Question

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.

1. lnY_t=0.627-1.273 ln X_2t + 0.937 ln X_3t + 1.713 ln X_4t - 0.182
2. ln X_5t

                                    (0.327)            (0.659)           (1.201)             (0.128)

            R² = 77.8%                              D.W. = 1.78                             N = 16

B.        ln Y_tÙ = 10.462 - 1.39 ln X_2t

                                       (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 analysis? Test the joint significance of these variables.        

h) Starting from model B, assuming that at the time point of January, 1973, there was a disaster that heavily affected the quantity of roses produced. Suggest a model to check if we have to use two different models for the data before and after the disaster. (Using dummy variable).

Answer 1