EqCMs vs. dVARs in macroeconometric forecasting

The development of macroeconometric models in the course of the 1980s and 1990s, with more emphasis on dynamic specification and on model evaluation, meant that the models became less exposed to the critique against earlier generations of models, namely that models that largely ignore dynamics and temporal properties of the data, will necessarily produce suboptimal forecasts; see, for example, Granger and Newbold (1986: ch. 6). At the same time, other model features also changed in response to developments in the real econ­omy, for example, the more detailed and careful modelling of the supply-side factors and the transmission mechanism between the real and financial sectors of the economy; see Wallis (1989) for an overview. Given these developments, macroeconomic model builders and forecasters may be justified in claiming that modern models of the EqCM type, would forecast better than models that only use differenced data, dVARs. Forecast competitions between models of these two types have been reported in Eitrheim et al. (1999, 2002a). This chapter draws on these results, and extends the horse race competition between the different inflation models reported in Chapter 8 (Section 8.7.6).

As noted above, Michael Clements and David Hendry have re-examined several issues in macroeconometric forecasting, including the relative merits of dVARs and EqCMs (see, for example, Clements and Hendry 1995a, b, 1996, 1998). Assuming constant parameters in the forecast period, the dVAR is mis-specified relative to a correctly specified EqCM, and dVAR forecasts will therefore be suboptimal. However, if parameters change after the forecast is made, then the EqCM is also mis-specified in the forecast period. Clements and Hendry have shown that forecasts from a dVAR are robust with respect to certain classes of parameter changes. Hence, in practice, EqCM forecasts may turn out to be less accurate than forecasts derived from a dVAR. Put differ­ently, the ‘best model’ in terms of economic interpretation and econometrics, may not be the best model for forecasts. At first sight, this is paradoxical, since any dVAR can be viewed as a special case of an EqCM, since it imposes additional unit root restrictions on the system. However, if the parameters of the levels variables that are excluded from the dVAR change in the forecast period, this in turn makes also the EqCM mis-specified. Hence, the outcome of a horse race is no longer given, since both forecasting models are mis-specified relative to the generating mechanism that prevails in the period we are trying to forecast.

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