Name:_______________________
Economics 345 Final
Prof. Bryan Caplan
Fall, 1997
Instructions:
Part 1: True, False, and Explain
(10 points each - 3 for the right answer, and 7 for the explanation)
State whether each of the following propositions is true or false. Using 2-3 sentences AND/OR equations, explain your answer.
Country |
Growth Rate |
U.S. |
2% |
Britain |
3% |
Japan |
1% |
Mexico |
4% |
T, F, and Explain: The estimated population variance is 1.25.
2. T, F, and Explain: The covariance between the dependent variable and the error terms is equal to .
3. You regress Y on X, getting the equation: Y=1.237 + .847*X.
T, F, and Explain: Therefore, if you regress Y on ln(X), the equation will be of the form Y=constant + 2.33*ln(X). (Note that e^{.847}=2.33).
4. You have a dependent variable with N observations.
T, F, and Explain: You can always get an R^{2}=1 if you regress the dependent variable on any N variables (including the constant).
5. T, F, and Explain: R^{2} always increases when you add additional variables to a given regression specification.
6. You do two regressions: in both cases, your dependent variable is cancer severity (on a scale of 1-10; higher is worse), and the independent variable is a dummy variable equal to 1 if the patient received a new drug, and 0 otherwise. Your results are as follows:
Regression #1: Severity_{i}=3+4*Drug_{i}
Regression #2: Severity_{i}=3-2*Drug_{i}
T, F, and Explain: One plausible explanation for the difference is that patients were randomly selected for Regression #1, but self-selected for Regression #2.
Income_{i}=$15,000 + $1200*Education + $7850*Grad
($2000) ($200) ($1000)
T, F, and Explain: The typical annual salary benefit of completing the final year of college was about $8000.
Problems #8 and #9 refer to the following regression:
Snails can be either male, female, or hermaphrodite - and they must be one of the three. You run the following regression on a randomly selected box of 10,000 snails to estimate their lifespan (in days):
Lifespan_{i}=a + b1*Male_{i} + b2*Female_{i}
8. T, F, and Explain: It will be possible to run this regression on your computer.
9. T, F, and Explain: The predicted lifespan of hermaphrodite snails will be .
Problems #10 and #11 refer to the following regression:
Unemployment_{t}=5 -.6*Inflation_{t} +.8*Inflation_{t-1} +.5*Unemployment_{t-1}.
10. T, F, and Explain: The equation is consistent with the simple version of the Phillips curve.
11. T, F, and Explain: The implied estimate of the natural rate of unemployment is 5%.
T, F, and Explain: The economist's model could be fixed if he added a new independent variable, TOTALDOWNS to his list of regressors, where TOTALDOWNS is defined as the total number of downs a team gets.
Problems #13 and #14 refer to the following regressions:
(A) NPER= 3 + .9*M2PER + .3*(G1PER) +.3*(G2PER)
(1) (.2) (.1) (.1)
(B) RPER= 1 + .1*M2PER + .3*(G1PER) -.3*(G2PER)
(1) (.2) (.1) (.1)
NPER=percentage change in nominal GDP; RPER is the percentage change in real GDP; M2PER is the percentage change in M2; G1PER is the percentage change in the unpredictable part of government spending - such as military spending; and G2PER is the percentage change in the predictable part of government spending, such as Social Security and Medicare.
T, F, and Explain: If the random walk hypothesis holds for the price of oil, then none of the coefficients on these three independent variables will be significantly different from zero.
16. Suppose you define the variable INDEX=1 if a fund is an index fund, and 0 if it is a managed fund. Then you regress the funds' gross ROR (gross rate of return) and net ROR (gross ROR minus management fee) on INDEX:
Gross ROR_{i}=10 + .2*INDEX_{i} (3) (.5) |
Net ROR_{i}=7 +2.2*INDEX_{i} (3) (.5) |
T, F, and Explain: Even though managed funds have higher management fees than index funds, this suggests that management fees "pay for themselves" with a higher return.
17. Black markets, though difficult to measure, are usually thought to be much larger in more tightly regulated and heavily taxes economies. GDP figures, however, do not count black market output.
T, F, and Explain: Adding black market output to legal output would probably make the positive correlation between economic freedom and prosperity bigger.
18. T, F, and Explain: According to Sachs' article, rich countries with bad economic policies will grow more slowly than poor countries with similar policies.
Part 2: Short Answer
(20 points each)
In 4-6 sentences AND/OR equations, answer all of the following questions.
1. PROVE: The residuals in a regression necessarily sum to zero.
2. GIVEN: Y=10 +3*X1 has an R^{2} of .7.
PROVE: The regression Y=a+b1*X1+b2*X2 will have an R^{2} of at least .7.
3. Both inflation and unemployment in the U.S. are currently very low. What does the evidence on the expectations-augmented Phillips curve suggest is likely to happen over the next 3 years?
6. Compare the 1995 Economic Freedom rating of the U.S. to the rating of any other country of your choice. What specific components of the index contribute most to the disparity? Is there any reason to think that these components are caused by prosperity rather than causes of prosperity?