ProblemSet5 Answers - Professor Mumford Econ 360 - Spring...

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Unformatted text preview: Professor Mumford Econ 360 - Spring 2010 mumford@purdue.edu Problem Set 5 Answers True/False 1. TRUE If the distribution of j becomes more tightly distributed around j as the sample size increases, then j is consistent. 2. TRUE Under the Gauss-Markov Assumption, ( j- j ) se ( j ) is asymptotically normally dis- tributed. 3. FALSE Without Assumption MLR.6 (Normality), we can still perform statistical in- ference if we have a large sample size. See #2 above. 4. FALSE The p-value is the probability of obtaining an estimate as extreme or more extreme than j under the null hypothesis. 5. TRUE While it does not violate any of the Gauss-Markov Assumptions, multicollinear- ity causes the OLS estimates to have large standard errors. This reduces our ability to perform inference. 1 Long Answer Questions 6. College GPA (a) The 95 percent confidence interval for the effect of high school GPA on college GPA is .412 1.96(.094), or about .228 to .596. (b) No, because the value .4 is well inside the 95% CI. (c) Yes, because 1 is well outside the 95% CI. 7. Job Training Program (a) Ability of the worker has been omitted from the regression, so we should think of u as containing unobserved worker ability. 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 say that the OLS esti- mator of 1 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. (b) If the t-statistic is 2, this indicates that we can reject the null hypothesis of 1 = 0. Knowing that 1 is likely negatively biased means that we are no any less confident in our conclusion. 2 8. Wage Normality (a) The histogram for the level-level model is given below: .05 .1 .15 .2 .25 Density-10-5 5 10 15 Residuals (b) The correlation between the residuals, u and educ is exactly zero. The same is true for exper and tenure . This is a mathematical result of minimizing the sum of squared residuals. (c) The histogram for the log-level model is given below: .2 .4 .6 .8 1 Density-2-1 1 2 Residuals (d) The residuals from the log( wage ) regression appear to be more normally dis- tributed. Certainly the histogram in part (c) fits under its comparable nor- mal density better than in part (a), and the histogram for the wage residuals is notably skewed to the left. In the wage regression there are some very large...
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This note was uploaded on 02/06/2012 for the course ECON 360 taught by Professor Na during the Spring '10 term at Purdue University-West Lafayette.

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ProblemSet5 Answers - Professor Mumford Econ 360 - Spring...

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