A forecasting model for y , based on its relationship to exogenous variables (e.g. x,) must use i,, the forecast of x,. An example is given where commercially available I,'s are sufficiently inaccurate that a univariate model for y , appears preferable. For a variety of types of models inclusion of an exogenous variable xf is shown to worsen the y , forecasts whenever x, must itself be forecast by I, and MSE(i,) > Var(x,). Tests with forecasts from a variety of sources indicate that, with a few notable exceptions, MSE(I,) > Var (x,) is common for macroeconomic forecasts more than a quarter or two ahead.
Thus, either: (a) available medium range forecasts for many macroeconomic variables (e.g. the GNP growth rate) are not an improvement over the sample mean (so that such variables are not useful explanatory variables in forecasting models), and/or the suboptimization involved in directly replacing x, by 1, is a luxury that we cannot afford.
(b)
KEY WORDS Box-Jenkins Bivariate Commercial forecasting Transfer function
On average, a multivariate model will yield better conditional forecasts than a univariate model, provided that the chosen explanatory variables do matter and that both models are well specified and estimated. The multivariate model's superiority increases as the forecast horizon lengthens. This is because it is well known that the univariate model's forecasts are actually just extrapolations from the sample data that decay to the sample mean. Moreover, if sufficiently accurate forecasts are available for the explanatory variables, then the multivariate model retains its superiority in unconditional forecasting as well.
One might well ask, what constitutes sufficient accuracy in forecasting an explanatory variable? In particular, suppose that this explanatory variable is the growth rate in U.S. GNP. Considerable effort has been expended in constructing models to forecast this particular growth rate. Is it safe to
The Gunning Fog Index for this paper is less than 15.