For my Engel Curve, I estimated the effect of annual household disposable income (hdi) on annual gambling consumption expenditure (gamblingconsumption). It combines 24 between 1992-2015 (N=24) and was pulled from the FRED website. For this sample, the model predicted that a 1 billion dollar increase in aggregate disposable household income was associated with a 10.9 million dollar increase in aggregate gambling consumption (p-value < 0.0001; t-stat = 26.53). The model as a whole fit very well (R2= 0.9697) and was statistically significant (p-value < 0.0001). However, using the Durbin-Watson test, I discovered positive autocorrelation in the model (d= 0.2686) that was statistically significant (p-value < 0.0001 for positive autocorrelation). Multicollinearity was not an issue because the model only contained one independent variable (hdi) and heteroskedasticity was not present in the error terms.
In correcting for autocorrelation, I used proc autoreg, which by default uses the Yule-Walker estimation method to correct. I lagged the model using the 2nd order autoregressive process (NLAG=2) because lagging it only one period (NLAG = 1) still showed statistically significant positive autocorrelation within the model and a higher sum of squared errors then when using the 2nd order. After correcting, the model again predicted that a 1 billion dollar increase in aggregate disposable household income is associated with a 10.9 million dollar increase in aggregate gambling consumption. The coefficient was again highly statistically significant (p value < 0.0001; t-stat 17.24). The transformed model fit very well as a whole (R2= 0.9369). More importantly, the Durbin Watson t statistic in this transformed model is now 1.6072 and statistically insignificant p-value (0.1335), suggesting that we cannot reject the null hypothesis that correlation between the two variables is 0. Although the Durbin-Watson statistic is not above 2, which is the accepted value for a model showing no autocorrelation, this is a great improvement from the original Durbin-Watson statistic of 0.2686. From this model we can deduce that gambling is a normal good (as income increase, consumption increases). Below I included SAS code.
proc import datafile=”/home/blumjt0/sasuser.v94/gamblin_consumption.xls”
var hdi gamblingconsumption;
model gamblingconsumption = hdi/ DW white;
plot gamblingconsumption * hdi;
model gamblingconsumption = hdi/ NLAG=2 DWPROB;