RDP 8802: Var Forecasting Models of the Australian Economy: A Preliminary Analysis 5. Conclusions and Future Directions
January 1988
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We have considered the ex-ante forecasting performance of three relatively large (fifteen variable) vector autoregression models of the Australian economy. The first two models approach the issue of detrending in a fairly mechanical way – applying a linear time trend in one case and first differences in the other. The final model mechanically applied Litterman's (1986a) random walk priors on the coefficients of the VAR.
The main lesson to be drawn from the analysis of these models is the importance of capturing the “trends” in the variables in order to induce covariance stationarity into the data. This has some implications for the development of a better VAR forecasting model, which are canvassed below. The implications for other macroeconometric research are perhaps more important. Non-stationarity is an important property of most macroeconomic data, yet it is typically ignored.
Classical examples of this problem are provided by the Murphy (Murphy, 1987) and NIF 88 (Simes, 1987) models of the Australian economy. Both lay claim to a certain amount of “econometric purity” by apparently extensive use of statistical diagnostics during model development. Yet many of these diagnostics, as well as the parameter estimates on lagged dependent variables, are inappropriate if the data are difference stationary.
We do not claim that the solutions to these problems are trivial (see, for instance. Stock and Watson, 1987). Nonetheless, they do suggest that accuracy in ex-ante forecasting should become an important part of a model builder's toolkit. It may be that forecasts from VAR models will set the standard by which these other models are judged.
Given our “cheap and simple” approach, the ex-ante forecasts, produced up to six quarters ahead by the VAR models, are generally competitive with forecasts prepared by private sector economists for many of the variables. However, an evaluation of the ex-ante forecasting performance of the three VAR models combined with some results from the economics literature, suggests two main ways in which the forecasting performance of VARs may be improved.
The first method would replace the VARs estimated with a time trend or first differences by a single VAR estimated on individually detrended variables. The potential importance of this is clear from the graphs; the forecasts from the model based on first differences are markedly superior for several variables. Techniques such as those used by Stock and Watson (1987) would be applied to each variable to determine the order and number of deterministic and/or stochastic time trends exhibited, and these would be allowed for in the estimation of the VAR. The resulting model would be more complex (in terms of its use of technical expertise) than those considered above, but still relatively cheap to develop and run.
However, this procedure is likely to have at least three limitations. First Meese and Rogoff (1983) and others have shown (in the case of exchange rates) that good estimation period fit does not necessarily produce good forecasts. Second, the floating of the dollar and other financial deregulation of the eighties suggests that one may not want to let the data from the regulated regimes of the sixties and seventies speak too loudly in some of the equations. Given limited data availability from the deregulated period, one cannot simply throw out the sixties and seventies data. However, it may be possible to allow for structural change by imposing fairly strong priors in the equations for the financial variables. Finally, and probably most importantly, the sheer size of the VARs suggests that considerable payoffs in forecasting precision may be had from applying some kind of restrictions.
These arguments lead us to the second method of building a better VAR – namely, a more thoughtful application of priors in the Bayesian model. In the foregoing analysis, we mechanically applied Litterman's random walk prior to all variables. Yet both theory and empirical work suggest that stock prices, exchange rates (e.g. Meese and Rogoff, 1983) and interest rates (e.g. Trevor and Donald, 1986) are extremely likely to be well modelled by a tight random walk prior; consumption (e.g. Hall, 1978, Flavin, 1981 and Johnson, 1983) is likely to do well with a similar prior, perhaps without the mean of unity on the first own lag; but there is little reason to expect, for example, that the ratio of the change in stocks to real gross domestic product will follow a random walk.
Our models provide some evidence on this issue. An examination of the graphs presented above, and the impact of each variable in each equation of the three VARs,^{[11]} suggests some areas where the priors need to be modified.
In particular, the random walk prior could be substantially tightened in the equations where the BVAR model performs best: stock prices, the exchange rate, interest rates and the money supply. Substantial loosening of this prior, especially in increasing the weights assigned to other variables, is required in the equations for output, consumption, trade and prices where the results of the other models suggest that other variables are important in these equations.
These results suggest that gains in forecast accuracy may be achieved by modifying the priors used in the estimation of the Bayesian VAR. The resulting model would still be relatively simple and cheap to develop and run. Of course, once it has been developed, we will need to await the passage of time to generate a new set of data to evaluate the new ex-ante forecasts.
Footnote
Tables documenting these effects may be obtained from the authors on request. [11]