Question: 18.13 Consider the heterogeneous regression model Yi = b0i + b1iXi + ui, where b0i and b1i are random variables that differ from one observation

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) are distributed independently of Xi and that the observational units are randomly drawn from the population.

a. Let b nOLS 1 denote the OLS estimator of b1 given in Equation (18.2). 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 Xi) = 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.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

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

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Econometrics Questions!

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)...

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

13.10 Consider the regression model with heterogeneous regression coefficients Yi = b0i + b1iXi + vi, where (vi, Xi, b0i, b1i) are i.i.d. random variables with b0 = E(b0i) and b1 = E(b1i). a. Show...

13.10 Consider the regression model with heterogeneous regression coefficients Yi = b0 + b1iXi + vi, where (vi, Xi, b1i) are i.i.d. random variables with b1 = E1b1i2. a. Show that the model can be...

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)....

NAME: Don't forget your name! WARNING: Be careful when you enter the letter answers. Any extra character in the cell, including a blank space, will cause your answer to not match the key and Excel...

Consider the regression model with heterogeneous regression coefficients \[ Y_{i}=\beta_{0}+\beta_{1 i} X_{i}+v_{i} \] where \(\left(v_{i}, X_{i}, \beta_{1 i} ight)\) are i.i.d. random variables with...

Question 1 (28 points]: Consider a heterogeneous computer architecture that has two types of processors: a CPU (of which there is only one) and p small capacity processors (called small processors...

Question 1 [40 points]: Consider a heterogeneous computer architecture that has two types of processors: a powerful processor (of which there is only one) and p small capacity processors (called...

University of California, Los Angeles Department of Statistics Statistics 100C Instructor: Nicolas Christou Homework 3 EXERCISE 1 Answer the following questions: a. Suppose y1 , y2 , . . . , yn are...

Can capitalism lead to human happiness? Read issues one from taking sides. Which viewpoint do you side with? Why? Explain.

Nueva Vizcaya Company has the following accounts included in its December 31 trial balance: FA@FVTPL FA@FVTOCI FA@AC Investment in associate Interest rate swap receivable Forward contract receivable...

What are the main factors used to calculate the year of a bond?

What steps could a company take to avoid making product design and marketing mistakes when introducing new products into East Germany? How would you go about hiring a plant manager for a facility you...