The Italian Job

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.

…The average robbery lasts 4.27 minutes and leads to a haul of approximately 16,000 euros. Given that more than half of all bank robberies involve two or more perpetrators, the average haul per criminal is approximately equal to 8,700 euros.

…only about 40 percent of all bank robbers disguise themselves when robbing a bank.

Those are a few interesting facts from a bold new paper, Optimizing Criminal Behavior and the Disutility of Prison. The authors, Mastrobuoni and Rivers, use extensive data on bank robberies to model bank robbery as a second by second optimization problem:

The key insight of our model is that bank robbers face a trade-off when deciding how long to stay in the bank. By staying an extra minute, the robbers can collect more money, but they also run the risk of getting caught and sent to prison. The cost of being apprehended is a function of the disutility each individual places on going to prison. By equating the marginal benefit with the marginal cost of time spent in the bank, we can back out the unobserved disutility that robbers assign to prison.

The authors create a sophisticated model of optimizing behavior which they estimate using extensive data. In their conclusion, they focus attention on their finding that higher ability bank robbers have a higher disutility of prison. Thus higher ability offenders can be (especially) deterred by longer sentences. The authors focus attention on high-ability offenders because those are the offenders most likely to fit the assumptions of their rational-actor model. I think it’s actually better to focus on the contra-positive conclusion: its hard to deter idiots.

Moreover, there are plenty of idiots:

Not surprisingly, traveling to the robbery by foot and targeting a bank with a security guard are both consistent with lower ability offenders….

The existence of idiots, however, calls into question the optimizing assumptions of the model. As I argue in What was Gary Becker’s Biggest Mistake? the poorly-socialized-child theory of crime can suggest other approaches to combatting crime (e.g. cognitive behavioral therapy):

Here’s a simple test for whether crime is in a person’s rational interest. In the economic theory if you give people more time to think carefully about their actions you will on average get no change in crime (sometimes careful thinking will cause people to do less crime but sometimes it will cause them to do more). In the criminal as poorly-socialized-child theory, in contrast, crime is often not in a person’s interest but instead is a spur of the moment mistake. Thus, even a small opportunity to reflect and consider will result in less crime.

The guy who robs a bank that has a security guard and then attempts to run away seems like a poor fit for a rational actor model. Perhaps more thinking would have led a better planned bank robbery but more plausibly it would have led to no robbery at all. Thus, I’d frame the author’s contributions in this path-breaking paper as telling us not just about rational bank robbery but about the limits and bounds of rational bank robbery.


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