Your estimate of a quarterly consumption model on 50 observations is:
Consumption (Y) = -48.7+0.68Income (X1) -0.04intrate (X2)
R2= 0.75, Dw = 1.55
Is autocorrelation present? If autocorrelation is present what can be said about
the results of the estimation?
To determine if autocorrelation is present, we need to examine the Durbin-Watson (Dw) statistic. The value of Dw is 1.55, which is lower than the critical values of 1.66 and 1.36 at 5% and 1% significance levels respectively for a sample size of 50 and two explanatory variables. This indicates the presence of positive autocorrelation in the residuals.
Positive autocorrelation means that the residuals are correlated with each other over time, suggesting that the model is not fully capturing all the relevant explanatory variables. As a result, the coefficients estimated may be biased and inefficient. Therefore, the results of the estimation should be interpreted with caution, and further investigation is needed to improve the model. One possible approach is to include additional explanatory variables that might account for the missing factors that are causing the autocorrelation. Another approach is to use a time series model that explicitly accounts for the autocorrelation in the data.