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?

Question

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?

Quizplus · Accepted Answer

The Answer is

\begin{array} { l c c c c } ext { (a) Coefficient } & \beta _ { \mathrm { p } } & \beta _ { \mathrm { Y } } & \beta _ { \mathrm { A } } & \beta _ { \mathrm { R } } \ ext { Expected sign } & - & + & + & - \ ext { Calculated } t ext {-score } & - 4.0 & 5.0 & 3.0 & - 3.0 \ ext { Decision } & ext { reject } & ext { reject } & ext { reject } & ext { reject }\end{array}

(given a 1% critical t-score of 2.528)
In addition, the DW =1.86 is higher than the d_U of 1.77, so there is no evidence of positive serial correlation.
(b) There may be theoretically sound variables that have been omitted, for instance some measure of competition from foreign-made cars, but the results themselves give no indication of any problems.
(c) These results are clear indications of multicollinearity but not of heteroskedasticity.
(d) Unless a theoretically sound variable can be added measuring competition, the regression need not be changed at all.

A Model of the Number of Cars Sold in the United