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Unformatted text preview: Professor Mumford Econ 360 - Fall 2010 [email protected] Problem Set 5 Due at the beginning of class on Tuesday, September 28 True/False (10 points) Please write the entire word. No explanations are required. 1. If the distribution of ˆ β j becomes more tightly distributed around β j as the sample size increases, then ˆ β j is consistent. 2. Under the Gauss-Markov Assumption, ( ˆ β j- β j ) se ( ˆ β j ) is asymptotically normally distributed. 3. Without Assumption MLR.6 (Normality), we cannot perform statistical inference. 4. The p-value is the probability of obtaining ˆ β j under the null hypothesis. 5. Multicollinearity causes the OLS estimates to have large standard errors. Long Answer Questions (90 points) 6. (9 points) Consider the following estimated equation which can be used to study the effects of skipping class on college GPA: d colGPA = 1 . 39 ( . 33) + . 412 ( . 094) hsGPA + . 015 ( . 011) ACT- . 083 ( . 026) skipped n = 141 , R 2 = . 234 where colGPA denotes college GPA, hsGPA denotes high school GPA, ACT denotes achievement test score and skipped is the average number of lectures missed per week. (a) Using the standard normal approximation, find the 95% confidence interval for β hsGPA . (b) Can you reject the hypothesis H : β hsGPA = . 4 against the two-sided alternative at the 5% level? (c) Can you reject the hypothesis H : β hsGPA = 1 against the two-sided alternative at the 5% level? 1 7. (6 points) To test the effectiveness of a job training program on the subsequent wages of workers, we specify the model log ( wage ) = β + β 1 train + β 2 educ + β 3 exper + u. where train is a binary variable equal to one if a worker participated in the program. Suppose that less able workers have a greater chance of being selected for the program. (a) What can you say about the likely bias in the OLS estimator of β 1 ? (b) Suppose the t-statistic, t ˆ β 1 , is equal to 2. Given the bias, how confident are you that β 1 6 = 0? 8. [Stata] (12 points) Use the data in WAGE1.DTA for this exercise. (a) Estimate the equation wage = β + β 1 educ + β 2 exper + β 3 tenure + u. Save the residuals (use the command: predict varname , resid ) and plot a histogram as well as the normal density that best fits the data (use the command histogram varname , normal ). Include this histogram in your write-up....
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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.
- Spring '10