E6 15. Consider the following data generating process (DGP): y = a + fx + u, where x ~ N(2,2²¹), u ~ N(0₂ex(x)), a=1,and ß = 2. <a) Consider a weighted least squared (WLS) regression: <yαXU1√(x)=√(x) + √(x) B+ √(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):αXน+ B + where h(x)=x².<√h(x) √h(x) √h(x) √h(x)9Calculate Var(x). Is the WLS estimator BLUE? Explain why or why not. <[h(x)c) Use Stata to generate a random sample of n = 1,000 from the DGP. Set "seed" to be your student number soyou can replicate the same results. Estimate the WLS regressions in (b) and (c). In real-world applications,do we know h(x)?↔

Solution !! a.) No, the WLS estimator is not BLUE. The reason is that the variance of the WLS…

~N(0₂exp(x) 5. Consider the following data generating process (DGP): y = a + ßx+u, where x ~ N(2,2²¹), u ~] and ß = 2. ( a) Consider a weighted least squared (WLS) regression: < y α u 1 √h(x) √h(x) √h(x) ' exp(x) Calculate Var(x). Is the WLS estimator BLUE? Explain why or why not.< = + √h(x) B+ where h(x)= = H b) Consider another weighted least squared (WLS) regression but with a misspecified h(x): < y α x √h(x)=√h(x) + √h(x) B+ where h(x) = x².< u √h(x) ' Calculate Var(x). Is the WLS estimator BLUE? Explain why or why not. < a=1, 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)?<

~N(0₂exp(x) 5. Consider the following data generating process (DGP): y = a + ßx+u, where x ~ N(2,2²¹), u ~] and ß = 2. ( a) Consider a weighted least squared (WLS) regression: < y α u 1 √h(x) √h(x) √h(x) ' exp(x) Calculate Var(x). Is the WLS estimator BLUE? Explain why or why not.< = + √h(x) B+ where h(x)= = H b) Consider another weighted least squared (WLS) regression but with a misspecified h(x): < y α x √h(x)=√h(x) + √h(x) B+ where h(x) = x².< u √h(x) ' Calculate Var(x). Is the WLS estimator BLUE? Explain why or why not. < a=1, 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)?<

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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