Re: st: first-difference regression

[Sami Alameen <samialameen@gmail.com>]

Correcting previous post, I was talking about the dependent variable
all the time.

It's, I guess, a matter of of what we believe about the data: if the
data is very long (t is large) and we believe the dependent variable
is constant, on average, over time (the sum of its differences over
time should be zero) then not including a constant is ok.

but usually the mean change in the dependent variable is not zero
especially in short panels (short t), then the constant measures the
average of changes in the dependent variable and a constant should be
included.

I don't know of a theoretical justification of which, but this piece
of information is the usual practical justification.

If we believe that the unemployment rate is 6 (the hypothesized
natural rate), then if the difference in the unemployment rate is the
independent variable, the expected value is zero, thus no constant.

However, if the dependent variable is differences of inflation rate.
In advanced economies, in normal times, the expected and targeted
inflation rate is 2% for example, then a constant is needed. (assuming
a continuously updated chain price index for example)
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