Industrial Concentration in Belgium: Empirical Comparison of Alternative Seller Concentration Measures

Abstract

A. INTRODUCTION RECENT information on industrial concentration in Belgium is rather scarce. Van Meerhaeghe [22] reported Gini coefficients based on I960 employment data, absolute concentration measures for the I, 2, 3, 4, 8, 12, I6 and 20 largest firms based on equity for the year 1959-60 and Herfindahl indices derived from national statistics on industrial output at plant level (I959-60). Phlips [I8], using employment data of the I963 census compiled by the Statistical Bureau of the E.E.C., calculated absolute concentration measures for the 4, 8, 20 and 50 largest firms as well as plants based on the NICE threedigit classification. The same data (for Belgium, December 3 1St, 1962) have been used by Horowitz [I2] to calculate entropy measures of industrial concentration for 26 two-digit sectors. It seemed to us that more recent and detailed information was badly needed. At our request the National Institute of Statisticsl calculated a series of concentration measures on the basis of 1970 data on industrial output at plant level. Besides the more classical measures such as the absolute concentration ratio C4 and the Herfindahl index, a number of alternative measures were included in this study. Most of these were discussed in Hart's articles [6], [7] which show the mathematical relationship between the various concentration measures in terms of moments and moment distributions. If the size distributions of plants in Belgium took an exact mathematical form, such as the lognormal or Pareto distributions, it would be possible to state the exact relationships between the various concentration measures. But the observed distributions of plants in Belgium do not follow an exact mathematical form and thus we estimate an empirical relationship between these measures without specifying any particular theoretical distribution. Whereas Hart limited himself to a theoretical a priori comparison of various concentration measures, our objectivebesides filling the information gap on industrial concentration in Belgiumwas to arrive at an empirical comparison of various measures. This objective allows us to de-emphasize the importance of the fact that the primary data from which the concentration measures are derived are gathered at plant level. Since all concentration measures relate to the size 1 The authors are grateful to Professor Dereymaeker, Director General of the National Institute of Statistics and to Mr. Demeulenaere for their kind co-operation.