How to interpret the coefficient of the variable that takes first difference?

[mia lin]

Panel data model.
x takes first difference to become stationary.
Then how to interpret the coefficient of d.X?

[Oscar Ozfidan]

Stationary means the mean and variance does not change overtime. Most economic variables that is not true because everything GDP, Price levels etc grows overtime. So, if you look at GDP and Price level without differencing you will find that they are likely appear related but they may in fact not. That is generally true fro most economic variables. So, in order to investigate if variable A is related to variable B you have to make sure that they are stationary. So, that what you would be modeling then is the difference of the dependent variable. So, if variations from the stationary mean turns out to have significant relationship to your independent variable then you can reliably say that they are in fact related to each other. So, if X is related to difference of Y by a coeffcient of b then the interpretation is one unit change in X's level cause b times change in the Y's difference.

[Phil Bromiley]

To add to Oscar's comment, if you are differencing both X and Y, then a one unit change in the change in X is associated with a b change in the change in y. But this should also be the correct parameter for the original b because

if y(t)=b x(t)

then

y(t) - y(t-1) = b x(t) - b x(t-1)
= b (x(t) - x(t-1))