psviii140a

# psviii140a - University of California D Steigerwald...

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Unformatted text preview: University of California D. Steigerwald Department of Economics Economics 140A Problem Set VIII 1. Consider the simple model in deviation-from-means form (1) Y t = β X t + U t . Inspection of the distribution of the residuals reveals that V(U t ) = σ 2 2 t Z , where Z t is known, so that you know the error variance up to a multiplicative constant. a) How would you correct for this form of heteroskedasticity? Show that the variance of the OLS estimator is higher than the variance of the generalized least squares (GLS) estimator you would obtain after the appropriate transformation. b) Assume now that you found instead that the V(U t ) = σ 2 X t . How would you transform the model now? Derive the expression for the estimator . B GLS c) Another case where error variances are often unequal involves grouped data. To motivate grouped data for the above model, suppose that the n observations are divided into K groups, with n k observations in the k th group ( k=1,2,...K ). We estimate the equation ( 2 ) , V X Y k k k + = β where k Y is the average value of Y t and k X is the average value of X t for group k . If you know that V(U t )= σ 2 , what is the variance of V t ? How can you use this information to transform (2) into one for which OLS is...
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psviii140a - University of California D Steigerwald...

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