An Iterative GLS Procedure for Estimating the Parameters of Models with Autocorrelated Errors Using Data Aggregated over Time.

This article describes an iterative generalized least-squares procedure for estimating the parameters of economic relations characterized by first-order autocorrelated disturbances when the available data have been aggregated over time. The general problem of aggregating economic relations over time has already received considerable attention in the literature. Economist H. Theil explained the difficulties of obtaining the correct aggregate relation when lagged variables appeared in the micro relationship, but he did not consider the role of the disturbance term. Y. Mundlak studied the effects of aggregation over time on the partial adjustment model and developed the relationship between the parameters of the micro relation and those of the mispecified time-aggregated macro model. In this article, the variance-covariance matrix of the aggregate disturbances was explicitly derived from that of the disturbances of the disaggregate model. Acceptance or rejection of the model was seen to depend crucially on the data collection interval being utilized. The results obtained in this study raise interesting questions concerning some of the results reported in studies of cumulative advertising effects measurement.