Empirical evidence from Euro-area data
In this section, we present estimated reduced form versions of the AWM and ICM inflation equations in order to evaluate the models and to compare forecasts based on these equations with forecasts from the inflation models referred to in Section 8.5, that is, the P*-model and the NPCM. The models are estimated on a common sample covering 1972(4)-2000(3), and they are presented in turn below, whereas data sources and variable definitions are found in Jansen (2004).
We establish the reduced form inflation equation from the AWM by combining the wage and price equations of the AWM (see appendix B of Jansen 2004). The reduced form of the equation is modelled from general to specific: we start out with a fairly general information set which includes the variables of the wage and price block of the AWM: three lags of inflation, Apt, as well as of changes in trend unit labour costs, Aulct, and two lags of the changes in: the wage share, Awst, the world commodity price index, Ap)aw; the GDP deflator at factor prices, Aqt, unemployment, Aut, productivity, Aat, import prices, Apit, and indirect taxes, At3t. The output gap is included with lagged level (gapt_ 1) and change (Agapt_ 1). The dummies from the wage and price block of AWM, AI82.1, AI82.1, 192.4,177.4178.1, 181.1, and AI84.2, are included and a set of centred seasonal dummies (to mop up remaining seasonality in the data, if any). Finally, we include into the reduced form information set two equilibrium-correction terms from the structural price and wage equations, ecmpAWM and ecmwAWM, defined in Section 8.5.1.
The parsimonious reduced form AWM inflation equation becomes:
Apt = 0.077 + 0.19Apt_ з + 0.08Aulct_ 1 + 0.34Aqt_ 1
(0.017) (0.06) (0.05) (0.08)
- 0.07Aat_2 + 0.07Apit_ 1 + 0.82Af3t_ 1 (0.04) (0.01) (0.28)
— 0.051 ecmpAW1M — 0.01 ecmwAW, M + dummies (0.011) t 1 (0.0015) t 1
Far(i-S)(5, 94) = 0.41[0.84] Farch(i-4)(4, 91) = 0.43[0.78] X2normaiity(2) = 1.01[0.60] Fhetx? (23, 75) = 1.35[0.17]
Freset(1, 98) = 0.06[0.80]
All restrictions imposed on the general model leading to (8.18), are accepted by the data, both sequentially and when tested together. We note that the effects of the explanatory variables are much in line with the structural equations reported in appendix B in Jansen (2004) and that both equilibrium - correction terms are highly significant. If we deduct the respective means of the equilibrium-correction terms on the right-hand side, the constant term reduces to 0.5%, which is significantly different from zero with a t-value of 5.36. The fit is poorer than for the structural inflation equation, which is mainly due to the exclusion of contemporary variables in the reduced form. If we include contemporary values of Apit, Aat, and Ap)aw, the standard error of the equation improves by 30% and a value close to the estimated a of the inflation equation in appendix B in Jansen (2004) obtains. Figure 8.6 contains recursive estimates of the model’s coefficients. We note that there is a slight instability in the adjustment speed for the two equilibrium terms in the period 1994-96.