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

The authors examine the advertising-sales relationship in the framework of the Koyck model. They note that if only macro (e.g., annual) data are available, it is necessary to approximate micro (e.g., monthly) data in order to minimize the ‘data interval bias’ in estimating the microparameters. They examine two previously proposed models for minimizing the data interval bias and propose a direct aggregation model that avoids some of the problems common to those two models. The proposed constrained search estimation method eliminates the problem of infeasible parameter estimates present 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 microparameters more accurately than the other two models.