THE ECONOMETRICS OF MACROECONOMIC MODELLING

Aggregate wage-price dynamics in the United Kingdom

In Section 5.6 we showed that, using aggregate wage and price data for the period 1976(3)-1993(1), the following long-term wage and price equations were identified (see Table 5.3).

(1) w = p + a — t1 — 0.065m + constant; (6.43)

(2) p = 0.89(w +11 — a)+0.11p* + 0.6t3 + constant. (6.44)

Next, consider the model in Table 6.1 which is estimated by full information maximum likelihod (FIML). Equations (6.43) and (6.44) are incorporated into the dynamic model as equilibrium-correction terms, and their importance is clearly shown. In addition to the equilibrium-correction term, wages are driven by growth in consumer prices over the last two periods and by productiv­ity gains. With an elasticity estimate of 0.66 and a standard error of 0.039, short-run homogeneity is clearly rejected.

The negative coefficient estimated for the change in the indirect tax-rate (At3t) is surprising at first sight. However, according to equation (6.44), consumer prices respond when the tax rate is increased which in turn is passed on to wages. Hence, the net effect of a discretionary change in the indirect tax rate on wages is estimated to be effectively zero in the short run and positive in the intermediate and long run. The effect of an increase in the payroll tax rate is to reduce earnings, both in the short - and long-run.

According to the second equation in Table 6.1, prices respond sharply (by 0.96%) to a 1 percentage change in wage costs. Hence short-run homogene­ity is likely to hold for prices. In addition to wage increases and equilibrium - correction behaviour, price inflation is seen to depend on the output gap, as captured by the variable gap.

Finally, note that the two dummy variables for incomes policy, BONUS and IP4, are significant in both equations, albeit with different signs. Their impact in the first equation is evidence of incomes policy raising wages, and their reversed signs in the price equation indicate that these effects were not completely anticipated by price-setters.

The diagnostics reported at the bottom of Table 6.1 give evidence of a well - determined model. In particular, the insignificance of the overidentification x2 statistic, shows that the model encompasses the implied unrestricted reduced form—see Bardsen et al. (1998) for evidence of recursive stability.

The significant equilibrium correction terms are consistent with previous cointegration results, and are clear evidence against a Phillips curve NAIRU, that is, 9q > 0 and 9w > 0 in the theory model. As for the wage curve NAIRU, note that the model formulation implies ш = 1 in the theory model, rather than ш = 0 which is one necessary requirement for correspondence between uw

Table 6.1

The model for the United Kingdom

The wage equation

Awt = 0.187 Awt_і + 0.332 (A2pt + Aat) — 0.341 A2t1t (0.075) (0.039) (0.100)

— 0.162 A^t3t — 0.156 (wt-2 — Pt—2 — at-і + t1t-2 + 0.065ut-i) (0.064) (0.023)

+ 0.494 + 0.013 BONUSt + 0.003 IP4t (0.071) (0.003) (0.001)

a = 0.45%

The price equation

Apt = 0.963 Awt — 0.395 Aat + 0.153 A(p + a)t_і (0.149) (0.118) (0.059)

— 0.044 Awt_ 1 + 0.536 At3t

(0.019) (0.092)

— 0.480 [pt_і — 0.89(w + t1 — a)t_2 — 0.11pit_2 — 0.6t3t_ 1] (0.047)

+ 0.238 gap, ! — 1.330 — 0.019 BONUSt — 0.005 IP4t (0.099) (0.131) (0.005) (0.001)

a = 0.71%

Diagnostic tests

x2vendentification(16) = 24.38[0.08]

FAR(i-5)(20, 94) = 0.97[0.50]

X2o^mality(4) = 3.50[0.48] FHETx2 (84, 81) = 0.63[0.98]

Note: The sample is 1976(3)-1993(1), 67 observations. Estimation is by FIML. Standard errors are in parentheses below the estimates. The symbol a denotes the estimated percentage residual standard error. The p-values of the diagnostic tests are in brackets.

and uss. In addition, although the estimates suggest that dynamic homogene­ity can be imposed in the price equation, a similar restriction is statistically rejected in the wage equation.