Asymptotic Minimum-MSE Prediction in the Cobb-Douglas Model with a Multiplicative Disturbance Term
A nonparametric framework for deriving the asymptotic MSE-optimal predictor for a multiplicative model is presented. The resulting predictor is compared to several known competitors in a limited Monte Carlo experiment. RECENT PAPERS BY Zellner [10] and Teekens and Koerts [7] address themselves to the problem of minimum-MSE prediction in a Cobb-Douglas-type multiplicative model under a lognormal distribution assumption for the disturbance term. Each derives the finite sample predictor (which turns out to be a function of the familiar least-squares predictor) for the model based on the assumption that ?2, the variance of the lognormally distributed disturbance, is known. An approximately optimal finite sample predictor is then suggested, where an estimate of w2 is utilized. Under certain conditions the approximately optimal predictor poses a computational burden. Under others, the predictor is easily computed, but no longer are small sample properties guaranteed. Our purpose in this note is to present a general framework for deriving the asymptotically optimal-MSE predictor for this multiplicative model without the imposition of a distributional assumption at the outset. Not only does this exercise provide us with a convenient vehicle for discussing further the aforementioned contributions, it also yields a viable distribution-free predictor that may