And a Hockey Game Broke Out: Crime and Punishment in the NHL

I. INTRODUCTION The economic theory of crime predicts that an increase in policing resources will lead to a decrease in the crime rate. Empirically determining the magnitude of this effect has proved difficult, however, because of an endogeneity problem. Although variations in the allocation of policing resources are expected to affect crime rates, the reverse may also hold true (Cornwell and Trumbull, 1994; Levitt, 1997). The endogeneity problem can be avoided to a large degree by studying situations in which changes in the allocation of policing resources occur independent from crime rates. In an innovative and influential study, McCormick and Tollison (1984) apply the economic theory of crime to rules infractions in a sports contest. They analyze a policy change in the Atlantic Coast Conference (ACC) basketball tournaments. In 1979, the ACC increased the number of referees in the tournament games. McCormick and Tollison analyze the effect of increasing the number of referees on the number of fouls called. Their approach is unlikely to suffer from a severe endogeneity bias because the policy change occurred only once and furthermore occurred between tournament seasons. On the other hand, insofar as rules infractions in sports contests are analogous to criminal activity, McCormick and Tollison measure arrests, rather than crimes. The effect of an increase in policing resources on arrests cannot be resolved by theory. For a given crime rate, increases in police budgets and forces enable greater monitoring of criminal activity and consequently lead to more arrests. The crime rate, however, is itself a function of the level of policing resources. Rational criminals realize that greater monitoring increases the probability that their actions will result in arrest and may be deterred from committing crimes. This decreases the crime rate. The net effect on the total number of arrests is ambiguous because it depends on whether the monitoring or deterrent effect dominates. McCormick and Tollison find that increasing the number of referees leads to a reduction in the number of fouls called. This suggests that the deterrent effect dominates the monitoring effect. Shortly after their study was published, it was recognized in surveys of both sports economics, by Cairns et al. (1985), and crime, by Cameron (1988). We examine a natural experiment in sports to further understand the monitoring and deterrent effects. In the 1999-2000 season, the National Hockey League (NHL) games had either one or two referees. (1) We find that games with two referees have more penalties called, suggesting that the monitoring effect dominates the deterrent effect. We then use an instrumental variables technique to determine the effect of the number of referees on the number of infractions actually committed by players in the game. We find that the number of referees does not significantly affect the number of infractions committed. This is direct evidence that the deterrent effect is inconsequential in this context. Our results are unlikely to suffer from an endogeneity bias because the variation in the number of referees is independent of the rate of infractions in the individual games. II. THE NHL EXPERIMENT Enforcement of the rules in an NHL game is done by referees and linesmen. The NHL has historically utilized one referee and two linesmen. The linesmen are responsible for identifying infractions that result in a stoppage of play, such as icing (sending the puck from one end of the rink to the other) and off-sides (entering the offensive zone before the puck). The referee is responsible for identifying more severe infractions, such as slashing (swinging a stick at an opponent), hooking (using a stick to impede the progress of an opponent), and fighting (fisticuffs). When one of these infractions is identified by the referee, a penalty is called and the offending player is removed from the ice for a period of time depending on the severity of the penalty. …