Inflation equations derived from the P*-model
The P*-model is presented in Section 8.5.4. The basic variables of the model are calculated in much the same way for Norway as for the Euro area in the previous section. Figure 8.16 shows the price gap (p — p*)t and the real money gap (rm — rm*)t along with the corresponding level series using Norwegian data. The price gap is obtained from equation (8.16) after first applying the HP filter to calculate equilibria for output (y*) and velocity (v*), respectively. As for the Euro area we have used A = 1600 to smooth the output series y* and A = 400 to smooth velocity v*. Then p* can be calculated from (8.14), as well as the price - and real money gaps. It is easily seen from the figure that (p — p*)t = —(rm — rm*)t.
The reference path for money growth A4mt is calculated in a similar way as in Section 8.5.4. Recall that if we know A4p"t, the inflation target (or reference path for inflation in the case when no explicit target exist), we can use equation (8.17), that is, A4mt = A^ + A4y* — A4v*, to calculate the corresponding reference path for money growth. The equilibrium paths for output, y*, and velocity, v*, are defined above (calculated by the HP-filter). We let the reference value for inflation vary with the actual level of smoothed inflation for the larger part of the sample period, from 1969(1) to 1995(4). The heuristic interpretation is that the monetary authorities changed the reference path according to the actual behaviour, adapting to the many shocks to inflation in this period and we calculate the reference value of inflation with a HP-filter with a large value of the parameter which penalises non-smoothness, that is, we set A = 6400 to avoid volatility in A4pt. For the period from 1996(1) to 2001(1) (end of sample)
we have set the reference value to 2% which is consistent with the actual level of inflation in this period as well as corresponding to the upper limit of inflation in the Euro area in this period. Although Norway formally followed a managed float exchange rate regime in this period, there were substantial deviations from the target exchange rate level in this period, and towards the end of the century the monetary policy regime in Norway was for all practical purposes equivalent to an inflation targeting regime with a target geared towards the Euro-area inflation target (Figure 8.17). Finally we define A4pgapt as the change in the difference between the actual inflation A4pt and the reference path A4pt, and A4mgapt is defined accordingly as A4mt — A4mt.
The basic version of the P*-model for Norway corresponds to the model we have reported in Section 8.6.3 for the Euro area. In addition to the potential effect from the real money gap (rm — rm* )t-1, we have also included lagged values of the reference money growth gap indicator, A4mgapt_ 1 (see Figure 8.18), the deviation from the reference value of inflation (inflation gap for short), A4pgapt i, and the yield spread deviation from its trend value, RBRMgapt_ 1. We also follow Gerlach and Svensson (2003) in including variables which account for temporary shocks to inflation from changes in energy prices, Apet, and output growth, Ayt. Moreover, we augment the equation with the change in household wealth (Awht) and the dummies Wdumt and Pdumt. As shown in Table 8.14 changes in energy prices and output growth come out as significant explanatory factors, while the empirical support is less convincing for the gap variables. Only the real money gap, (rm — rm*)t-1, and the inflation gap, A4pgapt_ 1, are significant at the 10% level. The real money gap has a positive effect, and the inflation gap a negative effect on inflation. When we include the gap variables in this model one at a time, only the real money gap and the inflation gap come out as significant at the 5% level. The reported
1965 1970 1975 1980 1985 1990 1995 2000
Figure 8.18. Money growth objective and gap. Norwegian data.
The P*-model for annual CPI inflation, A4pt
Aypt = + 1.2763Азр4_ і + 0.0436Apet + 0.0481Ayt_ 2 + 0.0303AuAt_ 3 (0.0191) (0.0107) (0.0109) (0.0173)
— 0.0824A4pgapt_ 1 + 0.0491rmgapt_ 1 + 0.0217 gd, pgapt_ 1
(0.0323) t і (0.0292) t і (0.0474) t і
— 0.0024A4mgapt_ 1 — 0.0202RBRMgapt_ 1 — 0.0116P dumt + 0.0006
(0.0271) (0.0548) (0.0010) (0.0010)
<7 = 0.46%
Far(i-S)(5, 113) = 2.1491[0.0647]
Farch(i-4)(4, 110) = 2.3686[0.0570] xX normality (2) = 4.9067[0.0860]
FHETx2(20, 97) = 3.7178[0.0000]**
FHETxiXj(65, 52) = 1.7848[0.0160]*
FREsET(1, 117) = 5.5016[0.0207]*
Note: The sample is 1969(1)-2001(1), quarterly data.
mis-specification tests indicate that the model only barely passes the tests for residual autocorrelation, ARCH and normality tests at a 5% significance level, but fails to meet the tests of zero heteroskedasticity and the RESET test of functional form. The findings that the money growth indicator A4mgapt_ 1 is insignificant whereas the real money gap, (rm — rm*)t-1, picks up a significant effect are in line with our results for the Euro area as well as those found in Gerlach and Svensson (2003).
The enhanced P*-model (P*_enh) for annual CPI inflation, A4pt
Aypt = + 1.0653Д3р^ і + 0.2606Apt_ 2 + 0.0496Apet (0.0259) (0.0552) (0.0087)
+ 0.0302Д2уи^_і — 0.0574Ayt_і + 0.0650 Дт(
(0.0133) (0.0137) (0.0252)
— 0.0647 (mt-і — pt-і — 0.9yt-i + 2.5(RBt-i — RMt-і))
+ 0.1234rmgapt_ 1 + 0.1373RBRMgapt_ 1 + 0.0024 CS2 (0.0178) t (0.0496) t (0.0012)
—0.0121Pdumt — 0.0033^ dumt — 0.3113 (0.0007) (0.0012) (0.0536)
a = 0.35%
Far(i-S)(5, 111) = 1.2569[0.2877]
Farch(i-4)(4, 108) = 0.7746[0.5441] x2 normality (2) = 1.8738[0.3918]
FHETx2(23, 92) = 1.6716[0.0452]*
FHETxiXj(82, 33) = 0.6567[0.9353]
FREsET(1,115) = 0.6076[0.4373]
Note: The sample is 1969(1)-2001(1), quarterly data.
As for the Euro area, we have tried to improve on the P*-model by including a wider set of variables from the other inflation models. Most importantly, we have lifted the equilibrium-correction term ecmmd from the (improved) money demand function in Section 8.4.1 (see Table 8.4) into the P*-model. The model is derived general to specific using the liberal PcGets modelling strategy and it is seen from Table 8.15 that this model which we have dubbed the enhanced P*-model (P*-enhanced for short) improves strongly on the previous P*-model: the model fits the data better, and the estimated standard error is reduced from a = 0.46% in Table 8.14 to a = 0.35%. The model is also well designed and with the exception of the Fhetx2-test it passes all the reported mis-specification tests.