THE ECONOMETRICS OF MACROECONOMIC MODELLING

Cointegration and Norwegian manufacturing wages

We analyse the annual data set for Norwegian manufacturing that was used to estimate a main-course Phillips curve in Section 4.6. We estimate a vector autoregressive model (VAR), check for mis-specification and then for coin­tegration, and discuss identification. Several of the variables were defined in Section 4.6.

The endogenous variables in the VAR are all in log scale and are denoted as follows: wct (wage cost per hour), qt (producer price index), at (average labour productivity), tut (the total rate of unemployment, that is, including labour market programmes), rprt (the replacement ratio), and we (the real-wage wedge in manufacturing). The operational measure of the wedge is defined as

wet = Pt - qt + 11t + t2t = Pq, t + t1t + t2t,

where t1 and t2 denote payroll and average income tax rates respectively. The annual sample period is 1964-98, so there are only 36 observations of the six variables. We estimate a first-order VAR, extended by four conditioning variables:

two dummies (i1967t and IPt);

the lagged inflation rate, Acpit-b;

the change in normal working hours, Aht,

all of which were discussed in Section 4.6. Table 5.1 contains the residual diagnostics for the VAR. To save space we have used * to denote a statistic which is significant at the 10% level, and ** to denote significance at the 5% level. There are only two significant mis-specification tests and both indicate heteroskedasticity in the residuals of the replacement ratio.[34]

The results of the cointegration analysis are shown in Table 5.2 which con­tains the eigenvalues and associated maximum eigenvalue (Max) and trace (Tr) statistics, which test the hypothesis of (r — 1) vs. r cointegration vectors, and r vs. less than (r — 1) cointegrating vectors, respectively. These eigenvalue tests are corrected for degree of freedom (see Doornik and Hendry 19976), and give formal evidence for one cointegrating relationship, namely

wct = mwc + 0.93qt + 1.20at — 0.0764tut + 0.0318wet + 0.11614rprt + ecmb, t,

(5.21)

when we normalise on wc, and let ecmb, t denote the I(0) equilibrium correc­tion term.

Equation (5.21) is unique, qua cointegrating relationship, but it can either represent a wage equation or a long-run price-setting schedule. Both interpreta­tions are consistent with finding long-run price homogeneity and a unit long-run elasticity of labour productivity. The joint test of these two restrictions gives X2(2) = 4.91[0.09], and a restricted cointegrating vector becomes

wct — qt — at = mwc — 0.069tut + 0.075wegt + 0.1644rprt + ecmb, t.

The real-wage wedge can be omitted from the relationship, and thus imposing ш = 0, we obtain the final estimated cointegration relationship as:

wct — qt — at = mwc — 0.065tut + 0.184rprt + ecmb, t (5.22)

and the test statistics for all three restrictions x2(3) = 5.6267[0.1313]. Equation (5.22) is the empirical counterpart to (5.11), with ш = 0 and

mb = mwc + 0.184rpr.

In simplified form, the six variable I(0) system can be written as:

which shows that there is significant evidence of equilibrium correction in wage-setting.

Interestingly, the real-wage wedge wet also appears to be endogenous. However, since wet does not enter into the cointegration relationship, its endo­geneity poses no problems for identification. A set of sufficient restrictions that establishes (5.22) as a long-run wage equation is given by the weak exogene­ity of qt, at, ut, and rprt with respect to the parameters of the cointegrating relationship (5.22). The test of the 4 restrictions gives x2(4) = 2.598[0.6272], establishing that (5.22) has been identified as a long-run wage equation.

Of particular interest is the significance (or otherwise) of the adjustment coefficients of the product price index qt and average productivity at, since the answer to that question relates to whether the causality thesis (H4mc) of Aukrust’s main-course model in Section 3.2.1 applies to the Norwegian manufacturing sector. Again, from (5.23) there is clear indication that the ecmb, t-^coefficients of Aqt and Aat are insignificant, and a test of their joint insignificance gives x2(2) = 0.8315[0.6598]. Thus, we not only find that the cointegration equation takes the form of the extended main-course equation discussed in Chapter 3, but also that deviations from the long-run relationship seem to be corrected through wage adjustments and not through prices and productivity.[35]

Visual inspection of the strength of cointegration is offered by Figure 5.2, where panel (a) shows the sequence of (largest) eigenvalues over the period 1980-98. Although the canonical correlation drops somewhat during the 1980s, it settles at a value close to 0.92 for the rest of the sample. Panels (b) and (c) show that the elasticities of the rate of unemployment and of the replacement

15.0 -
12.5

1980 1985 1990 1995 2000

Figure 5.2. Norwegian manufacturing wages, recursive cointegration results
1981-98: (a) Sequence of highest eigenvalue; (b) and (c) coefficients of
identified equation; (d) sequence of x2 test of 7 overidentifying restrictions.

ratio are stable, and significant when compared to the ±2 estimated standard errors.8 Over the period 1964-98, the joint test of all the 7 restrictions yields X2(7) = 8.2489[0.3112]. Figure 5.2 shows that we would have reached the same conclusion about no rejection on samples that end in 1986 and later.

The findings are interpretable in the light of the theories already discussed. First, equation (5.22) conforms to an extended main-course proposition that we discussed in Chapter 3: the wage share is stationary around a constant mean, conditional on the rate of unemployment and the replacement ratio. However, it is also consistent with the wage curve of Section 5.2. The elasticity of the rate of unemployment is 0.065 which is somewhat lower than the 0.1 elasticity which has come to be regarded as an empirical law following the comprehens­ive empirical documentation in Blanchflower and Oswald (1994). Finally, the exogeneity tests support the main-course model assumption about exogenous productivity and product price trends, and that wages are correcting deviation from the main course. The analysis also resolves the inconsistency that ham­pered the empirical Phillips curve system in Section 4.6, namely that there was little sign of an equilibrium correction which is necessary to keep the wage on the main course. In the cointegration model, wages are adjusting towards the main course, and the point where the Phillips curve goes wrong is exactly by [36]
insisting that we should look to unemployment for provision of the equilibrating mechanism. In Chapter 6 we develop the theoretical implication of this type of dynamics further. Specifically, in Section 6.9.2, we incorporate the long-run wage curve in (5.22) into a dynamic model of manufacturing wages and the rate of unemployment in Norway.