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Unformatted text preview: 73261 Econometrics October 7, 2009 Midterm 1
Student name:______________________________ 50 minutes. 50 points. Feel free to detach the table, and use it's back side as scratch paper. 1. Short/Multiple choice questions [5 points] You estimated the equation y = xβ + u, and you want to make a prediction for x = x0. ˆ ˆ The estimate of β is β , the estimate of V(ux) is σ 2 , ˆˆ ˆ ˆ and you define y0 = x0β + u, y = x β , e = y − y .
0 0 1.a Which of the following could be an actual set of estimates: ˆ ˆ ˆ Case σ s.e.(e) s.e.( y ) A. 3 5 4 B. 3 4 5 C. 5 4 3 D. 4 3 5 1.b Which s.e. would you use in constructing confidence interval for y0? ˆ A. σ ˆ B. s.e.(e) ˆ C. s.e.( y ) ˆ D. s.e.( β ) 1.c Which distribution would you use to compute the critical value for that CI? A. Chisquared B. Student's t C. Fdistribution D. Poisson (pick one answer) (pick one answer) (pick one answer) 1.d You have 15 observations and 2 variables, and you want a 99% confidence interval. What is the appropriate critical value c? (write your answer in the provided space) 1.e Given the s.e. from 1.b, and critical value c from 1.d, what is the formula for the confidence interval? ˆ A. y ± c * se
2 ˆ B. y ± c * (se ) (pick one answer) C. y0 ± c * (se ) ˆ D. y ± c * se 2 2. [15 points] You are trying to estimate the following equation: y = β0 + u You have N observations of x and y, denoted as Xi and Yi respectively. 2.a [5 points] Derive the estimator of β0:  write out the sum of squared residuals  Compute its derivative and set it equal to zero ˆ  solve for β 0 2.b [3 points] What assumption is necessary to make your estimate unbiased? Prove it. 2.c [5 points] Assuming that V[ux] = σ 2, derive the population variance of your estimate. 2.b [2 points] You have the following data: X = 4.9, Y = 2.4, X 2 = 31, Y 2 = 7, XY = 15 Compute the estimate of β0. 3. [13 points] You decided to check whether controlling for economic growth eliminates the link between global warming and pirate activity, but your dog has chewed up the output, and you're left with: Dependent Variable: TEMPERATURE Included observations: 15 Variable Coefficient Std. Error tStatistic Prob. C Log GDP Piracy Rsquared Adjusted Rsquared 0.4 3.a [2 points] Is correlation between piracy and global warming eliminated? 3.b [7 points] Fill in the blank cells. 3.c [2 point] Somebody suggests that your R2 could be higher, and you might improve the fit by adding add a variable measuring heat output of the sun. Name one test or criterion that you would use to check whether adding the variable leads to a meaningful improvement. 5 0.65 3 1. 1.666 2.6 0.2 3.d [2 points] Same somebody also suggests that increasing R2 will reduce standard errors. What is the basis for this claim, i.e. what is the quantity that affects both R2 and standard errors? 4. [17 points] You have the following regression output:
Dependent Variable: LWAGE Included observations: 526 Variable Coefficient S. Error tStatistic Prob. C 0.387817 0.102322 3.790171 0.0002 EDUC 0.083533 0.006861 12.17532 0 EXPER 0.003164 0.001655 1.911744 0.0565 TENURE 0.015684 0.002921 5.369541 0 MALE*MARRIED 0.292091 0.055389 5.273454 0 FEMALE*(1MARRIED) 0.09675 0.057463 1.68368 0.0928 FEMALE*MARRIED 0.12024 0.057984 2.07358 0.0386 and a subset of the variancecovariance matrix:
MALE*MARRIED FEMALE * (1MARRIED) FEMALE*MARRIED MALE*MARRIED 0.003068 0.001917 0.002101 FEMALE*(1MARRIED) FEMALE*MARRIED 0.001917 0.002101 0.003302 0.001947 0.001947 0.003362 Male, female and married are "dummy" variables, i.e. they are equal to 1 if individual is male, female or married (respectively), and 0 otherwise. 4.a [2 points] What is the approximate wage difference between single male and married male? Specify whether it is absolute or relative. 4.b [5 points] What is the exact wage difference between single male and married male? 4.c [6 points] Test whether there is a wage difference between married and unmarried females, vs. twotailed alternative, at 10% significance level. Compute the test statistic, describe its distribution (t, F, χ2, Normal, etc.) and d.f.'s, report critical value and your conclusion. 4.d [4 points] On the basis of this regression, can you claim that getting married would increase the wage of a given male? Why? Use back side of this page if you need more space. ...
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This note was uploaded on 01/21/2011 for the course ECON 73261 taught by Professor Kyrkv during the Fall '09 term at Carnegie Mellon.
 Fall '09
 Kyrkv
 Econometrics

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