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# RE: st: first difference and time dummies.

 From "Vasilis Sarafidis" To Subject RE: st: first difference and time dummies. Date Thu, 18 Oct 2007 09:02:47 +1000

```If you believe that there are common time-specific effects in your errors, these will remain despite first-differening your model. Therefore, you should include dummies (or time-demean the data) in the first-differenced model too.

Let's consider this example:

Y(i,t) = b*X(i,t) + u(i,t), u(i,t) = e(i,t) + g*f(t)

where f(t) is the common time effect.

Transforming the data in terms of deviations from time-specific averages you obtain

Y(i,t)-Y.t = b*[X(i,t)-X.t] + [e(i,t)-e.t)]

so the common time-effects have been removed. You can then take first differences.

You may use xttest2 to test for the presence of common time effects or xtcsd.

Best

Vasilis

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Brent Fulton
Sent: Thursday, 18 October 2007 3:29 AM
To: statalist@hsphsun2.harvard.edu
Subject: RE: st: first difference and time dummies.

Hi Alessia,

I am not sure of your exact problem, but you want to include time dummies if you think they will explain some of the variance of the first-differenced
(FD) dependent variable. Wooldridge (2003) pp. 448+ goes through an example of how to incorporate time dummies in a FD model, which David also described below. If you FD the time dummies, then the FD model does not contain an intercept, which can be inconvenient. Wooldridge then recommends replacing the FD time dummies with an intercept and regular 0/1 time dummies. So if you originally had t periods, then the FD model will have an intercept and
t-2 time dummies. His example of 3 periods (2 after FD) includes an intercept and a single dummy variable for period 3.

In the next chapter, he then goes through the relative advantages and disadvantages of a fixed-effects versus a FD model, which will give different results when t is greater than 2.

Hope this helps.

-Brent

Wooldridge, Jeffrey M. (2003), Introductory Econometrics: A Modern Approach (2nd ed.), Mason, Ohio: Thomson South-Western.

______________________________________________________
Brent D. Fulton, PhD
Health Services Researcher
Petris Center, School of Public Health, UC Berkeley
Phone: 510-643-4102
Fax: 510-643-4281
Email: fultonb@berkeley.edu
www.petris.org

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of alessia matano
Sent: Wednesday, October 17, 2007 6:45 AM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: first difference and time dummies.

Many thanks,

may i ask you also how should I evaluate if it is better to include
time dummies or not in the first difference equation? Should I look at
the residual pattern?

Can you help me?
alessia

2007/10/17, David Roodman (DRoodman@cgdev.org) <DRoodman@cgdev.org>:
> First-differencing time dummies is OK. It is consistent with the levels
model.
>
> But actually it hardly makes any difference whether you enter the time
dummies directly into the differenced regression without differencing, or
you difference them too. This is because the joint *linear span* of the time
dummies is the same before and after differencing, so their coefficients
will differ but none of the other coefficients should change. There's a
brief mention of this in footnote 18 of my "How to Do xtabond2" paper.
>
> For basically the same reasons, if you are including time dummies anyway,
it shouldn't matter whether you include the constant or not in the
differenced regression. If you do include it, one of the time dummies should
drop out but not much else should change.
> --David
>
> > -----Original Message-----
> > From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
> > statalist@hsphsun2.harvard.edu] On Behalf Of Sebastian F. Büchte
> > Sent: Wednesday, October 17, 2007 8:27 AM
> > To: statalist@hsphsun2.harvard.edu
> > Subject: Re: st: first difference and time dummies.
> >
> > Alessia
> >
> > this is a repeat post of your message to the list for which you so far
> > did not receive any answers. I guess this may be due to an
> > inconclusive presentation of your "problem". You should try to give
> > more details as
> >
> > - you regression command
> > - variables used and what they mean
> > - ...
> >
> > This will certainly increase your chances to be helped out by other
> > list subscribers.
> >
> > Regards
> > Sebastian
> >
> > 2007/10/17, alessia matano <alexis.rtd@gmail.com>:
> > > Hi,
> > > I would like to ask you one thing i do not well understand: I am
> > > performing a regression in first differences. In the level equations i
> > > was using time dummies, now i do not know.
> > > 1) if i use them in differences (which take value1 0 -1) the
> > > regression does not work anymore. I think it is not correct to use
> > > such modified dummies (they are not more dummies)
> > > 2) if i use them in levels (they are 0 1), also the regression does
> > > not work and i think it is not right to assign to a single year the
> > > impact of the difference between two years
> > > 3) if i do not use them it works, and it has closer results for the
> > > level equation.
> > >
> > > I am asking also if not trying to create such dummies which take value
> > > of 1 for the two years the difference concerns, but i am not sure it
> > > has sense..
> > >
> > > Another question: stata automatically put the constant in rthe
> > > regression. To mantain the structure of the level equation should it
> > > be not right to take it off??
> > >
> > >
> > > Anyone of you can help me or suggest me something to read about?
> > >
> > > Many thanks
> > > alessia
> > >
> > > p.s. I am sorry, I already sent this email, but it was yesterday in
> > > the night. so I am trying again last time
> > > *
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