THE ECONOMETRICS OF MACROECONOMIC MODELLING

The stable solution of the conditional wage-price system

If the sufficient conditions in (6.18) hold, we obtain a dynamic equilibrium— the ‘tug of war’ between workers and firms reaches a stalemate. The system is stable in the sense that, if all stochastic shocks are switched-off, piq, t ^ piq, ss(t) and wq, t ^ wqss(t), where piq, ss(t) and wqss(t) denote the deterministic steady-state growth paths of the real exchange rate and the product real wage. The steady-state growth paths are independent of the historically determined initial conditions piq,° and wq,° but depend on the steady-state growth rate of import prices (gpi), of the mean of ut denoted uss, and of the expected time path of productivity:

Wq, ss (t) = i°gpi + rfu ss + ga(t - 1) - Л (6.19)

piq, ss (t) = Є0gpi + U°Uss +----- 1- '~T ga (t - 1) - d°, (6.20)

Ц1 - ф)

where ga is the drift parameter of productivity.4 The coefficients of the two steady-state paths in (6.19) and (6.20) are given by (6.21):

£° = (1 - Фqw - Фqi)/0q,

П0 = gq/6q,

5° = (Cq - 9q mf )/9q + coeff X ga,

(6.21)

e = [°q (1 - Фwq - Фwp) + dw (1 - Фqw )}/вw $q^(1 - Ф),

n (@q gw + @w gq )/@w@q ^(1 ф),

d — [^q (cw + @w mb) + @w (cq @q mf)] /@w @q ^(1 ф) + coeff X ga.

One interesting aspect of equations (6.19) and (6.20) is that they represent formalisations and generalisations of the main-course theory of Chapter 3. In the current model, domestic firms adjust their prices in response to the evolu­tion of domestic costs and foreign prices, they do not simply take world prices as given. In other words, the one-way causation of Aukrust’s model has been replaced by a wage-price spiral. The impact of this generalisation is clearly seen in (6.19) which states that the trend growth of productivity ga(t - 1) traces out a main course, not for the nominal wage level as in Figure 3.1, but for the real wage level. It is also consistent with Aukrust’s ideas that the steady state of the wage share: wsss(t) = wq, s(t) - ass(t), is without trend, that is,

wsss = £,°gpi + n°Uss - 5° (6.22)

but that it can change due to, for example, a deterministic shift in the long-run mean of the rate of unemployment.

Implicitly, the initial value ao of productivity is set to zero.

According to (6.20), the real exchange rate in general also depends on the productivity trend. Thus, if i < 1 in the long-run wage equation (5.10), the model predicts continuing depreciation in real terms. Conversely, if i = 1 the steady-state path of the real exchange rate is without a deterministic trend. Note that Sections 5.5 and 5.6 showed results for two data sets, where i = 1 appeared to be a valid parameter restriction.

Along the steady-state growth path, with Auss = 0, the two rates of change of real wages and the real exchange rate are given by:

Using these two equations, together with (6.7)

Apss = фAqss + (1 - ф)9рі,

we obtain

It is interesting to note that equation (6.23) is fully consistent with the Norwegian model of inflation of Section 3.2.2. However, the existence of a steady state was merely postulated in that section. The present analysis improves on that, since the steady state is derived from set of difference equations that includes wage bargaining theory and equilibrium correction dynamics. Equa­tions (6.24) and (6.25) show that the general solution implies a wedge between domestic and foreign inflation. However, in the case of i = 1 (wage earners benefit fully in the long term from productivity gains), we obtain the standard open economy result that the steady-state rate of inflation is equal to the rate of inflation abroad.

What does the model tell us about the status of the NAIRU? A succinct summary of the thesis is given by Layard et al. (1994): ‘Only if the real wage (W/P) desired by wage-setters is the same as that desired by price-setters will inflation be stable. And, the variable that brings about this consistency is the level of unemployment.'

Compare this to the equilibrium consisting of ut = uss, and wq, ss and piq, ss given by (6.19) and (6.20): clearly, inflation is stable, since (6.23)-(6.25) is implied, even though uss is determined ‘from outside’, and is not determined [40]
by the wage - and price-setting equations of the model. Hence, the (emphasised) second sentence in the quotation is not supported by the steady state. In other words, it is not necessary that uss corresponds to uw in equation (5.7) in Chap­ter 5 for inflation to be stable. This contradiction of the quotation occurs in spite of the model’s closeness to the ICM, that is, their wage - and price-setting schedules appear crucially in our model as cointegration relationships.

In Sections 6.5 and 6.6, we return to the NAIRU issue. We show there that both the wage curve and Phillips curve versions of the NAIRU are special cases of the model formulated above. But first, we need to discuss several important special cases of wage-price dynamics.