THE ECONOMETRICS OF MACROECONOMIC MODELLING

# Cointegration

Equation (3.1) captures the price taking behaviour characterising the exposed industries, and (3.2)-(3.3) define foreign prices of traded goods (pft) and labour productivity as random walks with drifts. Equation (3.4) serves a double function: first, it defines the exposed sector wage share we, t - qe, t - ae, t as a stationary variable since v4,t on the right-hand side is I(0) by assumption; second, since both qe, t and ae, t are I(1) variables, the nominal wage we, t is also non-stationary I (1).

The sum of the technology trend and the foreign prices plays an important role in the theory since it traces out a central tendency or long-run sustainable scope for wage growth. Aukrust (1977) refers to this as the main course for wages in the exposed industries. Thus, for later use, we define the main-course variable: mct = ae, t + qe, t. The essence of the statistical interpretation of the theory is captured by the assumption that v1>t is ARMA, and thus I(0).

It follows that we, t and mct are cointegrated, that the difference between we, t and mct has a finite variance, and that deviations from the main course will lead to equilibrium correction in we t (see Nymoen 1989a and Rpdseth and Holden 1990).

Hypothetically, if shocks were switched off from period 0 onwards, the wage level would follow the deterministic function

E[we, t I mco ]= me + (gf + sv )t + mc0, mc0 = pf0 + ae, o, (t = 1, 2,...).

(3.9)

The variance of we t is unbounded, reflecting the stochastic trends in productivity and foreign prices, thus we, t ~ I(1).

In his 1977 paper, Aukrust identifies the ‘controlling mechanism’ in equation (3.4) as fundamental to his theory:

The profitability of the E industries is a key factor in determining the wage level of the E industries: mechanism are assumed to exist which ensure that the higher the profitability of the E industries, the higher their wage level; there will be a tendency of wages in the E industries to adjust so as to leave actual profits within the E industries close to a ‘normal’ level (for which, however, there is no formal definition). (Aukrust 1977, p. 113)

In our reconstruction of the theory, the normal rate of profit is simply 1 — me. Aukrust also carefully states the long-term nature of his hypothesised relationship:

The relationship between the ‘profitability of E industries’ and the ‘wage level of E industries’ that the model postulates, therefore, is certainly not a relation that holds on a year-to-year basis. At best it is valid as a long-term tendency and even so only with considerable slack. It is equally obvious, however, that the wage level in the E industries is not completely free to assume any value irrespective of what happens to profits in these industries. Indeed, if the actual profits in the E industries deviate much from normal profits, it must be expected that sooner or later forces will be set in motion that will close the gap. (Aukrust 1977, pp. 114-15)

Aukrust goes on to specify ‘three corrective mechanisms’, namely wage negotiations, market forces (wage drift, demand pressure) and economic policy. If we in these quotations substitute ‘considerable slack’ with ‘vi, t being autocorrel - ated but I(0)’, and ‘adjustment’ and ‘corrective mechanism’ with ‘equilibrium correction’, it is seen how well the concepts of cointegration and equilibrium correction match the gist of Aukrust’s original formulation. Conversely, the use of growth rates rather than levels, which became common in both text book expositions of the theory and in econometric work claiming to test it (see Section 3.2.3) misses the crucial point about a low frequency, longterm relationship between foreign prices, productivity, and exposed sector wage-setting.

Aukrust coined the term ‘wage corridor’ to represent the development of wages through time and used a graph similar to Figure 3.1 to illustrate his ideas. The main course defined by equation (3.9) is drawn as a straight line since the wage is measured in logarithmic scale. The two dotted lines represent

Figure 3.1. The ‘wage corridor’ in the Norwegian model of inflation |

what Aukrust called the ‘elastic borders of the wage corridor’. In econometric terminology, the vertical distance between the lines represents a confidence interval, for example, E[wtmco] ±2 standard errors, where the standard errors are conditional on an initial value mc0. The unconditional variance does not exist, so the wage corridor widens up as we move away from mc0.

Equation (3.5) incorporates two other substantive hypotheses in the Norwegian model of inflation: stationarity of the relative wage between the two sectors (normalised to unity), and wage leadership of the exposed sector. Thus, the sheltered sector is a wage follower, with exposed sector wage determinants also in effect shaping sheltered sector wage development.

Equation (3.6) allows a separate trend in labour productivity in the sheltered sector and equation (3.7) contains the stationarity hypothesis of the sheltered sector wages share. Given the nature of wage-setting and the exogenous technology trend, equation (3.7) implies that sheltered sector price-setters mark up their prices on average variable costs. Thus sheltered sector price formation adheres to so-called normal cost pricing.

To summarise, the three cointegration propositions of the reconstructed main-course model are:

H1mc we, t - qe, t - ae, t = me + U4,t, U4,t ~ I(0),

H2mc We, t = Ws, t + v5}t, v5}t ~ I(0),

H3mc Ws, t - qs, t - as, t = ms + v7,t, vr, t ~ I(0).

H1mc states that the exposed sector wage level cointegrates with the sectorial price and productivity levels, with unit coefficients and for a constant mean of the wage share, me. However, the institutional arrangements surrounding wage-setting change over time, so heuristically me may be time dependent. For example, bargaining power and unemployment insurance systems are not constant factors but evolve over time, sometimes abruptly too. In his 1977 paper, Aukrust himself noted that the assumption of a completely constant mean wage share over long time spans was probably not tenable. However, no internal inconsistency is caused by replacing the assumption of unconditionally stationary wage shares with the weaker assumption of conditional stationarity. Thus, we consider in the following an extended main-course model where the mean of the wage share is a linear function of exogenous I(0) variables and of deterministic terms.

For example, a plausible generalisation of H 1mc is represented by

H1gmc we, t qe, t ae, t = me,0 + fte,1 ut + [^e,2Dt + u4,t:

where ut is the log of the rate of unemployment and Dt is a dummy (vector) that along with ut help explain shifts in the mean of the wage share, thus in H1gmc, me,0 denotes the mean of the cointegration relationship, rather than of the wage share itself. Consistency with the main-course theory requires that the rate of unemployment is interpreted as I (0), but not necessarily stationary, since ut may in turn be subject to changes in its mean, that is, structural breaks. Graphically, the main course in Figure 3.1 is no longer necessarily a straight unbroken line (unless the rate of unemployment and Dt stay constant for the whole time period considered).

Other candidate variables for inclusion in an extended main-course hypothesis are the ratio between unemployment insurance payments and earnings (the so-called replacement ratio) and variables that represent unemployment composition effects (unemployment duration, the share of labour market programmes in total unemployment); see Nickell (1987), Calmfors and Forslund (1991). In Section 3.5 we shall see that in this extended form, the cointegration relationship implied by the main-course model is fully consistent with modern wage bargaining theory.

Following the influence of trade union and bargaining theory, it has also become popular to estimate real-wage equations that include a so-called wedge between real wages and the consumer real wage, that is, pt — qe, t in the present framework. However, inclusion of a wedge variable in the cointegrating wage equation of an exposed sector is inconsistent with the main-course hypothesis, and finding such an effect empirically may be regarded as evidence against the framework. On the other hand, there is nothing in the main-course theory that rules out substantive short-run influences of the CPI, that is, of Apt in a dynamic wage equation. In Chapter 6 we analyse a model that contains this form of realistic short-run dynamics.

The other two cointegration propositions (H2mc and H3mc) in Aukrust’s model have not received nearly as much attention as H1mc in empirical research, but exceptions include Rpdseth and Holden (1990) and Nymoen (1991). In part, this is due to lack of high quality wage and productivity data for the private service and retail trade sectors. Another reason is that both economists and policy makers in the industrialised countries place most emphasis on understanding and evaluating wage-setting in manufacturing, because of its continuing importance for the overall economic performance.