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March 21, 2005
Dummy Variables
Exact collinearity: some linear combinations of the regressors (possibly including 1 for the intercept) is zero.
The problem with exact collinearity is that no amount of data can yield estimates of the parameters.
If there are three states, we could construct three state dummies. Adding all three to an equation with a constant term produces exact collinearity. The solution is either to add two of the three dummies or to suppress the constant term.
The Chow test is for the alternative hypothesis that a data sample could be broken up into m subsamples where the regression parameters differ across subsamples.
A closely related idea is to put in slope dummies and do an F test. This imposes the restriction that the error variance is the same across subsamples.
The choice among these two approaches sometimes comes down to computational convenience.
Posted by bparke at March 21, 2005 10:37 PM