The Effects of Serial Correlation and Data Aggregation on Advertising Measurement

Many annual data series for the sales of branded consumer goods exhibit marked autocorrelation which provides significant fits with lagged-variable advertising sales response models. Concern continues to be expressed that the source of such autocorrelation is not advertising efforts but spurious effects from temporal data aggregation, and some researchers have criticized advertising studies using annual data as being misleading. The authors investigate the source of autocorrelation in annual series and show that temporal data aggregation is unlikely to be the primary cause of upwardly biased estimates of the coefficient (λ) of the lagged dependent variable. Sampling and specification error are more likely causes. The authors develop the aggregate form of the brand loyal model for data aggregated over time and derive a formula to calculate the amount of autocorrelation that is induced by aggregation. They present a new estimation approach which takes into account the impact of aggregation on estimates of coefficients and the error terms of such models. They compare the effects of specification error on the estimate of λ for two well known approximations to the aggregate function as well as for the approximation developed here.