# Re: st: Constant terms in AR1 error regressions

 From "Clive Nicholas" To statalist@hsphsun2.harvard.edu Subject Re: st: Constant terms in AR1 error regressions Date Fri, 19 Dec 2008 21:27:58 +0000

Michael Hanson replied:

> You've defined your "task" very narrowly as using -regress- to estimate an
> AR(1) equation on residuals from (what I presume to be) a prior regression.
>  If you could give a more general idea of what you are trying to accomplish,
> I and others on the list might be able to make better suggestions.  For
> example, one might give different advice if you were concerned that the
> residuals were I(1) than if you were fairly confident they were stationary.

This example probably best illustrates what I was originally getting at:

webuse union
xtset idcode year
reg grade south union black if year==70
predict r70, r
forval i=71(1)73 {
local j = i'-1
reg grade south union black if year==i'
predict ri', r
reg ri' rj' if year==i'
reg ri' rj' if year==i', nocons
}

Notice that the coefficients on \rho and their attendant t-ratios are
not always the same. Unit-root tests via -pperron- and -dfuller-,
within unit, suggests my pooled time-series is stationary.

> That said, Wooldridge (2006, p. 418) discusses testing for AR(1) serial
> correlation with strictly exogenous regressors, and advises "this regression
> may or may not contain an intercept; the t statistic for \hat{\rho} will be
> slightly affected, but it is asymptotically valid either way."  Later, he
> notes that strictly exogenous regressors are not very common with time
> series data, and that such simple tests are not robust to higher order
> autocorrelation.  (You did test for higher order terms before settling on an
> AR(1) specification, right?)  Wooldridge recommends a Breusch-Godfrey test,
> but there are others:  see -help regress postestimationts- (yes, that is a
> "ts" at the end) for discussion of what is implemented in Stata.

Because, like -union-, my dataset is pooled, I ran -corrgram- with
selected units (i.e., those possessing a long enough time-series to be
worth performing Q tests on) and found one AR1 process and one AR3
process; the rest had none at all. That said, a pooled regression
using BSS's -xtivreg2, bw(2) small robust i() t() fe- showed my lagged
dependent variable to be significant; running (mean-centered) pooled
regressions using -xtpcse-, however, showed my LDV failed to reach
significance.

I did look carefully at -help regress postestimationts-, as it would
be much easier to run any of those AC tests automatically than do it
'by hand', as I had to. However,

quietly reg grade lagrade south union black if year==73
estat bgodfrey
sample may not include multiple panels
r(459);

estat archlm
sample may not include multiple panels
r(459);

estat durbinalt
sample may not include multiple panels
r(459);

estat dwatson
sample may not include multiple panels
r(459);

and so on.

> Two final thoughts:  First, if you include the intercept in a regression of
> a residual series on its first lag, and the estimated intercept is
> significantly different from zero, then you probably should revisit your
> prior estimation: your residuals should be mean-zero by definition.  Second,
> if your results are very different when the intercept is excluded -- if that
> one extra degree of freedom is enough to change your results -- then I would
> caution you to be very skeptical of them to begin with, as you are working
> with large-T asymptotics by using -reg-.

Indeed, my T has a maximum of 13 in this pooled dataset, and I'm
running -reg- on single cross-sections in order to obtain \rho by
hand.

--
Clive Nicholas

[Please DO NOT mail me personally here, but at
<clivenicholas@hotmail.com>. Please respond to contributions I make in
a list thread here. Thanks!]

"My colleagues in the social sciences talk a great deal about
methodology. I prefer to call it style." -- Freeman J. Dyson.
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