Interpretation of coefficients:
Consider the simple dynamic model outlined in equation.
Taking partial derivatives we have
Thus, the lag structure in equation implies that changes in X result in a set of dynamic responses in Y. 'The immediate response is given by β. This is also referred to as the impact or short-run multiplier. We can obtain the medium-run response as the accumulated effect of a stimulus now, i.e.,
The long-run effect (or equilibrium multiplier) of a unit changein Xt can be computed by summing up all the regression coefficients/partial derivatives. Given |φ|< 1, this sum will be equal to [β/(1 -φ,)].