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Skip to 0 minutes and 1 second Understanding the effect of police on crime has been of great interest to economists. The common wisdom is that having a bigger, more efficient police force reduce crime. But it’s not easy how we can actually quantify the effect of police on crime. Imagine you are asked to quantify the effect of police force size on crime. What would you do? Following our discussion from last week, the obvious first step is to collect data on police and crime, and run a linear regression to estimate the relationship between two variables. And I did this using data from year 2010. This figure compares the number of law enforcement employees and the rate of violent crimes in American cities with population greater than 100,000.

Skip to 0 minutes and 49 seconds This figure shows that more violent crimes take place in cities with more police officers. But we would not take this as a sign that more police causes more crime. A more reasonable interpretation is that in cities with more crimes, they tend to hire more police officers. To some extent, we can alleviate this problem if we have data on police and crime from multiple years. Suppose that some cities historically had high crime rates and large police forces for many years, and other cities had low crime rates and small police forces. This historical difference between them can be eliminated by using city-fixed effects and looking at the within-city differences in crime rates and the size of police force.

Skip to 1 minute and 39 seconds I did this, based on the 2005 and 2010 UCR data, and obtained this figure. The regression line tells us that the relationship between police officers and crime is still positive, but the slope is a lot flatter this time. This figure makes more sense to me than the last one, but it still tells us that having more police is associated with more crimes. Before we conclude that having more police may be really detrimental to public safety, let’s talk about one more potential problem with this analysis. The problem is that the change in the number of police officers within a city is probably not random.

Skip to 2 minutes and 21 seconds Let’s say I find that the number of police officers in a city has gone down between 2005 and 2010. This decline in the size of the police force may be a response to some change in the city over this period time. For example, crime may have been falling during this period of time, and the city government may have thought that it could maintain public safety with a smaller police force.

Skip to 2 minutes and 47 seconds In this case, my regression analysis will pick up what’s called a reverse causation: an increase in crime will lead to increase in police force, and a decrease in crime will lead to a decrease in police force size. This makes sense, but it does not answer the question of whether having more police reduce this crime or not. Ideally, this problem will be eliminated if I can run a random experiment on police and crime. For example, I may randomly assign each of the police districts in Seoul to one of the two groups. For police district assigned to the first group, I will double the size of their police force.

Skip to 3 minutes and 26 seconds For the district assigned to the second group, I will do nothing and keep the number of police officers the same. And I will compare the crime rates between the two groups. In this case, the difference in crime rates between the two groups can be plausibly viewed as the causal effect of doubling the size of police force on crime. Crucially, in this thought experiment, whether a police district increases the number of its police officers has nothing to do with their crime trend in the police district. And that’s because the assignment to the first group or the second group was random. Of course, running an experiment like this is not going to be easy for obvious reasons.

Skip to 4 minutes and 9 seconds First, I must have a lot of resources to double the size of police forces in about a half of the police district in Seoul. Second, even if I obtain the resource somehow, there will be a lot of political and ethical concerns about an experiment that deals with public safety. Because such experiments are very hard to run in real life, economists often use quasi-experimental research designs that allow them to recover a causal relationship from a non-experimental data. In the current context, the main idea is to look for some variation in the size of police force, which takes place randomly, or at least in a way not related to crime itself.

Skip to 4 minutes and 54 seconds After this video, we will see a number of examples of such quasi-experimental variations used by economists.

Empirical analysis on the Effect of police on crime

That cities with more police may be systematically different from cities with fewer police is a classic example of a “self-selection” problem, which can make it very difficult to establish a causal relationship from non-experimental data. (How do we separate the effect of police on crime from the effects of other factors?)

The strength of an empirical research in economics often depends on how successfully it mitigates the selection problem.

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Economics of Crime

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