st: RE: Difference-in-difference, serial correlation, and robust standard errors

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

Glenn,

In general, the use of the -robust- option in Stata addresses
heteroskedasticity only.  -cluster-, on the other hand, gives you SEs
that are robust to both heteroskedasticity and within-group correlation,
and the latter, in the panel data context, would normally mean
within-panel serial correlation.

In the case of -xtreg-, however, -robust- automatically triggers the use
of cluster-robust SEs.

One thing worth checking - are your fixed effects at the state or county
level?  The problem is that the asymptotics behind the cluster-robust
covariance estimator rely on the number of groups going off to infinity.
If your FEs are at the county level, and you use cluster-robust SEs,
there's no problem in your case - you have 840 counties.  But if your
FEs are at the state level, then you have a problem - you have only 17
states, and 17 isn't very far on the way to infinity.

HTH,
Mark

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
> statalist@hsphsun2.harvard.edu] On Behalf Of Glenn Landers
> Sent: 02 September 2012 14:28
> To: statalist@hsphsun2.harvard.edu
> Subject: st: Difference-in-difference, serial correlation, and robust
standard
> errors
> 
> I am a novice. I am using StataIC V11.
> 
> Does the robust option correct for serial correlation as well as
> heteroskedasticity? Wooldridge seems to say so in his Introductory
> Econometrics 4th ed. text (although his comment is specific to robust
> standard errors and not specifically Stata), and I have seen a few
references
> here.
> 
> I am running an OLS difference in difference. I am testing state and
county
> laws at the county level with quarterly data for three years for each
> state/county. I have 17 states, 840 counties, and 12 periods per
county =
> 10,800 observations. I am trying to be conscious of serial
correlation, as
> Bertrand et al (2000) as well as others point out, but I am also aware
my data
> seem to fit the case Bertrand describes where laws are not all
implemented
> at the same time, and the serial correlation problem goes away.
> My data range from 2002 to 2009, but I have three years for each
> state/county, so the laws are implemented at varying times across
those
> eight years. Still, I would like to run a test for serial correlation
just to be sure.
> 
> Colleagues have suggested xtreg, and I have implemented that and
xtserial,
> but it seems in arraying the 840 counties in panels of 12 periods each
> (1-12) and bringing the implementation dates of the laws more into
> alignment, I am imposing the serial correlation problem on the data
that I am
> trying to test for. In fact, the data demonstrate serial correlation
when
> implementing xtserial.
> 
> I know the data are heteroskedastic. Does implementing the the robust
> option also correct for any serial correlation that might be present,
short of
> having a test for serial correlation that does not implementing xtreg
or
> xtserial?
> 
> Thank you.
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