THE ECONOMETRICS OF MACROECONOMIC MODELLING

Wage-price dynamics: Norwegian manufacturing

In this section, we return to the manufacturing data set of Section 4.6 (Phillips curve), and 5.5 (wage curve). In particular, we recapitulate the cointegration analysis of Section 5.5:

1. A long-run wage equation for the Norwegian manufacturing industry:

wct — qt — at = — 0.065 tut + 0.184 rprt + ecmw t, (6.58)

(0.081) (0.036)

that is, equation (5.22). rprt is the log of the replacement ratio.

2. No wedge term in the wage curve cointegration relationship (i. e. ш = 0).

3. Nominal wages equilibrium correct, 6w > 0.

4. Weak exogeneity of qt, at, tut, and rprt with respect to the parameters of the cointegration relationship.

These results suggest a ‘main-course’ version of the system (6.51)-(6.57): as shown in Section 6.4.4, the no-wedge restriction together with one-way causality from product prices (qt) and productivity (at) on to wages imply a dynamic wage equation of the form

Awt = kw + фwpApt + фwq Aqt — 9w [wq, t-i — at-1 + шщ_і] + £w, t,

(6.59)

(cf. equation (6.34)). The term in square brackets has its empirical counterpart

in ecmw, t.

Given items 1-3, our theory implies that the real exchange rate is dynam­ically unstable (even when we control for productivity). This has further implications for the unemployment equation in the system: since there are three I(1) variables on the right-hand side of (6.53), and two of them cointe­grate (wq t and at), the principle of balanced equations implies that [3u4 = 0. However, the exogeneity of the rate of unemployment (item 4) does not neces­sarily carry over from the analysis in Section 5.5, since zut in equation (6.53) includes I(0) conditioning variables. From the empirical Phillips curve system in Section 4.6, the main factor in zut is the GDP growth rate (Aygdpjt-1).

We first give the details of the econometric equilibrium-correction equation for wages, and then give FIML estimation of the complete system, using a slightly extended information set.

Equation (6.60) gives the result of a wage generalised unrestricted model (GUM) which uses ecmw, t defined in item 1 as a lagged regressor.

Awt = — 0.183 — 0.438 ecmt-1 + 0.136 At1t + 0.0477Apt (0.0349) (0.0795) (0.387) (0.116)

+ 0.401 Apt_ 1 + 0.0325 Apt_2 + 0.0858Aat + 0.0179 Aat_ 1 (0.115) (0.114) (0.102) (0.0917)

— 0.0141 Aat_2 + 0.299 Aqt + 0.0209 Aqt_ 1 — 0.000985Aqt_2 (0.0897) (0.0632) (0.0818) (0.0665)

— 0.738 Aht — 0.0106 Atut + 0.0305 *1967t — 0.0538 IPt (0.185) (0.00843) (0.0128) (0.00789)

(6.60)

It is interesting to compare equation (6.60) with the Phillips curve GUM for the same data; cf. equation (4.42) of Section 4.6. In (6.60) we have omitted the second lag of the price and productivity growth rates, and the levels of tut-1 and rprt-1 are contained in ecmwt-1, but in other respects the two GUMs are identical. The residual standard error is down from 1.3% (Phillips curve) to 0.89% (wage curve). To a large extent the improved fit is due to the inclusion of ecmt-1, reflecting that the Phillips curve restriction 9w = 0 is firmly rejected by the t-test.

The mis-specification tests show some indication of (negative) autoregressive residual autocorrelation, which may suggest overfitting of the GUM, and which no longer represents a problem in the final model shown in equation (6.61):

Awt = — 0.197 — 0.478 ecmw t_ 1 + 0.413 Apt_ 1 + 0.333 Aqt (0.0143) (0.0293) (0.0535) (0.0449)

— 0.835 Aht + 0.0291 U967t — 0.0582 IPt (0.129) (0.00823) (0.00561)

(6.61)

The estimated residual standard error is lower than in the GUM, and by FpGUM, the final model formally encompasses the GUM in equation (6.60). The model in (6.61) shows close correspondence with the theoretical (6.32) in Section 6.4.4, with 6w =0.48 (t§ =16.3), and tpwp + rtpwq = 0.75, which is significantly different from one (F(1, 27) = 22.17[0.0001]).

As already said, the highly significant equilibrium-correction term is evid­ence against the Phillips curve equation (4.43) in Section 4.6 as a congruent model of manufacturing industry wage growth. One objection to this con­clusion is that the Phillips curve is ruled out from the outset in the current specification search, that is, since it is not nested in the equilibrium-correction models (EqCM-GUM). However, we can rectify that by first forming the union model of (6.61) and (4.43), and next do a specification search from that starting point. The results show that PcGets again picks equation (6.61), which thus encompasses also the wage Phillips curve of Section 4.6.

Figure 6.5 shows the stability of equation (6.61) over the period 1978-94. All graphs show a high degree of stability. The two regressors (Apt-1 and Aqt) that also appear in the Phillips curve specification in Section 4.6 have much

Table 6.3

FIML results for a model of Norwegian manufacturing wages, inflation,
and total rate of unemployment

Awct = — 0.1846 — 0.4351ecmw t_ 1 + 0.5104Apt_ 1 + 0.2749 Aqt (0.016) (0.0352) (0.0606) (0.0517)

— 0.7122 Aht + 0.03173 i1967t — 0.05531 IPt + 0.2043Ay„dp t_ 1 (0.135) (0.00873) (0.00633) (0.104)

Atut = — 0.2319 tut_1 — 8.363 Aygdpt-1 + 1.21 ecmw t_ 1 (0.0459) (1.52) (0.338)

+ 0.4679 i1989t — 2.025 A2pit (0.148) (0.468)

Apt = 0.01185 + 0.1729 Awt — 0.1729Aat — 0.1729Aqt_ 1 + 0.3778 Apt_ 1 (0.00419) (0.0442) (—) (—) (0.0864)

+ 0.2214 A2pit — 0.4682 Aht + 0.04144 i1970t (0.0325) (0.174) (0.0115)

ecmw, t = ecmw, t-1 + Awct — Aqt — Aat + 0.065Atut — 0.184Arprt

tut — tut-1 + Atut-1,

Note: The sample is 1964-98, T = 35 observations. &Aw = 0.00864946 o~Atu = 0.130016 aAp = 0.0110348 Far(1-2)(18, 59) = 0.65894[0.84]

X20;maiity(6) = 4.5824[0.60] x2vendentfication(32) = 47.755[0.04].

narrower confidence bands in this figure than in Figure 4.2. In sum, the single­equation results are in line with earlier ‘equilibrium correction’ modelling of Norwegian manufacturing wages; see, for example, Nymoen (1989a). In partic­ular, Johansen (1995a) who analyses annual data, contains results that are in agreement with our findings: he finds no evidence of a wedge effect but reports a strong wage response to consumer price growth as well as to changes in the product price.

Thus, the results imply that neither the Phillips curve, nor the wage-curve NAIRU, represent valid models of the unemployment steady-state in Norway. Instead, we expect that the unemployment equilibrium depends on forcing variables in the unemployment equation of the larger system (6.51)-(6.57). The estimated version of the model is shown in Table 6.3, with coefficients estimated by FIML.

It is interesting to compare this model to the Phillips curve system in Table 4.2 of Section 4.6. For that purpose we estimate the model on the sample 1964-98, although that means that compared to the single equation results for wages just described, one year is added at the start of the sample. Another, change from the single equation results is in Table 6.3: the wage equation in augmented by Aygdp, t-i, that is, the lagged GDP growth rate. This variable was included in the information set because of its anticipated role the equa­tion for unemployment. Finding it to be marginally significant also in the wage equation creates no inconsistencies, especially since it appears to be practically orthogonal to the explanatory variables that were included in the information set of the single equation PcGets modelling.

The second equation in Table 6.3 is similar to (6.53) in the empirical Phillips curve system estimated on this data set in Section 4.6. However, due to coin­tegration, the feedback from wages on unemployment is captured by ecmwt-1, thus there are cross-equation restrictions between the parameters in the wage and unemployment equations. The third equation in the table is consistent with the theoretical inflation equation (6.33) derived in Section 6.4.4.[53]

The model is completed by the two identities, first for ecmw, t which incorp­orates the cointegrating wage-curve relationship, and second, the identity for the rate of unemployment. The three non-trivial roots of the characteristic equation are

0.6839 0 0.6839

0.5969 0.1900 0.6264

0.5969 -0.1900 0.6264

that is, a complex pair, and a real root at 0.68. Hence the system is dynamically stable, and compared to the Phillips curve version of the main-course model of Section 4.6 the adjustment speed is quicker.

Comparison of the two models is aided by comparing Figure 6.6 with Figure 4.5 of Section 4.6. For each of the four endogenous variables shown in Figure 6.6, the model solution (‘simulated’) is closer to the actual values than in the corresponding Figure 4.5. The two last panels of Figure 6.6 show the cumulated dynamic multiplier of a point increase in the rate of unemploy­ment. The difference from Figure 4.5, where the steady state was not even ‘in sight’ within the 35 years simulation period, is striking. In Figure 6.6, 80% of the long-run effect is reached within four years, and the system is clearly stabilising in the course of a 10-year simulation period.

6.8 Summary

This chapter has discussed the modelling of the wage-price subsystem of the economy. We have shown that under relatively mild assumptions about price - and wage-setting behaviour, there exists a conditional steady-state (for infla­tion, and real wages) for any given long-run mean of the rate of unemployment. The view that asymptotic stability of inflation ‘requires’ that the rate of unem­ployment simultaneously converges to a NAIRU (which only depends on the

Figure 6.6. Dynamic simulation of the EqCM model in Table 6.3.
Panels (a-d): actual and simulated values (dotted line). Panels (e-f):
multipliers of a one point increase in the rate of unemployment

properties of the wage and price and equations) has been refuted both logically and empirically. To avoid misinterpretations, it is worth restating that this result in no way justifies a return to demand driven macroeconomic models. Instead, as sketched in the earlier section, we favour models where unemploy­ment is determined jointly with real wages and the real exchange rate, and this implies that wage - and price-equations are grafted into a bigger system of equations which also includes equations representing the dynamics in other parts of the economy. This is also the approach we pursue in the following chapters. As we have seen, the natural rate models in the macroeconomic lit­erature (Phillips curve and ICM) are special cases of the model framework emerging from this section.

The finding that long-run unemployment is left undetermined by the wage - price sub-model is a strong rationale for building larger systems of equations, even if the first objective and primary concern is the analysis of wages, prices, and inflation. Another thesis of this section is that stylised wage-price models run the danger of imposing too much in the form of nominal neutrality (absence of nominal rigidity) prior to the empirical investigation. Conversely, no inconsistencies or overdetermination arise from enlarging the wage-price­setting equations with a separate equation of the rate of unemployment into
the system, where demand variables may enter. The enlarged model will have a steady state (given some conditions that can be tested). The equilibrium rate of unemployment implied by this type of model is not of the natural rate type, since factors (in real growth rate form) from the demand side may have lasting effects. On the other hand, ‘money illusion’ is not implied, since the variables conditioned upon when modelling the rate of unemployment are all defined in real terms.

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