Knowledge that Transforms

IN A RECENT paper,' Frederick V. Waugh argues strongly for the use of ordinary least squares in simultaneous systems. His argument is not that least squares gives unbiased estimates of structural parameters2 but that they do (as consistent structural estimators do not) give unbiased estimates of the dependent variable in the regression equation given the values of the other variables and that this is what is needed for forecasting purposes. This note argues that Waugh's argument falls on its own grounds, that, even accepting all assumptions about no structural change and the like, least squares estimates of simultaneous equations when usedforforecasting purposes do not give unbiased forecasts of the dependent variables forecasted. The requirements of forecasting imply a different procedure. Suppose that we have made a least squares estimate of a structural equation and wish to use the result for forecasting purposes. We may assume that the system is not recursive and is in fact simultaneous, as otherwise nobody would quarrel with Waugh's position. Then, aside from the dependent variable to be forecast, there is at least one other endogenous variable in the equation. In order to forecast the dependent variable, however, one must know (or be told or forecast) the values of all the variables on the right-hand side of the equation. So long as all such variables are exogenous, this presents no problem. There is no reason why forecasts of exogenous variables (such as the weather, say) cannot be given the econometrician from outside his system. This is not the case with endogenous variables, however, for the values of endogenous variables in the system will be influenced by the value of the dependent variable being forecast and thus cannot be known before the forecast is made. They must also be forecast at the same time. Waugh states in this regard :3 .. . . I see no reason why I cannot estimate the expected future value of ce [the dependent variable to be forecast] associated with any stated value, or values, of yt [the other endogenous variable]. And unless the structure has changed, I think that in the future, as well as in the past, the least squares

The response of manufacturers' inventory holdings to changes in the volume of sales and the backlog of unfilled orders is examined on a quarterly basis for the period 1948-55 within a buffer-stock flexible accelerator framework. The hypothesis that manufacturers successfully hedge against increases in the price of purchased materials, enlarging their stocks in advance of actual price increases, is rejected. By introducing explicitly the impact of prediction errors it is possible to infer that manufacturers tend to underestimate actual changes in sales volume, but by a surprisingly small amount. An analysis of discrepancies between desired and actual inventory holdings reveals that manufacturers tolerated sizable deficiencies in stocks throughout the Korean conflict.

A. S. Goldberger, A. L. Nagar, H. S. Odeh, The Covariance Matrices of Reduced-Form Coefficients and of Forecasts for a Structural Econometric Model, Econometrica, Vol. 29, No. 4 (Oct., 1961), pp. 556-573