Bryan Caplan  

Does the U.S. Overpunish Violent Crime? Optimal Restitution on the Back of the Envelope

My Father's Day Essay for the ... Baiting Bryan...
I recently read a paper by Loyola prof (and GMU Ph.D.) Dan D'Amico.  The first part of the paper explained that among crime researchers, there is a strong consensus that the U.S. government is too punitive - even though the U.S. public believes the opposite. 

My presumption, as usual, is that experts are right and laymen are wrong.  But since most of these crime experts come from sociology and related far-left fields, maybe this consensus just reflects experts' ideological bias.  For victimless crimes, of course, I consider any punishment at all to be excessive.  But what about violent crime?  In a well-designed restitution-based system, how much would a criminal have to pay to, say, break your arm, and how long would it take him to repay his debt?

Let's start with willingness to pay.  If you have a comfortable First World existence, I doubt you'd settle for less than $10,000 to be the victim of a violent arm-breaking.  It's not just the pain; it's the fear.  If you add on medical expenses, that's probably another $5000.  If you count the willingness to pay of the people who care deeply about your well-being - most obviously your parents - that's probably at least another $5000.

This all adds up to $20,000.  But that is only reasonable restitution if the criminal is sure to be caught.  In the real world, the chance of catching an arm breaker is, say, more like 20%.  The roughly optimal restitution then comes out to $20,000/.2=$100,000.

How many years of indentured servitude in a prison factory would be required to repay this debt?  While violent criminals are generally healthy, young men, they're usually hard to monitor and manage and have few marketable skills.  Even if you could get their gross marginal productivity up to $20,000 a year, and hold room and board at the prison factory down to $15,000 a year, it would still take 20 years to work off the debt.  And that's ignoring interest!  At a 5% interest rate, $5000 per year just covers the interest on $100,000 of principal, so even an immortal arm breaker would never work off his debt.

Admittedly, there are some countervailing factors.  Victims might settle for less restitution than they're entitled to in order to improve convicts' work incentives.  Victims might prefer ankle bracelets and work release programs to get their money faster.  Prisons might offer criminals job training and split the rate of return.   And private prisons would certainly have an a strong incentive to curtail prisoner-on-prisoner violence, so they wouldn't be as awful as the prisons we've got.

Still, optimal restitution for even fairly minor assaults could easily justify a decade-plus of involuntary servitude.  And for violent crimes that do permanent physical and psychological damage, let alone murder, a criminal could easily burn up a lifetime's worth of human capital with a single offense.  Just imagine how quickly a kidnapper could rack up a million-dollar tab.

I'm the first to admit that these are only tentative calculations.  But as punitive as the U.S. is compared to other nations, it's simplistic to simply declare that the status quo is "too harsh."  That's obviously true for victimless crimes.  For violent crime, however, the central flaw of the status quo might well be excessive leniency.

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COMMENTS (24 to date)
Arnie writes:

This kind of post is why you add so much to this blog. Keep it up, Bryan.

OneEyedMan writes:

I completely agree that the purpose of justice should redress and that victimless crimes should be decriminalized and unpunished.

When we consider that the young men who commit most crimes have very high discount rates, we could easily end up in a situation where any number of serious crimes from aggravated assault on up to murder all consume same and entire life time earnings of the perpetrator. That eliminates the marginal incentives not to commit more serious crimes instead. Which is really bad. We don't want people committing murders instead of robberies because they carry the same punishments.

q writes:

I want to make an observation as a victim of a violent crime which was of the same scale as a violent arm-breaking -- never life-threatening, but harrowing nonetheless:

Redress and punishment cannot be reasonably specified by the victim. I became very emotional after the attack, and wanted this person (whom I had known for a long time) to suffer extreme pain. Nothing would have been too bad for this person. I could look at it rationally and see dissonance, and I was lucky in that -- I let other people counsel me for a while until I cooled down.

The lesson that I take from this is that it's dangerous to let victims specify punishments.

Andy Hallman writes:

Why are you using strict liability here? Are we assuming your arm was broken purposely? If it were not done purposely, would that change the amount of money you are owed?

Even if the criminal did break your arm intentionally, I'm not convinced that he should have to repay you in full if doing so is likely to reduce utility, on net. Maybe this would be a good time for you to explain why you do not take a utilitarian approach to punishment.

Bob Murphy writes:

Fascinating post, Bryan. This is why EconLog is one of the few blogs I allow myself to read when I'm putting off work.

A few points:

* Why are you assuming the convict has to work from within the prison? You lighten it up a bit, talking about ankle bracelets etc., but I still think you're not really gulping the idea of restitution vs. retribution. If the goal is to get the monetary debt paid off as fast as possible, then the judge simply rules how much the defendant owes the plaintiff. So the arm-breaker goes back to work on Monday, or maybe he even starts looking for a higher paying job. But it would be ludicrous to put him in a cell. Maybe he's a roofer or a plumber or a hairdresser? The ultimate threat of prison would only be needed for people who ignored judicial pronouncements or who were too dangerous to be allowed on anyone else's property.

* What about insurance? It would be analogous to malpractice insurance. Your take in this post could likewise "prove" that a free market in automobiles and roads wouldn't work, because if somebody hit me it might take years for him to pay me for the damage he caused with his car.

* For those interested, I wrote an essay [.pdf] on these issues in grad school that IMHO is still cutting edge.

Stephen Smith writes:

I think the issue of punishing violent crime would be a lot less relevant in a world without anti-drug laws. My understanding of America's murder high murder rate is that it's mostly due to our zealous prosecution of the drug war. As we've seen in Mexico in the last decade, drug wars induce violence among drug dealers and users, not just between them and the government.

Once you take the gang bangers out of the situation, you're pretty much only left with psychopaths, at which point I don't know that your rational cost/benefit analyses are very helpful.

Peter Twieg writes:

It seems like the conclusion that's going to be derived to the motivating question is heavily contingent upon particular assumptions about prisoner productivity and room-and-board costs. If you cut room-and-board costs by 1/3 in the example provided, you'd come to the conclusion that sentences should only be half as long. Or if room-and-board costs were increased by 1/3, then $1 of liability would lead to an infinite prison sentence.

If prisoners actually could choose their levels of productivity and have some control over their room-and-board fees, they'd probably spend less than 75% of their income on baseline expenditures. I'd guess.

JLA writes:

Professor - why use CV instead of EV as the baseline for payment?

David O writes:

First, it's far from clear that the optimal punishment rate is equal to the amount of damage done divided by the probability of being caught. If this were a zero sum game, and the victim got all of the benefits from the punishment, perhaps. But it surely depends on one's beliefs about recidivism and the utility of victims and wider society in imprisoning the convicts.

Second, this analysis is critically missing one significant factor: the non-zero risk of imprisoning an innocent. Disutility from imprisoning the innocent may not be symmetric with utility from imprisoning the guilty: statements like "it's better that 10 guilty men escape than that one innocent suffer" show that we also care about the extra-marginal effects on our sense of security before forces as powerful as the law, and these may currently be more important than the marginal effects of prison time on crime.

Dave Schuler writes:

The results are cooked. You can't draw any conclusions from the available data because the available data excludes too much.

The jail sentences of many criminal offenders doesn't mark the start or even the middle of their careers. It's closer to the end of their careers which probably began in childhood. Even in childhood their first arrests probably didn't mark their first offenses.

The parable of the broken window applies to criminal offenses, too. What about the years of robberies, assaults, and even murders that have been excused as first offenses or been expunged from the records since they were committed by juveniles?

seertaak writes:

I think Bryan's post is interesting, and I welcome the attempt to apply reason rather than emotion to these kind of questions. However, I think a) his calculus is incomplete, and b) it is wrong. a) causes his figure to be somewhat low, and b) causes it to be much too high.

Let me explain why.

a) It seems to me that a legal system should, in the allocation of jail time, pecuniary penalties, etc. according to the following pillars:

1. Punishment: if someone breaks the law, it is arguably appropriate that punishment be meted out. In Bryan's calculation, this is valued at 0.

2. Restitution: Bryan focuses solely on this.

3. Deterrence: It is reasonable for a penal system to allocate punishment above the direct or social cost of the behaviour in order to deter others, in future, from engaging in the same behaviour. In essence, this kind of punishment involves making the punishment higher than the infraction, so as "to make an example" of an individual (in other words, "pour encourager les autres"). Again, Bryan values this at 0. While the philosophical basis for such a type of punishment is no doubt questionable, it would be foolhardy to argue that, applied wisely and in a limited fashion, it can't contribute to overall lower crime, and it is in any case unwise to ignore it as it is a feature of almost all legal systems in use today.

4. Risk to society: Bryan's example involves breaking someones arm. Let's assume a more extreme infraction: say, child molesting, or murder. In these cases, above and beyond restitution, it is reasonable for a penal system to incarcerate the perpetrator simply as a protective measure to society. In other words, from a mathematical perspective the penal system, in effect, makes a determination of the future conditional probability of future infractions of a similar type, and allows this to influence the overall type, length, etc. of punishment. This is why in the penal system, past record is important.

b) I mentioned previously that I thought his calculation his wrong. More precisely, I think the "risk adjustment" aspect of his legal edifice is incorrect, and inconsistent with what I impute as his philosophical basis for punishment. Let me make this philosophical basis explicit, so that I may be taken to task for my premises: I think Bryan's overriding rule is, in very crude terms, "the non-violent equivalent of an eye for an eye". In other words, while he no doubt considers it vulgar for society to literally break the arm of someone who has done the same to a victim (and on this count I obviously agree!), he nevertheless feels that the perpetrator should suffer "equally", although perhaps spread out of over time. It is a utilitarian, cost-based approach to punishment.

And I think that's evident from his insistence that victimless crimes should not carry a punishment (not that I'm saying I disagree with this).

And by the metric of "U(eye) for eye", the risk metric seems unjust. Why should we adjust the penalty by the unconditional probability of getting caught? After all, the very fault that we are calculating the probability means that the perpetrator *has been* caught, whence the correct probability to use is that conditioning on being caught, in other words, 1! Another way of looking at this is: is it really just for the perpetrator to make good the lost utility on victims/society inflicted (potentially) by *others*, simply because he was the one caught? To put it again another way, let's imagine a crime in which detection was incredibly difficult and utterly random: detection rate was 1/1,000,000. Let's further assume that the cost at the victim's end was quite small, for the sake of argument, say $100. Would it then make sense for the perpetrator to receive a pecuniary punishment of $100,000,000? It seems to me this would be totally crazy.

It seems to me that the risk adjustment aspect of the calculation seems to incorporate aspects of deterrence into a calculation which is purported to only take into account restitution. Why else punish someone for the crimes of others?

Still, Bryan acknowledges that his calculation is crude, and I think the spirit of his approach is sound, so: great post!

Grant Gould writes:

Let me take up the risk adjustment step as well. I see three major adjustments.

(1) Questionable normative justiffiability -- punish A more harshly because unrelated criminal B was smart enough to avoid capture?

(2) Tricky line-drawing -- what if arm-breakers are caught 20% of the time, but right-arm breakers are caught 40% of the time, and white left-arm breakers are never caught at all... who decides how far to wander into that mathematical thicket?

(3) Incentive incompatibility -- the people punishing crime A want crime B to go unsolved so that crime A yields more compensation and/or jail time

In addition, I would note another questionable incentive that you allude to when you note that at some rates of interest a compensation claim may require a lifetime indenture: The people extracting compensation would have every incentive to make sure that this is so by setting interest rates so high and compensation so low (eg denying prisoners access to capital goods, selling their products below market rates, etc.) that even the debt for a stubbed toe could never be worked off.

Yancey Ward writes:

And if the violent criminal really doesn't have a marketable skill, he can always pay up through robbery and extortion.

Andy Hallman writes:

seertaak, you make many good points but I should tell you that this approach to punishment is not utilitarian:

...he nevertheless feels that the perpetrator should suffer "equally", although perhaps spread out of over time. It is a utilitarian, cost-based approach to punishment.

Utilitarians do not believe the guilty "deserve" to suffer. The suffering of the victim is in the past and thus is a sunk cost, and sunk costs are not counted when making a decision. Only expected costs are counted. The fact that a crime was committed does, however, count as a data point which figures in calculating an event's probability (such as how likely a criminal is to rob a bank given he has already done it twice), which is of course relevant for determining the proper punishment.

Eric Yu writes:

In order to deter crime, the expected punishment has to be more severe than the benefit the perpetrator receives from committing the crime, and in order to maximize total utility, the punishment should not be much more severe than this. Bryan uses the harm done to the victim to calculate the optimal punishment, but he should actually be using the benefit the criminal receives, which is usually less (i.e. murder costs the victim his/her life, but it does not give the killer an extra life; therefore, assuming the murderer is rational and has a 100% chance of being caught, the murderer should not be required to pay the full value of the victim's life.).

Ryan Singer writes:


Great Post! One note: In a system primarily based on restitution and liability, I expect liability insurance to be more common. Note that my $100/year renters insurance already covers over $100k in personal liability, and so does my auto-insurance.

The more we move towards restitution-based law, the more we can expect insurance companies to play a role in defining risk, insuring against it, determining fact, and collecting against liability.

Many apartment complexes require renter's insurance, and some careers require people to be bonded. I expect that in a restitution-based model, many more jobs, apartment complexes and such will require proof that you are insured against liability. I could easily imagine an America where the entirety of the middle-class is insured against these things, and has a parallel justice system to the one used by the poor. In fact, this is already the case when it comes to motor vehicles.

Henry writes:

One issue is that deterrence is bounded even if we adopted extremely harsh forms of punishment, because suicide is hard to stop. Now, punishing family members as well would give us greater deterrence. Aside from striking people as profoundly unjust, what's wrong with this? The main problem is that criminals may not care much about their family, so it would not provide much deterrence for its cost. In theory, we could create profiles for convicted criminals to determine who they would be upset at seeing suffer. In practice, everyone would have an incentive to claim that they did not have a close relationship with the person in question to avoid getting punished themselves, making the construction of such profiles difficult.

Rob writes:

In regards to Professor Murphy's post, it seems like the insurance scheme would be subjected to severe adverse selection and moral hazard problems. Addressing the former, the individuals most likely to buy insurance will be the ones hanging out in "the rough crowd". Also, once one has secured insurance, it is less costly to hang out in bad neighborhoods, provoke people who cut you off on the freeway, and pick up hitch hikers.

Now it can, and should be, argued that a private firm has incentives to screen applicants, mitigating the adverse selection problem and monitor customers, limiting the opportunities for moral hazard. But, if it's the case private firms can deal with the asymmetrical information problems, why don't private firms provide it already? When victims see the guilty thrown in jail, they are only compensated insofar as knowing he/she will suffer in incarceration. This surely does not come close to making the victim whole. Is it illegal to offer such insurance?

Ted Craig writes:

The so-called office of the drug czar was created in 1988. Violent crime started dropping steadily in 1993. I'm not saying there's a connection between the two, but maybe libertarians should at least consider a possible link. It makes more sense in many ways than Levitt's abortion theory, but doesn't fit many people's ideology as well.

Joshua Lyle writes:

Ted Craig,
I'm thinking the Ars Technica (somewhat tongue-in-cheek) thesis of a negative correlation between violent media and violent criminality is the most plausible of all.

Noah Yetter writes:

But since most of these crime experts come from sociology and related far-left fields, maybe this consensus just reflects experts' ideological bias. For victimless crimes, of course, I consider any punishment at all to be excessive.

Looks like it's pretty easy to test whether "crime experts" are actually experts or just ideologues (regardless of what that ideology might be). If they hold that victimless crimes should continue to be crimes (e.g. the Drug War should persist) then they're hacks and we can disregard every single thing they say.

Bob Murphy writes:

Rob wrote:

"Now it can, and should be, argued that a private firm has incentives to screen applicants, mitigating the adverse selection problem and monitor customers, limiting the opportunities for moral hazard. But, if it's the case private firms can deal with the asymmetrical information problems, why don't private firms provide it already? When victims see the guilty thrown in jail, they are only compensated insofar as knowing he/she will suffer in incarceration. This surely does not come close to making the victim whole. Is it illegal to offer such insurance?"

Great question. I don't know exactly which legal barriers currently are decisive, but I think at the very least, my proposed system couldn't go into effect right now, because it would be illegal for a store owner to kick out a customer who didn't have the appropriate insurance. It would also be illegal for a landlord to not rent to someone who didn't have this type of insurance too.

So in other words, right now the government insists that certain people have insurance--drivers need auto insurance, doctors need medical malpractice, roofers need some type, etc. But I'm pretty sure private people can't up the ante and say, for example, "For all I know you will kill people in this building, so I'm not renting an apartment to you unless you go get a policy which pays $1 million to the estate of anybody you are convicted of murdering."

Neverfox writes:

Am I the only one who finds it disturbing that Bryan simply assumes that indentured servitude is a legitimate option? If the perp does not presently have the money to pay, then they simply have a debt, like any other. No other debt legitimates indentured servitude.


I posted some of my thoughts after our second lunch last week, here:

Caplan on optimal restitution

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