Economics 435 1 Spring 1998 D. Maki Final Examination Instructions: There are three parts to this examination, each with two questions. Answer one question from each part (a total of three questions) Questions are equally weighted. Total time allowed = three hours. This is a closed book examination. Throughout the examination, I am not looking for SHAZAM commands as answers. Part I: Answer one of the following two questions. 1. The table below gives the estimated coefficients and standard errors (in parentheses) for several models dealing with the demand for cigarettes in Turkey, using annual data for 1960-1988. The variables are: LQ=logarithm of cigarette consumption per adult, LY=logarithm of per-capita real GNP, LP=logarithm of the real price of cigarettes, D82=1 from 1982 onward, zero otherwise, D86=1 from 1986 onward, zero otherwise, LYD1=LY*D82, LYD2=LY*D86, LPD1=LP*D82 and LPD2=LP*D86. (Intercepts estimated but not reported). Variable Model A Model B Model C Model D D82 23.36(5.55) -0.11(.21) -0.10(0.03) 21.79(5.25) D86 -36.26(12.86) -0.41(.24) -0.10(.04) -28.29(9.43) LY 0.73(.07) 0.71(.09) 0.62(.07) 0.73(.07) LYD1 -2.80(.66) -2.60(.62) LYD2 4.25(1.52) 3.30(1.10) LP -0.37(.10) -0.34(.13) -0.20(.09) -0.37(.10) LPD1 0.41(.21) 0.02(.25) 0.29(1.79) LPD2 -0.24(.26) 0.29(.25) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Rbar**2 0.921 0.859 0.852 0.921 RSS 0.018645 0.036444 0.04195 0.019427 a. In Model D, what are the estimated income and price elasticities of demand for each of the three periods? b. Calculate the value of the test statistic, and state its distribution, for testing the hypothesis: "there has been no change in the price and income elasticities over the three periods". c. Calculate the value of the test statistic, and state its distribution, for testing the hypothesis: "there has been no change in the price elasticities over the three periods, assuming income elasticities may have changed". d. Calculate the value of the test statistic, and state its distribution, for testing the hypothesis: "there has been no change in the income elasticities over the three periods, assuming price elasticities have not changed". 2 2. a. In the case of the three variable model: Y = b1 + b2X2 + b3X3 + u, show how the estimated variances of b2 and b3 are affected by the correlation of x2 and X3. What other factors affect these variances? Does your answer generalize to equations with more explanatory variables? Explain. b. Explain in a non-technical manner how ridge regression and principal components analysis "work". In what circumstances are these techniques a "solution" to the problem of multicollinearity? Explain. What other solutions to this problem are available, and when are they useful? Explain. Part II. Answer one of the following two questions. 3. The file DATA8-2 contains data on three variables for the 51 U.S. states as of 1993: ET=expenditures on travel (Bill $), Y=personal income (Bill $) and POP=population (mill). A SHAZAM command file is (several commands per line): file 11 a:data8-2; read(11) et y pop; ols et y/resid=r ols et y pop/resid=rr; genr etpy=et/y; genr poppy=pop/y genr ry=1/y; ols etpy ry poppy/resid=rrr; genr lr2=log(r**2) genr lrr2=log(rr**2); genr lrrr2=log(rrr**2); genr ly=log(y) ols lr2 ly; ols lrr2 ly; ols lrrr2 ly Some regression output is (t-values in parentheses): 1) ET = 0.4981 + 0.0556Y R-square=0.8532 (0.93) (16.88) 2) ET = 0.2164 + 0.0189Y + 0.8184POP R-square=0.8590 (0.38) (0.72) (1.40) 3) ETPY = 0.1360 + 0.6306RY - 1.5499POPPY R-square=0.1128 (2.56) (2.15) (-1.49) 4) LR2 = -5.9418 + 1.3057LY R-square=0.2591 (-4.44) (4.14) 5) LRR2 = -6.4237 + 1.4013LY R-square=0.3083 (-5.05) (4.67) 6) LRRR2 = -6.4227 - 0.4456LY R-squared=0.0464 (-5.24) (-1.54) a. What problems are apparent in the estimation of equation 2? Explain. b. What is the purpose of estimating equation 3? Explain. Is the coefficient of the income term in equation 3 non- significant? Explain (carefully). Use tabled t=2.00. c. Given the results above, what additional estimations would you perform to deal with the problems in equation 2? Explain. 4. The following ten observations of annual time series data yield the same regression equation for all i if Yi (i = 1, 1, ... 6) is regressed on X: Y = 0.0 + 1.0X, R2 =0.87. 3 Y1 Y2 Y3 Y4 Y5 Y6 X 1.98 2.69 2.17 1.82 0.53 -0.75 1.00 1.98 2.69 -1.01 2.14 1.63 3.90 2.00 1.48 2.69 3.83 2.46 2.83 1.67 3.00 4.98 3.19 4.66 2.78 3.93 5.11 4.00 3.48 3.89 5.49 3.10 5.73 5.93 5.00 7.48 4.69 6.32 7.92 6.53 6.54 6.00 5.98 5.89 7.15 8.24 8.03 6.35 7.00 8.98 7.69 7.98 8.56 6.93 7.22 8.00 7.98 9.69 8.81 8.88 11.03 8.54 9.00 10.70 11.79 9.64 9.20 7.83 10.38 10.00 For each of these six equations, note what econometric problems (if any) you suspect, how you would more formally test for the existence of each problem, and how you would correct if testing confirmed the existence of a problem. Part III. Answer one of the following two questions. 5. The file DATA9-1 contains data on the demand for ice cream for 30 four-week periods in the early 1950's. There are four variables, demand (DE) in physical units, income (IN) in dollars, price of ice cream (PR), and mean temperature (TE). A SHAZAM command file is (several commands per line): file 11 a:data9-1; read(11) de in pr te; genr lde=log(de) genr lin=log(in); genr lpr=log(pr); genr lte=log(te) ols lde lin lpr lte/rstat; auto lde lin lpr lte/rstat box de in pr te/all The regression output is (t-values in parentheses): 1) LDE = -6.761+0.733LIN-0.669LPR+0.419LTE, R-square=0.71 (-4.73) (2.67) (-1.06) (7.59) DW=0.98 2) LDE = -2.688-0.117LIN-0.711LPR+0.334LTE, R-square=0.79 (-1.27) (-0.25) (-1.26) (3.95) DW=1.86, Rho=0.77 3) DE = -5.0139 + 0.34IN - 0.71PR + 0.21TE, R-square=0.71 (-4.77) (2.69) (-1.09) (7.63) LLF(0.14)=59.3304, LLF(1.00)=58.6194), LLF(0.00)=59.3126 a. Equations 1 and 2 are run in LOGLOG form. Is this appropriate? Explain. b. What is the main problem exhibited by equation 1? Explain. c. Does equation 2 correct the problem exhibited by equation 1? In what sense? 6. Several equations are estimated using annual U.K. data for the period 1948-1989 on: CONS=per-capita consumption expenditure, DI=per-capita disposable income, CONS1=lagged CONS, DI1=lagged DI, and DDI=DI-DI1 (t-values in parentheses): 1) CONS = 168.31 + 0.864DI, R-square=0.991, DW=0.25 (3.89) (64.98) 2) CONS = -46.802 + 1.0219CONS1 + 0.7058DDI, R-square=0.998 (2.07) (123.0) (9.93) DW=1.54 4 3) CONS = -8.742 + 0.7040CONS1 + 0.2899DI, R-squared=0.994 (-0.17) (4.51) (2.26) DW=0.87 4) CONS = -56.095 + 1.0683CONS1 + 0.6840DI - 0.7230DI1 (-1.87) (10.98) (8.05) (-9.00) R-square=0.998, DW=1.60 a. Assume it is given that the 5% lower limit for the DW is around 1.3. Can you tell which of the above equations exhibit autocorrelation? Explain. b. What theoretical model do you suppose underlies equation 2? Is this model supported by the results? Explain. c. What theoretical model do you suppose underlies equation 3? Is this model supported by the results? Explain. d. What do you think would be the best estimation of the relation between CONS and DI (could be one of the above, or some other equation)? Explain.