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Re: st: Trends and Time dummies


From   Partho Sarkar <partho.ss+lists@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Trends and Time dummies
Date   Sun, 11 Sep 2011 12:10:46 +0530

Hello Vinod

I don't think your question is precise enough.  What kind of trend and
what sort of dummies do you mean?  The most obvious situation for each
is this:

trend:

Yt = b0 + b1X t + b2T t + ut,

where T is the trend term.   This is equivalent to a constant shift
(=b2) in the intercept term each period.  Now if you add a set of
"year dummies" to this, e.g.,

Yt = b0 + b1X t + b2T t + b3Dt1+ b4Dt2+...DtM +ut,

Now I try to give my interpretation of the regressions you mention, as
they would be in this sitution:

a) first, you obviously cannot have M=N (number of years), i.e. you
cannot have a dummy for every year, as that would leave you with
negative degrees of freedom!  So M<N.  Further

b) the coefficient of each Di measures the "extra" jump in the
intercept beyond the common upward shift=b2

Now if you were to rerun the regression without the trend, the
coefficients of the dummies would capture not only the "extra" shift
they were earlier capturing, but a part of the shift that was earlier
being captured by the trend term.  In other words, you would have an
omitted variable bias, as you are omitting the trend term.

Hope this helps.

Partha


On Sun, Sep 11, 2011 at 3:12 AM, Venkiteshwaran, Vinod
<Vinod.Venkiteshwaran@tamucc.edu> wrote:
> The following question is not really a Stata syntax/programming related but more of a statistical logic type query.
>  In pooled cross-sectional time series data what is the effect of including both a trend and  year dummy variables?
> Specifically can the coefficients on the year dummy variables thus obtained be related to a model without the trend but just the year dummies?
> Any useful references that I can look up would be extremely helpful.
>
> Thank you
>
> Vinod
>
>
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