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st: RE: First difference model for dynamic panel data xtabond2 xtivreg


From   "Salvati, Jean" <JSalvati@imf.org>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: First difference model for dynamic panel data xtabond2 xtivreg
Date   Fri, 8 Oct 2004 11:19:05 -0400

> I have some problems with estimating a dynamic panel data in 
> first differences of the following type:
> DY(it)=DY(it-1)+DX(it-1)+sector and time dummy variables
> 
> I would like to instrument DY(it-1) and DX(it-1) with 
> Y(it-2), respectively
> X(it-2) inline with Hsiao Anderson (1981) suggestions. 
> xtivreg...,fd seems to estimate the model but use the lagged 
> first differences as instruments.

Actually Anderson and Hsiao considered first-differenced instruments as
well as instruments in levels. Under their assumptions, both are equally
valid. In their paper, Arellano and Bond mention an estimator called
AHd. That's the Anderson-Hsiao estimator with first-differenced
instruments.

If, in your model, DY(it-2) and DX(it-2) are not valid instruments, then
I can't think of a reason why Y(it-2) and X(it-2) should be valid. My
guess is that the problem is somewhere else in your model.

A critical assumption in the papers by Anderson-Hsiao and Arellano-Bond,
and in the literature that followed, is that the idiosyncratic error
term in the levels equation is not autocorrelated. If this assumption is
rejected, then the orthogonality conditions involving lags of the
dependent variable or lags of the regressors are not valid, and
therefore the whole estimation procedure is not valid either.

The assumption that the idiosyncratic error term in the levels equation
is not autocorrelated has two testable implications: the error term in
the first-difference equation will exhibit negative first-order
autocorrelation, and 0 autocorrelation for orders 2 and beyond.
--xtabond-- reports the m1 and m2 statistics derived by Arellano and
Bond to test these implications.

Note also that that you can't use -xtivreg, fd- for inference and
hypothesis testing after Anderson-Hsiao estimation. The covariance
matrix of the coefficients reported by -xtivreg, fd- is not robust to
autocorrelation and, as I said, under the Anderson-Hsiao assumptions,
the error term in the FD equation will be negatively autocorrelated.

Jean Salvati

> Is it possible to estimate this kind of model maybe using any 
> other commands, for example, xtabond xtabond2? And how could 
> it be specified? 
> 
> I have tried the following: xi: xtabond2 y l.(y x) i.year 
> sec1-sec120, gmm(l.(x y),lag(1 1)) iv(i.year sec1-sec120 
> passthru) noleveleq robust but it do not do the trick.
> 
> I have estimated my model with system GMM and difference GMM 
> (xtabond2) but I keep rejecting that the instruments are 
> valid. Besides, the number of observations of each individual 
> is rather low (maximum of 7 observations) and the panel is unbalanced.
> 
> Any suggestions would be most appreciated
> 
> Fredrik Wilhelmsson
> Ph.D. Student
> University of Lund
> Department of Economics
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> 

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