Further results on estimating linear regression models with partial prior information

Abstract

This paper shows that Shiller's smoothness restrictions on the lag coefficients in a distributed lag model imply a singular normal prior distribution. The posterior mean for this prior is different from Shiller's estimator. Contradictions among specifying assumptions may arise if the moments of the singular normal prior are not properly determined. Sample data are used to guarantee that the estimated covariance matrix of an approximate generalized least squares estimator exceeds the estimatedmean square error matrix of the posterior mean by a positive semidefinite matrix. The posterior mean covers the generalized least squares and Almon estimators as special cases. We conclude with an empirical example which demonstrates the posterior mean's superiority in forecasting relative to both an approximate generalized least square estimator and Almon or ridge estimators.