# Are U.S. Cities Underpoliced?

on August 15, 2017 at 7:25 am in Economics, Law

Aaron Chalfin and Justin McCrary have a forthcoming paper in the Review of Economics and Statistics that takes a new approach to estimate the effect of police on crime. If you run an ordinary regression using the number of police to explain the number of crimes you typically find small or even positive coefficients, i.e. the police appear to have no effect on crime or maybe even a positive effect. The usual explanation is endogeneity. The number of police influence the number of crimes but the number of crimes also influences the number of police. The recent literature has focused on breaking this endogeneity circle by finding a change in the number of police that is exogenous, i.e. random with respect to crime. My paper with Jon Klick, for example, uses random movements in the terror alert level combined with the fact that the police go on double shifts when the terror alert level rises to estimate the effect of police on crime in Washington, DC. If the assumption of exogeneity is satisfied then you have pulled a random experiment out of natural data, hence a natural experiment. Obviously, if the exogeneity assumption isn’t satisfied the technique doesn’t work. But even if the exogeneity assumption is satisfied there is another problem–by focusing only on changes in police and crime when the terror alert level changes you are throwing out most of the variation in the data so the estimates are going to be less precise than if you used more of the variation in the data.

Chalfin and McCrary acknowledge the endogeneity problem but they suggest that a more important reason why ordinary regression gives you poor results is that the number of police is poorly measured. Suppose the number of police jumps up and down in the data even when the true number stays constant. Fake variation obviously can’t influence real crime so when your regression “sees” a lot of (fake) variation in police which is not associated with variation in crime it’s naturally going to conclude that the effect of police on crime is small, i.e. attenuation bias.

By comparing two different measures of the number of police, Chalfin and McCrary show that a surprising amount of the ups and downs in the number of police is measurement error. Using their two measures, however, Chalfin and McCrary produce a third measure which is better than either alone. Using this cleaned-up estimate, they find that ordinary regression (with controls) gives you estimates of the effect of police on crime which are plausible and similar to those found using other techniques like natural experiments. Chalfin and McCrary’s estimates, however, are more precise since they use much more of the variation in the data.

Using these new estimates of the effect of police and crime along with estimates of the social cost of crime they conclude (as I have argued before) that U.S. cities are substantially under-policed.

Hat tip Kevin Lewis.

Addendum: After writing this post I discovered that I had covered the Chalfin and McCrary paper when it was a working paper, five years ago! This tells you something about how long it can take to get an economics paper published.

1 Maz August 15, 2017 at 7:43 am

The fact that measurement error in independent variables causes downward bias in regression estimates seems to be almost always ignored in social science. E.g. we have lots of studies where values of Y are predicted from values of X with control variables A, B, C and D. If it is found that X is significant net of the control variables, it’s often concluded that X causes Y. Even assuming that the model is correct, this line of reasoning ignores the fact that X may be significant only because A, B, C and D are measured with less than 100% reliability.

2 Allen August 15, 2017 at 9:24 am

… so this Chalfin/McCrary “paper” is typical social science fluff and bs

3 Maz August 15, 2017 at 9:28 am

Umm, no.

4 Allen August 15, 2017 at 9:36 am

ahhh, so it’s atypicl fuff and bs. Please state of what practical use this paper is to the people dwelling in American cities.

5 Maz August 15, 2017 at 9:44 am

It seems like a decent paper. I don’t think research should always have immediate practical applications to be useful.

6 aMichael August 15, 2017 at 2:19 pm

This part seemed of practical use to people dwelling American cities:

“Using these new estimates of the effect of police and crime along with estimates of the social cost of crime they conclude (as I have argued before) that U.S. cities are substantially under-policed.”

7 dearieme August 15, 2017 at 8:02 am

But nobody knows how many crimes occur. All you know are reported crimes counts, with (I suspect) large margins of error and large biases. Moreover there’s every chance that the errors and biases vary with time and place. If economists wish to say anything useful about this topic they probably ought to go and serve on a police force for a few years to get a feel for the quality of the data.

8 Asher August 15, 2017 at 8:38 am

Furthermore it is quite plausible that reporting is also correlated with the number of police. Sources of correlation: likely to report a crime if it is likely to be investigated which is likely to be correlated with the number of police; likely to report a crime if it will impact level of policing which is likely to be correlated with the number of police; likely to report a crime if there happens to be a policeman nearby.

If the above is correct then the entire effect could be due to more reporting when there are more police about.

9 Maz August 15, 2017 at 9:14 am

If the error in crime reports is nonsystematic (random) then it’s not a big problem because random error in the dependent variable doesn’t bias OLS estimates. If it’s systematic, then it’s a problem. Victim surveys are better than official statistics in this sense, but they usually have only national rather than local data.

10 Willitts August 15, 2017 at 9:38 am

True, crime is also mismeasured, but error in measuring Y does not cause bias in the regression coefficients.

11 enoriverbend August 15, 2017 at 4:04 pm

“But nobody knows how many crimes occur. All you know are reported crimes counts, with (I suspect) large margins of error and large biases. ”

That’s true, but that’s also the reason for crime victimization studies, which give us a bit more information (although also under-, mis-, and occasionally over-reporting*). One way to handle this is to emphasize the types of crimes that are most likely to be reported (murder) over those less likely (larceny).

Not having read the paper yet, I don’t know if they utilized these.

*I ran a crime victimization survey some decades ago, and it was obvious that some people were so pissed off about crime rates that they would overstate their experience by including years other than the one being surveyed, and include experiences of family members and neighbors as if they had personally experienced it, etc. A few actually wrote additional comments on the survey instrument indicating they had done so “to make sure you get the point and do something about this”.

12 prior_test3 August 15, 2017 at 8:07 am

‘about how long it can take to get an economics paper published’

Maybe this could become a new crusade, trying to reform the economics paper approval process.

13 Axa August 15, 2017 at 8:38 am

I’d say this outcome arises because crime costs is distributed among a relatively low number of individuals (victims) while police costs are distributed among a much larger group of taxpayers. Thus, lack of empathy with victims.

14 Axa August 15, 2017 at 8:53 am

This is a bit sad: ” the recent crime literature has focused more on establishing that police reduce crime generally, rather than the extent to which police reduce violent crimes, or specific
crimes such as murder.”

So, it’s known that more police = less crime, but not which specific type of police such as patrol, detectives, narcotics, etc.

15 Taeyoung August 15, 2017 at 11:54 am

I think you’re right that there is a lack of empathy with victims, but I think it’s also complicated by the degree to which the populations that are most at risk from crime (poor, non-Asian, non-White, and geographically distinct) also send mixed messages about whether they want to be protected by the police or not. There’s certainly people in those neighbourhoods who would welcome greater police presence, but their voices are drowned out by the people who protest the police showing up in the neighbourhood at all. I can’t tell how much of that is real and how much of that is a kind of selection bias by a media, which regards the adversarial voices are more “authentic.” But I think there is some truth to the media portrayal.

16 Axa August 15, 2017 at 2:09 pm

Right, protests against police presence are another factor.

If most taxpayers are against higher police costs and some individuals are against more police in neighborhoods……that may explain the present situation.

17 Baked Alaska August 15, 2017 at 8:55 am

The Charlottesville Protests, and the absence of any violence there, shows that America is not under-policed. No one was maced, beaten up, or driven over–because the police kept the peace. Berkeley was also left without any property damage because the police kept everyone sane.

18 Tanturn August 15, 2017 at 11:05 am

+1

19 Art Deco August 15, 2017 at 9:06 am

I’m tired of having to grab my ankles every time a blackman walks down the street. Absolutely the cities are underpoliced.

20 Ray Lopez August 15, 2017 at 9:26 am

Or maybe you just enjoy it? Recall the scene of the pervert in Dirty Harry who begs for a beating…

21 Allen August 15, 2017 at 9:30 am

What is the proper level of “policing” in American cities?

How would one calculate that?

22 Willitts August 15, 2017 at 9:42 am

I haven’t read the original paper so I don’t know what under policed means. Generally it means that the benefit of increased policing will outweigh the costs. To calculate this one would have to know the cost of the marginal crime.

Perhaps this means we pay police officers too much.

23 John Thacker August 15, 2017 at 10:38 am

It could mean that we waste money on squad cars and technology that ought to be spend on more officers walking the beat, low technology staffed police boxes, etc. More lower tech officers with a consistent presence rather than a smaller number with occasional but rare overwhelming force.

24 Taeyoung August 15, 2017 at 12:05 pm

I don’t know how economists measure it, but I think that in general Americans underestimate the costs of crime. I think I’ve commented before how liberating it is to be in a place like Tokyo where people wander around in huge anonymous crowds with their wallets hanging out of their back pockets, or feel free to leave their \$800 smartphones on a cafe table while they go inside to order. The public spaces belong to ordinary people in a way they don’t in Washington DC, where you always have to be on guard for someone snatching your phone if you’re reading it inattentively in public and thieves are always stealing bicycles (even if DC bicyclists are mostly horrible and inconsiderate to pedestrians, they don’t deserve to have their bicycles stolen).

Even in DC, the proportion of people around you who are actually robbers and thieves is extremely low, yes. But in an anonymous crowd of a thousand people, they are enough. There’s a real cost to everyone in the community, there, even if it is almost impossible to value.

25 JWatts August 15, 2017 at 12:15 pm

“but I think that in general Americans underestimate the costs of crime.”

Most Americans don’t live in DC. I don’t really have to fear any of that kind type of crime living in the suburbs.

26 JWatts August 15, 2017 at 12:20 pm

Suburbs of Nashville, TN

27 dearieme August 15, 2017 at 12:31 pm

I incline to agree. People aren’t romancing when they talk, for instance, of how little fear of crime there was when they were growing up decades ago in XYZ. That lack of fear adds enormously to the douceur de vivre.

28 JonFraz August 15, 2017 at 1:34 pm

Quite a few people today grew up when crime rates were higher than they are now. You’re getting up into retirement territory if you grew up in a low crime era, though of course many people of all ages may have grown up in a low crime locality.

29 Mr. Econotarian August 16, 2017 at 1:27 am

I dropped a \$100 high speed train ticket on the ground in Tokyo station and before I could turn around someone grabbed it and ran off (and no, not to the lost & found).

30 Tanturn August 15, 2017 at 11:07 am

Basically, if more police than the current amount causes crime to go down, cities are under policed.

31 JWatts August 15, 2017 at 11:35 am

“Basically, if more police than the current amount causes crime to go down, cities are under policed.”

Meh, I would say that’s dependent on the nature and the cost of the crime.

Adding 100 cops to cut Jaywalking to nill is a waste of taxpayer’s money.

32 Art Deco August 15, 2017 at 3:11 pm

damn it I came here to post this but you beat me to it! Where’s the real Art when you need him.

33 Over Policed in Ramsey August 15, 2017 at 9:25 am

Maybe the problem is the definition of crime. Does policing stop certain crimes more than others? Should we make some of those not crimes?

34 Willitts August 15, 2017 at 9:47 am

White collar crime is usually independent of the number of beat cops.

I’m not certain that beat cops discourage crime by their presence as much as increasing the likelihood of getting caught, and punishment feeding back.

In my view, incarceration works not as a general deterrent but as a specific deterrent. Prison stops a criminal from committing more crimes.

35 John Thacker August 15, 2017 at 10:36 am

Isn’t discouraging crime by “increasing the likelihood of getting caught” a general deterrent? That’s my understanding of your usage, by contrast to specific deterrent being “this criminal is in prison and so will not commit more.”

36 Mark Thorson August 15, 2017 at 1:27 pm

There seems to be an implicit assumption that criminals decide on whether to commit a crime based on weighing the chance of getting caught and the cost of the penalty against the benefit of successfully commiting the crime. I submit that there are very few economist-criminals out there, and that most crimes are committed for less well-reasoned motives.

37 JonFraz August 15, 2017 at 1:37 pm

There are crimes of passion that happen without any prior thought given to them. However planned crimes usually do take into account the likelihood of getting caught.

38 JonFraz August 15, 2017 at 1:36 pm

Prisoners do commit crimes against other prisoners and sometimes against guards.
Moreover if you open up a niche by imprisoning a person who formerly filled it there’s a non-zero chance someone else will take his place.

39 Dave Smith August 15, 2017 at 9:53 am

What? We don’t know how many police there are? You have got to be kidding me. I would think that the measurement error would have to be in the number of crimes.

40 Rick Hyatt August 15, 2017 at 12:38 pm

We don’t. The US is not Scandinavia, all of our official statistics are junk. We don’t know even know how many people the police kill each year, because there are thousands of different police organizations unmotivated to report data in any consistent fashion. Perhaps you should read the paper before criticizing:

“We begin our discussion of the nature and extent of measurement errors in police personnel data using as an example the case of New York City in 2003. The UCR data for New York show 28,614 sworn police officers in 2003. Relative to the 37,240 and 35,513 sworn officers employed in 2002 and 2004, respectively, this is a remarkably low number. If the UCR figures are to be believed, New York lost a quarter of their sworn officers in 2003 and then hired most of them back the next year…The UCR data also indicate that New York lost a fifth of their civilian police employees in 2003 and then gained them all back in 2004, arguing against confusion over sworn officers versus civilian employees….Administrative data on police such as these are difficult to obtain. Some departmental annual reports are available, but they are not practical for econometric research. Annual reports do not circulate widely and even for cities and years where they are available, they do not always report the number of officers…Many people are surprised that there are errors in measuring the number of police officers.”

41 Dave Smith August 15, 2017 at 2:14 pm

Salary data? Clock in/out times? I am a pretty high-level college administrator. The state takes our student head counts very seriously. In fact, it is a scandal if we have one student that is improperly counted.

42 Rick Hyatt August 24, 2017 at 8:40 pm

Again:

“Administrative data on police such as these are difficult to obtain. Some departmental annual reports are available, but they are not practical for econometric research. Annual reports do not circulate widely and even for cities and years where they are available, they do not always report the number of officers”

Even if the police departments do, as one would hope, have accurate time data on their officers, that doesn’t mean *anyone else* and the *datasets in particular* have that data.

43 gregor August 15, 2017 at 11:11 am

If policing “doesn’t work” then why do people with the means pay for additional private policing?

44 dearieme August 15, 2017 at 12:27 pm

Indeed. And walls around their estates.

45 Ted Craig August 15, 2017 at 11:17 am

What parameters did the study use to define cities? There are a lot of very safe, very wealthy cities in the 100,000-resident range that are very safe and spend a lot on police, but the question has to arise if the police are the reason the residents are so safe, or is it the residents themselves? In other words, how to do you separate out spending on police out of need from spending in police as signaling?

I would add to the pro-spending that Coleman Young underinvested in the police force in general during the ’70s and ’80s in the name of fiscal responsibility and Detroit paid a heavy price. This included not buying equipment with a high upfront cost, such as helicopters, that might have saved money down the road.

46 John Thacker August 15, 2017 at 11:30 am

Personally I’d rather have more cops on the ground than the money spent on buying and operating choppers, but it could be a subject for further research.

47 Ted Craig August 15, 2017 at 12:31 pm

The thing about more cops is they stay on the books for decades.

48 John Thacker August 15, 2017 at 1:48 pm

Police helicopters cost quite a bit per hour of operation, unless you want to buy it and never fly it.

49 Ted Craig August 15, 2017 at 3:59 pm

True, but they don’t have pensions. And if one helicopter can replace two or three cops, the long-term savings might be higher. Anyway, my point isn’t police vs equipment, but underinvestment tends to be widespread. It’s typical of any poorly run enterprise, be it commercial or political.

50 Li Zhi August 15, 2017 at 11:45 am

So, the number of meter maids a city has matters?

51 Ted Craig August 15, 2017 at 4:00 pm
52 gregor August 15, 2017 at 11:53 am

I am reminded of this earlier post from Alex in which he argues seemingly the opposite:

http://marginalrevolution.com/marginalrevolution/2014/08/ferguson-and-the-debtors-prison.html

To be fair, though, I don’t actually think it’s contradictory to say there could be simultaneous over and under-policing in different respects (similar to the anarcho-tyranny idea). But that underscores the importance of who’s doing the policing, how they spend their time, and what their incentives are. There’s limited practical value in estimating the “optimal” headcount imo.

53 Taeyoung August 15, 2017 at 11:57 am

Well I think that makes sense. If you boost the number of police by 50%, but violent criminals are scary so they spend all their time going after parking infractions and jaywalkers, you’re not actually going to have much of an effect on violent crime.

54 The Other Jim August 15, 2017 at 12:25 pm

Sure, the cities are under-policed, but the real problem is that convicted criminals are under-imprisoned.

You need a lot more cops when you have to arrest each criminal eleven times throughout his lucrative “career.”

55 mulp August 15, 2017 at 2:30 pm

So, you advocate hiking taxes to fund confining 10% and up of the US population? About 10% are currently in prison, or parole, ie out of prison conditionally. The largest number of any nation.

56 Right Wing House Music August 15, 2017 at 7:43 pm

I question that statistic, mulp (30 million prisoners at any point in time?), but that’s besides the point. If America has 10x the number of criminals relative to the rest of the world, we need to have 10x the number of prisoners. And if they’re 10x harder to rehabilitate, then they need to be locked up for 10x as long.

Affirmative action-type quotas are stupid in virtually all contexts, but they’re especially stupid in the context of the criminal justoce system.

57 mulp August 15, 2017 at 2:31 pm

“Using these new estimates of the effect of police and crime along with estimates of the social cost of crime they conclude (as I have argued before) that U.S. cities are substantially under-policed.”

TANSTAAFL

Thus, Alex should have written:

Using these new estimates of the effect of police and crime along with estimates of the social cost of crime they conclude (as I have argued before) that U.S. cities are substantially under-TAXED.

58 Ted Craig August 15, 2017 at 4:01 pm

You do realize there is such a thing as misallocation, right?

59 john August 16, 2017 at 9:08 am

All spending is misallocated according to someone, or even many people. Doesn’t mean that spending/allocation not the economically efficient (in some paratian equalibrium cycle set context) in which case the additional police as a permenant feature would have to be increased taxes.

60 belisarius August 15, 2017 at 2:44 pm

The number of police have less to do with the crime rate than the number of laws. The fewer the laws, the lower the arrests for crime since there would be fewer crimes to commit. Remember history, late 19th century. When a mayor wanted to expand police powers or a prosecutor wanted to get re-elected on a tough on crime platform, they had their friends in the newspaper business report every little crime so it appeared there was a horrendous crime wave sweeping the city. Similar to the so-called opiate epidemic of today.
So much discussion about crime rates, police atrocities, and so on, without addressing the real problem. With thousands of laws on the books, it is easier for law enforcement to arrest just about anyone. With thousands of laws on the books, the number of crimes appears to rise.

61 chuck martel August 15, 2017 at 6:02 pm

Don’t forget that a percentage of criminals are policemen themselves. Like all the East Bay cops that were using teen-age Celeste Guap to satisfy their needs: http://www.news.com.au/world/north-america/former-underage-prostitute-wins-1m-in-huge-police-underage-sex-scandal/news-story/f53948490843c807c9e88ff1a79f3dd0 Or the Metro Gang Strike Force: http://www.citypages.com/news/metro-gang-strike-force-gets-off-scot-free-6537957 Or these members of Chicago’s finest: http://www.chicagotribune.com/news/local/breaking/ct-chicago-police-taco-burrito-beating-met-20161208-story.html

62 Boonton August 15, 2017 at 7:43 pm

Homeostasis— Your body typically is about 98.7 degrees. What would happen if you suddenly walked outside on a super hot and humid day wearing a temperature monitor that took your temp every 5 seconds? Or walked into a cold air conditioned room? Your body temp would probably change but after some time time your body’s metabolism would adjust to the ‘new normal’ and return to 98.7 or so.

So criminals in a city are used to a particular level of police presence on a ‘normal’ day and time. They are also probably aware of how police respond to dramatic events. Like if there was a shooting two blocks over, you probably should not be on the street doing crime because there will be a lot of cops riding around.

The insight in this paper seems to be that when the terror alert was raised, police suddenly were out more than ‘normal’. In other words, it’s almost as if the cops pretended there was a fake shooting somewhere, swarmed the area more than normal and made more arrests and deterred more crime than if they had just behaved as if nothing had changed.

However does this mean the city is underpoliced? Not so sure. If you permanently increased police you would simply reset the ‘normal’ and eventually crime would adjust to compensate….just as your metabolism would adjust if you turned off your home air condition and just stuck it out in the heat.

63 istanbul gezilecek yerler August 16, 2017 at 6:29 am

So, the number of meter maids a city has matters?

64 john August 16, 2017 at 9:00 am

I suppose certus paribus one might say the conclusion follows but it doe seem to beg the question why the incentive to crime. If the incenttives are simply part and parcel of human nature then the conclusion may hold (though then we’re stuck with the who polices the police — or how do we select the good for police and ensure that culture maintains it’s own accordingly).

However, if the incentives to crime are drivem more by other factors then it’s not clear the additional dollars spend in increasing policing actually is the best spending socially.

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