THE ECONOMETRICS OF MACROECONOMIC MODELLING

Aggregate wages and prices: UK quarterly data

Bardsen et al. (1998) present results of aggregate wage and price determination in the United Kingdom, that can be used to illustrate the third identification scheme above. In the quarterly data set for the United Kingdom the wage vari­able wt is average actual earnings. The price variable pt is the retail price index, excluding mortgage interest payments and the Community Charge. In this ana­lysis, mainland productivity at, import prices pit, and the unemployment rate ut are initially treated as endogenous variables in the VAR, and the validity of restrictions of weak exogeneity is tested. The variables that are treated as non-modelled without testing are employers’ taxes t1t, indirect taxes t3t, and a measure of the output gap gapt, approximated by mainland GDP-cycles esti­mated by the Hodrick-Prescott (HP) filter. Finally, two dummies are included to take account of income policy events.

The equilibrium relationships presented by Bardsen et al. (1998) are shown in Table 5.3 (to simplify the table, the constants appearing in equations (5.15)-(5.20) are omitted along with the residuals ecmb, t and ecmf, t). The first panel simply records the two long-run relationships (5.17) and (5.18), with the noted changes. Panel 2 records the unidentified cointegrating vectors, using the Johansen procedure (residual diagnostics are given at the bottom of the table). Panel 3 reports the estimated relationships after imposing weak exogeneity restrictions for ut, at, and pit. The estimated в coefficients do not change much, and the reported test statistic x2(6) = 10.02[0.12] does not reject the exogeneity restrictions. Panel 4 then applies the restrictions discussed in Section 5.4—ш = 1 and d = 0—hence the two estimated equations correspond to the theoretical model (5.19) and (5.20). The impact of the identification procedure on the estimated в coefficients is clearly visible. Panel 5 shows the final wage and price equations reported by Bardsen et al. (1998), that is, their equation (14a) and (14b). The recursive estimates of the cointegration coefficients (note the sign change in the graphs) together with confidence inter­vals and the sequence of tests of the overidentifying restrictions are shown in Figure 5.3.

The identifying restrictions are statistically acceptable on almost any sample size, and the coefficients of the two identified relationships are stable over the same period. Bardsen et al. (1998) perform an analysis of aggregate Norwegian

Table 5.3

Cointegrating wage - and price-setting schedules in the United Kingdom

Panel 2: No restrictions

w = 1.072p + 1.105a — 0.005m — 0.101pi — 0.892t1 — 0.395t3
p = 0.235w + 0.356a — 0.215m + 0.627pi — 0.775t1 + 3.689t3

Panel 3: Weak exogeneity

w = 1.103p + 1.059a — 0.005m — 0.139pi — 0.936t1 — 0.421t3
p = 0.249w + 0.325a — 0.212m + 0.535pi — 0.933t1 + 3.796t3
X2(6) = 10.02[0.12]

Panel 4: Non-linear cross equation restrictions, weak exogeneity w = 0.99p + 1.00a — 0.05m — 0.01pi — 1.32t1 — 0.05t3 (0.10) (0.01) (0.03) (0.31)

p = 0.89w — 0.89a + 0.11pi + 0.89t1 + 0.61t3 (0.02) (0.15)

X2(10) = 15.45[0.12]

Panel 5: Simplified linear restrictions, weak exogeneity

w = p + a + 0.065m — t1 (0.013)

p = 0.89w — 0.89a + 0.11pi + 0.89t1 + 0.62t3 (0.017) (0.17)

X2(13) = 20.08[0.09]

Diagnostic tests for the unrestricted conditional subsystem

FAR(1-5) =°.95[°.61]

X20;maiity(10) = 19.844[0.03]

(360,152) = 0.37[1.00]

Note: The sample is 1976(3) to 1993(1), 67 observations.

wages and prices, and show that the results are very similar for the two economies.

5.2 Summary

The Layard-Nickell wage-curve model of incomplete competition marks a step forward compared to both the Norwegian model and the Phillips curve, in that it combines formal models of wage bargaining and models of monopolistic price-setting. Thus, compared to Aukrust’s model, the hypothesised wage and

price cointegrating vectors are better founded in economic theory, and specific candidates for explanatory variables flow naturally from the way the bargaining model is formulated. We have shown that there are cases of substantive interest where the identification problem pointed out by Manning (1993) are resolved, and have shown applications with empirically stable and interpretable wage and price curves.

As a model of equilibrium unemployment, the framework is incomplete since only the cointegrating part of the dynamic system is considered. To evaluate the natural rate implication of the theory, which after all is much of the ration­ale for the whole framework, a broader setting is required. That also defines the theme of the next chapter.