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st: RE: RE: Prober Instrument for GMM xtabond2


From   "Salvati, Jean" <JSalvati@imf.org>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: RE: Prober Instrument for GMM xtabond2
Date   Mon, 17 Jul 2006 09:46:52 -0400

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Jo Gardener
> Sent: Monday, July 17, 2006 5:29 AM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: RE: Prober Instrument for GMM xtabond2
> 
> The mail again with a subject in the mail header.
> --------------------------------------
> Thanks for your answer, M. Parameswaran.
> However, I do not know if it is really that easy.
> 
> For instance if you have an AR(2) model like y=a1+a2*y(t-2)+...
> and the output gives shows you that there is autocorrelation 
> of 1., 2., and 3. order but no autocorrelation of 4. order 
> and onwards.
> 
> Then, referring to you, I can use instruments of 
> lag(4)-onwards for GMM-estimation.
> 
> But Arellano-Bond and in other books it is stated (for an 
> AR(1) model though), that the AR(1) is no problem because the 
> differenced residuals are expected to follow an MA(1) process 
> but if there is AR(2) autocorrelation, than the GMM-estimator 
> is inconsistent.
> 
> So the question should be: Is the AR(2) autocorrelation 
> always a sign, that the GMM-estimation is inconsistent (no 
> matter if the original model is an AR(1), AR(2) or AR(3) 
> model) or does it really depend on the instruments I use?
> 
> I think this question is not only important to me, but to 
> many others that use the GMM-estimator and do not get a 
> response from literature.

The Arellano-Bond paper is actually very clear about this. All the Arellano-Bond orthogonality conditions are established under the assumption that the error term in the levels equation is not autocorrelated. The purpose of the Arellano-Bond autocorrelation test is to test this assumption. If the error term in the levels equation is not autocorrelated, then the error term in the first-difference equation has negative first-order autocorrelation, and 0 second order autocorrelation.  

If you reject the hypothesis that there is 0 2nd order autocorrelation in the residuals of the first-difference equation, then you also reject the hypothesis that the error term in the levels equation is not autocorrelated. This indicates that the AB orthogonality conditions are not valid--no matter which lags you use as instruments.

Jean Salvati

> -------- Original-Nachricht --------
> Datum: Mon, 17 Jul 2006 13:58:54 +0530
> Von: "M.Parameswaran" <mpeswaran@gmail.com>
> An: statalist@hsphsun2.harvard.edu
> Betreff: st: Re:
> 
> > If there are second order serial correlation, then second 
> lags are not 
> > valid instruments, in this case one has to use 3rd lag onwards.
> > 
> > Parameswaran
> > 
> > On 17/07/06, Jo Gardener <1243go@gmx.net> wrote:
> > > Dear all,
> > >
> > > using a simple dynamic model (DPD) I currently face 
> following problem:
> > >
> > > Model: y=a1+a2*y(t-1)+ ...
> > > xi: xtabond2 y l.y i.year, gmm(y, lag(3!! 4) equ(both) coll) 
> > > iv(i.year,
> > equ(both)) small rob twostep arte(3)
> > >
> > > I use gmm(y, lag(3 4) and not lag(2 4) because the 
> AB-Test for AR(2) 
> > > -
> > not shown here - says that there is autocorrlation of second order. 
> > Thus I cannot use lag(2) as instrument.
> > > However, my question: Can I use lag(3 4), because the 3rd 
> lag is not
> > correlated with the differenced error term?
> > >
> > > Following output of the lag(3 4) estimation says, that the 
> > > differenced
> > residuals show no AR(3) correlation and the Hansen J is ok:
> > > Hansen test of overid. restr.: chi2(3) =   3,72     Prob 
> > chi2 =  0,432
> > > Arellano-Bond test for AR(1) in first diff: z =  -5,76  
> Pr > z =  0,000
> > > Arellano-Bond test for AR(2) in first diff: z =   2,21  
> Pr > z =  0,042
> > > Arellano-Bond test for AR(3) in first diff: z =  -0,75  Pr > z =  
> > > 0,433
> > >
> > > I am glad for any response I can get on this issue Jo gardener
> > >
> > > --
> > >
> > > --
> > >
> > >
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> > 
> > --
> > ___________________________________
> > M. Parameswaran,
> > Research Associate,
> > Centre for Development Studies,
> > Prasanth Nagar Road, Ulloor.
> > Trivandrum - 695 011,
> > Kerala, India.
> > Phone: +91-471-2448881 (O)
> >             +91 - 09446506388 (mobile)
> > e-mail: parameswaran@cds.ac.in
> >            mpeswaran@gmail.com
> > 
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