Threats Perceived When There Are None

Sendhil Mullainathan is one of the most thoughtful people in the economics profession, but he has a recent piece in the New York Times with which I really must take issue.

Citing data on the racial breakdown of arrests and deaths at the hands of law enforcement officers, he argues that "eliminating the biases of all police officers would do little to materially reduce the total number of African-American killings." Here's his reasoning:

According to the F.B.I.’s Supplementary Homicide Report, 31.8 percent of people shot by the police were African-American, a proportion more than two and a half times the 13.2 percent of African-Americans in the general population... But this data does not prove that biased police officers are more likely to shoot blacks in any given encounter...

Every police encounter contains a risk: The officer might be poorly trained, might act with malice or simply make a mistake, and civilians might do something that is perceived as a threat. The omnipresence of guns exaggerates all these risks.

Such risks exist for people of any race — after all, many people killed by police officers were not black. But having more encounters with police officers, even with officers entirely free of racial bias, can create a greater risk of a fatal shooting.

Arrest data lets us measure this possibility. For the entire country, 28.9 percent of arrestees were African-American. This number is not very different from the 31.8 percent of police-shooting victims who were African-Americans. If police discrimination were a big factor in the actual killings, we would have expected a larger gap between the arrest rate and the police-killing rate.

This in turn suggests that removing police racial bias will have little effect on the killing rate. 

A key assumption underlying this argument is that encounters involving genuine (as opposed to perceived) threats to officer safety arise with equal frequency across groups. To see why this is a questionable assumption, consider two types of encounters, which I will call safe and risky. A risky encounter is one in which the confronted individual poses a real threat to the officer; a safe encounter is one in which no such threat is present. But a safe encounter might well be perceived as risky, as the following example of a traffic stop for a seat belt violation in South Carolina vividly illustrates:

Sendhil is implicitly assuming that a white motorist who behaved in exactly the same manner as Levar Jones did in the above video would have been treated in precisely the same manner by the officer in question, or that the incident shown here is too rare to have an impact on the aggregate data. Neither hypothesis seems plausible to me.

How, then, can one account for the rough parity between arrest rates and the rate of shooting deaths at the hands of law enforcement? If officers frequently behave differently in encounters with black civilians, shouldn't one see a higher rate of killing per encounter? 

Not necessarily. To see why, think of the encounter involving Henry Louis Gates and Officer James Crowley back in 2009. This was a safe encounter as defined above, but may not have happened in the first place had Gates been white. If the very high incidence of encounters between police and black men is due, in part, to encounters that ought not to have occurred at all, then a disproportionate share of these will be safe, and one ought to expect fewer killings per encounter in the absence of bias. Observing parity would then be suggestive of bias, and eliminating bias would surely result in fewer killings.

In justifying the termination of the officer in the video above, the director of the South Carolina Department of Public Safety stated that he "reacted to a perceived threat where there was none."  Fear is a powerful motivator, and even when there are strong incentives not to shoot, it is still a preferable option to being shot. This is why stand-your-ground laws have resulted in an increased incidence of homicide, despite narrowing the very definition of homicide to exclude certain killings. It is also why homicide is so volatile across time and space, and why staggering racial disparities in both victimization and offending persist.

None of this should detract from the other points made in Sendhil's piece. There are indeed deep structural problems underlying the high rate of encounters, and these need urgent policy attention. But a careful reading of the data does not support the claim that "removing police racial bias will have little effect on the killing rate." On the contrary, I expect that improved screening and better training, coupled with body and dashboard cameras, will result in fewer officers reacting to a perceived threat when there is none.

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Update (10/18). I had a useful exchange of emails with Sendhil yesterday. I think that we both care deeply about the issue and are interested in getting to the truth, not in scoring points. But there's no convergence in positions yet. Here's an extract of my last to him (I'm posting it because it might help clarify the argument above):

Definitely you can easily make sense of the data without bias. The question is whether this is the right inference, given what we know about the processes generating encounters.

Suppose (for the sake of argument) that whites have encounters with police only if they are engaging in some criminal activity, while blacks sometimes have encounters with police when they are completely innocent. This need not be due to police bias: it could be because bystanders are more likely to think blacks are up to no good for instance (Gates and Rice come to mind).

Suppose further that those engaging in criminal activity are threats to the police with some probability, and this is independent of offender race. The innocents are never threats to the police. But cops can't tell black innocents from black criminals, so end up killing blacks and whites at the same rate per encounter. If they could tell them apart, blacks would be killed at a lower rate per encounter. What I mean by bias is really this inability to distinguish; to see threats when none are present. 

I believe that black cops are less likely than white cops to perceive an encounter with an innocent as threatening. If a suspect looks like your cousin, or a guy you sit beside to watch football on Sundays, you are less likely to see him as a threat when he is not. That's why I asked you in Cambridge whether you had data on officer race in killings - when the victim is innocent the officer seems invariably to be white. So a first very rough test of bias would be whether innocents are killed at the same rate by black and white officers...

I've found the twitter reaction to your post a bit depressing, because better selection, training and video monitoring are really urgent needs in my opinion, and the absence-of-bias narrative can feed complacency about these. I know that was far from your intention, and you are extremely sympathetic to victims of police (and other) violence. You also have a responsibility to speak out on the issue, given your close scrutiny of the data. But I do believe that the inference you've made about the likely negligible effects of eliminating police bias are not really supported by the evidence presented. That, and the personal importance of the issue to me, compelled me to write the response.

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Update (10/19).  This post by Jacob Dink is worth reading. Jacob shows that the likelihood of being shot by police conditional on being unarmed is twice as high for blacks relative to whites. The likelihood is also higher conditional on being armed, but the difference is smaller:

This, together with the fact that rates of arrest and killing are roughly equal across groups, implies that blacks are less likely to be armed than whites, conditional on an encounter. In the absence of bias, therefore, the rate of killing per encounter should be lower for blacks, not equal across groups. So we can't conclude that "removing police racial bias will have little effect on the killing rate." That was the point I was trying to make in this post. 

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Update (10/21). Andrew Gelman follows up. The link above to Jacob Dink's post seems to be broken and I can't find a cached version. But there's a post by Howard Frant from earlier this year that makes a similar point.