INTRODUCTION TO ECONOMETRICS II
ECO 306
NOUN
127
( )
( )
( )
( )
…[4.25] Now it is reasonable to suppose that lies between 0 and 1, in which case (1 – ) will also lie between 0 and 1. Thus (
becomes progressively smaller as s increases. Eventually, there will be a point where the term
( )
is so small that it can be neglected and we have a model in which all the variables are observable. A lag structure with geometricallydeclining weights, such as this one, is described as having a Koyck distribution. It is highly sparing regarding its constraint, requiring only one parameter more than the static version. Since it is nonlinear in the parameters, OLS should not be used to fit it, for two reasons. First, multicollinearity would almost certainly make the estimates of the coefficients so erratic that they would be worthless – it is precisely this problem that caused us to search for another way of specifying a lag structure. Second, the point estimates of the coefficients would yield conflicting estimates of the parameters.
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