Question: 18.8 Consider the regression model in Key Concept 18.1, and suppose that assumptions 1, 2, 3, and 5 hold. Suppose that assumption 4 is replaced

18.8 Consider the regression model in Key Concept 18.1, and suppose that assumptions 1, 2, 3, and 5 hold. Suppose that assumption 4 is replaced by the assumption that var(ui Xi) = u0 + u1 Xi , where Xi is the absolute value of Xi, u0 7 0, and u1 Ú 0.

a. Is the OLS estimator of b1 BLUE?

b. Suppose that u0 and u1 are known. What is the BLUE estimator of b1?

c. Derive the exact sampling distribution of the OLS estimator, b n

1, conditional on X1,

c, Xn.

d. Derive the exact sampling distribution of the WLS estimator (treating u0 and u1 as known) of b1, conditional on X1,

c, Xn.

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