For my SAS regression, I chose the following variables:

I decided to regress real gross domestic product (RGDP) per capita against United States gasoline consumption per year. My independent variable is total United States gasoline consumption while the dependent variable is RGDP per capita. I chose to use RGDP per capita because it measures the total economic output of a country divided by the number of people and is also adjusted for inflation. My data for gasoline consumption is time-series data.

The first model I decided to regress exhibits taking the natural log of overall gas consumption, RGDP per capita, and the real price of gas. The results:

The REG Procedure

Model: MODEL1

Dependent Variable: lncons

Number of Observations Read 68
Number of Observations Used 68

 

Analysis of Variance
Source DF Sum of
Squares
Mean
Square
F Value Pr > F
Model 2 11.94779 5.97390 288.44 <.0001
Error 65 1.34620 0.02071    
Corrected Total 67 13.29399      

 

Root MSE 0.14391 R-Square 0.8987
Dependent Mean 14.54070 Adj R-Sq 0.8956
Coeff Var 0.98972    

 

 

 

 

 

Parameter Estimates
Variable DF Parameter
Estimate
Standard
Error
t Value Pr > |t|
Intercept 1 4.34924 0.55492 7.84 <.0001
lnrgdp 1 1.02998 0.04289 24.01 <.0001
lnrpgas 1 0.08265 0.08058 1.03 0.3088
           

The first model results in a high R2 of 89.87% which shows the model has a high level of goodness of fit between the dependent and independent variables. The t-statistics for the beta coefficients are eye catching because the natural log of RGDP’s value is 24.01 while the natural log of real price of gasoline’s value is 1.03. This indicates that the natural log of the real price of gas is not statistically significant. In order to alter my regression, I decided not to take the natural log of variables. The results are the following:

 

The REG Procedure

Model: MODEL2

Dependent Variable: cons

Number of Observations Read 68
Number of Observations Used 68

 

Analysis of Variance
Source DF Sum of
Squares
Mean
Square
F Value Pr > F
Model 2 4.022103E13 2.011051E13 337.36 <.0001
Error 65 3.87478E12 59612003964    
Corrected Total 67 4.409581E13      

 

Root MSE 244156 R-Square 0.9121
Dependent Mean 2246161 Adj R-Sq 0.9094
Coeff Var 10.86991    

 

Parameter Estimates
Variable DF Parameter
Estimate
Standard
Error
t Value Pr > |t|
Intercept 1 176577 106930 1.65 0.1035
rgdp 1 69.23828 5.19396 13.33 <.0001
pgas 1 -68289 67426 -1.01 0.3149
           

My second model I regressed RGDP and the nominal price of gas against the overall consumption of gasoline in the United States. Although my R2 improved by 1.34%, the nominal price of gasoline has a low t-statistic of -1.01. The model implies that the nominal price of gas is statistically insignificant even though economical intuition implies that this is not the case. Now we take a look at the Engel curve.

(Created an Engel curve in excel that for some reason won’t transfer over to site but is included within my paper.)

When interpreting the first model, I conclude that a 1% change in RGDP per capita leads to a 1.02998% change in overall gas consumption in the United States. This conclusion is puzzling. If a 1% increase in RGDP leads to a greater than 1% increase in consumption of a good, it would be implied that it is a luxury good. Gasoline is classified as a normal good which means my model still has misspecification which is believed to be omitted variable bias. Potential variables that could be included within the model would be monthly gas consumption because consumers prefer to drive more while the weather is nicer (Spring and Summer) rather than when the weather is colder (Fall and Winter). Another factor is the advancement of technology of vehicles, more specifically engine efficiency. If cars have more energy efficient engines, then consumption of gas will decrease over time as the MPG per vehicles increase.

 

In conclusion, although my regression exhibits a high R2 and high F-statistic signifying overall model significance, this model will need additional research in order to produce a more accurate Engel curve.

Engel Curve for RGDP Per Capita against US Gasoline Consumption