Economists are (Potentially) Detectives

EUB（经济本科生委员会）杂志《The Economizer》供稿。

I recently attended the Annual Nobel Prize Lecture about Claudia Goldin, whose bio on the Nobel Prize webpage comes with a captivating title - “The Economist as Detective”. I could imagine her thrill when she haunted down the threads of evidence, those invaluable data that later contributed to her masterpiece, buried deep down in the basement at Penn. Broadly speaking, that’s exactly what detectives do, researching, digging out evidence, putting together those pieces, and illustrating the truth. Individuals with remarkable perceptions might argue that the subject matter is drastically different, which sadly is only partially true, for academic economists have already reached their invisible hands to the field of criminology.

Before diving into how economic approaches are used in criminal studies, I would like to introduce a four-book mystery series published by two economists, William L. Breit and Kenneth G. Elzinga (with the pseudonym Marshall Jevons[^1]). Those books[^2] were named after concepts that every student in our department should be familiar with. As an avid mystery reader, those books not only provide me with intellectual satisfaction in an academic environment but also because they illustrate how economists perceive the world, even in a fictional realm with an overly dramatic crime. The assumptions of rational decision and utility maximization are the fundamentals of our subject and of solving the crime. In the story, the key evidence is that when other things being equal, the suspect does not choose the option that maximizes its utility.

Of course, a perceptive student may quickly realize that a fictional world is not comparable to the complexity of our reality. Touché. Our world is packed with randomness and it is rare for police to arrest a suspect just because he or she does not pick the utility maximization option. Nevertheless, one only needs to reflect on Milton Friedman’s pool simile[^3], and our story about criminal economics can finally begin.

The first rigorous economic study of criminal behaviour was presented by Gary S. Becker in 1968[^4]. Although many criminologists believe the work to be oversimplified, it still greatly influenced later economists and gradually expanded into a new subject. Though the mathematical analysis is quite complicated, the ideas are simple. Economists propose that criminals possess no different traits than ordinary people because it is the preferences and laws that distinguish them. Thus, individuals obsessed with heroin are no more special than those addicted to tobacco. Furthermore, if there were no legal restrictions on heroin, the price would not have been drawn up so drastically and impelled those drug addicts to commit other crimes to maximize their purchasing power. Obviously, as economists usually do, the discussion above is under the ceteris paribus assumption as if heroin causes the same level of addiction and harm as tobacco do. Given the assumption that criminals are ordinary people with anomalous preferences, many economic properties could be applied to criminal behaviour analysis.

For example, why does crime even exist? Since criminals are no less rational than ordinary people, and given the fact that crimes do happen now and then, the only solution is that criminals can gain something, whether tangible or not, from those actions. With more economic jargon , they maximize their utility through criminal actions. If we denote utility with U as we usually do, then we could derive a general utility relationship between the payoff of honest work $U(W)$, legal punishment $U(S)$, and a successful and complete crime $U(W_C)$ with $q$ probability of being captured as:
$$
(1-q)U(W_C)-qU(S) > U(W), 0\le q \le 1
$$
This inequality states that a criminal’s payoff of a successful crime must strictly outweigh the benefit of doing honest work by their psychological and/or physical loss due to legal punishment. Perhaps this is why there have always been jokes about students studying criminology should pack their bags, go home, and urge the government to 1. increase the probability of police capturing criminals, and 2. increase the severity of punishment.

Nowadays, many impactful literatures are written in this field, and some modifications to the models are made to better fit the reality. In short, economic approach and rational analysis are becoming more important than ever to study and deter criminal actions, examples can be found in top-tier economic journals[^5]. Perhaps one day, economists would actually dig things that are deemed as genuine detective works.

Now, dear Watson, the game is afoot.

[^1]: As in Alfred Marshall and William Stanley Jevons.
[^2]: Those names are (by the publication order): Murder at the Margin, Fatal Equilibrium, A Deadly Indifference, and The Mystery of the Invisible Hand.
[^3]: See Microeconomic Theory by Walter Nicholson and Christopher Snyder, pp. 4
[^4]: Gary S. Becker, “Crime and Punishment: An Economic Approach”, Journal of Political Economy, March-April 1968, pp.169-217
[^5]: Such as Predicting and Preventing Gun Violence published in The Quarterly Journal of Economics by the University of Chicago Crime Lab.