THE ECONOMETRICS OF MACROECONOMIC MODELLING

Nominal rigidity and equilibrium correction

The understanding that conflict is an important aspect to take into account when modelling inflation in industrialised economies goes back at least to Rowthorn (1977), and has appeared frequently in models of the wage-price spiral; see, for example, Blanchard (1987).[37] In Rowthorn’s formulation, a dis­tinction is drawn between the negotiated profit share and the target profit share. If these shares are identical, there is no conflict between the two levels of decision-making (wage bargaining and firm’s unilateral pricing policy), and no inflation impetus.[38] But if they are different, there is conflict and inflation results as firms adjust prices unilaterally to adjust to their target. In the model presented later, not only prices but also wages are allowed to change between two (central) bargaining rounds. This adds realism to the model, since even in countries like Norway and Sweden, with strong traditions for centralised wage settlements, wage increases that are locally determined regularly end up with accounting for a significant share of the total annual wage growth (i. e. so-called wage drift, see Rpdseth and Holden 1990 and Holden 1990).

The model is also closely related to Sargan (1964, 1980), in that the dif­ference equations are written in equilibrium correction form, with nominal wage and price changes reacting to past disequilibria in wage formation and in price-setting. In correspondence with the previous chapter, we assume that wages, prices, and productivity are I(1) variables, and that equations (5.11) and (5.14) are two cointegrating relationships. Cointegration implies equilibrium correction, so we specify the following equations for wage and price growth:

Awt = 0W (wq, t-1 wq, t-1) + ^wp^Pt + фwqAqt yut-1 + cw + &w, t:

0 < фwp + 'Фwq < 1, У > 0, 9w > 0 (6.1)

and

Aqt = -6q (Wft-1 - Wq, t-1) + фqwAwt + — ЯЩ-1 + Cq + £q, t,

0 < Фqw + Фчі < 1, 0 < 0q, q > 0, (6.2)

where £w, t and £q, t are assumed to be uncorrelated white noise processes. The expressions for wq t-1 and wft-1 were established in Chapter 5, and they are repeated here for convenience:

wq t = mq + iat + upq, t — wut, 0 < i < 1, 0 < ш < 1, w > 0,

wf t = mf + at + dut, d > 0,

that is, (5.10) for wage bargaining, and (5.13) based on modified nor­

mal cost pricing. In Rowthorn’s terminology, the negotiated profit share is (1 — wq t — at), while the target profit share is (1 — wf t — at).

For the wage side of the inflation process, equations (5.10) and (6.1) yield

Awt = kw + ФwpApt + Фwq Aqt — gw Ut-1

+ 9w шpq, t-1 9w wq, t-1 + 9w lat-1 + £w, t, (6.3)

where kw = (cw + 9wmq). In equation (6.3), the coefficient of the rate of unemployment gw, is defined by

gw = 9ww (when 9w > 0) or gw = у (when 9w = 0), (6.4)

which may seem cumbersome at first sight, but is required to secure inter­nal consistency: note that if the nominal wage rate is adjusting towards the long-run wage curve, 9w < 0, logic requires that the value of у in (6.1) is zero, since ut-1 is already contained in the equation, with coefficient 9ww. Conversely, if 9w = 0, it is nevertheless possible that there is a wage Phillips curve relationship, hence gw = у > 0 in this case. In equation (6.3), long - run price homogeneity is ensured by the two lagged level terms—the wedge Pq, t-1 = (p — q)t-1 and the real wage wq, t-1 = (w — q)t-1.

For producer prices, equations (5.13) and (6.2) yield a dynamic equation of the cost markup type:

Aqt = kq + фqwAwt + Ф q%Ap%t — gq Щ-1 + 9q wq, t-1 — 9q a-1 + £q, t, (6.5)

where kq = (cq — 9qmf) and

gq = 9q d or gq = q. (6.6)

The definition of gq reflects exactly the same considerations as explained above for wage-setting.

In terms of economic interpretation (6.3) and (6.5) are consistent with wage and price staggering and lack of synchronisation among firms’ price-setting (see, for example, Andersen 1994, ch. 7). An underlying assumption is that firms preset nominal prices prior to the period and then within the period meet the demand forthcoming at this price (which exceeds marginal costs, as in Chapter 5). Clearly, the long-run price homogeneity embedded in (6.3) is joined by long-run homogeneity with respect to wage costs in (6.5). Thus we have overall long-term nominal homogeneity as a direct consequence of specifying the cointegrating relationships in terms of relative prices.[39]

In static models, nominal homogeneity is synonymous with neutrality of output to changes in nominal variables since relative prices are unaffected (see Andersen 1994). This property does not carry over to the dynamic wage and price system, since relative prices (e. g. wq, t) will be affected for several periods following a shift in, for example, the price of imports. In general, the model implies nominal rigidity along with long-term nominal homogeneity. Thus, care must also be taken when writing down the conditions that eventually remove short-run nominal rigidity from the system. Specifically, the conditions for ‘dynamic homogeneity’, that is, фwp + фwq = 1 and фqw + фф = 1, do not eliminate nominal rigidity as an implied property; see Section 6.4.2. As will become clear, there is a one-to-one relationship between nominal neutrality and the natural rate property, and a set of sufficient conditions are given in Section 6.5. First however, Section 6.3 defines the asymptotically stable solu­tion of the system with long-term homogeneity (but without neutrality) and Section 6.4 discusses some important implications.