Optimal aggregation by threshold accepting: An application to the German industrial classification system

A widely used method in the analysis of complex econometric models is to replace the "true model" by a highly simplified aggregative one in which the variables are grouped and replaced by sums or weighted averages of the variables in each group. The analysis of the problem of choosing an aggregative model optimally for modes of aggregation specified in advance leads to a formula for the aggregation bias. Taking this formula as objective function one would wish to choose a grouping that minimizes aggregation bias. Unfortunately this results in an optimization problem of a high degree of complexity, which means that there is probably no exact optimization algorithm that works in economic Computing time. In the last few years however, many efficient multiple-purpose optimization heuristics have been developed for complex problems as the traveling salesman problem, optimal chip layout or optimal portfolio composition. One example of such an algorithm is the Threshold-Accepting Algorithm (TA). We implement TA for the optimal aggregation of price indices. The algorithm and the resulting groupings are presented. The results show that the use of Standard or "official" modes of aggregation will in general be far from being optimal.