RE: st: RE: ivreg2 bandwidth

["Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>]

Mirko,

Hayashi's (2000) textbook "Econometrics", chapter 6, has a short and clear discussion.

But my original question is the first one you need to answer.  You have 3-day MAs.  Is the only reason for the autocorrelation the fact that these are 3-day MAs, and that therefore the autocorrelation disappears after 3 lags?  If so, then the unambiguous answer is that you should use the truncated kernel.  I think Hayashi has a discussion, but the intuition is fairly clear.  The truncated kernel puts weights of 1 on each of the lagged autocovariances.  If you want a kernel-robust VCV that is robust to any form of autocorrelation up to 3 lags, then the best thing to be doing is to be using all of them, and without weighting them by less than 1.  When you use other kernels, you put more weight on older lags that - in this case - actually aren't needed, and less weight on the lags that - in this case - you know a priori are the ones that matter.

HTH,
Mark

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Mirko
> Sent: 15 October 2011 17:29
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: RE: ivreg2 bandwidth
> 
> Mark,
> 
> I was just wondering whether you could provide some 
> references with respect to the choice of the bandwidth and 
> the kernel. And how this choice affects the weak instruments 
> tests. In few words this is what happens when varying 
> bandwidth and kernels
> 
> a) if I run IV regressions with non-truncated kernel and HAC 
> standard errors, my coefficients are all significant at 1% 
> level (using many specifications and IV estimators), but the 
> instruments are weak (F statistics ranging from 3 to 7);
> 
> b) if I run IV regressions using truncated kernel, my 
> coefficients are less robust across different regressions and 
> in some other specific cases never significant. The (AP) F 
> statistic is now around 9.6 or 10.4, with p-values ranging 
> from 0.001 to 0.01,  suggesting that the instruments are OK.
> 
> I wish to know more about the choice of the kernel and 
> bandwidth as the story to tell very much depends upon this. 
> Maybe is just better to show everything?
> 
> Mirko
> 
> 
> On 13 October 2011 16:51, Schaffer, Mark E 
> <M.E.Schaffer@hw.ac.uk> wrote:
> > Mirko,
> >
> > It depends partly on what you think the source of 
> autocorrelation is.
> >
> > If the autocorrelation is purely the result of the fact 
> that these are 3-day MAs - so that the autocorrelation will 
> disappear after 3 days - then the right kernel to use is the 
> truncated kernel (a.k.a. "Hansen-Hodrick") with a bandwidth 
> of 3.  It's not guaranteed to be PD in finite samples, but 
> this might not be a problem in practice in your case.
> >
> > If you suspect that there is autocorrelation beyond the 3rd 
> lag, you could try the automatic bandwidth selection option - 
> just say bw(auto).
> >
> > HTH,
> > Mark
> >
> >> -----Original Message-----
> >> From: owner-statalist@hsphsun2.harvard.edu
> >> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Mirko
> >> Sent: 13 October 2011 15:21
> >> To: statalist@hsphsun2.harvard.edu
> >> Subject: st: ivreg2 bandwidth
> >>
> >> Dear all,
> >>
> >> I am estimating a times-series equation where the 
> dependent variable 
> >> and the endogenous variable are 3-day moving averages.
> >>
> >> I am using -ivreg2- with -gmm2s- and -robust- to obtain 
> >> heteroskedasticity and autocorrelation-robust standard 
> errors such as
> >> this:
> >>
> >> qui count
> >> local band = round(r(N)^1/3)
> >> ivreg2 y x1 (x2=  z1 z2), gmm2s robust bw(`band') first
> >>
> >> I am not sure about the correct bandwidth specification in this 
> >> specific case as I am using moving averages. For a Bartlett kernel 
> >> function, it is usually suggested to use N^1/3. However, I am not 
> >> sure whether this is correct specification when using moving 
> >> averages.
> >>
> >> I would be grateful to receive any suggestion.
> >>
> >> Best wishes,
> >> Mirko
> >> --
> >> Mirko Moro
> >> Lecturer in Economics
> >> Economics Division
> >> University of Stirling
> >> FK94LA
> >> Scotland (UK)
> >> t: +44(0)1786467479
> >> f: +44(0)1786467469
> >> e: mirko.moro@stir.ac.uk
> >>
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