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st: First-Differece with or without a constant?

From   Hawal Shamon <>
To   <>
Subject   st: First-Differece with or without a constant?
Date   Mon, 7 May 2012 13:47:21 +0200

Dear Stata list,

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:

Δyit = α0 + Δx1it + . + Δx2it + Δeit , 

where α0 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 (Δxkit) 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 Δx1it will bedropped due to collinearity. This is understandable.

Other literature recommends to supress the constant as follows:

Δyit = Δx1it + . + Δx2it + Δeit

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. Δunem has a positive impact (.2074992) in the model with a constant and a negative impact (-.168085) on  Δmrdrte 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. 

What do you think? Which model is "in general" the better one and why? I kindly ask for your opionions. 

Thanks in advance and kind regards,

Hawal Shamon

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