7

5. Consider the following data generating process (DGP): y = a + Bx + u, where x~ N(2,22), u ~ NO, ), a=1, and B = 2. a) Consider a weighted least squared (WLS) regression: h(x) Jh(x) , where h(x) = exp(x) Calculate Var(- (x). Is the WLS estimator BLUE? Explain why or why not. b) Consider another weighted least squared (WLS) regression but with a misspecified h(x): h(x) H(x) [h(x) where h(x) = x2. Calculate Var(- x). Is the WLS estimator BLUE? Explain why or why not. c) Use Stata to generate a random sample of n = 1,000 from the DGP. Set "seed" to be your student number so you can replicate the same results. Estimate the WLS regressions in (b) and (c). In real-world applications, do we know h(x)? Y