# Summary and conclusions

The dominance of EqCMs over systems consisting of relationships between differenced variables (dVARs) relies on the assumption that the EqCM model coincides with the underlying data generating mechanism. However, that assumption is too strong to form the basis of practical forecasting. First, parameter non-constancies, somewhere in the system, are almost certain to arise in the forecast period. The example in Section 11.2.1 demonstrated how allowance for non-constancies in the intercept of the cointegrating relations, or in the adjustment coefficients, make it impossible to assert the dominance of the EqCM over a dVAR. Second, the forecasts of a simple EqCM were shown to be incapable of correcting for parameter changes that happen prior to the start of the forecast, whereas the dVAR is capable of utilising the information about the parameter shift embodied in the initial conditions. Third, operational macroeconometric models that are used for forecasting are bound to be mis – specified to some degree, for example, because of limited information in the data set, measurement problems or simply too little resources going into data and model quality control. Together, mis-specification and structural breaks, open the possibility that models with less causal content may turn out as the winner in a forecasting contest.

To illustrate the empirical relevance of these claims, we considered a model that has been used for forecasting the Norwegian economy. Forecasts for the period 1992(1)-1994(4) were calculated both for the incumbent EqCM version of the RIMINI model and the dVAR version of that model. Although the large-scale model holds its ground in this experiment, several of the theoretical points that have been made about the dVAR approach seem to have considerable practical relevance. We have seen demonstrated the automatic intercept correction of the dVAR forecasts (parameter change prior to forecast), and there were instances when the lower causal-content of the dVAR insulated forecast errors in one part of that system from contaminating the forecasts of other variables. Similarly, the large-scale EqCMs and its dVAR counterparts offer less protection against wrong inputs (of the exogenous variables) provided by the forecaster than the more ‘naive’ models. The overall impression is that the automatic intercept correction of the dVAR systems is most helpful for short forecast horizons. For longer horizons, the bias in the dVAR forecasts that are due to mis-specification tends to dominate, and the EqCM model performs relatively better.

Given that operational EqCMs are multi-purpose models that are used both for policy analysis and forecasting, while the dVAR is only suitable for forecasting, one would perhaps be reluctant to give up the EqCM, even in a situation where its forecasts are consistently less accurate than dVAR forecast. We do not find evidence of such dominance, overall the EqCM forecasts stand up well compared to the dVAR forecasts in this ‘one-off’ experiment. Moreover, in an actual forecasting situation, intercept corrections are used to correct EqCM forecast for parameter changes occurring before the start of the forecast. From the viewpoint of practical forecast preparation, one interesting development would be to automatise intercept correction based on simple dVAR forecast, or through differencing the EqCM term in order to insulate against a shift in the mean.

The strong linkage between forecasting and policy analysis makes the role of econometric models more important than ever. Policy makers face a menu of different models and an explicit inflation target implies that the central bank’s conditional forecast 1-2 years ahead becomes the operational target of monetary policy. The presence of non-stationary data and frequent structural breaks makes inevitable a tradeoff between the gain and importance of correct structural modelling and their cost in terms of forecasting robustness. We have explored the importance of this tradeoff for inflation forecasting.

Specifically, we considered the two popular inflation models, namely Phillips curves and wage curve specifications. We establish that Phillips curve forecasts are robust to types of structural breaks that harm the wage-curve forecasts, but exaggerate forecast uncertainty in periods with no breaks. Moreover, omitted relevant equilibrium correction terms induce omitted variables bias in the usual way. Conversely, for the wage curve model, the potential biases in afterbreak forecast errors can be remedied by intercept corrections. As a conclusion, using a well-specified model of wage-price dynamics offers the best prospect of successful inflation forecasting.

This appendix gives a proof of (4.29):

plim /?ols = «їв,

T

in Chapter 4, Section 4.5.

Since plim^^Q/3OLS is equal to the true regression coefficient between yt and xt, we express the regression coefficient in terms of the parameters of the expectations model. To simplify, we assume that {yt, xt} are independently normally distributed:

From (4.27), the conditional expectation of yt is:

E[yt I xt] = xtfi + E[nt I xt],

and, from (4.28):

E[nt I xt] = E[ey, t I xt] — fJE[ex, t I xt] = – pE[ex, t | xt].

Due to normality, E[ex t I xt] is given by the linear regression

E[tx, t I xt] = So + S^xt,

implying

E[£x, txt] E[^x, t(a1xt-1 + ex, t)] ae

Var[xt] Var[xt]

Since Var[zt] = a? /(1 — a2), we obtain

Sl = (1 — a),

which gives:

E[nt I xt] = —в(1 — o)xt,

since S0 = 0. Finally, using (A.7) in (A.2) yields the regression

E[yt | xt] = af3xt, (A.8)

and hence the true regression coefficient which is estimated consistently by /3qls is (not в).

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