Saul/Clive/John/Justina,
I just looked at -xtpcse- and it looks like you can't get it to
generate OLS coefficients and SEs that allow for autocorrelation (or,
more precisely, I couldn't get it to do it). As soon as the
corr(ar1) option is specified, the coefficients reported become Prais-
Winsten.
With respect to Justina's suggestion of -newey-: this will report OLS
coeff and SEs that are robust to heteroskedasticity and arbitrary
autocorrelation, not just AR(1). The price to be paid for the
greater AR robustness is that you need to believe that the
autocorrelations die out sufficiently to become negligible after a
number of periods (the -lag- option of -newey-), and for the
asymptotics to work you need not only the sample size to go to
infinity but also the number of lags to go to infinity (just at a
slower rate). For example, one of the recommendations I've seen for
the Newey-West estimator is that the number of lags should be set to
the cube root of the sample size. (Actually, I think this should
probaby be 1 + number of lags, because the recommendation refers to
"bandwidth", which includes the current period.) This is true even
if you believe the autocorrelation is AR(1) - you still need to send
the lags off to infinity when doing the estimation.
I'm not a time series expert, but I think this means that Saul needs
a long-ish time series in his panel if he wants to go down the
-newey- route. Wild guess: N=1000 would be OK, N=100 would be
wobbly, N=10 would not be legitimate.
--Mark
Date sent: Wed, 7 Jan 2004 15:28:43 -0000 (GMT)
Subject: Re: st: OLS with AR1 errors
From: "Clive Nicholas" <[email protected]>
To: [email protected]
Send reply to: [email protected]
> Saul,
>
> I think I'm right in saying that, in fact, -xtpcse- produces OLS
> estimators, not GLS ones, but with 'panel-corrected' standard errors. Beck
> and Katz, throughout all of their work, have gone out of their way to
> strongly recommend that GLS (or FGLS) should _never_ be used unless
> absolutely necessary, since they believe that the SEs contain "horrible"
> properties (to use Beck's word (2001)).
>
> Saul Lach wrote:
>
> > I have panel across individuals and time data and I want to estimate the
> > parameters of a linear model using OLS on the pooled data assuming that
> > the errors follow an AR1 process for each individual. Does anybody know
> > where I can get a program that does this? As far as I understand the
> > command xtpcse produces a GLS (prais-weinstein) estimator, not the OLS
> > estimator.
>
> Beck, N. (2001) "Time-Series-Cross-Section Data: What Have We Learned in
> the Past Few Years?", ANNU REV POLIT SCI 4: 271-93.
>
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