OSIPP Discussion Paper : DP-2012-E-011

The Effect of Additional Police Force on Crime Rate:
Evidence from Women’s Japan Basketball League

November 27, 2012

Hiroya Kawashima*
Ph.D. student, Osaka School of International Public Policy (OSIPP)【Abstract】This paper analyzes influence of an additional referee on number of fouls by using

the data from Women’s Japan Basketball League (WJBL) in order to examine whether numberof police officers affects the crime rate. For the season of 2010-2011, the upper league of the
WJBL introduced 3 referees system for the adaption of the international standard. Using thisnatural experiment, the Difference in Difference and the Instrumental Variable method are used
to remove endogeneity. The results indicate that increased number of referees decrease numberof fouls after considering both reverse causality and unobservable heterogeneity.
【Key Words】Police, Crime, Basketball【JEL Classification Codes】D0, K0*

Address: 1-31 Machikaneyama, Toyonaka, Osaka 560-0043 E-mail: h-kawashima@osipp.osaka-u.ac.jp

I would like to thank Miki Kohara (Osaka University) and Nobuo Akai (Osaka University) for providing valuable comments.
This Discussion Paper was made by permission of Nobuo Akai, who is my advisor at OSIPP.

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1. Introduction
Backer (1968)’s economic theory of crime shows that crime rate decreases when police
resource increase due to the rise in expected cost to be arrested. However, it is difficult to provethat empirically because it is often the case that police officers are employed more in acrime-ridden area. Hence, the reverse causality causes bias in the estimation.
Previous studies that have strived to overcome endogeneity problem are categorized into
four. Firstly, the most frequently used approach is to use the Instrumental Variable method as inCornwell and Trumbull (1994), Levitt (1997), Evans and Owens (2007), Lin (2009) and Worrall
and Kavandzic (2010). Secondly, there are studies used the allocation of police officers after theterrorism regardless the crime rate as in Klick and Tabarrork (2004), Draca, Machin and Witt(2011). Additionally, some researchers analyze by using monthly data sets as it takes time toactually increase the number of police force after the decision is made to an increase such as
Corman and Mocan (2000). Finally, there are studies conducted by using data sets of sports
match, which is the approach of this paper.
The seminal work using the data of sports match is McCormick and Tollison (1984).Their
paper uses the data from the Atlantic Coast Conference (ACC) Basketball Tournament. It uses
the natural experiment that the ACC introduced three referees system from two referees system
in 1979. By regarding referees as police officers, and fouls as illegal activities, it examines
whether the increase of referees (police officers) decreases the number of fouls (illegal
activities). This approach successfully overcomes the issue of above mentioned reverse
causality by using the natural experiment that the number of referee is increased randomly.
Although Hutchinson and Yates (2007) points out data-coding error for this work, McCormickand Tollison (2007) shows the similar result that the number of referees affects the number offouls even after correcting the data-coding error. However, Hutchinson and Yates (2006) claims
that the number of referees does not influence the number of fouls by analyzing the data set thatis created by adding data from subsequent years of the ACC tournament on the data set used by
McCormick and Tollison (1984) as well as using box score.
Other than the basketball, several researches also conduct analyses by using the data of the
National Hockey League (NHL). During 1998-99 season, the NHL randomly increased numberof referees in 20% of total number of game match. Levitt (2002), Allen (2002), and Heckleman
and Yates (2003) uses this natural experiment to investigate the influence of referee increase.
Heckleman and Yates (2003) uses the Instrumental Variable method to divide the effect into2

monitoring effect and deterrent effect. These researches using the data of the NHL find no
significant influence.
As seen, several researchers have already investigated the effect of the increased police
presences on crime by using sports data in order to consider reverse causality. Nevertheless,endogeneity problem between crime and police occurs not only because of the issue of above
mentioned reverse causality, but also unobservable factors that correlate with both police force
and crime such as recognition and reaction to the increased risk or the ability to commit a crime
without being noticed by the police. These issues also exist in the analysis by using the data ofsports match. Therefore, this paper firstly carries outs the analysis by using the Difference in
Difference estimation for the purpose of considering the reverse causality by using the WJBL
data. Then, this paper conducts the second analysis by using Instrumental variable method inorder to control for unobservable heterogeneity among players. As a result, the Difference in
Difference estimation, which considers only the reverse causalities, shows no significant
influence of increased number of referees on the number of fouls. This result is consistent withthe many previous researches. Nonetheless, when both reverse causality and unobservable
heterogeneity among players are considered by using Instrumental Variable estimation, the risein the number of referees decreases the number of fouls.
This paper is organized as follows. The natural experiment of the WJBL and the data arepresented in the following section. The Difference in Difference estimation is presented in
section three. The Instrumental Variable estimation is presented in section four. Finally, section
five concludes.
2. The WJBL experiment and data
The WJBL has the upper league (W league) and the lower league (W1 league). Before
2009-2010 season, both leagues basically had two referees system, and used three referees
system only during playoff. In the season of 2010-2011, the new system of three referees was
only introduced to the W league. This new system was introduced for the purpose of adapting
the rule to the international standard. So the number of referee was increased exogenously.
Figure 1 show the number of fouls per game for the past seven years. The number of fouls inboth the W league and the W1 league is the same level. So there isn’t the situation that more
fouls are likely to be observed in the games for the upper league.

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FIGURE 1 Number of fouls per game for the past seven years

16.5
16
15.5
15
14.5

w

14

w1

13.5
13
12.5
12
2004

2005

2006

2007

2008

2009

2010

When it comes to the homogeneity of the W league and the W1 league throughout the time,
between the season 2009-2010 and the season 2010-2011, there was only one exchange inleague members. Moreover, transfers of players only happen after each season, and registrationsof foreign players are basically not admitted. Therefore, the treatment group and the control
group are almost homogeneous throughout the time.
This paper uses this natural experiment to investigate whether the increased number ofreferees decreases the number of fouls. Data set to be used in the paper is the players’ statisticsof the WJBL 2009-2010 and the WJBL 2010-2011. They are available from the website of the
WJBL. Although box score (data of each game) can be obtained, it is impossible to identify
games that categorized as same in the analysis throughout two years. Hence, panel data cannot
be constructed. Additionally, box scores are more influenced by unobservable heterogeneity
among games. On the other hand, the data set of the seasons enable analysis to estimate theeffect of the increased number of referees without being less affected by heterogeneity among
each game, as well as utilizing the merit of panel data. Table 1 shows the descriptive statistics.
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Table 1. Descriptive statistics
Variablenumber of sample

averagestandard error

minimum

maximum

293

0.144

0.725

-2.485

1.273

W league dummy

293

0.608

0.489

0.000

1.000

number of game match

293

17.567

7.966

1.000

28.000success rate of two-point goal of other teams inthe same league

293

0.453

0.022

0.409

0.492

success rate three-point field goal of other teamsin the same league

293

0.311

0.016

0.293

0.343

success rate free throws of other teams in thesame league

293

0.752

0.015

0.719

0.774

average score of each game

293

6.372

4.406

0.000

20.140

the gap between the average height of players

293-172.569

7.216-191.253-153.240

the age differences between the head coaches

293

0.000

0.006

-0.010

0.014

Positiion: Center dummy

293

0.123

0.329

0.000

1.000

Positiion:Center Forward dummy

293

0.232

0.423

0.000

1.000

Positiion:Small Forward dummy

293

0.263

0.441

0.000

1.000

Positiion:Guard dummy

293

0.191

0.394

0.000

1.000

Positiion: Shooting Guard dummy

293

0.177

0.383

0.000

1.000

Positiion: Point Guard dummy

293

0.014

0.116

0.000

1.000

Dependent variable
logarithm of fouls per game
Independent variable

position dummies

As for the dependent variable, the log of number of fouls per game is used. As forindependent variables, in addition to the number of referees, variables referring McCormick andTollison (1984) are used. They are: number of game match, success rate of two-point goal,
three-point field goal and free throws of other teams in the same league, average score of eachgame, the gap between the average height of players belongs to other teams in the same league
and the height of each player, the age differences between the head coach of other teams in thesame league and the head coach of the team each player belongs to as a proxy for years ofexperience. And the position dummies are also used.
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3. Difference in Difference Estimation
Firstly, the Difference in Difference is used to overcome the reverse causality. Empiricalmodel is as follows.
ln

′

′

′

′

(1)

Where i indicates a player, t indicates year. YearDummy denotes a vector of year dummies,
WLeagueDummy is the vector of W league dummies. DD

is the vector of Difference in

Difference estimator. There DD term measures the effect of increased referees on the number offouls. A vector

indicates other independent variables.
Table2 Difference in Difference Estimation

DD estimator2010 dummy
W league dummy
number of game match
success rate of two-point goal of otherteams in the same league
success rate three-point field goal ofother teams in the same league
success rate free throws of other teamsin the same league
average score of each gamethe gap between the average height ofplayers
the age differences between the headcoaches(1)5.9955(5.9169)-1.3619(1.0351)-5.9360(5.4898)
0.0408***(0.0058)
5.0594(8.8016)130.5237(143.5017)
15.7396***(4.2518)
0.0686***(0.0075)-0.0085(0.0061)
101.0160(122.5971)

Positiion: Center dummy
Positiion:Center Forward dummy
Positiion:Small Forward dummy
Positiion: Shooting Guard dummy
Positiion: Point Guard dummy-54.7879(45.4912)293
0.55

Constant
Observations
R-squared(2)
5.9673(5.7111)-1.3769(1.0089)-5.9128(5.2830)0.0409***(0.0063)
4.3732(8.5159)129.2365(137.9341)
16.5888***(4.3472)
0.0684***(0.0074)-0.0127(0.0161)
98.5985(118.6231)
0.1023(0.1182)-0.0098(0.1494)0.1601(0.2626)
0.0565(0.1609)
0.1212(0.1855)-55.4952(43.5010)
293
0.56

Note 1. Cluster robust standard errors in parentheses
2. * significant at 10%; ** significant at 5%; *** significant at 1%
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Table 2 presents the result obtained by the Difference in Difference estimation. The focus of
this paper, the coefficient of the DD term which measures the effect of increased referees on thenumber of fouls does not show the significant influence for both specifications even at 10%
level. This means increase in the number of referees does not influence the number of fouls.
4. Instrumental Variable Estimation
The above Difference in Difference estimation has the possibility of correlation between thevariable of the number of referees and the error term if unobservable heterogeneity amongplayers, which may affect the number of fouls, changes over time. For instance, there isindividual ability that a player can make rule violation without being called. If she has the highability of deceiving referees, the number of fouls decreases. Moreover, it is expected that these
individuals have higher technique of ball handling and positioning. Consequently, these players
are likely to play in the upper league (W league) which has increased the number of referees. If
this is the case, the influence of increased number of referees appears to be small in theestimation.
In order to control for such unobservable heterogeneity among players, panel data of players
who are existed for both seasons is constructed and the Instrumental Variable estimation isconducted. The base model is as follows.
′

ln

′

(2)

Where i indicates a player, t indicates year. Error term is described as
unobserved heterogeneity among players.

~isX and Referee . In order to remove the effect of

0,

.

is

and does not correlate with, the first difference of (2) is taken. So thebasic econometric specification is as follows.
∆ln

′

∆

∆ ′

∆

Furthermore, for the purpose of taking endogeneity, which exists between Referee and Foul ,into consideration, the number of players registered by each team in the previous season is usedas the instrumental variable. Because the teams with larger number of players tend to havericher financial resources and better players, these teams are likely to play in the upper league(W league) in the following year, and to be the subject to the three referee system.

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Table 3 Instrumental Variable Estimation

number of referees
number of game match
success rate of two-point goal of otherteams in the same league
success rate three-point field goal ofother teams in the same league
success rate free throws of other teamsin the same league
average score of each gamethe gap between the average height ofplayers
the age differences between the headcoaches(1)-2.9020**(1.2815)0.0308***(0.0080)
6.1069(13.4472)
332.7990**(120.6080)-41.9051**(17.8380)
0.0870***(0.0168)-234.9237**(88.2572)
259.4096**(103.8170)

Positiion: Center dummy
Positiion:Center Forward dummy
Positiion:Small Forward dummy
Positiion: Shooting Guard dummy
Positiion: Point Guard dummy
5.2500**(1.9850)113
0.40

Constant
Observations
R-squared(2)-2.5417*(1.1926)0.0300***(0.0080)
3.2689(12.6536)
304.2878**(103.6706)-36.5209**(15.7843)
0.0863***(0.0168)-214.8362**(76.2010)
236.9946**(87.9387)
0.3369***(0.1043)0.0000(0.0000)
0.1621***(0.0468)0.0000(0.0000)
0.0000(0.0000)
4.7683**(1.7174)113
0.41

Note 1. Cluster robust standard errors in parentheses
2. * significant at 10%; ** significant at 5%; *** significant at 1%
Table3 shows the result of the Instrumental Variable estimation. This result shows that thecoefficient of the variable of the increased number of referees is statistically significant at 5%
and 10% level, respectively. This means the increase of referees decreases the number of fouls
when the reverse causality and unobserved heterogeneity among player are considered.
85. Conclusion
This paper analyzes influence of an additional referee on number of fouls by using the datafrom WJBL. The difficult problem of the empirical analysis of the relationship between thepolice existence and the crime rate is endogeneity problem. It is often the case that crime ridden
area increases the number of police officers. Moreover, unobservable factors, which correlatewith both number of police officers and crime rate, could cause bias in estimation. This paper
uses the natural experiment conducted in WJBL to overcome reverse causality. Additionally, theInstrumental Variable estimation is employed to control for unobservable heterogeneity that
correlate with the number of fouls and the number of referees.
First estimation using the Difference in Difference shows no significant influence ofincreased number of referees on the number of fouls. This is consistent with many previous
studies used data of sports match. However, this estimation only deals with the reverse causality.
Therefore, the second estimation uses the Instrumental Variable method to control forunobservable heterogeneity among players. This estimation revealed that increased number ofreferees decreases the number of fouls. This result is consistent with the result predicted in theeconomic theory of crime.
When applying the result of this paper to the reality of crime, the result, which is obtained
from the estimation taking both reverse causality and unobservable heterogeneity amongplayers into consideration, suggests that increasing policing force decrease crime rate. It isparticularly effective to prevent crime that was unplanned and committed by the quick
judgment like fouls in the basketball match.
Some issues still remain. This paper is unable to make a distinction between monitoring
effect and deterrent effect. Nonetheless, it is understood that deterrent effect is greater than themonitoring effect because the total number of fouls has declined. Hence, increasing policing
force has both effects, and consequently reduces crime. Also, players who are close to be achampion or not, or players who are facing to drop out to the lower league or promoted to theupper league may have different expected cost and benefit as other players. These differences
need to be concerned in the future analysis.

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