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Consider the model y, , + e, where for X= {r1,…..,¤N}, and for all i, E (e|X) = c # 0. and Var (eX) = the OLS estimator for Y. Which of the following is correct? O None of the above. O For all i. E (9+ ei|X) = y E + c

Consider the model y, , + e, where for X= {r1,…..,¤N}, and for all i, E (e|X) = c # 0. and Var (eX) = the OLS estimator for Y. Which of the following is correct? O None of the above. O For all i. E (9+ ei|X) = y E + c

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Consider the model y, =yi + ej where for X = {z1,..., IN}, and for all i, E (e,X) = c # 0. and Var (eX) =of. Denote by the OLS estimator for Y. Which of the following is correct? None of the above. O For all i, E (7 + e|X) = y 7 +c of Conditional on X. the variance of the OLS estimator, 7 of y is Var (§|X) O The OLS estimator for y is biased. O E (y|X) = c
Transcribed Image Text:Consider the model y, =yi + ej where for X = {z1,..., IN}, and for all i, E (e,X) = c # 0. and Var (eX) =of. Denote by the OLS estimator for Y. Which of the following is correct? None of the above. O For all i, E (7 + e|X) = y 7 +c of Conditional on X. the variance of the OLS estimator, 7 of y is Var (§|X) O The OLS estimator for y is biased. O E (y|X) = c
Expert Solution
Step 1

From the given information,

yi=γxi+ei

X=x1, x2, ...., XN

Eei|X=c≠0

Varei|X=σ2

Here, the ols estimator is unbiased estimator.

That is, Eγ^=γ

Hence, the option "the OLS estimator for γ is biased" is incorrect.

Consider,

Ey¯|X=Eγ^x¯+ei|X             =Eγ^x¯|X+Eei|X            =γ^Ex¯|X+c            =γ^x¯+c

Hence, the option Eγ^x¯+ei|X=γ^x¯+c is correct.

And Ey¯|X=c is incorrect.

 

 

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