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

I. 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.

II. 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 not provided by Fortune, O'Neill uses net sales data obtained from an alternative source, the Abstract. The use of such a procedure will be shown to produce inconsistent results and furthermore to be unnecessary. The following items make these points clear.
```Table I. Net Sales of All Manufacturing Firms and Gross Sales
of Fortune 500 Firms (Billion of Dollars)
Net Sales(a) Gross Sales(b)
Year A B A/B
1967 575 359 1.60
1968 632 405 1.56
1969 694 445 1.56
1970 709 462 1.53
1971 751 503 1.49
1972 850 558 1.52
1973 1017 667 1.52
1974 1061 831 1.28
1975 1065 865 1.23
1976 1203 970 1.24
1977 1328 1087 1.22
1978 1496 1216 1.23
1979 1742 1445 1.20
1980 1897 1650 1.15
1981 2145 1773 1.21
1982 2039 1672 1.22
1983 2114 1686 1.25
1984 2335 1753 1.33
1985 2331 1808 1.29
1986 2221 1712 1.30
1987 2378 1879 1.27
a. Source: Various issues of the Statistical Abstract of the
United States.
b. Source: Data published annually by Fortune.
```

(1) The reliability of net sales in the Abstract is questioned. This is primarily due to the way data are assembled. A warning in the tables states, "Data are not necessarily comparable from year to year due to changes in accounting procedures, industry classifications, sampling procedures, etc." Thus, the use of such data makes the adjustments on yearly entropy index values unreliable. As pointed out by Saghafi and Attaran |8~ in their reply to O'Neill |7~, the differences in the calculations may be due to differences in source and type of data used. For illustration, Table I provides net sales data from the Abstract (column 1) and total gross sales figures from Fortune (column 2) for the years 1967 to 1987. As shown in column 3, some consistency exists in the ratios between 1967 and 1973 where the values hover around 1.50. Suddenly the ratios are reduced to approximately 1.25 between 1974 and 1987, producing another set of consistent ratios. The result of such change is dramatically illustrated in Figure I in O'Neill |6, 265~, where there is a sharp jump in the graph corresponding to the value of the total entropy index in 1974.

(2) Pursuing the analysis a bit further, a series of simple regressions were conducted using the form of the regression equation

|Y.sub.i~ = a + b|T.sub.i~,

where |Y.sub.i~ is the entropy index for year i, a is the intercept, b is the trend, and |T.sub.i~ represents the year (1 for 1967,..., 21 for 1987). First, linear trend regressions for the years 1967 to 1987 TABULAR DATA OMITTED were performed on total entropy calculated by Nissan and Caveny (N&C), and on total entropy calculated by O'Neill (corrected) as the dependent variables. This data was obtained from Table I of O'Neill |6, 264~. Similar regression was performed again, with the period of interest this time being 1974 to 1987. The results are shown in Table II.

When the whole period 1967 to 1987 is used, the two regressions give different results. The Nissan and Caveny model produced a negative and significant slope of -.0207, indicating that there was a declining trend in the entropy index, and thus an increase in concentration. The O'Neill (corrected) model produced a positive slope of .0493, indicating a decrease in concentration. But this discrepancy is the result of the incompatibility of data as pointed out in (1) above.

When regression is performed for the period 1974 to 1987, a different picture emerges as shown in Table II. For this time span, the Nissan and Caveny model produced an almost identical slope of -.0206; however, the O'Neill (corrected) model reversed in trend had a slope with a negative sign (-.0336), indicating an increase in the trend toward concentration. This simple analysis shows that if data are comparable, as is the case for the period 1974 to 1987, the results are the same whether one uses the net sales of all the firms or the gross sales of the largest 500 firms only.

III. Summary and Conclusions

This comment addresses criticisms by O'Neill |6~ concerning indices of concentration of sales provided by Nissan and Caveny |51~. This analysis shows that the noted discrepancies were the result of using data that are not comparable, and it shows, as well, that when the data are comparable the original conclusions are obtained. In short, exclusive reliance on one set of data in reaching a conclusion in this type of study is better than basing such conclusions on a mixture of data.

References

1. Attaran, Mohsen and Massoud M. Saghafi, "Concentration Trends and Profitability in the U.S. Manufacturing Sector: 1970-84." Applied Economics, November 1988, 1497-510.

2. Hexter, Lawrence J., "Measuring Relative Concentration." Southern Economic Journal, January 1987, 777-78.

3. ----- and John W. Snow, "An Entropy Measure of Relative Concentration." Southern Economic Journal, January 1970, 239-43.

4. Nissan, Edward and Regina Caveny, "Relative Concentration of the Largest 500 Firms." Southern Economic Journal, January 1985, 880-81.

5. ----- and -----, "Relative Concentration of Sales and Assets in American Business." Southern Economic Journal, April 1988, 928-33.

6. O'Neill, Patrick B., "Measuring Relative Concentration of Sales in U.S. Manufacturing." Southern Economic Journal, July 1991, 263-67.

7. -----, "Concentration Trends and Profitability in U.S. Manufacturing: A Comment." Applied Economics, April 1991, 717-20.

8. Saghafi, Massoud M. and Mohsen Attaran, "Concentration Trends and Profitability in U.S. Manufacturing: A Reply and Some New Evidence." Applied Economics, April 1991, 721-22.