Consider the heterogeneous regression model Yi Icirc sup2 0i Icirc sup2 1iXi ui, where Icirc sup2 0i and Icirc sup2 1i are random variables that differ from one observation to the next Suppose that E(ui Xi) 0 and ( Icirc sup2 0i, Icirc sup2 1i) are distributed independently of Xi a Let Icirc sup2 1OLS denote the OLS estimator of Icirc sup2 1 given in Equation (17 2) Show that where E( Icirc sup2 1) is the average value of Icirc sup2 1i in the population b Suppose that where Icirc cedil 0 and Icirc cedil 1 are known positive constants Let Icirc sup2 1WLS denote the weighted least squares estimator Does Explain BOLS L, E(B1),

Question: Consider the heterogeneous regression model Yi = Î²0i + Î²1iXi + ui, where Î²0i and Î²1i are random variables that differ from one observation to

Consider the heterogeneous regression model Yi = Î²0i + Î²1iXi + ui, where Î²0i and Î²1i are random variables that differ from one observation to the next. Suppose that E(ui|Xi) = 0 and (Î²0i, Î²1i) are distributed independently of Xi.
a. Let Î²1OLS denote the OLS estimator of Î²1 given in Equation (17.2). Show that

where E(Î²1) is the average value of Î²1i in the population.
b. Suppose that

where Î¸0 and Î¸1 are known positive constants. Let Î²1WLS denote the weighted least squares estimator. Does

Explain?

BOLS L, E(B1),

Step by Step Solution

★★★★★

3.44 Rating (173 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a t he consideration following the equation b Write the regression model as Y i b 0 ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

909-M-S-L-R (8283).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Consider the regression model Yt = 0 + 1Xt + ut, where ut follows the stationary AR(1) model with mean 0 and variance a. Suppose that Xt is independent of uj for all t and j. Is Xt exogenous (past...

Consider the "constant-term-only" regression model Yt = 0 + ut, where ut follows the stationary AR(1) model with mean 0 and variance a. Show that the OLS estimator is b. Show that the (infeasible)...

Data set: WingLength2 If you completed the helicopter research project, this series of questions will help you further investigate the use of regression to determine the optimal wing length of paper...

18.13 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 Xi) = 0 and (b0i, b1i)...

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)...

Exercises Chapter 2 2.1 Marginal and conditional probability: The social mobility data from Section 2.5 gives a joint probability distribution on (Y1 , Y2 )= (father's occupation, son's occupation)....

Logarithms and polynomials Interaction effects Dummy variables ECMT1020: Introduction to Econometrics Lecture 10: Multivar. regr. & transformations Peter Exterkate peter.exterkate@sydney.edu.au...

Submitted to Management Science manuscript MS-0001-1922.65 Authors are encouraged to submit new papers to INFORMS journals by means of a style file template, which includes the journal title....

MATH S350 TMA 01 Hints Question 1 Let A and B be the event that water is contaminated with excessive amount of pollutant A and pollutatnt B respectively. Remarks: 1. Half of those communities whose...

AJPH RESEARCH Efcacy of a Computerized Intervention on HIV and Intimate Partner Violence Among Substance-Using Women in Community Corrections: A Randomized Controlled Trial Louisa Gilbert, PhD, Dawn...

The Fellercraft Corporation records manufacturing overhead costs initially in three service centres and three production departments and one non-departmental plant-wide cost pool called...

O's medical expenses paid during a 12-month period ending in the current year totaled $3,000. The medical expenses for O's 20-year-old son paid during the same 12-month period totaled $1,000. For the...

Very offen, a company's stock price will rise when it annousces that it plans to commence a share repurchase poogram due to signalling hypothesis. True False

13. SAT or ACT? Each year thousands of high-school students in the U.S. take either the SAT or the ACT, standardized tests used in the college admissions process. Combined SAT Math and Verbal scores...

The final test and exam averages for 20 randomly selected students taking a course in engineering statistics and a course in operations research follow. Assume that the final averages are jointly...

A random sample of 50 observations was made on the diameter of spot welds and the corresponding weld shear strength. (a) Given that r = 0.62, test the hypothesis that p = 0, using a = 0.01. What is...

A random sample of n = 25 observations was made on the time to failure of an electronic component and the temperature in the application environment in which the component was used. (a) Given that r...

Your fund is a VC fund in software services sector, where you are a general partner (GP). Your optimal portfolio size[1] is 10 ventures for this current fund of 20MM raised from your LPs. Company =...

QUESTION 23 Managed equity funds provide investors with advantages over index mutual funds because: a. They have lower operating costs. b. Their portfolio performance is generally superior. c. They...

An investor is considering the following opportunity: He will put capital into a start-up company today. He will not receive any cash flows from the investment until end of the 5th year. At that...