This assignment estimated a relationship between aggregate consumption and aggregate income by running an OLS regression in SAS. An Engel Curve is used to identify this relationship. The null hypothesis test states that a change in aggregate income will not lead to a change in aggregate consumption of alcoholic beverages.
CONSALC Personal consumption expenditures: Nondurable goods: Alcoholic beverages purchased for off-premises consumption, Billions of Dollars, Annual, Not Seasonally Adjusted
YDISP Disposable personal income, Billions of Dollars, Annual, Not Seasonally Adjusted
The annual time series data used in this regression ran from 1933 to 2015.
AUTOCORRELATION IN TIME-SERIES DATA
Time series data is often accused of serial correlation. Studenmund defines first-order serial correlation, as “The current value of the error term is a function of the previous value of the error term.” (Studenmund, A. H., and Henry J. Cassidy. Using Econometrics: A Practical Guide. Sixth ed. Boston: Addison-Wesley, 2011.) Autocorrelation will not lead to bias in coefficient estimates. However, OLS will estimate biased variances (see relevant output). To improve the OLS estimate for time series data, we will test and correct for autocorrelation.
TEST FOR AUTOCORRELATION
Two different methods were used to detect autocorrelation in the Engel Curve regression. The first, informal method of testing for serial correlation is to plot the estimates and note any unusual patterns. Our plotted data’s pattern clearly indicated the presence of positive serial autocorrelation (see relevant output).
A more formal and widely used method to test for first-order autocorrelation is the Durbin-Watson (D-W) d Statistic. This detection method was applied to this regression because it meets the assumptions of the D-W derivation: the regression model includes an intercept, does not include a lagged dependent variable as an independent variable, and the serial correlation is first-order in nature. (Studenmund, A. H., and Henry J. Cassidy. Using Econometrics: A Practical Guide. Sixth ed. Boston: Addison-Wesley, 2011.) The D-W statistic calculated in this regression is 0.142 (see relevant output), which indicates the presence of positive autocorrelation.
CORRECT FOR AUTOCORRELATION
To correct for first order autocorrelation, I ran PROC AUTOREG and produced Yule-Walker estimates for the regression model. This method corrects for first-order autocorrelation and “restores minimum variance to its estimation” (Studenmund, A. H., and Henry J. Cassidy. Using Econometrics: A Practical Guide. Sixth ed. Boston: Addison-Wesley, 2011.)
SAS results in Output B (see relevant output) show the AUTOREG procedure that OLS produced prior to correction.
SAS results in Output C (see relevant output) show the corrected output with Yule-Walker Estimates. Its D-W statistic increased from 0.1422 to 1.5394. Though still present, there is decreased autocorrelation as the D-W stat approaches 2, which strengthens the corrected model. The change in R2 gives a more accurate parameter estimate for the coefficient on disposable personal income.
The corrected regression suggests that a $1B increase in aggregate disposable personal income is associated with a $0.009465B (or, $9.465 million) increase in aggregate consumption expenditure of alcoholic beverages. These results are highly statistically significant with a p-value of < .0001 and we reject the null hypothesis.