Econ B2000, MA Econometrics

The questions are worth 120 points. You have 120 minutes to do the exam, one point per minute.
All answers should submitted electronically. Please submit all relevant computer files. Please no “pages” files, save as pdf or rtf. I prefer .Rmd files. No need to put your name, just last digits of ID to identify yourself, so grading is blind. You may refer to your books, notes, calculator, computer, or astrology table. The exam is “open book.” However, you must not refer to anyone else, either in person or electronically, during the exam time!
You must do all work on your own. Cheating is harshly penalized. Please silence all electronic noisemakers such as mobile phones. Good luck. Stay cool.

  1. (20 points) Please answer the following; you might find it useful to make a sketch.
    1. For a Normal Distribution that has mean 6 and standard deviation 6.7, what is the area to the right of 2.65 ?
    2. For a Normal Distribution that has mean -1 and standard deviation 3.8, what is the area to the right of -8.22 ?
    3. For a Normal Distribution that has mean 2 and standard deviation 2.7, what is the area to the right of 7.4 ?
    4. For a Normal Distribution that has mean 12 and standard deviation 9.8, what is the area to the left of -7.6 ?
    5. For a Normal Distribution that has mean -6 and standard deviation 3.4, what is the area to the left of -0.9 ?
    6. For a Normal Distribution that has mean 11 and standard deviation 5.7, what is the area in both tails farther from the mean than 16.7 ?
    7. For a Normal Distribution that has mean -1 and standard deviation 3.3, what is the area in both tails farther from the mean than -3.64 ?
    8. For a Normal Distribution that has mean -11 and standard deviation 5.8, what is the area in both tails farther from the mean than -24.92 ?
    9. For a Normal Distribution that has mean 2 and standard deviation 1.3 what values leave probability 0.815 in both tails?
    10. For a Normal Distribution that has mean -13 and standard deviation 4.2 what values leave probability 0.795 in both tails?
    11. A regression coefficient is estimated to be equal to 1.26 with standard error 6.3; there are 15 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero?
    12. A regression coefficient is estimated to be equal to -12.16 with standard error 6.4; there are 32 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero?

I created a dataset using the American Community Survey that includes info on college major (for those who completed college) and look at the different wages of those who majored in Business (largest single group) and those in Psychology (6th largest).

  1. (20 points) In Vermont, the average wage for graduates with a degree in Psychology is $12996 with a standard deviation of 32839; there are 125 of them. The average wage for graduates with a degree in Business is $33218 with a standard deviation of 62946; there are 191 of them.
    1. Find a 90% confidence interval for the difference in average wages.
    2. Does this seem plausible? What other factors do you suppose would be important?
  2. (20 points) From Blackboard you can download a little dataset (ACS_2015_avgs_by_state.RData) with average wages by state as well as the number of people in the sample who have either a major in business or psychology, the number who are female, the number in the labor force and unemployed, number working the full year and number fulltime.
    1. Estimate a linear regression where the dependent variable is the difference in average wage between Business and Psychology graduates. What independent variables might you include? Do you think you should change any of the measures provided? (eg use the number or proportion?)
    2. Explain your results. What coefficients are statistically significant? What other test statistics might you consider? Do these estimates seem reasonable?
    3. Can you provide graphs that can additionally show these results?
  3. (60 points) From Blackboard you can download the whole set of graduates with majors in Business or Psychology (ACS_2015__coll_buspsy.RData). Estimate a linear regression with wage as the dependent variable, a dummy for major, and other variables of your choice. Explain what other variables you think should be in the regression. Explain what additional restrictions to put on the dataset. Explain your results, giving details about the estimation and providing any relevant graphics. What are the changes from previous regression on state-level averages and why might this be so? How do changes in specification (e.g. logs) change the estimated coefficients? What are some relevant predicted values? Do those seem sensible? What additional information would be useful? Impress me.