Some economists have attempted to measure market power using indices based upon familiar theoretical considerations.67 However no satisfactory explanation of the size-distribution of firms has yet been derived from economic theory (for example, see Saving 1970). There is no concentration measure in existence that captures every conceivable aspect of business behaviour (Kwoka 1985). Therefore an ideal concentration index can be presumed not to exist, however it is possible to specify a collection of desirable properties.68 The following axioms are based on the assumption of the relative importance of a firm’s shares when formulating a concentration index:
i. A concentration index should be a one-dimensional measure. This ensures simplicity of use and interpretation.
ii. Concentration of an industry should be independent of the size of that industry. This implies that a firm’s share of an industry indicates it’s relative importance.
iii. An increase in the cumulative share of the ith firm, for all i, ranking firms 1, 2, 3…i…n in descending order of size, implies an increase in concentration.
iv. The principle of transfers should hold i.e. concentration should increase if the share of any firm is increased at the expense of the smaller firm.
v. The entry of new firms below some arbitrary significant size should reduce concentration.
vi. Mergers should increase concentration. In some instances, mergers would not be expected to influence concentration at all. Furthermore, mergers may lead to an increase in competition. The outcome will be determined by numerous factors, including the actual number and size distribution of firms following the mergers, the type of product or service provided, the structure of costs and the state of trade.
vii. Random brand switching by consumers should reduce concentration.
viii. If sj is the share of a new firm, then sj becomes progressively smaller, so too should its effect on the concentration index. Concentration should not be influenced by the total number of firms, but rather by the number of firms that are of significant size. ix. If all firms are divided into k equal parts, then the concentration index should be
reduced by a proportion of 1/k.
x. If there are n firms of equal size, concentration should be a decreasing function of n. xi. Random factors in the growth of firms should increase competition.
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Lerner (1934); Herfindahl (1950); Hirschman (1945); Stigler (1964); Horvath (1970); Horvath (1972); Gans (2007); Goppelsroeder, Schinkel and Tuinstra (2008); Lijesen (2004); Kate (2006); Campos and Vega (2003)
68 Curry and George (1983); Hall and Tideman (1967); Dansby and Willig (1979); Geithman, Marvel and Weiss (1981); Kilpatrick (1967);
Concentration indices embody, to a greater or lesser extent, information on the numbers of firms operating in an industry or market (Reekie 1989). Concentration, however measured, typically has been used as a proxy that describes the extent to which the structure, and consequently the conduct and performance of an industry is either believed to be competitive or presents monopoly conditions (Bailey and Boyle 1971). Economic theory suggests that all things being equal (for example, barriers to entry), the degree of competition is related positively to the number of firms in the relevant industry (Scherer and Ross 1990, p. 71). However, the number of firms (n) in an industry is an unsatisfactory index of market concentration unless all firms within an industry are the same size. Hence, the degree of inequality is important.69
A commonly accepted measure of market concentration [combining the elements of both firm numbers and inequality] is the Herfindahl-Hirschman index; also known as the Herfindahl index.70 The names Herfindahl and Hirschman are interconnected not because the two gentlemen worked together to develop the index, but rather because each developed it independently of one another.
Herfindahl (1950) used the index to measure gross changes in the concentration of the United States steel industry. Furthermore, Herfindahl proposed his version of the index because traditional measures of concentration were sensitive only to disparities in market shares and not the scarcity of competitors. Whereas Hirschman (1945) used a variation of the index as a measure of the concentration of a country’s foreign trade.
The HHI is a measure of the size of a firm relative to the total industry and hence is an indicator of the amount of competition amongst the participating firms (see Rhoades 1993). The HHI is calculated by squaring the market share of each firm competing in the market and then summing the resulting numbers as follows:
∑
= = n i i s 1 2 HHI (3.4–A)Where si is equal to the market share of firm i and the number of firms is represented by n.71
Thus, the HHI for a market consisting of three firms with shares of 50%, 30% and 20% respectively, is the sum of 502, 302, and 202 (2,500 + 900 + 400) is equal to 3,800. The HHI will take values between 0 and 10,000. An industry controlled by a single firm (a pure monopolist) has a HHI equal to 10,000 (1002); whereas the HHI for an industry populated by a very large number of
69 Atkinson (1970); Blackorby and Donaldson (1978); Kolm (1969); Sen (1973); Blackorby, Donaldson and Weymark (1982) 70 Herfindahl (1950); Hirschman (1964); Hirschman (1945)
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small firms (i.e. competitive market) would approach zero, which is the theoretical minimum value. Hence the value of the HHI decreases when the number of firms n increases.
Unlike the concentration ratio (Ck), the HHI decreases with the number of firms (n) and increases
with the variance in market share (σ2
).72 In order to measure market share in decimal form Equation (3.4–A) can be revised as
. / 1
HHI=nσ2+ n (3.4–B)
This demonstrates that HHI increases in value as the variance in market share increases. This also implies that when firms are equal size (i.e. σ2
= 0), the HHI = 1/n.73 The first term on the right- hand side of the equation is often referred to as the variance equivalent (nσ2) and the second term is known as the inverse of a numbers equivalent (1/n).74 Equation (3.4–B) can further provide a
numbers equivalent, such that a given value of HHI can be translated into a number of equal size
firms (n′). The numbers equivalent of a given value of HHI is n′=1/HHI when market share is measured as a decimal.
In other words, the HHI can be interpreted as a numbers equivalent by multiplying the HHI by 0.0001 and taking the reciprocal of that product. This means that one can readily compute the number of firms with equal market shares, which would be necessary in calculating any given HHI. For example, a HHI of 1,250 corresponds to a market of eight equal sized firms since the reciprocal of 0.125 (1,250 x 0.0001) is 8 (Calkins 1983, p. 406). Contrariwise, to obtain the HHI corresponding to a market with a specified number of equal sized firms the reciprocal of that number is multiplied by 10,000. Accordingly, the HHI corresponding of four equal sized firms would be (¼ x 10,000) equal to 2,500.
One of the major advantages of the HHI is that it is highly responsive to asymmetry in market shares. The HHI will be lowest when the share of the market is equal between firms and highest when one firm has an extremely large share of the market. For example, the HHI for a market consisting of three firms with equal shares (331
/32 +331
/32+331
/32 or 331
/32x 3=1,111 x 3) is equal to 3,333. Alternatively, the HHI for a market consisting of three firms where one firm has an 85% share (852 + 102 + 52 = 7,225 + 100 + 25) is equal to 7,350.
72 The k-firm concentration ratio is defined as the market share of the k largest firms in the industry.
73 In a monopoly market, the HHI has a value of 1; and diminishes as n increases and firms remain equal in size. 74
Another advantage of the HHI is that it reflects the shares of every firm in the market. In contrast, the k-firm concentration ratio requires an arbitrary selection method of which firms are included in the model. This all-inclusive characteristic is considered one of the key advantages of using the HHI as a measure rather than the k-firm concentration ratio. Whilst the number of firms in an industry is evident in its intuitive economic meaning, using the traditional variance measure of size dispersion has some shortcomings (see Kelly 1981).
One of the major disadvantages of the HHI is that small errors in estimating market shares of leading firms can produce large differences in the HHI.75 For example, the HHI for a market consisting of four firms, where two firms have a 40% and 10% share respectively (402 + 402 + 102 +102 = 1,600 + 1,600 + 100 + 100) is equal to 3,400. Now assuming that the market share of both the major firms are 45% and 35% respectively (rather than 40% each), the HHI would be equal to 3,450 (452 + 352 + 102 + 102 = 2025 + 1225 + 100 + 100). Whereas, if the market share of one large firm and one small firm is recalculated at 45% and 10% respectively, the HHI would be equal to 3,750. Hence, as summarised in Table 3-3, it is critical to avoid erroneously estimated market shares as this can impact on the value of the HHI (i.e. calculation error increases from 1.47% to 10.29%).
Table 3-3: Market share re-distribution implications
Group Market A Market B Market C
Overview Two large and two small
firms
Large firms redistributed Large and small firm redistributed
Market Share 40%, 40%, 10% and 10% 45%, 35%, 10% and 10% 45%, 40%, 10% and 5%
∑
= = n i i s 1 2 HHI 402 + 402 + 102 + 102 = 452 + 352 + 102 + 102 = 452 + 402 + 102 + 52 = 1,600 + 1,600 + 100 + 100 2,025 + 1,225 + 100 + 100 2,025 + 1,600 + 100 + 25 HHI 3,400 3,450 + 50 (1.5%) 3,750 + 350 (10.3%)Source: the author
As demonstrated, the HHI index weights more heavily the values for large firms than small firms when squaring the market shares in Equation (3.4–A). As a result, if precise data were not available on the market share of extremely small firms, the potential errors generated would not be large. Hence, it is important that market share data is available on the largest firms in order for concentration to be measured accurately. Obtaining all the markets shares of very small firms can
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be quite difficult. Therefore, the all-inclusive characteristic of the HHI can also be a disadvantage in the event of missing or unavailable data due to incompleteness. However given that fringe firms are unlikely to contribute significantly to the HHI, these firms would hardly raise any dominant position or anti-competitive behaviour (antitrust in the context of the US) concerns.
As highlighted by Calkins (1983), George J. Stigler was perhaps more important than either Herfindahl or Hirschman in bringing about the acceptance of HHI. Stigler (1964) investigated the issue of detecting secret price-cutting in the presence of a collusive agreement. Stigler assumes that the basic method of detection of a price cutter is that the seller is getting business, which would otherwise be unobtainable. Stigler used the HHI to measure the likelihood of effective collusion in the event that cheating on agreed prices were not detected. As a result, his evidence suggests that the more concentrated the industry structure, the larger the price reductions.
The relationship between market size and the maximum feasible number of firms is shown in Figure 3-6.76 The HHI is plotted on the vertical axis and is the reciprocal of the number of firms assuming that they are characteristically symmetrical. Each of the curves are downward sloping and the lower bound for H gets closer to zero as the market size expands. In other words, the theoretical minimum level of market concentration decreases as market size relative to economies of scale (S) increases as plotted on the horizontal axis. Hence, as S becomes large, market concentration will approach zero.
An industry with identical firms and no incumbent advantages can be represented by H =h0(s) and can be considered the lower bound for an unintegrated market. In practice, the size of firms is never identical. However, the smallest firms in an industry cannot make losses if they are to survive. This reduces the maximum number of sustainable firms and increases concentration; and is consistent with pushing the minimum level of concentration from points A to D. In contrast, the lower bound relationship between concentration and market size can be represented by H =h1(s). This would be reflective of an integrated market in the absence of the toughness of price
competition, suggesting that pricing behaviour remains unchanged irrespective of the increase in the
number of firms; and the equilibrium market share at s1 moves from point A to point B.
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Now assume that H =h2(s) represents the lower bound for a fully integrated European market prior to the launch of the euro (i.e. pre-EMU), where the equilibrium market share settles at point C. It is anticipated that the introduction of the euro will enhance competition across the region. Hence, the lower bound of the integrated market curve moves down, which can be represented by
) (
1 s
h
H = . Initially, this suggests that the market is more competitive as the equilibrium HHI moves from point C to point B. However as competition intensifies, the relationship between market size and the number of firms may move even further down the existing curve or recalibrate at H =h0(s).
Figure 3-6: Market concentration and size
Source: adapted from Davis and Garcés (2010)
The HHI is commonly used as preliminary benchmark in merger control, where the data on a post- merger situation cannot be observed (see Davis and Garcés 2010, p. 288).77 Both EU merger and US antitrust guidelines use the HHI screen for mergers which are unlikely to be of much concern; and to flag those mergers which need to be scrutinised. This assessment is undertaken by using the market shares to calculate the HHI pre merger (HHIP) and post merger (HHIM) as follows:
∑
= = n i pre i P s 1 2 ) ( HHI and∑
= = n i post i M s 1 2 ) ( HHI (3.4–C)77 Interestingly, the HHI has also been used to assess the relationship between concentrated industries and lower stock returns: see Hou and Robinson