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The Effects of Cartel Misdating under the

Forecasting Approach

Isabelle Slot

10676848

Supervisor: M. Bun

December 2017

University of Amsterdam, Bsc Econometrics

Abstract

The forming of cartels, where companies harm their competitors and customers through price-fixing, is a well-known form of antitrust. It is necessary to determine the start and end

date of the cartel to estimate the total damage caused by the cartel. In this paper the effects of misdating a cartel under the forecasting approach are analysed. Four different cases of misdating are brought into view. The results show that misdating the cartel leads

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Statement of Originality

This document is written by Student Isabelle Slot who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of

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Contents

1 Introduction 4

2 The Effects of Cartel Misdating 6

2.1 But-for Price . . . 6

2.2 The Dummy-variable Approach . . . 6

2.3 The Forecasting Approach . . . 8

2.4 Cartel misdating . . . 9

3 Methodology 10 3.1 Types of Misdating . . . 10

3.2 The Simple Forecast Model . . . 12

3.3 Model Specification . . . 14

3.4 Adjusted Coefficients . . . 16

4 Results 19 4.1 Estimation of ˜α1 and ˜β . . . 19

4.2 The Obtained Total Damage . . . 20

4.3 The Obtained Results under Several Adjustments . . . 21

4.3.1 Adjustments of cartel period TC . . . 21

4.3.2 Adjustments of the actual start and end date Tb and Te . . . 21

4.3.3 Adjustments of ρ . . . 22 4.3.4 Adjustments of α2 . . . 23 4.3.5 Adjustments of φ . . . 23 5 Conclusion 24 Bibliography Appendix

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1

Introduction

In June of this year the European Commission imposed a record antitrust fine of 2.42 billion euro on Google for illegally favoring search results for its own shopping service and thus demoting searches of its rivals. The New York Times reported that this is the biggest penalty issued by the European Commission in history when it comes to antitrust (Scott, 2017). Google, which is appealing the fine, is definitely not the only company which was confronted with antitrust practices recently.

Chip maker company Intel fought against their 1.06 billion euro fine in September of this year. In 2009 the company was accused by the European Commission of using illegal sales strategies to obstruct their rivals. The European Court of Justice assigned the Intel’s antitrust case for further legal inspection and therefore postponed the billion-euro penalty (Curia, 2017). Although the practice of any form of antitrust is illegal and fines are not mild, the companies who have been accused of antitrust are manifold. Moreover, the fact that multiple companies are still being penalized on antitrust violations shows that despite the strict regulations, this illegal practice is still being conducted nowadays.

A common type of antitrust are cartels, which make it possible for cartel members to broaden their market power by price-fixing and therefore harming their competitors and clientage. The imposed penalties are usually based on the magnitude of the affected business, which is established by the overcharge demanded by the cartel members. Regression analysis is being used to estimate the but-for price; the price that would have been set if there would have been no existence of cartels (Nieberding, 2006,p. 362). The two approaches that are frequently used for estimating the damage caused by antitrust are the so-called yardstick and the benchmark approach, (McCrary & Rubinfield, 2014). In the yardstick approach the prices in a market where cartels are present and believed to have an effect on the price are being compared to prices in markets with similar characteristics where cartels are not conducted. Conversely, the benchmark approach focusses solely on the market where cartels are being conducted and compares the price affected by the cartel to the price during the control period; the period before and/or after the presence of the cartel. Research has found that this last-mentioned benchmark approach is most common in evaluating damage caused by antitrust, since the data in the control period of the benchmark approach is known to have more corresponding characteristics with the cartel data (McCrary & Rubinfield, 2014).

The European Commission states two different benchmark approaches in their Practical Guide from 2013 that are used most frequently in the regression analysis for establishing but-for prices. In the forecasting approach, data from the control period is used to build up the regression equation and therefore forecasts the effect of cartel conduction on the price. In the

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dummy-variable approach, data from the control period as well as from the infringement period are being used to estimate the regression model, where the effect of the presence of a cartel is accounted by use of a dummy-variable.

However, a common difficulty in estimating the damage is establishing the begin and end date of the cartel. This could be a complicated aspect of the estimation, since the formal cartel dates do not per se correspond with the effective cartel dates as stated by Boswijk, Bun and Schinkel (2016, p.2). In their research they focused on the effects on estimating the but-for prices under the dummy-variable approach where the begin and end dates of cartel effects are misdated. They found that the misdating of the cartel leads to an overestimation of but-for prices and thus an underestimation of overcharges. In contrast with the paper of Boswijk et al.(2016), the center of interest in this paper is the forecasting approach. Furthermore, the purpose of this paper is to answer the question what the consequences are of misdating cartel effects under the forecasting approach.

In order to give answer to the central research question in this paper previous relevant literature is discussed in the next section which reviews the dummy-variable and the forecasting approach and pays attention to previous research on the causes and consequences of misdating cartel effects. Thereafter the research methodology used to investigate the effects of misdating cartels is discussed in section 3. A Monte-Carlo experiment is used to estimate the cartel damage in four different cases of misdating under the forecasting approach, taking into account the correlation between price and quantity. After the first Monte-Carlo analysis, the experiment is reproduced numerous times with several adjustments. Subsequently the results of the estimations are given in section 4. The paper occludes with a conclusion drawn from the obtained results. .

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2

The Effects of Cartel Misdating

As mentioned in the introduction the magnitude of damage caused by cartels is established through estimating overcharges. This section discusses the two most commonly used techniques for esti-mating the but-for prices that are used to calculate the overcharges stated by the European Commission. First brief definitions of the but-for price and overcharge are given in section 2.1. Thereafter the dummy-variable approach is discussed in paragraph 2.2, followed by the forecasting approach in paragraph 2.3. Attention is paid to the characteristics, main pitfalls and benefits of the approaches stated in previous published relevant literature. The conclusion of this section consists of the causes of appearance of cartel misdating and the involved additional consequences discussed in paragraph 2.4.

2.1

But-for Price

The damage that is caused by the presence of a cartel is evaluated by the magnitude of the overcharge, which is defined as the difference in price paid during the infringement period and the but-for price (Nieberding, 2006,p. 362). The but-for price is the price that would have prevailed in the absence of a cartel. To establish the size of the harm caused by the cartel, regression analysis are used to estimate the but-for prices. Subsequently the overcharges are calculated:

Ot= Pt− bf Pt t ∈ TC

(1) The total cartel damage (CD) is calculated as follows:

TE

X

t=TB+1

Ot∗ Qt t ∈ TC

(2) where Qtis the purchased quantity. TB is the start date of the cartel and TE the end date of the

cartel. Besides, the cartel period is defined as TC, the pre-cartel period as TN 1and the post-cartel

period as TN 2. Timeseries data derived from the market of interest are used to estimate the but-for

price. The two most common approaches for estimating the but-for prices are the point of focus in the following two paragraphs.

2.2

The Dummy-variable Approach

As mentioned before, one of the most common approaches to estimate the but-for price in con-spiratorial periods is the dummy-variable approach. This approach was introduced in 1983 by Finkelstein and Levenbach and estimates the regression model for all periods for which data is

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available and distinguishes between the infringement period and the control period by using a dummy-variable. This additional variable has value 0 in the absence of the cartel and a value of 1 otherwise. The effect of the presence of a cartel is expressed through the coefficient of the dummy-variable. The coefficient reveals if the presence of a cartel has a significant effect on the but-for price (Rubinfield & Steiner,1983). The model to estimate the effect of cartel on price through a dummy variable is given below:

Pt= α1+ α2Dt+ βXt+ et t ∈ TN 1, TC, TN 2

(3) Ptis the product unit price in period t, Xta set of explanatory variables which for instance consist

of demand and supply shifters and cost factors, Dt is the cartel dummy variable which equals 1

during the infringement period and 0 before and after the presence of the cartel and et is the

error term. In some researches, for example in the research of Boswijk et al. (2016), a lagged price variable Pt−1is added to the model. The reason for including this lagged variable is to cover

possible effects of the previous price on the current price. Due to the scope of this thesis, a lagged price variable is not included in the model.

The but-for price is defined as follows:

bf Pt= α1+ βXt+ et t ∈ TC

(4) As one can deduce from the model above, the dummy-variable Dtlogically has a value of zero

in the model for calculating the but-for price. The but-for price and unit price are obviously equal in the absence of the cartel.

The main pitfalls and benefits of the dummy-variable approach are discussed elaborately in previously published relevant literature. Notaro (2013, p.7) raises three conditions that need to be satisfied for the dummy-variable approach to be valid. First of all, the observable as well as the unobservable determinants of prices need to be exogenous and cannot be caused by the cartel. Secondly, the model must be specified correctly and the third condition states that the observable determinants of prices must be strictly exogenous with respect to the unobservable factors affecting the cartel and the price. Notaro states that if one of these conditions is not satisfied, the dummy-variable approach does not give an accurate estimation of the but-for price, since the ceteris paribus effect of the cartel on the price will not be captured correctly by the coefficient of the dummy-variable .

Furthermore, an issue that is mentioned in Rubinfield (2009, p.7) is the fact that the dummy-variable approach assumes that the price differential through the infringement period is constant. However, if this is not the case through the infringement period, the estimated but-for price is

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biased. Another pitfall of the dummy-variable approach described by Finkelstein and Levenbach (1983, p. 156) is the fact that the approach could be too simple since the model gives the impression that the presence of the cartel adds a fixed price or percentage to the price during the infringement period. However, if the price is affected in more complex ways, the use of one dummy-variable is too straightforward.

An advantage of the dummy-variable approach that is mentioned by Boswijk et al. (2016) is the fact that much more data is used in the dummy-variable approach than in the forecast approach and thus leads to a more accurate estimation. The latter approach is discussed in the following paragraph.

2.3

The Forecasting Approach

The most commonly used benchmark approach besides the dummy-variable approach discussed in the previous paragraph is the forecasting approach. The big difference with the dummy-variable approach is that the regression model is estimated with only data originating from the control period in which there was no cartel effective. Afterwards the but-for prices are predicted with the estimated model using data from the infringement period. Subsequently, the overcharges are calculated to determine the harm caused by the cartel. The following model is given by Rubinfield (2009,p.9) for the estimation using the forecasting approach:

Pt= α + βXt+ et t ∈ TN 1, TN 2

(5) Data from the control period, in the case of Rubinfield, the pre-conspiratorial period is being used to estimate the model. Ptis the product unit price in period t, α a constant, Xta set of explanatory

variables and et the error term. For the forecasting approach it is necessary to assume that the

same relations between the explanatory variables and prices prevail in the regression model during both the control and infringement period. If this same relationship does not hold, the forecasting approach may fail to give an accurate estimation of the but-for price (Nieberding, 2006, p.368). As mentioned in the previous paragraph, this assumption holds for the dummy-variable approach as well. When using the forecasting approach it is obligatory to take in account the effects on the price caused by other factors than the conspiracy. Ignoring these effects could lead to a biased estimation and thus give a distorted picture of the damage.

A question that is raised when using the forecasting approach is which data should be used if both pre- and post-cartel data are available. In this case three options are applicable, since one could solely use the pre- or post-cartel data or one could make use of both periods to estimate the model. When this latter option is used one must consider if the price-setting behavior is equivalent before and after the cartel. If this is the case and the factors that cause the different behavior

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are identifiable and can be controlled, this needs to be taken into account in the analysis. If there is no possibility to assign the factors that are responsible for the different price-setting behavior, one of the datasets must be excluded in the estimation (Nieberding, 2006, p.369).

In summary, the big difference between the forecasting approach and the dummy-variable approach is the data that is being used to estimate the model. Although opinions differ on which approach is preferred when establishing the damage caused by the cartel, the dummy-variable approach is used more frequently. An explanation for this could be that the forecasting approach requires more data over a wider period which is not available at all times (Harrington, 2004. p.530). Nevertheless, in the next paragraphs the effects of cartel misdating under both approaches are being discussed.

2.4

Cartel misdating

It is obvious that different start and end dates of cartels will result in different damage quantities, which go hand in hand with the outcome of the sum of the penalty. In this paragraph the method for establishing the start and end dates of cartels is being discussed. Thereafter the cause of misdating cartels is addressed, followed by the consequences of misdating.

When a company is suspected of forming a cartel, antitrust agencies determine the begin and end date of the cartel in order to set the period for which damage caused by the cartel must be established. Making use of relevant e-mail communications, scheduled presumable cartel meetings, memo’s, testimonies and other documented material, agencies can set the formal start date of the cartel (Boswijk et al., 2016, p.2). The day when the infringement is uncovered is usually set as the formal end date of the cartel period. Obviously this is easier than determining the actual start date, since the day of uncovering is known. Even if enough evidence is available to assign the start date of the cartel, it can still be a tough job, since a cartel is generally not established in one day. Also, at times evidence of the forming of a cartel is destroyed by the malfeasances, which makes it hard to determine the formal start date (Harrington, 2004, p. 534).

After the formal dates are being set, a next problem arises, since the effective time of the collusion does not always coincide with the formal period set by antitrust agencies. The European Commission (2013) states that effects of cartels can start gradually, which implies that the effective start date does not correspond with the formal start date. The American Bar Association declares in its manual Proving Antitrust Damages (2014,p.318) that the effect of a cartel might occur earlier or later, or will even last longer than the conduct. Evidence for these events must be used to determine the dates for which the cartel was effective.

The consequence of using the formal start and end date of a cartel in case the effective period of the cartel does not coincide with these actual dates is obvious: a different quantity of damage will be established which leads to a different antitrust penalty. Boswijk et. al (2016) found in their

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study that cartel misdating leads to an overestimation of the but-for prices under the dummy-variable approach. In extension to this research, the focus of this paper is on the effects of cartel misdating under the forecasting approach. The methodology used to do so is described in the next section.

3

Methodology

In this section the methodology to examine the effects of cartel misdating on the estimation of but-for prices under the forecasting approach is discussed. In paragraph 3.1 the different types of misdating and their causes are mentioned. Subsequently the most simple form of the forecasting model is being discussed in paragraph 3.2. Afterwards the specified model that is used in this thesis is explained in paragraph 3.3. Finally the adjustments that are applied to different coefficients are brought into view in paragraph 3.4. A Monte-Carlo analysis is executed using the specified model in paragraph 3.3 to estimate the effects of cartel misdating. The but-for prices are estimated under the four different scenarios that are described in paragraph 3.1. But first of all, the chosen benchmark period is being discussed.

As mentioned earlier, the forecasting approach uses data from non-cartel periods to estimate the but-for prices. The data that is used as benchmark period needs to be defined, since there are different options for selecting data as described in paragraph 2.3. In this paper the post-cartel period is being used as benchmark period. Harrington (2004, p.530) states two disadvantages of the pre-cartel data compared to the post-cartel data. First, the pre-cartel data is older and is therefore likely to provide a less accurate estimation of the but-for prices. The other reason that is mentioned by Harrington is the fact that this older data often is incomplete and at times not even available at all. This will obviously lead to less precise estimates of the but-for price. Taking these disadvantages into account, the post-cartel data is chosen as benchmark period in this thesis.

3.1

Types of Misdating

As described earlier, a cartel is misdated if the effective cartel dates do not correspond with the formal start and end date of the cartel. Four different scenarios of misdating are possible, since both the start and end date can be dated incorrectly. Tb and Te are respectively defined as the

formal start and end date of the cartel assigned by antitrust agencies. The effective start and end dates of the cartel are represented by TB and TE.

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The four cases described in the research of Boswijk et al.(2016) are:

Case 1: Tb< TB, T e < TE

Case 2: Tb< TB, T e > TE

Case 3: Tb> TB, T e < TE

Case 4: Tb> TB, T e > TE

Figure 1: Cases of Misdating

In case 1 the begin date and end date are both dated too early, which leads to a shift of the cartel period TC to the left in time. This is for example the case if a cartel does not have

an immediate effect and the effects of the cartel continue after the date of extrication. This is opposite to case 4 where both the effective start and end date of the cartel are earlier than the formal dates. In case 2 the start date of the cartel is dated too early and the end date is dated too late. In this case the cartel has no immediately effect on the price and the cartel has no effect anymore on the price before the formal end date. A cause for this latter point could be that the conspiracy is discovered when it was not effective anymore. Case 3 is the opposite: the cartel became effective before the formal start date and was not effective anymore before the formal end date.

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The following values for the actual start and end date in the different cases of misdating are chosen: Case: Tb Te Correct Dating 50 100 Case 1 47 98 Case 2 47 103 Case 3 53 98 Case 4 53 103 Table 1: Values of Tb and Te

The values of Tband Teare chosen quite close to the effective cartel dates to inspect the effects of

a small form of misdating. However, the values of Tb and Te are adjusted several times through

the research, to examine the effects of different lengths of misdating. In the next section the assumptions that are required to estimate the effects of the four misdating scenarios are pointed out.

3.2

The Simple Forecast Model

In this section the consequences of the four cases discussed in the previous section are being considered based on the following basic forecasting model:

Pt= α1+ α2∗ Dt+ t t i.i.d. ∼ (0, σ2) (6)

Where Dt is equal to 1 when t∈ TC and equal to 0 otherwise. The but-for price is logically

defined as follows:

bf Pt= α1+ t ti.i.d. ∼ (0, σu2) (7)

In this simple model the estimated but-for price is equal to the average of the prices in the benchmark period, which is the post-cartel period in this research:

g bf Pt= 1 T − Te T X t=Te+1 Pt= ˜α1 (8)

and it follows that the following holds if the cartel is dated correctly:

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In the appendix the proof of the following Lemma is given:

Lemma 1

E[αf1] = α1 if Te> TE (10)

E[αf1] > α1 if Te< TE (11)

This indicates that the but-for price is estimated correctly in case 2 and 4 when the post-cartel period is used as benchmark period. Lemma 1 shows that the estimated but-for price is biased upwards in the discussed misdating scenario’s 1 and 3, where Te< TE.

After estimating the but-for price, the estimated overcharge can be computed and subsequently the estimated cartel damage is calculated as follows:

f Ot= Pt− gbf Pt t ∈ TC (12) g CD = Te X t=tb+1 f Ot∗ Qt t ∈ TC

Where Qtwith t = 1, ...., T is the quantity purchased. It is obvious that quantity is related to

the price and that a higher price leads to a smaller quantity. Let Qtbe stochastic with:

         E[Qt] = QN 1, t ∈ TN 1 E[Qt] = QC, t ∈ TC E[Qt] = QN 2, t ∈ TN 2

where QN 1is the quantity purchased in the pre-cartel period TN 1, QN 2the quantity purchased in

the post-cartel period TN 2and QC the quantity purchased in the cartel period TC The following

assumption stated in Boswijk et al. (2016,p.10) is made:

Assumption 1

QN 1, QN 2≥ Qc and (13)

E[Qtt] ≥ 0, t = 1, ...T, j ≥ 0 (14)

As mentioned before, the cartel has a positive effect on the price, which leads to higher prices during the cartel period TC. This leads to a smaller purchased quantity during the cartel.

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In regard to the total cartel damage CD, the following theorem holds, based on Lemma 1 and the assumption above:

Theorem 1

E[ gCD] = E[CD] if Tb< TB and Te> TE (15)

E[ gCD] < E[CD] elsewhere (16) The proof of this theorem is given in the appendix.

Following this theorem, one can say that the total damage is unbiased if the cartel is dated wider than it should have been. This is the scenario in case 2. Theorem 1 states that the total cartel damage is underestimated in the cases 1, 3 and 4. This corresponds with the analysis of Boswijk et al. (2009,p.15).

3.3

Model Specification

A version of the basic model discussed in the previous paragraph expanded with an exogenous and stationary variable Xt is explained in this paragraph. A Monte-Carlo simulation is used for this

model to give a representative result of the effects of cartel misdating. The number of replications in this Monte-Carlo simulation is 10000. T is, to start of with, divided as follows: observations t1− t50 form the pre-cartel period TN 1, t51− t100 form the cartel period TC and t101− t150 form

the post-cartel period TN 2, which is the benchmark period in this paper. The values of Xt, Ptand

Qtare generated over these 150 observations of T.

Xt is an exogenous and stationary variable in the model used to estimate Pt. To meet the

requirements of exogeneity the following assumption is added for Xt:

E[etkXs] = 0 ∀s, t

which is the exogeneity assumption. This is a necessary assumption to obtain a consistent esti-mation. Xtis generated in the following way:

Xt= ρ ∗ Xt−1+ ωt t ∈ TN 1, TC, TN 2 (17)

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ρ < |1| (19)

ωt∼ N (0, σ2) (20)

The value of ρ must be < |1| to meet the stationary condition. ωt does not follow a standard

normal distribution but has a bigger variance. This is to add more weight to Xt in the model.

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of zero and a variance of 1−θσ22 which corresponds with a variance of a stationary AR(1) model. In

this research the following values for ρ and σ2 are chosen:

ρ = 0.40 (21)

σ2= 1.10 (22)

ρ = 0.4 is chosen as starting point, since 0.4 is a value that is not close to a unit root. To generate Ptthe following equation is used:

Pt= α1+ α2∗ Dt+ βXt+ et t ∈ TN 1, TC, TN 2

(23) where Dtis a dummy-variable which has a value of 1 if the cartel is effective and has a value of 0

otherwise. This model is in line with the model of Nieberding (2006), who presents and discusses the forecasting approach without including lagged prices. To start of with, the following values for the coefficients are chosen:

α1= 100

α2= 15.27

β = 1.00

The value of the coefficient α2 is based on the findings of Nieberding (2006), since Nieberding’s

model corresponds with the model used in this paper. Nieberding found an average overcharge of 15.27% in his model using the forecasting approach without a lagged price variable.This is why α2 has a value of 15.27% of α1. As discussed before, a lagged price variable is often included in

the model. However, in this paper these lagged variables are not included due to the scope of this paper.

Lastly Qtis generated using the following equation:

Qt= λ − φPt+ vt t ∈ TN 1, TC, TN 2 (24)

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The following values are chosen:

λ = 1000 φ = 1.50

λ is held constant through all the Monte-Carlo analysis. φ has a positive value in order to represent the negative relationship between price and quantity.

After estimating Pt, the but-for prices are estimated using the following model:

g

bf Pt = ˜α+ ˜βXt t ∈ (TC)

(26) where TC is the assigned cartel period. When the coefficients α1 and β are estimated with

the model above, the but-for prices in the four different cases are calculated with the average estimated coefficients. Subsequently the damage can be established by calculating the overcharges as follows:

f

Ot= Pt− gbf Pt t ∈ (TC)

(27) and finally the total damage:

g CD = Te X t=tb+1 f Ot∗ Qt t ∈ (TC)

3.4

Adjusted Coefficients

After the cartel damage is estimated with the model explained above, the Monte-Carlo analysis is executed several other times with adjusted coefficients or different values for the effective and actual start and end dates of the cartel. Obviously, all other coefficients are held constant when a certain coefficient is adjusted. This is necessary to give a reliable result of the effects of varying a particular coefficient, actual start and end date of the cartel, or the effective cartel period.

At first the start and end date of the effective cartel period and thus the end date of the pre-cartel period as well as the begin date of the post-cartel period, are adjusted after the first estimations to examine the effects of a different length of the effective cartel period on the estimated damage. In the model explained above, TC is defined as t51 − t100. Keeping all other values

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t56− t95. These adjustments are done to bring the effects of a longer and shorter effective cartel

period on the estimated cartel damage into view. To still meet the conditions of the different misdating cases defined in 3.1, the actual start and end date of the cartel need to be adjusted as well. The following values for Tband Teare chosen for TC= t46− t105respectively TC = t56− t55

Case: Tb Te Correct Dating 45 105 Case 1 43 94 Case 2 43 107 Case 3 50 94 Case 4 50 107

Table 2: Values of Tb and Te for TC= t46− t105

Case: Tb Te Correct Dating 55 95 Case 1 47 93 Case 2 47 100 Case 3 55 93 Case 4 55 100

Table 3: Values of Tb and Te for TC= t56− t95

The values of Tb and Teare adjusted in a way to stay as close to the original values of Tband

Teas possible in order to deviate from the original values as little as possible.

Subsequently the values of the actual start and end date Tb and Te are adjusted under the

original cartel period TC= t51− t100. The following adjustments are done:

Case: Tb Te Correct Dating 50 100 Case 1 40 90 Case 2 40 109 Case 3 56 90 Case 4 56 109

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Case: Tb Te Correct Dating 50 100 Case 1 45 95 Case 2 45 105 Case 3 54 95 Case 4 54 105

Table 5: Adjusted Values II of Tb and Te for TC = t51− t100

These adjustments are modified to determine the effects of bigger forms of cartel misdating on the estimated cartel damage.

Afterwards the value of ρ is modified in the original model discussed in the previous paragraph. ρ = 0.40 is chosen as starting point, since 0.40 is a value that is not close to a unit root. After Xt is simulated with ρ = 0.40, Xt is simulated with the values ρ = 0.90, ρ = 0.70 and ρ = 0.10,

keeping the other coefficients at the value of the starting point, to bring the effects of a different value of ρ on the estimated cartel damage into view.

Subsequently, the value of α2is adjusted. In the original model, a value of α2= 15.27 is chosen,

based on the findings of Nieberding (2009). In other previous relevant researches an overcharge between 10.00 and 20.00% of α1 was found. Therefore, after Pt is simulated with α2 = 15.27

with the cartel damage is estimated with values α2= 10.00 and α2= 20.00. α1 is logically held

constant.

Lastly, the value of φ is modified to estimate the cartel damage under different relationships between price and quantity. As starting value φ = 1.50 is chosen, which generates a negative relationship between price and quantity. This is the most likely situation, since a higher price usually leads to a smaller purchased quantity. First the value of φ is modified to φ = 0.00 With this adjustment, the cartel damage is estimated while the relationship between Qtand Ptis being

ignored. Afterwards φ is set equal to 1.5 to generate a positive correlation between Qtand Pt. In

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4

Results

In this section the results of the performed Monte-Carlo analysis using the methodology discussed in the previous section are presented. In paragraph 4.1 the estimated coefficients α1 and β under

the model characteristics described in paragraph 3.1 and 3.3 are given. Subsequently the calculated overcharges in the four different cases are discussed in paragraph 4.2. Lastly the obtained results under the executed adjustments explained in paragraph 3.4 are brought into view.

4.1

Estimation of ˜

α

1

and ˜

β

The estimations of α1and β using OLS are given in the figures below. The Monte-Carlo analysis

is performed for 10000 replications. Since the chosen benchmark period is the post-cartel period, it is obvious that the estimates of the coefficients ˜α1 and ˜β are equal in case 1 and 3 and case 2

and 4. 0 400 800 1,200 1,600 2,000 2,400 99.2 99.4 99.6 99.8 100.0 100.2 100.4 100.6 100.8 101.0 101.2 101.4 101.6 Alpha 1 Case 2 + 4 Alpha 1 Case 1 + 3 Alpha 1 Correct Dating

Fr eq ue nc y alpha 1 Figure 2: Estimation of ˜α1

Figure 2 gives the impression that the estimated ˜α1 is unbiased for case 2 and 4, since the

distribution overlaps the distribution of α1 where the effecst of the cartel are dated correctly. The

˜

α1for case 1 and 3 is overestimated. In cases 1 and 3 the formal cartel date Teis smaller than the

actual cartel date TE. This leads to inclusion of prices under cartel in the benchmark period. The

prices during the cartel period are higher and this could be an explanation for the overestimation of α1in the model for case 1 and 3.

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0 200 400 600 800 1,000 1,200 1,400 1,600 -0.8 -0.4 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 Beta Case 2 + 4 Beta Case 1 + 3 Beta Correct Dating

Fr eq ue nc y Beta Figure 3: Estimation of ˜β

In Figure 3 it seems that the estimated β is centered around 1 in all scenario’s. An explanation for this could be that the variable Xt is not influenced by the cartel. However, the estimated β

for cases 1 and 3 has a wider spread than the other estimators and therefore a bigger variance. The average over 10000 replications of the estimated coefficients of α1 and β are included in the

model to calculate the but-for prices in the four different cases. Subsequently the overcharge and corresponding average total cartel damage were computed. These results are given in the next paragraph.

4.2

The Obtained Total Damage

To calculate the estimated total damage caused by the cartel under the four different cases, the average of the 10000 replications of the coefficients α1 and β obtained through the Monte-Carlo

experiment are used to calculate the estimated but-for price and subsequently the corresponding overcharge and total cartel damage. The results are presented in the table below:

Case: Total Damage α1 β

Correct Dating 623722.17 100.19 1.07 Case 1 588847.80 100.71 0.46 Case 2 635122.80 100.20 1.06 Case 3 537739.80 100.71 0.46 Case 4 586517.70 100.20 1.06 Table 6: Estimated Total Cartel Damage, α1 and β

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line with the findings of Boswijk et al. (2016). Despite the numeric deviation, the estimated total cartel damage in Case 2 is similar to the estimated total cartel damage in case the cartel period is dated correctly. So on the base of these results it seems that dating the cartel too widely leads to an accurate estimation of the total cartel damage. This is in line with the expectations presented in Theorem 1. In the next paragraph the results are given under several applied modifications to the model.

4.3

The Obtained Results under Several Adjustments

4.3.1 Adjustments of cartel period TC

Two adjustments of the cartel period TC were executed to bring the effects of a different effective

cartel length TC in to view. In the tables below the results are given for these modifications:

Case: Total Damage for t51− t100 Total Damage for t46− t105 Total Damage for t56− t95

Correct Dating 623722.17 749984.09 502223.10

Case 1 588847.80 508279.30 474533.16

Case 2 635122.80 752506.25 509635.23

Case 3 537739.80 443141.57 460247.43

Case 4 586517.70 679924.56 500880.98

Table 7: Estimated Total Damage under Different Effective Cartel Periods

It is obvious that a longer effective cartel period leads to a bigger estimated damage in case the cartel is dated correctly, since prices under the effective cartel are higher. The contrary holds for a smaller effective cartel period. One can see in Table 7 that for all defined cartel periods TC,

the total damage is underestimated in case 1, 3 and 4. The total damage is estimated correctly in case 2. This is in line with Theorem 1. One can see that the proportional deviation of the estimated cartel damage in case 1 and 3 compared to the total damage under correct dating, is bigger when the effective cartel period is defined as t46− t105in comparison to the deviation of the

other effective cartel periods in case 1 and 3. An explanation for this is the fact that the length of the estimated cartel in the cases 1 en 3 for t46− t105 becomes smaller with respect to the effective

cartel period. This obviously leads to a bigger underestimation of the total cartel damage.

4.3.2 Adjustments of the actual start and end date Tb and Te

Two modifications were executed when it comes to the actual cartel dates. Below the results are presented for the different actual cartel dates discussed in paragraph 3.4:

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Case: CD Original Actual Dates CD Adjusted Actual Dates I CD Adjusted Actual Dates II Correct Dating 623722.17 623722.17 623722.17 Case 1 588847.80 443689.86 518036.20 Case 2 635122.80 621338.76 636356.24 Case 3 537739.80 360574.40 459657.75 Case 4 586517.70 540918.52 577031.32

Table 8: Estimated Total Damage under Adjusted Actual Cartel Dates

The estimated total damage under correct dating obviously does not change, since the effective cartel period is equal in all three situations. Table 8 shows that under the adjusted actual cartel dates the cartel damage is underestimated in cases 1, 3 and 4. The estimation in case 2 is unbiased. This shows that bigger forms of misdating still give the same results in estimating the total cartel damage.

4.3.3 Adjustments of ρ

Three modifications of ρ were applied to the model:

Case: CD ρ = 0.40 CD ρ = 0.90 CD ρ = 0.70 CD ρ = 0.10 Correct Dating 623722.17 623821.50 623424.10 623298.40 Case 1 588847.80 610670.40 592246.0 588741.90 Case 2 635122.80 635693.80 634952.00 634805.50 Case 3 537739.80 557330.60 538244.40 538665.90 Case 4 586517.70 586301.80 586169.40 585758.00

Table 9: Estimated Total Cartel Damage under Adjusted values of ρ Table 9 shows that when ρ meets the stationary condition of |ρ| < 1, the cartel damage is still underestimated in case 1, 3 and 4 and unbiased for case 2.

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4.3.4 Adjustments of α2

The results of the two modifications of α2are presented below:

Case: CD for α2= 15.27 CD for α2= 10.00 CD for α2= 20.00

Correct Dating 623722.17 409594.59 812361.30 Case 1 588847.80 387187.61 766510.02 Case 2 635122.80 416721.90 827526.42 Case 3 537739.80 354153.07 699456.13 Case 4 586517.70 385205.60 763865.41 Table 10: Estimated Total Cartel Damage under Adjusted values of α2

Table 10 shows that the cartel damage is still underestimated in case 1, 3 and 4 under different values for α2. The cartel damage is estimated correctly under the circumstances of case 2. One

can see that there is a positive relationship between the estimated cartel damage and α2: a smaller

value of α2 leads to a smaller estimated cartel damage. This is obvious, since a smaller value of

α2leads to a lower price, which results in a lower estimated cartel damage.

4.3.5 Adjustments of φ

Lastly the results for several adjustments of φ are presented in Table 11:

Case: CD for φ = 1.50 CD for φ = 0.00 CD for φ = −1.50 Correct Dating 623722.17 753900.06 884077.95

Case 1 588847.80 711929.10 835010.37 Case 2 635122.80 767775.22 900427.63 Case 3 537739.80 649991.77 762252.76 Case 4 586517.70 708847.35 831178.01 Table 11: Estimated Total Cartel Damage under Adjusted values of φ

For φ = 0.00, the correlation between price and quantity is being ignored. One can see that this adjustment of φ leads to the same result as when the relation between price and quantity is negative: Case 1, 3 and 4 underestimate the cartel damage, while Case 2 gives a quite accurate estimation of the total damage. The same holds for φ = −1.50 as well, when the relationship between price and quantity is considered to be positive. In the next section a conclusion is drawn based on the results presented.

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5

Conclusion

Despite the strict regulations and high fines issued by the European Commission when it comes to antitrust, common news reports prove that the practice of antitrust is still an ongoing phenomenon. One of the most common forms of antitrust is the practice of a cartel, where companies harm their customers and competitors through price-fixing.

When the presence of a cartel is revealed, it is a challenging task for the European Commission to determine the total damage caused by the cartel. Dating the effective period of the cartel makes this task ambitious, hence the effective start and end dates are difficult to determine. Since the fines issued by the European Commission are based on the estimated total damage, it is of great importance to estimate the total damage correctly. It is obvious that cartel misdating leads to a biased estimated damage.

In this paper the effects of different forms of cartel misdating were brought into view. First of all the chosen benchmark period was chosen. The post-cartel period was used as benchmark period, since the post-cartel data is the most recent data available, which leads to a more accurate estimation of the total damage caused by the cartel. Secondly the different cases of misdating were brought into view. Several arguments for the possible causes of the misdating were given. Subsequently the effects of cartel misdating were analysed algebraically on the basis of a simple forecasting model. Eventually a Monte-Carlo analysis was performed to determine the effects of cartel misdating for the four different scenario’s. The Monte-Carlo experiment was executed numerous times after several adjustments applied to the model.

On the basis of the results presented in section 4, one can conclude that misdating a cartel under the forecasting approach leads to an underestimation of the total damage. This is in line with the findings of Boswijk et al. (2016), who examined the effects of cartel mistating under the dummy-variable approach. This result suggest that it would be necessary for the European Commission to consider a wider cartel dating when determining the actual start and end date of the cartel. The results in this paper suggest that a wider dating range could give a more accurate representation of the harm caused by the cartel. However legal regulations are strict when it comes to determining the actual begin and end date, so a wider cartel dating is easier said than done. Perhaps these regulations can be revised in the future to determine a more suitable estimation of the damage caused by cartels.

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Bibliography

Boswijk, H. P., Bun, M. J. G., and Schinkel, M. P. (2016). Cartel Dating. Amsterdam Law School Research Paper No. 2016-62; Amsterdam Center for Law Economics Working Paper No. 2016-05. Commission of the European Communities (2013), Quantifying Harm in Actions for Damages Based on Breaches of Article 101 or 102 of The Treaty of The Functioning of The European Union. Practical Guide.

Court of Justice of the European Union, (2017). Judgment in Case C-413/14 P.

Retrieved from: https://curia.europa.eu/jcms/upload/docs/application/pdf/2017-09/cp170090en.pdf. Finkelstein, M.O. and H. Levenbach (1983). Regression Estimates of Damages in Price- Ficing Cases. Law and Contemporary Problems, 46 (4), 145–169.

Harrington, J. E. (2004). Postcartel Pricing during Litigation. The Journal of Industrial Eco-nomics, 52 (4), 517-533.

McCrary, J. and D.L. Rubinfeld (2014). Measuring Benchmark Damages in Antitrust Litigation. Journal of Econometric Methods, 3, 63–74.

Nieberding, J. F. (2006). Estimating overcharges in antitrust cases using a reduced-form approach: Methods and issues. Journal of Applied Economics, 9 (2), 361-380.

Notaro, G. (2013). Assessing Methods for the Quantification of Antitrust Damages. An Applica-tion to the Pasta Cartel in Italy. Journal of CompetiApplica-tion Law Economics, 10 (1), 1 March 2014, 87–106.

Rubinfeld, D. L. and Steiner, P. O. (1983). Quantitative methods in antitrust litigation. Law and Contemporary Problems, 46 (4), 69-141.

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Appendix

Lemma 1

E[αf1] = α1 if Te> TE (28) E[αf1] > α1 if Te< TE (29) Proof: Pt= α1+ α2∗ Dt+ twith t∼ i.i.d (0, σ2) bf Pt= α1+ t

Where Dtis equal to 1 when t ∈ Tc and Dt= 0 otherwise.

˜ α1=T −T1 e PT t=Te+1Pt E[bf Pt] = α1

For cases 2 and 4 where Te> TE :

E[ ˜α1] = T −T1 e ∗ (T − Te) ∗ α1= 1 ∗ α1= α1

This means that the estimation of α1is unbiased when Te> TE

For cases 1 and 3 where Te< TE:

˜ α1= T −T1 e ∗ ( PTE t=Te+1Pt+ PT t=TE+1Pt) ˜ α1= TT −TE−Te e ∗ 1 TE−Te PTE t=Te+1Pt+ T −TE TT e ∗ 1 T −TE PT t=TE+1Pt E[ ˜α1] = TT −TE−Tee ∗ (α1+ α2) +T −TT −TEe ∗ α1 E[ ˜α1] = TE−TT −Te+T −Te E ∗ α1+TT −TE−Tee ∗ αw E[ ˜α1] = α1+TT −TE−Tee ∗ α2

Which is bigger than α1 since 0 < TT −TE−Te

e < 1 and α2 > 0. So the but-for price is overestimated

in case 1 and 3. TE−Te

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Theorem 1

E[ gCD] = E[CD] if Tb< TB and Te> TE (30)

E[ gCD] < E[CD] elsewhere (31) With the following assumptions:

         E[Qt] = QN 1, t ∈ TN 1 E[Qt] = QC, t ∈ TC E[Qt] = QN 2, t ∈ TN 2 QN 1, QN 2≥ Qc and (32) E[Qtt−j] ≥ 0, t = 1, ...T, j ≥ 0 (33) QN 1= QN 2 (34) E[CD]=PTE t=TB+1E[Pt− bf Pt∗ Qt] E[CD]=(TE− TB) ∗ α2∗ QC g CD =PT t=Tb+1 e(Pt− gbf Pt) ∗ Qt Qt= λ − φPt+ vtwith vt∼ N (0, 1) E[ gbf Pt] = E[ ˜α1]

First the proof of equation 33 is given where Tb < TB and Te> TE. This is the scenario of Case

2: E[ gCD] =PTB t=Tb+1E[(Pt− gbf Pt) ∗ Qt] +PTE t=TB+1E[(Pt− gbf Pt) ∗ Qt] + PTe t=TE+1E[(Pt− gbf Pt) ∗ Qt] =PTB t=Tb+1E[(Pt− gbf Pt) ∗ (λ − φPt+ vt)] +PTE t=TB+1E[(Pt− gbf Pt) ∗ (λ − φPt+ vt)] + PTe t=TE+1E[(Pt− gbf Pt) ∗ (λ − φPt+ vt)] =PTB t=Tb+1E[λPt− φP 2 t − λ gbf Pt+ φPtbf Pgt)] +PTE t=TB+1E[λPt− φP 2 t − λ gbf Pt+ φPtbf Pgt)]

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+PTe t=TE+1E[(λPt− φP 2 t − λ gbf Pt+ φPtbf Pgt)] = (TB− Tb)(λα1− λα1− φa21+ φα 2 1) + (TE− TB)(λ(α1+ α2) − φ(α1+ α2)2− λα1+ φ(α1+ α2)α1) + (Te− TE)(λα1− λα1− φa21+ φα 2 1) = 0 + (TE− TB) ∗ (λα2− φα1α2− φα2) + 0 = (TE− TB)α2(λ − φ(α1+ α2))

Which is equal to (TE− TB)α2∗ QC, since E[Qt] = QC= λ − φ(α1+ α2)for t ∈ TC

E[ gCD] = (TE− TB)α2∗ QC= E[CD]

So under the assumptions mentioned above, the estimation of the total damage is unbiased in case 2.

Now the proof of equation 34 is given for cases 1, 3 and 4. Proof for case 1, with Tb< TB, Te< TE:

E[ gCD] =PTB t=Tb+1E[(Pt− gbf Pt)Qt] +PTe t=TB+1E[(Pt− gbf Pt)Qt] =PTB t=Tb+1E[(Pt− gbf Pt)(λ − φPt+ vt)] +PTe t=TB+1E[(Pt− gbf Pt)(λ − φPt+ vt)] = (TB− Tb)(λα1− φα12− λ(α1+ θα2) + φα1(α1+ θα2)) + (Te− TB)(λ(α1+ α2) − φ(α1+ α2)2− λ(α1+ θα2) + φ(α1+ α2)(α1+ θα2)) = (TB− Tb)(−λθα2+ φθα2α1) + (Te− TB)(−λα2(θ − 1) + φ(θ − 1)α1α2+ α22φ(θ − 1)) = (TB− Tb)(−θ ∗ α2QN 1) + (Te− TB)((θ − 1)α2QC)

< (TB− Tb)(−θ ∗ α2QC) + (Te− TB)((θ − 1)α2QC) since E[Qt] = QC= λ − φ(α1+ α2) for t ∈ TC

and E[Qt] = QN 1= λ − φα1for t ∈ TN 1

E[ gCD] = −TBθα2QC+ Tbα2θQC− Teθα2QC+ Teα2QC+ TBθα2QC− TBα2QC

= (Tb− Te)(θα2QC) − (Te− TB)α2QC

which is smaller than:

(Te− TB)α2∗ QC< (TE− TB)α2∗ QC= E[CD]

So the total damage is underestimated in case 1.

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E[ gCD] =PTe t=Tb+1E[(Pt− gbf Pt)Qt] =PTe t=Tb+1E[(Pt− gbf Pt)(λ − φPt+ vt)] = (Te− Tb)(α1+ α2− (α1+ θα2))(λ − φ(α1+ α2) = (Te− Tb)(α2(1 − θ))QC

Which is smaller than (Te− Tb) ∗ α2∗ QC < (TE− TB) ∗ α2∗ QC = E[CD]

And thus, the total damage is underestimated in case 3.

Proof for case 4, with Tb> TB, Te> TE:

E[ gCD] =PTE t=Tb+1E[(Pt− gbf Pt)Qt] + PTe t=TE+1E[(Pt− gbf Pt)Qt] = (TE− Tb) ∗ (α1+ α2− α1) ∗ (λ − φ(α1+ α2) + (Te− TE) ∗ (α1− α1) ∗ (λ − φα1) = (TE− Tb) ∗ (α1+ α2− α1) ∗ (λ − φ(α1+ α2)) = (TE− Tb) ∗ (α1+ α2− α1) ∗ QC

Which is smaller than (TE− TB) ∗ α2∗ QC= E[CD]

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