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MSc in Econometrics Thesis
Transfer strategies of European soccer clubs by
Rutger Goijen 5948878 Free Track
Date: 31-08-2015
Supervisor: Dr. Marco J. van der Leij Second marker: Dr. J.C.M. van Ophem Thesis coordinator: Dr. K.J. van Garderen
Abstract:
In the last two decades European soccer has encountered a huge financial expansion, and revenue growth has become a big priority for clubs and its shareholders. Furthermore, the takeovers of clubs by rich investors also had a big impact on the soccer business. The goal of this thesis is to investigate, in this financial expanding world, what transfer strategies work best. Is it wise to mainly buy expensive “superstar” players or is it maybe better to go for a balanced team with “normally” priced players? Using a Fixed Effect model with club dummy variables (OLS estimation) and a Dynamic Fixed Effects model (Arellano-Bond estimation) I investigate the effect of several buying and selling variables on the average points per game a club will earn in current and next year’s season. Finally I investigate if there is a positive effect of a takeover by a rich investor, who usually injects a lot of money into new expensive players. My dataset contains information about 100 soccer clubs from 12 different European competitions. The main findings of my research are that the best strategy is to increase the average acquisition amount per arriving player and to minimize the number of new players. Moreover, the negative effect of buying a lot of new players even increases after a takeover.
2 This document is written by Student Rutger Goijen who declares to take full
responsibility for the contents of this document. I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
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Contents
1. INTRODUCTION 4 – 6
2. THEORETICAL BACKGROUND 6 – 14
2.1 The Bosman Ruling and the growing inequality 7
2.2 The Money League 9
2.3 Rich investors versus an econometric approach 11 2.4 The superstar effect and image branding 13
3. DATA 14 – 18
3.1 Data overview 15
3.2 Variables explained 16
3.3 Descriptive statistics 16
4. METHODOLOGY AND TECHNIQUES 19 – 28
4.1 Fixed- and Random Effects model 21
4.2 Heteroskedasticity and serial correlation 23
4.3 Im-Pesaran-Shin unit root test 24
4.4 Arellano-Bond estimation 25
4.5 Break tests 26
5. RESULTS 28 – 36
5.1 Fixed Effect and Arellano-Bond 28
5.2 Lagged explanatory variables 31
5.3 Break tests 2 33
6. CONCLUSION 36 – 39
REFERENCES 40 – 42
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1. Introduction
Soccer, a game invented by the English to be enjoyed by the masses, is not only about goals, results and entertainment anymore. In the last two decades European soccer has encountered a huge financial expansion1, and revenue growth has become a big priority for clubs and its shareholders. For example, the total financial turnover of the English Premier League has increased by 900%2 in the period 1992 – 2006 (Hamil and Walters, 2010). And in 2006 soccer represented approximately 1.7% of total GDP of Spain (Callejo et al., 2006). Furthermore, the importance of broadcasting
revenues3, sponsorship deals and merchandise revenues has increased rapidly. The revenue of a club does not depend solely on the number of stadium tickets sold anymore. An important change in European soccer has been caused by the ‘Bosman Ruling’, which opened up the European transfer market.
One of the most visible results of the Bosman Ruling has been the growing interest and investments by Arab and Russian billionaires, mainly buying soccer clubs as a “hobby”, and turning them into successful enterprises, but there is also a prestige and political side of the story (Garcia and Amara, 2013). They spend hundreds of millions on new players based on skill, but also popularity. Examples are Abramovich with Chelsea (takeover in 2003) and Mansour Bin Zayed with Manchester City (takeover in 2008).
It is questionable if this strategy of instantly buying a lot of expensive players at once has a positive effect on the team results. Maybe it is better to buy just one or two crowd pullers? What is more important today when buying a new player: improving the team performance or improving revenues and popularity of the club? Or are these variables correlated at all time?
When looking at revenues and market values of clubs and players, we can clearly see that there is more and more money involved in the soccer business. For example, Real Madrid, which had a total revenue of 292 million euro in the season of 2005/2006, collected in 2013/2014 a total revenue of 550 million euro, having a total market value of more than 3,440 million euro4.
1
See Figure A1 for an overview of the huge financial expansion of the big five European competitions during the period 1999 – 2011.
2 From €244 million to €2.2 billion.
3 Money earned by games broadcasted on television. 4
5 Top striker of Real Madrid, Cristiano Ronaldo has a present market value of 120 million euro. When he started his professional career at Manchester United as a 19 year old he had a net worth of 18 million5. Of course, it is to be expected that a player will be worth more as he gains more experience, but to outline the issue here: Zinedine Zidane, in his days (1989 – 2006) a player of similar quality as Cristiano Ronaldo, had at the top of his career a market value of “only” 25 million euro5.
Another clear example to sketch that this business is getting more money grossing, is the fact that Sky and BT paid more than €7.4 billion for the rights to broadcast the Premier League for the upcoming three seasons. The payment and broadcasting rights for Sky are €6.0 billion and 126 matches, and for BT €1.4 billion and 42 matches. In comparison, the amounts paid for the broadcasting rights were €275 million and €2.5 billion for the period 1992-1997 and 2007-2010 respectively (BBC, 2015)6.
Is the soccer business today mainly about increasing revenues? Is it profitable to spend a lot of money on expensive, popular players? What is the best buying strategy for club managers? What effect do these different strategies have on the performances?
My research question is: What is the best transfer policy for a soccer club? I will investigate if there is a positive effect on the performances when a manager mainly buys expensive players. Maybe it is better to buy a lot of “normally” priced players instead? Furthermore I will investigate what improvements can be done on the selling side of the transfer business. Finally, next to looking at different buying
strategies, I will also investigate if there is a positive effect on the outcome of a season when a club has been taken over by a rich investor. Does a big capital input improve the results of a club?
I expect that a team full of (new) superstars is not a guarantee for better results. An evenly balanced team, with players with the same play style, will often perform equally or even better than a team full of top quality players.
I will investigate different buying strategies of clubs and the effect of a takeover by a rich investor, using data of 100 different clubs from 12 different
European competitions. Data, a total of 1056 observations, contain information about
5 Source: Transfermarkt.
6 See Figure A2 for the rise of Premier League broadcasting payments in pounds for different periods
6 transfer amounts, player trafficking and club performances (games played, points gathered and rankings). The data contain information about the seasons 1994/1995 until 2013/2014.
This article contributes to the existing literature by investigating the effect of different buying strategies towards expensive, “superstar” soccer players. Earlier research has shown that soccer players benefit from their superstar status, but I will investigate what effect it has on club performances. Furthermore, I will investigate if a club takeover by a rich investor has a positive effect.
The paper is organized as follows. In the next section I discuss earlier research about the superstar effect and the money grossing world of soccer. I will also talk about the Bosman Ruling, which had a huge impact on the transfer market.
Furthermore, the case of FC Midtjylland will be explained. FC Midtjylland is a club who bases its transfer policy on econometric models.. In Section 3, I describe the main features of the data set. Next, in Section 4 the different models and techniques will be clarified. In Section 5 I discuss the results of the regressions. Finally, Section 6 concludes and suggests further research.
2. Theoretical background
In this section previous research will be discussed. The ‘Bosman Ruling’, introduced in December 1995 by the Belgian court, abolished a couple of major transfer
restrictions in professional soccer (Antonioni and Cubbin, 2000). The effect of this “ruling” on the transfer market and the growing inequality between big and small soccer clubs after the opening of the European soccer market will be discussed in Section 2.1.
Next, Section 2.2 will be about the movement of the revenue sources. In the last two decades the importance of broadcasting, sponsorship and merchandise revenues has increased rapidly. The revenue of a club does not depend solely on the number of stadium tickets sold anymore.
Section 2.3 will be about the impact of rich investors, mainly oil sheiks from the Middle East, taking over soccer clubs. Besides trying to turn their soccer club into a money making enterprise, things like prestige and politics also play an important role. After the takeover, a big money injection usually follows. The new owner spends lots of money on new players, trying to improve the squad and ultimately win prices
7 (also prestige). Next to this takeover and injecting money policy, there is also a new phenomenon occurring in the soccer world; basing the acquisition policy of a club on econometric models. A good example is given by the club FC Midtjylland, a club in Denmark. This will also be discussed in this section.
Finally in Section 2.4 the so called ‘superstar effect’ of players will be
discussed. When improving a squad, managers are not only interested in the quality of a player, but also in their “crowd pulling” abilities. Earlier research has shown that these ‘superstars’ are usually just slightly better than other top players, but that their status give them a significant bigger salary (Lucifora and Simmons, 2003). So the superstar effect has a positive effect on superstars themselves, but in my thesis I am interested what effect it has on the results of a club.
2.1 The Bosman Ruling and the growing inequality
In 1990 Belgian soccer player Jean-Marc Bosman went to the court of justice to sue his former club RFC Liège. Bosman, with his contract expiring that year, wanted to transfer to the French club US Dunkerque, but RFC Liège refused to let him go and had put a transfer fee on his head. RFC Liège offered Bosman a new contract worth only 25% of value of his previous contract, and on top of that they would only let him go if a new club would pay 12 million Belgium Francs, about 600,000 euro
(Antonioni and Cubbin, 2000).
In 1995 the Belgian court ruled that two important transfer regulations were to be abolished, and the ‘Bosman Ruling’ was born (Simmons, 1997); First of all, the buying club is not required anymore to pay a transfer fee for a player with a expired contract at his present club: freedom of contract. And second, no limitations on buying foreign born players for soccer clubs: freedom of movement (Antonioni and Cubbin, 2000). Before the Bosman Ruling clubs could only buy 3 foreign players per season. It was also possible to buy up to 5 foreign players, but then there were
restrictions on a per match basis (Simmons, 1997). So what are the consequences of the Bosman Ruling for small and big European soccer clubs? And is there a difference between the ‘Big Five’7
and the rest of Europe?
One of the major results of the Bosman ruling is the exodus of the top soccer players of the minor competitions to the big foreign clubs (Kesenne, 2007). Clubs like
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8 Ajax, who won some big prices in the 90s, now have to compete on the transfer
market with big clubs like Manchester United, who has a budget of more than 10 times that of Ajax (Kesenne, 2007). And besides that the unit cost of talent has increased in small and decreased in big countries respectively (Kesenne, 2007).
Another result of the Bosman Ruling is that clubs want players to sign longer term contracts. Contract lengths have risen from 2-3 years to 5-10 years. With these long term contracts soccer clubs are trying to secure the player’s services (Simmons 1997). Obviously big clubs with bigger budget can offer better contracts to top talents and players.
Next, the international ‘UEFA Champions League’8
, a competition between the best performing clubs of each European country, does not give the desired result either. The goal was to open the European football market, but instead it even increased the gap between big and small soccer clubs (Kesenne, 2007). Participating in this international competition results in more revenues, and the further a team gets in this competition, the more money they get, and the more they can spend on new players for next season. So, highly ranked teams participate in the UEFA Champions League, their revenues increase, they can afford even more good players, their performances improve, they participate in the UEFA Champions League, etcetera. The same clubs gain from this European money league and dominate their domestic competition (Kesenne, 2007).
But the UEFA Champions League not only widens the gap between big and small clubs, but also between countries. For instance England has every year 3 clubs playing in the Champions League with an additional team playing qualifiers. The Dutch competition only delivers 1 club with a possible second team, playing qualifiers9. Moreover, the prize system is constructed in a way that clubs from big countries like England and Spain can get more money than minor countries like Austria and Belgium, even when they have the same performances. To illustrate the dominance of big European soccer nations: in the period 1994 – 1998 only 55 percent of the clubs who reached the semi-finals was from either England, Spain, Germany or Spain, while in the 4 seasons after that (1999 – 2003) it increased to 95% (Gerrard, 2003).
8 Founded in 1992.
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9 To conclude we can say that the Bosman Ruling has led to an opening of the European soccer market. It has widened the gap between the budgets and
performances of not only big and small clubs within a country, but also the gap between big and small soccer countries as a whole. Further, the UEFA Champions League, founded in 1992, has widened the gap even more. Kesenne (2007) proposes to abolish the UEFA Champions League and create a European soccer division where only the best clubs of each country meet, resulting in leaving their own domestic competition.
2.2 The Money League
Buraimo et al. (2007) state in their paper that market size can be considered essential for revenue, and therefore also for performances. One of the main income sources of clubs used to be the stadium gate revenues. The ticket sale is ultimately driven by the local fan base. Simply said; big clubs, mainly located in big cities with large
populations, have a bigger fan base and thus more gate revenues. But in the last two decades the importance of broadcasting, sponsorship and merchandise revenues has increased rapidly. The revenue of a club does not depend solely on the number of stadium tickets sold anymore. But again there is a difference between big and small clubs when it comes to revenues gained from broadcasting. For example matches of big English Premier League clubs like Arsenal Chelsea and Manchester United are more often shown on television. These big clubs therefore earn proportionally more money from broadcasting than smaller teams (Forrest et al., 2005).
An overview of the revenues of soccer clubs by source can be found in Figure 1. It shows the revenues of the season 2012/2013, of several European top clubs, by category in millions. ‘Matchday’ are primarily the ticket sale revenues and
‘Broadcasting’ are the television and media revenues from participation in the domestic league, domestic cup leagues and the European club competition. ‘Commercial’ is mainly the result from sponsorship deals and club merchandise.
First of all, we can see that for almost every club the biggest contribution to their revenues comes from sponsorship deals and merchandise (commercial).To get the attention of big companies for a sponsor deal, clubs need to be successful in the several soccer leagues (domestic and European), and work on their popularity. This can be accomplished by good results, buying popular players and working on the overall club status. Of course, clubs who rarely play in the European club competition
10 like the UEFA Champions League are less likely to attract an international company for a sponsor deal. In Section 2.4 I will elaborate on the importance of image
branding.
Figure 1. Revenue setup of several European club for the season 2013/2014 (Source: Deloitte Football Money League, 2014).
Second, broadcasting is also a big contributor to the revenues of clubs. Thanks to the audiovisual industry soccer has become a multimillion euro business sector (Garcia and Amara, 2013). In Figure A2 there is an overview of the payments for the broadcasting rights of the Premier League for several seasons from 1992 up to 2019. We can see a big increase of payments since 2013. The broadcasting costs for 2013 – 2016 were €4.3 billion and for 2016 – 2019 they are €7.4 billion. This is also
beneficial for the players, as the increasing television rights and commercial revenue go hand in hand with an increase in player salaries (Kesenne, 2007).
Finally, the third big revenue source ‘Matchday’: the money earned at “the gates of the stadium”. In Figure A3 the revenue source division for the period 2004 – 2013 is shown. We can clearly see that sponsorship deals and merchandise
11 (commercial) have increased in importance as a revenue source. The increase in commercial revenues is remarkable: 31.1% in 2004 to 42% in 2013.
However, in the last decade another important source of income for several European clubs became important: “The rich oil investors”. They mainly buy soccer clubs as a “hobby”, and turn them into successful enterprises, but there is also a prestige and political side of the story (Garcia and Amara, 2013)
2.3 Rich investors versus an econometric approach
One of the most visible results of the Bosman Ruling has been the growing interest and investments by (oil) billionaires10. A well-known takeover in the recent soccer history is Chelsea by the Russian businessman Roman Abramovich. In 2003 he took over the soccer club for an astounding €200 million. In the year of his acquisition he immediately bought Damien Duff (€24.5 mln.), Herman Crespo (€24.3 mln.), Juan Sebastian Veron (€21.5 mln.) and Claude Makélélé (€20 mln.), among others. Up to 2015 he has invested more than €3 billion in Chelsea (transfer amounts and wages)11. Figure A4 shows the transfer spending and earnings of Chelsea for the period 1994 – 2013. We can see a huge increase in arrival spending in the first couple of years after the takeover in 2003. The question remains: What has 12 years of Roman
Abramovich yielded for Chelsea (season 2003/2004 – 2014/2015)?
Since the takeover they have won 4 FA Cups, 4 Premier League Cups, 3 League Cups, 2 English Super Cups, 1 Champions League Cup and 1 Europe League Cup12, a total of 15 prices in only twelve years, of a total of 26 prices since the founding of Chelsea in 1905. In comparison: in the period 1991/1992 – 2002/2003, the 12 years before the takeover, Chelsea accomplished to gather 6 trophies, with a total transfer spending of €200 million13
. So is this great success all because of the takeover in 2003? Is it all about just buying a lot of good players for big amounts of money? Is money the key to success?14
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Manchester City: Mansour Bin Sultan Al Nahyan, 2007; PSG: Nasser Al Khelaïfi, 2011; Malaga FC: Abdullah Ben Nasser Al Thani, 2010; Monaco FC: Dmitry Rybolovlev, 2011; Vitesse: Merab Jordania, 2010.
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Source: The independent and Transfermarkt.
12
Source: Transfermarkt.
13 €1.227 million in 12 years of Abramovich.
14 Manchester City winning the Premier League in season 2011/2012 and 2013/2014. PSG winning the
12 Proof that a takeover is not always a blessing for a club has been given by Malaga FC. In 2010 the oil sheik Abdullah Ben Nasser Al Thani bought the Spanish club for 36 million euro. With the goal to consolidate the presence of the club in La Liga15 and reach the UEFA Champions League, he invested heavily in new top players. This goal was already reached at the end of season 2012/2013, as they finished fourth in La Liga. But after a couple of years of investing in new players, the Qatari sheikh pulled out the plug in 2013 because he lost his interest in soccer, leaving the club with debts since with all the expensive players he bought also came huge salaries.
Former owner of Tottenham Hotspur Sir Alan Sugar mentioned the “prume juice effect”; increased revenues enter the mouth of a soccer club and then rapidly exit the rear of the club in player salaries (Hamil and Walters, 2010). In this case the increase in revenues were the sheiks investments, but this suddenly stopped leaving Malaga FC with huge debts.
Besides this takeover and injecting money policy, the last couple years there is also a new phenomenon occurring in the soccer world; basing the acquisition policy of a club on econometric models. In 2010 English businessman Matthew Benham bought Danish club FC Midtjylland. Benham, who gathered his fortune with sports betting using algorithms, wants to bring rationalism back to the soccer world. His team now uses the ‘statistics first approach’; player selection is in the beginning purely model based. They apply a new ranking system, grading all European
professional soccer players, not only from the premier divisions, but also from second and third division European competitions. Their ranking is based on player statistics such as passing, assists (final pass before a goal), goals, tackles, etc. Using this model they found out that several second division players would be more than capable of playing in the first division. After players are selected by the model, scouts only have to look at the playing style of a player; will he fit in the team?
So will this latter approach of basing the transfer policy purely on econometric models prove to result in better performances? For starters, it costs much less than buying lots of expensive top players. But as mentioned before, increasingly more money is coming from merchandise and broadcasting. Clubs are more and more
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13 branding their club name, and attracting big and well-known players has proven to be very useful, for both performance and improving the club’s image.
2.4 The superstar effect and image branding
In the entertainment business it is very common that certain actors, singers or athletes earn astonishing amounts of money. Examples are for instance Tom Cruise, earning $20 million for his film Oblivion (2013) and Lionel Messi with a weekly salary of almost a million dollars a week in 2015 (The Richest, 2015). But in contrast, big talents in other fields like biology and astronomy don’t even come close to these amounts of earnings. The difference that in certain labour areas a few people can earn huge salaries and in other labour areas not, is called the ‘superstar phenomenon’ (Rosen, 1981). These “superstars” mainly appear in the entertainment and sports business. In the soccer world “the marginal revenue product of a soccer player is related to the extra price that a spectator is willing to pay to see him play (live or on television) times the number of spectators who are attracted” (Lucifora and Simmons, 2003). As mentioned before, revenues from broadcasting and international
competitions like the UEFA Champions League are increasing mainly for the top clubs, having “elite players”, resulting in higher than ever salaries for these superstar players (Garcia and Amara, 2013). Lucifora and Simmons (2003) stated that the increase in demand of a club is not driven by a price mechanism. Instead the large audience is attracted by the reputation of the superstar players.
As sponsorship deals and merchandise have become an important revenue source, soccer clubs are increasingly trying to improve their image. They want to increase their brand awareness and establish and improve their brand image (Cornwell and Maignan, 1998). One of the most direct strategies is to buy superstar players. They improve the image of the club, thus they make the club more interesting for companies to offer big sponsorship deals. Signing world class players not only contributes to the quality of the squad but it also has an important media impact, which can be exploited in the advertising market (Callejo et al., 2006).
A clear example of the success of image branding is given by Real Madrid. In 2000 Florentino Pérez was appointed as president of the club. His goal was to make Real Madrid the “top sports firm in Europe”: a debt free money making enterprise. Radically changing the club’s internal commercial structure he managed to double the
14 club’s income from €150 million in season 2000/2001 to €300 million in the
2004/2005 season16.
In this thesis I will not only look at how much a club spends every season and how many players they buy, but I will also look at the effect of ‘superstars’. Doing so, I will label players ‘expensive’ and ‘extremely expensive’, by installing a threshold when looking at the transfer amounts. In Section 3, the data, I will elaborate more on the implementation of these superstar variables.
So it is clear now that investing a lot of money on new and expensive, superstar players can have a positive outcome on the results. Examples are given by Chelsea, Manchester City and PSG. But on the other hand, a lot of money is not always necessary to improve a team, as we could see by FC Midtjylland. They base their transfer policy on econometric models, buying also “unknown” players from the second division.
My expectation is that a mix of these two strategies, that is buying just a few expensive “crowd pullers” and build the rest of the team around them, will work the best, in contrast to investing a lot of money in a club buying multiple superstars every season. Furthermore, I expect that the buying policy will be less efficient after a club has been taken over. The net investments will increase, but they have to invest relatively more to improve their results.
3. Data
This section contains information about the data I used in my research. I go through the different dependent and independent variables, the dummies and how I
constructed several variables. In Section 3.1 there is an overview of all the variables. Explanation about how the different variables are created can be found in Section 3.2. Finally, Section 3.3 discusses the descriptive statistics of the dependent and
explanatory variables.
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15 3.1 Data Overview
The data contains information about 100 soccer clubs from 12 different European competitions and is derived from transfermarkt.com, soccerway.com and
soccerassociation.com.
Results of the “sheik clubs”, Chelsea, Manchester City, Malaga FC, PSG, Monaco FC and Vitesse are about season 1994/1995 until 2013/2014. The other 94 clubs have data about the seasons 2004/2005 until 2013/2014. The data, a total of 1,056 observations, is about transfer amounts, player trafficking and club
performances (games played, points gathered and rankings). In my research I am only looking at results of playing in the premier domestic league. So dropping the
observations from the second and third domestic competitions results in 1,001 observations. Table 1 contains an overview of all the variables.
Variables Season 1994/1995 – 2013/2014
country Country
club Club
sheik Taken over by a rich investor: sheik = 1, zero otherwise firstdiv Playing in first division: firstdiv = 1, zero otherwise
season Season
ply Total number of matches played
pos Final ranking
pts Final points count
ptsx Average points scored per match totarr Total arrival (millions)
totdep Total departure (millions)
ndif Net difference (i.e. total departure – total arrival) (millions) avarr Average amount per player arrived (millions)
avdep Average amount per player departed (millions) totnumarr Total number of players arrived
exp1 Total number of expensive players arrived
exp2 Total number of extremely expensive players arrived totnumdep Total number of players departed
expp1 Total number of expensive players departed
expp2 Total number of extremely expensive players departed Table 1. Overview variables.
16 3.2 Variables explained
The variables totarr and totdep are the total value of all the players purchased and sold respectively in a year by a club. The net difference is the total departure of a club minus the total arrival (i.e. total revenues minus total expenses of the transfer policy).
The total number of players arrived and departed are created to get an insight into whether an extensive transferring policy has a positive or negative effect on the results of a club17. Often a transfer amount is zero because the arriving player comes from the youth section of the club. Also when a player ends his career the transfer amount is also zero.
To obtain information about the so called ‘superstar effect’ I have constructed variables exp1, exp2, expp1 and expp2 to distinguish “normally” priced players from expensive and extremely expensive players. By dividing total market value of 2015 of each by 150 and 75 respectively, I have created the variables for expensive and
extremely expensive transfers in a relative way. For instance, the total market value of the Dutch and English competition is respectively €530 million and €3.750 billion. So the threshold for an expensive and an extremely expensive player becomes €3.5- and €7 million for the Dutch competition and €25- and €50 million for the English
competition respectively. For a Dutch soccer club like Ajax the acquisition of a player of 7 million euro is quite a lot, but for a major English soccer team like Chelsea not a big deal. The variables exp1, exp2, expp1 and expp2 are then the number of players arrived and departed whose transfer value exceeded the respective threshold for expensive and extremely expensive players. See Table A1 for the total market values of the 12 European competitions and their expensive and extremely expensive player amounts.
3.3 Descriptive Statistics
In Table 2 we can see the descriptive statistics of the dependent-, explanatory- and some other interesting variables18. We can see that the median number of expensive and extremely expensive players for both arrival and departure is zero. This is to be expected, since only a hand full of clubs are able to acquire expensive and especially extremely expensive players. Further, Table 2 shows that the maximum amount of
17 When a player had as transfer amount ‘end of loan’, ‘-‘, ‘loan’, ‘?’ or ‘free transfer’, the transfer
amount is noted as zero euro.
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17 total arrivals is roughly twice as big as the maximum amount of total departures. With a median of respectively 4.95 and 5.45 million euro for total arrival and total
departure, we can conclude that there have been a couple big outliers in the dataset. We also see that the average number of points earned has a minimum of 0.5 and a maximum of 2.819. With a mean and median of respectively 1.613 and 1.6, we can determine that we have a heterogeneous group of observations, concerning the amount of average points gathered. The same applies to the total number of players that arrived. The minimum is 2 and the maximum is 47, with a mean and median of respectively 14.278 and 13. And the same goes for the total number of players
departed: a minimum and maximum of respectively 1 and 68, and a mean and median of 17.777 and 15 respectively.
In my data set of 100 European soccer clubs 67% has a positive balance over the period 2004 – 2013 when it comes to net difference between selling and buying players. But if we look at the total net difference of all the clubs in the period 2004 – 2013 we end up with -€3.1 billion. So there are clearly a few clubs who have invested a lot on new players. It will be no surprise that these clubs are mainly the clubs which were taken over by a rich investor in this period.
variables total points av. points per game total arrival (mln) total departure (mln) average arrival average departure total arrived mean 56.384 1.613 16.902 13.349 1.201 0.710 14.278 median 56 1.6 4.95 5.45 0.408 0.345 13 std dev 14.986 0.404 28.025 19.062 2.267 1.019 6.937 min 17 0.5 0 0 0 0 2 max 102 2.8 257.4 128.9 28.6 12.722 47 N 1001 1001 1001 1001 1001 1001 1001 variables expensive arrival extrem. expensive arrival transfer free arrival
total departed expensive departure extrem. expensive departure transfer free departure mean median std dev min max N 0.306 0 0.667 0 4 1001 0.074 0 0.391 0 5 1001 0.720 0.75 0.216 0 1 1001 17.777 15 9.674 1 68 1001 0.282 0 0.566 0 3 1001 0.204 0 0.524 0 3 1001 0.798 0.826 0.156 0.125 1 1001 Table 2. Descriptive statistics variables. Transfer free is the number of players arrived or departed
without a payment, divided by the total number of players arrived or departed respectively.
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18 Next in Figure 2 we can see that in the period 2004 – 201320 the total arrival amounts increased. There are a couple big outliers like Chelsea 200421 (€161,900), and Real Madrid 200922 (€257,400). In Figure A6 and A7 we respectively see the increase in total number of players bought each year and the increase of average amount per player. So there is not only an increase in total arrival amounts and total number of players bought, but also the average amount per player has increased.
Figure 2. Scatterplot of the increasing total acquisition amounts in period 2004 – 2013.
20
2004 stands for season 2004/2005, etcetera.
21 Roman Abramovich bought Chelsea in 2003.
22 Buying players like Cristiano Ronaldo (€94 mln.), Kaká (€65 mln.), Xabi Alonso (€35.4 mln.) and
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4. Methodology and Techniques
In this section I go through the different models and techniques I used in Stata. The main two models of my thesis are:
Fixed Effects model (OLS estimation)23:
𝑦𝑖𝑡 = ∑ 𝛼𝑗𝑑𝑗,𝑖𝑡+ ∑ 𝛾𝑠𝑑𝑠,𝑖𝑡+ 𝑥𝑖𝑡′𝛽 + 𝜀𝑖𝑡 𝑇 𝑠=2 𝑁 𝑗=1 (I) 𝑤𝑖𝑡ℎ 𝑑𝑗,𝑖𝑡 = 1 𝑖𝑓 𝑖 = 𝑗 𝑎𝑛𝑑 𝑑𝑠,𝑖𝑡 = 1 𝑖𝑓 𝑡 = 𝑠
Dynamic Fixed Effects model (Arellano-Bond estimation):
𝑦𝑖𝑡 = 𝛼𝑖 + 𝜌𝑦𝑖,𝑡−1+ 𝑥𝑖𝑡′𝛽 + 𝜀𝑖𝑡 (II) 𝑤𝑖𝑡ℎ 𝑖 = 1, … , 𝑁 𝑎𝑛𝑑 𝑡 = 1, … , 𝑇
In model (I) and (II) the dependent variable 𝑦𝑖𝑡 is 𝑝𝑡𝑠𝑥𝑖𝑡, the average number of points per game gathered by club 𝑖 in season 𝑡. The explanatory variables 𝑥𝑖𝑡 are: average amount per arriving (avarr) and departing player (avdep), total number of players arrived (totnumarr) and departed (totnumdep), number of expensive players arrived (exp1) and departed (expp1) and the amount of extremely expensive players arrived (exp2) and departed (expp2). Next, in model (I) 𝑑𝑗,𝑖𝑡 are the dummies for the different clubs with 𝑑𝑗,𝑖𝑡 = 1 𝑖𝑓 𝑖 = 𝑗 and 𝑑𝑠,𝑖𝑡 are the time-fixed effects for the different seasons with 𝑑𝑠,𝑖𝑡 = 1 𝑖𝑓 𝑡 = 𝑠. In model (II), 𝑦𝑖,𝑡−1, the average number of points per game gathered by club 𝑖 in season 𝑡 − 1, has been added as an explanatory variable. The error term 𝜀𝑖𝑡 is in both equations i.i.d. over 𝑖 and 𝑡 and normally distributed.
The reason for choosing average amount per arriving and departing player instead of the total amount of arrivals and departures is because these latter variables correlate with the total number of players arrived and departed respectively24. In
23
In the result section I will also compare this model (ordinary least squares with fixed effects) with the standard ordinary least squares estimation model (OLS): 𝑦𝑖𝑡 = 𝑥𝑖𝑡′𝛽 + 𝜀𝑖𝑡, 𝑖 = 1, … , 𝑁 𝑎𝑛𝑑 𝑡 = 1, … , 𝑇.
24 Correlation between total amount of arrivals and total number of players arrived is 0.377 and
20 addition, the chosen model is also better interpretable. The dataset, 1,001
observations, contains a large 𝑁 (100 clubs) and a small 𝑇 (average time span is 10.56).
When constructing model (I), I first tested for time varying effects and whether the model needs to contain fixed or random effects using the Hausman test. The Hausman test tests whether the errors (𝜀𝑖𝑡) are correlated with the regressors.
To determine what dummies to use, club- or country dummies, I have compared the 𝑅2 of the dummy models, using club- and country dummies. Using a Likelihood-ratio test, I investigate if there is a significant difference between the country- and club dummy model. The construction of model (I) is discussed in Section 4.1.
Next, testing and controlling for heteroskedasticity with a Wald test, and checking for correlation using the Wooldridge (2002) test for autocorrelation . This will be explained in Section 4.2.
Section 4.3 will be about the Im-Pesaran-Shin unit root test. This test based on the Dickey-Fuller procedure tests whether there are unit roots present in the panels.
In Section 4.4 I will discuss a different estimation model; Dynamic panel data model with the Arellano-Bond estimation. This method uses Generalized Method of Moments (GMM hereafter) (Hansen 1982) instead of Ordinary Least Squares (OLS hereafter) to estimate the panel data with lagged dependent variables. In my dataset there is a large N and a small T. Moreover, presence of autocorrelation and
heteroskedasticity have been verified (See Section 4.2). The Arellano-Bond
estimation has proven to perform well in these kind of situations (Roodman, 2009). The construction of this model (II) will be explained here.
Finally in Section 4.5 the Break tests will be discussed. These tests investigate if there is a positive effect when a club gets a huge money impulse from their new investor. In this case I use a slimmed down dataset containing data of only the “sheik clubs”. I will investigate whether there is a difference in (joint) coefficients of the parameters before and after the takeover.
comparison: correlation between average amount per arriving player and total number of players arrived is -0.016 and correlation between average amount per departing player and total number of players departed is 0.073.
21 4.1 Fixed- and Random Effects model
Fixed Effects model (FE):
The individual and time dummies model is:
𝑦𝑖𝑡 = ∑ 𝛼𝑗𝑑𝑗,𝑖𝑡+ ∑ 𝛾𝑠𝑑𝑠,𝑖𝑡+ 𝑥𝑖𝑡′𝛽 + 𝜀𝑖𝑡 𝑇 𝑠=2 𝑁 𝑗=1 (I) 𝑑𝑗,𝑖𝑡 = 1 𝑖𝑓 𝑖 = 𝑗 𝑎𝑛𝑑 𝑑𝑠,𝑖𝑡 = 1 𝑖𝑓 𝑡 = 𝑠
We test for time fixed effect, using an F-test. The null hypothesis of this test is
𝐻0: 𝛾𝑠 = 0: 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡𝑠 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑠𝑒𝑎𝑠𝑜𝑛𝑠 𝑎𝑟𝑒 𝑗𝑜𝑖𝑛𝑡𝑙𝑦 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜 𝑧𝑒𝑟𝑜, 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑠, 𝑠 = 2, … , 𝑇. Testing the time-fixed effects with a 𝐹(19,99) = 50.24 we get a p-value of 𝑝 = 0.000, so we reject the null. Since the coefficient for all seasons are not jointly equal to zero, I have to account for time-fixed effects.
Random Effects model (RE):
The Random Effects model is:
𝑦𝑖𝑡 = 𝑥𝑖𝑡′ 𝛽 + 𝛼 + 𝑢𝑖+ 𝜀𝑖𝑡, 𝑖 = 1, … , 𝑁 𝑎𝑛𝑑 𝑡 = 1, … , 𝑇 (1.1)
In this equation 𝑢𝑖 is the ‘between-entity error’ and 𝜀𝑖𝑡 is the ‘within-entity error’. In the RE the time-invariant variables are used as explanatory variables, since the entity’s error term are not correlated with the predictors.
We want to investigate whether to use the Fixed Effects or Random Effects model. Comparing both models we look at model (1.2), where the Fixed- and Random Effects model using the individual-specific effects are given:
22 In the fixed effects model (FE), 𝛼𝑖 is an unobserved random variable that might be correlated with 𝑥𝑖𝑡 and assumes 𝐸(𝜀𝑖𝑡|𝑥𝑖, 𝛼𝑖) = 0, 𝑡 = 1,2, … , 𝑇. This model estimates 𝛼1, … , 𝛼𝑁.
The random effects model (RE) treats the unobservable individual effect 𝛼𝑖 as a random variable that is independently distributed of 𝑥𝑖𝑡: 𝐶𝑜𝑣(𝑥𝑖𝑡, 𝛼𝑖) = 0. The RE also assumes that the random effects and error are independent and identically distributed: 𝛼𝑖~[𝛼, 𝜎𝛼2] and 𝜀
𝑖𝑡~[0, 𝜎𝜀2]. Further assumptions that are made: 𝐸(𝜀𝑖𝑡|𝑥𝑖, 𝛼𝑖) = 0, 𝑡 = 1,2, … , 𝑇 and 𝐸(𝛼𝑖|𝑥𝑖) = 𝐸(𝛼𝑖) = 0.
Using the Hausman test I investigate which model, FE or RE, I have to use with my data. With a null hypothesis is 𝐻0: 𝑐𝑜𝑟(𝑥𝑖𝑡, 𝜀𝑖𝑡) = 0 and alternative
hypothesis is 𝐻𝑎: 𝑐𝑜𝑟(𝑥𝑖𝑡, 𝜀𝑖𝑡) ≠ 0. If the null is not rejected, the preferred model is the RE and if the null is rejected the FE model is desired. The test statistic from the Hausman test is a 𝐻𝑀(8) = 47.48 with a corresponding p-value of 𝑝 = 0.000. So we can conclude that we can reject the null and thus have to use the fixed effects model: model (I).
Club or country dummies:
To determine what dummies 𝑑𝑗,𝑖𝑡 to use, club- or country dummies, I compare the 𝑅2 of the dummy models, using club- and country dummies. In Table A2 the results of the OLS and with the club and country dummies are shown. Using a Likelihood-Ratio I compare the club- and country dummy models.
The null hypothesis is 𝐻0: 𝛼𝑖𝑐 = 𝛼𝑐 𝑓𝑜𝑟 𝑎𝑙𝑙 𝛼𝑖𝑐 and the alternative hypothesis is 𝐻𝑎: 𝛼𝑖𝑐 ≠ 𝛼𝑐, 𝑤𝑖𝑡ℎ 𝑖 = 1, … , 100: 𝑐𝑙𝑢𝑏 𝑎𝑛𝑑 𝑐 = 1, … ,12: 𝑐𝑜𝑢𝑛𝑡𝑟𝑦 𝑓𝑜𝑟 𝑜𝑛𝑒 𝛼𝑖𝑐. If the null is rejected there is a significant difference between the club- and country dummy regression.
We have a test statistic of 𝐿𝑅 (88) = 502.06 resulting in a p-value of 𝑝 = 0.000. So rejecting the null, we know that there is a significant difference between the two regressions. Therefore, I prefer this latter model25.
25
Even though the country dummy model has more significant coefficients, with the club dummy model having a higher 𝑅2 (0.568 versus 0.284), I prefer this latter model. Because, although the country dummy model is less biased, there is a presence of omitted variable bias, because the lack of club dummies.
23 4.2 Heteroskedasticity and serial correlation
I test the model for heteroskedasticity and serial correlation; Using a modified Wald test26, I test for heteroskedasticity in my fixed effect regression model. The null hypothesis is 𝐻0: 𝜎𝑖2 = 𝜎2: ℎ𝑜𝑚𝑜𝑠𝑘𝑒𝑑𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦, 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑖, 𝑖 = 1, … , 𝑁. I have a test statistic of 𝑊𝑎𝑙𝑑(100) = 4212.89 resulting in a p-value of 𝑝 = 0.000, so I can reject the null; we know there is a presence of heteroskedasticity.
Next, testing for serial correlation I have used the simple test for
autocorrelation27. The first differences are shown in model (2.1), resulting in model (2.2), with the delta’s, obtaining the residuals by regressing ∆𝑦𝑖𝑡 on ∆𝑋𝑖𝑡.
𝑦𝑖𝑡 − 𝑦𝑖,𝑡−1= (𝑋𝑖𝑡− 𝑋𝑖,𝑡−1)𝛽1+ 𝜀𝑖𝑡− 𝜀𝑖,𝑡−1 (2.1) ∆𝑦𝑖𝑡 = ∆𝑋𝑖𝑡𝛽1+ ∆𝜀𝑖𝑡 (2.2)
𝑤𝑖𝑡ℎ 𝑖 = 1, … , 𝑁 𝑎𝑛𝑑 𝑡 = 1, … , 𝑇
Consider model (2.3) as the first-order serial correlation model. The null hypothesis is 𝐻0: 𝜌 = 0 and the alternative hypothesis is 𝐻𝑎: 𝜌 > 0, with −1 < 𝜌 < 1. So if the null is not rejected 𝜀𝑖𝑡 = 𝑣𝑖𝑡 and there is no serial correlation.
𝜀𝑖𝑡 = 𝜌𝜀𝑖,𝑡−1+ 𝑣𝑖𝑡, 𝑤𝑖𝑡ℎ 𝜌 =∑ 𝜀𝑖𝑡𝜀𝑖,𝑡−1
∑ 𝜀𝑖𝑡2 (2.3)
We have a test statistic of 𝐹(1,99) = 3.317 resulting in a p-value of 𝑝 = 0.0716, so we can reject the null and conclude that there is serial correlation. Controlling for heteroskedasticity and serial correlation will be done using clustered robust standard errors28, since N is large enough (i.e. 𝑁 > 50)29.
26
Source: Green, 2000.
27
Source: Wooldridge, 2002 and Drukker, 2003. Has good size and power properties in relative large samples.
28
Source: Torres-Reyna, 2007 and Cameron and Miller, 2013. Clustered robust for de FE models, and robust for OLS and AB.
29 I could also test for cross-sectional dependence/contemporaneous correlation using the
Breusch-Pagan Lagrange Multiplier test of independence or the Pesaran CD test, but since my dataset consist of a small 𝑡 (average t = 10.56) this is not necessary (Torres-Reyna, 2007).
24 4.3 Im-Pesaran-Shin unit root test
The Im-Pesaran-Shin (IPS hereafter) test is based on the Dickey-Fuller procedure tests whether there are unit roots present in the panels. Moreover, the IPS test uses separate unit root tests for N cross-section components.
The IPS test performs well with a fixed N and T, and when the panels are unbalanced. In my case the panels are unbalanced30 with a fixed 𝑁(= 100) and a fixed 𝑇 with an average timespan of 10.56. Furthermore, the IPS test has as null hypothesis that all panels have a unit root. The basic principle of the unit root test starts with a first-order autoregressive process31:
𝑦𝑖𝑡 = (1 − 𝜑𝑖)𝜇𝑖+ 𝜑𝑖𝑦𝑖,𝑡−1+ 𝜀𝑖𝑡, 𝑖 = 1, … , 𝑁 𝑎𝑛𝑑 𝑡 = 1, … , 𝑇 (3.1)
𝐻0: 𝜑𝑖 = 1 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑖
Subsequently, model (3.1) can be expressed by:
∆𝑦𝑖𝑡 = 𝛼𝑖+ 𝛽𝑖𝑦𝑖,𝑡−1+ 𝜀𝑖𝑡 (3.2)
𝑤𝑖𝑡ℎ 𝛼𝑖 = (1 − 𝜑𝑖)𝜇𝑖, 𝛽𝑖 = −(1 − 𝜑𝑖) 𝑎𝑛𝑑 ∆𝑦𝑖𝑡 = 𝑦𝑖𝑡− 𝑦𝑖,𝑡−1
𝐻0: 𝛽𝑖 = 0 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑖: 𝑢𝑛𝑖𝑡 𝑟𝑜𝑜𝑡𝑠 𝑖𝑛 𝑝𝑎𝑛𝑒𝑙𝑠 𝐻𝑎: 𝛽𝑖 < 0: 𝑠𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑟𝑦 𝑝𝑎𝑛𝑒𝑙𝑠
𝑤𝑖𝑡ℎ 𝑖 = 1,2, … , 𝑁1, 𝛽𝑖 = 0, 𝑖 = 𝑁1+ 1, 𝑁1+ 2, … , 𝑁
We have a unit root Im-Pesaran-Shin test with 1.81 average lags, resulting in a p-value of 𝑝 = 0.000. So we can reject the null and conclude that panels are stationary. So the model allows for adding 𝑦𝑖,𝑡−1 as an explanatory variables (instead of ∆𝑦𝑖𝑡 as dependent variable). This will be the case in the Arellano-Bond (see Section 4.4). Next to the normal FE and AB, I will also compare FE and AB with lagged explanatory variables.
30 6 out of the 100 clubs have data before 2004. 31
25 4.4 Arellano-Bond estimation
The Arellano-Bond estimation, using Generalized Method of Moments (GMM hereafter) (Hansen 1982), has proven to perform well in situations with large N and small T (Roodman, 2009) . In my fixed individual effects model there are 100 soccer clubs with an average timespan of 10.56 seasons. Moreover, Arellano-Bond is
designed for situations where the dependent variable is correlated with its own lagged version. In Section 4.2 I have proven the existence of autocorrelation (and
heteroskedasticity) within individual clubs. Finally, the Arellano-Bond estimation also assumes that the first differences of the instrumental variables and the fixed effects are uncorrelated, and therefore more instruments can be added to improve the efficiency of the model (Roodman, 2009).
Dynamic panel data model with the Arellano-Bond estimation32:
𝑦𝑖𝑡 = 𝛼𝑖 + 𝜌𝑦𝑖,𝑡−1+ 𝑥𝑖𝑡′ 𝛽 + 𝜀
𝑖𝑡, 𝑖 = 1, … , 𝑁; 𝑡 = 1, … , 𝑇 (II) We want to have a consistent estimator for 𝜌, the autocorrelation parameter33
. The variable 𝛼𝑖 is an individual effect, capturing the unobservable time-constant character of 𝑖. The error term 𝜀𝑖𝑡 is assumed to be uncorrelated over time. 𝑁 is large and 𝑇 is small. When using standard ordinary least squares, model (II) would give an inconsistent estimate of 𝛼𝑖. For the error term 𝜀𝑖𝑡 applies:
𝐸[𝜀𝑖𝑡] = 𝐸[𝜀𝑖𝑡𝜀𝑖𝑠] = 0, 𝑓𝑜𝑟 𝑡 ≠ 𝑠
𝐸[(∆𝜀𝑖𝑡)𝑦𝑖(𝑡−𝑠)] = 0, 𝑤𝑖𝑡ℎ (𝑠 = 2, … , (𝑡 − 1); 𝑡 = 3, … , 𝑇). 𝑤𝑖𝑡ℎ ∆𝑦𝑖𝑡 = 𝑦𝑖𝑡− 𝑦𝑖(𝑡−1) 𝑎𝑛𝑑 𝐸(∆𝜀𝑖𝑡∆𝑥𝑖𝑡) = 0
As instruments for differenced equation we have the first differences of the explanatory variables, and the constant is the instrument for the level equation.
32 Source: Arellano and Bond, 1991. 33
26 4.5 Break tests
To investigate the impact of a changing policy, in this case a money impulse from a new investor, I have used a classic Chow Break test (CB hereafter) to investigate if there is a significant difference in the joint coefficients of the parameters before and after the takeover. Next I have created a second Break test (BT hereafter) to
investigate if there is a significant difference in the coefficients of single parameters before and after the break34. I am especially interested if there is a significant
difference in the coefficients of the arrival parameters, since the acquisition policies of the clubs radically change after a takeover. The null hypothesis for the break tests is 𝐻0: 𝑛𝑜 𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑎𝑙 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑏𝑒𝑓𝑜𝑟𝑒 𝑎𝑛𝑑 𝑎𝑓𝑡𝑒𝑟 𝑎 𝑡𝑎𝑘𝑒𝑜𝑣𝑒𝑟.
The dataset, containing only data about the 6 “sheik clubs”, has 116
observations. After dropping the observations from domestic leagues different from the premier division, I have a dataset of 106 observations with small 𝑁 (6 clubs) and a small 𝑇 (average time span is 19.33)35
. So we have a total of 106 observations, with 76 observation before a takeover (𝑛𝑏𝑒𝑓𝑜𝑟𝑒 = 76) and 30 observation afterwards (𝑛𝑎𝑓𝑡𝑒𝑟 = 30).
Classic Chow Break test:
We want to test whether there is a significant difference in the joint coefficients of the parameters. We start with two separate regressions, model (5.1) and (5.2), and saving their Sum of Squared Residuals (SSR). Next, with the Chow Break test we have the F-test following an 𝐹(𝑔, 𝑛 − 𝑘) distribution under the null hypothesis of constant parameters (5.3). 𝑦𝑖𝑡 = 𝛼𝑖 + 𝑥𝑖𝑡′ 𝛽 + 𝜀 𝑖𝑡 (5.1) 𝑦𝑖𝑡 = 𝛼𝑖 + 𝑥𝑖𝑡′𝛽 + 𝛼𝑖𝑎𝑓𝑡𝑒𝑟𝐷𝑖𝑡+ 𝑥𝑖𝑡′𝛽𝑎𝑓𝑡𝑒𝑟𝐷𝑖𝑡+ 𝜀𝑖𝑡 (5.2) 𝑤𝑖𝑡ℎ 𝐻0: 𝛼𝑖𝑎𝑓𝑡𝑒𝑟 = 𝛽𝑎𝑓𝑡𝑒𝑟 = 0 𝑎𝑛𝑑 𝐻𝑎: 𝑎𝑡 𝑙𝑒𝑎𝑠𝑡 𝑜𝑛𝑒 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑖𝑠 𝑛𝑜𝑡 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜 𝑧𝑒𝑟𝑜 𝐹 =(𝑆𝑆𝑅(1) − 𝑆𝑆𝑅(2))/𝑔 𝑆𝑆𝑅(1)/(𝑛 − 𝑘) ~𝐹(𝑔, 𝑛 − 𝑘) (5.3)
34 Chow Break test (F-test) and Break test (Wald test).
35 In this model, due to a small N, controlling for heteroscedasticity will be done using robust standard
27 In (5.3) 𝑔 = 14 are the number of restrictions and 𝑘 = 14 are the number of
explanatory variables36. Furthermore, SSR(1) and SSR(2) are the Sum of Squared Residuals under the null of (5.1) and (5.2)37 respectively. Furthermore, all the 𝑛 = 106 error terms are i.i.d.
We have a SSR(1) and SSR(2) of respectively 9.3234 and 5.8066 resulting in an 𝐹 = 2.480~𝐹0.05(14,92) ≈ 1.8208. So we can reject the null and conclude that there is at least one coefficient not equal to zero, and thus there is a structural difference between before and after a takeover.
Break test 2:
Next, investigating whether there is a significant difference in the coefficients of single parameters I have constructed model (III).
𝑦𝑖𝑡 = 𝛼𝑖𝑏𝑒𝑓𝑜𝑟𝑒+ 𝑥𝑖𝑡′𝛽𝑏𝑒𝑓𝑜𝑟𝑒+ 𝛼𝑖𝑎𝑓𝑡𝑒𝑟𝐷𝑖𝑡+ 𝑥𝑖𝑡′𝛽𝑎𝑓𝑡𝑒𝑟−𝑏𝑒𝑓𝑜𝑟𝑒𝐷𝑖𝑡+ 𝜀𝑖𝑡 (III)
𝑤𝑖𝑡ℎ 𝐻0: 𝛽𝑎𝑎𝑓𝑡𝑒𝑟−𝑏𝑒𝑓𝑜𝑟𝑒 = 0, 𝑎𝑛𝑑 𝐻𝑎: 𝛽𝑎𝑎𝑓𝑡𝑒𝑟−𝑏𝑒𝑓𝑜𝑟𝑒 ≠ 0 𝑎𝑛𝑑 𝐷𝑠ℎ𝑒𝑖𝑘ℎ = {1 𝑖𝑓 𝑐𝑙𝑢𝑏 ℎ𝑎𝑠 𝑏𝑒𝑒𝑛 𝑡𝑎𝑘𝑒𝑛 𝑜𝑣𝑒𝑟 𝑏𝑦 𝑖𝑛𝑣𝑒𝑠𝑡𝑜𝑟0 𝑖𝑓 𝑐𝑙𝑢𝑏 ℎ𝑎𝑠 𝑛𝑜𝑡 𝑏𝑒𝑒𝑛 𝑡𝑎𝑘𝑒𝑛 𝑜𝑣𝑒𝑟
In model (5.1), (5.2) and (III) we have the same dependent and explanatory
variables38 as before with no constant. This is because I have added dummies for the six clubs39 that have been taken over in the past 10 years by a rich investor as extra explanatory variables. Furthermore, in model (III) 𝐷𝑠ℎ𝑒𝑖𝑘ℎ is the dummy variable for the takeover by a rich investor. Lastly, the error term 𝜀𝑖𝑡 is i.i.d. over 𝑖 and 𝑡 and normally distributed. Note that in the null- and alternative hypothesis of (III) the beta
36
Average amount per arriving (avarr) and departing player (avdep), total number of players arrived (totnumarr) and departed (totnumdep), total number of expensive players arrived (exp1) and departed (expp1), total number of extremely expensive players arrived (exp2) and departed (expp2) and six dummies for the clubs: 𝑘 = 14. Furthermore, 𝐻0: 𝛼𝑖𝑎𝑓𝑡𝑒𝑟= 𝛽𝑎𝑓𝑡𝑒𝑟= 0, where 𝛼𝑖𝑎𝑓𝑡𝑒𝑟 are the six club dummies (after) and 𝛽𝑎𝑓𝑡𝑒𝑟 are the eight other explanatory variables (after); so 𝑔 = 14.
37
SSR(1) over all observations, SSR(2) over 𝑛𝑎𝑓𝑡𝑒𝑟 observations.
38
Dependent variable: average number of points per game (ptsx). Explanatory variables: average amount per arriving (avarr) and departing (avdep) player, total number of players arrived (totnumarr) and departed (totnumdep), number of expensive players arrived (exp1) and departed (expp1), the number of extremely expensive players arrived (exp2) and departed (expp2) and six club dummies.
39
28 has a lower index ‘a’, because we are only testing the coefficients of single arrival variables.
5. Results
Here I discuss the results of the research that has been done. In Section 5.1 I will discuss the OLS, Fixed Effects and the Arellano-Bond models. Next in Section 5.2 the results from the FE and AB with lagged explanatory variables will be compared. And finally in Section 5.3 the results from the Break tests will be discussed. In the Fixed Effects models the individual club- and time effects dummies are included, but not displayed in the tables. Furthermore, all the standard errors are robust since we clustered over clubs28.
5.1 Fixed Effect and Arellano-Bond
In Table A3 the results from OLS with (I) and without fixed effects are shown. A part of the outcome is as expected: an increase in average amount per arriving player has a significant positive effect in both models (at a 0.01 significance level). Moreover, the acquisition of expensive and extremely expensive players also has a positive
outcome40. Furthermore, in both models we see that the more players you buy at once, the less average points a club will yield. In both models these coefficients are
significant at a 0.01 level.
In contrast we see that the departure of a lot of players does not have a negative effect on the outcome in both models. For every player that a club sells the average points per game increases with 0.010 and 0.007 in the OLS and FE regression respectively (at a significance level 0.01). Note that in the OLS regression selling an expensive (super expensive) player also significantly increases the average points per game by 0.039 (0.157). With a mean of 1.613 for the average points per game41 this has a huge impact (at a 0.01 significance level).
We can conclude that slimming down your team has a positive outcome, and clubs should go for quality rather than quantity. We have seen that increasing the average amount per arriving player and the acquisition of (extremely) expensive
40 OLS: significance level 0.01 for expensive and extremely expensive;, FE: significance level 0.05 for
extremely expensive.
41
29 players has a positive effect. A club can improve their results even more by selling a lot of players, even “superstar” players (in the OLS estimation).
Next in Table 3 we see the results of the two main models: The Fixed Effects model with club dummies (I) (OLS estimation) and the Dynamic Fixed Effects model with the lagged dependent variable as an explanatory variable (II) (AB estimation).
The signs of the coefficients of the arrival variables are as expected. In both models increasing the average amount per player has a positive effect, but only significantly in the FE regression. Next, the acquisition of one extra player decreases the average points per game by 0.010 in both models at a significance level of 0.01 and 0.05 in the FE and AB respectively. Furthermore we can even spot a significant positive effect of 0.046 (0.057) buying expensive (extremely expensive) players in the AB estimation (FE estimation).
Dependent variable: average points per game
FE (I) Coefficient (Rob. Std. Error) AB (II) Coefficient (Rob. Std. Error) constant 1.696*** (0.153) 1.308*** (0.186)
average points per game (t − 1) 0.223**
(0.093) average arrival amount 0.019***
(0.006)
0.010 (0.008) average departure amount -0.002
(0.015)
-0.018 (0.015) total arrived players -0.010***
(0.003) -0.010** (0.004) expensive arrival 0.038 (0.023) 0.046* (0.024) extremely expensive arrival 0.057**
(0.025)
0.036 (0.036) total departed players 0.007***
(0.002) 0.005 (0.004) expensive departure 0.035 (0.022) 0.042 (0.027) extremely expensive departure 0.005
(0.038) -0.019 (0.040) N Number of instruments 𝐖𝐚𝐥𝐝 𝐂𝐡𝐢𝟐 𝐑𝟐 1001 0.575 765 127 43.29 (19)
30 In contrast, the signs of the coefficients of the departing variables are very peculiar. The more players a clubs sells, even (extremely) expensive players42, the more points per game, but increasing the average amount per departing player has a positive effect on the outcome. Here we have a contradiction: Sell as many players, also (extremely) expensive players, but try to lower the average amount per departing player. But then again, none of these coefficients are significant except for the positive effect of selling more players in the FE estimation. So the results of the departing side of the
regression are not reliable.
Finally, looking at the lagged dependent variable as an explanatory variable in the AB estimation, we see that the results of this year’s season have a positive effect on next year’s season. For every point on average gathered in the current season a club will score 0.233 more points per game in next season (at a 0.05 significance level). The positive effect is quite large, since the mean of the average points per game is 1.61341.
Comparing the two main models we can mainly draw conclusions on the arrival side of the regression. Clubs should lower the number of players they buy and invest in expensive (extremely expensive) players according to the AB model ( FE model). There is only no significant proof in the AB estimation that increasing the average amount per player leads to better results.
Next, we have found that the coefficient signs of the departing variables cause a contradiction, but none of these coefficients are significant. So looking at the FE and AB regressions we cannot confirm that selling (expensive) players has a significant effect on the average points per match. The results of the departing side of the regression are not reliable.
Lastly, good performances in the current season will improve the results of next year’s season. This latter result is to be expected since better results lead to more revenues, media attention and popularity, allowing them to improve their team even more with the increase in revenues.
42 Except for extremely expensive player in the AB estimation. Selling an extremely expensive player
31 5.2 Lagged explanatory variables
We are also interested in what effect current transfer policies have on next year’s results. In Table 4 we see the results from the Dynamic Fixed Effects model
(Arellano-Bond estimation), with the standard lagged dependent variable, with (AB lags hereafter) and without (AB hereafter, model II) lagged explanatory variables and the Fixed Effects regression (OLS estimation) with lagged explanatory variables (FE lags hereafter).
Looking at the number of players arrived we immediately see a significant43 decrease in average points of 0.008 and 0.009 for current season but an (insignificant) increase of 0.004 and 0.003 for next season in the AB (lags) and FE (lags)
respectively. So you could argue that new arrived players need to adapt to their new club and will realize more points on average in the next season. Although it is to be expected that players will perform better after a year of adjustment to their new team, there is no significant proof for this.
Next, we see that increasing the average amount per players is not only positive for current season but also for the next season. Looking at the coefficients of the lagged average amount per player we see an significant44 increase of 0.015 (0.027) average points per game in the AB (lags) (FE (lags)).
In Section 5.1 we had found that buying superstar players has a positive effect. We even found significant proof that buying expensive (extremely expensive) players increases the average points per game in the AB (FE) regression. But there is no significant proof in the AB (lags) and FE (lags) that buying (extremely) expensive players has a positive effect.
Furthermore, looking at the lagged variables for expensive players, we mostly see negative coefficient signs. As mentioned before, new players seem to need some time to adapt, but this does not apply to superstar players. They have a positive effect on current season outcome, but a negative effect on next year’s results. These are not expected results, but all coefficient of the superstar variables are not significant in both the AB (lags) and FE (lags) estimations.
43 AB (lags): significance level 0.05; FE (lags): significance level 0.01. 44
32
Dependent variable: average points per game
AB (II) Coefficient (Rob. Std. Error) AB (lags) Coefficient (Rob. Std. Error) FE (lags) Coefficient (Rob. Std. Error) constant 1.308*** (0.186) 1.307*** (0.211) 1.883*** (0.178) average points per game (t − 1) 0.223**
(0.093)
0.198** (0.098)
average arrival amount 0.010
(0.008)
0.013 (0.009)
0.021*** (0.006)
average arrival amount (t − 1) 0.015*
(0.008)
0.027*** (0.007) average departure amount -0.018
(0.015)
-0.018 (0.014)
0.003 (0.016) average departure amount (t − 1) -0.021
(0.015)
-0.017 (0.018) total arrived players -0.010**
(0.004)
-0.008** (0.004)
-0.009*** (0.003)
total arrived players (t − 1) 0.004
(0.004) 0.003 (0.003) expensive arrival 0.046* (0.024) 0.033 (0.025) 0.026 (0.024) expensive arrival (t − 1) 0.009 (0.026) -0.001 (0.027) extremely expensive arrival 0.036
(0.036)
0.015 (0.038)
0.011 (0.024) extremely expensive arrival (t − 1) -0.015
(0.039)
-0.001 (0.026)
total departed players 0.005
(0.004)
0.003 (0.003)
0.005* (0.003)
total departed players (t − 1) -0.001
(0.004) 0.001 (0.003) expensive departure 0.042 (0.027) 0.053** (0.026) 0.045** (0.023) expensive departure (t − 1) 0.023 (0.026) 0.016 (0.023) extremely expensive departure -0.019
(0.040)
-0.029 (0.037)
0.014 (0.039) extremely expensive departure (t − 1) -0.038
(0.029) -0.022 (0.030) N Number of instruments 𝐖𝐚𝐥𝐝 𝐂𝐡𝐢𝟐 𝐑𝟐 765 127 43.29 (19) 765 135 73.29 (17) 879 0.590 Table 4. AB, AB with lags expl. var. and FE with lags expl. var. ∗ 𝑝 < 0.10; ∗∗ 𝑝 < 0.05; ∗∗∗ 𝑝 < 0.01
33 Next, increasing the average amount per departing player has a negative effect in the next season, but insignificantly in both the AB (lags) and the FE (lags) estimations. In contrast with the AB and FE models, in the AB (lags) and FE (lags) the positive effect of selling an expensive player is significant. The departure of one expensive player results in 0.053 and 0.045 more points on average for the AB (lags) and FE (lags) respectively at a 0.05 significance level. This positive effect preserves in the next season, but these coefficients are not significant.
Lastly we see in both lagged models that selling extremely expensive players has a negative effect on the outcome of upcoming season (as expected), but is not significant. The lagged AB results confirm that performances of current season increase the average points per game of next season. With an increase of 0.198 per point, this increase is slightly less than in the AB regression, but still significant at a 0.05 significance level.
Concluding, increasing the average amount per player has significantly been proven to be a good investment not only for current season, but also for next year’s season. Next, the significant negative effect of increasing the number of arriving players turns into a positive effect in the upcoming season. So it seems that players need some time to adjust, but this has not been proven at a significant level.
Furthermore, selling expensive players increases the average points per game at a 0.05 significance level. This positive effect continues in the next season, but is not significant. These results are quite contrary to our expectations, as one would expect that selling an expensive player will reduce the quality of the team.
A reason could be that selling expensive players will give clubs the
opportunity to buy more “semi top players” and create a more balanced team, since departing expensive players generate a lot of money. For instance, a team with several semi top players will perform better than a team with 1 top player and 10 mediocre players.
5.3 Break tests 2
In Table 5 the regression results of the explanatory variables before and after takeover are shown. These results will be used to construct Break test 2. In the model the individual club dummies are included, but not displayed in the table.
34
Dependent variable:
average points per game
Break test (III) Coefficient (Rob. Std. Error)
before average arrival amount 0.042
(0.051) average departure amount -0.060
(0.076) total arrived players † -0.004
(0.013)
expensive arrival -0.008
(0.130) extremely expensive arrival † -0.583***
(0.200) total departed players -0.020* (0.012)
expensive departure 0.006
(0.159) extremely expensive departure 0.545**
(0.250)
after average arrival amount -0.033
(0.033) average departure amount -0.091
(0.071) total arrived players † -0.041***
(0.013)
expensive arrival 0.063
(0.082) extremely expensive arrival † 0.018
(0.155) total departed players 0.014
(0.016)
expensive departure 0.167*
(0.098) extremely expensive departure 0.280
(0.197) N
𝐑𝟐 0.979 106
Table 5. Break test, with dependent variable ptsx. Regression with Chelsea, Manchester City, Malaga FC, PSG, Monaco FC and Vitesse as club dummies and no constant. ∗ 𝑝 < 0.10; ∗∗ 𝑝 < 0.05; ∗∗∗ 𝑝 < 0.01; † coefficient ‘after’ is significant different from coefficient ‘before’
We see some unexpected signs of the ‘before’ coefficients. The number of expensive (insignificant) and extremely expensive (0.01 significance level) arriving players have a negative effect on the average number of points. In contrast, departing expensive (insignificant) and extremely expensive (0.05 significance level) players have a positive effect. For every extremely expensive player a club buys (sells) the average
