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homework7s08_solution

homework7s08_solution - Economics 382 Instructor Jing Sun...

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Economics 382 Instructor: Jing Sun Homework #7 This homework is due on Tuesday April 8 th at the time of the class. 1. (Complete using calculator) Wooldridge Chapter 3, problem 3.10, page 114. Answer: 3.10 (i) Because 1 x is highly correlated with 2 x and 3 x , and these latter variables have large partial effects on y , the simple and multiple regression coefficients on 1 x can differ by large amounts. We have not done this case explicitly, but given equation (3.46) and the discussion with a single omitted variable, the intuition is pretty straightforward. (ii) Here we would expect 1 β % and 1 ˆ β to be similar (subject, of course, to what we mean by “almost uncorrelated”). The amount of correlation between 2 x and 3 x does not directly effect the multiple regression estimate on 1 x if 1 x is essentially uncorrelated with 2 x and 3 x . (iii) In this case we are (unnecessarily) introducing multicollinearity into the regression: 2 x and 3 x have small partial effects on y and yet 2 x and 3 x are highly correlated with 1 x .
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