ProblemSet4Ans - ECON 3200 Introduction to Econometrics...

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ECON 3200 Introduction to Econometrics Answers for Problem Set 4 Problem 1 (Wooldridge 7.6) In Section 3.3 – in particular, in the discussion surrounding Table 3.2 – we discussed how to determine the direction of bias in the OLS estimators when an important variable (ability, in this case) has been omitted from the regression. As we discussed there, Table 3.2 only strictly holds with a single explanatory variable included in the regression, but we often ignore the presence of other independent variables and use this table as a rough guide. If less able workers are more likely to receive training, then train and u are negatively correlated. If we ignore the presence of educ and exper , or at least assume that train and u are negatively correlated after netting out educ and exper , then we can use Table 3.2: the OLS estimator of 1 β (with ability in the error term) has a downward bias. Because we think 1 0, we are less likely to conclude that the training program was effective. Intuitively, this makes sense: if those chosen for training had not received training, they would have lowers wages, on average, than the control group. Problem 2 (Wooldridge 7.10) 1. Yes, simple regression does produce an unbiased estimator of the effect of the voucher program. Because participation was randomized, we can write 0 1 , score voucher u = + + where voucher is independent of u , that is, all other factors affecting score . Therefore, the key assumption for unbiasedness of simple regression, Assumption SLR.3, is satisfied. 2. No, we do not need to control for background variables. In the equation from part 1,
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ProblemSet4Ans - ECON 3200 Introduction to Econometrics...

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