THE ECONOMETRICS OF MACROECONOMIC MODELLING

An encompassing representation

The main alternatives to the NPCM as models of inflation are the Standard Phillips Curve Model (PCM) and the Incomplete Competition Model (ICM). They will therefore be important in suggesting ways of evaluating the NPCM from an encompassing perspective. To illustrate the main differences between alternative specifications, consider the following stylised framework—see also Bardsen et al. (2002a). Let w be wages and p consumer prices; with a as productivity, the wage share ws is given as real unit labour costs: ws = ulc — p = w — a —p; u is the unemployment rate, and gap the output gap, all measured in logs. We abstract from other forcing variables, like open economy aspects. A model of the wage-price process general enough for the present purpose then takes the form

Aw = aApe — fiws — yu,

Ap = S Ape + Z Aw + pws + figap,

where Ape is expected inflation, and the dynamics are to be specified separately for each model. Although the structure is very simple, the different models drop out as non-nested special cases:

1. The NPCM is given as

Apt = Sf Apl+l + SAp—i + mwst,

where the expectations term Ap(e+1 is assumed to obey rational expectations.

9 For example, in the Abstract of GGL the authors state that ‘the NPC fits Euro data very well, possibly better than United States data’. Also Gall (2003), responding to critical assessments of the NPCM, states that ‘it appears to fit the data much better than had been concluded by the earlier literature’.

2. The PCM is—Aukrust (1977), Calmfors (1977), Nymoen (1990), Blanchard and Katz (1997):

Awt = a^Apt - Y2Ut Apt = Z2 Awt + -&2gap t.

3. The ICM on equilibrium correction form—Sargan (1964), Layard et al. (1991), Bardsen et al. (1998), and Kolsrud and Nymoen (1998):

Awt = a3Apt - p3(ws - 72«)t-i

Apt = OiAwt - 6І[p - rn(ws + p)]t-i + fi3ga, Pt-i.

Of course, there exist a host of other, more elaborate, models—a notable omis­sion being non-linear PCMs. However, the purpose here is to highlight that discrimination between the models is possible through testable restrictions. The difference between the two Phillips curve models is that the NPCM has forward-looking expectations and has real unit labour costs, rather than the output gap of the PCM. In the present framework, the ICM differs mainly from the NPCM in the treatment of expectations and from the PCM in the latter’s exclusion of equilibrium correction mechanisms that are derived from conflict models of inflation; see Rowthorn (1977), Sargan (1980), Kolsrud and Nymoen (1998), Bardsen and Nymoen (2003) and Chapter 6. To see this, note that the NPCM can, trivially, be reparameterised as a forward-looking equilibrium-correction model (EqCM) with long-run coefficient restricted to unity:

Apt = 5{Apet+i + niAwst + SbiApt-i - ni[p - 1(ws + p)]t-i.

The models listed in 1-3 are identified, in principle, but it is an open question whether data and methodology are able to discriminate between them on a given data set. We therefore test the various identifying restrictions. This will involve testing against

• richer dynamics

• system representations

• encompassing restrictions.

We next demonstrate these three approaches in practice.