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 1. These are hypothetical demand data concerning a cross-sectional sample of 50 communities wherein a firm markets its output. The dependent variable is Q = number of units sold per month in each market; the available explanatory variables are P = price charged per unit in that market, and INC = median family income in thousands of dollars per year in that market.

a.) Taking into account the information in STATISTICS 1, if we neglected to include income in a model to explain quantity demanded, what would you expect to happen to the slope coefficient on P, compared to the results that appear in REGRESSION 1A? Explain.

b.) Comment on the theoretical plausibility of the parameter point estimates in REGRESSION 1A. What is implied by these estimates about the nature of demand for this good?

c.) In REGRESSION 1B, you attempt a more general specification. Based on the estimated parameters, what can you now infer about the nature of the relationship between quantity demanded and community incomes, controlling for variations in price? (Recall that goods for which an increase in income leads to an increase in quantity demanded are called "normal," whereas goods for which an increase in income leads to a decrease in quantity demanded are called "inferior.")

d.) At the means of the data (according to REGRESSION 1B), is demand price-elastic, or price-inelastic? Explain.

e.) Since the point estimate of the coefficient on INC in REGRESSION 1B is not statistically significantly different from zero at the 5% level, it would be alright to drop this variable from the model. True, False, Uncertain? Explain.

f.) What does REGRESSION 1C tell you about the properties of the estimates produced by REGRESSION 1B?

g.) Compare the results of REGRESSION 1B with those of REGRESSION 1D. Which specification would you prefer, and why? Does REGRESSION 1E have any bearing on your choice?

Preferred regression: ____________________

h.) REGRESSION 1D suggests that neither income term makes a statistically significant contribution to explaining the level of demand, implying that we could leave income out of the model without much compromise of its explanatory power. True, False, Uncertain? Explain.

i.) Based on the results of either REGRESSION 1C or REGRESSION 1E, choose among REGRESSIONS 1F through 1K for the next logical step in your analysis. Explain your choice.

Preferred regression: ______________________

j.) What is the estimated price elasticity of demand at the means of the data for your chosen specification? ________________ Is it possible that the true underlying demand relationship could have unit elasticity, such that a small adjustment in price would have no effect on the revenues of the sellers? Explain how you would test this.
 

2. The following questions pertain to EXHIBIT 2. These are real data, and we will explore a preliminary model to explain the observed quarterly time-series variation in automobile loans at commercial banks. The variables read by the program are defined as follows:

 a.) Which three variables in this data set are the most highly correlated?

c.) Based solely on REGRESSION 2B, does multicollinearity compromise our ability to discern the incremental effects on AUTOCRED of changes in any of the individual explanatory variables? Explain.

d.) Is there evidence of systematic "seasonal" variations in the level of AUTOCRED, according to REGRESSION 2B? Explain.

e.) What is the purpose of REGRESSION 2C? What does it imply about the results obtained from REGRESSION 2B?

f.) Is REGRESSION 2D likely to be adequate to correct the problems revealed by REGRESSION 2C? Why or why not? Explain.

g.) Suppose the REGRESSION 2E was your preferred model. Does this specification suggest the presence of seasonal effects in AUTOCRED? Which months tend to have the highest amount of outstanding car loans? ______________________ Which months tend to have the lowest amount of outstanding car loans? _____________________________.

h.) How do the implications of REGRESSION 2E differ from those of REGRESSION 2B concerning the effects on car loans of (a) nominal interest rates, and (b) car dealer inventories? Explain.

i.) Compare the goodness-of-fit of REGRESSION 2B with that of REGRESSION 2E.
 

3. Since she knows you have taken Economics 143 at UCLA, you have been asked by your manager to evaluate an empirical research proposal prepared by an economist in another division of your company. As a dependent variable, the researcher plans to use the sales of your firm's product (laundry soap) in each of its 20 sales regions. Price differs across regions, so price is one logical explanatory variable. Also, since women typically do more laundry than men, and wealthier people have a higher proportion of clothing that requires dry-cleaning, the researcher also plans to use gender and household income to explain household demand for this product. What will be your main comment(s) about this proposal?

 
4. If your dependent variable is a (0,1) dummy variable that indicates the category to which an observation belongs, ordinary least squares is still the best way to estimate the average effects of changes in the explanatory variables on category membership. True, False, Uncertain? Explain.

 
5. Suppose you are reading an article concerning the effects of citizenship status on earnings and you encounter the following estimated model:
 

EARN_i = 5.72 + 1.26 EXP_i - 0.92 NONC_i + 0.35 EXP_i*NONC_i
             (1.22)   (0.31)          (0.55)                 (0.20)

where EARN_i = earnings;
          EXP_i = job experience;
          NONC_i = 1 if noncitizen; = 0 if citizen; i = 1,...,468.

and the parameter standard errors are given in parentheses below each point estimate.

a.) Based on the point estimates, what is the average "starting salary" for a citizen? ______________ For a non-citizen? ___________________________

Based on the point estimates, what is the return to experience for a citizen? _________________ For a non-citizen? ____________________________

b.) Does citizenship status have a statistically significant effect on earnings? Explain.

c.) Does this model predict that citizens will always earn more than non-citizens (or vice-versa)? If not, how does the predicted earnings differential (citizens-noncitizens) change with experience? What formula would you use to determine the experience level at which the differential changes sign? To what would you compare the result of this calculation before concluding the relevance of a sign change in the differential?
 

6. Suppose you have supervised twenty different studies (for twenty different firms) of employee sick days. For each firm, you collected individual employee records on sick days taken per year (SICK_i) as a function of daily average intake of Vitamin C supplements (VITC_i) by that employee. For each firm, you have estimated a model of the following form:

          SICK_i = b₁ + b₂ VITC_i + e _i,      where i indexes individual employees.

Every one of these twenty different empirical models has shown that the coefficient b₂ is negative and strongly statistically significantly different from zero. The empirical evidence is extremely robust across studies. Are you ready to order a press release announcing that taking of Vitamin C should become company policy for any firm that wishes to reduce losses due to employee health problems? Explain.
 

BONUS: (5 points)

Suppose you use a classroom survey to collect data on average hours of sleep per night (SLEEP_i) as a function of age (AGE_i). Everybody reports a value for SLEEP_i, but 20% of your sample fails to report their ages. Suggest a model that will allow you to use all of the data and to estimate the effect of AGE on SLEEP, conditional on AGE being known, as well as expected SLEEP hours for the group that failed to report their age.