To estimate an Engel curve, I will look at the relationship between real disposable income per capita in the US and the total sales of car in the US from 1976 to 2016 with monthly data. I’m expecting for income to be positively correlated with the total sales of car. This means that an increase in income would be associated with some increase in total sales of car, making cars a normal good. Because of the limitations of our data, we will regard the total sales of cars as the consumption of cars and ignore the fact that some of the sales of cars might not be for the direct use of cars. We will run an OLS model using SAS with real disposable income as our independent variable and total sales of cars as dependent variable.
For this sample, an increase of 1 dollar in real disposable income is associated with an additional 0.000148 million total car sales. The coefficient was highly statistically significant with a (p<0.0001). The regression as a whole did not fit very well (R-Square 0.169 and adjusted R-square= 0.167) and was highly statistically significant (F=99.62 and p<0.0001).
Because this is a time series data ranging from 1976 to 2016, we suspect autocorrelation might be present. We run the Durbin Watson Test to detect for possible autocorrelation.
The Pr< DW is the p-value testing for positive autocorrelation. In this case, it looks like positive autocorrelation does exist for our sample (p<0.0001). I will correct for it by using PROC AUTOREG and NLAG=1 after the model statement.
It looks like correcting for autocorrelation did not change much of our estimates. The coefficient for INCOME is 0.000159 instead of 0.000147, which is a very small change. The p-value has gone up to p=0.0035 which still makes the coefficient a highly statistically significant one. The transformed regression R-square is very small 0.0173 while the total R-square for the Yule Walker estimate is 0.8132.