Cultures of illegality in the National Hockey League.

• Author: Allen, W. David

1. Introduction

   The economic model of crime demonstrates how an individual might decide to engage in illegal activity. It demonstrates that such activity may be motivated by incentives associated with a person's human capital skills, the availability of legitimate activity, preferences for risk, the potential sanction, and the probability of detection. But individualized as it may be, illegal activity still takes place in a social context. Fundamentally, a person who commits a crime has violated laws or other institutions formed by the larger social group. By the same token, society's collective experiences, fears, expectations, and reactions in relation to crime may well influence the individual decision to commit crime. Given crime's social content, can we disentangle the influence of social environment, or culture, from the individual factors that determine crime? (1) This article addresses this question.

   In the economic model of crime, hypothetical agents consider the various benefits and costs of legal and illegal activity and then decide how much time to devote to either activity. A more criminalized culture of illegality might enhance the potential benefit of clime through tacit or overt encouragement of crime and might reduce the potential cost of crime by relieving some of the stigma (social cost) associated with it. (2) If individuals experience a more pronounced culture of illegality, they might engage in more illegal activity on that basis; in principle, if we could remove them from that culture, they would less likely engage in illegal activity. But many factors complicate this possibility.

   Over time and over space, societal crime rates appear to vary in the opposite direction as overall wealth, whether measured in terms of legal wage opportunities or income level. (3) Therefore, any hypothetical change in a person's culture of illegality would almost certainly imply a change in his wealth or his opportunity to engage in legal time allocation. Furthermore, an individual who experiences a cultural change carries along a set of personal characteristics (e.g., tastes for illegality or for risk) that likely do not vary across cultures. Testing empirically for the influence of culture on individual-level crime thus requires a sample of individuals who engage in both legal and illegal activity, data on their personal incentives to engage in legal and illegal behavior (including their wealth), data on their cultures of illegality, and some exogenous cultural change that affects some subset of them. The data used in this study, relating to players in the National Hockey League (NHL), possess each of these features.

   As illustrated by Allen (2002), the NHL provides a useful setting for analyzing the economic model of crime, especially when one follows the legal and illegal behavior of a sample of players over a period of time, in a panel setting. Like citizens in society, hockey players react to a number of factors interpretable as benefits or costs associated with committing illegal activity (on-ice rules violations, which result in penalties). For example, a player's own history of involvement in illegality, such as measured by his career penalty minutes, likely indicates the manner by which he generally achieves success in the sport, while deficiencies in his current team at penalty killing (defending against goals while shorthanded) likely act as costs and, hence, as deterrents.

   Because hockey players have team-based objectives, their behavior may be influenced by the values and expectations of a larger social group (the team, the league, fans) with respect to physically aggressive play. In ice hockey, the culture of illegality may even have a situational character: In a given game, the degree to which one player's illegality is accepted may emanate in part from the level of illegality or violence demonstrated by the opposing team in that game. Also, because some players get traded from one team to another during the course of a season, we can observe economic agents who experience exogenous change in the culture of illegality around them. These elements of the NHL experience provide a rare opportunity to investigate how culture and cultural change influence illegal activity alongside individual-specific factors.

2. Culture and the Economic Model of Crime

   This section develops an economic model of crime participation that draws upon that advanced by Becker (1968) and extended by Block and Heineke (1975), Witte (1980), and Schmidt and Witte (1984). In the model, individuals decide whether to engage in illegal activity based on the benefits and costs of legal and illegal activity, each activity potentially generating income and, hence, utility. The variant of the model presented here incorporates the culture of illegality as an exogenous factor that influences the expected benefit and cost of illegality and the agent's wealth, as suggested in the Introduction. Having established the conditions for optimum illegal time, we consider the comparative statics of variation in three factors: wealth, illegal gains, and the culture of illegality. This analysis lays the foundation for the subsequent empirical investigation and discussion.

   Let [t.sub.L] and [t.sub.I] represent time that may be devoted to legal and illegal activity, respectively. Suppose legal activity offers a gain according to the function L([t.sub.L];[delta]), where [L.sub.t] = [partial derivative]L/[partial derivative][t.sub.L] > 0, [delta] is a shift parameter through which legal gains may change, and [L.sub[delta]] = [partial derivative]L/[partial derivative][delta] > 0. Suppose illegal activity offers a gain according to the function G([t.sub.I], c;[alpha]). In this function, c represents an index measuring the culture of illegality, that is, the attitudes and expectations of the agent's immediate social group in relation to illegal activity. In addition, [G.sub.1] = [partial derivative]G/[partial derivative][t.sub.I] > 0, [G.sub.c] = [partial derivative]G/[partial derivative]c > 0, and [alpha] is a shift parameter through which illegal gains may change, independent of time allocation and culture, such that [G.sub.[alpha]] > 0. We additionally assume [L.sub.I[delta]] = [[partial derivative].sup.2]L/[partial derivative][t.sub.I][partial derivative][delta] > 0, [G.sub.Ic] = [[partial derivative].sup.2]G/[partial derivative][t.sub.I][partial derivative]c > 0, and [G.sub.I[alpha]] = [[partial derivative].sup.2]G/[partial derivative][t.sub.I][partial derivative][alpha] > 0. (4)

   If the illegal activity is detected, there will accrue a penalty given by the function F([t.sub.I], c; [beta]). In this function, [F.sub.c] = [partial derivative]F/[partial derivative]c < 0, reflecting the assumption that a greater culture of illegality reduces social costs of illegal activity, while [beta] is a shift parameter through which the sanction may change exogenously. Finally, we shall characterize the agent's accumulated wealth, interpretable as income independent of the time-allocation decision at the margin, as a function of the culture of illegality, so that V = V(c). We make no assumption about the sign of [V.sub.c].

   If the illegal activity is undetected, income will be

   (1) [I.sub.u] = V(c) + L([t.sub.L]; [delta] + G([t.sub.I], c; [alpha]),

   while if the illegal activity is detected, income will be

   (2) [I.sub.d] = V(c) + L([t.sub.L]; [delta]) + G([t.sub.I], c; [alpha]) - F([t.sub.I], c; [beta]).

   Let the function p(N) represent the probability that any offense is detected, where N is the number of police officers at work and [p.sub.N] = [partial derivative]p/[partial derivative]N > 0. In the present application, the police officers are on-ice referees. (5) The individual's expected utility may then be written as

   (3) Z = E[U(I)] = [1 - p(N)]U([I.sub.u]) + p(N)U([I.sub.d),

   and the agent will select the levels of [t.sub.L] and [t.sub.I] that maximize Z, subject to the constraint [t.sub.L] + [t.sub.I] = T, the time available to the agent. (6)

   A necessary condition for the existence of an optimum level of illegal time is that

   [H.sub.1] = [partial derivative]Z/[partial derivative][t.sub.I] = (1 - p)[U.sub.G]([t.sub.I]; [theta])[G.sub.I]([t.sub.I], c; [alpha]) + p[U.sub.G]([t.sub.I]; [theta])[G.sub.I]([t.sub.I], c; [alpha]) = 0,

   where [theta] is a vector containing the shift parameters of the model and [U.sub.G] = [partial derivative]U/[partial derivative]G. In the present setting, we assume [F.sub.I] = [partial derivative]F/[partial derivative][t.sub.I] = 0, that is, that the penalty is independent of the amount of time allocated to illegality. (7) In the interest of brevity, the accompanying first-order condition for optimum legal time is not shown here. Following total differentiation of [H.sub.1], the generalized marginal effect on optimal illegal time of variation in any shift parameter may be expressed as

   (5) [partial derivative][t.sub.I]/[partial derivative][theta] = ([U.sub.G[theta]][G.sub.I] + [U.sub.G][G.sub.I[theta]])/[U.sub.II],

   where [U.sub.G[theta]] = [[partial derivative].sup.2]U/[partial derivative]G[partial derivative][theta], [G.sub.I[theta]]= [[partial derivative].sup.2]G/partial derivative][t.sub.I][partial derivative][theta],and [U.sub.II] = [[partial derivative].sup.2]U/partial derivative][t.sup.2.sub.I]. Using this expression, we may consider comparative-static results for any element of [theta].

3. Comparative Statics and Implications

   In illustrating comparative statics, we assume the economic agents are risk averse. (8) The relationships of interest in this study concern variation in optimal illegality given variation in accumulated wealth, illegal gains, and the culture of illegality. Comparative statics relating to variation in legal gains, the cost of illegality, and the presence of police in the context of the NHL are discussed by Allen (2002).

   Accumulated Wealth

   Other things equal, variation in accumulated wealth influences...