Optimal Industrial Classification: An Application to the German Industrial Classification System
A widely used method in the analysis of large-scale econometric models is to replace the ``true model'' by an aggregative one in which the variables are grouped and replaced by sums or weighted averages of the variables in each group. The modes of aggregation of the independent and dependent variables may in principle be chosen optimally by minimizing a measure of mean-square forecast error in predicting the dependent variables from the independent variables by using the aggregative rather than detailed variables. However, this results in an optimization problem of a high degree of complexity. Nevertheless, many efficient optimization heuristics have been developed for these kinds of complex problems. We implement the Threshold Accepting heuristic for the problem of optimal aggregation of price indices in a model of the transmission of external (import and export) prices on internal prices, using German data. The algorithm and the resulting groupings are presented. The results suggest that the use of standard or ``official'' modes of aggregation will in general be far from being optimal.
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