Faculty Economics and Business, Amsterdam School of Economics Bachelor thesis Econometrics
Effects of misdating cartels under the forecasting
approach
Laura Schim van der Loeff, 10016155
Supervisor: dhr. dr. Maurice Bun
December 2016
Abstract
This paper analyses the consequences of misdating a cartel period, where firms illegally take part in price-fixing activities, using the forecasting approach. Using both a simple and a more elaborate model, four misdating scenarios are considered. In line with expectations, it can be concluded that misdating a cartel will lead to underestimation of the total damage, regardless of the size and direction of the misdating.
Statement of originality
This document is written by Laura Schim van der Loeff, 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
Contents
1 Introduction 4
2 Effects of misdating cartels under both approaches 5
2.1 The dummy variable approach . . . 5
2.2 The forecasting approach . . . 7
2.3 Reasons and consequences of misdating cartels . . . 8
3 Assumptions and simple model 10 3.1 Assumptions . . . 10
3.2 Different types of misdating . . . 10
3.3 Basic form of the forecasting model . . . 11
4 Expanded version and Monte-Carlo analysis 13 4.1 Expansion of the model . . . 13
4.2 Monte-Carlo analysis . . . 15
4.2.1 Effects on ˆα1 and ˆβ . . . 15
4.2.2 Effects on estimated total damage . . . 18
5 Discussion & Limitations 19 6 Conclusion 21 7 Bibliography 22 8 Appendix 23 8.1 Proof Lemma 1 . . . 23 8.1.1 Case 1 + 3: Te< TE . . . 23 8.1.2 Case 2 + 4: Te> TE . . . 24 8.2 Proof Theorem 1 . . . 24 8.2.1 Case 1: Tb < TB,Te < TE . . . 25 8.2.2 Case 3: Tb > TB,Te < TE . . . 25 8.2.3 Case 2: Tb < TB, Te> TE . . . 26 8.2.4 Case 4: Tb > TB, Te> TE . . . 26
1 Introduction
In July of this year, DAF received a fine of 752 million euros due to participation in price fixing with four other truck manufacturers. According to the prosecution, this had been going on since 1997 (Klumpenaar & Bolle, 2016). Though conspiratorial price fixing is a felony, with costly consequences when caught, there have been a plethora of such scandals over the past decades, uncovering illegal antitrust activities. The list of uncovered cartels is endless; from the Lysine cartel, the Dairy cartel, the vitamin cartel, the Airline Cartel, to the infamous Libor Cartel, but also the banana cartel, the glass bulb cartel, the sodium chlorine cartel, the sugar cartel and the shrimp cartel. These examples are just a meager fraction of the uncovered illegal price fixing (European Commission, 2016).
When uncovered, on top of the fines imposed by governments, plaintiffs demand compen-sation for the economic damages suffered. However, it has proven to be difficult to assess the exact damages and therefore determining the appropriate fines.
The first issue while constructing a model to estimate the damages is the lack of data. Though examples of cartels are plentiful, obtaining the correct data proves to be a very diffi-cult task. Furthermore, from the data that is available, it is hard to draw conclusions for the general assessment about cartel damages, since every cartel is unique in its own way.
However, even when data is obtained, another complication arises. This complication is twofold; the first problem lies in the correct estimation of the so-called but-for price, the market price that would have prevailed in the absence of a cartel (White, 2001, p. 27). There are two main ways of computing this price; the dummy variable approach and the forecast-ing approach. The dummy variable approach consists of doforecast-ing a simple regression, addforecast-ing a dummy variable for periods where the cartel was active (White et al., 2006, p. 18). The impact of the cartel can then be measured by the coefficient of the dummy variable. The other approach, the forecasting approach, builds a predictive model using data from the so-called benchmark period, when there was no cartel activity (White et al., 2006, p. 18). The difference between the predicted prices and actual prices gives an indication of the overcharge during the cartel period. The principal difference between the two is that the latter only uses data of the benchmark period, whereas the dummy variable analysis uses data from the entire time period (Nieberding, 2005, p. 369).
The second issue concerns the actual dates the cartel has been active. As Boswijk, Bun and Schinkel remark, formal and effective cartel dates need not coincide (2016, p. 2). This thesis concerns itself with this issue. The importance of correctly dating cartel periods and the consequences when this is done incorrectly might stimulate a more secure and thorough
dating of cartels, improving the current way fines and compensations are calculated. Boswijk et al. (2016, p. 4) have analysed the consequences of misdating a cartel using the dummy variable approach; finding that cartel damages were underestimated by more than 25% in the sodium chlorate. This thesis focuses on the forecasting approach. The central research question is: What are the consequences of misdating a cartel using the forecasting approach? To answer this question, previous findings are discussed as a first step. Then, the effects of misdating the simplest form of the forecasting model are computed, taking into account multiple misdating scenarios. This is then also done for an expanded version of the forecasting model.
The rest of this paper is structured as follows: This introduction is succeeded by a lit-erature review. Besides theory, previous litlit-erature and empirical findings are discussed with respect to this topic. Consequently, the methodology is explained, for two versions of the fore-casting model, together with the underlying assumptions. Thereafter, the discussed method is applied to two forms of the forecasting approach and the outcomes are analysed. Finally, a conclusion is presented, followed by a discussion and limitations.
2 Effects of misdating cartels under both approaches
In this section past literature is discussed, focusing on previous research concerning the effects of misdating cartels. First, alongside some general theory and definitions about estimating cartel damages, the benefits and drawbacks of the dummy-variable approach are discussed, followed by the benefits and drawbacks of the forecasting approach. Those two models are then compared more directly to each other. This section concludes with explaining reasons for misdating the cartel period, together with empirical findings on the consequences of misdating, before moving on to the methodology in the next section.
2.1 The dummy variable approach
As explained in the introduction, the but-for price (bf Pt) is defined as the price that would
have existed in the market in the absence of a cartel (Nieberding, 2006, p. 362). The over-charge (Ot) in period t is defined as the difference between the price charged during the cartel
period and the but-for price: Ot = Pt− bf Pt. The total overcharge (CD) is defined as: TE
P
t=TB
Ot∗ Qt.
end date. Furthermore, periods that lie within the cartel period are denoted as TC, periods
that fall outside the cartel period are denoted as TN.
As mentioned before, the dummy-variable approach consists of estimating a model to predict prices, based on data from both the cartel period, as well as the benchmark period. The model looks as follows:
Pt= α1+ Xt∗ β + α2∗ Dt+ t, t ∈ TC, TN (1)
Where Dtis a dummy variable, with value 1 in the time a cartel was present and 0 otherwise.
Control variables are included in Xt, such as cost factors and demand and supply shifters
(Boswijk et al., 2016, p. 7). Thus, the cartel effect is measured by α2. The but-for price is
then predicted like this:
d
bf Pt= ˆα1+ Xt∗ ˆβ, t ∈ TC (2)
In some research, such as Boswijk et al. (2016), Harrington (2004), Nieberding (2006), a lagged price variable is added, making it a dynamic regression model:
Pt= α1+ Xt∗ β + α2∗ Dt+ δ ∗ Pt−1+ t, t ∈ TC, TN (3)
The main advantage of the dummy variable approach is that more of the available data is used, which could lead to more accurate results (Boswijk et al., 2016, p. 6).
However, as Finkelstein and Levenbach (1983, p. 156) note, a dummy variable model assumes that the cartel adds a fixed dollar amount (or percentage, when price is expressed in natural logarithms) to the price during the cartel period, with no effect during the competitive period. The authors point out that prices might have been effected in a more complex manner than suggested by this model. This issue is also named by Boswijk et al. (2016) and White, Marshall and Kennedy (2006). They contended that the other explanatory variables in the model might also be affected by the cartel, something which is now not measured in the model. Furthermore, they state that this method is highly misleading, since one can try out numerous different versions of the model, trying out different explanatory variables, until satisfying results are obtained (2006, p. 20). A possible solution to this problem might be using the forecasting approach, which is reviewed in the following paragraph.
2.2 The forecasting approach
This section focuses on the other approach to estimating the but-for price, the forecasting approach. Again, the general form of the model is given first, followed by the advantages and disadvantages. In contrast to the dummy variable approach, the forecasting approach focuses solely on data from outside the cartel period, the benchmark period. The reduced-form model is constructed as follows:
Pt= α1+ Xt∗ β + t, t ∈ TN (4)
β is then estimated by ˆβ, and the following model is used to predict the but-for prices:
d
bf Pt= ˆα1+ Xt∗ ˆβ, t ∈ TC (5)
In this model, it is also possible to add a lagged variable; the prediction model would then become:
d
bf Pt= ˆα1+ Xt∗ ˆβ + δ ∗ \bf Pt−1, t ∈ TC (6)
The overcharge is then computed as the difference between the actual prices and the pre-dicted prices (Nieberding, 2006, p. 369).
As Nieberding (2006, p. 369) remarks, using the forecasting approach requires that there is sufficient data available, after omitting the data from the cartel period, for the prediction to be reliable and accurate. The discussion arises which period to use as a benchmark pe-riod; the pre-cartel data or the post-cartel data (Harrington, 2004). According to the author, the advantage of using pre-cartel data is that they cannot be manipulated (2004, p. 530). However, he points out that this data is older, and therefore probably results in less reliable estimates, especially when the cartel period is long, but is also more likely to be incomplete. On the other hand, using post-cartel prices is problematic, since the price firms set during litigation influence the damages they have to pay (Harrington, 2004, p. 529). According to Finkelstein and Levenbach (1983, p. 161), post-cartel data is more commonly used than pre-cartel data.
As Finkelstein and Levenbach (1983, p. 156) remark, the outcomes of the damages differ in both models. They argue that a dummy-variable approach is more suitable, in contrast to most authors. Nieberding (2006) compares both models empirically, but does not advance
one in particular. However, most authors seem to prefer the forecasting approach to the dummy-variable approach, like White et al. (2006).
Despite the dummy-variable approach not being the most prefered one, it is used much more frequently throughout the literature, which is striking. This is probably due to the lack of enough reliable data points, to correctly build a statistically significant prediction model, when using the forecasting approach (Harrington, 2004, p. 539). Therefore there is less lit-erature and evidence available concerning consequences of wrongly dating cartels using the forecasting approach. The next paragraph will focus itself on the reasons and consequnces of misdating cartels.
2.3 Reasons and consequences of misdating cartels
Once a cartel is brought down, beginning and end dates are assigned. According to Boswijk et al. (2016), these dates can differ from the actual dates. In this paragraph, reasons for misdat-ing cartels are discussed. First of all, methods of formally datmisdat-ing a cartel are described. Then, reasons for the misdating of the start dates are analysed, followed by reasons of erroneous end dates. Both misdating issues are discussed together with previous empirical evidence on the consequences.
The formal start of a cartel is determined in hindsight, in the period when the cartel has ended. Though, formal end dates of cartels are often determined as the day of uncovering, beginning dates are then obtained throughout testimonies, confessions and plea deals and are then determined on basis of hard evidence on one specific day (Boswijk et al., 2016, p. 2).
According to Harrington (2004), it is more problematic to determine the exact beginning of the cartel than its end date. Finkelstein and Levenbach (1983, p. 162) agree with this point, noting that the beginning of the cartel is likely to be unclear, for multiple causes. Firstly, there is the legal reason. To strengthen their case in court, the prosecution might chose to decide upon a date they can prove with more ease, even though there might be strong suspicions and hints of the cartel being active for a more prolonged period of time (Boswijk et al., 2016, p. 2). An example of this can be found in the vitamin cartel, as described by Marshall et al. (2008), where the cartel did not plead guilty to price fixing before 1990, though there are strong indications that the price fixing had in fact begun in 1985. Boswijk et al. add another legal reason, namely that most cases end in a settlement, which leaves room for negotiation about the exact dates with the price-fixing firms (2016, p. 2).
of a more gradual process, making it near to impossible to pinpoint one specific day as the beginning. This can also lead to the length of the cartel being overestimated, for instance when the effect of a cartel takes some time and prices rise more slowly and gradually over time. Though there might be evidence of price agreements between firms on a specific date, the agreements made might have taken more time to have any effect (Finkelstein and Leven-bach, 1983, p. 162).
However, not only beginning dates are hard to estimate. Harrington (2004) found, when examining the graphite electrodes cartel, prices were still drastically above pre-cartel prices, up to two years after the cartel had formally ended. Though the author offers multiple possible explanations for the high cartel price, he believes that prices remain high during the litigation period and gradually decrease afterwards (2004, p. 521). He argues that a higher price is set by firms, since these data are used to compute the but-for price. The but-for price is then overestimated, leading to an underestimation of the damages firms have to pay (Harrington, 2004, p. 524). Another reason the formal end date might not correspond to the actual end date, is due to ‘residual collusion’. Though there is no explicit price fixing in the post-cartel period, the price effects can still be sustained for a while, leading to less competitive pricing in the aftermath of a cartel (Harrington, 2004, p. 531). Finkelstein and Levenbach (1983, p. 162) argue that the estimated damages differ significantly, when such a transition period is taken into account. Therefore, finding out if there is such a transition and how to practically adjust for this in the modelling of damages is crucial (Harrington, 2004, p. 534).
Boswijk et al. (2016) analyse the effects of misdating a cartel, using the dummy variable approach. They find that the but-for prices are overestimated and thus overcharges are un-derestimated. This overestimation is found regardless of the direction and size of the error. The only exception is when the cartel is dated to widely, then the total damage estimation is unbiased. They then apply their theory to the Sodium Chlorate cartel, which was active for about two years after the formal end date. They conclude that the total damage was underestimated by about 25 percent (2016, p. 4).
Following their method, this thesis focuses itself on the effects of misdating, while using the forecasting approach. In the next section, the methodology to answer the research question is outlined, together with the underlying (mathematical) assumptions.
3 Assumptions and simple model
In this paragraph, the methods for answering the research question are described, together with the underlying assumptions. To analyse the effects of misdating a cartel using the forecasting approach, this thesis closely follows the research conducted by Boswijk et al. (2016). First the benchmark period is determined, along with the assumptions underlying the model. This is followed by specifying the four different types of misdating. Hereafter, the methodology of estimating the effects on the most basic form of the forecasting model is explained, and the results are discussed before elaborating the model in the next paragraph. 3.1 Assumptions
First, the chosen benchmark period is discussed, followed by the way the overcharge is com-puted. Afterwards, the model-specific assumptions are discussed and finally the necessary Ordinary Least Squares assumptions are described.
The benchmark period is chosen as the period after the formal end date of the cartel. Though there are limitations to using this period, as discussed in the previous paragraph, it is the most commonly used, because of the availability of data. Therefore the results of the analysis can be more directly applied to real world settings.
Boswijk et al.(2016) focus their analysis on two different type of overcharges, namely the ones calculated with predicted cartel prices and the ones based on actual, observed cartel prices. This distinction is not possible when making use of the forecasting approach, since there is no predicted cartel price. Therefore only the overcharge based on the actual cartel price is used.
Furthermore, due to the scope of this thesis, lagged variables are not included in the model. Now that the assumptions underlying the method and model have been identified, the next paragraph focuses on the four different types of misdating that might arise.
3.2 Different types of misdating
As both the formal end date as well as the beginning date might be misspecified, there are four possible scenarios of misdating, as Boswijk et al. (2016, p. 12) point out. Defining Tb as
while TE represents the real end date, the following four cases of misdating are distinguished:
Case 1: Tb < TB and Te< TE
Case 2: Tb < TB and Te> TE
Case 3: Tb > TB and Te< TE
Case 4: Tb > TB and Te> TE
In Case 1, the formal dates are dated too early, the real start and end of the cartel were later. This could occur when effects linger on, but also took some time to arise in the first place. Case 2 is the situation in which the formal cartel period both starts earlier and ends later than the real cartel period, thus overestimating the length of the cartel. However, case 3 is the opposite, where the formal dates are set too narrow, and thus the length of the cartel is underestimated. This case is the most probable scenario for misdating, since in plea deals the formal beginning date is more likely to be set later than earlier than the the real start. Also, there is evidence that the effects linger on even when the cartel has officially ended. Case 4 resembles case 1, but now the beginning and end date are specified too late. The effects on the estimated total damages will be analysed for all four cases, first in the most basic form of the model, discussed in the next section, followed by a more elaborate model.
3.3 Basic form of the forecasting model
The most basic form of the forecasting model is used, where no cost factors are considered to influence the price. The model is defined as follows:
Pt= α1+ α2∗ Dt+ t, t i.i.d ∼ (0, σ2) (7) bf Pt= α1+ ut, ut i.i.d ∼ (0, σu2) (8) Dt= 1 t ∈ TC 0 otherwise.
The estimated but-for price is therefore simply the average of the prices in the non-cartel period: d bf Pt= ˆα1= 1 T − Te T X t=Te+1 Pt (9)
When the cartel is correctly dated, it follows that: E[ dbf Pt] = α1
It can be shown that the following Lemma holds (see appendix for proof): Lemma 1
E[ ˆα1] < α1 when Te< TE
E[ ˆα1] = α1 when Te> TE
From the estimated but-for price, the estimated overcharge, and total damage can be taken into account. As stated before, the overcharge is simply the difference between the observed price in the cartel period and the but-for price. The estimated total damage is defined as follows: d CD = Te X t=Tb+1 (Pt− dbf Pt) ∗ Qt
Regarding quantity, it is assumed that quantity during the cartel period, QC is lower than
the quantity in the non-cartel period, QN.
From Lemma 1, the following theorem holds regarding the total damage (see appendix for proof):
Theorem 1
E[ dCD] = E[CD] if Tb < TB and Te> TE
E[ dCD] < E[CD] elsewhere
So, only in the case of dating the model too widely, the estimation of total damage is unbiased. This is in line with the findings of Boswijk et al. (2016). It is to be noted that the longer the cartel has been misdated, the more substantial the underestimation. It is especially true for the misdating of the period which consists of the benchmark, in this analysis Te, since that
not only affects the time line, but the later TE is after Te, the more biased E[ ˆα] becomes, and
the stronger the underestimation.
In the next section a more elaborate model will be considered.
4 Expanded version and Monte-Carlo analysis
4.1 Expansion of the model
After analysing the most basic form of the model, it is expanded to the more general form of model (4), explained in section 2.3. The but-for price is estimated by model (5), determined in the same section.
In this model, Xtrepresents an exogenous, stationary, variable. Besides the assumptions
made in the first model, the assumption of exogeneity of Xt is added : E[t|X1, ..., Xt] = 0.
Also, due to the scope of this thesis it is assumed that the presence of a cartel does not affect Xt. So, it is assumed that the cartel only has an influence over the price and not over the
other variables in the model.
For this model, a Monte-Carlo simulation will be used. For this simulation, 120 observa-tions T will be used, dividing it between TC and TN. So, the first 40 data points are taken
as the competitive period before the cartel, 0 to TB, TC includes t41up to t80 and the last 40
data points represents the competitive period after the cartel. The simulation is done for a total of 10000 replications.
First, Xt is generated as follows:
Xt= ρ ∗ Xt−1+ ξt
X0= 0
ρ < 1
ξt∼ N (0, 1.1)
The reason ξt does not follow a standard normal distribution is to attribute more weight
to Xt in the model. This variance results in the model having a R2 value 0f 0.96.
Further-more, ρ < 1 due to the assumption of a stationary Xt. To get the process started, 20 extra
observations are generated (t−19 up until t0), to be discarded again later on.
Then, Pt is generated as follows:
Pt= α1+ α2∗ Dt+ β ∗ Xt+ t α1 = 100 α2 = 10 β = 1 Dt= 1 t ∈ TC 0 otherwise.
So, an one-on-one reaction to a change in Xt is assumed. Furthermore, from previous
studies, such as Nieberding (2006), Finkelstein and Levenbach (1983) and White (2001), the price-effect a cartel has, is typically estimated to be between 0 and 20 percent of α1. Therefore,
it is now assumed to be exactly in the middle, at 10% of α1. t is drawn from a standard
normal distribution, due to the underlying assumptions of white noise made earlier.
estimated as follows: d bf Pt= ˆα1+ ˆβ ∗ Xt, t ∈ [Tb, Te] c Ot= Pt− dbf Pt d CD = T e X t=tb+1 ˆ Ot∗ Qt Qt∼ N (100, 1)
Where ˆα1 and ˆβ are estimated by OLS in the period [Te+1, T ]. Qt is drawn that way for
simplicity reasons.
The analysis concerns itself with varying the dates of the model. So instead of the real beginning and end dates mentioned above, Tb is chosen at either t31 or t51 and similarly, Te
is chosen at either t70 or t90. After 10000 replications R, the average outcome for ˆOtand dCD
are computed by dividing their sum by the length of the formal cartel period, [Tb, Te]. When
correctly dated (Tb= TB, Te= TE), the average total damage should become this:
E[ dCD] = E[1 R R X r=1 ∗ dCDr] = (T − TE) ∗ E[Pt− dbf Pt] ∗ E[Qt] = 40 ∗ α2∗ 100
Now that both models have been discussed, the next section discusses their outcomes. 4.2 Monte-Carlo analysis
First the effects on ˆα1 and ˆβ are described, followed by the consequences on the effects on
d CD.
4.2.1 Effects on ˆα1 and ˆβ
Since ˆα1 and ˆβ are based on the benchmark period, it is to be noted that the estimates for
case 1 and 3 are identical, as are the estimates of case 2 and 4. Those cases therefore also overlap in the graphs shown below. The estimates can be shown graphically:
Figure 1: Estimates of α1
With respect to ˆα1, in case 2 and 4, the estimator can be seen to be unbiased. However,
in Case 1 and 3 (which overlap grafically), E[ ˆα1] overestimates α1. This means that a part of
the higher prices during the cartel period is misattributed to the base price being higher in general, as opposed to being caused by the cartel.
Figure 2: Estimates of β
It can be seen that ˆβ is centered around the real value of β in all 4 cases. This can be explained because of the assumption made earlier, that the cartel does not influence Xt.
4.2.2 Effects on estimated total damage
The effects on the average total damage are examined and can be observed in the figures hereunder:
Figure 3: Average total damage using estimated cartel length
The average total damage is underestimated in all 4 cases, which is nearly in line with expectations, except for case 2. This can be explained by the way the average damage was computed, by dividing the total overcharge by the estimated cartel period, [Tb+1; Te]. This
period is the longest in case 2, therefore the estimated total damage differs quite substantially from the correctly dated case.
Off course, when choosing a greater amount of time periods, or different dates, all 4 cases would still be found to underestimate the total damage; however their order of underestimation would alter. A more general result can be seen hereunder, where the average total damage is computed by dividing by the real cartel length (T=40), instead of the estimated cartel length, therefore giving a more general conclusion.
Figure 4: Average total damage using real cartel length
In figure 4 we see that the total damage is underestimated in all cases, except in case two, where the estimator is unbiased. This is in line with the results of the simple model and the expectations, based on the findings of Boswijk et al. (2016).
The results above also hold true, after altering ρ for different values between 0 and 1 (keep-ing Xt stationary). Furthermore, choosing different values of α2 and Qt, when determining
the real prices does not affect the conclusions of overestimation.
Now that the results have been analysed for both models, the next paragraph will concern itself with the conclusions and the limitations.
5 Discussion & Limitations
The analysis above has shown that misdating a cartel underestimates the total damage. The only scenario where misdating did not have an effect on estimating damages, was in the case where the cartel is estimated too widely, so the formal beginning date being before the actual beginning date and the formal end date being after the real end date. In that case, the
esti-mation is unbiased. However, this scenario is also the more unlikely one. Due to legal reasons, cartels are often formally dated to begin at a later time. Also, previous literature has pointed out that there are usually lingering cartel effects after the formal end date, meaning that in practice, the scenario of unbiased estimations is very unlikely and that the total damages are underestimated.
In this research the benchmark period, used to estimate the but-for price, had been cho-sen as the period after the cartel. The general conclusion would not change when using the pre-cartel period as the benchmark period, however, the four scenarios would be mirrored in their effects. However, it would be interesting in further research to combine both pre and post-cartel data to estimate a but-for price.
A limitation of this research is the assumption that quantity and price are unrelated to each other. This assumption had been made for the scope of this thesis, but is not a very probable one. More probable would be the assumption of a negative relationship between quantity and price, as assumed by Boswijk et al. (2016). The hypothesis is that the drawn conclusions about the underestimation would not change, but would become more general. Also, the assumption that the cartel does not influence other factors Xt, is something which
has been debated in the literature. This assumption could be relaxed in further research, to test whether the general results still hold, though it is expected that they will.
Furthermore, gathering sufficient, relevant data is often an issue when conducting eco-nomic research. However, in the case of cartels, this matter is even more relevant. Data are often not disclosed and even when they are, their reliability is questionable. That makes it challenging to test the economic theory in practice, and is the biggest limitation of this thesis. A suggestion for future research would be to apply the forecasting method on a real, misdated cartel, data which could not be obtained for this thesis. Using the sodium-chlorine cartel for this analysis, would also give a direct comparison to the underestimation using the dummy-variable approach, as done by Boswijk et al. (2016). Though theoretically, both models suffer the same consequences from misdating, it would be useful to know more about the exact scale of their misdating, which could lead to influencing the choice between the two approaches, since there is no consensus about that either.
6 Conclusion
Though illegal, and carrying costly consequences when discovered, price-fixing is still very common, with new scandals emerging every year. Correctly estimating the economic damages these cartels have caused is something which still needs a great deal of improving. Besides discussions about the correct approach to use, estimating the exact length of the cartel proves to be a complication too. Once a cartel has been discovered, formal dates are attributed to it, which often do not coincide with the real dates the cartel was active. This thesis concerned itself with the effects of misdating a cartel using the forecasting approach. After discussing previous literature concerning both the forecasting and the dummy-variable approach, two forms of the forecasting model were used to estimate the effects of misdating. First, a simple model was considered, where the but-for price simply consisted of the average price during the benchmark period. Afterwards, the model was elaborated with a stationary, exogenous variable. Based on previous literature, the expected outcome was that the damage would be underestimated as a result of misdating the cartel.
The effects were first evaluated algebraically, using the first model, the second model was estimated making use of a Monte-Carlo estimation. In the analysis, the four possible misdating scenarios were considered one by one. Furthermore, the Monte-Carlo analysis computed the average overcharge and average total damage in two manners. Once using the formal dates, and once using the real cartel length. Though the conclusions were very similar, the latter showed more general results, since the time frames were chosen quite arbitrarily. In both models, the results were similar to the ones found by Boswijk et al. (2016); misdating a cartel underestimates the total damages.
Concluding, since the effects of misdating a cartel seem to underestimate the total damages done, regardless of the approach used, it might be adviseable to date the cartel more widely, in order to get a more accurate estimation of damages. Dating the cartel too widely provides an unbiased estimation of damages, so this would not prove a problem. However, legal reasons and other, non-economic factors also play a major role in determining the formal cartel dates. Hopefully, the economic implications will be taken into account when deciding on the dates of the next uncovered cartel.
7 Bibliography
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8 Appendix 8.1 Proof Lemma 1 Pt= α1+ α2∗ Dt+ t, t ∼ i.i.d (0, σ2) bf Pt= α1+ t Dt= ( 1 t ∈ TC 0 otherwise. ˆ α1= 1 T − Te T X t=Te+1 Pt E[bf Pt] = α1 8.1.1 Case 1 + 3: Te< TE ˆ α1= 1 T − Te ∗ TE X t=Te+1 Pt+ T X t=TE+1 Pt ˆ α1= TE− Te T − Te ∗ 1 TE − Te TE X t=Te+1 Pt+ T − TE T − Te ∗ 1 T − TE T X t=TE+1 Pt E[ ˆα1] = TE− Te T − Te ∗ (α1+ α2) + T − TE T − Te ∗ α1 E[ ˆα1] = TE− Te+ T − Te T − Te ∗ α1+ TE− Te T − Te ∗ α2 E[ ˆα1] = α1+ TE − Te T − Te ∗ α2 > α1
This last step follows, since:
0 < TE− Te T − Te
< 1, α2> 0
For more clarity in the proofs that follow the following fraction is renamed: φ = TE− Te
T − Te
8.1.2 Case 2 + 4: Te> TE
E[ ˆα1] =
1 T − Te
∗ (T − Te) ∗ α1 = α1
So in cases 2 and 4 the estimator for α1 (and therefore the but-for price) are unbiased.
Concluding: E[ ˆα1] < α1 when Te< TE E[ ˆα1] = α1 when Te> TE 8.2 Proof Theorem 1 CD = TE X t=TB+1 (Pt− bf Pt) ∗ Qt Assumptions: E[Qt] = ( QN t ∈ TN QC t ∈ TC QN > QC Cov(Pt, Qt) = 0, ∀t E[CD] = TE X t=TB+1 E[Pt− bf Pt] ∗ E[Qt] E[CD] = (TE− TB) ∗ α2∗ QC d CD = Te X t=Tb+1 (Pt− dbf Pt) ∗ Qt E[ dbf Pt] = E[ ˆα1]
8.2.1 Case 1: Tb< TB,Te< TE d CD = TB X t=Tb+1 (Pt− dbf Pt) ∗ Qt+ Te X t=TB+1 (Pt− dbf Pt) ∗ Qt E[ dCD] = TB X t=Tb+1 E[Pt− dbf Pt] ∗ E[Qt] + Te X t=TB+1 E[Pt− dbf Pt] ∗ E[Qt] E[ dCD] = (TB− Tb) ∗ (α1− (α1+ φ ∗ α2) ∗ QN + (Te− TB) ∗ (α1+ α2− (α1+ φ ∗ α2) ∗ QC = (TB− Tb) ∗ (−φ ∗ α2) ∗ QN + (Te− TB) ∗ (α2∗ (1 − φ)) ∗ QC < (TB− Tb) ∗ (−φ ∗ α2) ∗ QC + (Te− TB) ∗ (α2∗ (1 − φ)) ∗ QC = −TB∗ φ ∗ α2∗ QC+ Tb∗ φ ∗ α2∗ QC+ Te∗ α2∗ (1 − φ) ∗ QC− TB∗ α2∗ QC+ TB∗ φ ∗ α2∗ QC = Tb∗ φ ∗ α2∗ QC+ Te∗ α2∗ QC− Te∗ φ ∗ α2∗ QC − TB∗ α2∗ QC = (Tb− Te) ∗ φ ∗ α2∗ QC+ (Te− TB) ∗ α2∗ QC < (Te− TB) ∗ α2∗ QC < (TE − TB) ∗ α2∗ QC = E[CD]
So in case 1, the total damage is underestimated. 8.2.2 Case 3: Tb> TB,Te< TE d CD = Te X t=Tb+1 (Pt− dbf Pt) ∗ Qt E[ dCD] = Te X t=Tb+1 E[Pt− dbf Pt] ∗ E[Qt] E[ dCD] = (Te− Tb) ∗ (α1+ α2− (α1+ φ ∗ α2)) ∗ QC < (Te− Tb) ∗ α2∗ QC < (TE − TB) ∗ α2∗ QC = E[CD]
8.2.3 Case 2: Tb< TB, Te> TE d CD = TB X t=Tb+1 (Pt− dbf Pt) ∗ Qt+ TE X t=TB+1 (Pt− dbf Pt) ∗ Qt+ Te X t=TE+1 (Pt− dbf Pt) ∗ Qt E[ dCD] = TB X t=Tb+1 E[Pt− dbf Pt] ∗ E[Qt] + TE X t=TB+1 E[Pt− dbf Pt] ∗ E[Qt] + Te X t=TE+1 E[Pt− dbf Pt] ∗ E[Qt] E[ dCD] = (TB− Tb) ∗ (α1− α1) ∗ QN + (TE− TB) ∗ (α1+ α2− α1) ∗ QC+ (Te− TE)(α1− α1) ∗ QN E[ dCD] = (TE − TB) ∗ α2∗ QC = E[CD]
so in case 2, the estimator for the total damage is unbiased. 8.2.4 Case 4: Tb> TB, Te> TE d CD = TE X t=Tb+1 (Pt− dbf Pt) ∗ Qt+ Te X t=TE+1 (Pt− dbf Pt) ∗ Qt E[ dCD] = TE X t=Tb+1 E[Pt− dbf Pt] ∗ E[Qt] + Te X t=TE+1 E[Pt− dbf Pt] ∗ E[Qt] E[ dCD] = (TE − Tb) ∗ (α1+ α2− α1) ∗ QC+ (Te− TE) ∗ (α1− α1) ∗ QN < (TE − TB) ∗ α2∗ QC = E[CD]
so in case 4, the total damage is underestimated. Concluding:
E[ dCD] = E[CD] if Tb < TB and Te> TE
