MIEF Quantitative Methods I (Basic Econometrics) Final Exam 2019
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Final Exam
MIEF Quantitative Methods I (Basic Econometrics)
August 27, 2019
Instructions. This is an open book, open note exam. Time limit: 3 hours. The variables for the problems are listed below. Other constructed variables are included with the individual outputs. Please show the formulas you are using and put any discussions into the context of the specific problem. Please try to carry three significant figures when working calculations. A calculator should be used for computations as needed. Please watch your time. There are 20 sub-questions (5 points each) so you will have 9 minutes on average for each sub-question. Some questions will take much less than 9 minutes, some more. Please try to answer each question as I can provide no partial credit with nothing written.
Questions 1 -8 use a Wooldridge data set “Sleep75” . Appendix 1 lists 40 observations of the 706 observations in the data set and an analysis of the data including two variables generated just before the data is listed. The variables are:
sleep Number of minutes per sleep per week at night
totwrk Minutes worked per week
age Age in years
educ Number of years of schooling in years
marr =1 if married; otherwise =0
gdhlth =1 if excellent or good health
clerical =1 if clerical worker
construc =1 if a construction worker
1. Regression #1 on Page 3 sets out to explain the minutes per week of nightly sleep in terms of a number of variables. Write out the model estimated (you do not need all the assumptions). Using that model, write out the hypothesis being testing with the F statistics computed. Draw a picture of the distribution and test that hypothesis with α=.01.
2. Regression #2 on Page 4 adds two constructed variables. What is the name of this test; what is being tested; and what are your conclusions? Use α=.10 and show a picture of the distribution to describe your conclusion.
3. Suppose a student enrolls in the MIEF program at age 25. After one year in the program, what is the change in sleep predicted using Regression #3 on page 5 Put that number into words. Assuming 16 years of education prior to enrolling in the MIEF program, what is the change in sleep predicted after one year in the program using Regression #3 on Page 5? Put that number into words.
Continuing with Regression #3 on Page 5, put into words the constant and the coefficient on clerical.
Using Regression #4 on Page 5, put in words the change in sleep based on one additional year of education.
Using Regression #4 on Page 5, Regression #6 on Page 7, and Regression #7 on Page 8, determine (using the SSR version of the formula) if the function in Regression #4 is different for men and women. Use α=.10 in your analysis with a clear picture of the probability distribution and your conclusion shown on the picture.
Using Regression #4 on Page 5 and Regression #5 on Pages 6 and 7, determine (using the R squared version of the formula) if the function in Regression #4 is different for men and women. . Use α=.10 in your analysis with a clear picture of the probability distribution and your conclusion shown on the picture.
Following Regression #8 on page 8 is the calculation of residuals and the listing of those residuals on Page 9. Describe those residuals clearly. State the slope coefficient in Regression #9 on Page 10 and put that number into words from Regression #9 and from Regression #4 on
Page 5.
Questions 9 through 17 use a Wooldridge data set “airplane” that consists of data on a large number of airline routes for the years 1997, 1998, 1999, and 2000. Only the data for 1997 and 2000 are used in this analysis. See page 1 of Appendix 2 for the first 40 observations. The variables are:
fare average one-way fare ($)
year 1997 or 2000
Id route identifier (1 to 1147 – therefore 2298 observations)
dist distance in miles
passen average number of passengers per day
bmktshr fraction of market, biggest carrier (ie, big market share)
y00 =1 if year == 2000, otherwise = 0
lfare log (fare) – Not shown
ldist log(dist) – Not shown
y00bmkshr y00 * bmkshr
9. Regression #1 on Page 2 of Appendix 2 produces a 95 percent confidence interval for the population coefficient on passen. Compute a 99 percent confidence interval. Explain why it is narrower or wider. Please show a clear picture of the probability distribution.
10. State in symbols and words the homoscedasticity assumption when Regression 1 was carried out. Regression #2 and Regression #3 on page 3 are run testing whether the homoscedasticity
assumption was violated. State clearly the names of these two tests and the assumptions involved for each test. What is your conclusion from these two tests? From Regression #2, can you tell which variable is causing the problem? Explain briefly.
11. Regression #4 on page 4 uses the same variables as Regression #1. Write down the function estimated from Regression #1 and Regression #4 with the standard errors from each regression written appropriately below each slope coefficient. Describe briefly why the standard errors from Regression #4 are more appropriate than the standard errors reported in Regression #1.
12. Discuss the assumptions made with Regression #5 on page 4. Do you think those assumptions are appropriate? Discuss briefly the variables that are used in this regression.
13. Using Regression #6 and Regression #7 on page 5 along with Regression #1 on page 2, carry out a Chow Test (the SSR version) to see if the coefficients on the function estimating fare changed in 2000 as compared with 1997.
14. Regression #8 on page 6 adds two additional variables. Explain clearly the meaning of the constant, the coefficient on bmktshr, and the coefficients on the two new variables.
15. Regression #9 on page 6 is used to for a prediction of fare. Calculations following that function continue on page 7 and page 8. What values of the independent variables are being used for this prediction? What is the point prediction? What is the standard error of the mean prediction? What does that tell us? What is the standard error of the individual prediction? What does that tell us? A confidence interval for prediction was computed. Put that confidence interval into words.
16. Regression #10 on page 8 uses variables described on page 2 of the test questions. Put in words the slope coefficients on ldist and bmktshr. Where appropriate calculate two values of the impact of the independent variable on the dependent variable.
17. Page 9 carries out some rearrangement of the data to prepare to carry out Regression #11 on page 10. Discuss briefly what type of data is being constructed and how that data is used in Regression #11. What are the assumptions made in Regression #11. What happened to the variable “dist”? What other variable might have been appropriate to include in the analysis from Regression #1 through Regression #10 and how would that variable be dealt with in Regression #11? What assumption of OLS would be violated if there were another appropriate variable that was correlated with one of the independent variables in Regression #1?
Questions 18– 20 use the analysis in Appendix 3 involving quarterly data from 2002 to 2019 taken from the Federal Reserve Bank of St. Louis (FRED Data). The data is listed on pages 1-2. The variables are:
DATE Quarterly identifier
Sequence Sequence numbers
Real_GPDI Real Gross Private Domestic Investment (2012 $) Not Seasonally
Adjusted (Billions of US$)
Real_GDP Real Gross Domestic Production (2012 $) Not seasonally Adjusted
(Billions of US$)
Bond Long-Term Government Bond Yields (10-year) Not Seasonally Adjusted
Real_ Exports Real Exports of Goods and Services (2012 $) Not Seasonally Adjusted
(Billions of US$)
Q1 =1 if observation is first quarter, =0 otherwise
Q2 =1 if observation is second quarter, =0 otherwise
Q3 =1 if observation is third quarter, =0 otherwise
Q4 =1 if observation is fourth quarter, =0 otherwise
18. Put in words the coefficient on Real_Exports and Q2 for Regression #1 on Page 3.
19 Put in words the regression coefficient for Regression #2 on page 3 and for Regression #3 on page 4. You should have two values for the coefficient for Regression #3. (Show any calculations)
20. From Regression #4 on Page 4, put in words the coefficient on Real_GDP and l2.Real_Exports. Graph the lag distribution.
Appendix 1
. gen ageeduc = age*educ
. gen educsq = educ^2
. list sleep totwrk age educ ageeduc educsq marr gdhlth in 21/56,clean
. list clerical construc male in 21/60,clean
clerical construc male
21. 0 0 1
22. 0 0 1
23. 0 0 1
24. 0 0 1
25. 0 0 1
26. 0 0 1
27. 0 0 1
28. 1 0 0
29. 0 0 1
30. 0 0 1
31. 0 0 1
32. 0 1 1
33. 0 0 1
34. 0 0 1
35. 0 0 1
36. 0 0 1
37. 0 0 1
38. 0 0 1
39. 0 0 1
40. 1 0 1
41. 0 0 1
42. 0 0 1
43. 0 0 0
44. 0 0 1
45. 0 0 1
46. 0 1 1
47. 0 0 1
48. 0 0 1
49. 0 0 1
50. 0 0 1
51. 0 0 1
52. 0 0 1
53. 0 0 1
54. 0 0 1
55. 0 0 1
56. 0 0 0
57. 0 0 1
58. 0 0 1
59. 0 0 1
60. 0 0 1
. /* Regression #1 */
. reg sleep totwrk age educ marr male
Source |
SS df MS |
|
Model Residual |
17023253.9 122216582 |
5 3404650.77 700 174595.117 |
Total |
139239836 705 197503.313 |
Number of obs
F(5, 700)
Prob > F
R-squared
Adj R-squared
=
=
=
=
=
=
706
19.50
0.0000
0.1223
0.1160
417.85
sleep |
|
|
Coef . |
Std . Err . |
t |
P> |t | |
[95% Conf . |
Interval] |
totwrk |
- . |
1 |
645387 |
.0180512 |
-9 .12 |
0.000 |
- .1999797 |
- .1290978 |
age |
1 |
. |
968593 |
1.443443 |
1.36 |
0.173 |
- .8654036 |
4.80259 |
educ |
-1 |
1 |
.59746 |
5.872449 |
-1 .97 |
0.049 |
-23 .12718 |
- .0677333 |
marr |
3 |
0 |
.35958 |
41.88 |
0.72 |
0.469 |
-51 .86588 |
112.585 |
male |
8 |
3 |
.13675 |
34.98239 |
2.38 |
0.018 |
14.45376 |
151.8197 |
_cons |
3 |
6 |
15.422 |
117.9382 |
30.66 |
0.000 |
3383.867 |
3846.977 |
. predict sleephat,xb
. generate sleephatsquared = sleephat^2
. generate sleephatcubed = sleephat^3
. /* Regression #2 */
. reg sleep totwrk age educ marr gdhlth male sleephatsquared sleephatcubed
Source |
SS df MS |
|
Model Residual |
18271077.8 120968758 |
8 2283884.73 697 173556.324 |
Total |
139239836 705 197503.313 |
Number of obs
F(8, 697)
Prob > F
R-squared
Adj R-squared
2022-08-22