17.13 Consider the heterogeneous regression model Yi = b0i + b1iXi + ui, where b0i and b1i are random variables that differ from one observation to the next.

Suppose that E(ui 0Xi) = 0 and (b0i, b1i) are distributed independently of Xi.

a. Let b nOLS 1 denote the OLS estimator of b1 given in Equation (17.2).

Show that b nOLS 1 ¡ p E(b1), where E(b1) is the average value of b1i in the population. [Hint: See Equation (13.10).]

b. Suppose that var(ui 0Xi) = u0 + u1X2i

, where u0 and u1 are known positive constants. Let b nWLS 1 denote the weighted least squares estimator.

Does b nWLS 1 ¡ p E(b1)? Explain.