This paper introduces a Laplace inversion technique for deriving unbiased p
redictors in exponential families. This general technique is applied to der
ive the exact optimal unbiased predictor in loglinear models with Gaussian
disturbances under quadratic loss. An exact unbiased estimator for its vari
ance is also derived. The result generalizes earlier work and unifies expre
ssions in terms of a simple hypergeometric function which has a number of a
dvantages. Nonlinear models rarely admit exact solutions and we therefore c
ompare the exact predictor with other predictors commonly used in nonlinear
models. The naive predictor which is biased and inconsistent, can be best
in terms of mean squared error, even for sample sizes of up to 40. (C) 2001
Elsevier Science S.A. All rights reserved.