HomeWork1_Econometrics - + = 3 2 1 3 2 1 3 2 1 X X X Y Y Y...

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ECONOMICS 598 ECONOMETRIC THEORY AND APPLICATIONS HOMEWORK 1 Due: 3PM on October 1, 2010 1 1. (20 pts) Consider the multiple linear regression model for which the classical conditions hold ε β + = X Y Suppose that instead of using Y, we use different units of measurement; that is, we use as data variable aY Y = * where a is a scalar constant. Find the ordinary least squares estimators of β (10 pts) and ( ) ˆ Var (10 pts) for this new model and compare them with ordinary least squares estimators of the original model. 2. (10 points) Question 2 from Econometrics Refresher Manual by David L. Ryan (page 43): Suppose that rather than finding ˆ as a solution to the minimization of e e , it is desired to find the expression for ˆ that will minimize Ae e , where A is nxn positive definite matrix. Derive the appropriate estimator. State any assumptions that you are making in your derivation and provide a reason why they are needed. 3. (20 pts) Consider the regression model
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Unformatted text preview: + = 3 2 1 3 2 1 3 2 1 X X X Y Y Y where Y 3 and X 2 are unobserved. The i are independently distributed N (0, 2 I) and the X i are nonstochastic. For each of the following sets of data derive the ordinary least squares (OLS) estimator of and determine whether it is biased or unbiased. Be precise what assumptions are necessary for your conclusion to be valid. a. (10 pts) OLS only on the complete observations for Y and X (that is, Y 1 and X 1 ) b. (10 pts) OLS of 2 1 Y Y on 2 1 X X where X 2 is replaced by a null matrix. 1 Please submit your assignment in the box on the 8 th floor of Tory (Room 8-14). If the office is closed, slide the assignment under the door of my office (Tory 7-26)....
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This note was uploaded on 11/30/2010 for the course ECON 598 taught by Professor Verabrenčič during the Fall '10 term at University of Alberta.

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