Tuesday, June 19, 2012

Dan Ariely on the Cost of Justice

We're getting the cognitive scientist hat trick today.  Today's guest is Duke professor Dan Ariely.  Dr. Ariely is a renowned author, psychologist, and behavioral economist.  He is the author of two New York Times bestsellers: Predictably Irrational and The Upside of Irrationality.  His most recent book, The Honest Truth About Dishonesty: How We Lie to Everyone--Especially Ourselves, came out earlier this month.  His TED talk on human irrationality has over one million views.

Dan asks,

How much do blue-collar criminals steal per year compared to white-collar criminals? How much do blue-collar criminals make per year on average?  How much money do we spend on the justice system in totality? How much economic gain do we get from it?  In other words, how much are we spending on the system and how much crime in economic terms are we preventing?

According to Wikipedia, white-collar crime

...was defined by sociologist Edwin Sutherland in 1939 as "a crime committed by a person of respectability and high social status in the course of his occupation."

In contrast, blue-collar crime is committed by individuals of lower social status. Using these definitions, there's not a sharp cutoff between blue- and white-collar crimes. Even if these terms were well-defined, getting precise statistics on how many of these crimes are committed is difficult since many of them go unreported. For this reason, I'll need to make a lot of assumptions in this problem.

According to at least one source, there are roughly 2.3 million people presently held in American prisons. If we use data from the Bureau of Prisons, we find the relative percentage of prisoners incarcerated for various crimes:

As mentioned above, there's some arbitrariness surrounding the definitions of blue- and white-collar crimes. Given the context of Dr. Ariely's question, I'm only going to consider crimes that have an inherent financial component.1 I'll further assume that drug, robbery, burglary, larceny, and property offenses all fall under blue-collar crime, while banking, insurance, counterfeit, and embezzlement offenses fall under white-collar crime.2 Using this categorization, over 50% of crimes would be considered blue-collar, which is in stark contrast to the 0.4% of crimes that are considered white-collar. According to Sutherland, "less than two percent of the persons committed to prisons in a year belong to the upper class," which is consistent with my assumptions. It's worth noting that these figures only count crimes where the crook was convicted and sentenced to serve time. There are undoubtedly a large number of crimes where the perpetrator has been either not apprehended, acquitted, or given a sentence that did not involve incarceration. Below is a chart illustrating the clearance rate (i.e., the fraction of time charges are filed for reported crimes) for various crimes:

Even these figures are fraught with peril. For example, robberies are more likely to be reported than money laundering, if for no other reason than the fact that a victim is immediately aware that a robbery is taking place when there's a gun pointed at his face.

For simplicity, I'm going to pull some numbers from Wikipedia and make some very basic assumptions.  According to the Wikipedia entry for "Crime in the United States", in 2009 roughly 3466 crimes were committed for every 100,000 people.3 Spread over a population of 300 million people, this means about ten million (~1×107) crimes are committed each year. Roughly 50% of these (~5×106) can be considered financially-motivated blue-collar crimes, while roughly 0.5% of these (~5×104) can be considered financially-motivated white-collar crimes.

I suspect the amount a blue-collar criminal steals each year varies quite a bit from person to person. A professional crook might be hitting a new house every day, but shoplifters and other petty thieves are less likely to be raking in the dough. You could steal anything from one dollar to over a million, but the average take, at least for professional crooks, is much more likely to be in the thousands. For concreteness, let's say $1000 per crime. If only to avoid being caught, I suspect the average criminal is not likely to rob more than 10 times a year (certainly fewer than 100). From these numbers we can conclude that the average blue-collar criminal steals at most $10,000 a year, with one-time offenders stealing much less and Ocean's 11-esque pros looting much more. Using this average as an upper bound, we can compute the maximum total amount our five million blue-collar criminals steal each year to be about $50 billion. Since this is an upper bound, we can reasonably argue that a realistic number is more likely in the one billion to $20 billion range.

White collar criminals are a different story. While fewer in number, they can use their fortunate disposition to gain control of much more money. A list of the top ten white-collar crimes shows thefts ranging from Martin Frankel's $200 million (~$2×108) swindling of insurance companies to Bernie Madoff's $65 billion (~$6.5×1010) ponzi scheme looting, but these are extreme cases.4 A more typical example might be Martha Stewart, who "avoided a loss of $45,673 by selling all 3,928 shares of her ImClone Systems stock...." If we assume a $100,000 (~$1×105) take, then our 50,000 white-collar criminals would rake in about $5 billion (~$5×109) each year.

There's a problem with this estimate. As one can easily see, Madoff alone took in more than ten times my estimate.5 What gives? While crimes like Madoff's are rare, they're significant because of the sheer volume of money involved. Significant rare events like these can be kryptonite to Fermi estimators. Moreover, as I pointed out earlier, blue-collar crimes are less likely to be reported. As such, my estimate is probably only good as a lower bound, so I'm going to need to up it a bit. Since we're talking order-of-magnitude estimates, it makes sense to bump my number up by a power of ten. This would give about $50 billion (~$5×1010) stolen each year by white-collar criminals. This is within an order of magnitude of the same numbers listed by the Wikipedia entry for "White-collar crime":
While the true extent and cost of white-collar crime are unknown, the FBI and the Association of Certified Fraud Examiners estimate the annual cost to the United States to fall between $300 and $660 billion.
At least one other source gives similar numbers:
It is estimated that white-collar crime cost the United States from $200 to over $300 billion every year. This is staggering compared to the estimated $15 billion to $20 billion in damages that blue-collar crime inflicts.
As you can see, my numbers are within a power of ten of these other estimates, but there is, admittedly, a huge error range associated with these figures.  

Let's try to put these numbers in context. The 2013 budget for the Department of Justice is set at $27.1 billion. Roughly $8.5 billion (~$8.5×109) of this is spent on prisons/detention facilities. Federal prisoners make up about 6% of the total incarcerated population, or about 138,000 people. As such, each federal prisoner would cost

($8.5 billion per year) / (138,000 people)
= $62,000 per person per year.

State prisons are a bit more efficient. According to the Wikipedia entry for "Incarceration in the United States"
In 2007, around $74 billion was spent on corrections. The total number of inmates in 2007 in federal, state, and local lockups was 2,419,241. That comes to around $30,600 per inmate.
In 2005, it cost an average of $23,876 dollars per state prisoner. State prison spending varied widely, from $45,000 a year in Rhode Island to $13,000 in Louisiana.
Even if we're building fairly efficient prisons at a net cost of $30,000 per prisoner per year, imprisoning blue-collar criminals costs the American taxpayer anywhere from 3 to 30 times more money than they would lose by letting these criminals run free. In contrast, letting 50,000 white-collar criminals run free would cost taxpayers 30 times more than it does to them lock up. This number skyrockets to 440 times as much money if we assume our white-collar criminals are stealing $660 billion.

A more efficient justice system would prosecute fewer of these guys...

...and more of these guys.

Economically, it seems drastically more efficient to lock up the high-class crooks and leave the petty thieves to themselves. However, this doesn't address Dr. Ariely's last question. Taken by itself, incarcerating blue-collar criminals is not cost-effective, unless you assume the mere threat of incarceration has prevented anywhere from 3 to 30 times more crimes. More on this in a moment. For now, let's naively assume the rate of crimes committed doesn't depend on the type of punishment doled out. If that's the case, taxpayers lose on average between $20,000 and $29,000 for every incarcerated blue-collar criminal. In contrast, taxpayers save between $70,000 and $13 million for every incarcerated white-collar criminal. Given five million (~5×106) blue-collar criminals and 50,000 white-collar criminals, the taxpayers would lose at most

($29,000) × (5×106) − ($70,000) × (5×104
= $140 billion

and potentially save

($29,000) × (5×106) − ($70,000) × (5×104
= $500 billion.

Given the huge error ranges, it's a little bit of a wash to say whether or not the justice system is cost effective for financial crimes. One thing that might shift the balance toward being a good system is the notion that the threat of punishment has prevented crimes from happening. Sadly, I don't really have a good way of estimating the number of crimes that would have occurred without a justice system. All I can really say is that you'd need to have prevented about five million crimes to break even.

So what have we learned from this? First off, whoever said crime doesn't pay was grossly misinformed. Second, the Department of Justice would do well to focus less on petty thieves and more on the white-collar criminals who got us into the financial mess we're currently in.

Dr. Ariely, thank you for a very challenging question. I feel like I learned a lot doing this one.

[1] For example, rape, murder, and jaywalking are all crimes, but there's no money exchanged, so I'm excluding these.
[2] Drug related offenses can be either possession (which does not have a financial component) or selling (which does have a financial component).
[3] It's unclear if this number represents the number of crimes committed or the number of crimes reported to police. I'm assuming the former for simplicity, but if it is the latter, one would need accurate clearance rates to compute the number of crimes committed.
[4] Seriously, who trusts a guy named Bernie Madoff? As in, "Bernie made off with my life savings!"
[5] Even if we take the $50 billion upper bound figure for the amount that all blue-collar criminals made in a year, it's still less than the amount that was stolen by one Bernie Madoff.

Aaron Santos is a physicist and author of the books How Many Licks? Or How to Estimate Damn Near Anything and Ballparking: Practical Math for Impractical Sports Questions.   Follow him on Twitter at @aarontsantos.

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