Importing Human Capital: The Effects of a
Foreign Football Manager on Club Performances
Alexander Schram
University of Amsterdam
Student number: 5935407 Supervised by: dr. J.C.M. van Ophem
Second reader: dr. M.J.G. Bun
December 17, 2014
Abstract
This empirical study investigates the effects on club performance of hiring a foreign football manager. First, we investigate the effects on seasonal results using both a fixed effects OLS and a random effects or-dered probit model. Ignoring the omitted variables bias, we find evidence that foreign managers have a positive effect on performance. This effect disappears, however, once the panel structure in the data is taken into account. We do find that, conditional on performance, the probability of getting the sack is higher for foreign managers than for local managers. The second part of this study shows the effect of sacking the manager on subsequent team performance. For this purpose we use a regression discontinuity design. The effect is estimated for all clubs with at least one within-season dismissal of the manager (the treatment group). The results show a positive effect of sacking the manager. However, we find the same effect in a control group consisting of evenly poor performing teams that did not sack their manager. We therefore attribute the perfor-mance effect not to managerial change, but instead to a classic example of regression to the mean.
1
Introduction
In modern organizations, managers are responsible for the day-to-day running of business. In this way, managers play a crucial role in organizational success or failure. However, measuring the quality of a manager’s work can be difficult in many businesses. There are several reasons underlying this lack of empirical evidence on managerial quality: (1) private firms are not required to reveal in-ternal data, and (2) many organizations are complex entities, where it is difficult to isolate the influence of a manager on organizational performance. Yet, there are various reasons why managers may fail; think of shirking, a lack of quality or bad luck.
An exception to this observation is the sports industry, which offers a more suitable environment to investigate manager quality. This is the case for various reasons. First, data are widely available on the output (results) of the manager’s work. Second, shirking seems unlikely in the sports industry, since club owners and directors are able to observe the production process every time a match is played, whereas this process might be much more complex and a lot less clearly defined in other industries. Furthermore, there is much more public attention in the sports industry than in others. Finally, in most sports, the number of managers is limited (often to only one) and responsibilities are clearly defined, which simplifies the isolation of any particular manager’s output. All this leads to a relatively clear measurement of managerial performance, and therefore to higher chance of being sacked after poor performance. In turn, this lowers the opportunity to shirk. Dismissing the manager has become such a regular phenomenon in football, that bookmakers offer odds for the next manager to be sacked. Third, firms in sports (clubs) are identical in several aspects: they produce the same output, compete under the same rules, and so on. They only differ in size1, for which one can control in statistical analyses, and have different owners and managers.
Being a football manager is probably one of the unsteadiest jobs one can get. In football, the manager is held responsible for the results of the team at all times. This means that a bad spell of results may lead to the manager being dismissed. Much research has been done on the effects of sacking the manager in the sports business. This paper contributes to this literature by investigating the effect of appointing a foreign football manager on club performances in European football. In theory, organizations only import employees from abroad if it increases human capital, which in turn increases performance. Aside from this effect on performance, we will also look at the probability of being sacked for both foreign and domestic managers.
The choice for a foreign employee is costly, (Bauer and Kunze [1]). First, obtaining a working permit could cause difficulties, although this is not likely to be the case in European football since most managers are from countries within the European Union. However, there are more specific difficulties, such as language problems and socio-cultural differences. For these reasons, orga-nizations are likely to only hire foreign workers if their qualifications outweigh these issues. Highly skilled workers tend to be costly, and importing a foreign manager is no exception. Therefore we expect that a club will only appoint a foreign manager if he is expected to significantly increase club performance.
An experimental study by Thomas and Ravlin [14] shows the existence of the Similarity-Attraction Paradigm2in a successful manager-employee relationship. Their results show that adaptation by a foreign manager to behaviours typical of native managers positively influenced the response by native employees: cultural adaptation resulted in higher levels of perceived similarity and higher perceived managerial effectiveness. This endorses the idea that extra effort is needed after appointing a foreign manager and hence further supports the hypothesis that an organization should only do so if it is expected to substantially increase performance.
When times are rough and results are disappointing, firing the manager is efficient if it increases the probability of winning subsequent matches3. The literature is ambiguous when it comes to this hypothesis. For example, De Dios Tena and Forrest [9] use an ordered probit model and find a modest positive difference in match results in Spanish football. This effect was entirely derived from an improvement in results in home matches. The authors argue that the home advantage is strengthened by sacking the manager after a series of poor results. By scapegoating the manager, the club lifts the morale of the supporters, which in turn boosts team performance. In contrast, Bruinshoofd and Ter Weel [3] use a difference-in-difference estimator and find that sacking a football manager is both ineffective and inefficient in Dutch football. They construct a control group of managers who on the basis of their performance could have been sacked but were not and a treatment group of managers who did get the sack. The current paper will partly build on these previous papers in analysing whether firing the manager has the desired effect, in particular when switching to a foreign manager.
In a related study, Dawson and Dobson [8] measure managerial efficiency
2The Similarity-Attraction Paradigm posits that people like and are attracted to others
who are similar, rather than dissimilar, to themselves. Similarity has also been related to positive outcomes other than attraction, such as trust and association, which may also play a key role in the success or failure of a professional relationship between manager and employee.
3Although clubs might also have a long term goal by sacking the manager, we consider a
in English professional football using stochastic frontier analysis. They find differences in efficiency across managers, which supports the idea that human capital is an important determinant of managerial performance. Their results show that the quality of a managers former career as a player and a prior affilia-tion with the current club have the strongest influence on managerial efficiency, while more experience as a manager in general is found to be less important. Generalizing to other industries, this would imply that initial specific experi-ence is more important than general working experiexperi-ence. Dawson and Dobson initially also include a dummy variable for managers from overseas (in other words, foreign managers), but drop it in their efficiency analysis. The current paper mainly focuses on this dummy variable by estimating its effect on club performances.
This paper examines the effects of appointing a foreign manager on the results of a football club using two approaches: a seasonal approach and a match-based approach. This allows us to compare the effects of a foreign manager on the (semi) long- and short run. In the seasonal approach, we first look at the probability of foreign and domestic managers being dismissed. Second, we focus on the effect of a foreign manager on two measures of success: the points earned in regular league matches and the final league ranking. We expect foreign managers to have a positive effect on results, hence we expect more points and a higher final league ranking. Note that for the seasonal approach, we consider the case where a club starts the season with a foreign manager. Thus the number of points and final league ranking are attributed to starting the season with a foreign or domestic manager, even though the manager may have been fired during the season. In the match-based approach, we investigate whether the probability of not losing the next match increases directly after the dismissal of the manager. We then check if there is any difference between clubs switching from a domestic to a foreign manager and vice versa. Again, we expect a positive effect of a foreign manager, hence an increase in the probability of not losing the next match, especially for clubs switching from a domestic to a foreign manager. The paper is organised as follows: Section 2 describes data and variables, Section 3 gives the model specifications, Section 4 lists the results and Section 5 concludes.
2
Data and variables
This section describes the data and variables of our analysis and is organized as follows: Section 2.1 describes the dataset for the research on seasonal results, while Section 2.2 gives an overview of the data and variables concerning the research based on match results.
2.1
Seasonal approach
For the seasonal approach, data was collected from Transfermarkt.de4. League results are collected for 24 countries for the seasons 2005-06 until 2013-14 for winter leagues and 2006 until 2013 for summer leagues5. The aggregate number of observations of league results is 3,331. For each of the seasons, we also collected information on the manager(s) and players of the clubs. Combining these with league results leads to our final dataset of 2,956 observations.
2.1.1 Dependent variables
The first dependent variable under consideration is a dummy variable sack which equals zero if the manager who started the season also finished it and one oth-erwise. Since a manager who underperforms is likely to be sacked by the board and successful managers are assumed to at least finish the season before consid-ering a move to another (bigger) club, we assume that all managers that leave before the end of the season have been sacked6. Table 1 shows the percentages of domestic and foreign managers leaving the club before the end of the season. Both for domestic and foreign managers, the percentage is close to 50%, with the percentage of sacked foreign managers being slightly higher.
Table 1: Percentage of managers sacked domestic foreign
not sacked 1,181 289
sacked 1,165 321
% sacked 49.7% 52.6%
Second, we measure performance by results per season. We take two mea-sures of team performance: (1) the total number of points earned during the season and (2) the position of the club in the final ranking of the league. Since every season takes on its own course, the total number of points does not al-ways reflect the same rate of success. For instance, when Martin Jol managed to collect 85 points in the 2009-10 Dutch Eredivisie campaign, AFC Ajax finished second behind FC Twente (86 points). In all four seasons thereafter, new man-ager Frank de Boer was able to become champion with fewer than 85 points.
4Transfermarkt is an independent website tracking results, transfers and the market values
of players in international football, see http://www.transfermarkt.de/.
5In most countries, the league runs from August until May the next year (winter league),
while others (Norway, Sweden and Russia until 2011) play during the summer due to weather conditions.
6In reality, some managers will have resigned instead of being sacked. However, successful
managers are not likely to resign and resignation is often motivated by outside pressure due to a string of bad results.
This shows that final league ranking may be a better measure of success than the total number of points earned.
In most of the countries considered, the league structure is a double round robin, in which each team plays the other teams twice (once at home and once away). The victor of each match is awarded three points, a draw yields one point to each team and the loser gets no points. The final ranking is based on the total number of points collected after playing each club twice. Leagues differ in rules when teams are level on points7 and the total number of teams competing.
Two league structures in the data are incompatible to the standard double round robin. First, starting in the 2009–10 season the format of the Belgium Pro League changed drastically. Playoffs were introduced after the regular season and the number of teams was decreased from eighteen to sixteen. Playoffs consist of the top six teams of the regular season playing each other twice for a total of ten additional games. Half of the points collected from the regular season plus the points from the playoffs then yield the final ranking. Second, a similar league structure was introduced in the Turkish S¨uper Lig at the start of the 2011-12 campaign. The only differences are that the number of teams was eighteen (instead of sixteen) while the number of clubs qualifying for the championship playoffs was four (instead of six). Therefore, the playoffs amounted a total of six additional games. Because both league structures still begin with a double round robin, it is natural to only consider the matches played during the regular season in our analyses.
Table 2: Correlation table Variables points position
points 1.000
position -0.8086 1.000
Based on 2956 observations.
Obviously, the final league rank of a team is correlated with the total number of points earned as can be seen in Table 2. Since a lower number of points yields a lower final league ranking, the correlation is negative. We find a correlation of -0.8086, which indicates a strong correlation, especially since position is a discrete variable. However, since every season takes on its own course, the correlation is not perfect. To illustrate the imperfect correlation between total number of points and final league ranking, Table 3 shows the minimum and maximum number of points collected by the national champions in the seasons considered in our dataset. It shows that in some countries, the variation across years in
7Most leagues either consider head-to-head records (for instance in Spain) or goal difference
Table 3: Minimum and maximum number of points collected by the champion
country min. max.
Austria 66 82 Belgium 65 77 Bulgaria 58 75 Croatia 62 92 Czech Republic 59 79 Denmark 62 81 England 80 91 France 76 89 Germany 69 91 Greece 70 86 Italy 76 102 Netherlands 71 86 Norway 53 69 Poland 50 77 Portugal 69 84 Romania 64 79 Russia 58 88 Scotland 78 99 Sweden 49 67 Switzerland 72 80 Serbia 51 80 Spain 76 100 Turkey 51 83 Ukraine 68 79
the number of points collected by the champion is quite large. For instance, we see a difference of as much as thirty points in Croatia, which equals ten league victories (approximately 30% of the total number of matches).
2.1.2 Explanatory variables
The most important explanatory variable in this study is the dummy variable foreign indicating whether or not the manager is from abroad. As can be seen in Table 4, there are quite some differences between countries in our dataset when it comes to the percentage of clubs starting the season with a foreign manager. For instance, the percentage of foreign managers is far below the European average of 20.6% in Croatia (3.4%), the Czech Republic (3.3%), Italy (7.2%) and the Netherlands (7.9%), while in countries such as Greece (48.1%) and Russia (42.5%) almost half of the managers is from abroad. In general, it seems as though Slavic countries are a lot less likely to appoint a foreign manager to start the season than other countries. Notice that a manager who works at a club for several seasons is counted for each season he starts. For instance, Ars`ene
Table 4: Percentage of foreign managers starting the season per country country foreign N Austria 31.2% 77 Belgium 30.2% 129 Bulgaria 11.1% 54 Croatia 3.8% 89 Czech Republic 3.3% 120 Denmark 23.5% 85 England 33.5% 179 France 16.2% 179 Germany 19.4% 160 Greece 48.1% 135 Italy 7.2% 180 Netherlands 7.9% 152 Norway 24.6% 114 Poland 8.6% 116 Portugal 12.2% 131 Romania 15.1% 119 Russia 42.5% 120 Scotland 12.5% 40 Sweden 16.8% 113 Switzerland 31.1% 90 Serbia 8.8% 102 Spain 29.1% 179 Turkey 23.6% 161 Ukraine 22.7% 132 Total 20.6% 2,956
Wenger was the manager of FC Arsenal in every season in our dataset, which means Wenger is observed nine times. Also, it is important to note that for these numbers, managers from England, Northern-Ireland, Scotland and Wales (Great Britain) are considered as domestic in each of those countries.
Table 5 shows the percentage of managers working abroad per origin country. Remarkably, there are no managers from Austria and Turkey working outside the borders of their origin countries. Furthermore, it seems that aside from the fact that clubs from the Netherlands are not likely to hire a foreign manager, as many as 28.9% of the Dutch managers work outside the Netherlands, indicating that Dutch managers are popular both in their home country and abroad. Also, with only 179 managers (6.1%) coming from outside the 24 European countries considered, it seems that European clubs are not likely to appoint a manager from outside Europe.
Table 6 shows that the percentage of foreign managers is reasonably stable across seasons for winter leagues. There seems to be no trend over time, with
Table 5: Percentage of managers from origin countries working abroad
origin country abroad N
Austria 0% 53 Belgium 15.1% 106 Bulgaria 14.3% 56 Croatia 11.3% 97 Czech Republic 12.9% 133 Denmark 8.5% 71 France 13.3% 173 Germany 30.6% 186 Great Britain 8.3% 168 Greece 1.4% 71 Italy 16.1% 199 Netherlands 28.9% 197 Norway 18.9% 106 Poland 1.9% 108 Portugal 21.2% 146 Romania 15.1% 119 Russia 12.7% 79 Sweden 23.0% 122 Switzerland 18.4% 76 Serbia 20.5% 117 Spain 21.1% 161 Turkey 0% 123 Ukraine 7.3% 110 Other 100% 179 Total 20.6% 2,956
percentages around the average of 20.6% for all winter leagues8. For summer leagues, there appears to be a decline in the percentage of foreign managers after the 2010 campaign. However, since there are not many summer leagues in our dataset (Norway, Sweden and Russia until 2011), these numbers are based on too few observations to jump to any sort of conclusion, especially since Russia has one of the highest percentages of foreign managers in the dataset. Naturally, then, the number of observations for summer leagues drops after Russia switched to a winter league after the 2011 campaign.
In addition to the dummy variable foreign, this paper considers the following explanatory variables. Besides the nationality of each manager, we also know his age. Almost all managers in football start their managing career after a career as a player. A playing career normally ends somewhere around the age of 35, followed by a short period as youth- or assistant trainer during which
8Winter leagues are denoted by combinations of two years in Table 6, while summer leagues
Table 6: Percentage of foreign managers per season season foreign N 2005-06 18.6% 226 2006-07 18.7% 273 2007-08 18.9% 286 2008-09 22.6% 296 2009-10 21.4% 308 2010-11 18.3% 301 2011-12 19.4% 310 2012-13 20.2% 327 2013-14 21.3% 314 2006 24.3% 37 2007 28.9% 38 2008 31.8% 44 2009 36.4% 44 2010 30.4% 46 2011 19.6% 46 2012 10.3% 29 2013 19.4% 31 Total 20.6% 2,956
courses must be followed at the nation’s football association. Table 7 shows the descriptive statistics of age, which are in line with this career path. We use age as a proxy for experience and expect experience of the manager to have a positive effect on performance.
To control for the different size of clubs, we need a proxy for each club’s financial status. Since data on finances in football are not widely available, we consider the aggregate market value, as given by Transfermarkt.de. This market value is the sum of the market values of the players in every season. The market value of a player is determined by various factors: performance, expected transfer sum, medial focus on the player and talent status. Based on these factors, the experts of Transfermarkt.de continuously discuss market values of nearly all professional football players around the world. At least twice a year they agree on a new value, which is then entered into the database. These experts are a mixture of data-scouts, experienced users, fans and moderators who are specially assigned to moderate the discussion on market values. It is important to realise that the market values are not to be seen as potential transfer fees, but merely represent the inherent value of a player for the club he is under contract at. Since football is the core business of a club, we assume that most clubs’ main investments aim at strengthening the squad and thus increase the market value of the selection. Table 7 shows the descriptive statistics. For better interpretation, we use total market value divided by 1,000,000 as a control
variable and of course we expect the market value to have a positive impact on performance.
We also include the variance of the market value of the players in each selection. This allows us to investigate whether or not a club is better off investing in a few highly valued players or in a selection of players of roughly the same value. This issue is fiercely debated by many experts. For example, Real Madrid’s president Florentino P´erez introduced a transfer strategy called Zidanes y Pav´ones when he first took control of the club in 2000. The strategy was to sign one major superstar per year (for instance Zinedine Zidane in 2001) and promote youth players to fill up the remainder of the selection (Francisco Pav´on was also added in 2001). Initially the Zidanes y Pav´ones strategy was successful, with Real winning the Spanish Primera Divisi´on in 2000–01 and 2002–03 and claiming the UEFA Champions League in 2001–029. However, subsequent seasons showed limited success on the pitch, with Real failing to win any trophy for three seasons after the 2002-03 campaign.
We also control for the age of the players. This variable will typically have an inverted U-shaped relationship with performance at the player level: early on, a player will improve his physical- and playing skills by gaining experience; later in his career the physical constraints outweigh the benefits of experience. Since most managers will try to find a balance between experienced players and youngsters, the distribution is peaked around the average of 24.4, as can be seen in Table 7. Since we take the average age of the selection, the inverted U-shaped relationship will be hard to find. We will however be able to observe whether it is beneficial for a club to have an above average age of the selection or not. Furthermore, we include the variance of the age of the players to see if clubs are better off with a balanced or unbalanced selection with regards to the age of the players. In football, it is generally believed that a selection should consist of a mix of talented (younger) and experienced (older) players, which suggests a positive relationship between this variance and team performance.
One could argue that a manager has an indirect effect on results by training and buying players and thus enhancing their market value. However, since we are only considering the market value and average age of the selection at the beginning of the season, this effect will be small and is not expected to bias our results. This study will not focus on the question whether foreign managers are better able to increase the total market value of a selection, but merely on whether foreign managers are able to achieve better results, conditional on the market value and average age of their selection at the beginning of the season.
Table 7: Descriptive statistics of the explanatory variables
age manager market value age selection
mean 48.0 49,300,000 24.4 median 47.2 21,300,000 24.4 sd 7.5 73,400,000 1.3 min 29.4 50,000 19.4 max 73.1 622,000,000 29.7 N 2,956 2,956 2,956
2.2
Match-based approach
For the match-based approach, data is taken from Infostrada Sports and Hy-percube Business Innovation. The data consists of matches played in seasons 2007-08 until 2013-14 (winter leagues) and 2007 until 2013 (summer leagues). We only consider results in domestic leagues, hence results in the European and domestic cups are omitted from the data. In total, the data consists of 99,902 observations, from which we sample both a treatment and a control group. In total, 22.5% of the league matches are coached by a foreign manager, which is close to the percentage of foreign managers found in the seasonal approach (20.6%). Note that each match is observed twice, both for the home and the away team, unless one of the managers is unknown (only 1.2% of the matches are in the data only once).
2.2.1 Treatment group
For the treatment group we consider league matches in seasons where there is at least one within-season dismissal of a manager of one of the clubs concerned. Again, there is assumed to be no difference in voluntary and forced resignation of the manager. In order to correctly interpret the results after the managerial change, we do not consider changes in the last five league games, since there may be nothing to play for in those matches or a disproportional pressure to achieve somewhat unrealistic goals like avoiding relegation when results have been poor all season. Furthermore, we only consider the first dismissal within a season, hence we do not include more than one managerial change per season per club.
In our treatment group, we consider the results of 33,629 league matches in seasons where a club switches to another manager. Of those matches, 13,316 were played before the switch and 20,313 after. Table 8 shows the number of managerial changes per league per season. The total number of clubs changing at least one manager within a season is reasonably stable from 2009-10 onwards
(around 150). Before then, data from some leagues are missing, which explains the lower number of managerial changes in those seasons. The total number of managers not finishing the season is well above the average of 37 in the English Championship, the Turkish S¨uper Lig, the Italian Serie A and B and the Spanish Primera and Segunda Divisi´on. Note that the total number of teams differs across leagues; hence we cannot straightforwardly conclude from these numbers that managers working in those leagues should fear for their job more than others.
Table 8 also shows the number of times a club switched from a domestic to a foreign manager and vice versa. The total number of changes from one to the other is quite similar (143 vs. 150). Obviously, both are far beneath the number of managerial changes from a domestic manager to another domestic manager, but above a change from foreign to foreign (570 vs. 63, not shown in Table 8). Hence given that a club was forced to switch to another manager during the season, a club chose a foreign manager 20.1% of the time when the first manager was domestic and 29.6% of the time when the first manager was also from abroad. Note that these switches imply no major changes to the total distribution of domestic/foreign managers, since before the switch there were 570 + 143 = 713 domestic and 150 + 63 = 213 foreign managers about to get the sack, while after the switch 570 + 150 = 720 domestic and 143 + 63 = 206 foreign managers took over. Since all other managers were not replaced, the total distribution remains almost exactly the same. In our treatment group, 23.6% of the matches are coached by a foreign manager.
2.2.2 Control group
A potential pitfall for this study is the fact that results are typically bound to get better after a string of bad results: a positive effect after the dismissal of the manager might be incorrectly attributed to the managerial change, while in fact we only confirm a well-known phenomenon called regression to the mean. Therefore, we construct a control group of clubs who had similar poor results as in the treatment group, but did not sack the manager. The data provides an excellent way to construct such a control group, since for every match we also know the Euro Club Index (ECI) score of both teams. The ECI is a ranking of football teams of all European countries and is developed by Hypercube Business Innovation. It shows the relative strengths of European football teams at any given point in time and is updated after every match. For a detailed description of the ECI, see Appendix C.
To construct the control group, we first look at the average loss of ECI points at the moment a club fires its manager during a season. Thus for each club in
T able 8: Num b er of managerial changes p er league p er season Coun try League 2007-08 2008-09 2009-10 2010-11 2011-12 2012-13 2013-14 T ota l Austria Bundesliga 1 [0] (0) 3 [0] (1) 3 [1] (1) 3 [0] (0) 2 [1] (0) 5 [0] (1) 4 [0] (1) 21 [2] (4) Belgium Jupiler Pro League 8 [3] (1) 6 [3] (0) 5 [0] (1) 4 [2] (0) 6 [1] (2) 8 [1] (1) 8 [2] (3) 45 [12] (8) Denmark Sup erligaen 1 [0] (0) 7 [0] (1) 3 [0] (0) 5 [0] (1) 4 [1] (2) 1 [0] (0) 3 [1] (0) 24 [2] (4) England Premier League 8 [1] (2) 7 [1] (1) 5 [3] (1) 5 [2] (2) 4 [2] (1) 5 [1] (1) 7 [1] (1) 41 [11] (9) England Championship 3 [0] (1) 8 [2] (1) 10 [2] (4) 10 [2] (3) 7 [1] (1) 12 [1] (2) 10 [3] (2) 60 [11] (14) F rance Ligue 1 5 [1] (0) 5 [0] (0) 3 [0] (1) 3 [2] (0) 5 [2] (1) 3 [0] (1) 5 [1] (1) 29 [6] (4) F rance Ligue 2 6 [1] (2) 4 [0] (1) 4 [1] (1) 6 [0] (1) 6 [1] (0) 26 [3] (5) German y Bundesliga 4 [1] (0) 3 [0] (2) 6 [1] (2) 8 [1] (3) 7 [3] (0) 5 [0] (1) 4 [2] (0) 37 [8] (8) German y 2. Bundesliga 2 [1] (0) 8 [1] (0) 10 [1] (0) 5 [1] (0) 9 [0] (1) 7 [2] (0) 8 [1] (1) 49 [7] (2) German y 3. Liga 7 [1] (0) 7 [1] (1) 7 [2] (1) 9 [0] (3) 30 [4] (5) Italy Serie A 5 [0] (0) 7 [0] (0) 10 [1] (0) 9 [1] (0) 7 [0] (1) 8 [0] (1) 8 [2] (2) 54 [4] (4) Italy Serie B 9 [0] (0) 8 [0] (0) 9 [0] (0) 8 [0] (0) 9 [0] (0) 43 [0] (0) Netherlands Eredivisie 5 [0] (0) 7 [2] (0) 4 [0] (1) 4 [1] (0) 5 [1] (1) 2 [1] (1) 4 [1] (0) 31 [6] (3) Netherlands Jupiler League 1 [0] (0) 6 [0] (0) 4 [0] (1) 5 [0] (0) 5 [1] (0) 4 [0] (0) 6 [0] (1) 31 [1] (2) P oland Ekstraklasa 1 0 [2] (0) 9 [3] (2) 8 [1] (3) 4 [1] (0) 10 [4] (2) 41 [11] (7) P ortugal Primeira Liga 6 [0] (0) 6 [0] (4) 10 [3] (0) 8 [0] (2) 8 [0] (1) 5 [0] (0) 6 [1] (0) 49 [4] (7) Russia Premier League 10 [3] (4) 6 [3] (1) 13 [1] (3) 29 [7] (8 ) Scotland Premie rs h ip 4 [2] (1) 1 [1] (0) 6 [1] (2) 4 [0] (0) 4 [3] (0) 3 [0] (1) 2 [0] (1) 24 [7] (5) Spain Primera Divisi´ on 7 [0] (1) 8 [2] (3 ) 8 [1] (1) 7 [2] (0) 9 [1] (3) 7 [0] (1) 4 [2] (1) 50 [8] (10) Spain Segunda Divisi´ on 13 [1] (1) 9 [0] (0) 10 [0] (0) 10 [1] (1) 11 [0] (0) 53 [2] (2) Switzerland Sup er League 2 [1] (0) 5 [2] (1) 2 [0] (1) 4 [1] (0) 4 [1] (0) 7 [0] (3) 2 [0] (0) 26 [5] (5) Switzerland Challenge League 3 [2] (0) 5 [0] (2) 6 [3] (0) 4 [1] (2) 4 [1] (1) 3 [0] (0) 5 [1] (1) 30 [8] (6) T urk ey S ¨up er Lig 7 [1] (2) 11 [1] (1 ) 5 [0] (1) 10 [0] (3) 9 [2] (3) 10 [1] (2) 11 [1] (3) 63 [6] (15) 2007 2008 2009 2010 2011 2012 2013 T otal Norw a y Tipp eligaen 4 [1] (1) 2 [0] (1) 4 [0] (1) 1 [0] (0) 2 [1] (0) 0 [0] (0) 13 [2] (3) Russia Premier League 9 [1] (5) 3 [1] (1) 12 [2] (6) Sw eden Allsv ensk an 2 [0] (1) 1 [0] (1) 2 [1] (0) 3 [1] (0) 3 [0] (1) 3 [1] (1) 1 [1] (0) 15 [4] (4) T otal 74 [13] (9) 108 [16] (19) 151 [23] (26) 145 [22] (21) 151 [27] (28) 141 [16] (21) 156 [26] (26) 926 [143] (150) T otal n um b er of clubs sw itc hing at least o nc e within a season: total, [domesti c to foreign] and (foreign to domestic) p er league.
the treatment group, we compare the clubs ECI score at the first dismissal to the ECI score at the beginning of the season (the first league match). Note that this way, we also control for the size of the club, since bigger clubs start the season with a higher ECI score and lose more points following a bad result. Taking only match results would not differentiate between a major club like Real Madrid losing twice in a row compared to a small club such as Sporting Gij´on. On average, the first within season dismissal of the manager came after losing approximately 65 points on the ECI ranking. Hence the control group consists of all matches played in seasons where a club lost 65 ECI points compared to the first match for the first time during a season and did not sack the manager. In total, the control group consists of 28,810 matches, with 10,397 matches played before the loss of 65 points and 18,413 after. The percentage of matches played before is similar to that in the treatment group (36.1% compared to 39.6%). Only 19.2% of the matches in the control group were coached by a foreigner, compared to 23.6% in the treatment group.
2.2.3 Dependent variables
Our main focus in this part of the study is the probability of collecting points from a match by either a win or a draw directly after the dismissal of the man-ager. Our dependent variable is the dummy variable not losing, which equals one if the number of goals scored by the team is greater than or equal to the number of goals scored by the opponent and zero otherwise. Table 9 shows the distribution of the result of the matches in the total sample, the treatment and the control group. The fact that there are a few more wins than losses in the total sample is because not every match is present twice (data on managers is incomplete for some teams). We see that 26.3% of the matches end in a draw, meaning that 73.7% of the matches is won by one of the teams. Not surprisingly, the percentage of losses is greater in the treatment group, since the treatment group contains all matches from seasons where there was a managerial change, which is likely to be caused by disappointing results. The percentage of matches ending in a draw is very close to that in the total sample. On the other end, the distribution in the control group is surprisingly similar to the total sample, while we expected it to be more like the treatment group. It appears that big-ger clubs are more present in the control group, since such clubs lose more ECI points per lost match.
Secondly, one could argue that the strength of the opponent is crucial to our analysis. It could be the case that a manager is sacked after a string of bad results against a series of strong teams, while his successor faces weaker oppo-nents immediately after his appointment. Therefore, we also take the quality of
Table 9: Distribution of match results
Total sample Treatment group Control group
loss 36,721 36.8% 14,281 42.5% 10,770 37.4%
draw 26,288 26.3% 8,931 26.6% 7,551 26.2%
win 36,893 36.9% 10,417 31.0% 10,489 36.4%
total 99,902 33,629 28,810
the opponent as a dependent variable. If the above scenario is true, we expect to see a fall in opponent quality. To measure the strength of the opponent, we again use the ECI score, but now of the opposing team. Because the ECI value of a team is updated after every match, it provides a good proxy for the playing strength of the opponent per match.
Table 10 gives the descriptive statistics of the ECI per league in our dataset. It shows the relative playing strength of each league, but more importantly a degree of the inequality between teams within each league. For instance, it shows a large gap between the top and bottom teams in the English Premier League and the Spanish Primera Divisi´on. In general, it seems that teams are more evenly matched in lower leagues than in a country’s top division. It also shows quite a large overlap between the worst team in the top division and the best team in the lower division for each country where lower leagues are available, but one should note that this is not necessarily true for each season since the reported maximum and minimum are based on all seasons. The inequality within each league shows the importance of checking the strength of the opponent to exclude the scenario that a team faces weaker opponents after the dismissal of the manager.
2.2.4 Explanatory variables
In a regression discontinuity design such as ours, there are two explanatory variables: treat and treatday. The dummy variable treat equals zero for all observations up to and including the final game before the dismissal of the first manager and one after. As mentioned before, there are 13,316 observations where treat equals zero and 20,313 where it equals one, indicating that on average the first within season dismissal happens before the season is halfway (although one should note that these numbers do not include dismissals in the last five league games). The coefficient of treat gives the effect of the managerial change on the probability of not losing the following match.
The other explanatory variable treatday contains the number of days to or from the first managerial change. Hence when treat equals zero, treatday is negative and counts down to the managerial change, while it is positive and
Table 10: Descriptive statistics: ECI per league
Country League mean sd max min
Austria Bundesliga 1,828 391 2,788 850
Belgium Jupiler Pro League 1,954 380 2,912 1,073
Denmark Superligaen 1,867 333 2,792 1,058
England Premier League 2,660 575 4,094 1,467
England Championship 1,651 229 2,368 1,086 France Ligue 1 2,406 420 3,684 1,377 France Ligue 2 1,594 216 2,365 912 Germany Bundesliga 2,538 437 4,230 1,465 Germany 2. Bundesliga 1,566 305 2,404 964 Germany 3. Liga 1,066 183 1,689 620 Italy Serie A 2,497 438 3,854 1,462 Italy Serie B 1,519 245 2,255 920 Netherlands Eredivisie 2,137 407 3,111 1,322
Netherlands Jupiler League 1,106 274 1,827 583
Norway Tippeligaen 1,776 319 2,519 574
Poland Ekstraklasa 1,500 322 2,430 917
Portugal Primeira Liga 2,258 450 3,598 1,564
Russia Premier League 2,304 373 3,200 1,542
Scotland Premiership 1,684 427 2,797 740
Spain Primera Divisi´on 2,726 559 4,520 1,792
Spain Segunda Divisi´on 1,805 243 2,640 1,281
Sweden Allsvenskan 1,694 351 2,406 796
Switzerland Super League 2,023 376 2,892 1,161
Switzerland Challenge League 1,049 298 1,890 533
counting upwards thereafter. The coefficient of treatday does not have a causal interpretation, but does show the trend in performance before and after the switch. The descriptive statistics given in Table 11 confirm the thought that the first managerial dismissal is before half of the season has passed, since on average there are 78.8 days before and 101.6 days after.
Table 11: Descriptive statistics: treatday by treat
mean sd min max N
treat = 0 -78.8 59.3 -289 13,316
treat = 1 101.6 70.0 388 20,313
3
Model specifications
Many of the models used in this study are extensively described in Cameron and Trivedi [5]. This section gives an overview of the models for both the seasonal approach (Section 3.1) and the match-based approach (Section 3.2). Estimation of the models is done using Stata and results are discussed in Section 4.
3.1
Seasonal approach
3.1.1 Ordinary Least Squares
For all our dependent variables in the seasonal approach (sack, points and posi-tion), we first estimate the coefficients of our explanatory variables by standard OLS. All models are identically given by
y = Xβ + u,
where y is an N × 1 vector of dependent variables, X is an N × K matrix of regressors, and u is an N × 1 error vector. The OLS estimator is defined as the estimator that minimizes the sum of squared errors and is probably the most widely used estimator. It is given by
ˆ
βOLS= (X0X)−1X0y.
For a detailed study of the properties of the OLS estimator, see Cameron and Trivedi [5].
To illustrate our use of the OLS estimator, we consider model (5) for depen-dent variable points, for which results are given in Section 4.1.2. All other OLS models ((1), (4), (7) and (8)) are similar to this model and therefore moved to
Appendix A. Model (5) for each observation i is given by
pointsi= β0+ β1foreigni+ β2age manageri+ (5) + β3age selectioni+ β4Var [age selection]i+
+ β5market valuei+ β6Var [market value]i+ ui,
for which both the dependent and explanatory variables are described in Section 2.1. One problem with this approach is the possibility of correlated errors, which would violate standard assumptions for the OLS model. In our case, errors might be correlated between observations of the same club and observations from the same league. This is dealt with in Section 3.1.5.
3.1.2 Probit and random effects probit
As discussed in Section 2.1, the first research question under consideration is whether the probability of dismissal is different for foreign managers. Because we are dealing with a binary dependent variable, we estimate the coefficients of model 2 using a probit model. For binary outcome data the dependent variable y takes one of two values. In our case, manager i gets the sack with probability pi and gets to keep his job with probability 1-pi:
sacki= (
1 with probability pi 0 with probability 1-pi
The probit model estimates the probability p, which depends on the regres-sor vector x and a K × 1 parameter vector β. Our regresregres-sor vector x consists of our dummy variable foreign. Since we know that bad results (a low number of points) are a reason for dismissal, we also include points as a control variable. We add the market value of the selection to investigate if higher market values lead to a higher chance of getting fired. We expect this to be the case, since higher market value will increase the expectations of both the executives and fans and we expect disappointing results to be more detrimental for the man-ager’s position when expectations are high. Lastly, dummy variables for each season are added to see if in some seasons, the probability of getting the sack is significantly higher than in others. The probit model specifies the conditional probability pi ≡ Pr(yi = 1|xi) = F (x0iβ) = = Φ(x0iβ) = Z x0iβ −∞ φ(z)dz,
where Φ(·) is the standard normal cumulative distribution function. Estimation of β is done by maximum likelihood which maximizes our log-likelihood function
LN(β) = N X
i=1
{sacki· ln Φ(β0+ β1f oreigni+ β2pointsi+ (2) + β3market valuei+ βsdummy seasons)+
+ (1 − sacki) ln Φ(1 − (β0+ β1f oreigni+ β2pointsi+ + β3market valuei+ βsdummy seasons))},
where βs is a 17 × 1 vector of parameters consisting of the seasonal dummies. The resulting coefficients are not interpreted the same way as in OLS. For probit models, the marginal effects are ∂pi/∂xij = φ(x0iβ)βj and are easily calculated using Stata.
Because our data has both a cross-sectional and a temporal structure we also use the natural extension of the probit model for panel data: the random effects probit model (model 3). Now we consider
pit≡ Pr(yit= 1|xit, β, νi) = Φ(νi+ x0itβ),
where Φ(·) is the standard normal cdf. Note that the subscript has changed from i to it. The random effects MLE assumes that the individual effects are normally distributed, with νi∼ N [0, σ2ν]. Using random effects we assume that the individual specific effects are uncorrelated with the explanatory variables. It maximizes the panel-level likelihood with respect to β and σ2
ν: N X i=1 ln Z Φ(yit|Xit, νi, β) · 1 p2πσ2 ν exp−νi 2σ2 ν 2 dνi (3)
where Φ(·) is the standard normal cdf. There is no closed-form solution to the log-likelihood of model (3), but Stata is able to compute it numerically. Unfortunately, no fixed effects probit estimator exists, as discussed by Greene, Han and Schmidt [11]. Fixed effects might be more appropriate, since the fixed effect assumption is that the individual specific effects are correlated with the explanatory variables, which in our case could be true. For instance, the total market value of the selection could be correlated with the financial capabilities of a club.
3.1.3 Fixed Effects
Since we observe the number of points collected by a team over several years, we also consider another panel data regression technique to further exploit the
data on seasonal results. There are two kinds of information in our panel data: the cross-sectional information reflected in the differences between clubs, and the within-subject information reflected in the changes within clubs over sea-sons. OLS may not be optimal, because the estimated coefficients are likely to suffer from the omitted variable bias. This bias is a problem that arises when there are unknown variables that cannot be controlled for, but that do affect the dependent variable. Using panel data regression techniques, it is possible to control for the omitted variable bias without observing these variables, by observing changes in the dependent variable over time. This controls for omit-ted variables that differ between cases but are constant over time (fixed effects, considered in this section).
Our fixed effects model is given by
pointsit= αi+ β1f oreignit+ β2age managerit+ (6) + β3age selectionit+ β4Var [age selection]it+
+ β5market valueit+ β6Var [market value]it+ it
where the individual-specific effects αi measure unobserved heterogeneity that are possibly correlated with the regressors. The fixed effects esimator ˆβF E is estimated by subtracting the time-averaged model ¯yi= αi+ ¯x0iβ + ¯i from the original model. The estimator is given by
ˆ βF E= hXN i=1 T X t=1 (xit− ¯xi)(xit− ¯xi)0 i−1XN i=1 T X t=1 (xit− ¯xi)(yit− ¯yi),
which can be estimated by OLS. We are mainly interested in the coefficients of β10. Interpretation of the estimated coefficients is similar to OLS. Model (6) incorporates possible correlation of the errors at the club level, but again we also cluster the errors at a league level (see Section 3.1.5).
3.1.4 Ordered probit and random effects ordered probit
Lastly, one could also argue that the final league ranking is a natural ordering of alternatives, which calls for a model that takes into account this ordering, such as an ordered probit model. Ordered probit is a generalization of the probit analysis to the case of more than two outcomes of an ordinal dependent variable, in this case the final league position. The starting point of our ordered probit
10The individual specific effects α
iare easily calculated by ˆαi = ¯yi+ ¯x0iβˆF E but are not
of particular interest. They include omitted variables that differ between clubs and are a measure of the size of each club. The estimated variables show a positive correlation of 0.6982 with the average ECI score of the club. For a detailed description of the ECI, see Appendix C.
model is
yi∗= x0iβ + ui,
where yi∗ is not directly observed and xi does not contain an intercept. As y∗ crosses a series of increasing thresholds we move up in the ordering of alterna-tives of position, the observed yi. Now consider a league consisting of C clubs. Then for our C-alternative ordered probit model, we define
yi = j if αj−1< yi∗≤ αj,
where j = 1, . . . , C and α0 = −∞ and αC = ∞. The ordered probit model is a parameterization of both the coefficients β and the thresholds α. For the probability pij we know that
pij ≡ Pr[yi= j] = Φ(αj− x0iβ) − Φ(αj−1− x0iβ), (◦) where Φ(·) is the standard normal cdf. Estimation is by maximum likelihood of the log-likelihood function
LN = N X i=1 C X j=1 1(yi= j) ln pij, (9)
where pij is defined as in ◦ and 1(·) is the indicator function indicating if po-sition equals j. Maximization of (9) over the parameters yields the maximum likelihood estimators ˆβ, ˆα1, . . . , ˆαC−1.
Again, the interpretation of the coefficients requires some attention. We can interpret the sign and significance of the ˆβ’s as usual. For marginal effects we now have
∂ Pr[yi= j] ∂xi
= φ(αj−1− x0iβ) − φ(αj− x0iβ)β,
where φ(·) is the standard normal probability density function. Stata computes these marginal effects and the interpretation is given in Section 4.1.3.
Lastly, we estimate the coefficients of our explanatory variables using a panel data approach by including random effects in the ordered probit model. For a detailed study of the random effects ordered probit model, see Crouchley [7] and Boes [2]. The starting point of model (10) is
y∗it= x0itβ + νi+ uit,
where y∗it is not observed, the added random effects νi are independent and identically distributed N (0, σ2ν) and errors uit are independent of νi. We do
observe position, which is given by yit: yit= 1 if yit∗ ≤ α1 2 if α1< y∗it≤ α2 .. . C if yit∗ > αC−1
where just as before the α’s represent the thresholds. Now similar to ◦, we can derive the probability of observing outcome j for response yitas
pitj ≡ Pr[yit= j] = Φ(αj− x0itβ − νi) − Φ(αj−1− x0itβ − νi), (◦◦) where Φ(·) is the standard normal cdf. The random effects MLE is very similar to our random-effects probit model given in Section 3.1.2, but now we maximize the panel-level log-likelihood with respect to β, σ2
ν and thresholds α: N X i=1 ln Z Φ(yit|Xit, α, νi, β) · 1 p2πσ2 ν exp−νi 2σ2 ν 2 dνi, (10)
where Φ(·) is the standard normal cdf. Again, there is no closed-form solution to the likelihood function of model (10), but Stata computes it numerically using a C-point Gauss-Hermite quadrature approximation.
3.1.5 (Non-nested) Two-way clustering
In order to conduct accurate statistical inference, it is important to estimate the standard errors correctly, as argued by Cameron, Gelbach and Miller [4]. The main potential problem is the posibility of correlated errors. Controlling for clustering is very important, as failure to do so can lead to underestimation of the standard errors and consecutively the acceptance of non-significant estimation results.
Our data asks for two-way clustering since errors are likely to be non-independent at both a cross-section level and a temporal level: non-non-independent over both clubs and seasons per league. For leagues, points (and thus position) are always gathered at the expense of another club in the same league, hence errors will be correlated within leagues. Each observation belongs to his own group of observations per club c ∈ {1, 2, ..., C} and to a group of clubs in the same season per league s ∈ {1, 2, ..., S}. Now consider a basic model
yics = x0icsβ + uics
observation of C clusters and s denotes the sthobservation of S clusters. Now for the error term, we assume that
E[uicsujc0s0|xics, xjc0s0] = 0 unless c = c0 or s = s0.
For non-cluster-robust standard errors to be correct, we assume they are uncorrelated. However, if errors belong to the same group in any of our two dimensions, they may very well be correlated. This might bias the standard errors and hence upset statistical interference.
For our two-way clustering, the variance estimator uses those elements of ˆ
uˆu0 with ˆu = y − X ˆβ where the ith and the jth observation share a cluster in one or both of the dimensions. Now we can estimate
ˆ
B = X0(ˆuˆu0× SCS)X ()
where SCS is an N × N indicator matrix with ijth entry equal to one if the ith and jth observation share a cluster and zero otherwise. This allows us to estimate the cluster-robust variance matrix
ˆ
V [ ˆβ] = (X0X)−1B(Xˆ 0X)−1. () Since Stata allows one to calculate cluster-robust standard errors for one-way clustering, we use the following decomposition of SCStaken from Cameron, Gelbach and Miller [4]:
SCS= SC+ SS− SC∩S, ( )
where SC is an N × N indicator matrix with ijth entry equal to one if the ith and jthobservation belong to the same cluster c ∈ {1, 2, ..., C}, SS is an N × N indicator matrix with ijth entry equal to one if the ith and jth observation belong to the same cluster s ∈ {1, 2, ..., S}, and SC∩S is an N × N indicator matrix with ijth entry equal to one if the ith and jth observation belong to the same cluster c ∈ {1, 2, ..., C} and the same cluster s ∈ {1, 2, ..., S} and zero otherwise. Now we substitute into to get
ˆ
Finally, substituting ? into yields ˆ
V [ ˆβ] = (X0X)−1X0(ˆuˆu0× SC)X(X0X)−1+ (??) + (X0X)−1X0(ˆuˆu0× SS)X(X0X)−1+
− (X0X)−1X0(ˆuˆu0× SC∩S)X(X0X)−1,
our two-way cluster-robust variance matrix. Note that in panel data regressions such as our fixed effects regression, we are dealing with non-nested cluster-ing, since the clustering at the league level is non-nested within the panel-level (club). Stata is able to compute all three elements of our cluster-robust variance matrix given by ?? seperately. Stata commands and programming methods are described in Appendix B.
3.2
Match-based approach
3.2.1 Regression Discontinuity Design
In our regression discontinuity design, we estimate the effect of a managerial change on the probability of not losing the next match. First, estimation is done by OLS, as briefly described in Section 3.1.1. In the match-based approach, the model is given by
not losingi= β0+ β1treati+ β2treatdayi+ ui,
for which both the dependent and the explanatory variables are described in Section 2.2. As a robustness check, we also evaluate the model without the results of matches played in the last thirty days prior to the managerial change in the treatment group and prior to the loss of 65 ECI points in the control group (the ‘donut’ estimation). To check whether there is a difference in the playing strength of the opponent directly after the dismissal of the manager, we also evaluate the following model:
ECI opponenti= β0+ β1treati+ β2treatdayi+ ui.
In these models, we again have to be cautious for the possibility of correlated standard errors. Details are given in the next section.
One of the major benefits of a regression discontinuity design is that it offers a ideal platform for graphical analysis. Not only can we plot the linear fit of the OLS models, we can also do a robust locally weighted regression. Robust locally weighted regression is a method for smoothing a scatterplot. Consider our data (xi, yi) with i = 1, . . . , n, where x is the number of days since the arrival of the
new manager and y is the possibility of not losing the match. The fitted value at xk is the value of a polynomial fit to the data using weighted least squares, where the weight for each observation is large if xi is close to xk and small if it is not. For a detailed study of robust locally weighted regression, see Cleveland [6].
Lastly, since not losing is a binary dependent variable, we check if the OLS estimates are reasonable by performing a probit model. A more detailed de-scription of a probit model is given in Section 3.1.2. In this section, estimation is done by maximum likelihood which maximizes the log-likelihood function
LN(β) = N X
i=1
{not losingi· ln Φ(β0+ β1treati+ β2treatdayi+
+ (1 − not losingi) ln Φ(1 − (β0+ β1treati+ β2treatdayi))} with respect to β. In order to compare the coefficients of this probit model to the OLS estimates, we have to look at the marginal effects. Once again, we have to be wary of the possibility of correlated errors, which is discussed in the next section.
3.2.2 Two-way clustering
In Section 3.1.5, we describe the necessity and theory underlying two-way clus-tering. In order to conduct correct statistical interference, we also need to correctly cluster the standard errors in the match-based approach.
In our total sample, each match is represented by two observations: one for the hometeam and one for the awayteam. Although both observations are not necessarily part of either the treatment or the control group, some matches will be present twice. For instance, if two teams from the same league have sacked their manager during a particular season, their two mutual matches from that season will both be in the treatment group twice. Obviously, the standard errors of these matches are correlated, requiring clustering on matches.
In addition, the results of one team are correlated with those of any other in the same league. A strong team will win most of its league matches, while weaker teams are condemned to struggle for success week in week out. Therefore, the errors might also be correlated at a team level. To control for this correlation, we cluster the standard errors both on a match and a team level in the match-based approach.
4
Results
This section presents the results of our study. First, we describe the effect of foreign managers on seasonal results in Section 4.1. This is done for our dependent variables sack, points and position. Next, the results of our match-based approach are given in Section 4.2.
4.1
Seasonal approach
4.1.1 Probability of getting the sack
First we estimate whether the probability of getting the sack is different for foreign managers than for domestic managers. We estimate the probability using both the OLS and probit models given in Section 3.1. Results are given in Table 12. Insignificant coefficients of seasonal dummies are not given in the table, but are included in the models. Note that the standard errors in models (1), (2) and (3) are robust since we clustered over clubs. For these models, it is not necessary to use two-way clustering as discussed in Section 3.1.2, since errors are not likely to be correlated at a league level.
The sign of the coefficient for points is as expected in all models: more points decreases the probability of getting fired. Remarkably, the market value of the selection plays no significant role in models (1) and (2), while it is highly significant and positive in model (3), where the sign is as expected: a higher market value of the selection seems to lead to a higher probability of getting the sack conditional on the number of points. More importantly, our results show that foreign managers are more likely to be fired. Note that in probit models, the interpretation of the coefficients is not as straightforward as in standard OLS. Although we can interpret the sign and significance of a coefficient the same way, we cannot directly interpret its magnitude. By looking at the margins fixed at the 25th percentile value of points (35.5) given in Table 13, we conclude that 52.8% of the foreign managers would have been given the sack during a season where only 35.5 points where earned, while only 38.6% of the domestic managers would suffer the same fate.
The random effects probit estimation of model (3) also allows us to predict the probability of a manager getting the sack conditional on the number of points earned that season. To illustrate the fragile position of a foreign manager, we highlight the case of Ars`ene Wenger (born in Strasbourg, France). Wenger is the manager of (the London-based team) FC Arsenal for all nine seasons in our data. Figure 1 shows the probability of Ars`ene Wenger getting the sack for each season of the English Premiership. It shows both the actual estimated probability (Wenger is a foreign manager) and the hypothetical estimated probability (if
Table 12: Estimation results on dependent variable sack
(1) (2) (3)
Variable(a) Coefficient Coefficient Coefficient
(Rob. Std. Err.) (Rob. Std. Err.) (Rob. Std. Err.)
foreign 0.074∗∗ 0.199∗∗ 0.142† (0.026) (0.072) (0.078) points -0.009∗∗ -0.025∗∗ -0.040∗∗ (0.001) (0.003) (0.003) market value 0.0002 0.0004 0.002∗∗ (0.0002) (0.0005) (0.0006) dummy 2006 -0.124 -0.332 -0.490† (0.087) (0.228) (0.266) dummy 2010 -0.145† -0.374† -0.518∗ (0.082) (0.218) (0.258) dummy 2011-12 0.079∗ 0.220∗ 0.219† (0.039) (0.104) (0.122) dummy 2012-13 0.080∗ 0.214∗ 0.213† (0.040) (0.105) (0.126) constant 0.896∗∗ 1.052∗∗ 1.679∗∗ (0.052) (0.146) (0.179) N 2,956 2,956 2,956 F 10.05 (19,583) Wald chi2 145.92 237.82 (19) (19)
Coefficients estimated by OLS in model (1), by probit in model (2) and by random effects probit in model (3).
(a)Insignificant coefficients of seasonal dummies are not shown.
Significance levels : † : 10% ∗ : 5% ∗∗ : 1%
Table 13: Margins at the mean of points
Variable Margin 95% CI (Delta-method Std. Err.) domestic 0.386∗∗ [0.285 ; 0.487] (0.052) foreign 0.528∗∗ [0.377 ; 0.679] (0.077)
Margins based on the coefficients of model (3), fixed at the 25thpercentile value of points (35.5).
Figure 1: The probability of FC Arsenal’s manager Ars`ene Wenger getting the sack per season
.1 .2 .3 .4 .5 Probability of firing 2005-06 2006-07 2007-08 2008-09 2009-10 2010-11 2011-12 2012-13 2013-14 foreign domestic
Wenger had been a domestic manager). It shows that in each of the seasons, the probability of losing his job is higher for Wenger the foreigner.
4.1.2 Dependent variable points
The second dependent variable we consider is the number of points earned during the regular season. As discussed in Section 3.1.1 and 3.1.3, we use both OLS and fixed effects models to estimate the effect of a foreign manager on points. Results are shown in Table 14.
The results of model (4) show a significant positive effect of foreign on the number of points earned. This suggests that starting the season with a foreign manager will yield a club almost five extra points. However, since the coeffi-cient most likely suffers from an omitted variables bias, we first add the control variables. Immediately, the coefficient of foreign loses its significance (95% con-fidence interval [-0.707 ; 2.987]). As expected, the age of the manager shows an increasing relationship with points, although small (0.061) and insignificant. Raising the average age of the selection by one year has a negative effect of ap-proximately one point. Of course, this does not suggest that a club should lower the average age of the players indefinitely. It only suggests that a club is better off with a below average age of the selection. The variance of age is
insignif-Table 14: Estimation results on dependent variable points
(4) (5) (6)
Variable Coefficient Coefficient Coefficient
(Rob. Std. Err.) (Rob. Std. Err.) (Rob. Std. Err.)
foreign 4.939∗∗ 1.140 -0.730 (1.339) (0.942) (0.656) age manager 0.061 -0.007 (0.043) (0.034) age selection -1.032∗∗ 0.860∗∗ (0.270) (0.246)
Var [age selection] -0.037 -0.130∗∗
(0.054) (0.044)
market value 0.138∗∗ 0.030
(0.013) (0.018)
Var [market value] -6.98e-14∗∗ 2.69e-14
(2.24e-14) (2.52e-14) constant 45.169∗∗ 62.684∗∗ (0.630) (6.567) N 2,956 2,956 2,862 F 13.54 21.90 3.61 (1,199) (6,199) (6,199) Coefficients estimated by OLS in models (4) and (5) and by fixed effects OLS in model (6).
Significance levels : † : 10% ∗ : 5% ∗∗ : 1%
icant, so model (5) provides no evidence to support the idea that a selection should consist of a mixture of talented and experienced players. Increasing the market value of the selection by 1,000,000, which can be done by both training the current players and buying new ones, gives an expected increase of 0.138 points. Lastly, the variance of the market value plays a highly significant role. The effect seems small, but since the variance of the market value in a selection is very large, the coefficient strongly suggests that increasing the variance of the market value of the selection has a significant negative effect on performance. Therefore, it appears that a club is better off investing in an evenly balanced selection when it comes to player values.
Lastly, we use the panel structure of the data to estimate the coefficients using our fixed effects model. As the results of model (6) show, the sign of for-eign has changed but remains insignificant. The same holds for age manager. Remarkable is the change in sign of age selection from negative to positive: apparently, an above average age of the players improves the performance in-stead of lowering it like model (5) suggests. The sign and significance of Var [age selection] shows that increasing the variance of the age of the players in the selection has a negative effect on points. Hence clubs are better off with
a selection where players are roughly the same age, which contradicts common belief that a selection should contain of a mixture of talented and experienced players. Surprisingly, model (6) shows that both the total market value and its variance do not have a significant effect. The coefficient of market value how-ever still suggests a positive effect and only slightly misses the 10% significance (p-value of 0.103) mark. A careful reader notices the loss of 94 observations, which were dropped because they are singleton groups.
The results show that manager specific characteristics such as nationality and age have no significant effect on the total number of points. Player charac-teristics as average age of the selection and total market value of the selection do however seem to affect performance, while a high variance in players age lowers it. As mentioned before, foreign managers might have an indirect positive effect on performance by increasing both the market value and the average age of the selection. Table 15 shows that in our dataset, foreign managers tend to work with teams with both a higher market value and a slightly higher age. However, since bigger clubs are known to be more internationally oriented, they are more likely to appoint a foreign manager. Hence this result is not surprising and does not tell us that foreign managers are better able to enhance the total market value of the selection. Further research must be done to show if foreign man-agers enhance performance by training and buying players such that it increases the market value of the selection, which in turn increases performance.
Table 15: Average market value and age of selection Average market value Average age
domestic 42,700,000 24.3
foreign 74,700,000 24.4
4.1.3 Dependent variable position
The last dependent variable in our seasonal approach is position. Section 3.1 gives the model specification used: OLS and ordered probit (both normal and random effects). The results are listed in Table 16.
As can be seen in Table 16, model (7) shows a significant negative effect of foreign on the final league ranking of a club. Note that the lower the league ranking, the higher the sporting performance (champions are number 1). There-fore, model (7) suggests that starting the season with a foreign manager results in a better league ranking of 1.479 positions. However, once again this result may be biased due to omitted variables. Adding the control variables leads to a slightly lower impact of foreign. Model (8) suggests that foreign managers who start the season are expected to finish approximately one place higher in
Table 16: Estimation results on dependent variable position
(7) (8) (9) (10)
Variable Coefficient Coefficient Coefficient Coefficient
(Rob. Std. Err.) (Rob. Std. Err.) (Rob. Std. Err.) (Rob. Std. Err.)
foreign -1.479∗∗ -0.931∗∗ -0.205∗∗ -0.055 (0.355) (0.332) (0.075) (0.077) age manager -0.027† -0.005 -0.003 (0.016) (0.004) (0.003) age selection 0.686∗∗ 0.135∗∗ -0.018 (0.106) (0.022) (0.022)
Var [age selection] -0.025 -0.005 0.011∗
(0.022) (0.005) (0.004)
market value -0.017∗∗ -0.004∗∗ -0.004∗∗
(0.004) (0.0004) (0.001)
Var [market value] -9.53e-16
(7.75e-15) constant 8.967∗∗ -5.194† (0.201) (2.665) N 2,956 2,956 2,956 2,956 F 17.28 13.23 (1,199) (6,199) Wald chi2 357.28 34.41 (5) (5)
Coefficients estimated by OLS in models (7) and (8), ordered probit in model (9) and random effects ordered probit in model (10).
Significance levels : † : 10% ∗ : 5% ∗∗ : 1%
the final league ranking. Both the variance of the market value and the age of the players are insignificant. All other explanatory variables are highly signifi-cant and show the same relationship to performance as they did in model (5) of Section 4.1.2: a positive effect of the age of the manager, a negative impact of higher average age of the selection and, of course, a positive impact of the total market value of the selection.
Table 16 reports no coefficients for the variance of the market value of the selection in model (9) and (10). Including them resulted in Stata reporting the Wald chi2 as missing, meaning that the covariance matrix is not of full rank. There are several reasons that can cause the rank of the covariance matrix to be too small to perform the overall Wald chi2test, one of which is that some of the regressors may be sparse indicators. The lack of significance and the size of the coefficient indicate that the model is better specified without Var [market value]. Model (9) shows the results of ordered probit estimation of the coefficients. The coefficients are not interpreted in the same way as OLS estimates, except for sign and significance. All variables show the same sign and significance as in model (8). Marginal effects are given in Table 17. These show that foreign
managers increase the probability of becoming champion of the league by 2.4%. The marginal effect of age selection shows that increasing the average age by one leads to a 1.6% lower chance of the league title. Lastly, the total market value again plays a role in the chance of success: increasing the market value by 1,000,000 increases the chance of becoming champion by 0.04%. This seems like a relatively small effect, but means that buying a player worth 25,000,000 euros increases the chance of becoming champion by 1% for any club. Finally, as expected, all insignificant coefficients also show an insignificant marginal effect.
Table 17: Marginal effects of model (9) on position=1
Variable dy/dx 95% CI (Delta-method Std. Err.) foreign 0.024∗∗ [0.006 ; 0.042] (0.009) age manager 0.0006 [-0.0002 ; 0.0014] (0.0004) age selection -0.016∗∗ [-0.021 ; -0.010] (0.003)
Var [age selection] 0.0005 [-0.0005 ; 0.0016]
(0.0005)
market value 0.0004∗∗ [0.0003 ; 0.0006]
(0.0001)
Marginal effects based on the coefficients of model (9), probability of becoming champion (position=1).
Significance levels : † : 10% ∗ : 5% ∗∗ : 1%
Lastly, model (10) incorporates the panel structure of the data by estimating a random effects ordered probit model. Just as for our other dependent variable points, most explanatory variables including foreign lose their significance. In this model, only the total market value and the variance of the age of the players in the selection prove to have significant effects on the final league ranking. Therefore, model (10) teaches us that starting the season with a foreign manager does not have the desired effect on final league ranking while investing in the market value of your selection is key in being successful. Just as in model (6), our results show that a higher variance of the age of the players in a selection has a negative effect on performance: a club is better off with a selection balanced in age than having a mixture of talented and experienced players. All in all, our analyses show that modeling the data correctly is crucial in estimating the effect of a foreign manager on performance. If we ignore the panel structure of the data, we conclude that foreign managers have a direct positive effect on final league ranking. Model (10) however shows us that this is not necessarily the case.
