More on measuring relative concentration of sales in U.S. manufacturing.

• Author: Nissan, Edward
• Position: Communications

1. Introduction

   In a recent communication in this journal, O'Neill |6~ claims that computing entropy indices for concentration as was done by Hexter and Snow |3~, Hexter |2~, and Nissan and Caveny |4; 5~ were incorrect because the use of data for sales and assets of the Fortune 500 sample manufacturing companies is just a fraction of the total companies. Instead, data of the actual number of companies, which number in the hundreds of thousands, should be used in the computation, O'Neill says. Because working with data on such a scale is prohibitive at best and perhaps impossible because of unavailability, O'Neill computes the shares of sales of the Fortune 500 as percentages of total net sales for the years 1967 to 1987 taken from various issues of the Statistical Abstract of the United States, herein referred to as Abstract. O'Neill then recomputes, as an example, sales entropy for the years 1967 to 1987 which he calls the "corrected" index and makes comparisons with the results of Nissan and Caveny for the same period. Similar arguments by O'Neill |7~ were forwarded on the work of Attaran and Saghafi |1~ concerning concentration trends and profitability in U.S. manufacturing. O'Neill proposes that the use of net sales as the basis of computing the shares of the 500 firms results in a reversal of conclusions. Whereas the aforementioned authors claim that the trends in concentration were on the increase, O'Neill says that concentration is instead, on the decrease. The purpose of this comment is to provide a response to O'Neill's criticisms and to show that using either method, one obtains similar conclusions when the data are compatible.

2. Comparisons

   Theil's entropy measure "E" on which all computations are based is

   |Mathematical Expression Omitted~

   where |S.sub.i~, in the present study, stands for the share of sales of firm "i" as a ratio of total sales, and n is the number of firms. If all n firms have an equal share, entropy is at maximum and concentration is at a minimum. When one company controls all shares, entropy is at a minimum, and E = 0. Thus, a decrease in E over time implies an increase in concentration. The reverse is true when "E" increases.

   The gist of the argument profferred by O'Neill is that in calculating the entropy of the largest 500 firms listed in Fortune, the shares "|S.sub.i~" should be ratios of sales to total sales of all manufacturing firms rather than just the total of the 500 firms alone. Because such data are...