Temporal Aggregation, the Data Interval Bias, and Empirical Estimation of Bimonthly Relations from Annual Data

In an important study reviewing the literature on econometric studies of the relationship between advertising and sales Clarke (Clarke, Darral G. 1976. Econometric measurement of the duration of advertising effects on sales. J. Marketing Res. 13 (November) 345--357.) concluded that the implied duration interval of the effects of advertising on sales were too long when the studies used annual data. A theoretical explanation is provided here for the observation of parameter estimates which vary with the data interval employed in the analysis. Parameter estimates are developed on the basis of data aggregated at various levels of temporal aggregation and compared with theoretical values. It is demonstrated that it is possible to recover bimonthly parameters when only annual data are available.