The NPCM in Norway
Consider the NPCM (with forward term only) estimated on quarterly Norwegian data:
Apt = 1.06 Apt+1 + 0.01 wst + 0.04 Apit + dummies (7.21)
(0.11) (0.02) (0.02)
x2(10) = 11.93[0.29].
The closed economy specification has been augmented heuristically with import price growth (Apit) and dummies for seasonal effects as well as special events in the economy described in Bardsen et al. (2002b). Estimation is by GMM for the period 1972(4)-2001(1). The instruments used (i. e. the variables in z1) are lagged wage growth (Awt-1, Awt-2), lagged inflation (Apt-1, Apt-2), lags of level and change in unemployment (ut-1, Aut-1, Aut-2), and changes in
Figure 7.2. Rolling coefficients ±2 standard errors of the NPCM, estimated on Norwegian data ending in 1993(4)-2000(4). Graph (a) shows the coefficient of wst and graph (b) shows the coefficient of Apt+1.
energy prices (Apet, Apet-1), the short term interest rate (ARLt, ARLt-1), and the length of the working day (Aht).
The coefficient estimates are similar to GG. Strictly speaking, the coefficient of E[Apt+i I It] suggests that a backward solution is appropriate. But more importantly the estimated NPCM once more appears to be a modified random walk model. We also checked the stability of the key parameters of the model by rolling regressions with a fixed window of 85 observations. Figure 7.2 shows that the sample dependency is quite pronounced in the case of Norway.
Next, we define an equilibrium correction term from the results in Bardsen et al. (2003) and use that variable as the additional instrument, z2,t:
ecmpt = pt – 0.6(wt – at + т 1t) – 0.4pq + 0.5т3t.
The results, using GMM, are
Apt = -0.02 Apt+1 + 0.04 wst – 0.06 Apit – 0.10 ecmpt_ i
(0.125) (0.025) (0.017) (0.020)
Xj(10) = 12.78[0.24],
showing that the implication of the NPCM is refuted by the finding of (1) a highly significant (price) equilibrium correction term defined by an existing study, and (2) the change in the estimated coefficient of Apt+1, from 1.06 and statistical significance, to -0.02 and no statistical significance.
Earlier researchers of the NPCM have concluded that the NPCM represents valuable insight into the driving forces of inflation dynamics. Our evaluation gives completely different results. In particular we show that by including variables from the list of instruments as explanatory variables, a statistically adequate model for the Euro area is obtained. In this respecified model, the forward term vanishes, and the Euro area ‘inflation equation’ can be reinterpreted as a conventional price markup equation. Encompassing implies that a model should be able to explain the results of alternative specifications. In many countries, empirical inflation dynamics is a well researched area, so studies exist that any new model should be evaluated against. Applying the encompassing principle to the NPCM models of United Kingdom inflation as well as Norwegian inflation, leaves no room for the NPCM. The conclusion is that economists should not accept the NPCM too readily.
On the constructive side, our analysis shows that the NPCM can be seen as an equilibrium-correction model augmented by a forward term. This means that although our conclusion refutes the NPCM hypothesis as presently implemented, this does not preclude that forward expectations terms could be found to play a role in explaining inflation dynamics within statistically well-specified models, using the procedures for testing forward terms.