# Problem Set 5-Solution.pdf - Introductory Econometrics...

• No School
• AA 1
• 4

This preview shows page 1 - 2 out of 4 pages.

Introductory Econometrics - Problem Set V (Suggested Solutions) 1 . Stock and Watson, Exercise 9 . 2 (a) When Y i is measured with error, we have ˜ Y i = Y i + w i , or Y i = ˜ Y i - w i . Substituting the 2 nd equation into the regression model Y i = β 0 + β 1 X i + u i gives ˜ Y i - w i = β 0 + β 1 X i + u i , or ˜ Y i = β 0 + β 1 X i + u i + w i . Thus v i = u i + w i . (b) i. The error term vi has conditional mean zero given X i : E ( v i | X ) = E ( u i + w i | X i ) = E ( u i | X i ) + E ( w i | X i ) = 0 + 0 = 0. ii. ˜ Y i = Y i + w i is i.i.d since both Y i and w i are i.i.d. and mutually inde- pendent; X i and ˜ Y j ( i 6 = j ) are independent since X i is independent of both Y j and w j . Thus, ( X i , ˜ Y i ) , i = 1, · · · , n are i.i.d. draws from their joint distribution. iii. v i = u i + w i has a finite fourth moment because both u i and w i have finite fourth moments and are mutually independent. So ( X i , v i ) have nonzero finite fourth moments. (c) The OLS estimators are consistent because the least squares assumptions hold. (d) Because of the validity of the least squares assumptions, we can construct the confidence intervals in the usual way. (e) The answer here is the economists’ “On the one hand, and on the other hand.” On the one hand, the statement is true: i.i.d. measurement error in X means that the OLS estimators are inconsistent and inferences based on OLS are invalid.

Subscribe to view the full document.

• Fall '19

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask You can ask ( soon) You can ask (will expire )
Answers in as fast as 15 minutes