Appendix B:  Diagnostic tests

This appendix presents the results of the various diagnostic tests of the short-run error correction models in more detail.

Table A1 below presents the pairwise correlation matrix between the contemporaneous variables contained in the initial and parsimonious ECMs. The correlations do not appear too strong, with the strongest between the change in the unemployment rate and income growth at –0.48. This suggests that there is no presence of strong multicollinearity in the EMCs. The pairwise correlation matrix was also done for all the lagged variables (not reported), with a similar conclusion.

The results for the test for normality using the Jarque-Bera method is presented in Table A2 below. In all cases, the Jarque-Bera statistic was not significant, indicating that the residuals from the ECMs are normally distributed.

The presence of redundant variables was tested only for the parsimonious ECMs, with the F-statistics presented in Table A3 below (the null hypothesis being that the variable tested is redundant). In both parsimonious ECMs, a number of redundant variables are present. However, in most cases the variables are included in the models to preserve the lag structure in order to adequately model the dynamic effects. While inclusion of redundant variables will mean that the estimated coefficients are inefficient, the estimates themselves remain unbiased and consistent.

Note: Reported values above are F -statistics.

** Reject null hypothesis that variable is redundant at the 1% level.

* Reject null hypothesis that variable is redundant at the 5% level.

^ Reject null hypothesis that variable is redundant at the 10% level.

Ramsey’s Reset test against a quadratic form was used to test for mis-specification error in the ECMs, with the results presented in Table A4. At both the 1% and 5% levels, the null hypothesis of mis-specification can be rejected for all the models. However, mis-specification cannot be rejected at the 10% level for the parsimonious ECM (B).

Note: Estimated based on 2 fitted values.

^ Cannot reject null hypothesis that model is mis-specified at the 10% level.

The Chow test was used to look for evidence of structural breaks over the estimated period of the models. Due to insufficient observations, the Chow test could not be applied to the initial ECMs. Based on the residual plot in Figures 1 and 2, the most likely point for a structural break in the parsimonious ECMs could be in 1998, the period where the models consistently under-estimated the actuals. Table A5 below presents the F-statistics from the Chow test for each quarter of 1998. The null hypothesis of no structural break cannot be rejected over the entire 1998 period. For completeness, the Chow test was carried out over every quarter of 1996 and 1997 (not reported). In all cases, there was no evidence of a structural break.

Note: Reported values above are F-statistics. The initial equations have insufficient observations to carry out the Chow test.

To test for the presence of serial correlation, the Breush-Godfrey Lagrange multiplier test was used, with the F-statistics from the test reported in Table A6 below. The null hypothesis is that there is no serial correlation in the residuals. The result of the Breush-Godfrey test suggests that serial correlation is not present up to order four.

Note: Reported values above are F-statistics.