A Model of the Number of Cars Sold in the United

question 1

Essay

A model of the number of cars sold in the United States from 1980 through 2004 produced the following results (standard errors in parentheses):
$$\begin{array} { l } \hat { \mathrm { C } } _ { \mathrm { t } } = 3738 - 48.0 \mathrm { P } _ { \mathrm { t } } + 10.0 \mathrm { Y } _ { \mathrm { t } } + 6.0 \mathrm {~A} _ { \mathrm { t } } - 360.0 \mathrm { R } _ { \mathrm { t } } \\\begin{array} { l l l l } ( 12.0 ) \quad ( 2.0 ) \quad ( 2.0 ) \quad ( 120.0 )\end{array} \\\overline { \mathrm { R } } ^ { 2 } = 0.85 \quad \text { DW } = 1.86 \quad \mathrm {~N} = 25 \text { (annual) } \\\end{array}$$ where: C_t = thousands of cars sold in year t
P_t= price index for domestic cars in year t
Y_t = disposable income (billions of dollars) in year t
A_t = billions of dollars of auto industry advertising expenditures in year t
R_t = the interest rate in year t
(a) Hypothesize the expected signs of the coefficients and test the appropriate null hypotheses at the 1% level.
(b) What econometric problems appear to be present in this equation? Why?
(c) 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 Park test with Y as Z produced a t-score of 0.50. Would your answer to part (b) above change? Why or why not? How would it change?
(d) What suggestions would you have for another run of this regression?

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Definitions:

Cross Elasticity

A measure of the responsiveness of the demand for one good to a change in the price of another good.

Soft Drinks

Carbonated, non-alcoholic beverage options often flavored with various sweeteners, fruits, or other flavorings.

Substitutes

Products or services that can be used in place of each other, where the increase in price of one leads to an increase in demand for the other.

Cross Elasticity Coefficient

A measure of how the quantity demanded of one good changes in response to a price change in another good.