Answers+Exam+2+-+2011

Answers+Exam+2+-+2011 - Department of Economics University...

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Department of Economics Professor Dale J. Poirier University of California, Irvine November 15, 2011 Answers to Exam 2 ECON 123A Econometrics I Directions : You must answer each of the following questions. Points (out of 100) are allocated as noted to the left of each question. Allocate your time according to these points. To receive any partial credit, you must show your work. 1. Consider the multiple regression model with three independent variables, under the classical linear model assumptions MLR.l through MLR.6: You would like to test the null hypothesis H 0 : $ 1 - 3 $ 2 = 1. (10) (a) Let and denote the OLS estimators of $ 1 and $ 2 . Find Var( - 3 ) in terms of the variances of and and the covariance between them. What is the standard error of $ 1 - 3 $ 2 ? (10) (b) Write the t statistic for testing H 0 : $ 1 - 3 $ 2 = 1. (10) (c) Define 2 1 = $ 1 - 3 $ 2 and . Write a regression equation involving $ 0 , 2 1 , $ 2 , and $ 3 that allows you to directly obtain and its standard error. Solution: (a) Use Property VAR.3 from Appendix B: Var( - ) = Var( ) = Var( ) + 9Var ( ) – 6 Cov( , ). (b)
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Answers+Exam+2+-+2011 - Department of Economics University...

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