Engel Curve Assignment

For this assignment I was interested in how aggregate food expenditures fluctuated with aggregate disposable income. I obtained annual aggregate food expenditure information, in 1988 dollars, dating from 1953-2014 from the website of the United States Department of Agriculture (USDA). Consequently, from the USDA I also obtained a dataset containing information concerning  the annual per capita available food supply adjusted for loss, in Kilocalories, dating from 1953-2014. From the Federal Reserve of St. Louis (FRED) I obtained a dataset chronicling the U.S. civilian noninstitutional population per year from 1953-2014. I also obtained, from FRED, a dataset containing seasonally adjusted and end of period aggregated real disposable personal income for the period 1953-2014 as well as the annual personal savings rate as a percentage of disposable income, for the same period, also aggregated end of period.

My initial model OLS model was as follows:


Where CPEXP is annual aggregate food expenditures in millions of 1988 dollars, RDI is annual seasonally adjusted real disposable income in billions of 2009 chained dollars, POP is annual civilian noninstitutional population of the U.S. in thousands of persons, SUPPLY is the loss-adjusted annual supply of kilocalories available per capita in the U.S., and SAVINGR is the annual personal savings as a percentage of personal disposable income. This model yielded the following SAS output:

As can be seen from the output, my initial R-squared and adjusted R-squared indicated that my model had good fit, with over 99% of the variance in CPEXP explained by the variance in the statistically significant independent variables. Since this assignment concerns an Engel curve I will only talk briefly about the variables POP, SUPPLY, and SAVINGR and focus instead on the effect that RDI has on CPEXP.  In my initial model the effect of RDI was statistically significant at the 5% level, as well as the 1% level as indicated by the p-value, and the parameter estimate predicates that an increase of $1 billion in aggregate real disposable income would cause an increase of $21.27 million in aggregate food expenditures holding the supply of food, as well as the civilian noninstitutional population, and personal savings rate as a percentage of personal disposable income constant. Consequently, POP is also significant at the 5% and 1% level but both SUPPLY and SAVINGR are insignificant at the 5% level.

However, looking at the residual plots of the independent variables, there is a hint that autocorrelation is present given the cyclical nature of the residuals. To check for this I conducted a Durbin-Watson test and obtained the following output:


Given this result, I am able to conclude that my model is suffering from positive autocorrelation since the Durbin-Watson statistic is 0.693 but the dL is 1.455 and the dU is 1.729 at the 5% significance level. To correct for this, I run a second regression model, using the same variables as in the above model, but using the SAS autoreg procedure with the maximum likelihood estimator enabled, and lag of 3. This autoregressive model yields the following parameter estimates:

The Durbin-Watson test statistic of 1.9230 indicates that, at the 5% significance level with dL being 1.455 and dU being 1.789, the autocorrelation has been corrected. The parameter estimate for RDI indicates that, at the 5% as well as 1% significance level, an increase of $1 billion in real disposable income leads to an additional $21.5 million in aggregate expenditures on food holding supply of food, civilian noninstitutional population, and personal savings as a percentage of personal disposable income constant. Consequently, POP is statistically significant at the 1% and 5% significance level and SAVINGR is significant at the 5% level. However, SUPPLY still remains insignificant at the 5% level. Additionally, the R-squared of this model indicates that 99% of the variation in CPEXP is explained by the variation in the statistically significant dependent variables.

Finally, in order to create a visual of the Engel Curve for aggregate food expenditures in the U.S., I create a scatter plot of the RDI on the vertical axis and CPEXP on the horizontal. The output is given below and shows a clear positive relationship between the two variables:

Aggregate Food Engel Curve