THE ECONOMETRICS OF MACROECONOMIC MODELLING

Evaluation of the inflation models’ properties

In this section, we summarise the statistical properties of the different infla­tion models, in order to make more formal comparisons. In Table 8.6 we have collected the p-values for the mis-specification tests for residual autocorrela­tion, autoregressive conditional heteroskedasticity, non-normality, and wrong functional form. With the exception of the normality tests which are x2(2), we report F-versions of all tests, as in the previous sections. We also report k, the number of estimated coefficients, and aAp%, the estimated standard error.

One way of condensing this information is to perform encompassing tests.[80] In Table 8.7 we consider AWM as the incumbent model, the one we want to

Mj encompasses M is tested by running the regression of the residuals from model Mj, £j, t, on the same difference (with changed sign). The simple F-test of the hypothesis that the difference has no (linear) effect is reported in the table. Following Mizon and Richard (1986) and Hendry and Richard (1989), a congruent encompassing model can account for the results obtained by rival models, and hence encompassing tests form a richer basis for model comparison than ordinary goodness-of-fit measures.

Tables 8.7 and 8.8 show results from the two encompassing tests explained above, and in addition we report a test for parsimonious encompassing. We have embraced all five models in forming their minimal nesting model, and report p-values of FEncGum tests in the fourth column of the two tables.[81] We see that only the AWM parsimoniously encompasses the general unrestricted model (GUM[82]). For all the other models we reject the corresponding set of restrictions relative to the GUM (at the 5% level). In some cases, neither of the pair of models encompasses the other. When both tests lead to rejection this is prima facie evidence that both models are mis-specified; see Ericsson (1992).