A Fallacy of Composition

Peter Moskos is a sociologist by training, a professor at John Jay College of Criminal Justice, and a former Baltimore City police officer. In responding to the shooting of Philando Castile, he had this to say:

Honestly, in this shooting, with this cop, in this locale, I don't think there's a chance in hell Castile would have been shot had he been white. 

Nor did he think this was an entirely isolated incident; it reminded him of the (non-fatal) shooting of Levar Jones by Sean Groubert at a traffic stop in South Carolina. I had exactly the same reaction when I saw the Castile video, as did others. Even the Governor of Minnesota conceded that the shooting "probably would not have happened if he were white."

And yet, Moskos was unsurprised by Roland Fryer's recent claims of an absence of racial bias in police shootings:

I was not surprised by Fryer's conclusions... if one wishes to reduce police-involved shootings... there are good liberal reasons to de-emphasize the significance of race in policing.

Jonathan Ayers, Andrew Thomas, Diaz Zerifino, James Boyd, Bobby Canipe, Dylan Noble, Dillon Taylor, Michael Parker, Loren Simpson, Dion Damen, James Scott, Brandon Stanley, Daniel Shaver, and Gil Collar were all killed by police in questionable to bad circumstances... What they have in common is none were black and very few people seemed to know or care when they were killed. 

Moskos is not arguing here that the police can do no wrong; he is arguing instead that in the aggregate, whites and blacks are about equally likely to be victims of bad shootings. 

How can these two views be reconciled? If there is bias in individual incidents, ought it not to show up in aggregate data? Doesn't the congruence between the racial composition of arrestees nationwide and the racial composition of victims of police killings indicate an absence of bias, as Sendhil Mullainathan claimed a few months ago?

I have argued previously that it does not, because of systematic differences in the qualitative nature of encounters. If police initiate more encounters with blacks that are not objectively threatening (but may in some cases be subjectively perceived to be threatening) then parity in killings per encounter can indicate the presence rather than absence of bias. As Andrew Gelman put it at the time, it's all about the denominator. 

But Moskos offers another, quite different reason why bias in individual incidents might not be detected in aggregate data: large regional variations in the use of lethal force. 

To see the argument, consider a simple example of two cities that I'll call Eastville and Westchester. In each of the cities there are 500 police-citizen encounters annually, but the racial composition differs: 40% of Eastville encounters and 20% of Westchester encounters involve blacks. There are also large regional differences in the use of lethal force: in Eastville 1% of encounters result in a police killing while the corresponding percentage in Westchester is 5%. That's a total of 30 killings, 5 in one city and 25 in the other.

Now suppose that there is racial bias in police use of lethal force in both cities. In Eastville, 60% of those killed are black (instead of the 40% we would see in the absence of bias). And in Westchester the corresponding proportion is 24% (instead of the no-bias benchmark of 20%). Then we would see 3 blacks killed in one city and 6 in the other. That's a total of 9 black victims out of 30. The black share of those killed is 30%, which is precisely the black share of total encounters. Looking at the aggregate data, we see no bias. And yet, by construction, the rate of killing per encounter reflects bias in both cities. 

This is just a simple example to make a logical point. Does it have empirical relevance? Are regional variations in killings large enough to have such an effect? Here is Moskos again:

Last year in California, police shot and killed 188 people. That's a rate of 4.8 per million. New York, Michigan, and Pennsylvania collectively have 3.4 million more people than California (and 3.85 million more African Americans). In these three states, police shot and killed... 53 people. That's a rate of 1.2 per million. That's a big difference.

Were police in California able to lower their rate of lethal force to the level of New York, Michigan, and Pennsylvania... 139 fewer people would be killed by police. And this is just in California... If we could bring the national rate of people shot and killed by police (3 per million) down to the level found in, say, New York City... we'd reduce the total number of people killed by police 77 percent, from 990 to 231!

This is a staggeringly large effect. 

Additional evidence for large regional variations comes from a recent report by the Center for Policing Equity. The analysis there is based on data provided voluntarily by a dozen (unnamed) departments. Take a close look at Table 6 in that document, which reports use of force rates per thousand arrests. The medians for lethal force are 0.29 and 0.18 for blacks and whites respectively, but the largest recorded rates are much higher: 1.35 for blacks and 3.91 for whites. There is at least one law enforcement agency that is killing whites at a rate more than 20 times greater than that of the median agency.

On the reasons for these disparities, one can only speculate:

I really don't know what some departments and states are doing right and others wrong. But it's hard for me to believe that the residents of California are so much more violent and threatening to cops than the good people of New York or Pennsylvania. I suspect lower rates of lethal force has a lot to do with recruitment, training, verbal skills, deescalation techniques, not policing alone, and more restrictive gun laws. 

Moskos expands on these points in a recent conversation with Glenn Loury.

All of this must be interpreted with caution, since the information we have available is so patchy and deficient. As I wrote in a recent opinion piece with Willemien Kets, there is a desperate need for better data, collected and distributed in a comprehensive and uniform manner. Without this we are just groping in the dark.