The variables will each be tested for individual significance and the overall strength of the model will also be measured. After the initial regression the model will be tested for problems such as autocorrelation, multicollinearity and misspecification bias. The model shall also be tested in the long run. As mentioned before, if there is sufficient time the ca variable will be looked at. Estimation The regression results from our original basic model are reproduced in appendix, (a). The signs of the two explanatory variables are as expected, i.e. the level of disposable income has a positive relationship with the demand for money while the interest rate has a negative one. The t-values obtained from the coefficients of RNET and IA reject the null hypothesis that they are individually insignificant at both the 5% and 1% level of significance. The model has a fairly strong R2 of 0.68154 as well which is promising.
Unfortunately the Durbin-Watson d statistic that we obtain, once run through the Durbin-Watson test is suggestive of positive autocorrelation. The Durbin-Watson test for autocorrelation does, however, have it limitations, some of which include the fact that there are zones of “indecision” and more importantly is not appropriate to use when a lagged dependent variable is included which will occur later when the basic model starts to evolve. The Breusch-Godfrey test will therefore be used to test for autocorrelation. The Breusch-Godfrey test also says that autocorrelation is present in the model at both the 5% and 1% level especially at the first order serial correlation. The Whites General Test also reveals heteroscedasticity. These results mean than the variables in the model are not BLUE.
In an attempt to counteract the adverse effects above the model will have to be changed. The variables in the basic model will remain but lagged values of the variables will be included, meaning that the new model will now be: The results of this regression can be found in the appendix under part (c). The new Chi squared figures indicate that we can accept the null hypothesis that there is no heteroscedasticity present at the 5% and 1% levels. We can also accept the null hypothesis that there is no longer autocorrelation at the same levels of significances as above. The R2 value has shot up to 0.994653 and by using the F-test is significant. Although we seem to have dealt with the worst of the autocorrelation and heteroscedasticy, the t-ratios now seem to be insignificant. A high R2 value and few significant t-ratios is a classic indicator of multicollinearity. Multicollinearity is undesirable as it leads to large standard errors of the estimators.
Remedial measures to combat multicollinearity. The simplest model to attempt to control multicollinearity is to drop variables, we can do this confidently seeing as we have so many. The new model (now greatly cut down) is: The regression results for this model can be found in appendix (d). The results for this model look proimising. We have a high R2 value, the t-values (apart from the intercept) seem to all be significant, suggesting we have lost the problem of multicollinearity. We can accept the null hypothesis that there is no autocorreation present at the 1% level and it is tantilisingly close to being accepted at the 5% level. We can also accept the null hypothesis that there is no heteroscedasticity at both the 1% and 5% levels of significance. At last, we seem to have found a valid final model.