{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

e2-245a - X ∗ t other than X t − V t In e f ect we need...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Economics 245A Exercise 2 Consider the errors-in-variables model (that is, measurement error in the re- gressor) Y t = X t β + U t , in which the regressor is latent. We observe X t = X t + V t . We assume that X t , U t and V t are independent Gaussian random variables with zero mean. a) For the ordinary least squares estimator P n t =1 X t Y t P n t =1 X 2 t , discuss why replacement of X t with X t V t results in an expression that we cannot easily use to calculate the exact ° nite sample bias. b) To evaluate the exact ° nite sample bias, we use an expression for
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: X ∗ t other than X t − V t . In e f ect, we need to & nd the part of V t that is uncorrelated with X t . To do so, we construct W t = aV t − bX ∗ t , for values of a and b to be determined. The values of a and b must be such that E ( X t W t ) = 0 and also satisfy X ∗ t = cX t − W t . Find the values of ( a,b, c ) and use the resultant W t to derive the exact & nite sample bias of the OLS estimator....
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern