THE ECONOMETRICS OF MACROECONOMIC MODELLING
The dynamic wage-price model
When modelling the short-run relationships we impose the estimated steady state from (9.3) to (9.4) on a subsystem for {Awt, Apt} conditional on {Aat, Ayt, Aut-1, Apit, At1t, At3t} with all variables entering with two additional lags. In addition to energy prices Apet, we augment the system with {Aht, Wdumt, Pdumt} to capture short-run effects. Seasonalt is a centred seasonal dummy. The diagnostics of the unrestricted I(0) system are reported in the upper part of Table 9.2.
The short-run model is derived general to specific by deleting insignificant terms, establishing a parsimonious statistical representation of the data in I(0)-space, following Hendry and Mizon (1993) and is found below:
Awt = -0.124+ 0.809Apt - 0.511Aht + 0.081Aat (0.017) (0.109) (0.123) (0.017)
— 0.163 (wt-1 — pt-1 — at-1 + 0.1ut_2) + 0.024 Seasonal^2 (0.021) (0.002)
— 0.020Wdumt + 0.023 Pdumt (9.5)
(0.003) (0.004)
a = 0.0089.
Table 9.2
Diagnostics for the unrestricted I(0) wage-price
system and the model
Unrestricted I(0) system 52 parameters
Far(! - 5) (20,154) 0.68[0.85]
Molality (4) 4.39[0.36]
FHETx2 (141,114) 0.81[0.88]
Final model
19 parameters
Xoveridentification (33) 33.72[0.43]
FAr(i-5) (20,188) 1.45[0.10]
xnormaiity (4) 6.82[0.15]
FHETx2 (141,165) 1.23[0.10]
Note: References: overidentification test (Anderson and Rubin 1949, 1950; Koopmans et al. 1950; Sargan 1988), AR-test (Godfrey 1978;
Doornik 1996), Normality test (Doornik and Hansen 1994), and Heteroskedasticity test (White 1980; Doornik 1996). The numbers in [..] are p-values.
The sample is 1972(4)-2001(1), 114 observations.
Apt = 0.006 + 0.141Awt + 0.100Awt_i + 0.165Apt_2 - 0.015Aat (0.001) (0.026) (0.021) (0.048) (0.006)
+ 0.028Ayt_ 1 + 0.046Ayt_ 2 + 0.026Apit + 0.042Apet (0.012) (0.012) (0.008) (0.007)
- 0.055 (pt-з - 0.7(wt-2 +11t-i - a—) - 0.3pi—i - 0.5f3—i) (0.006)
- 0.013 Pdumt (9.6) (0.001) t
a = 0.0031
T = 1972(4)-2001(1) = 114.
The lower part of Table 9.2 contains diagnostics for the final model. In particular, we note the insignificance of x2veridentification (33), which shows that the model reduction restrictions are supported by the data.
The wage growth equation implies that a one percentage point increase in the rate of inflation raises wage growth by 0.8 percentage point. The discretionary variables for incomes policies (Wdumt) and for price controls (Pdumt) are also significant. Hence, discretionary policies have clearly
succeeded in affecting consumer real wage growth over the sample period. The equilibrium-correction term is highly significant, as expected. Finally, the change in normal working-time Aht enters the wage equation with a negative coefficient, as expected. In addition to equilibrium-correction and the dummies representing incomes policy, price inflation is significantly influenced by wage growth and output growth (the output gap), together with effects from import prices and energy prices—as predicted by the theoretical model.
The question whether wage-price systems like ours imply a NAIRU property hinges on the detailed restrictions on the short-run dynamics. A necessary condition for a NAIRU is that wage growth is homogenous with respect to the change in producer prices, Aqt. Using, Apt = (1 — 4>)Aqt + 4>Apit, and since Apit does not enter the wage equation, it is clear that a homogeneity restriction does not hold in the wage growth equation (9.5): using the maintained value of ф = 0.3 from (9.4) the implied wage elasticity with respect to the change in producer prices, Aqt is 0.56. The wage equation therefore implies that we do not have a NAIRU model. Hence, the conventional Phillips curve NAIRU, for example, does not correspond to the eventual steady-state rate of unemployment implied by the larger model obtained by grafting the wage and price equations in a larger system of equations.
 |
 |
The model has constant parameters, as shown in Figure 9.3, which contains the one-step residuals and recursive Chow-tests for the model. Finally, the lower left panel of Figure 9.3 shows that the model parsimoniously encompasses the
Figure 9.3. Recursive stability tests for the wage-price model. The upper
panels show recursive residuals for the model. The lower panels show recursive
encompassing tests (left) and recursive Chow tests (right)
system at every sample size. As noted in the introduction, improperly modelled expectations in the dynamic simultaneous equations model could cause the model’s parameters to change when policies change, generating misleading policy simulations, as emphasised by Lucas (1976). However, as Figure 9.3 shows, there is no evidence of any mis-specified expectations mechanisms.
