The model is The parameter is estimated by OLS b X 0X 1 X 0Y and GLS e X 01X 1 X 01Y Let be Y X b and e Y X e denote the residuals Let b R2 1be0be (Y 0Y ) and e R2 1ee0ee (Y 0Y ) denote the equation R2 where Y Y Y If the error ei is truly heteroskedastic will b R2 or e R2 be smaller Y XB ei Ele X 0 E ex 0 diag(, , 0

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Question: The model is The parameter is estimated by OLS b X 0X 1 X 0Y and GLS e X 01X

The model is Y = XB+ei Ele|X]=0 E[ex] = 0 = diag(,..., 0}.

The parameter ¯ is estimated by OLS b¯ Æ
¡
X 0X ¢¡1 X 0Y and GLS e¯ Æ
¡
X 0§¡1X ¢¡1 X 0§¡1Y . Let be Æ Y ¡X b¯
and e Æ Y ¡ X e¯ denote the residuals. Let b R2 Æ 1¡be0be/(Y ¤0Y ¤) and e R2 Æ 1¡ee0ee/(Y ¤0Y ¤) denote the equation R2 where Y ¤ Æ Y ¡Y . If the error ei is truly heteroskedastic will b R2 or e R2 be smaller?

Y = XB+ei Ele|X]=0 E[ex] = 0 = diag(,..., 0}.

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