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This and the next two exercises are based on the test statistic usually used to test a set of J linear restrictions in the generalized regression model: where β is the GLS estimator. Show that if Ω is known, if the disturbances are normally distributed and if the null hypothesis, Rβ = q, is true, then this statistic is exactly distributed as F with J and n − K degrees of freedom. What assumptions about the regressors are needed to reach this conclusion? Need they be nonstochastic? |
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