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Standard Errors of Forecast of a Complete Econometric Model

T. M. Brown

Abstract

An attempt is made here to carry the concept of the standard error of forecast, which has long been used with single equations, into the realm of the complete econometric model. The analysis is begun by reviewing the problem and developing the error formula for the single equation situation. This background is then used for approaching the analogous problem for the full model. The equation system forecasts a vector of endogenous variables which are essentially random variables with probability distributions. Hence a vector of standard errors is desirable. Formulas for estimating the elements of this vector are worked out in matrix form convenient for computation. The problem of presenting the forecast as a vector of distributions is discussed in terms of confidence intervals and tolerance intervals. Finally the reduced form, as distinct from the full structure method of estimating the forecast distributions, is considered.