THE ECONOMETRICS OF MACROECONOMIC MODELLING

Evaluation of the system

The nature of the solution for the rate of inflation is a system property, as noted in Section 7.3. Hence, unless one is willing to accept at face value that an oper­ational definition of the forcing variable is strongly exogenous, the ‘structural’ NPCM should be evaluated within a system that also includes the forcing variable as a modelled variable.

For that purpose, Table 7.1 shows an estimated system for Euro-area infla­tion, with a separate equation (the second in the table) for treating the wage share (the forcing variable) as an endogenous variable. Note that the hybrid NPCM equation (first in the table) is similar to (7.14), and thus captures the gist of the results in GGL. This is hardly surprising, since only the estimation method (full information maximum likelihood—FIML in Table 7.1) separates the two NPCMs.

An important feature of the estimated equation for the wage share wst is the two lags of the rate of inflation, which both are highly significant. The likelihood-ratio test of joint significance gives x2(2) = 24.31[0.00], meaning that there is clear formal evidence against the strong exogeneity of the wage share. One further implication of this result is that a closed form solution for the rate of inflation cannot be derived from the structural NPCM alone.

The roots of the system in Table 7.1 are all less than one (not shown in the table) in modulus and therefore corroborate a forward solution. However, according to the results in the table, the implied driving variable is emugapt, rather than wst which is endogenous, and the weights of the present value

Table 7.1

FIML results for the NPCM system for the
Euro area 1972(2)-1998(1)

Apt = 0.7696Apt+1 + 0.2048Apt_ 1 + 0.0323wst (0.154) (0.131) (0.0930)

+ 0.0444 (0.1284)

wst = 0.8584wst_ і + 0.0443Apt_ 2 + 0.0918Apt_ 5 (0.0296) (0.0220) (0.0223)

+ 0.0272 emugap t_ 2 — 0.2137 (0.0067) t (0.0447)

Apt+i = 0.5100wst_ 1 + 0.4153Apt_ 1 + 0.1814 emugapt_ 1 (0.0988) (0.0907) (0.0305) t

+ 0.9843 (0.1555)

Note: The sample is 1972(2) to 1998(1), T = 104.

aApt = 0.290186

aws = 0.074904 &Apt+1 = 0.325495 Far(1-5)(45, 247) = 37.100[0.0000]**

FHETx2 (108,442) = 0.94319[0.6375]

FHetxx (324, 247) = 1.1347[0.1473]

X2oVmaiity(6) = 9.4249[0.1511]

calculation of emugapt have to be obtained from the full system. The stat­istics at the bottom of the table show that the system of equations has clear deficiencies as a statistical model, cf. the massive residual autocorrelation detected by FAr(1-5). Further investigation indicates that this problem is in part due to the wage share residuals and is not easily remedied on the present information set. However, from Section 7.5.2 we already know that another source of vector autocorrelation is the NPCM itself, and moreover that this mis-specification by and large disappears if we instead adopt equation (7.16) as our inflation equation.

It lies close at hand therefore to suggest another system where we utilise the second equation in Table 7.1, and the conventional price equation that is obtained by omitting the insignificant forward term from equation (7.16). Table 7.2 shows the results of this potentially useful model. No mis-specification is detected, and the coefficients appear to be well determined. In terms of economic interpretation the models resemble an albeit ‘watered down’ version

Table 7.2

FIML results for a conventional Phillips curve for the
Euro area 1972(2)-1998(1)

Apt = 0.2866wst + 0.4476Apt_ і + 0.1958Др^4 (0.1202) (0.0868) (0.091)

+ 0.1383emugap t_ і + 0.6158 (0.0259) (0.1823)

wst = 0.8629wst_ і + 0.0485Др^ 2 + 0.0838Др^ 5 (0.0298) (0.0222) (0.0225)

+ 0.0267 emugap t_ 2 — 0.2077 (0.0068) t (0.0450)

Note: The sample is 1972(2) to 1998(1), T = 104.

aApt = 0.284687

crws = 0.075274

FAR(1-5)(20,176) = 1.4669[0.0983]

FHETx2 (54, 233) = 0.88563[0.6970]

FHetxx (162,126) = 1.1123[0.2664]

X^Vmaiity (4) = 2.9188[0.5715]

Xoveridentification (10) = 10.709[0.3807]

of the modern conflict model of inflation and one interesting route for further work lies in that direction. That would entail an extension of the information set to include open economy aspects and indicators of institutional developments and of historical events. The inclusion of such features in the information set will also help in stabilising the system.11