Dynamic price modelling in antitrust cases : application of the German cement cartel

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Dynamic price modelling in

antitrust cases

Application of the German cement cartel

Abstract

Although proven effectively in numerous fields, dynamic price modelling finds little application in practice to estimate overcharges in antitrust cases. This research takes a

step in exploring this possibility by examining the influence of AR dynamics on the accuracy of cartel effect estimations. The 1990’s German cement cartel is analysed as case study, and used as a point of departure for an experimental analysis in the form of simulation. For this cartel, the dynamic estimated long term effect yielded a 29% higher outcome compared to a static estimated effect. On the basis of the estimation models for the case study, dynamic and static data generating processes are established. By working in a controlled, and simultaneously realistic, environment, AR model specifications are

associated with the accuracy of cartel effect estimations. Adding redundant AR dynamics to a model resulted to be effectively harmless for the estimated cartel effect.

On the other hand, omitting relevant AR dynamics resulted in highly underestimated estimations of the cartel effect. These findings suggest important advantage in using AR

models instead of static models. It also indicates that the dynamic estimation of the German cement cartel seems more reliable than the static estimated values. With direct

implication on imposed fines of millions, the enhancement of cartel effect estimation accuracy by AR dynamics seems an opportunity with high potential.

Rik Helwegen

supervisor: Maurice J.G. Bun

23 December 2016

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Statement of Originality

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

I declare that the text and the work presented in this document is 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 the work, not for the contents.

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1 Introduction

“People of the same trade seldom meet together, even for merriment and diversion, but the conversation ends in a conspiracy against the public, or in some contrivance to raise prices.”

- Adam Smith, The Wealth of Nations, 1776 Adam Smith commented in 1776 already that we need to be cautious for conspiracy when people in the same industry come together. Maybe this legacy inspired the European commission while imposing almost 3 billion euro in fines for a truck producer cartel earlier this year. This amount rates as the highest fine for a single antitrust case the European commission has imposed since the recordings started in 1969. (European commission, 2016b)

Pricing is the way the market brings supply and demand in equilibrium. For this process, corporations need to operate under competitive market conditions, according to Gabszewicz and Thisse (1979). They argue this market competitiveness causes companies to be fair opponents, to be subject to free choice of consumption. When companies try to overcharge their customers, some company competing in the same industry will provide a homogeneous product for a lower price, causing the customers to choose for the latter. However, if the competing companies all together agree to ask a higher price, they leave the customer no way out, so Gabszewicz and Thisse (1979) say. Among else to keep the market prices natural, governments prohibit anti-competitive agreements between companies in the so called antitrust laws.1 Punishment can be severe, as seen this year2, but it still occurs regularly that companies attempt to increase their profit by means of a cartel. When such an infringement comes to light, it is custom to model the cartel effects in order to understand what damage the cartel has done.

In this paper the scope will be on those cartels in which companies horizontally agree on including an overcharge in the price, also known as hardcore cartels. That companies include an overcharge, implies that there must be a natural price equilibrium lower than the charged price. This natural price is called the but-for price. A visual understanding of the but-for price can be obtained through Figure 1. For the estimation of these but-for prices in antitrust cases, econometricians commonly use regression analysis. A development of the latest decade has been to include short-run dynamics in the overcharge estimation models3. Dynamic modelling has been applied in a wide range of fields, it receives both critique and support, which is further elaborated in the following section. However, little is known

1

See European Commission (2016a)

2_{See European commission (2016b)} 3

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Figure 1: The actual price, predicted price and but-for price as estimated by Nieberding (2006) via an ECM-DV approach

about the consequences of making empirical overcharge models ’dynamic’. Researchers are facing the challenge that they need to base their decision of dynamic variable inclusion on literature in which the dynamics are applied to different sorts of problems. To attribute to a robust base for dynamic variable inclusion decisions in antitrust cases, this paper examines one aspect of the dynamic modelling, namely the inclusion of autoregressive (AR) dynamics. The paper answers the question in what way AR dynamics influence the accuracy of long term cartel effect estimations.

In order to do so, relevant findings from earlier research is discussed in the next section. Section 3 elaborates on an empirical analysis of a cartel case study. Section 4 discusses an experimental analysis to obtain more profound results. In section 5 the results are interpreted and discussed to finally come to an overall conclusion.

2 Dynamic models for overcharge estimation

This section reviews relevant literature on what is already known on the consequences of estimating overcharge estimation models with an incorrectly specified dynamic model. The combination of cartels and the implications of dynamic modelling decisions is relatively scarce in earlier literature4. Nieberding (2006) phrases it as most articles on these matters focus on ’higher-level’ issues. Therefore, both overcharge estimation models, as well as the

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statistical implications of the inclusion of variables are given in overview. Accordingly, a subsection discusses the specifics of dynamic models, defining which dynamic procedures fall under the scope of this paper. The section concludes with bringing all elements together, discussing what consequences can be expected for inclusion decisions of AR variables in overcharge estimation models.

2.1 Overcharge estimation models

Within the estimation of but-for prices by regression analysis, two methods are custom to use, both of which many applications can be found in the literature.5 In the Practical Guide published by the European Commission (2013), the main difference between these two methods is formulated. Either the model uses only data from non-infringements periods, in which case is spoken of the forecasting approach, or the model uses data from both inside and outside the infringement period, being the dummy variable (DV) approach. When the forecasting approach is used to estimate but-for prices, an explanatory re-gression model is fitted to the available data outside the cartel period. Next, the values of the explanatory variables within the cartel period determine with their estimated coef-ficients what the product price would be if the price stayed in line with the model. White et al. (2006) argue that since the forecasting model only uses data from outside the cartel period, an advantage of this approach is that the explanatory variables are not influenced by the cartel, assuming the cartel period is well defined6. An exception to this is when the cartel has changed the market with its influences, and therefore causing consequences until after the infringement period. (White et al., 2006, p. 21)

This advantage of data being clear of cartel influences does not hold for the DV ap-proach, according to White et al. (2006). With this apap-proach, all the available data is used for the estimation of the coefficients. Different here is that a dummy variable is added to the regression as an explanatory variable. This dummy variable equals the value 0 outside the cartel period and turns to 1 during the cartel period. This way, Nieberding (2006) explains, when the price rises during the cartel period in a way which cannot be explained by the other variables, this will be absorbed in the coefficient of the dummy variable, directly indicating the relative overcharge. White et al. (2006) argue that this method is misleading in most cases, and could be very easily manipulated. In their paper, White et al. (2006) mention that actions like supply restriction, or redirecting marketing by the cartel members, can heavily influence the explanatory variables, and therefore cause biases in the estimated coefficients.

5

See White et al. (2006) and Nieberding (2006)

6_{When the cartel period is not correctly specified, this may influence overcharge estimation according}

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Furthermore, Nieberding (2006) mentions an important assumption that is taken on for both approaches. The relationship between dependent and the independent variables, estimated by the model, needs to hold over the entire set of observations, within and out-side the cartel period. As remark to the forecasting approach he makes the notion that enough data is needed before and/or after the cartel period in order to successfully apply the forecasting approach. Either way, both Nieberding (2006) and White et al. (2006) support the idea that antitrust cases need a case specific investigation into which method-ology is most ideal and how the model should look like. Therefore, it seems reasonable to consider both approaches when setting up a regression analysis of but-for prices.

2.2 Variable inclusion

Because this paper considers the effects of including and excluding variables in a regres-sion model, it is important to get a clear understanding of the underlying theory. Before zooming into the specific case of dynamic models, the general consequences of omitting relevant variables and including redundant variables is discussed in this paragraph. Con-sider a hypothetical data generating proces (DGP) which has the following form in the population:

y = X1β1+ X2β2+ (1)

A standard process in which y is depending on influences from X1 and X2, including an

error term . When one of the explanatory variables, say X2, is omitted the estimated

model equals:

y = X1β11+ (2)

According to Heij et al. (2004), the estimated value of b1₁ for this model, under (1) as DGP, equals:

b1₁= (X₁0X1)−1X10y = β1+ (X10X1)−1X10X2β2+ (X10X1)−1X10

So that, E(b1₁) = β1+ (X10X1)−1X10X2β2, which means the estimator is not consistent as

long as β2 6= 0, which won’t be the case if the omitted variable is relevant. However,

the variance of the estimated coefficient will decrease, therefore this estimation might be desirable if the bias is acceptable for the gain in variance. (Heij et al., 2004, p. 136)

Contrarily, the model used for estimation also might contain redundant variables. This is the case when, for example, under DGP (1), b2₁ is derived from the next equation:

y = X1β12+ X2β22+ X3β32+ (3)

The assumptions for the linear regression are not harmed in this case, which makes b2₁ a consistent estimator of β1. Nevertheless, the variance of the estimated b21 obtains an extra

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term now, depending on how X1 interacts with the other variables and their variances.

Therefore, Heij et al. (2004) conclude adding redundant variables leads to inefficiency. Besides evaluating the model with statistical tests, it is highly important to keep in mind that inclusion of variables has to be based on economic theory. The inclusion of a variable with no relevance whatsoever to the price, but a similar trend, leads to spurious results. This causes a non existing explanation for the price in the model, which deteriorates the forecasting performances needed for the but-for price estimation. (White et al., 2006, p. 21)

In short, the selection of variables should first of all be based on economic theory. Thereafter, leaving out or including a variable while forming the model turns out to be a trade-off between variance and a possibly implied bias. Hereafter, a subsection goes into detail about dynamic models, on which these findings need to be implied in order to understand the inclusion of AR variables.

2.3 Dynamic models

There are various ways of including dynamics in a regression model. A general way of describing a large number of dynamic models is as follows (Heij et al., 2004, p. 637):

yt= α + p X k=1 φkyt−k+ r X k=0 βkxt−k+ q X k=1 φkt−k+ t (4)

In this equation, the term including yt−k causes the model to be autoregressive, the lagged

values of the dependent variable help predicting the current depending variable. The term including xt−k makes this a distributed lag model, both current as previous values

of an explanatory variable are used as regressors7. Finally, the inclusion of t−k makes

this a moving average model, it causes random shocks to have a direct effect on the dependent variable which diminishes over time. The focus of this paper will be on the first part, i.e., the AR variables in the estimation model. This is the included dynamic most often purposed for antitrust cases, e.g., by White et al. (2006) and Nieberding (2006). Nieberding also explored the application of an ECM, which is another interesting model type to combine with cartels, but falls outside the scope of this paper.

2.4 Autoregressive overcharge estimation model

Combining overcharge estimation with AR models has numerous advantages (White et al., 2006, pp. 20-21). Two reasons jump out in making clear why a lagged price variable must be considered for overcharge estimation models.

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First of all, especially of importance for the DV approach, the implication of the dummy variable being either on or off seems unrealistic. At the beginning of a cartel, it takes time for the companies’ non-competitive actions to develop towards their full consequences. This process will more likely be gradual, instead of being a binary shift (Boswijk et al., 2016, p. 4). One approach to ease this problem is given by H¨uschelrath et al. (2013), in which they implement dummy fractions in order to divide the price shift over a number of steps in time. Creating many of these fractions might lead to a more smooth transition, but would yield a model difficult to comprehend and work with. A much more natural solution for this is making the model auto-regressive. Adding a lagged version of the objective variable is a common and proven successful approach to create smooth transitions of the dependent variable. Although the forecasting approach does not include a dummy variable, it still concerns a model with the price as objective. Because prices have a certain stickiness, the smoothing of transitions is also a preferred characteristic of the model. (H¨uschelrath et al., 2013)

Another reason to make an overcharge estimation model dynamic is to capture vari-ables which are difficult or impossible to observe. In many cases proxy varivari-ables are used to account for such missing variables. Not in all cases, such alternatives are available how-ever. In fact, often it is even unknown which variable is still missing from the model. The previous section inclusion of variables shows that neglecting influential variables leads to inconsistent coefficient estimates. The lagged version of the price, as mentioned by White et al. (2006), already naturally includes much of the factors on which the current price depends. Therefore, they argue, this lagged variable can function as a tool to lesser the effects of neglecting variables which are difficult to include in the model otherwise.

It seems many preach the advantages of including dynamics in regression analysis, but on the other hand there has also been wide stretched critique on the use of AR variables. A major part of the opposing arguments shows from an elaborate paper by Achen (2001). He states that often lagged versions of the dependent variable are inserted without any clear theoretical reason to do so. Although the inclusion might create a model which fits the sample data much better, the coefficients of other variables collapse, and can even switch sign, so Achen (2001) says. He argues that the inclusion of AR variables therefore often misleads researchers, and he stresses the importance of selecting variables based on economic grounded theory. This precaution unmistakably has to be taken serious for the inclusion of AR variables in overcharge estimation models. Important to notice is that White et al. (2006) and others, do give reasons why the implementation of AR variables in overcharge estimation is justified. Smoothing the transition of the objective variable because it concerns a price value is one of these.

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implications of AR overcharge estimation models. Available literature suggests that omit-ting relevant AR variables leads to inconsistent coefficients, whereas including redundant AR variables causes inefficiency. It is important the inclusion of variables is grounded on economic theory. In this case, this approach seems justified since lagged price variables will smooth out transition periods and account for unobservable variables. To test these findings in practice, the following section contains an empirical analysis of an actual cartel case.

3 Empirical analysis

The last paragraph created an overview of findings, thoughts, and warnings relevant to inclusion of AR variables and overcharge estimation models. Although it gives an indica-tion of what to expect, precisely the lack of empirical research on including dynamics in overcharge models has dealt as incentive for setting up this research. This research inves-tigates the dynamic modelling of a German cement cartel. This cartel has been analysed before, e.g., H¨uschelrath et al. (2013) and Frank and Schliffke (2013), but has not been subjected to models including AR variables. These papers yielded overcharge estimates around 20 - 26% and 7 - 9% respectively. The vast difference between their estimates is due to the modelling of the post-cartel period, which H¨uschelrath et al. did not pay major attention to.

3.1 Specific conditions of the German cement cartel

As mentioned by Nieberding (2006) and White et al. (2006), market characteristics and economic developments around a cartel demand a case specific model analysis. It was in the early nineties that a group of the major cement suppliers in Germany decided to engage in a hardcore cartel.8 H¨uschelrath et al. (2013) mention why the cement industry has a relatively high tendency to engage in anti-competitiveness; the industry has typically a low number of producers, the product can be considered homogeneous, and the expenses to enrol in the industry are high, making it difficult for new companies to enter the market. As a result, the market did not automatically shift the price back to its natural level, and the companies succeeded in overcharging their costumers.

In July 2002, the German Federal Cartel Office launched its investigation after one of the members of the cement cartel approached them, Readymix AG. This company reported the cartel in the hope its own punishment would be waved under the leniency 8_{Although there is no causality proven empirically, it is relevant to know this was a turbulent period in}

German economics. It coincides with the fall of the Berlin wall, and the reunification of the economy of east and West Germany.

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program. Readymix AG had started lowering prices in February that year, which they had announced 3 months earlier. During the process, it was argued that a price war started right after the ending of the cartel.9 _{This price war seems to have caused a drop in price,}

which reached a level below the competitive price of cement. The company Readymix AG was taken over by a competing company in September 2004, the court which handled the case declared this as the moment where the price was back at its but-for level. (Berget, 2014)

3.2 Historical data retrieval

Deciding which variables to include in the analysis depends on both the demand and the supply side of the price equilibrium. Cement is primarily used in the construction indus-try. The most important material used in the production of cement is lime10, besides, production requires a lot of electricity (Berget, 2014). On the demand side of the equilib-rium, a measurement of construction is used, including executed construction work such as the construction of roads, government buildings, and housing. Hüschelrath et al. (2013) note that there might exist interdependence between the price of cement and construc-tion, reflecting demand. Consequently, they estimate a 2SLS model in which instrumental variables account for omitting of the construction variable. The resulting overcharge turns out to be very similar to the estimation in which construction was included (Hüschelrath et al., 2013, pp. 112). Berget (2014) argues that the cost of cement is a very slight part of the cost of construction, therefore not being a significant factor of influence on the amount of construction. Altogether, this study takes on the assumption that construction can be included as an exogenous variable. The price of cement and electricity are non-stationary time series. Hüschelrath et al. (2013) and Frank and Schliffke (2013) ignore the differ-ent order integrations of the variables, a consensus this research will hold on to, staying focused on the addressed problem.

Often the data used for overcharge estimation of a cartel is not available for public because it concerns evidence used in lawsuits.11 In the case of the German cement cartel, a lot of relevant data is available at www.destatis.de, allowing researchers to analyse this cartel case, eg., H¨uschelrath et al. (2013), Berget (2014), and Frank and Schliffke (2013). This organisation Destatis has also been the major source for this case study. The available data goes back until the first quarter of 1991. From this moment until the third quarter of 2010, data sets are retrieved from Destatis for different variables. In addition, the 9_H¨_{uschelrath et al. (2013) state the price war is brought up by the convicted companies, Frank and}

Schliffke (2013) argue this is incorrect, and the price war was suggested by experts of the court.

10_{In papers occasionally referred to as ’kalk’, the German word for lime.} 11

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appendix of Berget (2014)12 is used to complete the data set for the needed time frame. All data is obtained quarterly, since this is the smallest interval available for a number of the required variables. Resulting, between q1 1991 and q3 2010, 79 consecutive moments in time are considered for the analysis.

3.3 Dummy variable inclusion

As discussed, the price establishment during and after the infringements period was sub-jected to unnatural influences. The anti-competitive agreements between the companies first caused an overcharge in the price, while shortly after, a price war caused the price to fall below its natural level. Because this caused noticeable price changes according to the discussed information about the case, a model simulating the cement price during and after the infringement period has to account for this.13 One way to do this is by using the forecasting approach. A requirement for this approach is sufficient benchmark data in order to forecast, or backcast, the price level (White et al., 2006). Since the price war would mean that the benchmark period is either unreliable or far apart from the infringe-ment period, this research makes use of the dummy variable approach. This means a dummy variable will be included for both the cartel period, as well as the transition pe-riod which comprises the price war. These dummy variables take on the value ”0” outside their respective period and the value ”1” during the period.

Concerning the cartel dummy, this research holds on to the consensus of starting the cartel period for the analysis in q1 1990.14 This means the cartel dummy is already influential at the start of the analysis. The cartel started to fall apart when AG Reademix announced they would deviate from it in November 2001. The court determined December 2001 as the final month of the cartel, a consensus which was followed by H¨uschelrath et al. (2013), Frank and Schliffke (2013), and Berget (2014). However, no company actually deviated from the cartel until February 2002, when AG Readymix started to lower prices. Therefore, in this research, the first quarter of 2002 is also included in the cartel period.

Frank and Schliffke (2013) elaborately tested the consequences of different ways of accounting for the after-cartel transition period. They show H¨uschelrath et al. (2013) overestimated the overcharge by not including correcting dummy variables in the after-cartel period. Frank and Schliffke (2013) argue, that directly after the after-cartel a punishment phase followed, and that shortly after the cartel a price war broke out. The court included a dummy variable accounting for both of this from August 2002 until February 2005. In this research, the dummy variable accounting for this transition period runs similarly from

12

Available at: //studenttheses.cbs.dk/bitstream/handle/10417/4728/jacobberget.pdf ?sequence = 1

13_{Frank and Schliffke (2013) show that neglecting to account for the after cartel transition period results}

in misspecification of the model.

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the last quarter of 2002 until the second quarter of 2005. With both the historical data and the artificial dummy variables, a complete view can be obtained of the price establishments of cement in Germany during and after the cartel period. The next subsection explains how these variables are used in order to get a model which follows the cement price development as realistic as possible.

3.4 Model specification

The research is set up so that the influences of AR features in overcharge estimation models can be optimally observed and analysed. Therefore, a static model is compared to a dynamic model. The static model derives its form from the known price influences and cartel specific circumstances. It is specified relatively similar to the initially suggested form by H¨uschelrath et al. (2013), for which a transition dummy is added15, and the trend variable is omitted. There is no theoretical indication of why a trend has to be included in the regression. Including a rising trend means that there would be a steady increasing difference over time between the explaining and explained side of the equation, this is an undesirable result. This linear regression model is estimated with OLS, and defined by the following equation:

Pt= α1+ βc1Dct+ βtr1Dtrt + βli1limet+ βel1electrt+ βcon1 constrt+ 1t (1)

In the equation, Dc_t, is the cartel dummy variable and D_ttr is the transition dummy. The included supply and demand variables each have their own β with their respective abbreviation as subscript. The superscript indicates which estimation the value belongs to. The estimation of this model with Newey-West standard errors is given in table 1.

Coefficient Related variable estimation Newey-West standard error

β_c1 Cartel dummy 12.7074 5.5616 β1 tr Transition dummy -3.7208 2.9001 β_li1 Lime price 1.8753 0.3160 β1_el Electricity price 0.0596 0.2666 β1 con Construction 0.0911 0.0412 α1 Constant -85.1816 18.9708

Table 1: OLS regression, static estimates on cement price

All coefficients fall in line with the ones of Frank and Schliffke (2013), in terms of sign. The relationship between the coefficients also reflects these earlier findings. The Newey-West standard errors allow for up to 5 lags of autocorrelation in this regression.

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This ’standard’ static model is compared to a dynamic AR model. The dynamic model includes lagged cement price variables in order to fulfil the smooth transition requirement coming from the theory, but also to reduce autocorrelation and enhance the forecasting properties. In order to decide on the number of AR regressors in the model, the effect on the residuals is examined. The residual autocorrelation decreases by adding a first and second lagged price variable. A third or fourth AR variable barely has further influence. Therefore the dynamic model will be defined as the static model with the first two AR regressors included in addition:

Pt= α2+ φ1Pt−1+ φ2Pt−2+ βc2Dct+ βtr2Dttr+ βli2limet+ β2elelectrt+ βcon2 constrt+ 2t (2)

The added φ1 and φ2 are the autoregressive coefficients. For the rest, all variables are

named the same but assigned with a 2 instead of 1 to distinguish the models. Also this es-timate is not completely free of autocorrelation. The Breusch-Godfrey LM test now shows autocorrelation in the residuals from the 3rd lag onwards. This residual autocorrelation is disregarded in the rest of the analysis. The estimation of this model with Newey-West standard errors is given in table 2.

Coefficient Related variable estimation Newey-West standard error

φ1 Cement price, first lag 0.8849 0.1021

φ2 Cement price, second lag -0.1869 0.0936

β2 c Cartel dummy 4.9669 1.3855 β2_tr Transition dummy -1.3411 1.0252 β_li2 Lime price 0.4357 0.0737 β2 el Electricity price 0.1151 0.0477 β_con2 Construction 0.0124 0.0076 α2 Constant -19.9599 6.6698

Table 2: OLS regression, dynamic estimates on cement price

Relevant results such as the long term cartel effect and the but-for prices are discussed in the following subsection.

3.5 Empirical results

The two models (1) and (2) provide an explanation of the observed price levels. The main goal of such models is to derive but-for prices, which can be found by excluding the cartel caused factors from the fitted estimates.16 In the static model, this is simply a matter

16

As defined by Boswijk et al. (2016) as ˆO1. They argue it is preferred to subtract cartel effect from the observed prices, instead of the fitted values, in case the cartel period is unknown and might continue outside the specified cartel period. Since the analysis starts during the cartel and the end is clearly marked, it seems reasonable to assume this case study is not subjected to such circumstances.

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of subtracting the cartel coefficient during the cartel period from the fitted values. Since there is also a transition period included in the model, the transition coefficient also needs to be distracted during its active period in order to obtain the but-for price. In case of the static model, there is no difference between the long term and short term effect of the cartel, since there is no transmission of influence over time.

Concerning the dynamic model, the cartel effect grows over time, approaching a long term effect. The example of Nieberding (2006) can be followed to write out the first number of cartel effect periods (pp. 374). Since Nieberding uses one lagged variable instead of two, the form looks slightly different:

( ˆP − Pbf)1 = ˆβ

( ˆP − Pbf)2 = ˆβ(1 + ˆφ1)

( ˆP − Pbf)3= ˆβ(1 + ˆφ1(1 + ˆφ1) + ˆφ2)

( ˆP − Pbf)4= ˆβ(1 + ˆφ1((1 + ˆφ1(1 + ˆφ1) + ˆφ2)) + ˆφ2( ˆβ(1 + ˆφ1)))

etc. The cartel effect takes on the recursive form:

( ˆP − Pbf)n= ˆβ(1 + ˆφ1(( ˆP − Pbf)n−1)) + ˆφ2(( ˆP − Pbf)n−2))

Therefore, the level of influence will eventually stabilise while approaching γ = βˆ

1− ˆφ1− ˆφ2 , interpreted as the long term effect. An overview of the cartel effects is given in table 3.

Short term cartel effect SD Long term cartel effect SD Static model (1) 12.7074 5.5616 12.7074 5.5616 Dynamic model (2) 4.9669 1.3855 16.4467 2.3385

Table 3: Estimated cartel effects

The table provides Newey-West standard deviations, except for the long term cartel effect in the dynamic model. This effect estimate is a combination of three model coefficients, so that the Delta method can be applied to obtain its variance. The Delta method calculates the long term effect variance as follows: V ar(d

b

γ) = ˆG ˆV ˆG0, for which G contains the partial derivatives of γ, and V is the covariance matrix of the estimated coefficients.

The cartel is assumed to start one year ahead of when the analysis starts. For this reason, the cartel effect will have gained power, but did not reach a close approximation to its long term effect yet at q1 1991, the first included moment. The influences over time

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of the dummy variables in the dynamic model are presented in figure 2.

Figure 2: Dynamic cartel and transition effect

As derives from figure 2, the dummy influences have a fade in and a fade out. This causes the smooth transitions of price levels desired. In order to obtain dynamic but-for price results, the cartel and transition effect as shown in figure 2 are subtracted from the fitted price values.16 _{A graph plotting the actual price levels, the fitted static and dynamic price}

levels, and the static and dynamic but-for prices is shown in figure 3.

Figure 3: Observed prices, fitted prices, and but-for prices of the German cement cartel A first thing that stands out is that the but-for prices of the static and the dynamic model follow a roughly similar price level. The static but-for price during the cartel period is higher than the dynamic but-for price, which logically follows from relation between static and dynamic long term cartel effect. Another observation is that the dynamic but-for price makes a very smooth progression over time. The static but-for prices shows more short-run volatility. The but-for prices of both the static and dynamic estimation seem to

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have an intuitive development, being on a lower level than the observed prices during the cartel, and exceeding the observed prices during the price war.

With this information, it cannot be fully determined which of these but-for prices is the better one. Therefore, a more broad analysis of the dynamics influence is desirable. The next section achieves this by examining variations in model dynamics in a controlled environment.

4 Experimental analysis

In addition to examining this specific cartel case, the German cement cartel, the estimates are used for a cartel data simulation study. With this approach, an environment is created in which the effect of AR dynamics inclusion can be measured in scenarios for which the DGP specifics are known. This allows for creating a more generalised understanding of what AR dynamics inclusion does to estimated long term cartel effects in antitrust cases.

4.1 Generating price data

In order to simulate realistic data, the cement cartel will be used as a base for simulating new data. The model structures of equation (1) and (2) are used to define two different data generating processes. The data obtained for the German cement cartel is used in combination with the estimated coefficients of (1) and (2) to generate simulated price values. These realisations are randomised by including an error term for every step in time the prices make. The error terms are White Noise, independent and identically normal distributed with expectation 0. The variance of this error terms equal the squared standard error of regression (1) and (2) respectively. The simulation of both the models is executed 10,000 times. The two generating processes have the following equation form:

Simst_t = a1+ b1_cDc_t+ b1_trD_ttr+ b1_lilimet+ b1elelectrt+ b1conconstrt+ νt1

Simdy_t = a2+ψ₁2Simdy_t−1+ψ₂2Simdy_t−2+b2_cDc_t+b2_trDtr_t +b2_lilimet+b2elelectrt+b2conconstrt+νt2

For which ν_ti ∼ N( 0, MSE(i) ), for i = 1, 2.

4.2 Analysis structure

Both the static and the dynamic simulated data are regressed on a static model, a dynamic AR1 model, and a dynamic AR2 model. The three estimation models are shown in equation (3), (4) and (5):

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Simt= α4+ φ41Simt−1+ βc4Dct+ β4trDtrt + β4lilimet+ βel4electrt+ βcon4 constrt (4)

Simt= α5+φ51Simt−1+φ25Simt−2+βc5Dct+βtr5Dttr+βli5limet+βel5electrt+βcon5 constrt (5)

The denotation is the same as used for estimation model (1) and (2). Estimations are obtained with the models (3), (4) and (5) for both the dynamic and the static generated data. The relation between the structure of the estimation model and the used process through which the data is generated is shown in table 4.

Estimation

Static Dynamic AR(1) Dynamic AR(2)

Static DGP Correctly specified 1 redundant AR coefficient 2 redundant AR coefficients Dynamic AR(2) DGP 2 omitted AR coefficients 1 omitted AR coefficient Correctly specified

Table 4: Relation cases for estimation model and DGP

This way, it can be observed what happens with the estimates when the estimation model deviates from the DGP properties in terms of AR dynamics. Possible biases can be detected since the population parameters of the simulated data are known. The obtained results for this experimental analysis are presented in the following subsection.

4.3 Simulation results

Each combination of DGP and estimation model yields a distribution of estimated cartel influences. In table 5, the means and the standard deviations of these outcomes are presented. Additionally, the nominal 5% t-test value is provided. This statistic reflects the rejection probability of the null hypothesis that the estimated cartel effect equals the effect of its respective DGP. Analogue to the one case in table 3, the coefficient variations used for this t-test are obtained using the Delta method.

Long term Effect

DGP Value

Static estimation AR(1) estimation AR(2) estimation cartel effect (SD) Nominal 5% t-test cartel effect (SD) Nominal 5% t-test cartel effect (SD) Nominal 5% t-test Static DGP 12.707 12.696 (1.635) 0.06 12.734 (1.724) 0.06 12.518 (1.671) 0.08 Dynamic DGP 16.446 11.393 (1.703) 0.89 16.360 (2.704) 0.10 15.947 (2.602) 0.10

Table 5: Long term cartel effect estimations: mean, SD and nominal 5% t-test For the upper left and lower right case in the table, the estimation model is correctly specified in relation to the DGP. Because this implies the coefficients should be unbiased, the mean of the cartel effect estimations is expected to converge towards the cartel effect in the population. Overall, the results seem to be compliant with this expectation, however, it is noteworthy the dynamic model seems to obtain a small bias on average, which is reflected in the nominal 5% t-test rejecting the null hypothesis in 10% of the cases.

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For the static generated data, it seems like all the estimation models yield similar results for the long term cartel effect. The three estimates are approximated towards the true population value of the cartel effect. Within the estimates of the dynamic generated data, the mean estimated cartel effects show more variability. What jumps out is the static estimate for the dynamic data, being over 30% below the parameter value, and as such, making a significant underestimation of the long term cartel effect. The 5% t-test shows that the null hypothesis of an unbiased estimate is rejected in 89% of the cases.

Another angle of looking at these long term effect estimations, is considering the short term effects. The short term effects form an important part of the composition of the long term effect, and besides, have the intuitive interpretations of short term influences on price levels. The estimated short term cartel effects are given in overview in table 6.

Short term Effect

DGP Value

Static estimation AR(1) estimation AR(2) estimation

cartel effect (SD) Nominal 5% t-test cartel effect (SD) Nominal 5% t-test cartel effect (SD) Nominal 5% t-test Static DGP 12.707 12.696 (1.635) 0.06 12.702 (1.846) 0.06 13.206 (1.948) 0.08 Dynamic DGP 4.9669 11.393 (1.703) 0.98 5.603 (0.960) 0.17 5.275 (0.889) 0.09

Table 6: Short term cartel effect estimations, mean, variance and nominal 5% t-test It shows from these estimates that the dynamic estimation models tend to overestimate the short term cartel effect. Both for the static and the dynamic generated data, the estimates are higher than the population parameter.

Figure 4 and 5 display the distributions of the estimated long term cartel effects in a histogram. Figure 4 shows the estimations concerning the static generated data.

Figure 4: Simulation long term cartel effect estimations, static DGP

The figures give visual oversight in how the distributions of estimated cartel effects compare to eachother for the different combinations of DGP and estimation model. As confirming with the findings of the means and variances, for the data which is simulated with a static

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process, the estimation distributions of the cartel effect are really comparable for the three different models. All the models seem to estimate the cartel effect without significant bias with respect to the population parameter value. Furthermore, the shape and variance of the distributions do not show any prominent disparities. Figure 5 displays the distributions as estimated for the dynamic generated data.

Figure 5: Simulation long term cartel effect estimations, Dynamic AR(2) DGP The histogram makes it decidedly clear that the static model is an outlier opposed to the dynamic models. Both the dynamic models show a considerable variance in their estimates, but the mean is close to the value as initiated by the DGP. The static model however, shows a distribution with a low variance around a strongly underestimated long term cartel influence.

These results, together with the results of the case study, provide insight in how the accuracy of long term cartel effect estimations reacts on the inclusion of AR dynamics in the model. The interpretation of these results follows in the upcoming section. Section 5 also puts the results into theoretical perspective, and formulates an overall conclusion.

5 Discussion and conclusion

From both the results of the empirical, as well as the experimental analysis, this section abstracts the relevant interpretations for this study. The findings are put into context, considering the theoretical expectations, and the limitations to which this study was bound are discussed. The section finalises with a conclusion, providing answer to the question of how AR dynamics influence the accuracy of cartel effect estimations, and making a suggestion for further research.

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5.1 Interpretation of the results

The insights from the simulation help interpreting the case study results. Therefore, the simulation is now discussed first, after which the interpretation of the German cement cartel results follows. When not explicitly stated otherwise, cartel effect now refers to the long term cartel effect.

In case of the static simulated DGP, all overcharge estimation models estimated the cartel effect without significant bias. The distributions of the overcharge estimates are similar in variance and shape. This means that the dynamic models are, although dif-ferently specified from the actual DGP, still accurate. The addition of redundant AR dynamics is no problem for the cartel effect estimation in this case. This implies that the static and dynamic estimation of the overcharge will tend to be similar when the price is only influenced by static factors.

For the dynamic DGP on the contrary, the simulation results show that omitting necessary AR dynamics does disturb the estimated overcharge. When the dynamic price data is modelled with a static model, an underestimated cartel effect results. The static estimation shows a very low variance, creating a false idea of significance for the incorrectly estimated coefficient.

The simulation has shown, with almost the same data as in the actual case study, that the dynamic model and the static model are likely to yield similar cartel effects when there is no dynamic influence in the price of cement. However, for the German cement cartel, the dynamically estimated cartel effect is 29% higher compared to the static estimated cartel effect.17 _{This scenario seems more likely to occur in a case where the price data}

actually has AR factors included in its composition. Therefore, the dynamic estimate of the German cement cartel seems more realistic than the static one.

As a whole, the results are notably in favour of including AR dynamics in overcharge estimation models. It will substantially improve estimation results when it turns out to be needed, and does not harm the results when the dynamics are redundant.

5.2 In perspective of theoretical background

In order to place the findings within the relevant field of study, this subsection discusses them in the light of earlier conducted research.

According to Heij et al. (2004), adding redundant variables does not lead to a bias, but might lead to a greater variance. From the static simulation, it clearly shows that the overcharge estimators are consistent although redundant AR variables are added to the model. The variance does increase for the dynamic models, but on a very marginal

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scale. Heij et al. also argue that omitting a variable of significant importance does lead to biased estimators. In case the AR dynamics do occur in the DGP but are not included in the model, the overcharge results are indeed biased. The results of the simulation are consistent with the findings by Heij et al. (2004), but show there is no need to refrain from including AR dynamics out of fear of a greater variance.

The most relevant papers on the German cement cartel are conducted by H¨uschelrath et al. (2013) and Frank and Schliffke (2013). Their overcharge estimates vary both above and under the estimates of this study, depending on the modelling of the after cartel period. This research builds upon the known information and adds a new layer of analysis by including AR dynamics in the models, an addition to their work.

Overall, the results seem to fit logically within the theory and earlier conducted re-search. Only the findings of Achen (2001) are in contrast with this paper. He warns that the inclusion of redundant AR dynamics will heavily undermine the other coeffi-cients accuracy. However, the results show that this is not applicable in the investigated situations.

5.3 Limitations

Because a forecasting approach requires more benchmark data than available in this case, this study solely focuses on the DV approach. As White et al. (2006) state, within the DV approach the explanatory variables might obtain biases due to cartel influences, such as collective effort by engaged companies to reduce production costs. If this is the case, this affects the case study estimates. A solution for this could be to estimate but-for levels of the explanatory variables, this is not within the scope of this paper however.

Another consideration for the German cement cartel is that it has quite strong specific conditions, which might influence the outcomes. Especially the price war directly after the cartel causes an unusual price development, and therefore unreliability of the used benchmark data. The case study shows the importance of creating a complete overview of the situation when analysing a cartel.

The decision to base the simulation process on the estimated overcharge models brings this unusual price path of the case study into the simulation. Therefore, the simula-tion deals with similar complicasimula-tions for the cartel effect estimasimula-tion as encountered while analysing the German cement cartel. This seems restrictive, but precisely the analysis of realistic situations is what is lacking in the current pool of relevant research. One concession has been made in mirroring reality, namely the neglecting of higher order au-tocorrelation in the residuals of estimation (2). This was necessary to be able to compare estimates to their parameter values, and might have caused the slight difference between the estimates and parameter values of the correctly specified AR(2) model.

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5.4 Conclusion

Cartels appear as a disrupting influence on the natural establishment of prices. To measure the caused damage, researchers quantify the effect of cartels on price levels by using overcharge estimation models. This research explains how the accuracy of cartel effect estimations is influenced by the inclusion of AR dynamics in the models.

A German cement cartel, originating from the early nineties, provided ground for em-pirical analysis and a simulation study. Based on openly available data, the long term cartel effect is estimated with both a static and a dynamic model, deriving their form from findings of earlier conducted research. With estimations of 12.71 and 16.45 respec-tively, the dynamic model yields a 29% higher cartel effect compared to the static model. To improve understanding of the effect of including AR dynamics, artificial price data is generated by processes which follow the static and dynamic estimation models, making use of their respective estimated coefficients. In this controlled environment, cartel effect estimation distributions are obtained for models with a known misspecification. This way, AR dynamics inclusion is linked to accuracy performances of the cartel effect estimations. The results show that including irrelevant variables has minor effect on the estimated overcharges or their variances. Omitting relevant AR variables however, results in signifi-cant underestimation and a drop in variance. It needs to be taken into account that the available data did not allow for a forecasting approach, so that these findings derive from the DV approach only. Nevertheless, these findings place the dynamic model notably in favour of the static model. The cartel effect estimation is not harmed when redundant AR dynamics are added to the model, but when AR dynamics are part of the price es-tablishment, the AR dynamics in the model are shown to be an absolute necessity. These findings form a valuable example within this developing field of research.

Active further investigation into the accuracy of dynamic cartel effect estimations seems desirable. A first step would be to expand the number of case studies, in which the influence of including AR dynamics is examined elaborately. Furthermore, quantitative analysis of the influences of dynamics while using the forecast approach would be valuable. Testing AR dynamics within the two approaches on several quantitative cases would yield a more robust understanding of how the accuracy of cartel effect estimations is influenced.

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Dynamic price modelling in antitrust cases : application of the German cement cartel