Ki Young Park <[email protected]> asked about why his attempt to estimate
a model with -xtabond- failed.
The short answer is that his call to -xtabond- specified too many
instruments.
Now for some details.
Ki noted that
> I am currently working on panel data estimation with predetermined
> variables. My panel data has i=50 and t=123.
If Ki's data is balanced with no missing observations and Ki was interested
in a model with only one lag of the endogenous variable then a full
-xtabond- specification would include (123-2)*(123-1)/2 = 7381 instruments.
Since Ki specifies predetermined variables, Ki is actually asking for many
more instruments.
It is worth while to review the properties of some of the different
estimators in dynamic panel data models with predetermined variables when
the number of panels, n, goes to infinity and the number of time periods, T,
is fixed.
1) Standard Random- and Fixed-effects estimators are inconsistent
2) There are simple instrumental variables estimators derived by
Anderson and Hsiao that provide consistent but inefficient
estimates. One of these estimators cannot identify an
autoregressive lag coefficient of .5, the other can. (See
Arellano and Bond (1991) for details.)
3) The Arellano-Bond estimator provides consistent estimates that
are more efficient than the Anderson-Hsiao estimators. In
addition, since the Arellano-Bond estimator is explicitly derived
as a GMM estimator, the Arellano-Bond estimator has many nice
generalizations that handle heteroskedasticity, specification
testing, et cetera.
4) The GMM literature, and its more recent counterpart in Generalized
Empirical Likelihood, has shown that using too many instruments
for a given sample size in a GMM estimator can produce
significant finite sample bias.
The properties of the above estimators are derived under the assumptions
that n -> infinity and that T is fixed. Since Ki's data has n = 50
and T = 123, it is not clear that Ki would want to choose an estimator based
on n -> infinity and T fixed asymptotics.
While -xtabond- should exit more quickly, when asked to estimate models with
too many instruments, it is not clear that Ki actually wants to use -xtabond-.
Ki can restrict the number of lags of the dependent variable that -xtabond-
uses to create instruments by specifying the -maxlags()- option and
similarly for the number of lags of the predetermined variables in the -pre(
varlist, lagstruct(prelags, premaxlags)- option. However, even setting
maxlag(1) will specify more instruments than is likely desirable. The
reason is that you can still create a lot of instruments from that first lag
of the dependent variable.
Ki may want to use a simpler Anderson-Hsiao estimator estimator using
-xtivreg-. With T so large, Ki is probably better off carefully specifying
the instruments by hand than letting any Arellano-Bond estimator pick them
up automatically.
-- David
[email protected]
References
Arellano, M. and Bond, S. 1991. ``Some Tests for Specification for Panel Data:
Monte Carlo Evidence and an Application to Employment Equations". The Review
of Economic Studies, 58(2), pages 277-297.
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