Optimal Industrial Classification in a Dynamic Model of Price Adjustment

It is common practice in econometrics to base a model to be applied to data on pure theory, and yet to replace the variables of the pure theory by aggregates of them. But if one must aggregate, there are many alternative ways of doing so; we present an approach using heuristic optimization for optimal aggregation. The method is applied to the study of the international transmission of price changes. The basic idea of our approach is easily explained. One wishes to find a partition of industries into a certain number of groups so as to obtain the best possible prediction of the resulting indices of prices of the corresponding commodity groups within a country, given data on the corresponding indices of external prices. The criterion for the optimal prediction is mean-square forecast error, which is to be minimized. The problem of finding a partition of a given number of industries into a smaller number of groups that minimizes mean-square forecast error falls under the heading of integer programming problems. A simple enumeration algorithm is not feasible, since even for modestly problem instances the number of possible groupings is enormous. One way to by-pass this problem is represented by the use of heuristic combinatorial optimization algorithms. We use a refined local-search algorithm similar to the Simulated Annealing approach which is known as Threshold Accepting algorithm (cf. Dueck and Scheuer (1991)).