A Direct Aggregation Approach to Inferring Microparameters of the Koyck Advertising-Sales Relationship from Macro Data

This paper examines the advertising-sales relationship in the framework of the Koyck model. We note that if only macro (e.g., annual) data are available then it is necessary to approximate micro (e.g., monthly) data in order to minimize the “data interval bias” in estimating the micro parameters. We examine two previously proposed models to minimizing the “data interval bias” and propose a direct aggregation model that avoids some of the problems common to the previous two models. The proposed constrained search estimation avoids the problem of infeasible parameter estimates prevalent in the OLS estimation of the two previous models. A comparison of the constrained search estimation of the three models in a simulation setting indicates that the proposed model recovers the micro parameters more accurately that the other two models.