GBA6230, Midterm Exam. Deadline: 3\/21 8:00 PM. I need help writing my essay – research paper submit
\nyour answers in a single pdf file along with your R code file via Blackboard.
\nIf you are using other software than R-studio, please also submit your code
\nfor your software.
\n1. True or False. Explain your answer in detail. Your score will be based on your
\nexplanation.
\n(a) E(u|X1, X2) = 0 implies E(u) = 0. It also implies that (1) u is uncorrelated with X1 and X2; and (2) X1 and X2 is uncorrelated. (5 pt)
\n(b) In order for our regression estimators to be unbiased, we need the variance
\nof X to be as small as possible. In the best scenario, we want the variance
\nof X to be 0. (5 pt)
\n(c) R2 measures how much of the variation in data can be explained by linear
\nregression model, and it never increases when we try to control more X in
\nthe model. (5 pt)
\n(d) E(u|X1, X2) = 0 implies E(u) = 0. It also implies that u is uncorrelated
\nwith X1 and X2 and X1 and X2 is uncorrelated. (5 pt)
\n(e) Suppose we are interested in testing the null hypothesis: H0 : \u03b21 =
\n0 and \u03b22 = 0, we can apply t test and test H0 : \u03b21 = 0 and H0 : \u03b22 = 0
\nseparately. (5 pt)
\n(f) When there are 3 groups in the sample, we should define 3 dummy variables and use all of them in the regression model to control all the group
\ndifferences. (5 pt)
\n2. Consider the following two models relates education to wage:
\nlog(wage) = \u03b20 + \u03b21educ + u
\nlog(wage) = \u03b20 + \u03b21educ + \u03b22sibs + e
\nwhere wage denotes monthly wage; educ is the education level measured by
\nyear; and sibs is the number of siblings. Let \u03b2e1 denotes the estimator of \u03b21
\nfrom the simple regression, and \u03b2b1 denotes the estimator from the multiple
\nregression.
\n1
\n(a) Suppose educ and sibs are positively correlated in the sample, and sibs
\nhas negative effects on log(wage), would you expect \u03b2e1 and \u03b2b1 to be very
\ndifferent? If yes, which one will be larger? Explain your answer in detail.
\n(5 pt)
\n(b) Suppose educ and sibs are positively correlated in the sample, and sibs has
\nno effects on log(wage), would you expect \u03b2e1 and \u03b2b1 to be very different?
\nIf yes, which one will be larger? Explain your answer in detail. (5 pt)
\n(c) In the same circumstance in part (b), would you expect se(\u03b2e1) and se(\u03b2b1)
\nto be very different? If yes, which one will be larger? Explain your answer
\nin detail. (5 pt)
\n3. Use wage1 data for this question. Consider the following model,
\nlog(wage) = \u03b20 + \u03b21educ + \u03b22exper + \u03b23tenure + \u03b24educ \u2217 tenure + u
\n(a) Holding other factors fixed, what is the marginal effect of educ to log(wage)
\nbased on the estimation result? (5 pt)
\n(b) State the null hypothesis that the educ has no effect on log(wage) against
\nthe alternative hypothesis that it has effect. (5 pt)
\n(c) Test the hypothesis in part (b). Explain your answer in detail. (5 pt)
\n4. Use ceosal1 data for this question. Consider the following model that links
\nCEO\u2019s salary to the type of industry, company\u2019s sales and roe,
\nlog(salary) = \u03b20 + \u03b21f inance + \u03b22consprod + \u03b23utility + \u03b24sales + \u03b25roe + u
\nwhere we have 4 types of industry in the data: industrial, financial, consumer
\nproducts, and utilities industries. f inance, consprod, and utility are binary
\nvariables indicating the financial, consumer products, and utilities industries.
\n(a) Which industry is the base group? (5 pt)
\n(b) Compute the approximate percentage difference in estimated salary between the industrial and utilities industries, holding sales and roe fixed. Is
\nthe difference statistically significant at the 1% level? (5 pt)
\n2
\n(c) Compute the approximate percentage difference in estimated salary between the utilities and finance industries, holding sales and roe fixed. (5
\npt)
\n(d) Test whether the difference in part (c) is significant at 5% level. Explain
\nyour answer in detail. (5 pt)
\n5. Use hprice1 data for this question. Consider the following model that links
\nhouse price to its square feet, lot size, and number of bedrooms,
\nprice = \u03b20 + \u03b21sqrf t + \u03b22lotsize + \u03b23bdrms + u
\n(a) Test whether sqrf t has the same effect as lotsize on price at 5% level.
\nReport the results under traditional standard error and robust standard
\nerror. Do you find different conclusions? Explain your answer in detail. (5
\npt)
\n(b) We have two types of house in the data, colonial style and non-colonial
\nstyle. Define colonial as a dummy variable for colonial style house. Consider the following model,
\nprice = \u03b20 + \u03b40colonial + \u03b21sqrf t + \u03b41sqrf t \u2217 colonial + \u03b22lotsize
\n+\u03b42lotsize \u2217 colonial + \u03b23bdrms + \u03b43bdrms \u2217 colonial + u
\nExplain what does the null hypothesis, H0 : \u03b40 = \u03b41 = \u03b42 = \u03b43 = 0 imply?
\n(5 pt)
\n(c) Test the null hypothesis in (b). Report the results from traditional F-test
\nand the robust F-test. Do you find different conclusions? Explain your
\nanswer in detail. (5 pt)
\n(d) Perform Breusch-Pagan and White tests on the model in part (b). What
\nare your conclusions based on these two tests? (5 pt)
\n3<\/p>\n","protected":false},"excerpt":{"rendered":"
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