Economics 315 Econometrics
Jim Vincent Fall 2009 Final Exam
Be sure to show all work and provide thorough explanations. For this exam you will answe...
Be sure to show all work and provide thorough explanations. For this exam you will answer all of the questions. 2-1. You are conducting an empirical investigation into the beer expenditures of male and female office employees of a company. You data are a random sample of observations on 40 office employees, 21 of whom are females and 19 of whom are males. The sample data provide observations on the following observable variables: BEi = the annual beer expenditures of employee i, measured in dollars per year; INCi = the annual income of employee i, in thousands of dollars per year; AGEi = the age of employee i, in years; Fi = a dummy variable defined such that Fi = 1 if employee i is female and Fi = 0 if employee i is male. Your research assistant provides you with OLS estimates of the following beerexpenditure equation on a sample of 40 employees: BEi = β1 + β2INCi + β3AGEi + β4Fi + β5Fi INCi + β6Fi AGEi + εi
(1)
OLS estimation results for the full sample of N = 40 employees are given in the following table (with estimated standard errors given in parentheses below the coefficient estimates). OLS Sample Regression Results Expl. Var. Intercept
Note: The figures in parentheses below the coefficient estimates are the estimated standard errors. (a) Using the full model (equation and column 1), what is your estimate of the marginal effect of income on beer expenditures for males? …for females? Is it statistically significant? Be precise. That is, on average, another thousand dollars of income translates into how much additional beer expenditure annually?
(b) Suppose that you wanted to test the hypothesis that there was no difference between male and female beer expenditure in model 1. State the null and alternative hypotheses. (Be careful to observe all occurrences of the variable F.)
(c) Write out your unrestricted and restricted models.
(d) Some have suggested that it is possible that the AGE variable is misspecified. They note that is likely that beer consumption increases into middle age and then drops as people get into their 50s and 60s. How would you respecify the model to explore that possibility? Write out your model indicating how you would respecify AGE to account for this possibility. What sign(s) would you expect on the AGE variable(s)?
2-2. In the following regression u is a variable giving average total cost and q is cumulative production. It is from a “learning curve” study in which the hypothesis is that a company’s ATC falls as experience (cumulative production) grows. These are annual time-series data. ln(u) = β0 + β1ln(q) + εi a)
When working with time series data you should be alert to what problem? Be specific about the mathematical form that describes this problem and the consequences of ignoring it.
Dependent Variable: LOG(U) Method: Least Squares Date: 12/15/09 Time: 08:21 Sample: 1 16 Included observations: 16 Variable
Coefficient
Std. Error
t-Statistic
Prob.
C LOG(Q)
6.019093 -0.385696
0.274869 0.036011
21.89803 -10.71037
0.0000 0.0000
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
b) What does this panel of statistics tell you about this common time-series problem? \ c)
Describe in detail how you would employ GLS (generalized differencing and the Cochrane-Orcutt 2-Step) to try to remedy the problem.
2-3. Some researchers estimated the following logit model (t statistics in parentheses): ln[Pi/(1-Pi)] = .7752 + .001798 Ci - .03807 INCi - .08307 EDUCi (1.958) (7.263) (-2.601) (-2.850) where Pi is the estimated probability that a resident of Minnesota will vote NO to support a policy to reduce toxic air pollution. Ci is the annual monetary cost of the air pollution policy to that resident. INCi is an index of the resident's income level and EDUCi is years of education for that resident. A qualitative dependent variable, Yi, equals 1 if the person voted NO and 0 if the person voted YES. Z-statistics are in parentheses. a. What is the estimated probability that a resident of Minnesota will vote YES on the toxic-air-pollution policy if the person has 14 years of education, has an income index of 10 (which represents an income range of $50-55,000), and will bear an annual cost of $120 if the policy is adopted?
b. What effect would an extra $5,000 of household income (income index of 11) have on the estimated probability of voting YES, other things being equal.
2-4. The following regression results are from a study of vacation-taking behavior. It is a cross-sectional study of 200 families where miles is distance traveled on a family vacation, income is household disposable income, age is the average age of adult members of the household, and kids is the number of children under age 16. a) When working with data of this type you should be alert to what type of problem? Why? Describe the problem and the consequences of ignoring it.
Dependent Variable: MILES Method: Least Squares Date: 12/15/09 Time: 09:33 Sample: 1 200 Included observations: 200 Variable
Coefficient
Std. Error
t-Statistic
Prob.
C INCOME AGE KIDS
-391.5480 14.20133 15.74092 -81.82642
169.7752 1.800256 3.757370 27.12960
-2.306273 7.888506 4.189346 -3.016131
0.0221 0.0000 0.0000 0.0029
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
b) What test would you perform to detect this common cross-sectional problem? Describe how the test is conducted, what test statistic is used and what its distribution is under the null hypothesis. What do you conclude based on the following panel of statistics?
Dependent Variable: RESID^2 Method: Least Squares Date: 12/15/09 Time: 09:35 Sample: 1 200 Included observations: 200 Variable
Coefficient
Std. Error
t-Statistic
Prob.
C INCOME INCOME^2 INCOME*AGE INCOME*KIDS AGE AGE^2 AGE*KIDS KIDS KIDS^2
