INSTRUCTIONS: Answer all questions in the space provided (or indicate clearly where you have continued your answer on the back of the page). Calculators are NOT permitted. Reduce all computations to the simplest form so that anyone with a calculator could attain the answer easily. Show your work and reasoning to the fullest extent possible so that part marks can be assigned as warranted. You have three hours to complete this exam. There are 25 questions worth 5 points each. Total points = 125. Budget your time carefully. Exhibit pages should not be turned in with your exam. Remember: answer questions in a manner that reflects the econometric reasoning you have learned in this course.
1. The following questions refer to the computer output in EXHIBIT A. These are hypothetical data concerning a cross-sectional sample of 30 individuals. The dependent variable is MOVIES = number of movies seen per year; the available explanatory variables are FAMINC = family income in tens of thousands of dollars per year, PRICE = typical admission price paid, and POPCORN = typical price for a small order of popcorn. You are trying to characterize the demand for movie admissions.
a.) Is there any relationship between admission prices and neighborhood incomes? Explain. Is there any relationship between admission prices and popcorn prices? Explain and offer an economic rationale. [ANSWER]
b.) Suppose you began by estimating the model in REGRESSION A1. Comment on the "demand curve" you estimate. If there is a problem, speculate upon its source.[ANSWER]
c.) Now you elect to employ all of the available regressors, as in REGRESSION A2. Since the R-squared values of PRICE and POPCORN on the other regressors are higher than the ordinary and adjusted R-squared values for the main model, the specification suffers from too much multicollinearity and we cannot make any inferences. True, False, Uncertain? Explain.[ANSWER]
d.) Around the means of the data, according to REGRESSION A2, a slight increase in admission and popcorn prices will raise revenues for the theaters, and movies appear to be inferior goods, in the economic sense. True, False, Uncertain? Explain.[ANSWER]
e.) What does REGRESSION A3 suggest about any interpretation you may have made regarding REGRESSION A2? Explain. How would you test whether PRICE and POPCORN make a jointly statistically significant contribution to explaining the magnitude of e2, and why might you want to conduct such a test?[ANSWER]
f.) Consider REGRESSION A4 and REGRESSION A5. Which would you prefer and why? How do the revised regression results differ qualitatively from those in REGRESSION A2? [ANSWER]
g.) Paying close attention to all SHAZAM commands after the OLS command that produces REGRESSION A5, and ignoring for now the issue of weights, consider REGRESSION A6 and REGRESSION A7. Can the goodness-of-fit in the context of the current sample be compared across these two models? Between either of these models and REGRESSION A2? Explain carefully.[ANSWER]
2. The following questions pertain to EXHIBIT B. The data consist of five years of hypothetical monthly time-series data for total TRIPS to a fictitious amusement park. The available explanatory variables are PRICE = adult full-price admission, UR= unemployment rate, INC=median family income (annualized), RAIN= total inches of rain per month.
a.) These data suggest that the amusement park price-discriminates, charging higher prices to people with higher incomes. True, False, Uncertain? Explain.[ANSWER]
b.) Since greater unemployment rates mean many households have lower incomes, comment on the validity of the pairwise correlation between INC and UR in this sample. Is this possible?[ANSWER]
c.) Observing the results from REGRESSION B1, which variables appear to have the greatest influence on TRIPS? Also evaluate the sign on the INC variable and explain whether you would like to draw any inferences about TRIPS being a normal or inferior good in the minds of consumers.[ANSWER]
d.) SUMMER seems to make a difference to expected TRIPS. The variable is sufficiently statistically significant that you might be curious about whether the effects of PRICE or INC or RAIN differed between the summer and non-summer months. Interpret the point estimates in REGRESSION B2? Why do you suppose the research might have declined to differentiating between the effects of RAIN on TRIPS between non-summer and summer months?[ANSWER]
e.) According to REGRESSION B2 and the subsequent diagnostics, is the relationship between TRIPS and the basic list of explanatory variables the same in summer and non- summer months? Explain.[ANSWER]
f.) Consider REGRESSION B3. To a naive observer, does the unemployment rate now seem to have a statistically significant effect on TRIPS? Sketch the apparent nature of the relationship between TRIPS and UR (controlling for PRICE, INC, RAIN, and SUMMER). Identify clearly any "interesting" features of your diagram. Can you invent a rationale for this finding?[ANSWER]
g.) Is multicollinearity a problem in REGRESSION B3? Explain.[ANSWER]
h.) Is serial correlation in the errors a problem in REGRESSION B3? Explain. What are the implications for any interpretation of the results of REGRESSION B3? [ANSWER]
i.) What is going on during the "iterations" in REGRESSION B4? [ANSWER]
j.) Can we conclude unambiguously from the results of REGRESSION B4 that the unemployment rate and incomes have no effect on TRIPS? Why or why not? Explain carefully.[ANSWER]
3. The following questions refer to EXHIBIT C. This data set is a hypothetical survey of 24 undergraduates, concerning the duration (DUR) of each student's most recent previous mixed-gender romantic relationship. (Since the study addressed mixed-gender relationships, anyone with no prior relationships, or no prior mixed- gender relationships, was excluded from the sample.) Potential explanatory variables include AGEDIF = the age of the male minus the age of the female in the relationship in question, HOURS = average daily hours of waking time spent together during the relationship, FEMALE = 1 if the respondent is female, 0 otherwise.
a.) From REGRESSION C1, we can conclude that if one wishes a relationship to last a long time, then the partners should spend as much time as possible together. Explain your answer very carefully.[ANSWER]
b.) How might you improve the model?[ANSWER]
4. Concerning the American Statistical Association's "Ethical Guidelines for Statistical Practice" (pamphlet on reserve at Towell)
a.) It is NOT appropriate to inform potential survey respondents about the general nature and sponsorship of an inquiry and the intended uses of the data. T, F, U?[ANSWER]
b.) Statisticians should inform a client or employer of all factors that may affect or conflict with their impartiality. T, F, U?[ANSWER]
c.) Statisticians should maximize the usefulness of any survey data set by collecting as many additional variables as possible, even if they are not required for the purposes of the current inquiry. T, F, U?[ANSWER]
d.) In writing up statistical results, statisticians should delineate the boundaries of the inquiry as well as the boundaries of the statistical inferences which can be derived from it. T, F, U?[ANSWER]
e.) Statisticians should NOT accept contingency fee arrangements. T, F, U?[ANSWER]
5. Suppose you have a sample of survey data, wherein some respondents chose not to answer the question about income. You do not wish to throw away the rest of the information you collected from them, so you create an additional variable for each respondent called HAVINC=1 if you have income data for them, and =0 if you do not have income data for them. You then interact this HAVINC variable with the raw income variable, producing a variable called INC that takes on the value zero if income is unavailable and contains the reported income level if the question was answered. Suppose your regression model is as follows (t-ratios in parentheses):
Yi = 25.21 + 3.125 HAVINCi + 1.21 INCi + 6.35 X1i - 4.24 X2i + ei(2.30) (1.62) (4.33) (2.43) (-3.11)
Does the presence or absence of income data have a statistically significant effect on the expected value of Y? Explain. What does this regression allow you to say about the effect of income on the expected value of Y? Explain carefully.[ANSWER]
6. You ask a subordinate employee to put together a proposal to study the effects of community demographics upon sales at each location of the chain of coffee bars which you manage. The employee proposes to regression monthly branch sales on a set of explanatory variables: PHOUSE = price of small house blend coffee at each location, PLATTE = price of small latte at each location, PESPR = price of small espresso at each location, INC = median household income in Census tract where bar is located, GENDER = 1 if the customer is female, AGE = age of the customer, ETH1 through ETH6 (set of dummy variables for six categories of "non-white" ethnicity, including "other"). Summarize your memo to the subordinate re: this proposal.[ANSWER]
7. Multicollinearity can almost always be "fixed." True, False, Uncertain? Explain.[ANSWER]
8. Since the parameter point estimates under heteroscedasticity or serially correlated errors are unbiased, you do not really have to worry about these problems. People who feel compelled to "correct" their models for either problem are just being excessively nit-picky, and employers certainly are not going to want anybody to waste time fixing something that really doesn't matter. Evaluate.[ANSWER]
9. Many of the challenging problems in econometric practice stem from the fact that the data that economists must work with are "non- experimental." Explain what this means. Then evaluate the claim: "If economists could do experiments, there would be no need for multiple regression models."[ANSWER]
BONUS QUESTION (OPTIONAL) Explain "non-response bias," giving an example of a scenario wherein failure to respond by some survey recipients might bias the estimated slope(s) relative to their true value in the overall population.[ANSWER]