Questions 1 (Total 20 points) Suppose that the true model is Y; = Bo+B1X1i+B2Xy+ (1) where E(1|Xli, X2;) = 0 and you are

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Questions 1 Total 20 Points Suppose That The True Model Is Y Bo B1x1i B2xy 1 Where E 1 Xli X2 0 And You Are 1 (122.95 KiB) Viewed 65 times

Questions 1 (Total 20 points) Suppose that the true model is Y; = Bo+B1X1i+B2Xy+ (1) where E(1|Xli, X2;) = 0 and you are interested in estimating B1-. However, you do not have data of X2i, thus you run a regression without X2i, i.e., you run the following regression: Y = 0 + BX1 +ũiwhere [ = P2X2 + li (2) a) (4 points) Discuss what factors determine the sign of bias of the OLSestimator of B, obtained from the short regression (2). b) (4 points) Discuss how the factors in your answer to part (a) determine the magnitudes of the bias. c) (4points) Your text book extends the simple regression analysis of Chapters 4 and 5 by adding an additional explanatory variable, the percent of English learners in school districts (PctEl). The results are as follows: Testscore = 698.9 -2.28 X STR and Testscore = 698.0 - 1.10 STR - 0.65 x PctEl. Explain why you think the coefficient on the student-teacher ratio has changed so dramatically (been more than halved). d) (4 points) Find two special cases where the estimator of B1 from the short regression (2) actually has zero bias. Discuss intuitively why the estimator has no bias in these two cases. e) (4 points) Consider a special case where X1; and X2i are independent. Also suppose that you also have data of Xz; and you believe that Xzi should have some effects on Yi. To estimate B1, which regression do you prefer, the long regression (1) or the short regression (2)? Explain your answer briefly. 9