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# Re: st: First-Differece with or without a constant?

 From Christopher Baum To "statalist@hsphsun2.harvard.edu" Subject Re: st: First-Differece with or without a constant? Date Tue, 8 May 2012 08:08:59 -0400

<>
On May 8, 2012, at 2:33 AM, Hawai wrote:

> I like to estimate a First-Difference-Model on the basis of two waves.
>
> Some literature (e.g. Wooldridge 2008) recommends to estimate First Differenceusing the constant as follows:
>
> Äyit = á0 + Äx1it + . + Äx2it + Äeit ,
>
> where á0 denotes the difference of the intercepts of y for both years which isnothing else than the change. A disadvantage occurs when any change in x (Äxkit) does not varybetween the units. E.g., having a panel dataset with employees over twosubsequent years means that job experience is increasing for all of them overthe two subsequent years by one year. In this case Äx1it will bedropped due to collinearity. This is understandable.
>
>
> Other literature recommends to supress the constant as follows:
>
> Äyit = Äx1it + . + Äx2it + Äeit
>
>
> The first suggestion sounds very plausible to me. However, I am confused by the suggestions not to use a constant. Both models may lead to conflicting results. E.g., I regressed changes in murder rates on changes in unemployment rates over the years 1987 and 1990 and once with a constant and once without a constant. Äunem has a positive impact (.2074992) in the model with a constant and a negative impact (-.168085) on  Ämrdrte in the model without a constant. I would go for the model with the constant because it allows for a change in the intercepts. Ignoring the constant might lead tobiased estimates.

This is not an arbitrary choice. If you write down a model in levels containing the regressors (X, t), where t is a time trend, and you take
first differences (the equivalent of differentiation in discrete time), you end up with \delta y regressed on \delta X and a constant. If you do not have
a time trend in the level equation, you won't have a constant in the differenced equation, because it will be differenced away. If your model
of the process in levels conceptually includes a time trend, then you should include a constant in a FD equation; otherwise not.

Kit

Kit Baum   |   Boston College Economics & DIW Berlin   |   http://ideas.repec.org/e/pba1.html
An Introduction to Stata Programming  |   http://www.stata-press.com/books/isp.html
An Introduction to Modern Econometrics Using Stata  |   http://www.stata-press.com/books/imeus.html

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