For my SAS regression, I chose the following variables:
- RGDP per Capita (RGDP per capita) stated in dollar terms
- Overall United States gasoline consumption (overall gas consumption) stated in thousand barrels
- Consumer Price Index (CPI Index)
- Average nominal price of gasoline (average nominal price of gas) in dollars per gallon
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 R^{2} 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 R^{2} 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 R^{2} and high F-statistic signifying overall model significance, this model will need additional research in order to produce a more accurate Engel curve.