(This article was originally published at Statistical Modeling, Causal Inference, and Social Science, and syndicated at StatsBlogs.)
Rajiv Sethi points to a discussion of Peter Moskos on the recent controversy over racial bias in police shootings.
Here’s Sethi:
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. . . .
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.
This is all important in its own right but I also wanted to highlight it as an example of a more general principle about different levels of variation when considering policy interventions.
One of my favorite examples here is smoking: it’s really hard to have an individual-level intervention to help people quit smoking. But aggregate interventions, such as banning indoor smoking, seem to work. This seems a bit paradoxical: after all, aggregate changes are nothing but aggregations of individual changes, so how could it be easier to change the smoking behavior of many thousands of people, than to change behaviors one at a time? But that’s how it is. Individual decisions are not so individual, as is most obvious, perhaps, in the variation across populations and across eras in family size: nowadays, it’s trendy in the U.S. to have 3 kids; a couple decades back, 2 was the standard; and a few decades earlier, 4-child families were common. We make our individual choices based on what other people are doing. And, again, it’s really hard to quit smoking, which can make it seem like smoking is as inevitable as death or taxes, but smoking rates vary a lot by country, and by state within this country.
To return to the policing example, we’ve had lots of discussion about whether or not particular cops or particular police departments are racially biased—lots of comparisons within cities—but Moskos argues we have not been thinking hard enough about comparisons between cities. An interesting point, and it would be good to see it on the agenda.
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