THE FIRST MOMENT OF AN ORDINARY LEAST SQUARES ESTIMATE FOR BIVARIATE KOYCK DISTRIBUTED LAG MODELS

A class of models generalizing Koyck distributed lag models is applied to the problem of measuring market response Yt to a communications mix Zt-s consisting of media advertising or promotional expenditures. Rewriting these models as Yt=αYt-1+βZt+error term, α: 2×2, an ordinary least squares (OLS) estimate of α is obtained and the analytical expression for the first moment of an OLS estimate is derived under the assumption that Yt is normally and independently distributed. These results, in combination with an asymptotic expansion of the generalized hypergeometric function, yield a new approximate first moment formula for the OLS estimate.