THE ECONOMETRICS OF MACROECONOMIC MODELLING
A main-course interpretation
In Chapter 3 we saw that an important assumption of Aukrust’s main-course model is that the wage-share is I(0), and that causation is one way: it is only the exposed sector wage that corrects deviations from the equilibrium wage share. Moreover, as maintained throughout this chapter, the reconstructed Aukrust model had productivity and the product price as exogenous I(1) processes.
The following two equations, representing wage-setting in the exposed sector, bring these ideas into our current model:
wbq t _ ть + at — wut, 0 < 1 < 1, w > 0, (6.31)
and
Awt @w (wq, t— 1 wq, t-1) + фwpApt + ФwqAqt + cw + ^w, t,
0 < Фwp + Фwq < 1, 9w > 0. (6.32)
In Section 3.2 we referred to (6.31) as the extended main-course hypothesis. It is derived from (5.10) by setting ш _ 0, since in Aukrust’s theory, there is no role for long-run wedge effects, and in the long run there is full pass-through from productivity on wages, 1 _ 1. Equation (6.32) represents wage dynamics in the exposed industry and is derived from (6.1) by setting <p = 0 (since by assumption 9w > 0). Note that we include the rate of change in the consumer price index (CPI) Apt, as an example of a factor that can cause wages to deviate temporarily from the main course (i. e. domestic demand pressure, or a rise in indirect taxation that lead to a sharp rise in the domestic costs of living).
The remaining assumptions of the main-course theory, namely that the sheltered industries are wage followers, and that prices are marked up on normal costs, can be represented by using a more elaborate definition of the CPI than in (6.7), namely
Apt = фlAqt + ф^2(Awt - Aat) + (1 - фі - ф^2)Apit, (6.33)
where фі and ф2 are the weights of the products of the two domestic industries in the log of the CPI. The term ф2Awt amalgamates two assumptions: followership in the sheltered sector’s wage formation and normal cost pricing.
The three equations (6.31)-(6.33) imply a stable difference equation for the product real wage in the exposed industry. Equations (6.31) and (6.32) give
Awt = kw + ФwpApt + ФwqAqt - 6W [wq, t-i - a-i + шщ-і] + £w, t, (6.34)
and when (6.33) is used to substitute Apt, the equilibrium correction equation for wqt can be written as
Awq, t = kw + (VWq 1)Aqt + ^PwpiApit ^PwpaAat
- kw [wq, t-i - at-1 + wut-i + £w, t, (6.35)
with coefficients
kw kw/(1 Фwpфl'),
Фwq (^wq + Фwpф1)/ (1 Фwpф1),
Фwpi Фwpф2/(1 Фwpфl'),
Фwpi Фwp (1 ф1 ф2 ) / (1 Фwpф1) ,
@w @w/(1 Фwpфl'),
and disturbance £w, t = £w, t/(1 - ф^фі).
In the same manner as before, we define the steady state as a hypothetical situation where all shocks have been switched off. From equation (6.35), and assuming dynamic homogeneity for simplicity, the steady-state growth path becomes
wq, ss(t) kw, ss шиБв + 9a(t 1) + a0, (6.36)
where kw, ss = {kw + (фwpф2 - 1)qa}/9w. This steady-state solution contains the same productivity trend as the unrestricted steady-state equation (6.19), but there is a notable difference in that the long-run multiplier is - ш, the slope coefficient of the wage curve.
In Section 6.9.2 we estimate an empirical model for the Norwegian manufacturing industry which corresponds closely to equations (6.31)-(6.33).
