EVOLUTION OF COMMUNITY DETERRENCE: EVIDENCE FROM THE NATIONAL HOCKEY LEAGUE - SSRN papers
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EVOLUTION OF COMMUNITY DETERRENCE: EVIDENCE FROM THE
NATIONAL HOCKEY LEAGUE
CRAIG A. DEPKEN II, PETER A. GROOTHUIS and MARK C. STRAZICICH∗
Community and specialized enforcement are recognized as important components of
deterring antisocial behavior. To provide insights on the interplay between deterrence
methods, we examine the empirical evolution of fighting and scoring in the National
Hockey League using time series data. We identify structural changes that correlate with
changes in player behavior and rules. In particular, we find that player behavior related
to fighting changed 4 or 5 years prior to most rule changes aimed at reducing fighting.
We conclude that the decline in fighting in hockey was more closely associated with a
change in community rather than specialized deterrence methods. (JEL Z22, D71, L83)
I. INTRODUCTION is not involved in granting priorities, customers
must use community enforcement to sustain a
Deterring antisocial behavior has generally queuing equilibrium.
come in two forms. First, there are rules enforced In this paper, we examine these two ways of
by a specialized centralized enforcer such as a reducing antisocial behavior by asking whether
manager, police officer, or referee. These agents community or specialized deterrence occurs first
monitor and punish antisocial behavior and other when considering the reduction in fighting in the
private actions that run counter to the established National Hockey League (NHL). Utilizing time
rules. Second, there are community enforcement series data from 1957 to 2013, we empirically
methods that discourage antisocial activity using investigate whether specialized or community
norms and sanctions developed and delivered by enforcement initiated the decline in fighting that
the community. Posner and Rasmusen (1999) occurred over the sample period. Because fight-
define a social norm as “a social rule that does not ing is semi-legal in professional hockey, we iden-
depend on government for either promulgation or tify if changes in the prevalence of fighting were
enforcement.” They further suggest that “norms more closely associated with changing rules, that
are an attractive method of social control because is, specialized deterrence, or changing culture,
a rule may be desirable but too costly a project that is, community deterrence. In the context of
for the state to undertake relative to the benefits.” hockey, the community norm is less aggressive
In this regard, Allon and Hanany (2012) develop play. Fighting in hockey is a way to maintain
a dual system of specialized enforcement and this community norm because there are clear and
community enforcement for waiting in a queue, accepted “rules” for a fight. Furthermore, the his-
for example, at a bank or airport security check- torical term of “enforcer” suggests an informal,
point. They find that when the queue manager community-enforcement of this norm.
Because of hockey’s physical nature, history,
∗ We thank David M. Singer for access to his NHL fight and culture, both injuries and fights have been
data obtained from hockeyfights.com, and two anonymous common in the sport. To help regulate the anti-
referees for helpful comments and suggestions. social behavior of players, both formal rules of
Depken: Professor, Department of Economics, Belk Col- specialized deterrence and informal social norms
lege of Business, University of North Carolina at Char-
lotte, Charlotte, North Carolina 28223, E-mail cdepken@ of community deterrence arose to regulate play.
uncc.edu Coincident with increasing evidence that head
Groothuis: Professor, Department of Economics, Walker trauma has long-term health consequences, the
College of Business, Appalachian State University,
Boone, North Carolina 28608, E-mail groothuispa@
appstate.edu
ABBREVIATIONS
Strazicich: Professor, Department of Economics, Walker
College of Business, Appalachian State University, ADF: Augmented Dickey–Fuller Test
Boone, North Carolina 28608, E-mail strazicichmc@ LM: Lagrange Multiplier
appstate.edu
NHL: National Hockey League
289
Contemporary Economic Policy (ISSN 1465-7287)
Vol. 38, No. 2, April 2020, 289–303 doi:10.1111/coep.12461
Online Early publication January 9, 2020 © 2020 Western Economic Association International
Electronic copy available at: https://ssrn.com/abstract=3593694290 CONTEMPORARY ECONOMIC POLICY
number of fights in hockey has diminished over breaks in our four measures of fighting where
time. This leads to the question: to reduce fight- the trend changes from positive to negative 4 or
ing, did the players themselves change the culture 5 years before major rule changes aimed at reduc-
of the game by changing community deterrence ing fighting. We conclude that changes in social
or did the NHL change specialized enforcement norms or “community deterrence” in the NHL
by changing the rules of the game? occurred prior to changes in formal rules or “spe-
Our paper is most closely linked to DeAn- cialized deterrence.”
gelo, Humphreys, and Reimers (2017) who use The remainder of the paper proceeds as fol-
disaggregated NHL event-level data from 2007 lows. In Section II we provide a brief history
to 2013 to identify whether community and spe- of the NHL and the culture of fighting within.
cialized enforcement measures are substitutes or In Section III, we discuss the hypotheses that
complements. They find that when rules are lack- we examine. Section IV describes our testing
ing community enforcement acts as a substitute. methodologies and the data that we utilize. Our
However, in contrast to DeAngelo, Humphreys, test results are described in Section V. Conclud-
and Reimers (2017), we use season level data ing remarks are provided in Section VI.
with time series tests to identify whether com-
munity deterrence preceded changes to formal
deterrence or vice versa. Our analysis pro- II. THE NATIONAL HOCKEY LEAGUE: HISTORY
AND CONTEXT
vides additional insights to the interconnection
between community and specialized enforcement The NHL started in 1917 with three teams
mechanisms. and has expanded over time to 31 teams in the
Time series econometrics provides a unique 2019–2020 season.2 In 1922, a 5-minute penalty
way to identify structural changes that can pro- for fighting was established replacing the more
vide new insights into how deterrence methods in severe punishment of expulsion for the remain-
the NHL have changed over time. Sports histori- der of the game. This made hockey unique among
ans and scholars often assume exogenous changes team sports as fighting became semi-legal and
in a sport based on specific known historical gave rise to what became known as the “en-
events such as particular rule changes, changes in forcer.” Rockerbie (2012) states: “[t]he new sys-
hiring practices, or changes in league structure. In tem encouraged each club to carry a few players
contrast, we make no prior judgments about the that would act as “enforcers” on the ice, expected
timing of any particular era. Instead, our tests let to deal with the other club’s enforcers in a con-
the data speak to endogenously identify eras. By trolled battle of fisticuffs. This established a long-
doing so, we hope to identify changes in the NHL standing code of conduct in the NHL that still
that may not be apparent when focusing a priori exists today. Skilled players are not expected or
on particular historical events. encouraged to fight in their own defense when
Applying time series tests to sports data has rules are ignored, instead, an enforcer comes to
only recently become more popular in the liter- the aid of the stricken skilled player, with the
ature. For example, Fort and Lee (2006, 2007), expectation of being met by the other club’s
Lee and Fort (2005, 2008, 2012), and Mills and enforcer. This system of on-ice détente worked
Fort (2014) employ unit root and structural break well.”3
tests to examine competitive balance in a vari- Notwithstanding the culture of fighting and
ety of sports. More recently, Groothuis, Rot- the potential pressure-valve release that fighting
thoff, and Strazicich (2017) use structural break
tests to measure changing performance eras in 2. During the sample period 1957–2013, both the num-
major league baseball.1 In this paper, we adopt ber of teams and the makeup of players in the NHL
a methodology similar to Groothuis, Rotthoff, changed providing a unique economic laboratory to investi-
gate changes in both community and specialized deterrence
and Strazicich (2017) applied to the NHL to measures. At the beginning of the sample period, there were
examine twelve measures of fighting and perfor- six NHL teams and by the end of the sample period there were
mance. We find that all but one of these time thirty teams. During the sample period, the national origin of
series are stationary around one or two struc- players changed from about 2% European in 1957 to 23.5%
European in 2013. For detailed discussion of these institu-
tural breaks. Most notably, we identify structural tional changes, see Rockerbie (2020).
3. Rockerbie (2012) further states “Rule 47 (which
1. See also Scully (1995), Palacios-Huerta (2004), replaced Rule 56) now even specifies the allowable behavior
Schmidt and Berri (2004), and Nieswiadomy, Strazicich, and during a fight: the players must first drop their gloves and fight
Clayton (2012). bare-knuckled; third-men are not allowed into a fight between
Electronic copy available at: https://ssrn.com/abstract=3593694DEPKEN, GROOTHUIS & STRAZICICH: EVOLUTION OF COMMUNITY DETERRENCE 291
TABLE 1 used hockey as an economic laboratory and two
Major Rule Changes in the NHL Pertaining to streams of literature have developed. The first
Fighting focuses on the demand for hockey through the
question of whether fighting and physical play
Season Rule Description
generate higher revenue for owners or higher
1976–1977 Instigator rule adds major penalty and game wages for players. The second focuses on the
misconduct penalty for starting a fight “law and economics” of the NHL and asks
1992–1993 Diving penalty implemented; game
misconduct penalty for starting a fight whether rule changes and enforcement influence
2000–2001 Second referee added for all games the semi-legal behavior of fighting?
2009–2010 Greater enforcement of instigating The literature on fan attendance and team rev-
enue finds that teams are rewarded for fighting
and physical play. Jones (1984), Jones, Ferguson,
might provide, over time the NHL has imple- and Stewart (1993), Jones, Steward, and Sunder-
mented many rules that aim to increase the costs man (1996), and Paul (2003) all find that fighting
and decrease the benefits of fighting. We iden- increases attendance at NHL games. Paul, Wein-
tify four such major rule changes that we use as bach, and Robbins (2013) find this same rela-
a heuristic in our empirical analysis. Table 1 lists tion for the American Hockey League, the main
these four major rule changes and their year of development league for the NHL. Stewart, Fer-
implementation.4 guson, and Jones (1992) and Coates, Battré, and
In 1976, the league implemented an instiga- Deutscher (2011) both find that fighting reduces
tor rule that penalized the player who started a the probability of winning games in the NHL but
fight with a major penalty and a game misconduct has the direct effect of increasing attendance. In
penalty. The major penalty entails the player stay- addition, Coates, Battré, and Deutscher (2011)
ing off the ice for 5 minutes without replacement. find weak evidence that highly penalized teams
The game misconduct penalty entails the player have higher revenues. Rockerbie (2016) finds that
staying off the ice for 10 minutes with replace- fighting slightly reduced attendance through the
ment. This particular rule change increased the mid-1990s but had little relationship with atten-
cost of instigating a fight to be equivalent to one- dance thereafter. Overall this stream of literature
fourth of a game’s 60 minutes of play. In 1992, the suggests that team owners, at least in the past, do
league reinforced the game misconduct penalty not have financial incentives to reduce fights or
for starting a fight. In 2000, the league added a physical play in hockey.
second referee to all games, which was expected The literature on player salaries suggests that
to increase enforcement of minor infractions and players are rewarded for fighting and physical
reduce the benefits from fighting, especially for play. Both Jones, Nadeau, and Walsh (1997) and
enforcers. The last rule change that occurred dur- Haisken-DeNew and Vorell (2008) find a pay
ing our sample period is the greater enforcement premium for unskilled wing players who fight
of instigating implemented in 2009. more often. Haisken-DeNew and Vorell (2008)
Given that fighting and physical play are suggest, however, that the wage premium may be
common in hockey, the economic literature has a compensating wage differential for the physical
harm suffered from fighting.
two players (immediate expulsion from the game); kicking A second strand of literature focuses on
with skates is strictly forbidden and severely punished; play- applying the economics of crime to the sport of
ers must end the fight at the instruction of the referee if they
separate, and; pulling the opponent’s sweater over his head is hockey. Given the semi-legal nature of fighting
not permitted.” This rule provides the case for the semi-legal in the NHL both changes in rules and enforce-
nature of fighting in the NHL. ment has served as an economic laboratory.
4. As pointed out by a helpful referee, it is possible As noted above, DeAngelo, Humphreys, and
that there are announcement effects of the rule changes if
coaches, players, and referees knew about the potential rule Reimers (2017) use NHL game level data to
changes in advance. This could occur if there were widespread identify whether community and specialized
knowledge of the debate surrounding the rule changes and enforcement measures are substitutes and com-
the likelihood that the rule changes would be adopted. Using
newspaper archives, we identified that the rule changes were plements. They utilize disaggregated event-level
announced during the off-season before they went into effect data in panel regressions and find that when
but could find no dates certain about when the rule changes rules are lacking community enforcement acts as
were debated nor whether there was widespread knowledge a substitute.
of the potential rule changes. Therefore, we do not model
potential announcement effects here but recommend the topic Most of the additional literature has focused
for future research. on the natural experiment of the introduction of
Electronic copy available at: https://ssrn.com/abstract=3593694292 CONTEMPORARY ECONOMIC POLICY
a second referee to NHL games in 1998–1999. be thought of as attitudes and values attributed to
Allen (2002) finds that the second referee did not a group. Hockey has a tradition of a “tough guy”
reduce violent behavior but did increase the level culture. For example, one norm that was slow to
of detection. Levitt (2002) found no effect on change was wearing a helmet. Wise and Scott
either behavior or detection. Depken and Wilson (2012) analyze the changing norm of helmet
(2004) and Wilson (2005), however, both find that use in the NHL. They suggest that “since new
fighting is reduced and scoring increased. Allen players were required to use helmets and players
(2005) uses the same natural experiment but asks tend to have relatively short careers, the effect
whether the culture of violence or rules enforce- of this policy was to ensure that helmets would
ment changes behavior? He argues that changing eventually be universally adopted. In effect, the
rules matter more than changing culture. NHL policy removed any stigma associated
with helmet usage and encouraged adoption.”
One reason norms and community enforcement
III. COMMUNITY OR SPECIALIZED ENFORCEMENT measures can change relatively quickly in sports
is because of short careers and how quickly the
The analysis of community enforcement or
community can change.
social norms has a long history in economics.
Acemoglu and Wolizky (2015) develop a theo-
On the theoretical side, Axelrod (1986) provides
retical model of deterrence to sanction antisocial
a discussion of the evolution of social norms.5
behavior that uses both community and special-
Elster (1989) and Posner (1997) discuss how
ized enforcement mechanisms. One of their key
economists define social norms relative to legal
results is that a single enforcer is not optimal in
norms, private norms, and group norms. Huang
cases where there is imperfect monitoring. We
and Wu (1994) develop a psychological game
suggest that both norms and rules have arisen in
theory model to suggest that emotions, such
sports and particularly the NHL due to these mon-
as remorse, can strengthen the ability of social
itoring imperfections.
norms to punish antisocial behavior. Applying
In the NHL, the referees enforce rules, which
their model to corruption, they suggest that
is costly. Posner and Rasmusen (1999) sug-
expectations about the likelihood of corrupt
gest that, depending on which social norms
behavior by others will impact an individual’s
prevail, enforcement can occur in many ways.
decision to engage in such behavior. In a com-
Enforcement can be automatic wherein violating
ment paper, Posner (1998) notes that social
the norm leads to automatic punishment, for
norms and laws interact and can serve as substi-
example, driving into oncoming traffic on the
tutes and complements; he also notes that norms
left side of the road in the United States. Other
can be the source of laws or the target of laws.
enforcement mechanisms can include guilt,
Muehlheusser and Roider (2008) investigate
shame, ostracism, and informational punishment.
the phenomenon that certain team (societal)
Posner (1997) suggests that some norms are
members do not report objectively bad behavior
enforced by bilateral costly sanctions or multi-
on the part of other team (societal) members.
lateral costly sanctions. In hockey, the enforcer
Dequech (2009) distinguishes between moral
arose to punish players on the other team who
and epistemic values which, in turn, generate
used too much physical force on star talent. For
different types of social norms. All of these
instance, when Wayne Gretzky was traded to
studies provide interesting hypotheses that can
the Los Angeles Kings in 1988, he required that
be applied to real-world examples.6 Culture can
Marty McSorley be included in the trade. McSor-
ley served as his enforcer and, with over 3,300
5. Axelrod (1986) notes that social norms and laws are penalty minutes in his career, is the fourth-most
often (but by no means always) reflections of each other: “In
short, social norms and laws are often mutually supporting. penalized player in NHL history. Given the nature
This is true because social norms can become formalized of their job, enforcers provide costly sanctions
into laws and because laws provide external validation of and thus the quantity of penalty minutes for these
norms. They are also mutually supporting because they have
complementary strengths and weaknesses. Social norms are players should be high.
often best at preventing numerous small defections where the However, over time the audience for NHL
cost of enforcement is low. Laws, on the other hand, often games might have sufficiently changed to cause
function best to prevent rare but large defections because
substantial resources are available for enforcement” (p. 1107).
players to alter existing social norms. This
6. Azar (2004) investigates the social norm of tipping and change might be necessary for players to max-
Morgulev et al. (2014) investigate the social norm of flopping imize the internalized returns generated by
in professional basketball. their behavior. For example, if NHL fans began
Electronic copy available at: https://ssrn.com/abstract=3593694DEPKEN, GROOTHUIS & STRAZICICH: EVOLUTION OF COMMUNITY DETERRENCE 293
rewarding scoring and offense more than defense and to identify structural breaks, we utilize the
and fighting, the empirical question would one- and two-break minimum Lagrange multi-
focus on which group of individuals noticed plier (LM) unit root tests proposed by Lee and
this change first: the players or the league/team Strazicich (2003, 2013).
owners? If the players initiated a change in the As shown by Perron (1989), ignoring existing
social norms of hockey such that fighting was structural breaks when implementing unit root
reduced without formal rule changes by the tests can reduce the ability to reject a false unit
league, then we should see changes in player root null hypothesis.10 To overcome this draw-
behavior before formal actions by the league. back, Perron proposed including dummy vari-
On the other hand, if the league or team owners ables in the usual augmented Dickey–Fuller unit
discovered that fan preferences were changing, root test (ADF test) to allow for one known,
we would expect rule changes before observing or “exogenous,” structural break. In subsequent
changes in player behavior. work, Zivot and Andrews (1992, ZA hereafter),
In both cases, player behavior is expected among others, proposed unit root tests that allow
to change, perhaps to the extent that a notable for one unknown break to be determined “en-
change or “structural break” is introduced into a dogenously” from the data. The ZA test selects
time series measuring a particular behavior. The the break where the t statistic testing the null of a
key difference is the timing of any changes in unit root is minimized (i.e., the most negative).
player behavior relative to formal rule changes. The ZA test, however, and other similar ADF-
Following the established definitions of commu- type endogenous break unit root tests derive their
nity and specialized deterrence, if the change in critical values assuming no break under the null
behavior takes place after a formal rule change, hypothesis. Nunes, Newbold, and Kuan (1997)
then the change in behavior would be interpreted and Lee and Strazicich (2001), among others,
as the result of specialized deterrence. On the show that this assumption can lead to spurious
other hand, if the change in behavior takes place rejections of the unit root hypothesis in the pres-
before a formal rule change then the change in ence of a unit root with break. As a result, when
behavior would be interpreted as the result of using these tests, researchers can incorrectly con-
community deterrence.7 clude that a time series is “trend-break stationary”
when in fact the series has a unit root with break.
To avoid these drawbacks, we utilize the one-
IV. EMPIRICAL METHODOLOGY AND DATA and two-break minimumLM unit root tests devel-
a. Empirical Methodology oped by Lee and Strazicich (2003, 2013), which
has the desirable property that its test statistic is
To create time series to identify structural not subject to spurious rejections. Thus, conclu-
breaks in the NHL, we calculate the mean and sions are more reliable since rejection of the null
coefficient of variation of several measures of hypothesis unambiguously implies that the series
fighting, performance, and penalties across play- is stationary around one or two breaks in the level
ers and games for each season from 1957–1958 and/or trend.
through 2012–20138 ; where each time series Our testing methodology can be summarized
consists of 55 observations.9 To determine if each as follows.11 According to the LM “score” princi-
time series is stationary (i.e., has a “determin- ple, the test statistic for a unit root can be obtained
istic trend” where following a shock the series from the following regression:
reverts to a stable trend) or nonstationary (i.e., ∑
has a “stochastic trend” where following a shock (1) Δyt = δ′ ΔZt + ϕ̃ St−1 + γΔ̃St−i + εt ,
there is no tendency to revert to a stable trend)
where ̃ ̃ x − Z t̃
S = yt − ψ δ, t = 2, … , T; ̃
δ are the
7. Axelrod (1986) provides a descriptive model of the coefficients from the regression of Δyt on ΔZ t ;
empirical hypothesis outlined here: “Norms often precede and ψ̃ x is the restricted MLE of ψ x (≡ψ + X 0 )
laws but are then supported, maintained, and extended by
laws … As [a] norm becomes firmer, there is growing support
to formalize it through the promulgation of laws defining 10. By “structural break,” we imply a significant, but
where [an act] is and is not permitted” (p. 1106). infrequent, permanent change in the level and/or trend of
8. The coefficient of variation is utilized to allow a more a time series. See Enders (2010) for additional background
suitable measure of dispersion when comparing our differing discussion on structural breaks and unit root tests.
time series. We thank a referee for this suggestion. 11. Gauss codes for the one- and two-break minimum
9. Data are not available for 2004–2005 because of the LM unit root test are available on the web site https://sites
season-cancelling lock-out by team owners. .google.com/site/junsoolee/codes
Electronic copy available at: https://ssrn.com/abstract=3593694294 CONTEMPORARY ECONOMIC POLICY
given by y1 − Z1̃ δ. The Δ̃St−i terms are included, lagged term is found, or k = 0. Once the maxi-
as necessary, to correct for serial correlation; εt mum number of lagged terms is found, all lower
is the contemporaneous error term assumed to lags remain in the regression.13 The process
be independent and identically distributed with is repeated for each combination of two break
zero mean and finite variance; Z t is a vector of points to jointly identify the breaks and the test
exogenous variables contained in the data gener- statistic at the point where the unit root test statis-
ating process. Z t is described by [1, t, D1t , D2t , tic is minimized.
DT ∗1t , DT ∗2t ]′ , where Djt = 1 if t ≥ T Bj + 1, j = 1, After identifying that all of our time series are
2, and zero otherwise, DT ∗jt = t if t ≥ T Bj + 1, and stationary around one or two breaks, except for
zero otherwise, and T Bj is the time period of mean goals, which is nearly so, we additionally
structural break j. Note that the testing regres- perform tests to see if more than two breaks are
sion (1) involves ΔZ t instead of Z t so that ΔZ t present. To do so, we utilize the multiple break
is described by [1, B1t , B2t , D1t , D2t ]′ , where tests suggested by Bai and Perron (1998, 2003,
Bjt = ΔDjt and Djt = ΔDT ∗jt , j = 1, 2. Thus, B1t BP hereafter), which are valid only for stationary
time series.14
and B2t , and D1t and D2t , correspond to structural
changes or breaks in the level and trend under the
(stationary) alternative, and to one period jumps b. Data
and permanent changes in the drift under the (unit The data employed in this study describe mea-
root) null hypothesis, respectively. The unit root sures of fighting, penalties, and performance,
null hypothesis is described by ϕ = 0 and the LM for the NHL from the 1957–1958 through the
test statistic is defined by: 2012–2013 seasons.15 We focus on the NHL
(2) ̃
τ ≡ t statistic testing the null since it is the oldest professional league in the
Hockey Database. Our sample period begins
hypothesis ϕ = 0. (ends) in 1957/1958 (2012/2013) because that is
the period for which we have fight data.
To endogenously determine the location of Table 2 reports descriptive statistics for the
two breaks (λj = T Bj /T, j = 1, 2), the LM unit variables investigated. First, we describe the
root test uses a grid search to determine the com- fight-related data. We use several different mea-
bination of two break points, λ = (λ1 , λ2 )′ over sures of how much fighting occurred in a given
the time interval [.1 T, .9 T] (to eliminate end NHL season: the average number of fights per
points), where the unit root test statistic is min- game, the percentage of games with at least one
imized. Since the critical values for the model fight, the percentage of games that had more
with trend-break vary depending on the location than one fight, and the percentage of players who
of the breaks (λj ), we employ critical values cor- fought in a given year. As can be seen in Table 1,
responding to the location of the breaks.12 there is considerable variation over the sample
To determine the number of lagged augmented period across these four variables suggesting that
terms Δ̃ St−i , i = 1, … , k, included to correct the level of fighting has not been static over the
for serial correlation, we employ the following sample period.
sequential “general to specific” procedure. At Unlike the fight data, measured across games
each combination of two break points we begin within a given season, the performance variables
with a maximum number of k = 4 lagged terms are measured across players within a given season
and examine the last term to see if its t-statistic (as is the percentage of players who fought in
is significantly different from zero at the 10% a given season). The performance and penalty
level (critical value of 1.645 in an asymptotic nor- statistics include the following variables: mean
mal distribution). If insignificant, the k = 4 term and coefficient of variation in penalty minutes,
is dropped and the model is re-estimated using
k = 3 terms, and so forth, until the maximum 13. This type of method has been shown to perform better
than other data-dependent procedures to select the optimal k
12. While one might consider allowing for more than two (e.g., Ng and Perron 1995).
breaks in the unit root tests, we do not consider this possibility 14. See Prodan (2008) for a discussion of pitfalls that can
in the present paper. The computational burden of allowing arise when applying the Bai and Perron (1998, 2003) type
for three or more breaks in the unit root tests in conjunction tests to nonstationary time series.
with determining the number of first differenced lagged terms 15. The NHL fight data were obtained from David M.
would increase significantly. However, allowing for more than Singer at www.hockeyfights.com. The penalty and perfor-
two breaks may not be a concern here since we reject the unit mance data come from the Hockey Database version 9.0,
root hypothesis with one or two breaks in all but one series. available at www.hockeydb.com, last accessed January 2019.
Electronic copy available at: https://ssrn.com/abstract=3593694DEPKEN, GROOTHUIS & STRAZICICH: EVOLUTION OF COMMUNITY DETERRENCE 295
TABLE 2 V. EMPIRICAL RESULTS
Descriptive Statistics of the Data
The LM unit root test results are reported in
Variable Mean Std. Dev. Min Max Table 3 for the fight, penalty, and performance
FPG 0.57 0.26 0.14 1.12 variables. In each case, we begin by applying the
PCTGF 36.93 13.05 11.90 60.60 two-break LM unit root test. If only one break
PCTGMF 12.96 7.49 1.43 28.81 is identified (at the 10% level of significance) in
PCTPF 36.30 7.78 22.47 53.61
MPM 36.40 8.35 16.75 55.15 the two-break test, we re-examine the series using
CVPM 118.07 7.57 95.64 131.32 the one-break LM unit root test.16 We first con-
MG 10.98 1.43 8.39 13.96 sider the results for the fight and penalty series.
CVG 110.79 6.16 98.38 130.57 The evidence suggests that all fight and penalty
MA 18.72 2.33 14.84 24,03
CVA 88.77 5.21 78.86 100.57 series are stationary around two structural breaks.
MPTS 29.70 3.74 23.57 37.66 Table 4 reports results from regressions on the
CVPTS 87.71 4.24 78.93 97.69 level and trend breaks reported in Table 3.17 To
better visualize these results, Figure 1 displays
Notes: Variables are defined as follows: number of fights
per game (FPG), percentage of games with a fight (PCTGF),
plots of the actual and fitted values from the
percent of games with multiple fights (PCTGMF), percent of regressions along with the identified breaks and
players who fought in a given season (PCTPF), the mean and the most important rule changes relating to fight-
coefficient of variation of penalty minutes across players in ing described in Table 1.
a given season (MPM and CVPM), mean and coefficient of
variation of the number of goals scored across players in a Figure 1A displays the series related to fight-
given season (MG and CVG), mean and coefficient of varia- ing. In the percentage of games with a fight and
tion of assists across players in a given season (MA and CVA), the percentage of players who fought, the first
and the mean and coefficient of variation in points across play-
ers in a given season (MPTS and CVPTS). Data obtained from structural break occurs in 1966 and 1967, respec-
www.hockeyfights.com and the Hockey Database version 9.0. tively.18 In the percentage of games with a fight,
The sample period spans the 1957–1958 through 2012–2013 following the 1966 break there is a significant
NHL seasons, except for season 2004–2005 where data are upward trend. For the percentage of players who
not available because of the owner lock-out. Each series con-
tains 55 observations. fought, following the 1967 break the downward
trend changes to an upward trend. In the case
of fights per game and the percentage of games
the mean and coefficient of variation in goals
with more than one fight, each series has a struc-
scored, the mean and coefficient of variation in
tural break in 1974 and 1975, respectively. Both
assists, and the mean and coefficient of variation
breaks indicate an upward shift and steepening of
in points.
the upward trend towards more fights per game
During the sample period, the average number
after 1974 and 1975, respectively. One possi-
of fights per game was just over one-half (0.57);
ble explanation for the upward trend in fighting
in an average NHL season, approximately 37%
after 1966–1967 and 1974–1975 could be the
of games had at least one fight and 13% had
rapid expansion in the number of NHL teams that
more than one fight. On average, 36% of players
occurred during this period. Such rapid expan-
participated in at least one fight during a season
sion could be expected to lead to a shortage of
and the standard deviation was 7.78. The average
highly skilled players that resulted in an increase
number of penalty minutes per player was 36 with
in lesser skilled players who may be more prone
a standard deviation of 8.35 and coefficient of
to fighting.19
variation of 118.07, reflecting the wide dispersion
of penalty minutes across players. All four of the time series related to fighting
In the performance measurements, the average have a second structural break in either 1987 or
number of goals per player (excluding goalies) 1988, with three of the series having a structural
was approximately 11, the average number of
assists was 19, and the average number of total 16. If no break is significant (at the 10% level) in the one-
break unit root test we could then utilize a no-break unit root
points was 30. The standard deviation and coef- test. However, one or two significant breaks were identified in
ficient of variation of goals scored, assists, and each series.
total points were 1.43, 2.33, and 3.74 (standard 17. Given that these series were found to be stationary
deviations) and 110.79, 88.77, and 87.71 (coeffi- around breaks, the spurious regression problem found when
utilizing nonstationary times series can be avoided.
cient of variations), respectively. The number of 18. Throughout our paper, a break in 1966 indicates that
assists is greater than the number of goals because a break occurred during the 1966–1967 season.
many times more than one assist is awarded on a 19. See our discussion in footnote 2. We thank an anony-
given goal. mous referee for suggesting this.
Electronic copy available at: https://ssrn.com/abstract=3593694296 CONTEMPORARY ECONOMIC POLICY
TABLE 3 penalty minutes. The first structural break in the
LM Unit Root Test Results for NHL Fight, mean penalty minutes occurs in 1978 and in
Penalty, and Performance Data, 1957–1958 the coefficient of variation in 1969. While mean
through 2012–2013 penalty minutes had an upward trend prior to
the break, the upward trend slope increases after
Time Series k Breaks Test Statistic Break Points 1978. Following the second structural break in
FPG 0 1975, 1988 −5.402* λ = (.4, .6) 1993, the trend in mean penalty minutes shifts
PCTGF 0 1966, 1988 −5.737** λ = (.2, .6) downward and becomes negative, similar to what
PCTGMF 0 1974, 1988 −5.368* λ = (.4, .6) occurs in the series related to fighting. Particu-
PCTPF 0 1967, 1987 −5.409** λ = (.2, .6) larly noteworthy is that the second break occurs 5
MPM 1 1978, 1993 −6.190** λ = (.4, .6)
CVPM 4 1969, 2002 −6.474*** λ = (.2, .8) or 6 years after the 1987–1988 breaks in fighting,
MG 0 1978, 1997 −5.256 λ = (.4, .8) suggesting that a change in social norms occurred
CVG 0 1962, 1987 −7.951*** λ = (.2, .6) prior to the change in formal enforcement by ref-
MA 0 1984 −4.222* λ = (.6) erees. Interestingly, this break occurs at the same
CVA 0 1986 −7.791*** λ = (.6) time hockey implemented stricter rules on fight-
MPTS 0 1979, 1996 −5.535* λ = (.4, .8)
CVPTS 0 1970, 1987 −9.776*** λ = (.2, .6)
ing that should have increased penalty minutes,
ceteris paribus. Similar to the series describing
Notes: Variables are defined as follows: number of fights fighting, after the second break the mean penalty
per game (FPG), percentage of games with a fight (PCTGF), minute time series continues to fall through the
percent of games with multiple fights (PCTGMF), percent end of our sample period in 2013. The decrease
of players who fought in a given season (PCTPF), the mean in mean penalty minutes continued even after a
and coefficient of variation of penalty minutes across players
in a given season (MPM and CVPM), mean and coefficient second referee was introduced for all games in
of variation of the number of goals scored across players 2001, which further suggests that a change in cul-
in a given season (MG and CVG), mean and coefficient of ture and behavior had already occurred and rule
variation of assists across players in a given season (MA and
CVA) and the mean and coefficient of variation in points changes followed.
across players in a given season (MPTS and CVPTS). The We next consider the results from Tables 3
Test Statistic tests the null hypothesis of a unit root, where and 5 for the performance series. The bottom
rejection of the null implies a trend-break stationary series.
k is the number of lagged first-differenced terms included
panel of Figure 1C plots the series related to goals
to correct for serial correlation. The critical values for the scored and Figure 1C plots the series related to
one- and two-break LM unit root tests come from Lee and assists and total points. Looking first at Table 3,
Strazicich (2003, 2013). The critical values depend on the except for the mean goals series, we find that all
location of the breaks, λ = (T B1 /T, T B2 /T), and are symmetric
around λ and (1 − λ). *, **, and *** denote significance at the performance series are stationary around one or
10%, 5%, and 1% levels, respectively. two structural breaks.20 The evidence suggests
that for the mean performance series with two
breaks (mean goals, mean points) the first break
break in 1988. Following these second breaks, occurs in either 1978 or 1979. In sum, these series
all four fight series show a downward shift and a show a slow upward trend that shifted upward
trend that goes from positive to negative. To sum- and turned downward after the break. The second
marize, all four of these series show that fight- structural break for these series occurs in 1995
ing in hockey increased to a peak in 1987–1988 or 1996, after which the trends of these series
and declined thereafter. In contrast, three of the shifts downward and levels off or begins a slight
four major rule changes to deter fighting occurred turn upward. Most notable, the results show that
in 1992, 2000, and 2009, which is 4 or 5 years the offense-related measures of mean points and
after the establishment of a downward trend in assists peaked ten years before fighting peaked.
fighting. Although hockey has always had a cul- Then both series showed a decline that bottomed
ture of fighting, fighting in the NHL reached a out for the offense-related measures in 1996 but
zenith in the late 1980s and declined prior to continued to decline for fighting. In sum, the
most of the major rule changes implemented to results suggest a rise and fall in the role of fighting
reduce fighting. in hockey driven by changing social norms rather
Turning next to penalty minutes, both the
mean and coefficient of variation are station- 20. While the Mean Goals series could not reject a unit
ary around two structural breaks. Table 5 reports root (at the 10% level), it nearly does so and has two structural
breaks like those identified in the other five performance
results from the regressions on the level and series. Given this outcome, we include Mean Goals in the
trend breaks reported in Table 3. The upper panel discussion that follows while some caution is warranted when
of Figure 1B displays the time series related to interpreting the regressions and visual plots of this series.
Electronic copy available at: https://ssrn.com/abstract=3593694DEPKEN, GROOTHUIS & STRAZICICH: EVOLUTION OF COMMUNITY DETERRENCE 297
TABLE 4
OLS Regressions on Level and Trend Breaks of NHL Fight and Penalty Data 1957–1958 to
2012–2013
FPGt = 0.073 + 0.389D1975 + 0.580D1988 + 0.015Trend + 0.026T 1975 – 0.015T1988 + lags(1) + et
(2.276)** (5.061)*** (5.749)*** (4.589)*** (2.925)*** (−4.557)***
R2 = 0.890 SER = 0.086
PCTGFt = 15.745 + 4.472D1966 + 36.322D1988 + 0.211Trend + 1.769T 1966 − 0.825T 1988 + lags(0) + et
(11.760)*** (1.921)* (16.585)*** (0.939) (11.543)*** (−6.554)***
R2 = 0.904 SER = 4.048
PCTGMFt = 0.495 + 8.324D1974 + 15.936D1988 + 0.363Trend + 0.886T 1974 – 0.465T 1988 + lags(1) + et
(0.577) (4.615)*** (5.847)*** (4.224)*** (3.537)*** (−4.142)***
R2 = 0.871 SER = 2.683
PCTPFt = 34.142 + 2.513D1967 + 4.563D1987 − 0.795Trend + 0.718T 1967 − 0.465T 1987 + lags(0) + et
(16.297)*** (0.974) (1.802)* (−2.685)*** (5.276)*** (−4.884)***
R2 = 0.813 SER = 3.364
MPMt = 28.585 + 12.652D1978 + 11.511D1993 + 0.308Trend + 0.744T 1978 − 0.786T 1993 + lags(0) + et
(23.185)*** (4.045)*** (3.098)*** (3.623)*** (2.462)** (−2.517)**
R2 = 0.759 SER = 4.104
CVPMt = 104.443 + 20.905D1969 − 4.029D2002 + 1.714Trend − 0.265T 1969 + 1.961T 2002 + lags(0) + et
(31.475)*** (5.756)*** (−0.465) (4.419)*** (−3.976)*** (1.673)
R2 = 0.546 SER = 5.102
Notes: Variables are defined as follows: number of fights per game (FPG), percentage of games with a fight (PCTGF), percent
of games with multiple fights (PCTGMF), percent of players who fought in a given season (PCTPF), the mean and coefficient
of variation of penalty minutes across players in a given season (MPM and CVPM). t statistics are shown in parentheses. D and
T represent dummy variables for the identified intercept and trend breaks respectively. Trend denotes a common trend. White’s
robust standard errors were utilized to control for heteroscedasticity. Lagged values of the dependent variable were included to
correct for serial correlation as described in Section III. SER indicates the standard error of the regression. ***, **, and * denote
significance at the 1%, 5%, and 10% levels, respectively.
than formal rule changes, the latter of which began prior to formal deterrence changes, that is,
occurred 4 or 5 years after the structural breaks. community deterrence began 7 or 8 years prior
The results on fighting when applying the BP to formal rule changes instead of 4 or 5 years
tests for multiple breaks are consistent with our prior.
findings that a change in trend from positive to
negative occurred prior to a formal change in
rules by the NHL. For fights per game and percent VI. CONCLUSION
of games with a fight there is a change in the trend
from positive to negative in 1988 in both sets of Sometimes community deterrence changes
results. For percent of games with multiple fights before formal deterrence and sometimes the
and percent of players who fought when using the other way around. Hockey is a violent game
BP test the trend in fighting changes from pos- and is the only major team sport where fighting
itive to negative in 1985 and 1984, respectively, does not result in an automatic ejection. His-
instead of 1988 and 1987 as with the LM unit root torically, hockey had so-called enforcers who
test. While the results in these cases for the trend aimed at deterring dirty play against star players
break occur 3 years prior to our LM unit root test and goalies by responding aggressively to such
results, these results can be said to provide even behavior through fighting. However, over time
greater support to our hypothesis that changes in the NHL implemented rules aimed at reducing
community deterrence about fighting in the NHL the need for the enforcer by increasing the costs
Electronic copy available at: https://ssrn.com/abstract=3593694298 CONTEMPORARY ECONOMIC POLICY
FIGURE 1
Rule Changes and Structural Breaks in NHL Fights, Penalties, and Performance Data
A
and decreasing the benefits of fighting. Our The empirical evidence provided in this paper
research question is whether such rule changes shows that all four series related to fighting in the
predated changes in player behavior or vice- NHL have an upward trend that peaks around the
versa? This question is related to the strain of time of a structural break in 1987–1988 and turns
literature focusing on the use of formal and downward thereafter. While the NHL imple-
community deterrence measures. mented several rule changes in 1992, 2000, and
Electronic copy available at: https://ssrn.com/abstract=3593694DEPKEN, GROOTHUIS & STRAZICICH: EVOLUTION OF COMMUNITY DETERRENCE 299
FIGURE 1
Continued
B
2009, to increase the costs and decrease the ben- the form of major rule changes to reduce fight-
efits of fighting, all of these rule changes occurred ing. We conjecture that these changing social
at least 4 or 5 years after the structural breaks in norms among players might have been influenced
fighting. In sum, these findings suggest that com- by growing concerns about head injuries or by
munity enforcement in the NHL changed before a decreased preference for fighting on the part
the implementation of specialized enforcement in of fans. The identification of the source of these
Electronic copy available at: https://ssrn.com/abstract=3593694300 CONTEMPORARY ECONOMIC POLICY
FIGURE 1
Continued
C
changes in social norms is an interesting avenue While our empirical investigation focuses on a
for future research.21 specific community, there is anecdotal evidence
21. Additionally, we expect that other social norms flagrant and technical fouls in professional basketball can
within sport such as hit batsmen in professional baseball, potentially all be addressed using the same methodology
unnecessary roughness penalties in American football, and employed herein.
Electronic copy available at: https://ssrn.com/abstract=3593694DEPKEN, GROOTHUIS & STRAZICICH: EVOLUTION OF COMMUNITY DETERRENCE 301
TABLE 5
OLS Regressions on Level and Trend Breaks of NHL Performance Data 1957–1958 to 2012–2013
MGt = 7.474 + 2.338D1978 − 1.177D1997 + 0.048Trend − 0.157T 1978 + 0.016T 1997 + lags(1) + et
(4.090)*** (2.583)** (−2.742)*** (2.075)** (−2.852)*** (0.916)
R2 = 0.841 SER = 0.575
CVGt = 118.221 − 5.125D1962 − 2.220D1987 − 3.031Trend − 0.393T 1962 − 0.120T 1987 + lags(0) + et
(28.195)*** (−1.057) (−0.502) (−3.110)*** (−2.858)*** (−1.387)
R2 = 0.471 SER = 4.701
MAt = 6.482 + 0.842D1984 + 0.078Trend − 0.064T 1984 + lags(2) + et
(3.048)*** (0.951) (1.998)* (−1.892)*
R2 = 0.775 SER = 1.127
CVAt = 88.622 + 5.449D1986 − 0.215Trend − 0.087T 1986 + lags(0) + et
(64.695)*** (2.826)*** (−2.914)*** (−1.345)
R2 = 0.600 SER = 3.299
MPTSt = 29.002 + 8.846D1979 − 4.848D1996 + 0.148Trend − 0.605T 1979 + 0.105T 1996 + lags(0) + et
(42.120)*** (10.453)*** (−6.014)*** (3.328)*** (−9.986)*** (2.374)**
R2 = 0.860 SER = 1.398
CVPTSt = 108.166 − 3.972D1970 + 7.616D1987 + 0.030Trend + 0.038T 1970 − 0.158T 1987 + lags(1) + et
(7.989)*** (−1.534) (3.795)*** (0.163) (0.270) (−2.981)***
R2 = 0.592 SER = 2.725
Notes: Variables are defined as follows: mean and coefficient of variation of the number of goals scored across players in
a given season (MG and CVG), mean and coefficient of variation of assists across players in a given season (MA and CVA)
and the mean and coefficient of variation in points across players in a given season (MPTS and CVPTS). Dependent variable is
the number of mean number of goals per player, coefficient of variation of goals per player, mean number of assists per player,
coefficient of variation of assists per player, mean number of points per player, and coefficient of variation of points per player per
season, respectively. t statistics are shown in parentheses. D and T represent dummy variables for the identified intercept and trend
breaks respectively. Trend denotes a common trend. White’s robust standard errors were utilized to control for heteroscedasticity.
Lagged values of the dependent variable were included to correct for serial correlation as described in Section III. SER indicates
standard error of the regression. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively.
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