UNIVERSITY OF CALIFORNIA, LOS ANGELES

Department of Economics

Economics 143 - Midterm Examination

• 1. Imagine you have been retained as a consultant by the local public transit authority to analyze demand for city bus services by urban residents. The research department of the transit authority has collected bus demand data from 17 central city areas. Quantity (Q) is measured in number of one-way trips per week per capita. Price (P) is the price of a single-zone bus fare or token. From other separate sources, you have compiled data on per-capita disposable income (Y) in each of these inner- city areas. The statistical analyses you perform are given in Exhibit A. [ANSWER]
  • a.) Fill in the blanks: [ANSWER]
    • Across these 17 cities, what is the mean number of weekly bus trips per capita? ______
    • What is the maximum single-zone bus fare? ________
    • What is the standard deviation in per-capita disposable income? ________
    • Do the descriptive statistics you have just provided refer to the joint distribution of these three variables, or to their marginal distributions? ______________
    • What is the correlation between quantity and price in this sample? ________
    • What are the units for this correlation measure? ________
  • b.) Consider Regression A1. If the transit authority had chosen to rely only on its data on trips and fares: [ANSWER]
    • What would have been the point estimate of the effect of a one-unit increase in bus fares on the expected number of per-capita bus trips (on average, across these 17 cities). Does this make sense, given typical numbers of bus trips? Explain.
    • What would have been the point estimate of the effect of a ten-cent increase in bus fares on trips (on average, across these 17 cities).
    • How do you interpret the intercept in this model?
  • c.) A community activist acquires the same data as the transit authority (via the Freedom of Information Act) and uses it to argue that demand for public transportation is completely inelastic. Inner city residents have to ride busses. Thus, a proposed 20% increase in bus fares will mean a 20% increase in aggregate transportation costs for this group. Test the activist's assertion statistically, using the results of Regression A1. Explain. [ANSWER]
  • d.) Based on Regression A1, your public transit authority wants a prediction about the likely average weekly ridership figures if they set fares at $1.20. How would you calculate this point prediction? ______________________________________. Furthermore, they want a likely range of ridership levels that would result. What statistical measure would you give them and how should it be calculated? [ANSWER]
  • e.) You are concerned that the activist doesn't have income data and is thus failing to control completely for all relevant determinants of demand for public transportation. In Regression A2, you include your additional income data corresponding to each observation. What happens to the point estimate of the effect of a one-unit increase in bus fares on per-capita weekly ridership as you move to this more-general model? Why? [ANSWER]
  • f.) Perform an appropriate statistical test of the activist's assertion based on Regression A2. What do the data now imply? If there is a difference in statistical significance, compared to the results from Regression A1, what accounts for it? [ANSWER]
  • g.) Microeconomics tells us that the price elasticity of demand reveals whether a price increase will make revenues larger or smaller. Price elasticity is %þQ/%þP, which is roughly equal to (þQ/Q)/(þP/P) = (þQ/þP)*(P/Q). Recall that a linear demand curve does not have constant elasticity, so we generally "measure" elasticity at the means of the data. Where in Exhibit A would you find (þQ/þP), sample average P, and sample average Q? [Answer here] SHAZAM might just be smart enough to calculate these elasticities for you. In Regression A2, what is the elasticity of demand for bus trips at the means of the data? ____________________. Explain what this implies for the expected effect of a price increase on transit revenues (or equivalently, aggregate transportation costs of the affected population) for a hypothetical inner- city area with mean transit prices and mean incomes. To increase revenues, is a price increase the right policy? [ANSWER]
• 2. Suppose you have a counterpart at a transit authority in another country (say Canada). Your counterpart has been watching your study with interest, because urban public transit is a similar policy problem there. Her data set consists of analogous information for 15 Canadian cities. Activists in her city have also been using these data to support claims of inelastic demand and to make the point that any increase in fares is a direct transfer from low-income city dwellers to the transit authority. Information for her data set is contained in Exhibit B. [ANSWER]
  • a.) The Canadian activist group has based their campaign on Regression B1. Test their implicit hypothesis. [ANSWER]
  • b.) Your counterpart has heard about what happened in your study when you added income, so she collects similar income data for her cities, promising her boss that when the income data are added, the activists will be proved "wrong." Regression B2 shows what happens. Test the activist's assertion in the context of this model. [ANSWER]
  • c.) Now your counterpart has to explain to the boss why things didn't go the same in the Canadian case as they did in the U.S. case when the omitted income variable was added to the model. What is the story? [ANSWER]
  • d.) Comment on the effect of income on quantities of bus trips demanded in Canada versus the U.S. [ANSWER]
  
  SHORT QUESTIONS:
• 3. Adjusted R-squared values are preferred to regular R-squared values when you are comparing two regressions with different dependent variables? True, False, Uncertain? Explain. [ANSWER]
• 4. In ordinary least squares regression, the maintained hypotheses of "homoscedasticity" and "no serial correlation in the errors" do not matter in our derivation of the formulas for b1 and b2. They only come into play as we determine whether these two estimators are unbiased. True, False, Uncertain? Explain. [ANSWER]
• 5. When we construct a t-test statistic of the null hypothesis that some true underlying population parameter Bj = c (where c is some number), and we find a value for our test statistic of, say, 6.3, what are the two possible conclusions we could draw, which one do we usually draw, and why? [ANSWER]
• 6. What is perfect multicollinearity and why do we require that it not be present if we are going to run a multiple regression? [ANSWER]
• BONUS QUESTION: In Regression A1, what is the R- squared value? What is the adjusted R-squared value? Show your work. [ANSWER]