Stochastic response restrictions

This paper considers the implementation of prior stochastic information on unknown outcomes of the response variables into estimation and forecasting of systems of linear regression equations in the context of time series, cross sections, pooled and longitudinal data models. The established approach proves particularly useful when only aggregated information on the response variables is available, as is frequently the case in applied statistics. We address the combination of prior stochastic and sample information as an extension of standard Gauss–Markov theory. Prior stochastic information could be given in the form of expertsʹ expectations, or from estimations and/or projections of other models. A classical (i.e. non-Bayesian) regression framework for the incorporation of prior knowledge in generalized least-squares estimation and prediction is developed.