悉尼大学计量经济学作业

University of Sydney Department of Economics ECMT2110 Semester 2, 2012 Kadir Atalay ASSIGNMENT #2 DUE: 4 pm Friday, October 5th Deadline: 4pm, Monday, October 8th . INSTRUCTIONS: Use STATA to conduct the following analysis. Hand in your log file. Use an editor to add your names and student numbers to the file, and to add your written responses. Iwould suggest after completing your log file you copy it into a Word document (with nice font so the result come out (try Courier New, size:8) then type your answers after you have preformed the command. HANDWRITTEN ASSIGNMENTS will get “0” point. Q1- 70 points Asset Pricing Models. A w ell know n m odel o f t he r eturns t o financial as sets i s t he C apital A sset P ricing M odel (CAPM). It asserts that the (expected) excess return on stock i in period t should be proportional to the excess return of the market as a whole. Excess returns are returns above those generated by a risk free asset, such as t bill. rit-rft = i*(rmt-rft) Note that the factor of proportionality, i, v aries a cross i ndustries ( possibly c ompanies) depending on how risky they are. An e xcellent di scussion of t he C APM c an be f ound i n Berndt, E . ( 1991) The P ractice o f Econometrics. . It is also discussed in your textbook, on page 160. Note that this relationship lends itself naturally to estimation by linear regression: rit-rft = i + i*(rmt-rft) + i a) Retrieving and Manipulating the Data ( 5 points) The file market.dta is a STATA data file containing the monthly stock market returns of a selection of companies over a 10 year period. It also contains the market return and the return on a risk free asset (t-bills). Choose two companies from those in the data. For each company, create a variable for the excess returns. Create a variable equal to the excess returns for the market. For each of your companies, plot the excess returns over the period against the excess market return b) Bivariate Regression and t tests: the CAPM .(15 points) For each of your companies, regress the excess returns over the period against the excess market return. The of each company is a measure of its riskiness. Which of yo ur companies is riskier? Do your results surprise you? One of the implications of the CAPM is that the intercept i. Report a t-test of this hypothesis. c) Reverse Regression (10 points) For one of your companies, estimate the reverse regression of excess market returns on excess returns. Does this regression estimate the same line? If not, why not? Compare the fit of the two regressions. d) Chow test for Structural Stability (15 points) Another implication of the CAPM is that the Betas should be fairly stable over time. One way to test the stability of a regression parameter is a type of F test known as a Chow test. Use this test to test the stability of the for each of your companies. e) Multiple Regression and F tests: The Asset Pricing Model (25 points) A competitor to the CAPM is the Asset Pricing Model (APM). While the CAPM asserts that excess stock returns should only be related to the excess returns of the market, the APM counters that excess stock returns may be (contemporaneously) related to other features of the economy. Add the following data to your worksheet (see the end of this pdf, or use the market_add.txt ): The new variables are: POIL Nominal Price of oil in $ FRBIND Federal R eserve Board i ndex of i ndustrial P roduction ( 1972=100, seasonally adjusted) CPI Consumer Price Index (1967=100) Generate a v ariable f or the r eal p rice o f o il ( RPOIL=POIL/CPI). G enerate v ariables capturing the growth rate in RPOIL, FRBIND and CPI (note that the last will be the rate of inflation). Growth rate in X = (Xt-Xt-1)/Xt (Note that the data in above starts one month earlier than the data in market.dta). Generate variables capturing the “surprise” in the growth rates in each month by taking deviations from sample means. Estimate the multiple regression of excess stock returns on excess market returns, the surprise in the inflation rate, rate of growth in real oil prices and rate of growth of industrial production. and Use an F test to test for the exclusion of the new variables . This is a test of the CAPM against the more general APM (Why?). Discuss your results. Q2- 30 points Use t he d ata i n LOANAPP.DTA for t his e xercise. T he bi nary va riable t o be e xplained i s approve, which is equal t o one i f a m ortgage l oan t o an i ndividual was approved. The ke y explanatory variable is white, a dummy variable equal to one if the applicant was white. The other applicants in the data set are black and Hispanic. To test for discrimination in the mortgage loan market, a linear probability model can be used: approve = 0 + 1 white + other factors (i) If there is discrimination in loan approvals against minorities, and the appropriate factors have been controlled for, what is the sign of 1 ? (ii) Regres approve on white and report the results in the usual form. Interpret the coefficient on white. Is it statistically significant at the 1% level? Is it practically large ? Would you conclude that there is discrimination (or no discrimination) in the market for loans? Explain. (iii) As controls, add the variables obrat, loanprc, unem, male, married, dep, sch and cosign. Is th ere s till evidence of di scrimination a gainst nonw hites ( using a 1 % l evel of significance)? See below, where the data is described, for the definition of these variables (iv) Now allow the effect of race to interact with the variable measuring other obligations as a percent of income (obrat). Is the interaction term significant at the 1% level? What do you conclude from the hypothesis test? (v) Re-estimate the model in part (iii) with the inclusion of an interaction term between white and male. Test the null hypothesis that the coefficient on the white male interaction term is equal to zero (against a two-sided alternative) using a 1% significance level. Are white males treated differently in the market for loans? Note: The LOANAPP.DTA data set can be downloaded from the course Blackboard page. The data set has 1000 observations and 10 columns. The columns corresponds to , , , , , , , and respectively. The definition of each variable is: = 1 if the loan is approved (= 0 otherwise) = 1 if the applicant is white = other obligations (as a % of income) = amount of loan / price of the property = unemployment rate in applicants industry of employment = 1 if the applicant is male = 1 if the applicant is married = number of dependents = 1 if the applicant has more than 12 years of schooling = 1 if there is a cosigner Market_add nth year poil frbind cpi mnth year poil frbind cpi 12 1977 7.93 126.5 166.3 01 1983 28.85 151.4 260.5 01 1978 7.90 125.9 166.7 02 1983 34.10 151.8 263.2 02 1978 7.87 127.6 167.1 03 1983 34.70 152.1 265.1 03 1978 7.79 128.3 167.5 04 1983 34.05 151.9 266.8 04 1978 7.86 128.7 168.2 05 1983 32.71 152.7 269.0 05 1978 7.89 129.7 169.2 06 1983 31.71 152.9 271.3 06 1978 7.99 129.8 170.1 07 1983 31.13 153.9 274.4 07 1978 8.04 130.7 171.1 08 1983 31.13 153.6 276.5 08 1978 8.03 131.3 171.9 09 1983 31.13 151.6 279.3 09 1978 8.39 130.6 172.6 10 1983 31.00 149.1 279.9 10 1978 8.46 130.2 173.3 11 1983 30.98 146.3 280.7 11 1978 8.62 131.5 173.8 12 1983 30.72 143.4 281.5 12 1978 8.62 133.0 174.5 01 1984 30.87 140.7 282.5 01 1979 8.50 132.3 175.3 02 1984 29.76 142.9 283.4 02 1979 8.57 133.3 177.1 03 1984 28.31 141.7 283.1 03 1979 8.45 135.3 178.2 04 1984 27.65 140.2 284.3 04 1979 8.40 136.1 179.6 05 1984 27.67 139.2 287.1 05 1979 8.49 137.0 180.6 06 1984 28.11 138.7 290.6 06 1979 8.44 137.8 181.8 07 1984 28.33 138.8 292.6 07 1979 8.48 138.7 182.6 08 1984 28.18 138.4 292.8 08 1979 8.62 138.1 183.3 09 1984 27.99 137.3 293.3 09 1979 8.63 138.5 184.0 10 1984 28.74 135.8 294.1 10 1979 8.72 138.9 184.5 11 1984 28.70 134.8 293.6 11 1979 8.72 139.3 185.4 12 1984 28.12 134.7 292.4 12 1979 8.77 139.7 186.1 01 1985 27.22 137.4 293.1 01 1980 8.68 138.8 187.2 02 1985 26.41 138.1 293.2 02 1980 8.84 139.2 188.4 03 1985 26.08 140.0 293.4 03 1980 8.80 140.9 189.8 04 1985 25.85 142.6 295.5 04 1980 8.82 143.2 191.5 05 1985 26.08 144.4 297.1 05 1980 8.81 143.9 193.3 06 1985 25.98 146.4 298.1 06 1980 9.05 144.9 195.3 07 1985 25.86 149.7 299.3 07 1980 8.96 146.1 196.7 08 1985 26.03 151.8 300.3 08 1980 8.05 147.1 197.8 09 1985 26.08 153.8 301.8 09 1980 9.15 147.8 199.3 10 1985 26.04 155.0 302.6 10 1980 9.17 148.6 200.9 11 1985 26.09 155.3 303.1 11 1980 9.20 149.5 202.0 12 1985 25.88 156.2 303.5 12 1980 9.47 150.4 203.3 01 1986 25.93 158.5 305.4 01 1981 9.46 152.0 204.7 02 1986 26.06 160.0 606.6 02 1981 9.69 152.5 207.1 03 1986 26.05 160.8 607.3 03 1981 9.83 153.5 209.1 04 1986 25.93 162.1 308.8 04 1981 10.33 151.1 211.5 05 1986 26.00 162.8 309.7 05 1981 10.71 152.7 214.1 06 1986 26.09 164.4 310.7 06 1981 11.70 153.0 216.6 07 1986 26.11 165.9 311.7 07 1981 13.39 153.0 218.9 08 1986 26.02 166.0 313.0 08 1981 14.00 152.1 221.1 09 1986 25.97 165.0 314.5 09 1981 14.57 152.7 223.4 10 1986 25.92 164.5 315.3 10 1981 15.11 152.7 225.4 11 1986 25.44 165.2 315.3 11 1981 15.52 152.3 227.5 12 1986 25.05 166.2 315.5 12 1981 17.03 152.5 229.9 01 1987 24.28 165.6 316.1 01 1982 17.86 152.7 233.2 02 1987 23.63 165.7 317.4 02 1982 18.81 152.6 23