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 (or sections) 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 demand data concerning a cross-sectional sample of 100 individuals and their annual consumption of frozen waffles (y). Available explanatory variables include the income of the individual in thousands of dollars per year (x) and the cost of electricity to prepare waffles in cents per dozen waffles (z). Assume that all individuals face the same price of waffles, but marginal costs of electricity vary across individuals (according to how much electricity their household consumes in total each month).
a.) Consider Regression A1 and Regression A2. If these specifications satisfied the maintained hypotheses for ordinary least squares regression, would you conclude that frozen waffles were a normal good, an inferior good, or both, depending upon the level of income. Explain your reasoning.
b.) Regression A2
is
followed by a diagnos command. What do the results of this command
suggest, and what are the implications for your interpretation of Regression A2?
c.) Consider Regression
A3, Regression A4, and Regression A5. What do these regressions reveal
about the nature of any systematic variations in the magnitude of si2? If you had to choose just
one
variable that was strongly correlated with the magnitude of si2, what would it be, and why?
d.) Just prior to Regression
A6, a number of potential weighting variables are generated. Which of these
weights is more appropriate, and hence, which of
Regression A6,
Regression A7, or
Regression A8 is preferred as a "correction" for
the problems besetting the naive model in Regression
A2? Explain.
e.) Are the standard errors for the estimated
parameters
in your preferred model smaller than those for the naive model in Regression A2? _______ For a single sample,
is it necessary that the weighted least squares estimator always produce smaller
parameter standard errors than the ordinary least squares estimator?
Explain.
f.) Under what circumstances will the use of a
log-log
version of your model be a remedy for heteroscedasticity? Explain.
g.) Consider Regression
A9. If we did not have to worry about heteroscedasticity, would you prefer
this log-log model to the linear-in-variables model in Regression A2? Why or why not?
h.) Do the different implications of the models
in Regression A2 and Regression A9 regarding the income elasticity (or
inelasticity) of demand for waffles cause you any concern? Why or why not?
i.) Do the various point estimates of the
coefficient on z
(electricity cost for heating waffles) conform with economic theory?
2. The following questions pertain to EXHIBIT B. These are real data, and we will explore a preliminary model to explain the observed monthly time-series variation in private school construction expenditures. The variables read by the program are defined as follows:
a.) According to the results of Descriptive Statistics B and Regression B1, does new construction of private schools mimic new construction of public schools, or are private schools built when public school construction is inadequate? Explain.
b.) According to Regression B1, is new construction of private schools growing over time, even controlling for activity levels of public school construction and for the relevant demographics of school-age children? Explain.
c.) According to Regression B1, is there seasonality in private school construction? If so, summarize in words the form of this seasonality? Is it plausible?
d.) What is the purpose of Regression B2 and what is implied from the results of this regression for the validity of Regression B1? Why?
e.) What is the main qualitative difference between the results from Regression B1 and Regression B3?
f.) Consider Regression B4. Is the extent to which private school construction mimics public school construction increasing or decreasing over time? Explain.
g.) In Regression B4, the estimated coefficient on the T variable (the time trend variable) is no longer statistically significantly different from zero. Thus we cannot say that private school expenditure is changing systematically over time. It is statistically constant. True, False, Uncertain? Explain.
h.) In Regression B3 and Regression B4, why is an ORDER=12 option chosen for the AUTO command?
i.) Describe briefly what goes on "behind the scenes" when you ask SHAZAM to estimate your regression parameters using the AUTO command, rather than the OLS command.
3. In addition to causing flood damage, El Nino has created social costs by interfering with Southern Californians' enjoyment of their public beaches. Suppose the Department of Beaches has asked you to assess the welfare effects of beach closures due to storm-drain runoff from El Nino events. To do this, you need to estimate a model of local demand for public beaches, and then see how consumer's surplus from beach trips changes as this demand function shifts according to the number of days of beach closures (CLOSURES) each month. You collected survey data each month from a different random sample of Angelenos concerning the number of beach trips (TRIPS) they have made in that month as a function of the distance (DIST) they live from the beach. (Since beach access is free in most of Southern California, you will use this distance times average-travel-cost-per-mile as a rough proxy for the price of access). In the process of analyzing the effects of closures, you model demand by regressing TRIPS on DIST and CLOSURES and a set of sociodemographic characteristics such as age, income, and gender. Suppose a 1% change in DIST corresponds roughly to a 1% change in the "price" of a beach visit. Why should you be cautious about taking the results from this regression at face value (especially those concerning the price elasticity of demand for beach visits)? By analogy to one of the examples used in lecture, discuss a potential problem with this model and assess its implications for the estimates produced.
4. If your dependent variable is a (0,1) dummy
variable that indicates the category to which an observation belongs, you probably
want to try a PROBIT or a LOGIT method for estimating your model. How does the
interpretation of set of PROBIT or LOGIT results differ from the
interpretation of the analogous set of OLS results?
5. Suppose you have been hired by a large national
recreational equipment cooperative to assess individual consumer expenditures on
the types of products sold by the cooperative. You are provided with some survey
data on individual expenditures (EXP) by AGE, gender (FEM=1 if female) and income
(INC, in thousands of dollars per year). The best-fitting model you discover is
displayed in Exhibit C.
a.) Based on the point estimates, provide a formula that would give expected expenditures for a randomly selected female. (Two significant digits will be adequate.)
b.) Explain how you would go about testing whether expected expenditures differ by gender.
c.) What appears to be the main difference between the male and female age profiles of expenditure on recreational equipment in this sample?
d.) Does an extra $1000 of annual income have any statistically discernible effect on recreational equipment expenditures? Explain carefully.
6. In a regression model like that used for the time- series data in Exhibit B, can there be any multicollinearity among the dummy variables for each month? Explain your answer. If none of the individual t-test statistics on these monthly dummy variables is individually significantly different from zero, is it likely to be necessary to perform an F-test to assess the possible joint significance of the full set of dummies? Explain.
BONUS (4 points):
b.) For which topics would you have preferred less class coverage, and for which would you have preferred more?
c.) Which types of lab sessions did you find most useful to your understanding of the course material (if you remember any of them at all)? (Alternately, of the 8 lab sessions, how many were you able to attend?)
d.) For which topics might new WWWeb-based visualization aids be most helpful? (Consider the set of JAVA applets accessible from the current web site.)
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