concentration vs inequality measures of market structure

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Economic & Political Weekly EPW august 16, 2014 vol xlix no 33 59

Concentration vs Inequality Measures of Market StructureAn Exploration of Indian Manufacturing

Pulak Mishra, Ujjwal Singh Rao

This paper compares market structure in different

industries using conventional additive measures and

various indices of firm size inequality. It is found that

levels or changes in market structure are not exactly

consistent across various measures. However, as

compared to additive measures, inequality indices give

more consistent results, and hence can be used to

examine the structure of markets in different industries.

Nonetheless, since there are inconsistencies across

different inequality indices, efforts should be made

towards formulating a suitable criterion for selecting the

most appropriate measure.

The authors are grateful to Rakesh Basant for having useful discussions at the early stage of writing this paper. The authors are also thankful to an anonymous referee of this journal for valuable comments and suggestions. Usual disclaimers apply.

Pulak Mishra ([email protected]) is with the Department of Humanities and Social Sciences, Indian Institute of Technology Kharagpur. Ujjwal Singh Rao ([email protected]) is with American Express.

1 Introduction

Market competition is a desirable trait from both an economic as well as a societal point of view. The fi rst welfare theorem postulates that competitive equili-brium is Pareto-optimal and a deviation from this optimality results in a loss of effi ciency and welfare. The rationale of effi -ciency gain through competition has been instrumental in shaping economic policies of many of the countries across the globe. In general, such policies aim at developing an environ-ment which is conducive for market competition. In the Indian context, the basic objective of policy changes since July 1991 has been to facilitate effi cient functioning of market forces. But, with changes in policies resulting in oligopolistic rivalry, fi rms have adopted a variety of strategies to sustain and grow under new business conditions. Success of the new policy regime, therefore, largely depends on how fi rms strategically respond to policy changes and subsequent fi ne-tuning of policies by the government that impinge on fi rm-level choices (Basant and Mishra 2012). While economic reforms have deepened in many areas like foreign direct investment, competition policy, priva-tisation and intellectual property regulation during the last two decades, the strategy mix of fi rms has also changed fol-lowing the changes in the economic and policy environment.

Given such dynamic relationships, designing a comprehen-sive policy framework for greater competition requires a deeper understanding of structure of different markets and their changes over the years. A market is generally character-ised by the number and size distribution of buyers and sellers, barriers to entry and exit, and the extent of product differen-tiation. However, in empirical research, the structure of a mar-ket is examined in terms of degree of sellers concentration as it is an important feature of imperfect competition. Industrial organisation literature suggests a number of alternative meas-ures of market concentration such as n-fi rm concentration ratio (CRn), Herfi ndahl-Hirschman Index (HHI), price-cost margin (PCM), profi tability, etc, and conclusions on market structure may differ depending on the measure used.

Following the criteria suggested by Ginevicius and Cirba (2009), Mishra, Mohit and Parimal (2011) have attempted to examine the accuracy of various additive measures of market concentration in the Indian manufacturing sector. It is found that, although the HHI is widely used to examine market structure,1 it is not a very accurate measure, particularly in

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august 16, 2014 vol xlix no 33 EPW Economic & Political Weekly60

comparison with other additive indices.2 Instead, the GRS ap-pears to be the most accurate measure of market concentra-tion in the Indian context.3

Hence, a better understanding of market structure requires use of appropriate indices. This is very important as observed market structure can infl uence industry-specifi c policies. Further, while the thrust of the current policy regime is to enhance market competition, the relationship between competition and concentration is not very clear. A decrease in market con-centration may not necessarily correspond to an increase in market competition.4 A market even with high concentration may have stiff competition among fi rms.5 Similarly, a market with a low degree of sellers concentration may suffer from the problem of monopolistic behaviour of the dominant fi rms, particularly when the rest of the market is distributed across a large number of small fi rms.6 This means that the defi nition of competition should not be restricted to a low degree of sellers concentration alone and whether high market concentration will correspond to low competition also depends on the distri-bution of relative size of fi rms. Even if degrees of sellers con-centration in two markets are equal, the market with more uniform distribution of shares is likely to be more competi-tive.7 In other words, a low degree of sellers concentration is neither necessary nor suffi cient to have greater market compe-tition as the extent of inter-fi rm rivalry depends on their size distribution as well. Since additive measures fail to account for inequality of fi rm size distribution adequately,8 they may not be appropriate for understanding the extent of competition in the market. Further, inequality of market shares has important implications for strategic behaviour of fi rms. Hence, conclu-sions about market structures solely on the basis of additive measures may be misleading.

In this perspective, the present paper attempts to under-stand how conclusions on structure of different markets in Indian manufacturing sector may vary depending on the use of additive and inequality measures. Additive measures are more sensitive to the number of fi rms in the market whereas inequality measures are infl uenced by the distribution of mar-ket shares. The paper is divided into four sections. The second section provides an outline of different inequality measures. The structure of different markets in Indian manufacturing sector is then examined by using these inequality measures. A comparative analysis on observed market structure according to additive and inequality measures is carried out in the third section. The fourth section concludes the paper with some insights on the criterion that can be applied to examine appro-priateness of various inequality measures.

2 Inequality Measures and Market Structure

The present paper uses four measures of dispersion, viz, relative mean deviation (RMD), coeffi cient of variation (CV), relative entropy coeffi cient (REC), and the Gini coeffi cient (GINI) to ex-amine inequality in fi rm size distribution. Although these in-equality measures are generally used to measure income ine-quality, they have often been applied to understand fi rm size in-equality as well. For example, Barla (2000) used GINI on capacity

shares9 as a measure of fi rm size inequality. On the other hand, Hannan (1997) used CV of fi rm output to capture fi rm size in-equality, whereas Du and Chen (2010) examined the extent of inequality in size of fi rms on the basis of CV, GINI, RMD, REC, and variance of logarithms. The mathematical formulae and the basic properties of each of these measures are discussed below.

Relative Mean Deviation: RMD is a dimensionless number which is computed using the following formula: 1 nRMD = | xi x | 2 n x i = 1Here, xi refers to size of ith fi rm (measured by sales of goods),

10 x to average fi rm size, and n for number of fi rms in the indus-try. The measure captures the extent to which size of an indi-vidual fi rm differs from the average fi rm size in the industry. Higher the RMD, greater is the inequality in size distribution of fi rms, and hence lesser is the extent of market competition.

Coeffi cient of Variation: CV is a standard measure of disper-sion. It is the standard deviation of size of all the fi rms in the industry normalised by its average. Like RMD, CV is also a unit free measure and is comparable across industries due to its normalisation. Mathematically, CV is computed as, 1 1 nCV = (xi x)2 x n i = 1Here xi stands for size of ith

fi rm (measured by sales of goods), and x for average fi rm size and n for number of fi rms in the in-dustry. A higher CV indicates lesser competition in the indus-try. However, the basic difference between RMD and CV is that the former gives equal weight to all the deviations irrespective of their size, whereas CV assigns larger weight to larger devia-tion with the deviation itself being the weight.

Relative Entropy Index: The entropy index is a measure of uncertainty in information theory. In its basic form, the value of the index lies between 0 and ln(n), where n stands for the number of fi rms in the industry. This makes the index incom-parable across industries. In order to make the index compara-ble, the entropy index is divided by ln(n) so that it is restricted to the interval [0,1]. Mathematically, the relative entropy in-dex is computed as follows: 1 n 1RE = si ln ( ) ln(n) i = 1 siHere si refers to the share of ith fi rm in total sales of goods in the industry.

Gini Coeffi cient: GINI is computed by taking the ratio of the area between the Lorenz Curve and the equality line to the total area under the equality line. Being a ratio of two similar quantities, GINI is also a dimensionless measure and hence is comparable across industries. Mathematically, GINI can be cal-culated as 1 n n GINI = | xi xj | n2 x i = 1 j = 1 Here xi stands for size of ith fi rm (measured by sales of goods), x for average fi rm size and n for number of fi rms in the industry.

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For an infi nite sample, the GINI coeffi cient varies between zero and unity, whereas the upper bound is (1 1/n) for a fi nite sample. Closer the value is to zero, greater is the extent of competition in the market.11

Given these defi nitions, what follows is an attempt to under-stand market structure of 34 major industries in Indian manu-facturing sector. We measure fi rm size inequality in different markets using all the four indices for the period 1988-89 to 2007-08. Necessary data are collected from the Prowess Database of the Centre for Monitoring Indian Economy (CMIE). The decision criteria used for relative classifi cation of markets is mentioned in Table 1.12

Table 2 presents the relative classifi cation of industries on the basis of average value of the four inequality measures during 1989-2008.13 It is observed that, like additive measures (Mishra, Mohit and Parimal 2011), there are inconsistencies in

classifi cation of industries across various inequality measures. For example, inequality in market share in information techno logy appears to be high according to all the four indices. On the other hand, three out of the four indices show that ine-quality is moderately high in electricity, petroleum products and polymers, and reasonably low in automobile ancillaries. But, while REC shows high inequality in electrical machinery, it is not so for rest of the measures. Likewise, according to RMD and GINI, inequality is high in alkali, but none of the industries appears to be in the same category when CV and REC are considered. Such inconsistencies are also observed when the industries are grouped according to moderately high or moderately low inequality in market share. Even in case of indecision, the group of industries is not consistent across different inequality measures.

3 Comparison of Additive and Inequality Measures

This section attempts to compare the relative positions of industries across inequality indices and additive measures. In addition to inequality indices, a separate ranking of industries is done on the basis of additive measures as well. The four ad-ditive measures used for the measurement of market concen-tration include the HHI, HOR, entropy index (ENT), Ginevicius index (GIN) and GRS index.14

Ranks of different industries using both additive and in equality measures are given in Table 3. Here, the highest rank, i e, 1 stands for the industry with the highest value of the measure (except ENT and REC). In case of ENT and REC, the 1st rank has been assigned to the industry with lowest

Table 1: Decision Criteria Used for Classification of IndustriesCriteria Decision

C > C + 2 High inequality of market share for RMD, CV, and GINI

Low inequality of market share for REC

C + < C < C + 2 Moderately high inequality of market share for RMD, CV, and GINI

Moderately low inequality of market share for REC

C < C < C + IndecisionC 2 < C < C Moderately low inequality of market share for RMD, CV, and GINI

Moderately high inequality of market share for REC

C < C 2 Low inequality of market share for RMD, CV, and GINI

High inequality of market share for REC

Here, C denotes average value of the measure and denotes its standard deviation.

Table 2: Classification of Industries Based on Average Values of the Inequality IndicesGroup RMD CV REC GINI

High Information Technology Information Technology Electrical Machinery, Information Information Technology Technology

Moderately High Electricity, Non-ferrous Metals, Ferrous Metals Cosmetics, Electricity, Petroleum Cosmetics, Electricity, Electronics, Petroleum Products, Polymers Products, Polymers Ferrous Metals, Petroleum Products, Polymers

Moderately Low Automobile Ancillaries, Diversified, Automobile Ancillaries Automobile Ancillaries, Inorganic Chemicals, Readymade Diversified, Inorganic Chemicals, Garments Ready-made Garments

Low Alkali Alkali

Indecision Automobile, Alkali, Automobile, Alkali, Automobile, Automobile, Beverages and Tobacco, Automobile Ancillaries, Beverages and Tobacco, Beverages and Tobacco, Cosmetics, Cotton Textiles, Beverages and Tobacco, Cosmetics, Cotton Textiles, Diversified, Cotton Textiles, Drugs and Pharmaceuticals, Diversified, Drugs and Pharmaceuticals, Drugs and Pharmaceuticals, Dyes and Pigments, Drugs and Pharmaceuticals, Dyes and Pigments, Electronics, Dyes and Pigments, Electrical Machinery, Electronics, Dyes and Pigments, Ferrous Metals, Fertilisers, Electrical Machinery, Fertilisers, Ferrous Metals, Fertilisers, Electrical Machinery, Electricity, Food Products, Food Products, Food Products, Misc Manufacturing, Electronics, Fertilisers, Inorganic Chemicals, Misc Manufacturing, Non-electrical Machinery, Food Products, Inorganic Chemicals, Misc Manufacturing, Non-electrical Machinery, Non-metallic Mineral Products, Misc Manufacturing, Non-electrical Machinery, Non-ferrous Metals, Organic Chemicals, Other Chemicals, Non-electrical Machinery, Non-ferrous Metals, Non-metallic Mineral Products, Other Textiles, Paints and Varnishes, Non-ferrous Metals, Non-metallic Mineral Products, Organic Chemicals, Pesticides, Plastic Products, Non-metallic Mineral Products, Organic Chemicals, Other Chemicals, Other Textiles, Rubber and Rubber Products, Organic Chemicals, Other Chemicals, Other Chemicals, Other Textiles, Paints and Varnishes, Synthetic Textiles, Textile Processing, Other Textiles, Paints and Varnishes, Paints and Varnishes, Pesticides, Pesticides, Tyres and Tubes Pesticides, Petroleum Products, Plastic Products, Plastic Products, Plastic Products, Polymers, Readymade Garments, Rubber and Rubber Products, Ready-made Garments, Rubber and Rubber Products, Synthetic Textiles, Rubber and Rubber Products, Synthetic Textiles, Textile Processing, Synthetic Textiles, Textile Processing, Tyres and Tubes Textile Processing, Tyres and Tubes Tyres and Tubes

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value of the measure. Similarly, in case of number of fi rms (n), the highest rank refers to the industry having the least (average) number of fi rms during 1988-89 to 2007-08.15 It is observed that ranking of industries in respect of market structure differs across different measures. In addition, there are inconsistencies in ranking of industries within different additive or inequality measures as well. For example, in case of non-electrical machinery, there is disparity in ranks assigned by both additive and inequality measures. Among additive measures, the GIN index ranks this industry towards the bottom end, whereas the GRS index ranks it at nine. Similarly, among inequality measures, CV ranks this industry as fi fth, whereas it is in the 13th position according to REC.

Such inconsistencies have been refl ected in high coeffi cient of variations in ranking across different measures for many of the industries (Table 4). Such high coeffi cients of variation for a majority of the industries indicate inconsistencies in their ranking across different measures. However, for some of the industries, variation in ranking is less across different

inequality indices vis--vis that across additive measures. This means that, when compared to additive measures, ine-quality indices are more consistent. For example, ranking of alkali by inequality indices is more consistent as compared to that by additive measures. Moreover, for industries like cos-metics, electricity, information technology, organic chemicals and other chemicals, the ranking is the same across all the inequality measures.

The pairwise correlation coeffi cients between the values of various indices are presented in Table 5 (p 63). It is observed that ENTs and RECs have a negative correlation with other measures due to their defi nition. While a high value of other measures denotes a high degree of market concentration, the opposite is true for ENT and REC. A high value of these meas-ures denotes a more egalitarian distribution of market shares across fi rms. It is seen that there exists a high degree of corre-lation among different inequality measures as well as among various additive indices. But, the correlation across these two sets of measures is not very strong. For example, GINI does not show a statistically signifi cant correlation with ENT and GIN

Table 3: Ranking of Industries Based on the Additive and the Inequality MeasuresIndustry Additive Measures Inequality Measures

n HHI HOR ENT GIN GRS RMD CV REC GINI

Alkali 1 8 8 7 1 9 34 33 33 34

Automobile 12 10 10 11 15 10 12 14 12 12

Automobile ancillaries 25 31 29 32 26 29 32 30 34 30

Beverages and tobacco 18 6 7 9 18 4 8 4 7 8

Cosmetics 10 3 4 6 7 3 6 6 6 6

Cotton textiles 31 33 33 33 32 34 28 34 32 27

Diversified 8 25 25 19 16 25 33 31 31 33

Drugs and pharmaceuticals 28 32 32 30 28 32 16 16 25 16

Dyes and pigments 7 15 14 13 12 17 21 23 20 22

Electrical machinery 26 30 31 29 27 30 22 17 2 20

Electricity 17 4 5 4 9 5 3 3 3 3

Electronics 24 22 20 22 25 19 9 8 11 7

Ferrous metals 33 13 12 25 33 8 7 2 8 5

Fertilisers 9 18 22 15 17 24 17 28 19 21

Food products 34 34 34 34 34 33 19 13 28 17

Information technology 30 1 1 1 3 1 1 1 1 1

Inorganic chemicals 13 23 21 18 13 21 31 29 27 32

Misc manufacturing 32 29 28 31 31 28 14 11 22 13

Non-electrical machinery 27 20 17 26 29 12 10 5 13 10

Non-ferrous metals 15 11 11 10 19 14 5 12 10 9

Non-metallic mineral products 29 27 26 27 30 26 11 9 16 11

Organic chemicals 21 24 24 21 21 23 18 18 18 18

Other chemicals 19 16 16 17 20 16 15 15 15 15

Other textiles 22 19 19 23 23 15 23 32 21 19

Paints and varnishes 2 7 6 5 2 7 13 19 9 14

Pesticides 6 14 15 14 11 18 24 26 23 26

Petroleum products 5 5 3 2 6 6 2 10 4 2

Plastic products 23 28 30 28 24 31 26 20 29 23

Polymers 4 2 2 3 4 2 4 7 5 4

Ready-made garments 14 17 18 16 8 20 30 27 26 31

Rubber and rubber products 11 12 13 12 10 13 25 21 17 25

Synthetic textiles 20 26 27 24 22 27 27 24 30 28

Textile processing 16 21 23 20 14 22 29 22 24 29

Tyres and tubes 3 9 9 8 5 11 20 25 14 24The column n shows ranking of industries on the basis of average number of firms between 1988-89 and 2007-08.

Table 4: Coefficient of Variation in Rankings of Industries across Different Measures of Market StructureIndustry Coefficient of Variation in Rankings

Additive Measures Inequality Measures All

Alkali 0.49 0.02 0.87

Automobile 0.19 0.08 0.14

Automobile ancillaries 0.08 0.06 0.09

Beverages and tobacco 0.62 0.28 0.57

Cosmetics 0.39 0.00 0.36

Cotton textiles 0.02 0.11 0.08

Diversified 0.19 0.04 0.33

Drugs and pharmaceuticals 0.06 0.25 0.27

Dyes and pigments 0.14 0.06 0.31

Electrical machinery 0.05 0.59 0.38

Electricity 0.38 0.00 0.79

Electronics 0.11 0.20 0.43

Ferrous metals 0.57 0.48 0.79

Fertilisers 0.19 0.23 0.27

Food products 0.01 0.33 0.30

Information technology 0.64 0.00 2.22

Inorganic chemicals 0.20 0.07 0.30

Misc manufacturing 0.05 0.32 0.35

Non-electrical machinery 0.33 0.35 0.49

Non-ferrous metals 0.28 0.33 0.33

Non-metallic mineral products 0.06 0.25 0.40

Organic chemicals 0.07 0.00 0.12

Other chemicals 0.10 0.00 0.11

Other textiles 0.17 0.24 0.21

Paints and varnishes 0.38 0.30 0.65

Pesticides 0.17 0.06 0.39

Petroleum products 0.41 0.84 0.56

Plastic products 0.10 0.16 0.14

Polymers 0.34 0.28 0.42

Ready-made garments 0.29 0.08 0.36

Rubber and rubber products 0.10 0.17 0.36

Synthetic textiles 0.09 0.09 0.12

Textile processing 0.18 0.14 0.22

Tyres and tubes 0.26 0.24 0.60Neg - Negligible.

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and its correlation with other additive measures is less than 0.6. Similarly, the correlation of GIN with the inequality meas-ures is not statistically signifi cant. It is interesting to note that unlike additive measures, most of the inequality measures

show poor correlation with the number of fi rms operat-ing in the market.

Table 6 shows changes in market structure of different industries during the post-reform period. In order to understand these changes, all the measures of market struc-ture are averaged for the periods 1993-94 to 1999-2000 and 2000-01 to 2007-08, and then a comparison is made

between the average values. It is observed that, like the level, changes in market structure also appear to be inconsistent across different measures for most of the industries. There are a few industries like alkali, cosmetics, pesticides and tex-tile processing, for which changes in market structure are consistent across different measures. On the other hand, changes across different measures are contradictory for many industries like cotton textiles, non-metallic minerals, plastic products, ready-made garments, etc. However, changes across inequality indices are found to be more consistent vis--vis the additive measures.

4 Selection of an Appropriate Measure

Thus, while levels as well as changes in market structure differ across alternative measures, the observations are more consistent for inequality indices. However, even within inequality measures, there are variations in conclusions on market structure. This raises an important question, how does one choose between various inequality measures? Ginevicius and Cibra (2009) have suggested a criterion to judge the accuracy of various additive measures of market concentration, and on the basis of this criterion they found the GRS to be a better measure than others as it keeps the dis-tortion in relative importance of fi rms to the minimum.16 Since inequality measures are not additive in nature, it is diffi cult to apply this criterion for these indices. Besides, the overall contribution of each fi rm to inequality measures cannot be segregated easily. However, the existing literature (e g, Allison 1978) suggests that every inequality measure should satisfy two desirable properties, viz, (i) scale invari-ance, and (ii) the principle of transfers. According to the property of scale invariance, if all individual entities are multiplied by a constant (say k), value of the inequality measure should remain unchanged. On the other hand, if a constant is added to each value then the inequality measure should decline. According to the principle of transfers, for any two entities xi and xj, such that xi < xj, if a transfer is made from xi to xj then the value of inequality measure should increase (Dalton 1920).

Selection among the above four inequality measures can be done on the basis of these two criteria. Since RMD, CV GINI are normalised by the mean (x) and REC is calculated using mar-ket shares, the property of scale invariance is satisfi ed.17

Table 5: Correlation Coefficients between Various Measures of Structure Concentration Measures Inequality Measures

N HHI HOR ENT GIN GRS RMD CV REC GINI

Concentration N 1.0000

Measures HHI -0.2311 1.0000

HOR -0.3901* 0.9576* 1.0000

ENT 0.6523* -0.8493* -0.9331* 1.0000

GIN -0.5722* 0.6989* 0.7642* -0.8422* 1.0000

GRS -0.2396 0.9761* 0.9713* -0.8390* 0.6591* 1.0000

Inequality RMD 0.1374 0.7167* 0.6788* -0.4985* 0.1243 0.7249* 1.0000

Measures CV 0.3407* 0.7227* 0.5956* -0.3890* 0.1680 0.7021* 0.7806* 1.0000

REC 0.0243 -0.7694* -0.7163* 0.5690* -0.3143 -0.7580* -0.8038* -0.7083* 1.0000

GINI 0.2481 0.5852* 0.5447* -0.3310 -0.0627 0.6220* 0.9717* 0.7312* -0.7449* 1.0000*Statistically significant at 5% level.

Table 6: Changes in Market Structure during 1993-94 to 2007-08Industry Concentration Measures Inequality Measures


Alkali + + + + + + + + + +

Automobile - - - - - - + - - +

Automobile ancillaries - - - - - - N + - N

Beverages and tobacco - + + - N + - + N N

Cosmetics - - - - - - - - - -

Cotton textiles - N + + N N + + + +

Diversified + + + + + + + + + +

Drugs and pharmaceuticals - + + + - + + + + +

Dyes and pigments - + + - - + - + N -

Electrical machinery - + N + N N + + N +

Electricity - + + + - + + + + +

Electronics - + + + N + + + + +

Ferrous metals - - - - - - + - - +

Fertilisers + N + + + + + - + N

Food products - N N - - N + + + +

Information technology - + + + + + + + + +

Inorganic chemicals - N - - - - + + + +

Misc manufacturing - - - - - - + + + +

Non-electrical machinery - + + + N + + + + +

Non-ferrous metals - + + + N + + + + +

Non-metallic mineral products - N N - N N + + + +

Organic chemicals + N + + N + + + + +

Other chemicals - - - - - - + - - +

Other textiles - - - - - - - + - -

Paints and varnishes - + + + + + + + + +

Pesticides - - - - - - - - - -

Petroleum products - - - - - - N - - N

Plastic products - + + + - N + + + +

Polymers - - - - - - - - - N

Readymade garments - + + - - + + + + +

Rubber and rubber products - - - - - - N - - N

Synthetic textiles - + + + N + + + + +

Textile processing + + + + + + + + + +

Tyres and tubes - + + + - + + + + +Here, + stands for an increase in concentration or inequality, - for a decline and, and N stands for no change. Given the nature of their interpretation, necessary adjustments have made for ENT and REC. The comparison is made between average values of the index for the periods 1993-94 to 1999-2000 and 2000-01 to 2007-08. The values have been rounded off to two decimal places for comparison. In case of GIN, three decimal points have also been considered.

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If sales of all the fi rms in a market segment increase by a con-stant factor, values of these measures will remain unchanged. However, RMD fails to satisfy the principles of transfers. In case of RMD, if a transfer is made between any two entities on the same side of the mean, value of the measure remains un-changed. While the other three measures do satisfy this princi-ple, there is a catch. Corresponding to any particular transfer, the change in each measure has a different functional depend-ency on the entities.18

In case of CV, the change depends on the difference in the entities, whereas for REC, it varies with the changes in the ratio of entities. When GINI is considered, the change depends

on the relative ranks of the entities involved in the transfer. As stated earlier, one of the most popular uses of the measures of dispersion is to account for income inequality. In this case, the assumption of diminishing marginal utility of income simplifi es the choice. However, in the present context, choice across different measures is not that straightforward due to absence of such assumption. Hence, further research is neces-sary for designing a criterion that can potentially address these issues and help in selecting the most appropriate ine-quality measure. This is very important as conclusions on market structure appear to be more consistent across different inequality measures.

Notes

1 The popularity of the HHI can be gauged from the fact that it forms the basis on which the United States Federal Anti-trust Authorities make their decisions on market competition.

2 Majority of the additive measures of concentra-tion are ridden with bias. For details in this regard see Mishra et al (2011).

3 The GRS index, suggested by Ginevicius and Cirba (2009), is based on Taylors series. Unlike other additive measures, weights to different fi rms in this index are assigned in such a way that (i) the value of the index ranges from 0 to 1, (ii) if all fi rms in the industry have equal market share, GRS=1/n, and (iii) it gives a more accurate measure of market concentra-tion. For the details on derivation of this index see Ginevicius and Cirba (2009).

4 The majority of existing studies have relied heavily on measures of concentration to draw conclusions on market structure with the un-derlying assumption that higher the concentra-tion less is the competition. However, a crucial condition for this assumption to hold true is that measures of concentration must capture all other relevant aspects like distribution of market size across fi rms. But, using data on the Chinese manufacturing sector, Du and Chen (2010) found evidence of a weak correlation between some inequality measures (like the

entropy index) and additive measures of con-centration, and thereby raised questions about the reliance on additive measures alone.

5 For example, let us consider two markets each with two fi rms. Let us further assume that in the fi rst market the fi rms have market share 0.60 and 0.40, and market share of the fi rms in the second market are 0.5 and 0.5. Hence, the HHI in the two markets are 0.52 and 0.50 respectively. Here, following the guidelines of the US Department of Justice, both the markets should be termed as concentrated. But from data on market share it appears that the second market is more competitive vis--vis the fi rst one as the fi rms have equal market share.

6 For example, let us consider a market with 100 fi rms with the top-three fi rms having market share 0.3, 0.15, and 0.05, and the rest of the market is equally distributed among 97 small fi rms. The HHI for this market is as low as 0.117, but the distribution of market share clearly shows dominance by the top three fi rms in the market.

7 Let us consider two markets each with three-fi rm concentration ratio of 0.6. Let us further assume that, in the fi rst market, market shares are distributed as 0.2, 0.2, and 0.2, and it is distributed as 0.5, 0.05, and 0.05 in the other. The fi rst market (with no inequality) represents

an oligopoly with high competition among fi rms, whereas the second market (with high inequality) is closer to a monopoly.

8 According to Rhoades (1995), the HHI, the most widely used additive measure of market concentration, fails to capture inequality in size distribution of fi rms adequately.

9 Here, capacity share of a fi rm is defi ned as share of the fi rm in total productive capacity in the market.

10 Although there are various competing vari-ables that can be taken as a proxy for fi rm size such as assets, labour employment, capital employed etc, the present paper use sales of goods (in value) to understand the structure of different markets. As most of the fi rms want to maximise their share in the relevant market segment, sales of goods is expected to capture the structural changes adequately. Also, the heterogeneity in the industry stand-ards for other competing proxies makes them less relevant.

11 In this study, GINI coeffi cient has been calcu-lated by using relative distribution package (reldist) in R language developed by Handcock and Morris (1999). The underlying mathemati-cal formula used by this package is same as that stated above in the text.

12 Here, inequality in market share is used as an indicator of market concentration. Following

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Appendix IAverage Values of the Inequality and Concentration Indices (1989 to 2008)Industry Concentration Measures Inequality Measures


Alkali 13 0.16 0.42 2.13 0.09 0.28 0.38 1.03 0.84 0.48

Automobile 49 0.12 0.36 2.58 0.02 0.25 0.63 2.23 0.67 0.78

Automobile ancillaries 190 0.03 0.13 4.38 0.01 0.10 0.47 1.26 0.85 0.63

Beverages and tobacco 72 0.22 0.49 2.42 0.02 0.44 0.68 3.81 0.58 0.83

Cosmetics 48 0.31 0.58 1.93 0.04 0.53 0.69 3.65 0.52 0.84

Cotton textiles 292 0.02 0.09 4.68 0.00 0.07 0.50 0.48 0.83 0.67

Diversified 44 0.06 0.20 3.14 0.02 0.12 0.46 1.23 0.83 0.60

Drugs and pharmaceuticals 250 0.02 0.11 4.28 0.01 0.08 0.58 2.13 0.79 0.74

Dyes and pigments 44 0.09 0.29 2.82 0.03 0.18 0.55 1.64 0.76 0.69

Electrical machinery 199 0.03 0.12 4.23 0.01 0.08 0.54 2.01 0.34 0.71

Electricity 70 0.27 0.56 1.68 0.04 0.42 0.77 3.92 0.46 0.86

Electronics 186 0.07 0.24 3.44 0.01 0.17 0.68 3.30 0.67 0.83

Ferrous metals 429 0.11 0.33 3.73 0.00 0.29 0.68 6.31 0.62 0.84

Fertilisers 46 0.07 0.24 2.89 0.02 0.14 0.57 1.52 0.76 0.70

Food products 554 0.01 0.09 5.03 0.00 0.07 0.57 2.41 0.81 0.73

Information technology 272 0.57 0.77 0.99 0.06 0.72 0.88 11.43 0.24 0.94

Inorganic chemicals 51 0.07 0.24 3.09 0.03 0.16 0.48 1.48 0.81 0.63

Misc manufacturing 366 0.03 0.14 4.30 0.00 0.11 0.61 2.72 0.76 0.77

Non-electrical machinery 231 0.07 0.26 3.77 0.01 0.23 0.65 3.81 0.70 0.81

Non-ferrous metals 65 0.12 0.35 2.57 0.02 0.21 0.71 2.57 0.63 0.82

Non-metallic mineral products 250 0.04 0.17 3.99 0.00 0.12 0.63 2.92 0.73 0.80

Organic chemicals 84 0.06 0.22 3.29 0.02 0.14 0.57 1.96 0.76 0.73

Other chemicals 75 0.08 0.28 3.08 0.02 0.21 0.59 2.15 0.73 0.74

Other textiles 110 0.07 0.26 3.49 0.01 0.21 0.54 1.20 0.76 0.71

Paints and varnishes 21 0.22 0.52 1.87 0.06 0.37 0.62 1.90 0.63 0.75

Pesticides 44 0.09 0.28 2.83 0.03 0.17 0.53 1.53 0.77 0.67

Petroleum products 36 0.26 0.58 1.64 0.04 0.42 0.78 2.88 0.47 0.88

Plastic products 179 0.03 0.13 4.10 0.01 0.08 0.53 1.89 0.81 0.69

Polymers 35 0.36 0.63 1.64 0.06 0.57 0.72 3.35 0.47 0.85

Ready-made garments 60 0.08 0.26 3.01 0.04 0.17 0.48 1.52 0.80 0.63

Rubber and rubber products 48 0.12 0.32 2.77 0.04 0.23 0.53 1.79 0.75 0.68

Synthetic textiles 83 0.04 0.17 3.57 0.01 0.11 0.51 1.57 0.81 0.66

Textile processing 69 0.07 0.23 3.20 0.02 0.16 0.50 1.66 0.79 0.66

Tyres and tubes 24 0.14 0.39 2.25 0.05 0.23 0.56 1.55 0.71 0.69

Mishra, Mohit and Parimal (2011), inequality is levelled as high medium and low in a relative sense, i e, in comparison with other industries in the sector.

13 For the actual values of the indices, see Appendix I.14 For details on each of these measures, see

Mishra, Mohit and Parimal (2011).15 Industries have been ranked in descending or-

der of market concentration/inequality. Hence, the 1st rank stands for an industry with the highest concentration or highest inequality whichever is the case.

16 For example, if the two fi rms have market shares in the ratio of 1:2, their contribution to the HHI is in the ratio 1:4. Thus, there is a dis-tortion in the relative importance of the two fi rms. Among all the additive measures, the GRS keeps such a distortion to the minimum.

17 One can view RMD, CV and GINI as fractions with the numerator consisting of a deviation and the denominator consisting of mean (x). If each entity is multiplied by a constant k, the ratio remains the same as this constant cancels out. If a constant k is added to each entity, then the numerator is unchanged but the denomina-tor increases by k thereby decreasing the value of the fraction. The logic is similar for REC as well. Multiplication by a constant does not

affect market shares whereas addition of a constant distorts the relative value of market shares.

18 Allison (1978) has pointed out the following changes in different measures:

xjCoV = ( xj xi ); RE = ( ); Gini = ( j i) xi

References

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Dalton, H (1920): The Measurement of the Ine-quality of Incomes, The Economic Journal, Vol 30, No 119, 348-61.

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concentration vs inequality measures of market structure

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