevent xtabond2 from using orthogonality conditions for a
particular regressor and a particular equation.
For example, if x is orthogonal to the idiosyncratic error but not
orthogonal to the individual effect, you should use the following
options:
ivstyle(x, equation(diff))
This will prevent x from being used in orthogonality conditions for the
levels equation.
> and in general: What is exactly the difference between system
> GMM and 2SLS?
At least in the context of dynamic panel data models, "System-GMM"
refers to the GMM estimation method that uses the levels equation as
well as the first-difference equation. References are given in the help
file for xtabond2.
More generally, 2SLS and GMM are two ways of dealing with
overidentification (the case where you have more independent
instrumental variables than parameters to estimate). 2SLS reduces the
dimension of the set of instruments by projecting the regressors on the
instrumental variables, and using the fitted values of these regressions
as instruments. GMM stacks the non-necessarily-null members of all the
orthogonality conditions in a vector and minimizes the (generalized)
norm of that vector. 2SLS can be seen as a special case of GMM.
A very good book about 2SLS and GMM in general is Fumio Hayashi's
"Econometrics" (Princeton).
I hope this helps.
Jean Salvati
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