Aggregate Concentration in Corporate America: The Case of the

Nissan and Caveny, International Journal of Applied Economics, 2(1), March 2005, 132-152 132

Aggregate Concentration in Corporate America: The Case of the Fortune 500

Edward Nissan and Jennifer Caveny

The University of Southern Mississippi

Abstract: This article provides a look at business concentration for sales and assets for the period 1967 to 2002 based on Theil’s entropy, a measure adopted by several authors in earlier publications. For contrast, three other well-known measures of concentration, the Hirschman-Herfindahl (HHI) index and the 4-firm and 8-firm concentration ratios, CR4 and CR8, were utilized. Data used were sales and assets of the largest 500 companies provided by Fortune magazine. In addition to detailed results on concentration, the paper found that the inclusion of service firms with the industrial firms in the list of 500 in 1994 somewhat changed the levels and trends in concentration. Keywords: Theil’s entropy, HHI, concentration ratios, Fortune 500 JEL Classifications: L10, L22, L40 Introduction

Sorkin (2004), in assessing future trends of mergers and takeovers, claims that although 2002 and 2003 did not witness a great deal of activity due to financial and political instabilities, there is a renewed interest in megadeals in corporate America. Despite the “lack of activity,” the deal volume last year was $525 billion, and was $429 billion the year before. The prediction is that merger mania will return, and that the top Fortune 100 are poised for action at the first sign of the return of growth.

The growth of a company, according to Greer (1992), can be accomplished either internally because of its efficiency in a given market or externally through mergers. In either case, there is a potential for business concentration, which may lead to monopolization. A practical way to gauge the level of business concentration in the United States is to view the pattern of growth of the largest companies for which sales and assets data is provided by Fortune magazine’s publication of the Fortune 500. In 2003, the companies included in the list accounted for $7.5 trillion in revenues and $445.6 billion in profits.

The purpose of this paper is to provide an assessment of industrial concentration of the largest U.S. companies between 1967 and 2002, as provided annually by Fortune magazine. Note that there is a one-year lag between the reported results and the year of the publication of the data. For instance, the results shown in this paper for the year 2002 are based on data published by Fortune in 2003.


Literature Survey

According to Adams and Brock (2004), merger mania at the turn of the last century marked the initial corporate consolidations in corporate America. The second round, occurring between World War I and the beginning of the Great Depression, was followed by a third wave in the 1960s, which peaked in 1969 and diminished during the 1970s. Resumption occurred through the “leveraged buyout/junk bond/hostile takeover” activity in the 1980s but crashed through bankruptcies in the late 1980s and early 1990s. In the mid 1990s, a fourth wave exploded to new heights. Adams and Brock provide a sense of the magnitudes by pointing out that announced mergers and acquisitions of $130 billion in 1991 skyrocketed to $1.7 trillion in 1999. During the Clinton administration alone, they say, some 70,000 mergers took place with a combined value of $6 trillion, which is equivalent to the U.S. gross domestic product in 1992.

Crook (1996) traces the peaks in aggregate merger activity in the United States, occurring in 1920, 1929, 1968, 1986 and 1992.Crook documents his evidence through eleven scholarly studies, each of which provides an economic reasoning for the occurrence of these peaks. Taking these together, he summarizes the economic variables that induced the merger peaks. The variables appear to suggest that such activities were related to Tobin’s Q, which is an index computed as a function of share prices, fuel prices, unemployment, real expenditures on housing, business failure rate and credit rationing. The first two variables are positively related to Tobin’s Q, while the other four are negatively related. Two other variables included in the index – bond yields and industrial production – had ambiguous relationships.

Crook goes on to show newer long-run relationships between the levels of merger activity and a host of their determinants for the period 1930-1979. The dependent variable was the annual number of completed mergers and acquisitions of manufacturing and mining companies with assets of $1 million and more. The independent variables were cost of funds, output, growth rate of output, spare capacity and Tobin’s Q index. His findings appear to suggest that the number of mergers and acquisitions in the long run is positively related to both the level of manufacturing production and the level of nominal bond yield. In the short run, mergers and acquisitions were found to be positively related to current changes in Tobin’s Q and changes in Q lagged one, two and four years, and to changes in the current bond yield, but negatively related to changes in the yield in the previous year.

Shleifer and Vishny (1988, 1991) and Sikora (1995) blamed the administering of antitrust laws as the strongest single cause in the increase in the number of mergers and acquisitions as witnessed in the 1980s as compared to the 1960s. They say lax policies of the 1980s made it possible to divest and acquire assets and to resell peripheral divisions to companies who could manage them better. Adams and Brock (2004) also note the role merger policies play in increasing the levels and numbers of mergers during the Reagan and Bush administrations through the merger guidelines of 1982, 1984, 1988 and 1992. These guidelines view mergers and takeovers as valuable instruments to force management to heed stockholder-owner interests. Restraints to takeovers would be counterproductive by protecting inefficient managers from the discipline of the merger market.

Amoto (1995) explains the dichotomy of scholarly opinions related to the so-called structure performance model of industrial organization. The model hypothesizes a strong correlation between concentration as a consequence of business organic growth and/or mergers and profit. The other side of the dichotomy discredits the structure-performance model, suggesting that individual firm efficiency explains profits. This revisionist view -- introduced by


Demsetz (1973) and supported by Ravenscraft (1983), Branch (1980) and Gale and Branch (1982) -- showed that concentration is found to have a negative impact on profits. More recently, Bhuyan (2002), in his study of the relationship between vertical mergers and profitability, has shown that the relationship is negative.

Grone and Spikes (2004), commenting on the recent $58 billion merger of J.P Morgan Chase & Co. with Bank One Corp. and Bank of America Corp.’s agreement to acquire Fleet Boston Financial Corp for $49 billion, say a major benefit of such mergers is the provision of larger access to the U.S. retail market. The retail market, according to Langley, Pacelle and Sapsford (2004) includes services to consumers, such as lending and credit cards. Yet, Hamel (2004) questions the wisdom of such mergers, contending that his research on twenty industries suggests no correlation between size and profitability. He goes on to say that the cost of integration far exceeds the benefit of anticipated economies. A major acquisition is simply a way to compensate for organic growth, which, when free of accounting trickery, is of course desirable.

Paul (2003) provides an exception to this view by concluding that the U.S. beef packing industry consolidation of recent years resulted in significant scale economies substantiating cost-efficiency benefits outweighing pecuniary diseconomies associated with market power. Bley and Madura (2003), on assessing conglomerate mergers due to removal of cross-border barriers and the adoption of a single currency in the European Union, claim that diversification is the motivating factor. Conglomerates can gain financial benefits in improving their negotiation posture with banks, thus reducing the cost of capital. Bley and Madura cite many studies that confirm or refute their claim.

The above review of literature provides a brief look at the question of mergers and their consequences on the increase in business concentration. For this, Gallo et al (2000) investigated the number of antitrust enforcement cases undertaken by the Department of Justice (DOJ), including those involving the largest 500 enterprises as reported by Fortune. Between 1955 and 1997, according to their calculations, 454 out of 1,248 (34 percent) of the cases involved the Fortune 500.

The Computational Models

Hannah and Kay (1977) provide a list of the most commonly used mix of concentration measures. The list includes the coefficient of variation (CV) obtained by dividing the standard deviation by the mean. Two popular measures are the k firm concentration ratio where k indicates how many leading firms are taken into account to define concentration (usually k = 4 or k = 8) denoted by CR4 and CR8, and the Hirschman-Herfindahl Index (HHI) obtained by squaring and summing the companies’ share in a sample. A less often used measure is the Gini concentration coefficient (G), which, according to Sherman (1974), is a summary representation of the Lorenz Curve, whereby cumulative percentages of shares are plotted against the cumulative percentages of firms. Two other notable measures are the Theil’s entropy, H(s), derived from the notion of entropy in information theory, according to Sen (1973), and the variance of logarithms. According to Creedy (1985), variance of logarithms describes a process known as the Gibrat’s law of proportionate effect, whereby if the growth of firms follows the lognormal distribution, the variance of this distribution will increase steadily. Each of the measures outlined possesses some inherent weaknesses and strengths according to Caswell


(1987). However, they are expected to correlate well according to Sherman (1974), plausibly because of consistency and validity of time trends inherent in each of the measures.

Miller (1972) describes Theil’s (1967) entropy as the current front runner in rivalry with the popular concentration ratios and the Hirschman-Herfindahl index, especially on the finding that the contributions to knowledge by other measures are marginal. Besides, Theil’s entropy has one distinct advantage over the others in that it can be decomposed into a “between sets” and “within sets” components. Champernowne (1974), recognizing that there is no single “best” coefficient of inequality, compared the performance of various indexes of inequality according to three aspects. These are inequality due to extreme relative wealth (α), inequality among the less extreme incomes (β), and inequality due to extreme poverty (ɤ). His conclusion was that the measures based on the coefficient of variations and Theil’s entropy were the most sensitive to α-type inequality associated with the exceptionally rich.

An early use of Theil’s entropy is by Jacquemin and Kumps (1971) in their study of the size structure of the largest European firms. Theil (1979, 1989) contributed two papers on the use of entropy to measure inequality, demonstrating in both papers the usefulness of disaggregating the measure into a “between” group portion and a “within” group portion. Cowell (1980) contributed to understanding the potentials of the measure and so also Kakwani (1980) and Slottje, Basmann and Nieswiadomy (1984). Attaran and Zwick (1987) provide an insight for Theil’s index for use in measuring industrial diversification. Attaran and Saghafi (1988), Saghafi and Attaran (1990) and Ng (1995) provide examples for its use in industrial organization research dealing with the subject of concentration.

Recently, many scholars have employed Theil’s entropy index in a variety of research having inequality as a common theme. Zanasi (1995) identified the most effective spatial performance of dairy cattle stock between and within areas of Italy. The work of Hubbell and Welsh (1998) is another application of Theil’s entropy in agriculture. In examining the geographic concentration in hog production in the United States, they also highlighted the attractiveness of Theil’s entropy to gauge dispersion or concentration and its ease of decomposition into within and between regions.

Mills and Zandvakili (1997) used Theil’s entropy to study youth earnings inequality, finding that during the latter half of the 1980s inequality within the cohort age groupings has decreased while between age-group, inequality has increased. Mills and Zandvakili explain that the ability of Theil’s index to compare inequality both within and between subgroups of the populations based on a variety of characteristics such as age, race and education is what makes it a desirable measure.

Again, because Theil’s is an additively decomposable measure, Fain (1999) employed the index to examine the impact of age, education, race, marital status, full-time work status and gender as factors influencing occupational outcomes. Fain found that gender and education were by far the most prominent factors explaining occupational inequality outcomes. Chowdhury (2003) -- with similar reasoning and enumerating some additional virtues of Theil’s index, such as freedom from bias and value judgment -- chose Theil’s entropy index to study income inequality between and within regions of the world. In this effort, Chowdhury grouped countries into eight geographic regions, finding that the between-region inequality component dominates the overall global inequality. He also found that within-region inequality has been decreasing over time, while between-region inequality has been increasing.

In every one of these studies, Theil was chosen because of the possibility of disaggregating the measure into “between” and “within” portions. For this reason, and because


the sundry measures of concentration in common use are highly correlated as explained earlier, this paper opted for Theil’s entropy as the index of choice of concentration in American businesses. Although not comparable with Theil’s index because they do not lend themselves to disaggregation, three other indexes are employed as well for contrast. They are the Hirschman-Herfindahl (HHI), the four-firm ratio (CR4) and the eight-firm ratio (CR8).

According to Batten (1983), the Theil's entropy measure for concentration is n

H(S) = − Σ Pi log Pi, (1) i = 1

where n is the number of firms and Pi is the market share (based on sales or assets) so that Σ Pi = 1.0. The logarithms in this study are taken to the base 2. The range for H(S) is between zero, when one firm dominates the market, and log n, when all firms control equal shares (1/n) of the market. Note that for the entropy index of equation (1), the smaller H(S) is, the larger the concentration. A disaggregation of equation (1) into n sets of firms G1, G2, …, Gn with shares P1*, P2*, …, Pn* is

n n

H(S) = − Σ Pj* log Pj* + Σ Pj* Sj* , j = 1, 2, …, n, (2) j = 1 j = 1

where Pj* = Σ Pi

i ε Gj

and Sj* = Σ (Pi / Pj*)log(Pi / Pj*) . (3)

i ε Gj

Equation (2) disaggregates total entropy into between-group entropy, indicated by the first part of the equation, and average within-group entropy, indicated by the second part of the equation. Equation (3) provides the separate within-group entropies. The second index of concentration employed in this study, the Hirschman-Herfindahl Index HHI, is obtained by summing the square of firm shares in the sample. That is,

n n

HHI = Σ PiPi = Σ Pi2.

i = 1

When one firm holds all shares, HHI = 1.00; when shares are held equally, H = 1/n. Note that HHI gives larger weights to larger firms, making it a favorite in the merger guidelines by the Department of Justice – Federal Trade Commission.

The third and fourth measures of concentration, CR4 and CR8, are obtained as sales or assets of the leading four or eight firms as ratios of totals. Amoto (1995), citing various empirical studies comparing HHI and concentration ratios, concludes that the HHI provides modest improvement and no additional explanatory power when compared to concentration ratios.


The Fortune 500 The data for computing the entropy index of equation (1) as well as HHI, CR4 and CR8 are obtained from Fortune's annual directory of the 500 largest firms in the United States. Prior to 1994, the directory listed the largest industrial corporations. Directory listings from 1994 and later added corporations that provide services, thus changing the title from “The Largest Industrial Corporations” to simply “The Largest Corporations.” For example, in the Fortune 1996 edition, the new entrant Wal-Mart Stores is ranked fourth with $93.6 billion in sales, trailing General Motors, Ford Motor and Exxon who ranked in the first three spots with respective sales in billions of $169, $137 and $110. In the 2003 Fortune edition, Wal-Mart Stores moved into the first slot with sales of $247 billion, leaving General Motors, Exxon and Ford behind with respective sales in billions of $187, $182 and $164 in respective ranks of second, third and fourth.

The inclusion of service industries among the industrial industries from 1974 and beyond reflects the radical change in the industrial output mix since the 1950s. Schwartz (2004) perhaps best described the phenomenon when he said (p.260), “Who could have imagined in the mid-1950s all the wonders that have since come to pass? That scientists would decode the human genome, or clone a sheep? Or that we’d be carrying tiny phones that not only don’t need wires but also can take photographs?”

The effect of such an industrial shift was brought to light on a regional level by Beeson and Tannery (2004) where they document the loss of jobs due to the shrinking manufacturing sectors, exemplified by the steel industry in Pennsylvania. Employment in durable manufacturing and especially the steel-dominated primary metals experienced drastic losses. For employment in durable goods for instance, a total of 250,000 jobs in 1979 was reduced to 91,400 by the end of 1987. The industrial restructuring experienced in Pennsylvania is amplified throughout the country affecting the distribution of earnings as a consequence.

Smith and Miller (2001) document the structural shift of the national economy from primary to secondary to tertiary sectors. The primary sector composed of agriculture, forestry, fishing and mining gave way to the secondary sector composed of manufacturing, construction and utilities, and this sector in turn is giving way to the tertiary sector composed of a wide range of service industries. Thus, through the course of economic development there is this sequential shift of employment from agriculture and other extractive industries to manufacturing to services. The shift from manufacturing to services is a reflection of economic progress, which, according to Aizenman (2001) was a consequence of the catching up of emerging economies with the high-income economies. De-industrialization in the high-income economies would have occurred without the presence of emerging markets but the process was speeded up. The disruption in the Fortune 500 listing described above makes the entries in Table 1 -- which lists the percent distribution of sales and assets of the 500 firms in five equal groups of 100 -- depart in magnitude at the break dates 1993 and 1994. Table 1 and subsequent tables list the results between 1967 and 2002. Table 1 shows that prior to 1994 the top 100 companies increased their share of sales from approximately 64 percent of the total in 1967 to approximately 71 percent in 1993. The share of sales of this group between 1994 and 2002, however, is reduced to much smaller levels, ranging for this period from between approximately 55 percent to approximately 59 percent. This reduction in the share of sales of the top 100 at the break dates 1993 and 1994 is translated into increases in shares of sales for the lower groups. On average, the changes in percent sales between the two periods for the five groups of 100


companies were 67.0, 15.9, 8.4, 5.2 and 3.5 to 57.1, 18.9, 11.1, 7.4 and 5.5. For assets in Table 1, the disruption in the Fortune 500 listing for the five groups operated in the opposite direction. For the top 100 companies, there was an increase in average share of assets from 69.8 percent to 75.1 percent, which is translated into decreases in shares of the four remaining groups of 100 companies. On average, the shares of assets of the five groups changed in percentages between the two periods from 69.8, 15.4, 7.8, 4.5 and 2.5 to 75.1, 13.9, 6.3, 3.3 and 1.5. Empirical Results Table 2 provides the results of using both sales and assets as bases in computing Theil’s entropy. The first two columns of Table 2 contain the total entropy of concentration for the 500 firms as computed by equation (1). The 500 firms were then grouped into two sets: the top 100 and the bottom 400. Thus, total entropies from the first two columns were disaggregated into between-sets and within-sets entropies from equation (2). In addition, the entropies within the top 100 firms and entropies within the bottom 400 firms were computed from equation (3). The effect of disruption in listings on the computed values reported in Table 2 seems to be somewhat minor with the exception of total entropy for both sales and assets, where noticeable breaks in magnitude are observed between 1993 and 1994. These findings indicate that, on average, there were slight increases in total entropies for sales and a slight decrease in entropy of assets between the two periods, giving the impression of a decrease in concentration for sales and a slight increase in concentration for assets. Table 3 reports results for grouping the 500 companies into five equal sets of 100 companies each. The first two columns of Table 3 are the between-sets entropy for sales and assets. The disruption in the listing of companies by Fortune affected substantially the between-sets entropies for sales, which increased from 1.39 in 1993 to 1.79 in 1994 and decreased thereafter to 1.72 in 2002. On average, the change for between-sets entropies between the two periods for sales was from 1.50 to 1.77, signaling a decrease in sales concentration. A reversal of pattern occurred for assets where a decrease in entropy on average was from 1.38 to 1.20, signaling an increase in concentration in the second period. Thus, when the 500 companies were viewed as five entities made up of 100 companies each, concentration among them in sales dropped while concentration among them in assets grew when comparing the two periods.

To make sense of the differences in sales and assets of the top 100 firms, it is advisable to observe data for the constituent companies. One way to do this is to compare the sales and assets of some of the prominent companies for 2002 (reported in Fortune 2003). The list below comprises a selection of companies designated as industrial and service, giving in each case the dollar magnitudes ($million) for sales and assets with the corresponding ranking in parentheses as provided by Fortune.


Industrial

Name Sales Assets Ratio Assets/Sales)General Motors 186,763 (02) 370,782 (10) 1.99Exxon Mobil 182,466 (03) 152,644 (28) 0.84Ford Motor 163,630 (04) 289,357 (15) 1.77General Electric 131,698 (05) 575,244 (06) 4.37Chevron Texaco 92,043 (07) 77,359 (53) 0.84IBM 83,132 (08) 96,484 (40) 1.16Conocophillips 58,394 (12) 76,836 (56) 1.32

Services Name Sales Assets Ratio (Assets/Sales)Wal-Mart Stores 246,525 (01) 94,552 (42) 0.38Citigroup 100,789 (06) 1,097,190 (01) 10.89Verizon Communication 67,625 (10) 167,468 (26) 2.48Fannie Mae 52,901 (16) 887,257 (02) 16.77State Farm Insurance 49,653 (21) 117,811 (31) 2.37Bank of America Corp. 45,732 (23) 660,458 (05) 14.44J.P Morgan Chase 43,372 (26) 758,800 (03) 17.50

These partial small lists tell the story regarding the discrepancies of decrease in

concentration for sales and increase in concentration for assets upon the inclusion of the service industries with the industrial services. The ratios (Assets/Sales) -- especially for those businesses engaged in finance and banking such as Citigroup, Fannie Mae, Bank of America Corp and J.P. Morgan Chase -- are much higher than those companies listed under the industrial category.

In fact, by computing the means and the standard deviation for the years of the break in the listing 1993 and 1994, average sales jumped from $4.7 billion to $8.5 billion corresponding to a jump in the standard deviation from $11.1 billion to $13.3 billion, an increase of 20 percent. For assets, the increase was from $5.4 billion to $19.1 billion with a corresponding change in standard deviation from $18.2 billion to $36.2 billion, an increase of almost 100 percent.

This exercise demonstrates the effect of including services with industrial in the Fortune 500 listing, in the sense that while the changes in sales were relatively moderate, the changes in assets were dramatic, giving rise to relatively small changes in concentration for sales and relatively larger concentration for assets. Thus, the inclusion of the services sector plays different roles in asset concentration and sales concentration in the two periods. The within-set entropies are shown in columns 3 through 12 of Table 3 for the five separate groups for both sales and assets. The top 100 companies as a group showed a continual slight increase in total entropy for sales after 1993, changing on average from 6.05 to 6.28. For assets, the change was from 6.02 to 6.13. In both instances, the indication is a decrease in concentration. However, looking particularly at assets entropies for individual years for the top 100 companies for the period 1988 to 1993 and again for the period 1994 to 2002, a decrease is noticed, indicating an increase in concentration. This is perhaps a consequence of mergers and acquisitions among the largest firms in recent years, as indicated by Pryor (2001). The increase in concentration here is irrespective of the component mixture of companies prior to and after 1994. With the exception of the top-100 group, it seems on inspection of Table 3 that the


changes in entropies were minor when comparing magnitudes of entropies prior to 1994 and after 1994. The indication is that the concentration among the bottom four groups of 100 remained unchanged. Summing up the findings of Table 3, the increase in assets concentration among the largest 100 companies is the most noticeable. Statistical Analyses for H(S) Following Ostle and Malone (1988) for inferences for paired (matched) observations, this paper investigated first whether the two modes of bases (sales or assets) in calculating total entropies between 1967 and 1986 differ significantly. The conclusion of this paper is that the observed differences in the measures of total entropy by sales and assets for each year were not statistically significant. That is, whether by using sales or assets as the basis on which entropies were calculated, the differences for each year were not statistically noticeable. A second form of analysis is to determine whether the trends in concentration indexes H(S) differ over the two periods 1967-1993 and 1994-2002, hereafter referred to as Periods I and II, respectively. A simple way to do this is to apply the suggestions by Lapin (1993) that time series covering a small number of years may be fitted by a straight line of the form

Y t = a + b t, (4)

where Yt is the computed value of the dependent variable and t is a code for time serving as the independent variable. Thus for Period I (between 1967 to 1993), t = 1, 2, …., 27, and for Period II (1994 to 2002), t = 1, 2, …, 9. The slope “b” measures the annual increase or decrease in the time series, and “a” is the intercept. The test statistic for significance of b is

t = b / Sb, (5)

where Sb is the standard error of the slope b. Equation (4) is applied to total entropies based on sales and assets (displayed in columns 1 and 2 of Table 2) and to the between-sets entropies as well as the individual within-sets entropies of the five groups based on sales and assets (displayed in all twelve columns of Table 3). In each case, the hypothesis of equality of trends for Periods I and II will be tested in accordance with the suggestion of Bailey (1985) by the test statistic

t* = (b1 – b2) / [s2b1 + s2

b2] ½, (6)

where b1 and b2 are the slope coefficients for Period I and II and s2b1 and s2

b2 are their squared standard errors. The results of these time series trends are shown in Table 4. The columns labeled “b1” and “b2” in Table 4 present the slope values for the two periods. For each slope, a test of the hypothesis of no trend is accomplished with the t-test given in equation (5). For significance level α = 0.05, the critical point for significance of each slope in Period I is ± t (0.025, 25) = ± 2.060 for a two-tailed test with 25 degrees of freedom. Similarly, the critical point for significance of each slope in Period II is ± t (0.025, 7) = ± 2.365. Table 4 also presents the t*


values for testing the equality of the slopes of the two periods by equation (6). The critical point for two-tailed testing with 36 degrees of freedom at the 0.05 significance level is ± 1.96.

As stated earlier, smaller entropies indicate larger concentrations of businesses. Therefore, a negative slope for the trend in entropies indicates an increase in concentration, while a positive slope indicates a decrease in concentration. It is evident from Table 4 that there are statistically significant increasing trends in concentration across Period I with both sales (except Set 5 but with the proper sign) and assets as the bases of the entropy calculations. However, in Period II, the bag is mixed. Concentrations based on assets only prove to have statistically significant trends in two of the sets of 100 firms, one an increase in concentration (Set 1) and one a decrease in concentration (Set 3). In Period II, the sales entropies followed significant increasing trends in concentration between the five sets and within Sets 2, 3 and 4, while Set 1 (top 100 firms) experienced a significant decrease in concentration. This is an interesting result. It shows that though the top 100 firms experienced an increase in concentration of their assets, due to the merger waves of the recent years, as explained earlier, their sales concentration was reduced -- perhaps due to the inclusion of service firms along with industrial firms. In other words, the largest firms swallowed assets of other firms, irrespective of the nature of their business without showing significant gains in their shares of sales. In comparing the slopes across the two periods, as shown by t* in Table 4 calculated from equation (6), in only two cases did the test statistic reject equality of trends between the two periods, meaning only two statistically significant differences were found. Specifically, entropies based on sales within the top 100 firms decreased over Period I and increased over Period II. Similarly, within Set 3, entropies based on assets decreased over Period I but increased over Period II. Overall, the results in Table 4 indicate that the trends in concentration of sales and assets did not change significantly between the two periods as a result of the change in composition of the Fortune 500 listing. Only two of twelve tests showed statistically significant results. Comparing H(S) with HHI, CR4 and CR8

As indicated earlier, although H(S) has the unique advantage of being additively decomposable as compared to other concentration indexes, nevertheless, it is of interest to investigate how it compares with HHI, CR4 and CR8. The first two columns of Table 5 provide the HHI scores for both sales and assets followed similarly by two columns for CR4 and again by two columns for CR8. The remarkable finding here is that the latter three indexes are almost mirror images of total entropy displayed in the first two columns of Table 2.

Concentration, according to the four indexes, decreased between Period I (1967-93) and Period II (1994-02) for sales, noting that H(S) operates inversely. The means of HHI for sales were reduced between the two periods from 0.01144 to 0.00643. For CR4, the means for sales were reduced from 0.15771 to 0.10579. A similar finding was true for CR8 where the corresponding reduction was from 0.23630 to 0.16441. For assets, HHI was in complete conformity with H(S), increasing from an average of 0.0129 to 0.01367. No such correspondence was observed for assets for either CR4 or CR8 where the mean levels of concentration for assets were reduced from 0.16026 to 0.13567 for the former and from 0.24348 to 0.22948 for the latter. It seems overall that HHI is more in conformity with H(S) on both counts, sales and assets, than are the other two indexes.


Of interest here is to find out whether these observed differences in means of the four indexes between Period II and Period I differ significantly by utilizing a t-test of two independent samples. The critical values of the test for a five percent significance level are ±1.96. The t-test results are

Sales

H(S) = 14.24 HHI = -17.20 CR4 = -18.28 CR8 = -15.54

Assets

H(S) = -1.27 HHI = 0.42 CR4 = -1.78 CR8 = -0.81

For sales, all four measures indicate a statistically significant decrease in concentration as indicated by the t-test. None of the t-values for assets showed statistical significance. None of the t-values are > 1.96 or < -1.96.

Perhaps a better way to judge the comparative relative performances of the four indexes is to evaluate their correlation, displayed in the matrix below

Sales Assets

H(S) HHI CR4 CR8 H(S) HHI CR4 CR8 H(S) 1.000 -0.992 -0.968 -0.9888 1.000 -.0957 -0.952 -0.967HHI 1.000 0.990 0.996 1.000 0.998 0.992CR4 1.000 0.985 1.000 0.992CR8 1.000 1.000

which gives an indication of high correlation among the sundry concentration indexes. The findings here substantiate to a great extent the comments reported earlier that in general the concentration indexes correlate highly.

A third form of analysis is to detect the nature of trends in concentration for the two periods for both sales and assets. The slopes of the trend regression (t-values in parentheses) applying equation (4) are


Period I Period II Sales Assets Sales Assets

H(S) -0.017940 -0.029940 -0.008670 -0.018830 (-16.20) (-7.68) (-1.56) (0.71) HHI 0.0001620 0.0005210 -0.000300 0.000928 (13.03) (6.80) (-0.01) (14.24) CR4 0.001323 0.004918 -0.000133 0.010692 (8.92) (6.33) (-0.19) (9.32) CR8 0.002458 0.005536 -0.00160 0.014973 (12.25) (7.12) (-0.16) (13.57)

This array of numbers allows a conclusion regarding trends of concentration that there is

complete unanimity among the four measures for sales and assets during Period I. All of them showed increasing trends, and the t-values of the trend coefficients were extremely high. All the measures were in agreement that no noticeable trends in concentration were evidenced. The t-values for trend coefficients indicate no statistical significance. The only departure from this consensus is the case for assets in Period II for entropy. Though with the proper sign for an increase in concentration, the coefficient is not significant. Agreement among the three remaining measures is complete, pointing to increasing concentration for assets during the second period. Summary and Conclusions The interest in concentration of business is a key element in industrial organization theory and an important guide when dealing with merger and acquisition issues (Scheffman and Coleman, 2002). This paper, through the use of Fortune 500 data, provided a survey of concentration in big business for both sales and assets. The measure of choice for concentration is Theil’s entropy H(S) because it has the unique feature among many other measures that total concentration can be disaggregated into “between groups” and “within-groups.” The rationale was to investigate the levels of concentration between and within sets grouped in a variety of ways. However, for the sake of comparisons, three other concentration measures were utilized – the Hirschman-Herfindahl (HHI) index and the four-firm and eight-firm concentration ratios CR4 and CR8. The time period under consideration was 1967-2002. A by-product of this research is the finding that the list of 500 U.S. companies identified by Fortune has changed in composition from strictly industrial firms to include service companies as well, beginning in 1994 (Fortune, 1995 edition). This paper, through the use of the four measures of concentration, also investigated whether the change in composition of the Fortune list has considerably impacted the levels of concentration. For this reason, the research dealt with the whole period 1967-2002 as well as subperiods 1967-1993, denoted as Period I, and 1994-2002, denoted as Period II. The findings, through the use of statistical analysis, attest, with minor exceptions, to a general agreement among the four measures in that:

(1) All four measures are highly correlated, (2) Differences in mean sales concentration between Period I and Period II were negative and statistically significant, implying a decrease in sales concentration during Period II,


while differences in mean concentration for assets were not statistically significant, implying minor change in concentration, and (3) Trends in concentration for sales and assets during Period I were statistically significant, implying an increase in concentration. For Period II, none of the four measures detected any statistically significant change in sales concentration. However, all agreed that there was an increase in concentration, although the coefficient of the Theil’s index was not statistically significant.

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Table 1. Percent Distribution of Sales and Assets of FORTUNE 500 Firms, in Groups of 100

Group1 Group2 Group3 Group4 Group5 Year Sales Assets Sales Assets Sales Assets Sales Assets Sales Assets 1967 63.7 68.5 16.8 15.2 9.4 8.4 5.9 4.9 4.2 2.9 1968 63.9 68.4 16.9 15.7 9.3 8.3 5.8 4.8 4.0 2.8 1969 63.0 67.6 17.6 16.5 9.3 8.4 5.9 4.8 4.2 2.7 1970 62.2 67.7 17.8 16.4 9.4 8.4 6.2 4.8 4.3 2.7 1971 62.6 66.6 17.4 16.6 9.5 8.7 6.2 5.2 4.3 2.9 1972 62.4 65.7 17.5 17.1 9.6 8.9 6.1 5.3 4.4 3.0 1973 62.5 65.9 17.3 17.0 9.5 8.8 6.2 5.3 4.5 3.0 1974 64.4 68.9 16.4 15.6 9.3 8.1 5.8 4.8 4.1 2.6 1975 64.9 65.9 16.4 17.0 9.1 8.9 5.7 5.3 4.0 2.9 1976 65.4 66.3 16.0 16.9 9.1 8.8 5.5 5.1 3.9 2.8 1977 66.0 66.9 15.9 16.7 8.9 8.7 5.4 5.0 3.8 2.8 1978 65.8 66.8 16.4 17.0 8.7 8.6 5.3 4.8 3.7 2.8 1979 66.7 67.0 16.4 17.1 8.5 8.5 5.1 4.8 3.4 2.7 1980 67.6 66.8 15.8 17.0 8.3 8.6 4.9 4.8 3.4 2.7 1981 68.1 65.7 16.0 17.4 8.1 8.9 4.8 5.1 3.1 2.9 1982 68.6 67.1 15.8 16.7 7.9 8.7 4.6 4.8 3.0 2.7 1983 68.8 67.2 15.6 17.1 7.9 8.1 4.7 4.8 3.0 2.7 1984 69.5 69.9 14.9 15.0 7.9 8.1 4.6 4.5 3.0 2.5 1985 70.0 70.4 14.7 14.8 7.8 7.5 4.6 4.7 2.9 2.6 1986 69.7 71.4 15.2 14.2 7.6 7.1 4.6 4.9 2.8 2.4 1987 69.6 72.5 15.3 14.5 7.6 7.0 4.7 4.0 2.9 2.0 1988 69.7 75.5 15.1 13.4 7.7 6.2 4.6 3.3 3.0 1.6 1989 70.1 76.2 14.8 12.9 7.6 6.0 4.5 3.3 3.0 1.6 1990 71.6 77.0 14.2 12.6 7.1 5.7 4.3 3.1 2.8 1.5 1991 71.5 77.4 14.3 12.2 7.1 5.7 4.2 3.1 2.9 1.5 1992 71.1 76.9 14.4 12.4 7.2 5.9 4.4 3.3 2.9 1.6 1993 70.7 77.2 14.5 12.0 7.4 5.7 4.5 3.3 3.0 1.7 1967-93 Mean 67.0 69.8 15.9 15.4 8.4 7.8 5.2 4.5 3.5 2.5 Std dev 3.2 4.1 1.1 1.8 0.9 1.2 0.7 0.7 0.6 0.5

1994 57.0 74.0 18.5 14.9 11.0 6.4 7.6 3.2 5.9 1.5 1995 56.1 73.9 19.0 15.1 11.4 6.5 7.6 3.1 5.9 1.4 1996 55.7 74.4 19.2 14.6 11.4 6.3 7.7 3.2 5.9 1.5 1997 55.7 75.8 19.1 13.6 11.6 5.9 7.8 3.3 5.8 1.5 1998 55.3 76.9 19.4 13.0 11.7 5.7 7.8 3.1 5.7 1.4 1999 57.0 77.6 19.0 12.3 11.2 5.8 7.3 3.0 5.5 1.3 2000 58.6 77.5 18.8 12.6 10.5 5.8 7.0 2.9 5.1 1.2 2001 59.6 78.3 18.7 12.3 10.4 5.5 6.6 2.7 4.8 1.1 2002 59.0 67.4 18.6 16.5 10.7 8.4 6.8 4.9 5.0 2.8 1994-02 Mean 57.1 75.1 18.9 13.9 11.1 6.3 7.4 3.3 5.5 1.5 Std dev 1.6 3.3 0.3 1.5 0.5 0.9 0.5 0.6 0.4 0.5

Based on data published annually by Fortune.


Table 2. Entropy of Sales and Assets of FORTUNE 500 Firms by Top 100 and Bottom 400

Total Entropy Between Sets Within Sets Within Top 100 Within Bottom 400 Year Sales Assets Sales Assets Sales Assets Sales Assets Sales Assets 1967 7.92 7.75 0.94 0.90 6.97 6.85 6.14 6.13 8.43 8.40 1968 7.90 7.76 0.94 0.90 6.95 6.86 6.12 6.15 8.42 8.36 1969 7.94 7.80 0.95 0.91 6.96 6.89 6.16 6.19 8.41 8.33 1970 8.00 7.80 0.96 0.91 7.03 6.89 6.21 6.20 8.42 8.33 1971 7.93 7.82 0.95 0.92 6.98 6.90 6.11 6.16 8.43 8.35 1972 7.93 7.84 0.96 0.93 6.97 6.91 6.09 6.15 8.43 8.35 1973 7.92 7.82 0.95 0.93 6.97 6.89 6.09 6.13 8.44 8.35 1974 7.86 7.52 0.94 0.90 6.92 6.62 6.08 5.84 8.43 8.34 1975 7.84 7.52 0.94 0.93 6.90 6.89 6.07 6.13 8.43 8.35 1976 7.79 7.79 0.93 0.92 6.86 6.87 6.03 6.11 8.43 8.34 1977 7.78 7.77 0.92 0.92 6.83 6.85 6.01 6.11 8.42 8.34 1978 7.76 7.78 0.93 0.92 6.84 6.86 6.02 6.13 8.40 8.32 1979 7.74 7.72 0.92 0.92 6.82 6.80 6.04 6.14 8.38 8.31 1980 7.69 7.78 0.91 0.92 6.78 6.86 6.02 6.14 8.39 8.32 1981 7.66 7.73 0.90 0.91 6.76 6.82 6.01 6.13 8.36 8.29 1982 7.64 7.68 0.90 0.89 6.77 6.79 6.01 6.12 8.35 8.27 1983 7.65 7.67 0.89 0.89 6.76 6.78 6.03 6.14 8.36 8.27 1984 7.61 7.53 0.89 0.86 6.73 6.67 6.01 6.04 8.37 8.26 1985 7.59 7.50 0.88 0.85 6.71 6.65 6.00 6.03 8.37 8.27 1986 7.60 7.49 0.88 0.85 6.72 6.64 6.02 6.02 8.34 8.27 1987 7.64 7.50 0.89 0.85 6.75 6.65 6.05 6.03 8.35 8.28 1988 7.60 7.14 0.89 0.80 6.72 6.33 6.01 5.72 8.36 8.22 1989 7.59 7.12 0.88 0.79 6.71 6.33 6.01 5.74 8.36 8.23 1990 7.53 7.07 0.86 0.78 6.67 6.30 6.01 5.72 8.35 8.22 1991 7.55 7.06 0.86 0.77 6.69 6.29 6.03 5.72 8.35 8.23 1992 7.56 7.08 0.87 0.78 6.69 6.30 6.01 5.71 8.36 8.25 1993 7.58 7.02 0.87 0.77 6.71 6.24 6.02 5.65 8.37 8.27 1967-93 mean 7.73 7.56 0.91 0.87 6.82 6.69 6.05 6.02 8.39 8.30 Std dev 0.15 0.28 0.03 0.06 0.11 0.23 0.06 0.18 0.03 0.05

1994 8.18 7.60 0.99 0.83 7.20 6.77 6.22 6.28 8.49 8.17 1995 8.21 7.58 0.99 0.83 7.22 6.76 6.24 6.26 8.49 8.14 1996 8.23 7.55 0.99 0.82 7.24 6.73 6.25 6.23 8.49 8.16 1997 8.25 7.46 0.99 0.80 7.26 6.66 6.29 6.17 8.48 8.20 1998 8.28 7.32 0.99 0.78 7.29 6.54 6.33 6.05 8.48 8.19 1999 8.22 7.31 0.99 0.77 7.23 6.54 6.30 6.06 8.47 8.21 2000 8.17 7.26 0.98 0.77 7.19 6.49 6.30 6.01 8.45 8.18 2001 8.14 7.18 0.97 0.75 7.17 6.42 6.32 5.95 8.43 8.15 2002 8.14 7.80 0.98 0.91 7.17 6.89 6.27 6.19 8.45 8.33 1994-02 mean 8.20 7.45 0.98 0.81 7.22 6.64 6.28 6.13 8.47 8.19 Std dev 0.05 0.20 0.01 0.05 0.04 0.16 0.04 0.12 0.02 0.05

Computations by equations 1-3


Table 3. Entropy of Sales and Assets of FORTUNE 500 Firms in Groups of 100

Between 5 Sets Within Set 1 Within Set 2 Within Set 3 Within Set 4 Within Set 5 Year Sales Assets Sales Assets Sales Assets Sales Assets Sales Assets Sales Assets 1967 1.60 1.46 6.14 6.13 6.62 6.61 6.63 6.63 6.63 6.63 6.64 6.60 1968 1.59 1.46 6.12 6.15 6.61 6.61 6.63 6.63 6.64 6.63 6.64 6.58 1969 1.61 1.47 6.16 6.19 6.61 6.61 6.62 6.63 6.64 6.63 6.64 6.57 1970 1.63 1.47 6.21 6.20 6.61 6.61 6.63 6.63 6.64 6.63 6.63 6.55 1971 1.63 1.51 6.11 6.16 6.61 6.61 6.62 6.63 6.64 6.63 6.64 6.58 1972 1.64 1.53 6.09 6.15 6.61 6.61 6.63 6.63 6.64 6.63 6.64 6.57 1973 1.63 1.52 6.09 6.13 6.62 6.62 6.63 6.63 6.64 6.63 6.63 6.57 1974 1.58 1.44 6.08 5.84 6.62 6.62 6.62 6.62 6.64 6.63 6.64 6.55 1975 1.57 1.52 6.07 6.13 6.62 6.62 6.63 6.62 6.64 6.63 6.64 6.56 1976 1.55 1.51 6.03 6.11 6.62 6.62 6.63 6.62 6.64 6.63 6.64 6.55 1977 1.54 1.49 6.01 6.11 6.62 6.62 6.63 6.62 6.64 6.63 6.64 6.57 1978 1.53 1.49 6.02 6.13 6.62 6.62 6.62 6.62 6.64 6.63 6.64 6.54 1979 1.50 1.48 6.04 6.14 6.62 6.62 6.63 6.62 6.63 6.63 6.64 6.58 1980 1.48 1.49 6.02 6.14 6.62 6.62 6.62 6.62 6.63 6.63 6.64 6.59 1981 1.46 1.45 6.01 6.13 6.62 6.62 6.62 6.62 6.63 6.62 6.63 6.57 1982 1.44 1.41 6.01 6.12 6.61 6.62 6.62 6.62 6.63 6.62 6.64 6.59 1983 1.44 1.39 6.03 6.14 6.61 6.61 6.62 6.62 6.63 6.62 6.64 6.56 1984 1.47 1.33 6.01 6.04 6.61 6.61 6.62 6.62 6.63 6.63 6.63 6.47 1985 1.41 1.31 6.00 6.03 6.61 6.61 6.62 6.62 6.63 6.63 6.64 6.53 1986 1.41 1.31 6.02 6.02 6.60 6.62 6.62 6.62 6.63 6.63 6.50 6.45 1987 1.42 1.31 6.05 6.03 6.60 6.61 6.63 6.62 6.63 6.63 6.62 6.50 1988 1.41 1.20 6.01 5.72 6.61 6.60 6.62 6.62 6.63 6.62 6.64 6.42 1989 1.40 1.18 6.01 5.74 6.60 6.60 6.63 6.62 6.63 6.62 6.64 6.42 1990 1.36 1.15 6.01 5.72 6.60 6.60 6.63 6.61 6.63 6.63 6.64 6.41 1991 1.36 1.14 6.03 5.72 6.60 6.60 6.62 6.61 6.63 6.63 6.63 6.43 1992 1.37 1.16 6.01 5.71 6.60 6.60 6.62 6.62 6.63 6.62 6.64 6.48 1993 1.39 1.15 6.02 5.64 6.60 6.59 6.63 6.62 6.63 6.63 6.64 6.55 1967-93 mean 1.50 1.38 6.05 6.02 6.61 6.61 6.62 6.62 6.63 6.63 6.63 6.53 Stddev 0.10 0.14 0.06 0.18 0.01 0.01 0.00 0.01 0.00 0.00 0.03 0.06

1994 1.79 1.23 6.22 6.28 6.62 6.60 6.63 6.61 6.64 6.61 6.64 6.57 1995 1.80 1.23 6.24 6.26 6.62 6.60 6.63 6.60 6.64 6.62 6.64 6.46 1996 1.81 1.22 6.25 6.23 6.63 6.59 6.63 6.60 6.64 6.62 6.64 6.52 1997 1.81 1.18 6.29 6.17 6.62 6.59 6.64 6.61 6.64 6.62 6.64 6.55 1998 1.82 1.15 6.33 6.05 6.62 6.59 6.63 6.61 6.64 6.62 6.64 6.55 1999 1.78 1.13 6.30 6.06 6.61 6.60 6.63 6.62 6.64 6.62 6.64 6.55 2000 1.73 1.12 6.30 6.01 6.61 6.59 6.63 6.62 6.64 6.61 6.64 6.52 2001 1.70 1.09 6.32 5.95 6.61 6.60 6.63 6.62 6.63 6.61 6.64 6.49 2002 1.72 1.47 6.27 6.19 6.62 6.61 6.63 6.63 6.64 6.63 6.64 6.57 1994-02 mean 1.77 1.20 6.28 6.13 6.62 6.60 6.63 6.61 6.64 6.62 6.64 6.53 Stddev 0.04 0.11 0.04 0.12 0.01 0.01 0.00 0.01 0.00 0.01 0.00 0.04

Computations by equations 2 and 3.


Table 4. Summary of Trends in Entropy

Period I (1967 - 1993) Period II (1994 - 2002) b1 t b2 t t* Total Entropy Sales -0.0178 -16.201 a -0.0089 -1.558 -1.540 Assets -0.0299 -7.677 a -0.0188 -0.708 -0.413 Between 5 Sets Sales -0.0116 -16.598 a -0.0123 -3.228 b 0.168 Assets -0.0150 -8.827 a 0.0048 0.314 -1.280 Within Set 1 Sales -0.0056 -6.189 a 0.0092 2.495 b -3.888 c Assets -0.0178 -6.143 a -0.0307 -2.644 b 1.075 Within Set 2 Sales -0.0007 -7.253 a -0.0014 -2.867 b 1.389 Assets -0.0006 -2.900 a 0.0008 0.926 -1.533 Within Set 3 Sales -0.0001 -0.965 -0.0005 -2.667 b 1.954 Assets -0.0006 -5.556 a 0.0032 4.524 b -5.264 c Within Set 4 Sales -0.0003 -3.199 a -0.0003 -3.167 b -0.023 Assets -0.0002 -2.137 a 0.0005 0.556 -0.788 Within Set 5 Sales -0.0006 -0.891 -0.0002 -2.333 -0.552 Assets -0.0055 -5.452 a 0.0015 0.294 -1.338 "b" and "t" for Periods I and II are calculated from equations (4) and (5), respectively; "t*" is calculated by equation (6) for testing statistical significance of equality of trend slopes of the two periods; "a" indicates significant trend in entropy for Period I (critical value = 2.060); "b" indicates significant trend in entropy for Period II (critical value = 2.365); and "c" indicates significant difference in slopes of Periods I & II (critical value = 1.96).


Table 5. HHI, 4-Firm and 8-Firm Concentration of Sales and Assets of FORTUNE 500 Firms HHI 4-Firm Ratio 8-Firm Ratio

Year Sales Assets Sales Assets Sales Assets 1967 0.00970 0.01031 0.14364 0.13759 0.20620 0.21296 1968 0.00991 0.00998 0.14633 0.13401 0.21051 0.21019 1969 0.00938 0.00935 0.14038 0.12662 0.20050 0.20026 1970 0.00830 0.00923 0.12787 0.12344 0.18882 0.19964 1971 0.00982 0.00959 0.14473 0.13168 0.20842 0.20899 1972 0.00985 0.00945 0.14553 0.13266 0.21213 0.21083 1973 0.00986 0.00956 0.14439 0.12918 0.21236 0.20804 1974 0.01015 0.00991 0.14503 0.13276 0.22447 0.21618 1975 0.01042 0.00969 0.14922 0.13066 0.22567 0.21208 1976 0.01114 0.00996 0.15574 0.13277 0.23639 0.21524 1977 0.01163 0.00996 0.16479 0.13063 0.24284 0.21397 1978 0.01158 0.00977 0.16535 0.13003 0.24147 0.21107 1979 0.01156 0.00977 0.16171 0.12929 0.24135 0.20841 1980 0.01214 0.00969 0.16455 0.12810 0.24347 0.20731 1981 0.01223 0.01002 0.16525 0.12962 0.24506 0.20603 1982 0.01200 0.01027 0.15795 0.13193 0.24115 0.20776 1983 0.01176 0.01027 0.15555 0.13309 0.24053 0.20769 1984 0.01242 0.01184 0.16152 0.14226 0.25413 0.24282 1985 0.01259 0.01219 0.16140 0.14945 0.25710 0.24716 1986 0.01260 0.01251 0.16742 0.15332 0.25255 0.24708 1987 0.01199 0.01262 0.16183 0.15850 0.24619 0.24825 1988 0.01294 0.02070 0.17441 0.23695 0.25680 0.33190 1989 0.01291 0.02067 0.17280 0.23862 0.25664 0.32886 1990 0.01316 0.02161 0.17264 0.24646 0.26032 0.33841 1991 0.01290 0.02208 0.16829 0.25206 0.25813 0.34166 1992 0.01299 0.02249 0.17009 0.25520 0.25779 0.33996 1993 0.01289 0.02498 0.16990 0.27009 0.25918 0.35107 1967-93 Mean 0.01144 0.01291 0.15771 0.16026 0.23630 0.24348 STD 0.00135 0.00504 0.01181 0.04881 0.02068 0.05270 1994 0.00685 0.00915 0.10973 0.10017 0.17147 0.18151 1995 0.00662 0.00928 0.10865 0.10000 0.17012 0.18126 1996 0.00640 0.00979 0.10654 0.10744 0.16600 0.19039 1997 0.00610 0.01080 0.10392 0.11293 0.15656 0.20439 1998 0.00573 0.01306 0.09505 0.14958 0.15016 0.24019 1999 0.00629 0.01292 0.10788 0.14543 0.16220 0.23821 2000 0.00650 0.01408 0.10708 0.16575 0.16708 0.26347 2001 0.00650 0.01509 0.10122 0.16592 0.16541 0.27538 2002 0.00686 0.01604 0.11205 0.17382 0.17066 0.29052 1994-02 Mean 0.00643 0.01367 0.10579 0.13567 0.16441 0.2948 STD 0.00036 0.00184 0.00511 0.03044 0.00709 0.04178 Based on data published annually by Fortune.

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Aggregate Concentration in Corporate America: The Case of the