Econometric Exam
m Problem1: The demand for roses was estimated using quarterly figures for the period 1971 (3rd quarter) to 1975 (2nd quarter). Two models were estimated and the following results were obtained: Y = Quantity of roses sold (dozens) X2 = Average wholesale price of roses ($ per dozen) X3 = Average wholesale price of carnations ($ per dozen) X4 = Average weekly family disposable income ($ per week) X5 = Time (1971.3 = 1 and 1975.2 = 16) ln = natural logarithm The standard errors are given in parentheses. A. ln Yt = 0.627 - 1.273 ln X2t + 0.937 ln X3t + 1.713 ln X4t - 0.182 ln X5t (0.327) (0.659) (1.201) (0.128) R2 = 77.8% D.W. = 1.78 N = 16 B. ln Yt = 10.462 - 1.39 ln X2t (0.307) R2 = 59.5% D.W. = 1.495 N = 16
Correlation matrix: | ln X2 | ln X3 | ln X4 | ln X5 | ln X2 | 1.0000 | -.7219 | .3160 | -.7792 | ln X3 | -.7219 | 1.0000 | -.1716 | .5521 | ln X4 | .3160 | -.1716 | 1.0000 | -.6765 | ln X5 | -.7792 | .5521 | -.6765 | 1.0000 |
a) How would you interpret the coefficients of ln X2, ln X3 and ln X4 in model A? What sign would you expect these coefficients to have? Do the results concur with your expectation? b) Are these coefficients statistically significant? c) Use the results of Model A to test the following hypotheses: i) The demand for roses is price elastic ii) Carnations are substitute goods for roses iii) Roses are a luxury good (demand increases more than proportionally as income rises) d) Are the results of (b) and (c) in accordance with your expectations? If any of the tests are statistically insignificant, give a suggestion as to what may be the reason. e) Do you detect the presence of multicollinearity in the data? Explain. f) Do you detect the presence of serial correlation? Explain g) Do the variables X3, X4 and X5 contribute significantly to the
Correlation matrix: | ln X2 | ln X3 | ln X4 | ln X5 | ln X2 | 1.0000 | -.7219 | .3160 | -.7792 | ln X3 | -.7219 | 1.0000 | -.1716 | .5521 | ln X4 | .3160 | -.1716 | 1.0000 | -.6765 | ln X5 | -.7792 | .5521 | -.6765 | 1.0000 |
a) How would you interpret the coefficients of ln X2, ln X3 and ln X4 in model A? What sign would you expect these coefficients to have? Do the results concur with your expectation? b) Are these coefficients statistically significant? c) Use the results of Model A to test the following hypotheses: i) The demand for roses is price elastic ii) Carnations are substitute goods for roses iii) Roses are a luxury good (demand increases more than proportionally as income rises) d) Are the results of (b) and (c) in accordance with your expectations? If any of the tests are statistically insignificant, give a suggestion as to what may be the reason. e) Do you detect the presence of multicollinearity in the data? Explain. f) Do you detect the presence of serial correlation? Explain g) Do the variables X3, X4 and X5 contribute significantly to the