Everyone Keeps Getting Becker's Crime Model Wrong

In a recent JPE article, Steven Levitt claims that Gary Becker's 1968 paper on crime makes predictions that are at odds with reality. Specifically, he claims that Becker's model predicts that the most efficient way to deter criminals is by combining a low probability of punishment (p) with an extremely severe penalty or fine (f) when a criminal is caught. Obviously, no developed country has a criminal justice system that functions this way. So, either the whole world is wrong or Becker was mistaken. Right?

I really respect Levitt, but this just isn't so. 

Becker's predictions depend on the risk preferences of criminals. If criminals are risk averse (or risk neutral), then Levitt is right that the optimal policy is to have a very low p and a very high f. To see why, suppose you start off with the opposite policy--a high p and low f. What happens if you decide to cut p in half and double f? The expected value of the penalty stays the same (pf = (p/2)*(2f)), but crime becomes more risky because you have increased the variance of the outcomes. On the one hand, this is bad news for risk averse criminals because they receive less utility from riskier crimes (see Figure 1). On the other hand, this is good news for taxpayers because imposing penalties is typically cheaper than trying to catch criminals. In other words, you are deterring criminals more and at a lower cost. If you keep increasing f and decreasing p, you will find that the cheapest way to deter risk averse criminals is to have a very low p and very high f. Just like Levitt said!

Unfortunately for Levitt, Becker did not think that criminals are risk averse. Instead, he spends a good chunk of his 1968 article arguing that criminals are risk lovers. In that case, making crime riskier actually INCREASES their incentive to commit crimes (see Figure 2). So, having a very low p and very high f is no longer the optimal policy. Becker goes on to argue that actual US policy seems consistent with the implications of his optimality analysis. In other words, Becker argues the exact opposite of what Levitt says.

Levitt is not the first person to mischaracterize Becker's paper in this way. In 2015, Alex Tabarrok wrote a blog post making a similar argument. Tabarrok's post was later boosted by Tim Worstall and Noah Smith. It is a shame that this keeps happening, especially in places like the JPE! It leaves the impression that Becker's paper is inherently flawed, possibly not worth reading. In reality, it is actually a good example of how to apply theory to understanding real-world problems.

Figure 1. Making Crime Riskier Deters Risk Averse Criminals

Following Becker (1968), these figure assumes the following. If a criminal is not caught, they get to keep all of the income they "earned" (Y). If they are caught, they have to pay some penalty or fine (f), leaving them with (Y-f). The probability the criminal is caught is p. In this figure, I illustrate the impact of increasing f from f to 2f and decreasing p from p to p/2 on a risk averse criminal.


Figure 2. Making Crime Riskier Encourages Risk Loving Criminals

Following Becker (1968), these figure assumes the following. If a criminal is not caught, they get to keep all of the income they "earned" (Y). If they are caught, they have to pay some penalty or fine (f), leaving them with (Y-f). The probability the criminal is caught is p. In this figure, I illustrate the impact of increasing f from f to 2f and decreasing p from p to p/2 on a risk loving criminal.