The optimising behaviour of Italian bank robbers

One of 1992 Nobel Prize winner Gary Becker's many contributions to economics was the development of an economic theory of crime (see the first chapter in this pdf). Becker argued that criminals, like other rational decision-makers, weigh up the costs and benefits of their actions, and will take the action that offers the greatest net benefits. That assumes we are talking about a discrete decision (a yes or no decision) based on incremental benefits and incremental costs. The benefits of crime include the monetary gains, and any 'rush' associated with committing the crime. The costs include any punishment that might be received, conditional on the probability of being caught (and convicted).

However, not all criminal decisions are yes/no type decisions. That is, not all decisions are made on the extensive margin. Some decisions are instead made on the intensive margin, such as how long to spend inside a bank while committing a robbery. The trade-off here is that the longer a criminal spends in the bank, the greater their haul of loot, but also the greater the risk of the police arriving and the criminal being caught. When a question is about the optimal amount of something (e.g. the optimal amount of time for the bank robber to spend in the bank), a rational decision-maker will optimise at the quantity where marginal benefit is equal to marginal cost. In this case, that will be whatever time in the bank where the last minute spent there equates the additional loot collected with the disutility (the negative utility) of being caught and punished.

In a recent discussion paper, Giovanni Mastrobuoni (University of Essex) and David Rivers (University of Western Ontario) exploit this equality using data on nearly 5,000 bank robberies in Italy, to estimate the disutility of imprisonment. Their dataset is quite rich and, while it doesn't include data on the robbers, it includes a lot of data about the robbery including, crucially, the exact duration of the robbery (which is often able to be confirmed using CCTV camera footage). They find that:

...the most successful robbers in terms of hauls use weapons, wear masks, and rob banks with fewer security devices and no guards. Those who work in groups, wear masks, target banks around closing time, and target banks with no security guards and few employees, achieve lower rates of apprehension. Offenders who use a mask and target banks without security guards have higher disutilities of prison. Robber ability is also found to be a strong driver of larger hauls, lower probabilities of arrest, and larger disutilities of prison. The latter finding is consistent with higher ability offenders having a larger opportunity cost of prison.

That latter finding is most interesting. Higher ability offenders tend to earn more from crime (and possibly have better earning opportunities outside of crime as well). So, the foregone earnings (from crime or otherwise) are higher for these offenders if they are imprisoned, which explains their higher opportunity cost of prison and their higher disutility of prison. The other results are mostly unsurprising. Mastrobuoni and Rivers also find that:

...heterogeneity in robber ability generates a positive correlation between criminal harmfulness and disutility. An importance consequence of this is that policies designed to affect those with higher disutilities of prison (for example simply raising overall sentences) have the added benefit of disproportionately targeting the more harmful (higher ability) offenders.

What that means is that the offenders who create the most harm (by being least likely to be caught, and generating the greatest hauls of loot) are also those with the greatest disutility of punishment. So, increasing the punishment for bank robbery would disproportionately deter the highest ability criminals, and have a large effect on reducing bank robberies. Whether the benefits to the state of greater punishment (less bank robbery) exceed the costs (more prisoners who cost money to house and feed) is not considered in the paper. However, for Italy it may well be the case, since:

Each year there are more bank robberies in Italy (approximately 3,000) than in the rest of Europe combined, with a 10 percent chance of victimization on average (there are about 30,000 bank branches).

Over the period 2000-2006, on average 8.7 percent of Italian banks were robbed each year. That compares with 2.2 percent in New Zealand (and a surprising 14.1 percent in Canada!). So, even if the benefits of greater prison terms for bank robberies exceed costs in the case of Italy, they may not do so for New Zealand.

[HT: Marginal Revolution]