>Jo Gardener <1243go@gmx.net>:
> Thanks a lot Jean,
> this is what I also thought after reading again through the AB-article and
> the Baltagi book. However, there are some working papers on the net, that
> clearly state, that if there is autocorrelation of 2. order then simply take
> lags of order 3. or higher as instruments.
>
> I think, also the answer of M. Parameswaran shows, that this is a common
> mistake.
I would not regard this as a mistake. Autocorrelation
of order 2 in differenced residuals is certainly
evidence against the validity of lags of order 2 as
instruments, but not necessarily against lags of
order 3 and further.
Think about a more general Arellano and Bond model with
errors in levels that follow an MA(1) process. In this
case the errors in first differences will exhibit
autocorrelation of order 1 and 2 but not of order 3 and
further, so that lags of order three and further are
still valid instruments.
I think this is the rationale motivating the exclusion of
lags of order 2 in some empirical applications. In particular
this is the approach followed in Bond and Meghir (1994),
where you can find a detailed discussion of the issue.
Stephen Bond, Costas Meghir (1994)
"Dynamic Investment Models and the Firm's Financial Policy"
The Review of Economic Studies, Vol. 61, No. 2. (Apr., 1994),
pp. 197-222.
Giovanni
> -------- Original-Nachricht --------
> Datum: Mon, 17 Jul 2006 09:46:52 -0400
> Von: "Salvati, Jean" <JSalvati@imf.org>
> An: statalist@hsphsun2.harvard.edu
> Betreff: st: RE: RE: Prober Instrument for GMM xtabond2
>
> > > -----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.
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