# Are U.S. Cities Underpoliced?

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.