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In this short paper, cartel behaviour is analysed with respect to the market shares of cartel members. There is some evidence in previous theoretical and empirical research that market shares under collusion are more stable than in phases of competition. It is shown that this can be an artifact and that market share volatility may not be used by antitrust authorities as an exclusive indicator of tacit collusion. Using the Kolmogorov-Smirnov test, the distribution of market share changes during both the competitive and the collusive phases of ten recently discovered conspiracies is compared. Only in 3 of the 10 cartels were the distributions of market share changes significantly different.

In any market, firms have an incentive to coordinate their decisions and increase their collective profits by restricting output and raising market prices, which leads to a welfare loss. Antitrust authorities therefore require effective methods of detecting such collusion. Previous studies have revealed many different characteristics of collusive behaviour. For example, Porter and Zona1, and Bajari and Ye2 concentrate on some selected bidding markets and demonstrate the difference between collusive and competitive bidding behaviour. For studies that analyse price dispersion in order to detect collusive behaviour, see Abrantes-Metz et al.3 and Bolotova et al.4 Blanckenburg and Geist5 present a system of cartel markers (SCM), which includes a number of cartel markers based on expected behavioural patterns such as a low level of capacity utilisation, slackness of price adjustments to exogenous shocks, excess rates of return, near constant capacities, minimal price changes, a low variance of capacity growth rate and cost inefficiency.

In this paper, we extend the discussion to the stability of market shares as a further marker, as proposed by Harrington6, for example. The hypothesis is that market shares are more stable under collusion. If so, antitrust authorities may be able to detect cartels by identifying changes in market share volatility. However, no empirical verification of this marker has so far been undertaken. In order to do so, we analyse ten recently discovered instances of collusion and compare the distributions of market share changes during the competitive phase and under collusion. If the cartel members are able to agree on market shares (collusion), we expect a leptokurtic distribution of market share changes around zero because of more “near-zero changes” compared to a competitive situation. We employ the Kolmogorov-Smirnov test, which is a non-parametric (distribution-free) test comparing two distributions. All the cartels we analyse are German and the relevant organisations were recently prosecuted by the European Commission. The data was provided by the German Federal Statistical Office. The paper is structured as follows. Firstly, we discuss the theoretical background and hypothesis. We then present the data used for our analysis. Finally, the empirical results and some conclusions are presented.

Theoretical Background and Hypothesis

The stability of market shares has been the focus of both enforcement and academic efforts to analyse collusive behaviour. In a dynamic Bertrand game, Athey et al.7 show that under collusion market shares are more stable than in competitive equilibria, which holds for independent cost shocks across firms and over time and also when firms’ costs are consistent over time. Caves and Porter8 analyse the influence of market structure on oligopolistic behaviour and conclude that stable market shares provide an indicator of oligopolistic bargaining. When firms agree on a cost-minimising distribution of production, they effectively allocate market shares. If this constancy is interrupted, we expect that this instability will lead to less complete collusion. Shepherd9 states that the greater the stability, the higher the probability of overt or covert cooperation. Lorenz10 provides some empirical evidence of more stable market shares for the German cement cartel. Ogur11 finds that market shares in the turbine generator industry were more stable during its period of formal collusion.

However, no empirical verification of this marker by the analysis of numerous cartel cases has been undertaken so far. If firms are able to freeze their market shares, we expect to observe zero changes in market shares. Harrington12 warns that market share stability may only be observed when one uses the right measure. If the cartel is not all-inclusive, a particular cartel member’s market share may fluctuate if the non-cartel supply changes (the latter would generally be expected to increase due to the high prices created by cartel members) while at the same time its share of the cartel supply is stable. Therefore, we do not expect exact zero changes, but more changes near zero, compared to the competitive benchmark. Hence,

H0: the distribution of changes in market shares under collusion has a higher peak around zero.

The expected distributions of market share changes under collusion and competition are illustrated in Figure 1.

Figure 1
Expected Distribution of Market Share Changes

The introduced marker can only be used for antitrust screening and regulatory purposes if a change in the distribution of market shares changes is observable. There is some evidence supporting the hypothesis that stable market shares are not the consequence of a collusion but a precondition. Staiger and Wolak’s13 theoretical model states that under capacity constraints instable market shares across oligopolistic firms are an indicator of an inability to collude effectively. Grout and Sonderegger14 provide an empirical approach, analysing economic factors that are critical to the identification of cartels. They find that cartels are less likely in markets with significant changes in market share, or in markets with regular exits and entries.

Data Description

The present study uses quarterly data of market share changes provided on request by the German Federal Statistical Office (GFSO) for selected industries from 1995 to 2009. Because of data protection, the values of the market shares of the individual firms are not publicly available. In order to anonymise the data, we used the mean of the absolute market share changes ΔΩ of individual firms i,j = {1,...,n} at time t, which is sufficient to indicate the volatility of market shares. The market shares for the firms are calculated as a quotient Ωt of gross output Φt and the output sum of the industry. In the following analysis, ΔΩ is used as a “market share indicator”:

Table 1
Example for the Calculation of the Market Share Indicator ΔΩ
t = 0 t = 1
Gross output (Φ↓0)(€ m.) Market share(Ω↓0) Gross output (Φ↓1)(€ m.) Market share(Ω↓1) ΔΩ=Ω01
Firm 1 3.5 0.35 3.0 0.30 0.05
Firm 2 2.5 0.25 1.5 0.15 0.10
Firm 3 4.0 0.40 5.5 0.55 0.15
10.0 1.00 10.0 1.00
Mean of absolute market share changes (in t = 1) 0.10

ΔΩis given in Table 1. If there are no changes in market shares the mean is zero. All cartel industries in the study are grouped according to the statistical classification of economic activities in the European Community (NACE). The classification is designed to categorise data.15 The cases presented were of firms prosecuted by the European antitrust authority. The case descriptions also contain the cartel periods, which we use to differentiate between the periods of competition and the periods of collusion.16 Table 2 lists the product markets analysed. We were able to analyse cartel markets at the lowest possible of level aggregation. Finally, in Table 3 we list the companies involved and the total fines imposed by the European Commission.

Table 2
Descriptive Statistics of Cartel Cases by Data Periods
Product NACE Data Period Nall Cartel Period Ncartel
Coffee 108311 02/1995-04/2009 59 01/2000- 02/2008 30
Copper tubes, Copper fittings 244426 02/1995- 04/2009 59 02/1988- 01/2001 24
Gas insulated switchgear 271210 02/1995- 04/2009 59 01/1988- 04/2004 39
Hydrogen peroxide and perborate 201363 02/1995- 04/2009 59 01/1994- 04/2000 23
Marine hose 221930 02/1995- 04/2009 59 01/1986- 04/2007 53
Monochloro- acetic acid 20143220 02/1995- 04/2009 59 01/1984- 02/1999 17
Plasterboard 236210 02/1995- 04/2009 59 01/1992- 04/1998 15
Plastic industrial bags 222211 02/1995- 04/2009 59 01/1982- 02/2002 29
Synthetic rubbers 201710 02/1995- 04/2009 59 02/1996- 04/2002 26
Vitamins 21105 02/1995- 04/2009 59 04/1989- 01/1999 16
Figure 2
Density of Market Share Changes in Cartels and Competitive Markets

Empirical Results

In order to detect whether cartel market share volatility is different from that in situations of competition, let us first observe the distribution of market share changes under competition (continuous line) compared to the distribution of market share changes in a cartel (dotted line) in Figure 2. To illustrate the changes in market shares, we use our “market share indicator” ΔΩ, as introduced above. In particular, we show the kernel density of the distribution of ΔΩ.17

In Figure 2 mixed results can be observed. For only two industries (hydrogen, monochlor) is it immediately evident that in a cartel the market share changes are much less volatile. For all other industries, no large differences can be found.

Table 3
Descriptive Statistics of Cartel Cases by Companies and Fines
Product Companies Fines1
(€ million)
Coffee Tchibo, Melitta, Dallmayr no decision
Copper tubes, Copper fittings Mueller Industries, Austria Buntmetall, Boliden AB, Boliden Cuivre Zinc, Buntmetall Amstetten, Deno Acquisition, Deno Holding Company, Europa Metalli SpA, HME Nederland BV, Halcor SA, IMI Plc, KM Europa Metal AG, Mueller Europe Ltd, Outokumpu Oyj, Tréfimétaux SA, WTC Holding Company, Wieland Werke AG, Yorkshire Copper 222
Gas insulated switchgear Schneider Electric, ABB Ltd, AREVA T&D AG, AREVA T&D Holding SA, AREVA T&D SA, Alstom, Areva SA, Fuji Electric, Fuji Electric Systems, Hitachi Europe Ltd, Hitachi Ltd, Japan AE, Mitsubishi Electric, Nuova Magrini G, Siemens AG, Siemens AG Österreich, Siemens Transmis Ltd, Siemens Transmis SA, Toshiba Corporation, VA TECH Transmission 751
Hydrogen peroxide and perborate Degussa AG, Akzo Nobel Chemicals, Akzo Nobel NV, Arkema SA, Caffaro, Chemoxal, Edison SpA, Eka Chemicals, Elf Aquitaine, FMC Corporation, FMC Foret, KEMIRA OYJ, L’AirLiquide, SNIA, Solvay NV, Solvay Solexis, Total SA 388
Marine hose Yokohama Rubber Co, Bridgestone, Bridgestone Industri, ContiTech AG, Continental AG, Dunlop Oil & Marine, Manuli Rubber Indust, Parker Hannifin Corp, Parker ITR Srl, Trelleborg AB, Trelleborg Industrie 132
Monochloroacetic acid Hoechst AG, Akzo Nobel AB, Akzo Nobel Base Chem, Akzo Nobel Chemicals, Akzo Nobel Funct, Akzo Nobel NV, Akzo Nobel Nederland, Arkema SA, Clariant AG, Clariant GmbH, Eka Chemicals, Elf Aquitaine 217
Plasterboard BPB, Gyproc Benelux, Knauf W.G. KG, Lafarge SA 478
Plastic industrial bags UPM-Kymmene Oyj, Armando Álvarez SA, BPI, Bernay Film Plastiqu, Bischof + Klein FR, Bischof + Klein GmbH, Bonar Technical Fabr, Cofira-Sac SA, Combipac BV, FL Smidth& Co A/S, FLS Plast A/S, Fardem Packaging BV, Groupe Gascogne, JM Gesellschaft, KV Stempher CV, Kendrion NV, Low & Bonar plc, Nordenia IAG, Nordfolien GmbH, Plásticos Españoles, RKW, Sachsa Verpackung, Stempher BV, Trioplast Industrier, Trioplast Wittenheim 290
Synthetic rubbers Bayer AG, DOW Deutschland Inc, Dow Chemical Company, Dow Deutschland, Dow Europe GmbH, Eni SpA, Kaucuk as, Polimeri Europa SpA, Shell NL Chemie BV, Shell Nederland BV, Shell Petroleum NV, Trade-Stomil Ltd, Unipetrol as 519
Vitamins BASF AG, Aventis SA, Daiichi, Eisai Co Ltd, F. Hoffmann-La Roche, Kongo Chemical Co, Lonza AG, Merck KGaA, Solvay Pharmaceutic, Sumika Fine Chemical, Sumitomo Chemical Co, Takeda Chemical Ind, Tanabe Seiyaku Co 855

1 http://ec.europa.eu/competition/cartels/statistics/statistics.pdf.

Furthermore, we employed the Kolmogorov-Smirnov test, which is a non-parametric (distribution-free) test which measures the distance between the empirical distribution functions of two samples. The null hypothesis of the test is that both samples are drawn from the same distribution. Formally, the test statistic is defined as follows:

D = sup | F0 (x) – F1 (x) |

where F0(x) and F1(x) are the empirical cumulative distribution functions for each of the two samples being compared. In other words, the empirical cumulative distribution functions are compared (as absolute differences in function values) at each point of distribution support, after which the largest absolute difference is taken as the Kolmogorov-Smirnov test statistic. If this supreme absolute difference exceeds a certain critical value, the null hypothesis of the two samples being drawn from the same distribution is rejected.

The results of the traditional Kolmogorov-Smirnov test data are reported in Table 4. In this case, the null hypothesis is rejected for three industries (switching, monochlor and hydrogen peroxide) and almost rejected for Vitamins. We can conclude that the distributions of market share changes under competition and cartels differ only in three of ten cases. These differences can be detected graphically and with the Kolmogorov-Smirnov test.

Table 4
Comparing Cartel and Competition Market Share Volatility
Kolmogorov-Smirnov test
D-statistic p-value
Coffee 0.198 0.457
Copper tubes 0.126 0.873
Switching 0.422*** 0.005
Hydrogen 0.296* 0.098
Tubes 0.304 0.315
Monochlor 0.480*** 0.004
Sacks 0.195 0.309
Plaster 0.239 0.361
Rubber 0.241 0.296
Vitamins 0.314 0.132

Notes: significance level: *** 0.01, ** 0.05, *0.1.


There is some evidence in previous theoretical and empirical research that market shares under collusion are more stable than in competition. If so, changes in market share volatility could be used by antitrust authorities as a possible marker of tacit collusion. In this paper,we test this hypothesis using data from ten recently discovered conspiracies. We use the Kolmogorov-Smirnov test to examine the differences in the distributions of market share changes during collusive and non-collusive periods. Only in 3 out of 10 cartels were the distributions of market share changes significantly different. In two out of these three cases (monochlor and hydrogen), however, the market share changes under competition are even less volatile than under a cartel. Hence, we find no support for the hypothesis that market shares in a cartel are more stable than under collusion. A possible explanation could be that market share stability is a condition for, rather than a consequence of, successful collusion. However, further empirical research would be necessary to verify this hypothesis.

Alexander Geist, Federal Institute for Public Administration, Muenster, Germany.
Korbinian von Blanckenburg, University of Muenster, Institute of Public Economics, Germany.

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  • 8 R.E. Caves, M.E. Porter: Market structure, oligopoly, and the stability of market shares, in: The Journal of Industrial Economics, Vol. 26, No. 4, 1978, pp. 289-313.
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  • 15 The NACE Classification is based on the International Standard Industrial Classification of all Economic Activities (ISIC Rev.2). Parts of ISIC Rev.2 were insufficiently aggregated to represent and monitor European national economies, and the necessary adjustments were therefore made accordingly.
  • 16 http://ec.europa.eu/competition/cartels/cases/cases.html.
  • 17 Our kernel density estimation is based on an Epanechnikov kernel.

DOI: 10.1007/s10272-011-0386-3

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