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Causal Friday: CSI: Regression Analysis…

January 23rd, 2015 · 2 Comments
Causal Friday · Fun With Data

My sarcastic intro comments aside (obviously part of the problem for the specific event is that CSI is not supposed to be funny), I still think that this should exist on a larger scale…

You probably guessed that I am more of a Law and Order gal, since I’m obviously guilty of mixing my metaphors. I did try though- in the name of research, I bought the first season of the original CSI on Amazon, and, well…I just couldn’t get into it, and, other than what I included, there wasn’t anything obvious enough to pull from. Maybe because it wasn’t about statistics, maybe because it didn’t have Olivia Benson, who knows. Anyway…you can see by the list of sources at the end of the video, you just learned the basics of three academic papers and a reply in under ten minutes and you didn’t even feel the pain! In case you weren’t paying attention, here’s the overall trajectory of (some of) the research on the causal impact of police presence on crime:

  • Early research (without the use of instrumental variables or natural experiments) either showed no relationship between police officers and crime or a positive association between police and crime. These findings are somewhat problematic due to potential for reverse causality (i.e. the crime increases could have called for an increase in police presence rather than the other way around). Some researchers tried to mitigate the reverse causality problem by looking at the relationship between yesterday’s police officers and today’s crime, but that didn’t really work for various reasons.
  • In 1997, Steve Levitt published a paper that used election cycles as an instrumental variable to confirm that more police officers does in fact cause a reduction in crime. Election cycles work well as an instrument because they’re on a fixed schedule and therefore not subject to the whims of things that would affect crime levels, but are correlated with police presence for reasons similar to those outlined in the video. Unfortunately, said paper had a math error that he got called out on that kind of broke a bunch of his conclusions.
  • Levitt published a reply to the aforementioned criticism that acknowledged the error and proposed using firefighters as an instrumental variable instead. Again, this seems valid because the data shows that increases in firefighters are correlated with increases in police officers, but it’s intuitively unreasonable that the number of firefighters would be correlated with things that other than police officers that affect crime rates. He again found a negative elasticity of crime with respect to police presence.
  • A few years later, Jonathan Klick and Alex Tabarrok did a similar analysis that uses terrorism alert levels and got a similar result regarding the effect of police officers on crime. The logic there is the more police officers are mandated when terror alert levels are higher, but terrorism isn’t really related to factors that would affect more day-to-day crime instances, so it can be used for the causal analysis of police on crime.

I think that this sort of approach- i.e. showing rather than telling- is so powerful, and there definitely should be more teaching that is done in this way. (I might be a bit biased since Mathnet was an important part of my childhood. In related news, you’re welcome.) Granted, it’s harder- I’m pretty sure it took more effort to write the script (reproduced below in case you want it) than it did to write the list of bullet points above. But I’m convinced that it’s worth it, especially with some production value thrown into the mix. Okay, here’s the script, and I’m (not even kidding) going to go back to watching Law and Order now.

CSI: Regression Analysis

*intro screen – The following story is sort of fictional but sort of depicts actual people and events.*

Cop: You guys from Internal Affairs?

Econ 1: Nope, we’re from…the Program Evaluation squad. *David Caruso sunglasses moment, with music/regression graphic*

Cop: *completely breaking the dramatic moment* The what?

Econ 1: The Program Evaluation squad- you know, you catch criminals who cause crimes, we identify the culprits that cause…well, a bunch of stuff.

Cop: So…nerd detectives, got it. What brings you here?

Econ 1: Well, we’ve been enlisted to study the effect of police presence on crime rates, so your department seemed like a natural place to start.

Cop: And what happens to my job if I’m found to be useless?

Econ 2: We’re economists, so such policy questions are outside of our jurisdiction. So…we’re going to need your data on number of police officers and number of crimes committed over time.

Cop: I’m not exactly inclined to share data that could cost me my job.

Econ 2: Story of my life. Do I need to get the Captain involved?

Cop: No, let me find what you’re looking for.

Econ 1: *looks at data on paper and writes some numbers on white board, then inputs into computer* Hmmm…from what I see here, it actually appears that more police officers leads to MORE crime. Weird, right?

Cop: Wait, what? That can’t be right…you have to keep looking- after all, the first suspect is never the true culprit, right?

Econ 2: We’re looking into the matter, sir.

*later*

Econ 2: He’s right, you know.

Econ 1: About what?

Econ 2: There’s a problem with our case. Look- I found these forms that request additional officers into the department. what do you notice?

Econ 1: *looks at forms* That the reason listed for the request is…oh. Increased crime prevalence. So that means…

Econ 2: …that we can’t tell whether the police officers cause crime increases or if the crime increases cause more police officers to be hired.

Econ 1: So are we back to square one?

Econ 2: *looks at data* Mayyyyyyybe not… Look at this- crime increases aren’t the only reason that officers are requested.

Econ 1: There’s no reason given at all, actually. What’s up with that?

Econ 2: *at white board* I have a theory….*does some math* Yep, what I suspected- the requests match up with election cycles.

Econ 1: Why would that be?

Cop: Welllllll…I probably should be saying this, but the mayor likes us to beef up our presence before elections because it makes him look good.

Econ 2: Even though crime doesn’t follow election cycles?

Cop: *sadly* Yeah…I know it’s wrong, but…

Econ 1: *cuts off cop* Perfect.

Cop: Huh?

Econ 1: If we look at the part of the increase in police presence that has to do with election cycles and not crime sprees, we can use that data to estimate the causal effect of police on crime.

*Instrumental Variables start playing*

Cop: What the…?

Band: Sorry, thought you called for us.

Econ 2: *doing math* Ok, this seems to make more sense. Now I see a negative elasticity of crime with respect to police, especially for violent crimes.

Cop: *breathes sigh of relief*

Econ 1: *looks at math on board* Actuallyyyyyyy…you made a math error.

Econ 2: Where?

Econ 1: *points* There.

Econ 2: Ughhhhhhhhh…. *fixes mistake* Well, there goes my result.

Cop: Can’t you try something else?

Econ 2: Let me see… *searches around* How about firefighters? The number of firefighters is correlated with the number of police officers, but we certainly don’t get more firefighters when we have more crime…

*Instrumental Variables start playing*

*everyone glares*

Band: Again, I thought…

Econ 1: Okay, that seems to work, but we need a corroborating witness if we’re going to be convincing. What else affects the amount of police presence?

Cop: Well, we have to send out more cops when Homeland Security sets a high terrorism alert.

Econ 2: Am I the only one who finds it funny that when the government is helpful for research it’s rarely on purpose? Ok, do we have historical data on terrorism levels?

Cop; *runs in* Way ahead of you- after all, my ass is on the line here.

Econ 1: Unbiased and unmotivated research at its best, right here. *rolls eyes* *puts data in computer and on board* Bingo- another negative elasticity estimate.

Cop: Meaning…

Econ 2: Meaning that the data shows that, when police presence increases for reasons other than increases in crime, the increased presence leads to decreases in crime.

Cop: It’s good to feel useful.

Econ 1 and Econ 2: You can say that again.

*Dick Wolf-type credit thing – Executive Producer Charles Wheelan*

Tags: Causal Friday · Fun With Data

2 responses so far ↓

  • 1 Slap On Tracker // Mar 8, 2015 at 1:24 pm

    Slap On Tracker…

    Causal Friday: CSI: Regression Analysis……

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