THE ECONOMETRICS OF MACROECONOMIC MODELLING

Revisiting empirical models of Norwegian inflation

The definitions of the variables are in line with those we presented for the ICM in Chapter 9, but the sample is different and covers the period 1966(4)-1996(4). The wage variable wt is average hourly wages in the mainland economy, exclud­ing the North Sea oil-producing sector and international shipping. The produc­tivity variable at is defined accordingly. The price index pt is measured by the official consumer price index. The import prices index pit is a weighted average of import price indices from trading countries. The unemployment variable ut is defined as a ‘total’ unemployment rate, including labour market programmes. The tax-rates t1t and t3t are rates of payroll tax and indirect tax, respectively.6

The output gap variable gapt is measured as deviations from the trend obtained by the Hodrick-Prescott (HP) filter. The other non-modelled variables contain first the length of the working day Aht, which captures wage com­pensation for reductions in the length of the working day—see Nymoen (19896). Second, incomes policies and direct price controls have been in operation on several occasions in the sample period; see, for example, Bowitz and Cappelen (2001). The intervention variables Wdum and Pdum, and one impulse dummy i80q2, are used to capture the impact of these policies. Finally, i70q1 is a VAT dummy.

The dynamic ICM As in the earlier chapters we have two simultaneous equations for Awt and Apt, with separate and identified equilibrium correction equations terms. Estimation is by full information maximum likelihood (FIML), and the coefficients and diagnostics of the final ICM for our current sample are shown in (11.54) and in Table 11.3.

Awt = Apt — 0.4 x 0.36Apit — At1t_2 — 0.36 At3t_2 — 0.3 Aht

(0.08) (0.11)

— (0.08)[wt_2 — pt-2 — at-i +0.1ut-2] + dummies (0.01)

aAw = 1.02%

Apt = 0.12 (Awt + At1t_2) + 0.05 gapt_. +0.4 x 0.07Apit — 0.07 At3t_2 (0.05) (0.02) t 1 (0.03)

— 0.08 [pt-3 — 0.6(wt_ 1 — at-1 + t1t-1) — 0.4pit-1 + t3t-3] + dummies (0.01) t t t t t t

&Ap = 0.41%. (1L54)

6 An income tax rate could appear as well. It is omitted from the empirical model, since it is insignificant. This is in accordance with previous studies of aggregate wage formation, see, for example, Calmfors and Nymoen (1990) and Nymoen and Rpdseth (2003), where no convincing evidence of important effects from the average income tax rate on wage growth could be found.

Table 11.3

Diagnostic tests for the dynamic ICMa

aAw = 1.02% aAp = 0.41%

Correlation of residuals = —0.4

x2vendentification(9) = 9.23[0.42]
FAr(i-5)(20, 176) = 1.02[0.31]

Xno^mality(4) = 6.23[0.18] FHETx2 (102,186) = 0.88[0.76]

aThe sample is 1966(4)-1994(4), 113 observations.

Table 11.4

Diagnostic tests for the PCMb

a Aw = 1.07% aAp = 0.47%

Correlation of residuals = —0.6

xLndentification(16) = 25.13[0.07]
Far(i-5)(20, 176) = 1.02[0.44]

XnOrmality(4) = 6.[113][0.18]

FHETx2 (102, 257) = 0.81[0.84]

(d)

Sequence of Chow statistics

1975 1980 1985 1990

Figure 11.4. Recursive stability tests for the PCM

Дwt = 1.11 Apt — 0.11ДрЬ — 0.65 At1t — 0.41 At1t_2 — 0.01 Ащ~3 (0.04) (0.22) (0.21) (0.005)

— 0.006 щ-1 — 0.16 Дt3t_ 1 — 0.34 Дt3t_2 — 0.30 ДЬі + dummies (0.001) (0.09) (0.09) (0.11)

aAw = 1.07%

Apt = 0.14 Дw^ + 0.07 Дwt_3 + 0.17 Др^ 1 + 0.27 Др4_2 + 0.05 Дрц

(0.03) (0.02) (0.05) (0.05) (0.02)

— 0.03Дat_1 + 0.05 gapt_ 1 + dummies (0.006) (0.01)

aAp = 0.47%. (11.55)

Parameter constancy of the PCM is demonstrated graphically in Figure 11.4. The two 1-step residuals with their ±2 estimated residual standard errors (±2a in the graphs) are in the upper panels, while the lower right panel shows the sequence of recursive forecast Chow tests together with their one-off 5% critical level. The lower left panel shows that the model encompasses the unrestricted reduced form as the sample size increases (i. e. the end point of the graph corresponds to Overidentification y2 (16) in Table 11.4).

Hence, using these conventional design criteria, the PCM seems passable, and it is attractive as a forecasting model since it is simpler than the ICM.