ABSTRACT
This chapter considers the estimation problem in a purely random coefficients model where the influence of the explanatory variable is distributed over a finite number of lagged values. It discusses the estimation of a lagged relationship in three situations: without smoothness priors; with polynomial deterministic priors; and with polynomial probabilistic priors. The specification of deterministic priors for the distributed lag model with purely random coefficients is also restrictive in the sense that the exact knowledge of the degree of polynomial is assumed whereas such prior knowledge is rarely available. The finite distributed lag with purely random coefficients model represents a class of weak specifications in that weak prior knowledge is assumed. The analysis of polynomial distributed lag in a purely random coefficients model with a single explanatory variable x can be generalised to a situation where more than one explanatory variable is involved on the lines of Tinsley and Almon papers in the context of the fixed coefficients model.
