A forecasting approach to estimat-ing cartel damages

The importance of considering estimation uncer-

tainty

By: Didrik Prohorenko Supervisor: Jonas Björnerstedt

Södertörn University | School of Social Sciences, Department of Economics

Master’s dissertation 30 credits

Economics | Spring 2020

2

A forecasting approach to estimating cartel

damages *

The importance of considering estimation uncertainty

Abstract

In this study, I consider the performance of simple forecast models frequently applied in coun-

terfactual analysis when the information at hand is limited. Furthermore, I discuss the robust-

ness of the standard t-test commonly used to statistically detect cartels. I empirically verify that

the standard t-statistics encompasses parameter estimation uncertainty when one of the time

series in a two-sided t-test has been estimated. Thereafter, I compare the results with those from

a corrected t-test, recently proposed, where the uncertainty has been accounted for. The results

from the study show that a simple OLS-model can be used to detect a cartel and to compute a

counterfactual price when data is limited, at least as long as the price overcharge inflicted by

the cartel members is relatively large. Yet, the level of accuracy may vary and at a point where

the data used for estimating the model become relatively limited, the model predictions tend to

be inaccurate.

Keywords: Forecasting approach, estimation uncertainty, merger simulation, cartels, t-test,

small sample size, damages, counterfactual analysis

________________________

* I would like to thank my supervisor PhD Jonas Björnerstedt for valuable discussions and piece of advice

throughout the process of writing this thesis. I would also like to thank PhD and Senior Economist at Copenha-

gen Economics Erik Lindén for giving me the idea and the topic to this thesis.

3

CONTENTS

1 Introduction 4

2 Background 6

2.1 Cartels 6

2.2 Methods for quantifying damages – an overview 8

3 Theoretical framework 14

3.1 Forecasting approach 14

3.2 The corrected t-test 15

3.3 Merger simulation 17

4 Data 22

5 Model specification 23

5.1 Cartel simulation 24

5.2 The forecasting models 27

6 Results 30

6.1 Scenario 1 30

6.2 Scenario 2 35

6.3 Scenario 3 38

7 Concluding remarks 42

8 References 44

9 Appendix A 47

4

1 INTRODUCTION Despite the fact that antitrust behavior through collusion is illegal in most jurisdictions, price-

fixing schemes, bid rigging and strategic output restrictions are frequently detected by compe-

tition authorities all over the world. The financial harm inflicted by colluding parties, i.e. cartels,

on consumers and/or trading partners can be severe. In 2016, the European Commission im-

posed fines amounting to about 3.7 billion euros on firms for violating Article 101 TFEU, the

article prohibiting collusion that prevents and/or distort competition on the internal market

within the European Union (European Commission, 2019)1.

Cartelization distorts market competition and results in negative effects in terms

of financial losses for the individual. Therefore, it is important to be able to quantify the finan-

cial losses in order to the affected parties, i.e. ultimately consumers, to seek compensation by

suing for financial damages in Court.

To quantify the magnitude of the financial harm on consumers, an analysis of the

evolution of the counterfactual scenario, i.e. where the cartel do not exist, typically has to be

carried out. One approach available to assess the counterfactual outcome is to apply a quantita-

tive model based on time series regressions, i.e. the forecasting approach (Davis & Garcés,

2010, p. 357). The forecasting approach first estimates a regression model based on observa-

tions outside the infringement period to establish the relationship between the competitive mar-

ket price and its determinants, i.e. its underlying cost and demand factors. Thereafter, a coun-

terfactual price is predicted by the estimated parameters from the regression. The predicted

price represents the counterfactual price, which is assumed to reflect the competitive price that

would have prevailed in a counterfactual scenario but for the cartel. In a third step, the price

predicted by the model is compared to the observable cartel price and if the two price series are

concluded to be statistically different from each other, the difference in price is assumed to

constitute the overcharge on the counterfactual price inflicted by the cartel members. To obtain

the financial damages, the overcharge is multiplied by the quantity of traded goods or services

during the entire cartel period (Davis & Garcés, 2010).

In order for plaintiffs to sue cartel members for financial damages, it is critical in

the procedure outlaid above to be able to determine whether the counterfactual price is statisti-

cally different from the observable cartel price. Failing to do so would infer that the collusion

has had no effect on the market price and plaintiffs would most certainly not be able to sue for

damages in Court (see e.g. Oxera, 2009).

1 The presented numbers are not adjusted for changes following judgments of the Courts.

5

A standard procedure typically adopted to determine whether two price series are

statistically different from each other, i.e. to conclude that a price overcharge has existed from

a statistical point-of-view, is to apply a standard two-sided t-test and test for a zero mean dif-

ference (see e.g. Oxera 2009, p. 50). However, Lindén & Lunde (2019) argue that the standard

t-test ignore additional estimation uncertainty stemming from the estimated price series (the

counterfactual price) and that applying a standard t-test, hence, will lead to a rejection of the

null hypothesis of a zero mean difference too often by increasing the Type 1 error. Instead, they

propose a corrected t-test, where the standard t-test has been adjusted for the estimation uncer-

tainty stemming from the predicted parameters.

To prove their hypothesis of a too high rejection frequency of the standard test

they perform a small simulation study where the two tests are compared. The results show that

the rejection frequency of the standard test increases in (i) small samples, (ii) when the relative

size of the infringement period increases in relation to the sample size, (iii) with the number of

covariates included in the regression, (iv) when multicollinearity among covariates exists and

(v) when covariates show trends and autocorrelation. The factors that was shown to have the

most distorting effect on the standard t-test and thus where the corrected test showed the most

significant improvement was when the infringement period was relatively large compared to

the outside period and when the sample size was small.

Lindén & Lunde’s (2019) findings are of interest as lack of data often can be a

practical problem in cartel investigations or in screenings (see e.g. OECD 2013, p. 41). The

reasons might be due to data collection often being time consuming or resource intensive but it

can also be completely inaccessible. Hence, it would be of interest for practitioners to have a

fairly simple tool to apply to detect cartels and to provide them with an estimate of the financial

damages. Yet, the study presented by Lindén & Lunde (2019) is a simulation study focusing on

statistical testing, where no real market data is presented. Instead data is being simulated. Thus,

for empirical use it would be of interest for practitioners to see (i) how a simple OLS-model

performs in terms of detecting a cartel and estimate its financial damages when data is limited

and (ii) to verify Lindén & Lunde’s (2019) results when the corrected t-test is performed on

real market data.

In this study I assess the corrected t-test on market data in the form of an unbal-

anced panel of 11 483 observations on product-level data over the European automobile indus-

try. Due to lack of real cartel data I adopt a structural merger simulation model to create a fictive

cartel where the cartel members constitute the merging parties. Once the fictive cartel is created

I collapse the dataset over its weighted sales quantities to obtain a time series-dataset covering

6

30 years, from 1970 to 1999. By varying the relation between the cartel period and the outside

period and performing the test in small samples, I investigate both the performance of the OLS-

model and the corrected t-test in a relatively complex setting characterized by a high level of

uncertainty due to lack of data. This study is of importance as lack of useful or disaggregated

data can be a plausible scenario for practitioners and/or competition authorities when calculat-

ing financial damages inflicted by cartels.

The outline of this study is as follows. In Section 2 cartels are reviewed and its

similarities with monopolies accounted for, to illustrate how a structural merger model can be

used to create a fictive cartel. The section also covers other methods for estimating cartel dam-

ages beside the forecasting approach to broaden the perspective of quantitative assessment in

cartel damages cases. Section 3 set the theoretical framework for the forecasting approach, the

corrected t-test and the structural merger simulation model. Section 4 reviews and explains the

data being used to carry out the analysis. Section 5 specifies the models adopted. Section 6

illustrate the results from the forecasting approach and the statistical testing and section 7 con-

cludes.

2 BACKGROUND

The first part of the section constitutes an introduction to cartels, where they stem from and

why they are illegal in most jurisdictions. Following, there is a discussion of the similarities

between cartels and monopolies to illustrate, from an economic theoretical perspective, how a

structural model for merger simulation can be applied to create a fictive cartel.

The second part of the section covers approaches to quantifying damages, focus-

ing on price overcharges in cartel damages cases. The aim is to provide an overview of existing

methods that are commonly applied by academicians and practitioners in competition econom-

ics, their advantages and drawbacks.

2.1 Cartels

In the 1800s America, numerous so called “trusts” operated with monopoly power, thus con-

trolling the American economy to a large extent by limiting the level of competition in many

industries (Hovenkamp, 1989). Two of the most well-known examples of American business

trusts, active in the late nineteenth century, are the United States Steel and Standard Oil. In

1901, U.S. Steel held two thirds of the American steel market (McCraw & Reinhardt, 1989).

Meanwhile, Standard Oil controlled more than 90 percent of the refining capacity in the United

States already in 1879 (Granitz & Klein, 1996).

7

The rise of business trusts, with monopoly power, set in motion the “anti-trust”

movement of the 1980s in the United States, which about ten years later resulted in the Sherman

Antitrust Act of the 1890 (Morley, 2016). The discussion that evolved further developed the

economic concept of marginalism, i.e. how market prices are set in relation to marginal costs

and marginal revenues, and constitutes the beginning of modern industrial organization theory

(Hovenkamp, 1989).

Two fundamental assumptions about firms competing in a competitive setting ac-

cording to the economic concept of marginalism are; (i) all firms are profit-maximizing and (ii)

all firms are considered being price takers (see e.g. Nicholson & Snyder, 2008).2 Consequently,

no single firm has the power to set the market price for the product being traded by itself. In-

stead, all firms consider the market price to be a fixed parameter in its profit-maximizing strat-

egy. The market price is determined by the level at which the marginal cost of producing one

more unit equals the marginal revenue of selling that same unit, and firms’ profits will be zero.3

At this state, the competitive market is usually said to be efficient, i.e. there are no deadweight

losses.

Consider instead a monopoly, where the market by definition is supplied by a

single firm which owns 100% of the market shares. The monopoly firm has no competitors to

consider. Typically, the single firm will increase the market price as part of its profit-maximiz-

ing strategy by adding a markup on the product’s marginal cost (see e.g. Nicholson & Snyder,

2008). The level of the markup is set with respect to the product’s marginal cost and the prod-

uct’s price elasticity of demand and can be determined by the inverse elasticity rule.4

By adding a markup on the market price, the marginal revenue no longer equals

the product’s marginal cost and the efficiency theorem of competitive markets no longer holds.

Consequently, deadweight losses are created due to the price increase and consumers are af-

fected negatively as welfare is transferred from them to the suppliers (Nicholson & Snyder,

2008).

2 To validate this assumption, a few more assumptions are needed. First, there has to be a large number of pro-

ducers, all producing the same homogenous product. Second, there has to be perfect information, i.e. all con-

sumers and producers (firms) know the market price. Third, the costs for trading products (transaction costs)

have to be zero or negligible. Four, the costs for entering or exiting the market have to be zero or negligible.

(Nicholson & Snyder, 2008). 3 If one firm tries to increase the price of its product it will lose all its market shares to its competitors. If the firm

instead tries to undercut the market price to increase its market shares, i.e. set a price where the marginal rev-

enue is lower than the marginal costs of production, the firm will create a loss and become bankrupt or even-

tually exit the market given its profit-maximizing strategy. 4 See e.g. Nicholson & Snyder (2008, p. 494).

8

The effects of a cartel on consumer welfare are very similar to those of a monop-

oly. By colluding, the cartel members often obtain a sufficiently high level of market shares

combined to have the power to implement price fixing schemes. The purpose of those schemes

are to increase, or sometimes, to maintain market prices at its current levels prior to an antici-

pated decrease in demand (Lindén & Lunde, 2019). The procedure distorts the market compe-

tition as the product price increase can be said to be “artificial” and decoupled from the devel-

opment of its determinants, i.e. its demand and cost factors (Lindén & Lunde, 2019). Thus, just

like monopolies, cartels reduce total welfare by creating deadweight losses and redistribute rent

from consumers to suppliers (Davis & Garcés, 2010). For that reason, cartels are illegal in most

jurisdictions (Harrington, 2005).

In Europe for example, Article 101 of the Treaty on the Functioning of the Euro-

pean Union (TFEU) states that actions and/or agreements that prevent, restrict or distort com-

petition in the European Union (EU) shall be prohibited (TFEU, 2008/C 115/ 01). To form a

cartel, or in any other aspect collude, in order to increase product prices by distorting competi-

tion is a violation of Article 101 of the TFEU.

The similarities between monopolies and cartels from an economic theoretical

perspective allow me to incorporate a structural merger model based on a two-level nested logit

model and Bertrand competition to form a fictive cartel. The price increase from the merger

illustrate the price increase in the beginning of the cartel and work as a starting point for the

following damage investigation and evaluation of the forecasting approach and the correction

of the standard t-test.

2.2 Methods for quantifying damages – an overview

To choose an approach when quantifying price overcharges due to collusion can be a difficult

task. Not only does cartels differ in their characteristics, so does the markets they belong to.

Determining a “but-for” price in a counterfactual scenario will never provide you with an exact

and correct answer. However, by carefully evaluating different approaches in assessing cartel

damages, robust and reliable estimates of the “but-for” price may be obtained. For that, several

different methods in assessing price overcharges in cartel cases have been developed by acad-

emicians and practitioners over the years. The conclusion, argued by Oxera (2009), among oth-

ers, is that there is no “one-size-fits-all” approach.

The choice of model should be selected with respect to economic facts, market

structure, economic theory and the data at hand. In investigations by competition authorities

9

and in prosecutions, the time aspect may also be a factor affecting the model selection. Hüsch-

elrath, Müller & Veith (2016) state that model selection should be done on a case-by-case basis

and that estimating several models is recommended in order to cross-check results and to obtain

a robust and reliable estimate of the “but-for” price.

Oxera (2009) provide an extensive overview of existing methods in damage quan-

tification, see Figure 1 below. The approaches can largely be classified into three different cat-

egories, comparator-based, financial-analysis-based and market-structure-based. As the cur-

rent discussion proceeds, several of them will be brought up and covered but to a varying extent.

Figure 1

An overview of a selected number of existing methods for quantifying damages

Source: Oxera (2009, p.44).

For the rest of this section a discussion around a number of selected approaches that are com-

monly used to estimate overcharges stemming from collusion will be held and set in context,

starting with a case from Spain.

Marcos (2015) examines the Spanish sugar cartel, active in 1995-1996, where the

plaintiffs were awarded €5 million by the Supreme Court. The method applied by the plaintiffs’

experts to compute the “but-for” price was the cost markup method. The cost markup method

estimates the competitive “but-for” price bottom-up by using information on production costs

and then adds a markup. The approach requires firm-level cost data and valid assumptions about

10

the level of competition in the industry in order to get a “reasonable” estimate of the competitive

long-run markup (van Dijk & Verboven, 2008). Though, Marcos (2015) notes that such a

method may not always be the most reliable. Typically, input costs of the product of interest

are not independent of the infringement and may thus also depend on other factors. However,

in the Spanish sugar cartel case, the main input cost, sugar beet, was made independent due to

regulations in the market.

Mariuzzo, Walsh & van Parys (2009) apply a structural model to estimate coor-

dinated effects in the Irish automobile industry. The model is estimated on product-level data

using a nested logit model of demand and a price setting scheme for firms following a multi-

product Bertrand-Nash equilibrium system. Their findings show average overcharge estimates

to be four and eight percent. Parameters are estimated using the generalized method of moments

(GMM). The structural approach allows for various counterfactual exercises, e.g. elaborating

on product ownership and mergers. It also allows the practitioner to calculate welfare losses to

consumers, and not only to focus on monetary overcharges. However, the model requires prod-

uct-level data that in practice may be hard to get in a restricted amount of time. Moreover, it

relies heavily on assumptions about demand and firms cost margins, which thus become very

critical and could be questioned in prosecutions.

Zona (2010) do also apply a structural model. He assesses the Vitamin A cartel

that was active from 1990 to 1999. The model is developed in a context of merger simulation

and is built upon two market process representations. The outcome of the first representation is

subject to the conspiracy and the outcome of the second representation to a competitive setting

“but for” the conspiracy. To obtain the average price overcharge in the collusive period, the

difference between the two market process representations is computed. The author claims the

proposed model to be less data-intensive than a standard benchmark model (e.g. the before-

and-after or dummy variable approach). However, the results demonstrate the structural

model’s sensitivity with respect to assumptions being made. The base case estimates the

weighted average overcharge to about 31 percent, yet the range goes from about ten percent to

about 51 percent. The author himself concludes that the estimate depends heavily on assump-

tions about values of margin, non-conspirator shares and industry elasticity and that it is crucial

that assumptions are consistent with economic facts.

Connor (2001) applies a before-and-after approach when estimating the “but-for”

price in the lysine cartel, active 1992-1995. Compared to previously discussed cases, the before-

and-after approach belong to a category of methods often referred to as reduced form models.

The model uses price information outside the collusive period, i.e. usually before or after or

11

before and after the conspiracy, which then becomes the basis of comparison. In such an ap-

proach, the “but-for” price is simply assumed to be similar to the price before and/or after the

conspiracy. The defendant’s experts, on the other hand, used a structural approach and assumed

the competitive behavior in the market to be characterized by Cournot competition. As we saw

in previously mentioned Zona (2010), structural models can be very sensitive to parametric

values and in the lysine cartel case Connor questions the defendants’ assumptions regarding

marginal costs and elasticities of demand by considering the “but-for” price to be too high.

Mncube (2014) examines the South African flour cartel, active from 1999 to 2007,

by applying the dummy variable (DV) approach. The DV approach uses regression techniques

to estimate the counterfactual scenario. Typically, all information in the dataset, i.e. inside and

outside of the infringement period, is being used to estimate the “but-for” price. By including a

binary variable in the regression model, a price shift due to the conspiracy is picked-up by the

dummy variable. The price shift is then assumed to be the overcharged price. The author re-

gresses an OLS model including four regressors and a binary variable for the conspiracy. The

regressors constitutes three cost determinants and one a demand factor. Several weaknesses of

the DV approach is brought up; (i) the cartel period has to be precisely defined, (ii) overcharge

measures may underestimate the harm on direct and indirect buyers by omitting potentially

significant volume effects and (iii) general time series issues, such as non-stationarity, may

distort the reliability of estimates and reduce the power of conventional statistical tests used for

inference. Mcnube estimate the average overcharges to range from seven to 42 percent. The

relatively large spread in the author’s findings could be due to one or several of the beforemen-

tioned weaknesses.

Hüschelrath, Müller, & Veith (2013) use publicly available data to compare two

different methodologies to quantify the effects of a cartel in the German market for cement. The

methods brought up are the before-and-after approach and the difference-in-difference ap-

proach. Focusing on the former approach, the authors start by estimating a basic model, i.e. a

simple ordinary least squares (OLS) regression model, including three cost factors, one demand

factor and a dummy variable for the conspiracy period. Thereafter, the basic model is extended

to a two-stage least squares (TSLS) regression, including several instruments besides the basic

model. The key econometric problem ignored by the OLS regression is the endogeneity issue

that arises from the interdependence of cement price and cement demand, which the TSLS-

regression handles. However, the OLS-model only overestimate the overcharges by 0,38 per-

centage points, compared to the TSLS-model.

12

Boshoff & van Jaarsveld (2019) investigate the South African cement market for

recurrent collusion by adopting a Markov regime-switching (RS) method. The price-fixing car-

tel was active from 1998 to 2006 and the authors estimate average cartel overcharges to 18

percent. The reduced-form model is regressed on quarterly data, including two cost drivers, two

demand determinants and a variable to determine the cartel overcharge. The RS model is quite

similar to the DV approach. However, the primary strength of the RS-method is that the collu-

sive, non-collusive and transition periods are determined implicitly, i.e. inside the model, in-

stead of explicitly (i.e. like in the DV approach). The different “states” (i.e. collusive, non-

collusive and transition) are rather identified by structural breaks in the data of the price series

of interest than by a binary variable that has been assigned its values ad hoc. The model thus

allows the practitioner to estimate the average overcharge over a sample period consisting of

more than one collusive period. However, the model fails to distinguish between rising prices

triggered by changes in cost and demand factors and those triggered by collusive behavior,

which would be a problem if not controlled for.

Khumalo, Mashiane & Roberts (2014) apply the yardstick method to calculate the

counterfactual price in the South African precast concrete products cartel. The market investi-

gated is characterized by low barriers to entry and unstable demand. The comparators used to

calculate the “but-for” price are non-cartelized products of similar cost and demand determi-

nants as the cartelized ones.. The yardstick method may however be infeasible if there are no

non-cartelized products with similar product characteristics and demand and cost determinants.

Friederiszick, & Röller (2010) apply a during-and-after approach when estimating the over-

charges in the German cement cartel. According to the authors, a benchmark approach seemed

more plausible than a yardstick approach due to the high likelihood of collusive behavior also

in all of the neighboring countries and a high level of heterogeneity in market structures.

Notaro (2013) compares three different methods when assessing the effects of a

cartel in the Italian market for pasta (2006-2008). The author discusses the dummy variable

(DV) approach, the dynamic treatment effects (DTE), and the straight-line methods (methods

that are similar to the yardstick approach). The regression models are estimated on publicly

available data and include a set of four cost factors related to the production price of pasta and

monthly dummy variables. In comparison to the DV approach, the DTE approach constitutes a

forecast model. The model uses information from outside the infringement period and based on

that information, a dynamic price equation is estimated. The estimated price equation is fur-

thermore applied to “predict” or forecast the “but-for” price, i.e. the price that would have pre-

vailed but for the conspiracy. In this case, the dynamic price equation is estimated using an

13

error-correction model (ECM) on the OLS-estimator. To obtain reliable estimates in time series

regression all series are assumed to be stationary and the regressors exogenous. However, No-

taro (2013) points out that the DTE method relies on milder conditions than the DV approach

and should thus be preferred over the latter. This follows from the DV approach requiring cor-

rect model specification and strict exogeneity, while the DTE method “only” requires included

variables to be conditionally independent given predictive proxies (CIPP). Notaro finds both

the DV and the DTE approach to estimate the average price overcharge to about 11 percent.

Nieberding (2006) discusses several models used to estimate cartel overcharges,

particularly focusing on reduced-form models such as the dummy variable (DV) approach and

the forecasting approach. Two illustrative examples are carried out, first an OLS estimation of

the DV approach and then an error correction model estimation (ECM) of the forecasting ap-

proach. No real pricing data or covariates are presented yet common endogeneity and time-

series issues, e.g. stationarity, are being discussed. Moreover, a discussion around how to pool

data in the forecasting approach is held. Short time series can be a practical problem in assessing

cartel damages and the practitioner might chose to pool pre-cartel with post-cartel data to obtain

a “richer” dataset outside the conspiracy. The alternative would be to forecast or backcast the

“but-for” price, using either pre- or post-cartel observations only. Price levels pre- and post-

cartel may therefore differ and could partly be taken in consideration by pooling data. Either

decision should however be supported by economic facts and theories. A good fit within the

benchmark period does not necessarily ensure that the model will perform well outside the

benchmark period, i.e. in the infringement period.

McCrary & Rubinfeld (2014) concentrate their discussion on the dummy variable

(DV) approach and the forecasting approach and distinguish the two of them from one another.

The authors carry out an illustrative example based on simulated data and conclude that the DV

approach might be slightly more robust than the forecasting approach in small samples. The

main reason for that is that the DV approach uses more information than the forecasting ap-

proach as the latter only uses information outside the infringement period. This becomes par-

ticularly evident when quantity varies over time and at the same time is related to unobserved

determinants of the price, i.e. omitted variables.

Bolotova, Connor & Miller (2008) use extended versions of the autoregressive

conditional heteroskedasticity model (ARCH) and the generalized ARCH model (GARCH) to

examine damages in the lysine cartel (1992-1995) and the citric acid cartel (1991-1995). The

models are estimated on monthly data using the maximum likelihood estimator (MLE). Com-

pared to previously discussed approaches, this method is dynamic and constitutes a forecasting

14

model. The “but-for” price is obtained by first estimating a price equation and in the second

step applying the fitted GARCH model to predict the counterfactual price. The estimates show

a 12 percent overcharge in the citric acid case and a 24 percent overcharge in the lysine case.

3 THEORETICAL FRAMEWORK In the first part of this section the theoretical foundation of the forecasting approach applied to

predict the overcharge due to the price increase from the colluding parties is laid out. Following

the first part, a discussion on parameter uncertainty and the corrected t-test is held. The second

part provides a theoretical explanation on how the conventional standard t-test is corrected for

the parameter uncertainty stemming from the estimated parameters of the counterfactual price.

In the last part of this section, the structure of the merger simulation, i.e. the creation of the

fictive cartel, is set up theoretically.

3.1 Forecasting approach

One available option to estimate cartel damages is to apply a forecasting approach. The fore-

casting approach is a reduced-form, multivariate approach, based on time series regression. It

involves estimating a multivariate regression model using data outside the infringement period

and incorporating the estimated parameters to forecast a counterfactual price that would have

prevailed but for the conspiracy (Davis & Garcés, 2010). To obtain an estimate of the direct

damages stemming from the collusion, the predicted but-for price is subtracted from the ob-

servable cartel price and multiplied by the quantity of products sold during the cartel period

(Davis & Garcés, 2010)

�̂� = (𝑃𝐶𝑎𝑟𝑡𝑒𝑙 − 𝑃 𝐶𝑜𝑢𝑛𝑡𝑒𝑟𝑓𝑎𝑡𝑐𝑢𝑎𝑙) × 𝑄𝐶𝑎𝑟𝑡𝑒𝑙

where �̂� is an estimate of the damages, PCartel is the observable cartel price, PCounterfactual the

predicted but-for price and QCartel the quantity of products sold during the infringement period.

However, the direct damages do not incorporate the indirect damages stemming

from collusion, i.e. the concept of deadweight losses explained for in Section 2.1. To account

for deadweight losses, the difference between the quantities sold during the cartel period and

the quantities that would have been sold in the counterfactual scenario needs to be taken in

consideration (Davis & Garcés, 2010). Although, just like the counterfactual price, the coun-

terfactual quantities sold would have to be estimated in a true cartel damages case and therefore

15

it is often neglected when damages are calculated in practice and focus is concentrated on the

direct damages.

By running a multivariate regression model to forecast the “but-for” price,

changes in demand and supply conditions are allowed and controlled for. However, the struc-

tural relationship between the dependent and the independent variables is assumed to remain

unchanged throughout the benchmark and the cartel period. If the structural relationship be-

tween variables in the infringement period is different from the relationship between variables

in the benchmark period, the forecast may provide unreliable estimates (Davis & Garcés, 2010).

Important to bear in mind, and pointed out by Nieberding (2006), is that a good fit of the model

inside the benchmark period does not necessarily assure a good fit outside it. This could also

be a potential weakness of the forecasting approach.

The multivariate regression model applied to estimate the product price consti-

tutes a simple ordinary least square model (OLS)

𝑃𝑡 = 𝛼 + 𝛽′𝑋𝑡 + 휀𝑡

where P is the product price, X a set of demand, supply and cost factors and ε the error term,

which is assumed to be independent and identically distributed (iid) and where the covariates X

are uncorrelated with the error term ε.

3.2 The corrected t-test

In a normal procedure of comparing two sample means a standard t-test is typically used. In

benchmark counterfactual analysis a two-sided t-test is commonly applied to determine whether

there is any statistical, significant difference between two price series (see e.g. Oxera 2009, p.

50). The two price series represent the predicted price, i.e. the counterfactual price, and the

observable cartel price. Once concluded that the counterfactual price is statistically different

from the cartel price, i.e. that an overcharge exists from a statistical point-of-view, plaintiffs

can sue for damages. Therefore, standard testing is a crucial part in prosecutions.

In the two-sided test, the mean, µ, of the two price series are tested against each

other. The null hypothesis can be formulated, 𝐻0: 𝜇𝑃𝐶𝑎𝑟𝑡𝑒𝑙 = 𝜇𝑃𝐶𝑜𝑢𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑡𝑢𝑎𝑙 and is tested

against the alternative hypothesis 𝐻𝑎: 𝜇𝑃𝐶𝑎𝑟𝑡𝑒𝑙 ≠ 𝜇𝑃𝐶𝑜𝑢𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑡𝑢𝑎𝑙 . Only if the null hypothesis can

be rejected in favor of the alternative hypothesis can we concluded that the two prices series

have a zero mean difference.

16

For the standard t-test, the test statistics follows a student’s t-distribution under

the null hypothesis (Stock & Watson, 2015). It can be formulated as

𝑡 =

1𝑁 (𝑃𝐶𝑎𝑟𝑡𝑒𝑙 − 𝑃𝐶𝑜𝑢𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑡𝑢𝑎𝑙)

√1𝑁 (𝑠𝑃𝐶𝑎𝑟𝑡𝑒𝑙

2 + 𝑠𝑃𝐶𝑜𝑢𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑡𝑢𝑎𝑙2 )

where N equals the size of the population and 𝑆𝑃𝐶𝑎𝑟𝑡𝑒𝑙 and 𝑆𝑃𝐶𝑜𝑢𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑡𝑢𝑎𝑙 are respective sam-

ple’s deviation from the mean (Lindén & Lunde, 2019).

However, as pointed out by Lindén & Lunde (2019), the conventional t-statistics

stated above relies on the assumption that observations representing the cartel price and the

counterfactual price are samples drawn from two populations, where the limiting distribution

depends on known population parameters and where the t-statistics is asymptotically normal

distributed with a variance equal to 1. Although, important to bear in mind is that a small sample

size can violate the normal approximation even if none of the series are predicted. The normal

approximation means that the variable’s sampling distribution asymptotically is considered nor-

mal in large samples. Hence, a small sample size may distort the results from the standard t-test

due to a relatively larger variance of the estimated β-values in a small sample, compared to in

a larger sample size.

Lindén & Lunde (2019) argue that the two-sided standard t-test is biased when

carried out on predicted time series variables due to estimation uncertainty stemming from the

estimated parameters of the forecasted price. This follows from that the estimated parameters

contain unknown population parameters and, hence the limiting variance of the t-statistics may

be greater than 1 and thus no longer apply to normal standard tables. The typical result, accord-

ing to Lindén & Lunde (2019), is a too often rejection frequency of the standard test. However,

by correcting the standard t-test for the estimation uncertainty a consistent test can be obtained.

To account for the estimation uncertainty ignored by the standard t-test Lindén &

Lunde (2019) propose a corrected formulation of the t statistics where the conventional t statis-

tics is corrected by the square root of κ

𝑡𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑 = 𝑡

√𝜅

where κ can be estimated by

17

κ̂ = 1 +N

M− N(1

N∑Xj

N

j=1

)

′

(1

M− N∑ XiXi

′

M

i=N+1

)

−1

(1

N∑Xj

N

j=1

)

where N is the number of observations in the cartel period, M is the number of observations in

the entire sample and X are covariates determining the price series.

From the previous expression, used in estimating κ, it can be seen that the estima-

tion uncertainty depends on (i) the sample size, (ii) the relative difference between the bench-

mark and prediction period and (iii) the price determinants. It becomes also clear that if there

is no existing estimation uncertainty, i.e. the second right term equals zero, the corrected t-

statistics will be equal to the standard one.

3.3 Merger simulation

To perform the merger simulation, a two-level nested logit model is adopted by following pre-

vious work on merger cases done by Verboven (1996), Ivaldi & Verboven (2005) and Björner-

stedt & Verboven (2013). The model considers the possibility of market segmentation by al-

lowing for consumer heterogeneity along two discrete product dimensions. The model is per-

formed in a Bertrand competition setting, where multiproduct firms compete with prices and

where the firms’ ultimate objective is to maximize profits.

In the model, it is assumed that there are I potential consumers, i = 1,…,I. Each

consumer choses one product to buy among J+1 differentiated products, or an outside good, o.

Expressed algebraically, j = 0,…,J, where zero denotes the outside good or no-purchase alter-

native. The outside good, or no-purchase alternative, represents a consumer choice which exists

outside the pre-defined market being studied. An example of an outside good in the automobile

industry could be a different mean of transport, i.e. a bicycle, a scooter or a transport card.

Moreover, there is always the no-purchase alternative where the consumer saves the money.

The J+1 differentiated products are classified into G groups, g = 0,…,G, where

zero, once again, denotes the outside good. Given a two-level nested logit model, each group g

is classified into Hg subgroups, h = 1,…,Hg, which implies that a consumer choice is assumed

to be made in two steps. For example, in Björnerstedt & Verboven (2014), a consumer i is

initially assumed to choose what segment, g, of cars she is interested in, i.e. a standard car, a

luxury car etc., and in the second step choose whether to buy a domestic car or not, h. Summed

up, each subgroup h consist of Jhg products, so that ∑ ∑ 𝐽ℎ𝑔𝐻𝑔ℎ=1

𝐺𝑔=1 . The interpretation of the

18

two-level nested logit is that products that belong to the same group have greater cross-price

elasticities than products that belong to different groups.

By purchasing product j, consumer i obtains the following conditional indirect

utility

𝑢𝑖𝑗 = 𝑥𝑗𝛽 + 𝜉𝑗 + 𝛼𝑓(𝑦𝑖, 𝑝𝑗) + 휀𝑖𝑗

First, there is a vector of observed product characteristics, xj, second, a random variable that

describes unobserved product characteristics, ξj, third, a function of consumer i’s income and

the price of product j, 𝑓(𝑦𝑖, 𝑝𝑗), and finally, a term that captures consumer i’s individual taste

for product j, εij, which follows the extreme value distributional assumptions of a two-level

nested logit model (Björnerstedt & Verboven, 2013).

Consumer i’s conditional individual demand from purchasing product j, dij, is ob-

tained by applying Roy’s identity

𝑑𝑖𝑗 = −𝜕𝑓(𝑦𝑖, 𝑝𝑗)

𝜕𝑝𝑗 𝜕𝑓(𝑦𝑖, 𝑝𝑗)

𝜕𝑦𝑖⁄

where f(yi, pj) = yi – pj.

According to standard microeconomic theory, the product j purchased by consumer i is chosen

to maximize the consumer’s random utility, uij,

𝑢𝑖𝑗 = 𝑥𝑗𝛽 + 𝜉𝑗 + 𝛼(𝑦𝑖 − 𝑝𝑗) + 휀𝑖𝑗

By rewriting previous expression, we obtain the following, simplified, expression for consumer

i’s conditional indirect utility, uij, upon buying product j

𝑢𝑖𝑗 = 𝐾𝑖 + 𝛿𝑗 + 휀𝑖𝑗

where Ki = αyi and δj ≡ xjβ – αpj + ξj, the latter denotes product j’s mean utility and it is nor-

malized to zero for the outside good, i.e. δ0 = 0 (Björnerstedt & Verboven, 2013).

19

According to McFadden’s (1978) generalized extreme value discrete choice

model, and based on studies on two-level nested logit models by Verboven (1996) and Björ-

nestedt & Verboven (2013), a consumer choice can be described by a specification of choice

probabilities for each purchase alternative. That is, given random utility maximization, the

probability that a consumer i choses product j follows

𝑠𝑗 = 𝑠𝑗(𝛿, 𝜎) ≡exp (𝛿𝑗/(1 − 𝜎1))

exp (𝐼ℎ𝑔/(1 − 𝜎1))

exp (𝐼ℎ𝑔/(1 − 𝜎2))

exp (𝐼𝑔/(1 − 𝜎2))

exp (𝐼𝑔)

exp (𝐼)

where,

𝐼ℎ𝑔 ≡ (1 − 𝜎1) ln∑𝑒𝑥𝑝

𝐽ℎ𝑔

𝑘=1

(𝛿𝑘

1 − 𝜎1)

𝐼𝑔 ≡ (1 − 𝜎2) ln∑𝑒𝑥𝑝

𝐻𝑔

ℎ=1

(𝐼ℎ𝑔

1 − 𝜎2)

𝐼 ≡ ln (1 +∑𝑒𝑥𝑝

𝐺

𝑔=1

(𝐼𝐺))

The mean utilities δj in sj(δ,σ), stated above, are denoted by a J × 1 vector, δ, and the nesting

parameters of the subgroups (σ1) and the groups (σ2) measure the correlation of preferences

across products that belong to the same subgroup or group (Björnerstedt & Verboven, 2013).

For the model to be consistent with random utility maximization, the nesting parameters must

fulfill the following condition (McFadden, 1978)

1 ≥ 𝜎1 ≥ 𝜎2 ≥ 0

To obtain the aggregated demand system qj for products J, the probability that consumer i buys

product j is multiplied by the consumer’s conditional individual demand dij and summed over

all consumers I, that is

20

𝑞𝑗 =∑ 𝑠𝑗 (𝛿, 𝜎) 𝑑𝑖𝑗𝐼

𝑖=1= 𝑠𝑗 (𝛿, 𝜎) 𝐼

The aggregated demand system qj contains four parameters, which need to be estimated. A price

parameter, α, a vector of mean valuations for observed product characteristics, β, a nesting pa-

rameter measuring consumer preference correlation for products in the same subgroup, σ1, and

a second nesting parameter measuring consumer preference correlation for products in the same

group, σ2. To obtain a simple linear regression model to estimate, i.e. where the error term ξj

enters linearly instead of non-linearly, the system of choice probabilities sj is inverted to solve

for the mean utilities δj as a function of the choice probability vector s in a first step (Berry,

1994; Verboven, 1996; Björnerstedt & Verboven, 2013)

𝛿𝑗 = ln(𝑠𝑗 𝑠0⁄ ) − 𝜎1 ln(𝑠𝑗|ℎ𝑔) − 𝜎2 ln(𝑠ℎ|𝑔)

Proceeding, the unobserved choice probabilities sj, sj|hg and s0 are rewritten in terms of observ-

ables using the aggregated demand system qj derived above

𝑠𝑗 =𝑞𝑗

𝐼

𝑠𝑗|ℎ𝑔 =𝑞𝑗

∑ 𝑞𝑗𝑗∈𝐻ℎ𝑔

𝑠ℎ|𝑔 =∑ 𝑞𝑗𝑗∈𝐻ℎ𝑔

∑ ∑ 𝑞𝑗𝑗∈𝐻ℎ𝑔

𝐻ℎ𝑔

ℎ=1

The previously unobserved choice probabilities are now expressed in volume terms of market

shares (Björnerstedt & Verboven, 2013).

Finally, by substituting the mean utility component of product j, δj ≡ xjβ – αpj +

ξj, into the inverted choice probability system and inserting the observable choice probabilities

sj, sj|hg and s0 into the equation, the following linear regression model is obtained (Björnerstedt

& Verboven, 2013)

21

ln𝑞𝑗

𝐼 − ∑ 𝑞𝑗𝐽𝑗=1

= 𝑥𝑗𝛽 − 𝛼𝑝𝑗 + 𝜎1 ln𝑞𝑗

∑ 𝑞𝑗𝑗∈𝐻ℎ𝑔

+ 𝜎2 ln∑ 𝑞𝑗𝑗∈𝐻ℎ𝑔

∑ ∑ 𝑞𝑗𝑗∈𝐻ℎ𝑔

𝐻ℎ𝑔

ℎ=1

+ 𝜉𝑗

The linear regression model to be estimated essentially depends on the products’ market share

in terms of volume, price, product characteristics and group and subgroup shares.

The model’s market structure is best described by multiproduct firms competing

with prices to maximize profits in a Bertrand-Nash equilibrium. Each firm f owns a set of prod-

ucts Ff and uses prices as its strategic variable to maximize its profits ∏f

∏𝑓(p) = ∑(𝑝𝑗 − 𝑐𝑗) 𝑞𝑗(p)

𝑗∈𝐹𝑓

where cj equals constant marginal cost, ∏f (p) equals profit, qj (p) equals demand and p is a J ×

1 price vector.

The price that is set by firms to maximize profits is defined by the following sys-

tem of first-order conditions

𝑞𝑗 (p) + ∑ (𝑝𝑘 − 𝑐𝑘)

𝑘∈𝐹𝑓

𝜕𝑞𝑘(p)

𝜕𝑝𝑗

The Nash-equilibrium stated above can be rewritten into matrix form and then solved for the

premerger marginal costs vector c, by first obtaining the inverted demand function (Björnerstedt

& verboven, 2013). Based on the premerger prices and estimated price elasticities of demand,

the rewritten equation is used to predict the postmerger equilibrium by capturing changes in the

product ownership matrix θ, from θpre to θpost

cpre = ppre + {θpre ʘ ∆(ppre)}−1 q(ppre)

where c and p are J × 1 marginal cost and price vectors, respectively, θ is a J × J block diagonal

product ownership matrix, q(p) is a J × 1 demand vector and ∆(p) is a J × J Jacobian matrix of

first order derivatives.

22

4 DATA

The data being used consists of an unbalanced panel of 11 483 observations on product-level

data over the European automobile industry. The panel covers almost all car models sold in five

European markets during 1970–1999. The dataset has previously been used to varying extent

in Goldberg & Verboven (2001), Goldberg & Verboven (2005) and Brenkers & Verboven

(2006). A reduced version of the dataset is used in Björnerstedt & Verboven (2014).5

The dataset constitutes a three-dimensional panel and the total number of obser-

vations amounts to 11,483. The three dimensions defining the panel are year, country and code.

The countries, or markets, included in the dataset are Belgium, France, Germany, Italy and the

United Kingdom, all together they account for about 85 per cent of annual car sales in Europe.

Code (shortened co) represents the model codes of the cars, e.g. Fiat 850, Opel Kadett, Toyota

Corolla etc., the total number of unique model codes are 351 and reflects the market heteroge-

neity.

Price represents car prices, measured in 1000 Euro in 1999 purchasing power. Qu

represents sales, measured in number of new car registrations. Segment represents groups, or

upper nests, and consists of five different car segments, namely, subcompact, compact, inter-

mediate, standard, and luxury. Domestic represents subgroups, or lower nests, and describes the

cars’ origin, i.e. domestic or foreign. Firm represents all existing firms and brand their portfolio

of brands (e.g. Volkswagen’s brand portfolio constitutes Audi, Seat, Skoda and Volkswagen).

The number of product characteristics included in the study are listed in Table 1

below

Table 1

List of product characteristics

Variable Abbreviation Unit Explanation

horsepower Kilowatt Cars’ horsepower

fuel Liter per kilometer Fuel efficiency at a

speed of 90 km/h

acceleration ac Seconds Time it takes to accel-

erate from 0 to 100

km/h**

width Centimeters Cars’ width

height Centimeters Cars’ height

5 The data has been made publicly available by Professor Frank Verboven, Department of Economics of KU

Leuven, Belgium, and is accessible at: https://sites.google.com/site/frankverbo/data-and-software.

23

weight Kilograms Cars’ weight

population pop Units Countries’ population

gross domestic product ngdp 1000 €* Countries’ gross do-

mestic product

* In 1999 purchasing power. ** Some car models are measured from 0 to 96 km/h.

Descriptive statistics of all variables included in the study are presented in Table

2 below.

Table 2

Descriptive Statistics

Variable Obs Mean Std.Dev. Min Max

year 11 549 1 985.43 8.53 1970 1999

country 11 549 2.91 1.44 1 5

co 11 549 223.38 206.14 1 980

segment 11 483 2.56 1.29 1 5

domestic 11 483 .19 .39 0 1

firm 11 483 14.5 8.57 1 34

qu 11 483 19 911.44 37 803.6 51 433 694

price 11 483 18.5 8.92 5.26 150.34

weight 11 483 980.23 225.15 520 1 910

height 11 483 140.44 4.63 117.5 173.5

width 11 483 164.46 9.57 122 188

horsepower 11 483 57.26 23.89 13 169.5

fuel 11 483 6.73 1.71 3.8 18.6

ac 9 232 15.24 5.23 7.5 50

pop 11 483 4.81e+07 2.18e+07 9 660 000 8.21e+07

ngdp 11 483 1.76e+14 4.73e+14 5.18e+10 2.13e+15

Source: Author’s own calculations.

5 MODEL SPECIFICATION

In the first part of this section the structural merger simulation model is specified. The frame-

work of the merger is presented, assumptions explained for and a discussion on how the simu-

lated merger will represent the fictive cartel is held. First, the market for passenger cars will be

presented followed by an estimation of the demand function. Thereafter, the cartel length will

be decided and its members presented. Finally, a few of the created, fictive, cartel’s character-

istics will be described.

24

5.1 Cartel simulation

Initially, the potential market size for passenger cars is defined. The total number of potential

consumers I is assumed to equal total number of households. I follow Björnerstedt & Verboven

(2014) and proxy the total number of households as the population divided by four, a rough

estimate. However, merger simulations do not tend to be sensitive to the specification of the

potential market size. Thus, slightly overestimating its size will not have any real effects on its

primary purpose of this study, i.e. to simulate a fictive cartel using market data.

The demand for passenger cars is best described by a unit demand function. Most

households are likely to buy only a single car and even though there are households in posses-

sion of more than one car, cars are usually bought one at a time and not in large quantities like

consumer goods, for example. Consequently, the demand for passenger cars is estimated by a

two-level nested logit model, where the upper nest is defined by the variable segment, reflecting

car segments such as subcompact, compact, intermediate, standard or luxury, and the lower nest

by domestic, i.e. a binary variable which takes the value one if the car is manufactured domes-

tically and zero otherwise. The specification implies that consumers are more likely to substi-

tute to another car from the same segment and manufacturing country and would rather substi-

tute to a car from the same manufacturing country than another segment (Björnerstedt & Ver-

boven, 2014).

The demand function is regressed on a set of product characteristics including the

variables horsepower, fuel, width, height, domestic, year and country (Björnerstedt & Ver-

boven, 2014). A fixed-effects regression and the ordinary least squares (OLS) estimator is ap-

plied to estimate the model. The results covering the most important variables from the regres-

sion can be seen in Table 3 below, a complete output-table of the regression can be found in

Appendix A.

All variables but height are significant on a one percent significance level and the

level of change in demand for passenger cars explained by the included regressors are fairly

high (about 90 percent). Furthermore, the included variables express the expected directions

according to economic theory, e.g. if the price for product j increases by thousand euros the

demand for that product decreases by approximately five percent, ceteris paribus. Price obvi-

ously has an impact on demand and the explanatory variables in logarithms represents the two-

level nests consumers are assumed by the specification of the model to make their decision

from when buying a new car. Additionally, the nesting parameters, 𝜎1 = 0,91 and 𝜎2 = 0,57,

fulfill the requirements for the model to be consistent with random utility theory, i.e. 1 ≥ 𝜎1 ≥

𝜎2 ≥ 0 (McFadden, 1978).

25

Table 3

Fixed effects estimation of the demand function

Log (share of product / share outside group)

Price (in 1000 Euro, 1999 purchasing power) -0.047***

(0.001)

Log (share of product j in subgroup h) 0.905***

(0.004)

Log (share of subgroup h in group g) 0.568***

(0.009)

Constant -8.193***

(2.246)

Observations 11483

R-squared 0.895

Adj. R-squared 0.891

F test 0.000

Standard errors in parentheses * p < 0.1, ** p < 0.05, *** p < 0.01

The demand determinants width and height constitute the size measures of a passenger car and

is primarily considered as factors of demand. A family with children living on the country side

might demand a bigger, more robust, car compared to a one-person household living in an urban

city where a smaller car would be preferable due to small parking lots and compact traffic. A

larger car also requires more material and consequently the production costs can be expected to

be higher, compared to a smaller one.

Proceeding to the variables horsepower and fuel. The engine’s effect in terms of

horsepower may be of importance if the consumer lives in a rural area with access difficulties,

or in a sports car. Fuel consumption, measured in liters at a speed of 90 kilometers per hour, is

often of interest for a potential consumer prior to a purchase of a new car.

The domestic car dummy shows that consumers tend to prefer to buy domesti-

cally. The reason could be of economic interest, i.e. to support a national brand, but also of

geographical practicalities, i.e. that it might be easier to get access to a domestic car if the supply

of those cars are higher. The country dummys simply reflects the willingness to buy a car from

any of the five European countries included in the dataset. Year does not have a significant

impact on demand according to the regression but from a theoretical perspective it could still

be of importance. Some people prefer to buy relatively new cars whilst other prefer older mod-

els.

The fixed-effects regression applied to estimate the demand function accounts for

the time varying effect but is not sufficient to get rid of the endogeneity problem that arises

26

from the dual causality running between the product price and the market share variables. To

fully address the endogeneity problem the practitioner would like to incorporate proper instru-

ments. However, given that the merger simulation exercise is carried out only to simulate a

fictive cartel, and thus the exact absolute effect on product prices following the merger is less

relevant, I chose not to identify any instruments as it would not change the conclusion of my

research topic. Yet, in an actual merger practice, neglecting the endogeneity problem give rise

to inconsistent parameter values and thus overestimated price effects due less elastic demand

elasticities (Björnerstedt & Verboven, 2013)6.

The length of the fictive price-fixing cartel is primarily set to eight years (1992-

1999). That is based on a study by Lande (1993), which findings point at an average cartel

duration of seven to eight years. However, cartel durations can vary significantly from case to

case. For example, Levenstein & Suslow (2006, p. 51) present a cross-section study where the

cartel duration ranges from one to 29 years. For simplicity the collusive price is assumed to go

back to its competitive level after the cartel has been dissolved by the Competition Authority7.

The structural model is simulated on all five European countries included in the

dataset (Belgium, France, Germany, Italy and the UK). Hence, the model incorporates all Eu-

ropean markets’ characteristics and the Nash-equilibrium exists across all five countries. How-

ever, the fictive cartel is eventually set up in France and consequently only effects the market

price for passenger cars in France. The results from the fixed effects panel regression visible in

table 2 show that consumers tend to prefer to buy domestic cars over foreign cars and therefore

I decide do geographically identify the market for passenger cars to a single country. However,

a European cartel could also be a plausible scenario8.

The cartel members constitute PSA, General Motors (GM), Volkswagen, Fiat,

Volvo, BMW, Ford, Rover and Toyota. From a merger simulation point-of-view the French car

manufacturer PSA buys the other manufacturers and that is how the fictive cartel is formed9.

The unweighted average price increase following the merger amounts to about 14 percent and

the four firm concentration ratio (C4) increases from 78 percent pre-merger to 96 percent post-

merger, i.e. at the start of the collusion in 1992. The newly formed, fictive, cartel possess about

60 percent of the market shares.

6 For a further discussion on how proper instruments can be identified and implemented in this particular dataset

the interested reader is referred to Verboven (1996, p. 253). 7 No tacit collusion following the collusion is taken into consideration. Neither is any partial coordination prior

to the cartel or any marginal cost savings in conjunction with the cartel. 8 A somewhat close example is the European truck cartel that existed for 14 years and where six truck manufac-

turer colluded on truck pricing and the pass-on of technology costs (Commission, 2017). 9 The cartel (merger) is simulated without any remedies.

27

In order to carry out time series regressions, i.e. applying the forecasting model,

the generated price series and its determinants from the unbalanced panel are collapsed over its

weighted quantities sold to obtain a new dataset consisting of a set of time series variables.

Hence, the new dataset consists of the same determinants as the previous dataset but now on an

aggregated level covering 30 years.

5.2 The forecasting models I run three different regression models based on data outside the infringement period, i.e. in the

benchmark period; one univariate model in its simplest form and two multivariate models. All

three models are differentiated and estimated with the OLS-estimator. The explanatory varia-

bles consist of a set of product characteristics that affect the price for passenger cars primarily

through demand, expect for the first model that is estimated on a trend variable. The models

take the following functional form, where Δ means that the variable has been differentiated

once, e.g. Δcar_pricet = car_pricet – car_pricet-1

∆𝑐𝑎𝑟_𝑝𝑟𝑖𝑐𝑒𝑡 = ∝ + 𝛽1𝑡𝑟𝑒𝑛𝑑 + ∆휀𝑡

where car_pricet is the observable price for passenger cars set by the cartel in time t (t is spec-

ified by an annual time format), β the parameter estimates to be estimated by the model, α a

constant term, trend a time trend and εt the residual, which explains the residual of the market

price that cannot be explained by the explanatory variable(s). The residual term is assumed to

be identically distributed and uncorrelated with the covariates.

∆𝑐𝑎𝑟_𝑝𝑟𝑖𝑐𝑒𝑡 = ∝ + 𝛽1∆𝑤𝑒𝑖𝑔ℎ𝑡𝑡 + 𝛽2∆ℎ𝑒𝑖𝑔ℎ𝑡𝑡 + 𝛽3∆𝑤𝑖𝑑𝑡ℎ𝑡 + ∆휀𝑡

where weight, height and width represent the car’s measurements (in kilograms and centimeters

respectively).

∆𝑐𝑎𝑟_𝑝𝑟𝑖𝑐𝑒𝑡 = ∝ + 𝛽1∆𝑤𝑒𝑖𝑔ℎ𝑡𝑡 + 𝛽2∆ℎ𝑒𝑖𝑔ℎ𝑡𝑡 + 𝛽3∆𝑤𝑖𝑑𝑡ℎ𝑡 + 𝛽3∆ℎ𝑜𝑟𝑠𝑒𝑝𝑜𝑤𝑒𝑟𝑡 +

𝛽3∆𝑓𝑢𝑒𝑙𝑡 + 𝛽3∆𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑡 + ∆휀𝑡

where horsepower represents the car’s horsepower (in kilowatt), fuel its fuel efficiency (in terms

of liter per kilometer at a speed of 90 kilometers per hour) and acceleration the time it takes to

accelerate from 0 to 100 kilometers per hour (in seconds).

28

Most of the included covariates in the three specified models above have been

described and motivated prior to the estimation of the demand function in section 5.1. However,

the trend variable in model (1) is included to estimate the simplest form of a model to study

how well such a model can predict a price given a fairly poor number of observations in the

benchmark period, i.e. the period prior to the infringement used to establish the relation between

price and underlying price determinants. Can such a simple model by any chance be of practical

use when resources are scarce and the time frame for damages investigations narrow?

Model (2) incorporates a third measurement, weight, besides the two previously

used in the demand regression. The inclusion of yet another potential proxy for demand by car

size and cost of material (a heavier car can be expected to be made of more material although

it also can be a result of the density of different materials rather than its costs) is primarily to

see how the estimation uncertainty, κ, of the predicted price series evolves as the number of

covariates increase.

Model (3) consists of six covariates and all but acceleration have been described

previously, either in section 5.1 or 5.2. Yet, acceleration can potentially be a crude proxy for

which segment a car belongs to, where cars that accelerate fast can be thought of as premium

cars and thus have an effect on peoples’ demand for a certain car.

The setup of the study, i.e. the three different scenarios containing three different

sample sizes, and the models to be estimated is summarized in Table 4 below.

Table 4

Scenario layout

Event Models to be esti-

mated

Benchmark pe-

riod

Cartel duration Sample size

Scenario 1 (1), (2) and (3) 22 years 8 years 30 years

Scenario 2 (1), (2) and (3) 12 years 8 years 20 years

Scenario 3 (1), (2) and (3) 8 years 8 years 16 years

Before the first regressions can be run, there are potential econometric issues that

must be properly addressed, the first one considering nonstationary variables. From an initial,

ocular inspection, certain variables seem to suffer from autocorrelation when plotted in levels,

among them the product price series, i.e. the dependent variable. The autocorrelation and partial

autocorrelation correlograms give support to the ocular inspection. Consequently, an Aug-

mented Dicky-Fuller (ADF) test is performed, first in levels and then in first difference of the

29

dependent variable. Both tests include a constant, a trend and no lags. The first test, performed

in levels of the dependent variable, do not reject the null-hypothesis that the variable contains

a unit root. Under regular circumstances, the practitioner might want to reperform the test and

include lags, but as the corrected t-test incorporated in the final part of this study is not yet

defined for dynamic models, i.e. where the variation in the dependent variable partly can be

explained by its own historical values, that option is ruled out (Lindén & Lunde, 2019). How-

ever, the second ADF test, performed in first difference of the dependent variable, do reject the

null-hypothesis that the variable contains a unit root, and thus all variables are transformed into

their first difference to become stationary.

The second potential econometric issue is the small sample size being used to

estimate the forecasting model. The sample at hand consists of 30 observations overall, i.e. the

years 1970-1999, and the cartel is assumed to be active for the last eight years of the sample,

i.e. from 1992 and onwards, leaving me with a benchmark period consisting of 22 observations.

Consider that all models are differentiated before they are run and consequently another obser-

vation is lost, leaving me with a sample size of 21 observations. The poor number of observa-

tions might violate the normal approximation, i.e. that parameter estimates have a jointly nor-

mal sampling distribution in large samples. The consequences could be inconsistent OLS-esti-

mators and consequently inconsistent statistical standard tests (Stock & Watson, 2015). Ideally,

the practitioner would try to obtain a larger sample size, perhaps by also incorporating post-

cartel observations. However, if that is not possible, e.g. due to lack of reliable data, the practi-

tioner might have to rely on the data at hand. Another, preferable, option would be to cross-

check the results by applying several different methods when estimating damages (Davis &

Garcés, 2010).

In practice, it can be hard to obtain large sample sizes when estimating damages

in cartel cases for several reasons. One of the objectives of this study is to investigate how

forecasting models and the estimation uncertainty surrounding predicted parameters behave in

small sample sizes and consequently I will proceed with the data at hand, although well-aware

of the prevailing econometric issues. In fact, in a second and third scenario analysis the sample

size will be further cut but first 10 years (the new sample size will consist of the years 1980-

1999) and then yet another four years (1984-1999). By cutting the sample size I will be able to

investigate how the fairly simple forecasting models perform when data is poor and especially

whether the estimation uncertainty surrounding predicted parameters will increase relatively

much, which is one of the main conclusions pointed out by Lindén & Lunde (2019).

30

6 RESULTS

In this section the results from the three scenarios previously stated are presented. Initially, I

estimate three models, one univariate and two multivariate, using data from the benchmark

period in the first scenario where the sample consists of 30 time periods and the ratio cartel

duration / benchmark period (CD/BP) is about 27 percent. In the second scenario the ratio

CD/BP has increased to 40 percent as the number of observations in the sample has decreased

by ten. In the third scenario the sample has been cut by another 4 years and the ratio CD/BP has

increased to 50 percent.

In the next step, I calculate the direct damages stemming from the simulated cartel

based on my estimates and compare the outcome to the true direct damages, i.e. where the “but-

for” price is replaced by the true competitive price given the in-sample predictions. In the last

step, I apply statistical testing procedures to conclude whether the potential price overcharges

due to the infringement is different from zero or not and whether the corrected t-test improves

the results from the standard test.

6.1 Scenario 1

In all three scenarios, the starting point is to estimate three forecasting models based on the

OLS-estimator. The models are further used to predict the counterfactual price, the price that

would have prevailed but for the anticompetitive cartel price. Eventually, the counterfactual

price is compared to the observable cartel price and tested for zero mean significance to com-

pare if the overcharge is statistically significant. If significant, an actual damage calculation can

be made and compared to the in-sample results. The results from the estimation in the first

scenario, where the sample contains 30 years and the cartel constitutes eight years are presented

in Table 5 below.

Though only two of the explanatory variables, width and acceleration, are signif-

icant, the directions of the parameter estimates are consistent across all models. The relatively

low level expressed by the adjusted R-squared measure, model 3 shows the greatest measure at

a level of almost 48 percent, indicates that the included explanatory variables Xt explain less

than half of the variation in the product price Yt. By adding cost and supply determinants to the

estimated models a greater share of the product price would be expected to be explained by the

regressions. Important input factors for the production of passenger cars are steel and labor,

among other. Including real steel prices and wages in the regressions could potentially improve

the results and increase the level of the variation in product prices being explained by the ex-

planatory variables.

31

Table 5

Results from model estimation in scenario 1 (1) (2) (3)

∆car_pricet ∆car_pricet ∆car_pricet

trend -0.005

(0.021)

∆weightt 0.006 0.010

(0.008) (0.009)

∆heightt -0.195 -0.506

(0.359) (0.319)

∆widtht 0.432* 0.605**

(0.226) (0.225)

∆horsepowert -0.182

(0.129)

∆fuelt -0.156

(0.210)

∆accelerationt -0.325**

(0.145)

Constant -0.006 -0.283* -0.433***

(0.277) (0.145) (0.138)

Observations 21 21 21

R-squared 0.003 0.367 0.634

Adj. R-squared -0.049 0.255 0.477

F test 0.809 0.046 0.015 Standard errors in parentheses * p < 0.1, ** p < 0.05, *** p < 0.01

The F-test of model (1) does not show statistical significance. However, all models will be used

to predict the counterfactual price in the next step. The reason why only two (width and accel-

eration) of seven explanatory variables show significance could potentially be explained by the

small sample size.

Once the forecasting model has been estimated, the analysis of the counterfactual

price, also “but-for” price, can be carried out. The “but-for” price, i.e. the competitive price that

would have prevailed but for the collusion, is predicted by the fitted values of the estimated

reduced form regressions. All forecasts are made “in-sample” to allow me to examine the ac-

curacy of each forecasting model against the actual outcome, i.e. to compare the estimated

counterfactual price with the “real” competitive price. The result from the forecasts are illus-

trated in figure 2 below.

32

Figure 2

Results from forecasts in scenario 1

Note: The results are based on a sample containing 30 observations and where the cartel duration, i.e. the pre-

diction period, equals eight years and the benchmark period equals 21 years. One year is lost due to dif-

ferentiation of the price series in the previous estimation step.

Source: The author’s own calculations.

All three models seem to predict the “but-for” price fairly well despite few significant variables,

a relatively low adjusted R-squared measure and a small sample size. The results may be due

to the cartel having relatively much market power so it can increase the market price above the

forecast intervals predicted by fairly poor models in terms of few covariates explaining the

evolution of the price series. Except for in model (3), the “true” competitive price lies within

the 95 percent forecast intervals of the predicted series. However, both model (1) and model (3)

predict the counterfactual price to be lower than the actual competitive price while model (2)

seems to follow the competitive price better despite larger forecast intervals. Yet, in scenario 1

with a CD/BP ratio of approximately 27 percent all three models, including the simple, non-

significant, univariate model, could be used for an initial screening in order to provide the prac-

titioner with a rough estimate of the damages.

33

To statistically conclude that the mean of the cartel price is significantly different

from the mean of the “but-for” price a two-sided t-test is implemented. Applying a two-sided t-

test is a common procedure to verify that the observable price is significantly different from the

estimated “but-for” price in cartel damages cases where a forecasting approach is adopted (Ox-

era, 2009). The procedure is used as fundamental evidence in Court to prove that the infringe-

ment caused by the cartel has had a significant impact on the product price in order for claiming

parties to sue for damages.

Thus, proceeding I apply both the standard t-test and the corrected t-test proposed

by Lindén & Lunde (2019) to compare the outcome of the two tests and to conclude if the

overcharges are statistically significant. The results are presented in Table 6 below.

Table 6

Results from statistical testing in scenario 1

Model 1 Model 2 Model 3

Cartel price 14.629

(0.197)

14.629

(0.197)

14.629

(0.197)

“But-for” price 12.829

(0.124)

13.432

(0.081)

12.517

(0.277)

Mean difference

Standard t-test

1.800

(0.179)

1.197

(0.155)

2.112

(0.226)

t-statistics 10.05 7.75 9.33

p-value

Corrected t-test

0.000 0.000 0.000

t-statistics 8.00 4.07 4.42

p-value

0.000 0.000 0.000

kappa (κ) 1.575 3.616 4.452

Standard errors in parentheses.

Note: The statistical tests test for a zero mean difference where the null hypothesis can be formulated according

to 𝐻0: 𝜇𝑃𝐶𝑎𝑟𝑡𝑒𝑙 = 𝜇𝑃𝐶𝑜𝑢𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑡𝑢𝑎𝑙 = 0. The prices displayed are mean prices for the cartel period 1992-1999.

The outcome from the two different versions of the two-sided t-test, standard and corrected,

both result in a rejection of the null hypothesis of a zero mean difference. For the standard t-

statistics, all three values for each of the three models respectively exceed the critical value at

a one percent significance level, which is 2,58 (model 1: 10,05; model 2: 7,75; model 3: 9,33).

The same result is obtained by the corrected t-test (model 1: 8,00; model 2: 4,07; model 3: 4,42).

34

The mean cartel price for the infringement period is approximately 14,6 thousand

euros and the predicted “but-for” price lies within a range from 12,5 to 13,4 thousand euros per

car, across all three models. The results from the tests confirm that the cartel has had an impact

on the market price by overcharging consumers. Consequently, consumers could go to Court to

sue the cartel members for financial harm.

Nevertheless, a difference can be spotted when comparing the outcome of the

standard t-test and the test that has been corrected for estimation uncertainty. In line with Lindén

& Lunde (2019), the t-statistics for the corrected test is lower than the standard test’s counterpart

albeit significant. Further, the results show that the estimation uncertainty, represented by κ, is

positively correlated with the number of covariates included in the model. Hence, the Model

(3) encompass the largest amount of estimation uncertainty. The result is evident given the

formulation of how κ is estimated (review Section 3.2). The uncertainty stems from each pa-

rameter that needs to be estimated, hence when the number of parameters increases so does the

uncertainty.

In the last step, the damages based on the predicted “but-for” price is estimated.

The results are presented in Table 7 below and are also compared to the “true” outcome, i.e.

where we know the true competitive price given the in-sample forecasts.

Table 7

Damages calculations in scenario 1 (Thousand euros)

Model 1 Model 2 Model 3 True

scenario

Damages 1 034 302 695 789 1 216 770 745 997

Note: For the “True scenario” the “but-for” price is represented by the mean of the true competitive price.

Source: The author’s own calculations.

According to the results from the damages calculation, presented in the table above, Model (2)

predicts the “true” competitive price most accurately. The model predict the damages to ap-

proximately seven hundred thousand euros compared to the true value of approximately 750

thousand euros. The other two models, one using less information (only a time trend) and the

other one more information (incorporates six covariates), both overestimate the damages. The

estimate of Model (3) is a relatively large over-estimation. A result of underestimating the coun-

terfactual price compared to the true competitive price as can be seen in Figure 2.

35

6.2 Scenario 2

In the second scenario the sample size has been reduced to an overall size of 20 years, 1980-

1999, instead of 30 years previously. The cartel duration remains at eight years and hence the

CD / BP increases to 40 percent from 27 percent.

The focus in scenario 2 and 3 is rather on a comparison of the results from scenario

1 than to analyze each scenarios result in isolation. Starting by the simple OLS-regression ap-

plied to estimate the model they all include the same number of variables as in the previous

scenario. The results of the estimated models are illustrated in Table 8 below.

Table 8

Results from model estimation in scenario 2 (1) (2) (3)

∆car_pricet ∆car_pricet ∆car_pricet

trend 0.009

(0.032)

∆weightt -0.006 -0.005

(0.011) (0.013)

∆heightt 0.038 -0.362

(0.564) (0.627)

∆widtht 0.789* 0.464

(0.344) (0.410)

∆horsepowert 0.301

(0.185)

∆fuelt -0.358

(0.208)

∆accelerationt 0.293

(0.273)

Constant -0.272 -0.345* -0.458*

(0.532) (0.181) (0.193)

Observations 12 12 12

R-squared 0.008 0.438 0.681

Adj. R-squared -0.091 0.227 0.299

F test 0.782 0.182 0.271 Standard errors in parentheses * p < 0.1, ** p < 0.05, *** p < 0.01

Many of the variables in Table 6 above have changed direction compared to the previous esti-

mation in scenario 1. Further, only one explanatory variable across all three models show sig-

nificance, i.e. ∆widtht in model (2) at a ten percent significance level. The poorly constructed

models are reflected in the result of the F-test. According to the test none of the three models

36

rejects the null hypothesis of all covariates in each model respectively to be zero. Hence, a

reduction of the sample size, which in scenario 2 consists of 11 observations in the benchmark

period compared to 21 previously, whilst the cartel duration remains the same at eight years

seems to have a large negative impact on simple models where the sample size originally is

small.

The forecasts of the estimated models are presented in Figure 3 below.

Figure 3

Results from forecasts in scenario 2

Note: The results are based on a sample containing 20 observations and where the cartel duration, i.e. the pre-

diction period, equals eight years and the benchmark period equals 11 years. One year is lost due to dif-

ferentiation of the price series in the previous estimation step.

Source: The author’s own calculations.

Proceeding to the forecasts they show similar results compared to the forecasts carried out in

scenario 1 despite the significantly worse performing models, if referring to the results of the

estimation in Table 7. The “true” competitive price still lies within the forecasting intervals of

37

Model (1) and (2) whilst Model (3) further tend to underestimate the counterfactual price. How-

ever, the first two models still predict the damages fairly well despite a drastically reduced

sample size (a 30 percent reduction) compared to scenario 1.

The results from the statistical tests are presented in Table 9 below.

Table 9

Results from statistical testing in scenario 2

Model 1 Model 2 Model 3

Cartel price 14.629

(0.197)

14.629

(0.197)

14.629

(0.197)

“But-for” price 13.232

(0.271)

13.339

(0.103)

12.462

(0.159)

Mean difference

Standard t-test

1.397

(0.193)

1.289

(0.161)

2.167

(0.156)

t-statistics 7.22 8.03 13.86

p-value

Corrected t-test

0.000 0.000 0.000

t-statistics 5.66 3.33 4.83

p-value

0.000 0.013 0.002

kappa (κ) 1.627 3.616 8.250

Standard errors in parentheses.

Note: The statistical tests test for a zero mean difference where the null hypothesis can be formulated according to

𝐻0: 𝜇𝑃𝐶𝑎𝑟𝑡𝑒𝑙 = 𝜇𝑃𝐶𝑜𝑢𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑡𝑢𝑎𝑙 = 0. The prices displayed are mean prices for the cartel period 1992-1999.

Both tests, standard t-test and corrected t-test, reject the null hypothesis of a zero mean differ-

ence between the cartel price and the counterfactual price. Although, the standard t-statistics

for Model (2) and (3) have increased and for Model (1) decreased. For the corrected t-test the

t-statistics for two out of three models have decreased. Further, the estimation uncertainty for

each model has increased compared to previous results in scenario 1. The increase in parameter

uncertainty is in line with Lindén & Lunde (2019) and the theoretical framework of the test,

which show that a reduction in number of observations in the sample and an increase in the

relative ratio between the cartel duration and the benchmark period will increase the uncertainty

and hence also increase the importance of the corrected test. In Table 8, the overcharge in Model

(2) is no longer significant at a one percent significance level.

The estimated damages in scenario 2 are presented in the Table 10 below.

38

Table 10

Damages calculations in scenario 2 (Thousand euros) Model 1 Model 2 Model 3 True

scenario

Damages 803 910 750 571 1 261 464 745 997

Standard errors in parentheses.

Note: For the “True scenario” the “but-for” price is represented by the “true” competitive price.

Source: The author’s own calculations.

Model (1) and (2) still predict the price fairly well, Model (2) really well, while Model (3) re-

main at the same level of accuracy as in scenario 1.

6.3 Scenario 3 Scenario 3 continues the comparison with the two previous scenarios concentrating on how

models, forecasts and parameter uncertainty change when the sample size decreases by another

4 years, compared to scenario 2. The entire sample now consists of the years 1984-1999 and

the ratio CD / BP is 50 percent.

The result of the OLS-estimation of the three models are presented in Table 11

below.

39

Table 11

Results from model estimation in scenario 3 (1) (2) (3)

∆car_pricet ∆car_pricet ∆car_pricet

trend 0.000

(0.071)

∆weightt -0.014 0.0182

(0.016) (0.022)

∆heightt 1.498 2.708

(1.339) (1.676)

∆widtht 0.861 -0.665

(0.503) (0.830)

∆horsepowert -0.102

(0.261)

∆fuelt -0.441

(0.258)

∆accelerationt -1.507

(0.932)

Constant -0.114 -0.194 -0.129

(1.324) (0.350) (0.319)

Observations 8 8 8

R-squared 0.000 0.606 0.935

Adj. R-squared -0.167 0.311 0.548

F test 0.999 0.249 0.456 Standard errors in parentheses * p < 0.1, ** p < 0.05, *** p < 0.01

The result is evident, the relatively small benchmark period containing information used to

estimate the models make them implode. The R-square measures increase while F-test become

even more non-significant compared to scenario 2. None of the coefficients across any of the

three models, including the constants, show significance even at a ten percent significance level.

The result is not surprising given the limited information at hand but forecasts and significance

test will still be proceed.

The forecasts of the estimated models are presented in Figure 4 below.

40

Figure 4

Results from forecasts in scenario 3

Note: The results are based on a sample containing 20 observations and where the cartel duration, i.e. the pre-

diction period, equals eight years and the benchmark period equals 11 years. One year is lost due to dif-

ferentiation of the price series in the previous estimation step.

Source: The author’s own calculations.

As illustrated by the result in Table 10, the results from the forecasts also implode but for

Model (1).

The results from the statistical tests are presented in Table 12 below.

41

Table 12

Results from statistical testing in scenario 3

Model 1 Model 2 Model 3

Cartel price 14.629

(0.197)

14.629

(0.197)

14.629

(0.197)

“But-for” price 12.933

(0.096)

15.357

(0.379)

16.085

(0.653)

Mean difference

Standard t-test

1.696

(0. 179)

-0.728

(0.480)

-1.456

(0.731)

t-statistics 9.49 -1.52 -1.99

p-value

Corrected t-test

0.000 0.173 0.087

t-statistics 7.20 −0.54 −0.54

p-value

0.000 0.606 0.606

kappa (κ) 1.738 7.761 13.609

Standard errors in parentheses.

Note: The statistical tests test for a zero mean difference where the null hypothesis can be formulated according

to 𝐻0: 𝜇𝑃𝐶𝑎𝑟𝑡𝑒𝑙 = 𝜇𝑃𝐶𝑜𝑢𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑡𝑢𝑎𝑙 = 0. The prices displayed are mean prices for the cartel period 1992-1999.

It is not surprising that the poor performance of the estimated models and its forecasts has an

impact on the outcome of the tests. The most interesting result in Table 11 is the one concerning

the estimation uncertainty kappa κ. Compared to previous scenarios, the estimation uncertainty

has further increased for each of the models and positive correlation between the number of

observations in a sample and the level of estimation uncertainty in accordance with theory can

be established.

The final results from the damages calculations are presented in Table 13 below.

Table 13

Damages calculations in scenario 3 (Thousand euros)

Model 1 Model 2 Model 3 True

scenario

Damages 974 907 - 407 680 - 827 410 745 997

Standard errors in parentheses.

Note: For the “True scenario” the “but-for” price is represented by the “true” competitive price.

Source: The author’s own calculations.

42

Like previous results in scenario 3, the calculation of damages for two of the models tend to

implode because of poorly estimated models resulting from a small benchmark period and a

small sample size. However, the result from Model (1) is still a fairly accurate estimation.

7 CONCLUDING REMARKS

In this study, the performance of simple forecast models based on OLS-estimations used for

cartel detection and counterfactual price prediction is investigated. The first contribution to the

existing literature is how such simple models perform when data at hand is aggregated and

limited to very limited, a plausible scenario in practical cartel investigations. The second con-

tribution is to empirically show that the standard two-sided t-test, commonly applied in cartel

investigations to statistically determine that a price overcharge has occurred, possesses param-

eter estimation uncertainty that increases the type 1 error of the test, when one of the series

under comparison is estimated. That is shown by using a corrected t-test, where the estimation

uncertainty has been accounted for and compare the results with the standard test.

The results show that even a simple OLS-model can be used to detect a cartel,

despite a small sample size and aggregated data, at least when the overcharge created by the

cartel is significantly large. However, its accuracy may vary significantly as the number of

observations included in the dataset goes from limited to very limited. Eventually, when the

sample size becomes too small and the parameters that need to be estimated relatively large, its

accuracy decreases significantly. Hence, the simple OLS-model would preferably be used as a

screening tool prior to further investigations.

The results of the two different t-tests carried out, standard and corrected version,

show that the standard t statistics encompasses parameter estimation uncertainty according to

previous findings from theoretical literature. Not only does it comprise estimation uncertainty,

the estimation uncertainty increases as the benchmark-cartel period ratio decreases, thus a neg-

ative correlation between the length of the benchmark period and the level of estimation uncer-

tainty in small samples can be established. However, the increase in the level of uncertainty

may partially stem from an overall reduction of the sample size. Furthermore, a positive corre-

lation between the number of parameters required to be estimated and the level of estimation

uncertainty exists. Hence, as the number of variables in the regression increase, the level of

estimation uncertainty increases due to an increases number of parameters to be estimated.

The results from the two different t-tests did not show, in this study, any signifi-

cant differences regarding the outcome of the detection of the cartel, i.e. either both tests re-

jected the null hypothesis of a zero mean difference or they failed to reject it. The outcome is

43

most likely a result of a significant price overcharge inflicted by the cartel. Nevertheless, the

corrected t-test could be useful in an investigation where the overcharge is less significant.

For future research it would be interesting to consider how more sophisticated

prediction models, e.g. two-stage least-squares (2SLS) or three-stage least-squares (3SLS), and

dynamic models, e.g. ARIMA, perform compared to the simple OLS-model. Including instru-

ments would require more parameters to estimate and hence would hypothetically result in a

larger estimation error given the outset of the corrected t-test. Further, it would be of interest to

carry out current and future methods on an actual cartel, where historical data is available, to

investigate if any deviations would occur.

44

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47

9 APPENDIX A

Fixed effects estimation of the demand function

Log (share of product / share outside group)

Price (in 1000 Euro, 1999 purchasing power) -0.047***

(0.001)

Log (share of product j in subgroup h) 0.905***

(0.004)

Log (share of subgroup h in group g) 0.568***

(0.009)

Horsepower (in kW) 0.004***

(0.001)

Fuel efficiency (liter per km at 90km/h) -0.027***

(0.005)

Width (in cm) 0.010***

(0.002)

Height (in cm) 0.000

(0.002)

Domestic car dummy 0.523***

(0.012)

Year 0.002

(0.001)

Country (France) -0.662***

(0.014)

Country (Germany) -0.588***

(0.015)

Country (Italy) -0.713***

(0.014)

Country (UK) -0.416***

(0.017)

Constant -8.193***

(2.246)

Observations 11483

R-squared 0.895

Adj. R-squared 0.891

F test 0.000

Standard errors in parentheses * p < 0.1, ** p < 0.05, *** p < 0.01