On the Optimal Use of Suboptimal Forecasts of Explanatory Variables

Ashley (1983) gave a simple condition for determining when a forecast of an explanatory variable (X_t ) is sufficiently inaccurate that direct replacement of X_t by the forecast yields worse forecasts of the dependent variable than does respecification of the equation to omit X_t . Many available macroeconomic forecasts were shown to be of limited usefulness in direct replacement. Direct replacement, however, is not optimal if the forecast's distribution is known. Here optimal linear forms in commercial forecasts of several macroeconomic variables are obtained by using estimates of their distributions. Although they are an improvement on the raw forecasts (direct replacement), these optimal forms are still too inaccurate to be useful in replacing the actual explanatory variables in forecasting models. The results strongly indicate that optimal forms involving several commercial forecasts will not be very useful either. Thus Ashley's (1983) sufficient condition retains its value in gauging the usefulness of a forecast of an explanatory variable in a forecasting model, even though it focuses on direct replacement.