THE ECONOMETRICS OF MACROECONOMIC MODELLING

Testing the encompassing implications

So far the NPCM has mainly been used to describe the inflationary process in studies concerning the United States economy or for aggregated Euro data. Heuristically, we can augment the basic model with import price growth and other open economy features, and test the significance of the forward infla­tion rate within such an extended NPCM. Recently, Batini et al. (2000) have derived an open economy NPCM from first principles, and estimated the model on United Kingdom economy data. Once we consider the NPCM for individual European economies, there are new possibilities for testing—since pre-existing results should, in principle, be explained by the new model (the NPCM). Specifically, and as discussed in earlier chapters, in the United King­dom there exist models of inflation that build on a different framework than the

Подпись: 11The largest root in Table 7.2 is 0.98.

NPCM, namely wage bargaining and cointegration; see, for example, Nickell and Andrews (1983), Hoel and Nymoen (1988), Nymoen (1989a), and Blan­chard and Katz (1999). Since the underlying theoretical assumptions are quite different, the existing empirical models define an information set that is wider than the set of instruments that are typically employed in the estimation of NPCMs. In particular, the existing studies claim to have found cointegrating relationships between levels of wages, prices, and productivity. These rela­tionships constitute evidence that can be used to test the implications of the NPCM.

Specifically, the following procedure is followed[61]:

1. Assume that there exists a set of variables z = [z1 z2], where the sub-set z1 is sufficient for identification of the maintained NPCM model. The variables in z2 are defined by the empirical findings of existing studies.

2. Using z1 as instruments, estimate the augmented model

APt = bpiEtApt+i + bpi Apt-i + bp2xt + ■ ■■ + z2,tbp4

under the assumption of rational expectations about forward prices.

3. Under the hypothesis that the NPCM is the correct model, bp4 = 0 is implied. Thus, non-rejection of the null hypothesis of bp4 = 0, corroborates the feed-forward Phillips curve. In the case of the other outcome: non­rejection of bf1 = 0, while bp4 = 0 is rejected statistically, the encompassing implication of the NPCM is refuted.

The procedure is clearly related to significance testing of the forward term, but there are also notable differences. As mentioned above, the motivation of the test is that of testing the implication of the rational expectations hypo­thesis; see Hendry and Neale (1988), Favero and Hendry (1992), and Ericsson and Irons (1995). Thus, we utilise that under the assumption that the NPCM is the correct model, consistent estimation of bfp1 can be based on z1, and supplementing the set of instruments by z2 should not significantly change the estimated bfp1.

In terms of practical implementation, we take advantage of the existing results on wage and price modelling using cointegration analysis which read­ily imply z2-variables in the form of linear combinations of levels variables. In other words they represent ‘unused’ identifying instruments that go beyond information sets used in the Phillips curve estimation. Importantly, if agents are rational, the extension of the information set should not take away the significance of Apt+1 in the NPCM, and bp4 = 0.

As mentioned earlier, Batini et al. (2000) derive an open economy NPCM consistent with optimising behaviour, thus extending the intellectual rationale of the original NPCM. They allow for employment adjustment costs, hence both future and current employment growth is included (Ant+1 and Ant), and

propose to let the equilibrium markup on prices depend on the degree of foreign competition, com. In their estimated equations, they also include a term for the relative price of imports, denoted rpi and oil prices oil. The wage share variable used is the adjusted share preferred by Batini et al. (2000). Equation (7.17) is our attempt to replicate their results, with GMM estimation using their data.[62]

Apt = — 0.56 + 0.33Apt+1 + 0.32Apt_ 1 + 0.07 gap t (0.20) (0.09) (0.04) (0.06)

+ 0.02com t + 0.13wst — 0.004 rpi t — 0.02 A oil t (0.01) (0.05) (0.01) t (0.003)

— 0.79Ant+1 + 1.03Ant (7.17)

(0.42) t (0.39) t

GMM, T = 107 (1972(3) to 1999(1)), a = 0.0099 Xj(31) = 24.92[0.77], Firei(40, 66) = 8.29[0.00].

The terms in the second line represent small open economy features that we noted above. The estimated coefficients are in accordance with the results that Batini et al. (2000) report. However, the Fire|, which still is the F-statistic from the first stage ordinary least squares (OLS) regression of Apt+1 against the instrument set, indicates that their model might have a potential problem of weak instruments.

In Section 5.6 we saw how Bardsen et al. (1998) estimate a simultaneous cointegrating wage-price model for the United Kingdom (see also Bardsen and Fisher 1999). Their two equilibrium-correction terms are deviations from a long - run wage-curve and an open economy price markup (see Panel 5 of Table 5.3):

ecmwt = (w — p — a + т 1 + 0.065u)t, (7.18)

ecmpt = (p — 0.6т 3 — 0.89(w + т 1 — a) — 0.11pi)t, (7.19)

where a denotes average labour productivity, т 1 is the payroll tax rate, u is the unemployment rate and pi is the price index of imports. The first instrument, ecmwt, is an extended wage share variable which we expect to be a better instrument than wst, since it includes the unemployment rate as implied by, for example, bargaining models of wage-setting (see the encompassing repre­sentation of Section 7.5.1). The second instrument, ecmpt, is an open economy version of the long-run price markup of the stylised ICM in Section 7.5.1.[63]

Equation (7.20) shows the results, for the available sample 1976(2)-1996(1), of adding ecmwt-1 and ecmpt-1 to the NPCM model (7.17):

Apt = — 1.51 + 0.03Apt+1 + 0.24Apt_ 1 — 0.02 gap t + 0.008com t (0.44) (0.13) (0.08) (0.11) (0.019)

+ 0.13 wst — 0.01rpi t — 0.003Aoil1 + 0.11Ant+i (0.07) (0.03) t (0.004) (0.27)

+ 0.87Ant — 0.35ecmwt-1 — 0.61 ecmpt_ 1 (7.20)

(0.19) (0.10) (0.12)

GMM, T = 80 (1976(2) to 1996(1)), <r = 0.0083 x2(31) = 14.39[0.99], Firei(42, 37) = 4.28[0.000].

The forward term Apt+1 is no longer significant, whereas the ecm-terms, which ought to be of no importance if the NPCM is the correct model, are both strongly significant.[64]

In the same vein, note that our test of GGL’s Phillips curve for the Euro area in Section 7.5.2 can be interpreted as a test of the implications of rational expectations. There z2 was simply made up of Apt-4 and emugapt-1 which modelling experience tells us are predictors of future inflation. Thus, from rational expectations their coefficients should be insignificant when Apt+1 is included in the model (and there are good, overidentifying instruments). Above, we observed the converse, namely Apt-4 and emugapt-1 are statist­ically and numerically significant, while the estimated coefficient of Apt+1 was close to zero.

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THE ECONOMETRICS OF MACROECONOMIC MODELLING

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