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Unformatted text preview: ECON 3200 Introduction to Econometrics Answers for Problem Set 2 Problem 1 (Wooldridge C3.8) We can use Table 3.2. By definition, 2 > 0, and by assumption, Corr( x 1 , x 2 ) < 0. Therefore, there is a negative bias in 1 % : E( 1 % ) < 1 . This means that, on average across different random samples, the simple regression estimator underestimates the effect of the training program. It is even possible that E( 1 % ) is negative even though 1 > 0. Problem 2 (Wooldridge 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 % and 1 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 ....
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- Spring '08