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Final Examination Semester 2 / Year 2018 COURSE COURSE CODE TIME DEPARTMENT LECTURER : FINANCIAL ECONOMETRICS : BBFN3523 : 2 1/2 HOURS : FACULTY OF BUSINESS AND MANAGEMENT : DR. JOHN ENG YONG HENG Student’s ID Batch No. : : INSTRUCTIONS TO CANDIDATES: 1) This question paper consists of 7 pages, 5 questions, and a t-table. 2) Answer ALL questions in the answer booklet provided within the duration allocated. 3) Return your answer booklet along with the question papers. FINANCIAL ECONOMETRICS Question 1 a) Basic labor economics theory tells us that among many variables, education is an important determinant of wages. You have collected the following data of 13 individuals and decided to estimate the regression line as Y = β0 + β1X Table 1 Impact of Education on Wages (Y, in RM) (X) Mean Hourly Wage Years of Schooling 4.4567 6 5.7700 7 5.9787 8 7.3317 9 7.3182 10 6.5844 11 7.8182 12 7.8351 13 11.0223 14 10.6738 15 10.8361 16 13.6150 17 13.5310 18 Observation 1 2 3 4 5 6 7 8 9 10 11 12 13 i) Calculate 0 and 1 manually for the regression line Y = β0 + β1X . (8 marks) ii) If an individual has 20 years of education, what is the mean hourly wage (in RM) would you guess that individual had? (4 marks) b) Consider the following regression results: = 798.7 – 1.18 × STR n = 420, R2 = 0.051, SER = 18.6 i) How would the slope coefficient of student-teacher STR change, if you decided one day to measure testscores in 100s, i.e., a test score of 650 became 6.5? Would this have an effect on your interpretation? (4 marks) ii) Do you think the regression R2 will change? Why or why not? 1/7 (4 marks) (Total 20 marks) FINANCIAL ECONOMETRICS Question 2 a) Consider the following regression equation for the Johor state (standard errors in parentheses): P̂t 4.00 0.010PRPt 0.030PRBt 0.20YD t (0.005) (0.020) R 2 0.98 (0.04) n 29 where: Pt = per capita pounds of chicken consumed in time period t PRPt = the price of chicken in time period t PRBt = the price of beef in time period t YDt = per capita disposable income in time period t i) Hypothesize signs and specify the appropriate null and alternative hypotheses for the coefficients of each of these variables. (4 marks) ii) State your decision rules and then test your hypotheses on the above results using the t-test at a 5% level of significance. (4 marks) iii) If you could add one variable to the regression, what variable would you add? Why? (2 marks) b) In a research, you have obtained measurements of height in inches of 30 female and 80 male students (Studenth) at a shopping center. A regression of the height on a constant and a dummy variable (Femme), which takes a value of one for females and is zero otherwise, yields the following result: = 69.0 – 4.89×Femme , R2 = 0.40, SER = 2.0 (0.3) (0.57) i) What is the interpretation of the intercept? What is the interpretation of the slope? How tall are females, on average? (6 marks) ii) Test the hypothesis that females, on average, are shorter than males, at the 1% level. (4 marks) (Total 20 marks) 2/7 FINANCIAL ECONOMETRICS Question 3 a) You would like to find the effect of gender and marital status on earnings. As a result, you consider running the following regression: ahei= β0 + β1×DFemmei + β2×DMarri + β3×DSinglei + β4×educi+...+ ui Where ahe is average hourly earnings, DFemme is a dummy variable which takes on the value of "1" if the individual is a female and is "0" otherwise, DMarr is a dummy variable which takes on the value of "1" if the individual is married and is "0" otherwise, DSingle takes on the value of "1" if the individual is not married and is "0" otherwise. The EViews regression program which you are using either returns a message that the equation cannot be estimated or drops one of the coefficients. Why do you think that is? What advice do you suggest to this problem? (5 marks) b) The faculty dean of a university has some disagreement with I. M. Smart (the director of the Computer Center) about an equation that Smart built to understand the number of applications that the school received from high school seniors. In need of an outside opinion, they turn to you to help them evaluate the following regression results (standard errors in parentheses): N̂ t 150 180A t 1.50 ln Tt 30.0Pt (90) R 0.50 2 (1.50) N 22 (60.0) (annual) where: Nt = the number of high school seniors who apply for admission in year t At = the number of people on the admission staff who visit high schools full time spreading information about the school in year t Tt = dollars of tuition in year t Pt = the percent of the faculty in year t that had PhDs in year t How would you respond if they asked you to: i) Discuss the expected signs of the coefficients. (3 marks) ii) Compare these expectations with the estimated coefficients by using the appropriate tests. (3 marks) iii) Evaluate the possible econometric problems that could have caused any observed differences between the estimated coefficients and what you expected. (3 marks) 3/7 FINANCIAL ECONOMETRICS Question 3 (Cont’) iv) Determine whether the semilog function for T makes theoretical sense. (3 marks) v) Make any suggestions you feel are appropriate for another run of the equation. (3 marks) (Total 20 marks) Question 4 a) A model of the number of cars sold in the United States from 1980 through 2004 produced the following results (standard errors in parentheses): Ĉt = 3738 - 48.0Pt + 10.0Yt + 6.0At - 360.0Rt (12.0) (2.0) (2.0) (120.0) R2 = 0.85 DW = 1.86 N = 25 (annual) where: Ct = thousands of cars sold in year t Pt = price index for domestic cars in year t Yt = disposable income (billions of dollars) in year t At = billions of dollars of auto industry advertising expenditures in year t Rt = the interest rate in year t i) Hypothesize the expected signs of the coefficients and test the appropriate null hypotheses at the 1% level. (3 marks) ii) What econometric problems appear to be present in this equation? Support your answer. (3 marks) iii) Suppose you were now told that the simple correlation coefficients between P, A, and Y were all between 0.88 and 0.94 and that a Breush-Pagan test produced a surprisingly low NR2. Would your answer to part ii) above change? Why or why not? How would it change? (4 marks) iv) What suggestions would you have for another run of this regression? (2 marks) 4/7 FINANCIAL ECONOMETRICS Question 4 (Cont’) b) If you run a regression in which the dependent variable and one or more independent variables are spuriously correlated, the result is a spurious regression, and the t-scores and overall fit of such spurious regressions are likely to be overstated and untrustworthy. One problem with time-series data is that independent variables can appear to be more significant than they actually are if they have the same underlying trend as the dependent variable. To test for non-stationarity, Dickey-Fuller test is employed to test the null hypothesis of whether a unit root is present in an autoregressive model. Describe and explain the test procedure. (8 marks) (Total 20 marks) Question 5 a) Consider the following distributed lag model: Yt = β0 + β1Xt + β2Xt-1 + β3Xt-2 + β4Xt-3 + ut where ut = φ1 ut-1 + ũt , AR(1) error term. ũt is serially uncorrelated, and X is strictly exogenous. Using the two equations of the model above, derive the ADL form of the model. (5 marks) b) Two authors published a study in 1992 of the effect of minimum wages on teenage employment using a U.S. state panel. The paper used annual observations for the years 1977-1989 and included all 50 states. The estimated equation is of the following type (Eit )= β0 + β1 (Mit /Wit ) + D2i + ... + D50i + B2t + ... + B13t + uit, where E is the employment to population ratio of teenagers, M is the nominal minimum wage, and W is average wage in the state. In addition, other explanatory variables, such as the prime-age male unemployment rate, and the teenage population share were included. i) Briefly discuss the advantage of using panel data in this situation rather than pure cross sections or time series. (5 marks) 5/7 FINANCIAL ECONOMETRICS Question 5 (Cont’) ii) Estimating the model by OLS but including only time fixed effects results in the following output it = 0 - 0.33 × (Mit /Wit ) + 0.35(SHYit) – 1.53 × uramit; R2 = 0.20 (0.08) (0.28) (0.13) where SHY is the proportion of teenagers in the population, and uram is the prime-age male unemployment rate. Coefficients for the time fixed effects are not reported. Numbers in parenthesis are homoskedasticity-only standard errors. Comment on the above results. Are the coefficients statistically significant? Since these are level regressions, how would you calculate elasticities? (5 marks) iii) Adding state fixed effects changed the above equation as follows: it = 0 + 0.07 × (Mit /Wit ) – 0.19 × (SHYit) – 0.54 × uramit; 2 = 0.69 (0.10) (0.22) (0.11) Compare the two results. Why would the inclusion of state fixed effects change the coefficients in this way? (5 marks) (Total 20 marks) ________ 000_________ 6/7 FINANCIAL ECONOMETRICS 7/7