st: Regressing a first differenced variable on levels

[Kuba Bembenek <kuba.bembenek1@gmail.com>]

Dear Statalists,

I want determine the dependence of liberalization across five
different industries (index i) and 30 countries (index c). My intended
regression is something of the following sort:

Ycit= Xit-1 + wYt-1 +Ac + Bi +ut

Ycit- liberalization index, xit-1 laggend controls, Ac - country
effects, Bi - industry effects, and wYt-1 is the spatial lag. The
spatiallag is the weighted sum of the dependent variable for industry
i across all OTHER countries.

The problem that arises when I regress this model, is that I have
strong serial correlation in the error terms. While country a is
influencend in t by the values of the other countries in t-1, these
countries are again influenced by the values of country A in t-2.  Im
afraid that this might bias (im not so worried about efficiency) my
estimates due to correlated error terms.

Instead of using a first difference estimator, I wonder if I can just
replace the dependent variable and the spatial lag by first diffrences
while still using levels for the controls? And if this is possible,
what would be the interpretation of the coefficient of variable that
is measured in levels? Note: the serial correlation disappears, and
the sign and significane are as expected. Just the relation of
absolute change and levels rattles me.

Many thanks ahead,

Kuba
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