Comparing the forecasting properties of the models

Figure 8.15 shows graphs of 20 quarters of one-step ahead forecasts with +/- two forecast errors to indicate the forecast uncertainty for the five models we have estimated. It is difficult to tell from the diagrams by means of ‘eyeball’ econometrics whether there are any differences between them. So there is a need for formal tests: Table 8.9 provides a summary of the forecasting prop­erties of the different inflation models as it reports root mean squared forecast errors (RMSFEs) along with their decomposition into forecast error bias and standard errors. The models are re-estimated on a sample up to the start of the forecasting horizon, and then used to forecast quarterly inflation until 2000(3)...

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Forecast errors of stylised inflation models

We formulate a simple DGP to investigate the theoretical forecasting capabilities of the ICM and the PCM, thus providing a background for the interpretation of the actual forecast errors in Section 11.3.3. The variable symbols take the same meaning as in the earlier chapters on wage-price mod­elling (see Chapter 6), hence (in logs) wt is the wage rate, pt is the consumer price index, pit denotes import prices, and ut is the rate of unemployment.

In order to obtain an analytically tractable distillation of the models, we introduce simplifying assumptions. For example, we retain only one cointegrating relationship, the ‘wage-curve’, and we also abstract from productivity.[112] Thus (11.44) is a simplified version of the dynamic wage equation of Chapter 6:

A(w – p)t = к – nw [(w – p)t-i ...

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Evaluation of the system

The nature of the solution for the rate of inflation is a system property, as noted in Section 7.3. Hence, unless one is willing to accept at face value that an oper­ational definition of the forcing variable is strongly exogenous, the ‘structural’ NPCM should be evaluated within a system that also includes the forcing variable as a modelled variable.

For that purpose, Table 7.1 shows an estimated system for Euro-area infla­tion, with a separate equation (the second in the table) for treating the wage share (the forcing variable) as an endogenous variable. Note that the hybrid NPCM equation (first in the table) is similar to (7.14), and thus captures the gist of the results in GGL...

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Mainland GDP output yt

The model for Ayt is adapted from the ‘AD’ equation in Bardsen and Klovland (2000). The growth in output Ayt is in the short run a function of public demand Agt, and growth in private demand—represented by growth in real private credit Acrt. Moreover, there is an effect from the change in the real exchange rate in the period after the deregulation of currency controls in Norway in 1990(2).

Ayt = 1.16 — 0.39Ayt_ і + 0.29Agt + 0.49Acrt_ 1 (0.30) (0.07) (0.06) (0.12)

— 0.17 ecmy t + 0.41 (s ■ A(v + pw — p))t-2 + 0.07Ydumt (0.05) ’ (0.12) (0.01)

— 0.06 Seasonal^ 1 — 0.07 Seasonal^2 — 0.03 Seasonal^3 (0.003) (0.005) (0.004)


T = 1972(4)-2001(1) = 114

d = 1.21%

Far(i-5)(5, 99) = 0.84[0.53]

X2 normality (2) = 0.78[0.67]

FHETx2 (14, 89) = 0.48[0.94].

(Reference: see Table...

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Inflation models for the Euro area

In Section 8.3 we found that an inverted money demand function did not pro­vide a sound basis for explaining inflation in the Euro area. Still, there may be a case for models of inflation that conceive of inflation primarily as a monetary phenomenon. In this section, we compare and evaluate four inflation models which have been used to analyse data for the Euro area. These include the P*-model, which relates the steady-state of the price level to the quantity theory of money, a hybrid New Keynesian Phillips curve model (NPCM) of inflation (see Chapter 7) and two reduced form inflation equations: one derived from the dynamic version of the Incomplete Competition Model (ICM) we developed in Chapters 5 and 6, and the other from the wage-price block of the AWM of the European Central Bank.


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Ex post calculated interest rate rules

To get a feel for the properties and implications of the different monetary policy rules in Table 10.1, we have calculated ex post interest rates corresponding to the different rules, by inserting the actual outcomes of the variables into the various versions of equation (10.1). The results are shown in the four charts in Figure 10.3. The upper left panel shows the realised interest rate together with the implied interest rate of following the flexible rule FLX. Following the rule would have meant a much higher interest rate during 1997, as a consequence of the spurt in output growth, shown in Figure 10.2(b). The strict rule ST of the upper right panel is basically reflecting the development of underly­ing inflation of Figure 10.2(a), while the smoothing rule SM appears more

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