Some Time Series Correlates of Mass Shooting Statistics

Figure 1: Mass shooting deaths (red), wounded (pink). February observation for data through 2/14. Light blue shading denotes assault weapon ban. Orange shading denotes implementation HJ Res 40. Source: Mother Jones, news accounts for 2/14, and author’s calculations.

HJ Res 40 ended the Obama era enhanced reporting requirements by Federal agencies regarding mental illness as part of gun purchase checks.

Figure 1: Mass shooting count. February observation for data through 2/14. Light blue shading denotes assault weapon ban. Orange shading denotes implementation HJ Res 40. Source: Mother Jones, news accounts for 2/14, and author’s calculations.

A regression analysis of fatalities yields:

f = -9.911.52ban – 0.91memo + 0.044pop

Adj-R2 = 0.04, NOBS = 427, DW = 1.78. bold face denotes significance at 10% msl using HAC robust standard errors.

f is mass shooting fatalities, ban is the assault weapons ban (dummy variable taking value of one 1994M10-2004M08), memo is a dummy variable measuring the Obama directive to insure communication of all Federal agencies communicate information regarding mental illnesses (2013M02-2017M02), pop is population in millions.

A count (Poisson) regression of events yields:

events = -7.060.49ban – 0.006memo + 0.020pop

Adj-R2 = 0.09, NOBS = 427. bold face denotes significance at 10% msl.

Where event is mass shooting events.

These time series regression results, albeit suggestive, are probably fragile. Different, and more detailed, analyses by Koper (2004), Gius (2014).

22 thoughts on “Some Time Series Correlates of Mass Shooting Statistics

    1. dilbert dogbert

      BooHoo!!! No one came up with the argument that one unlicensed car in an accident proves registration, licensing, insurance, testing, taxing is worthless.

    1. PeakTrader

      The 2011 mass shooting in Norway where 77 people were killed vaulted Norway to #1 in mass shooting fatalities adjusted for population and 21 times higher than the U.S..

      1. 2slugbaits

        Ugh. That was ONE mass shooting. The reason the number of victims was so high was because the killer used a semi-automatic .223 Ruger Mini-14.

        With a different weapon (e.g., single shot, bolt action), it’s highly unlikely that he could have killed anywhere near that number. He might have killed a couple, but he couldn’t have killed 77.

        The killer also passed all of the standard background checks. He had a history of owning other guns without incident. So maybe this is yet another case of guns creating criminals rather than criminals acquiring guns.

        1. PeakTrader

          There is always a percentage of the population, who are criminals whether or not they have a criminal record. Making guns illegal won’t stop criminals. If someone is intent on killing lots of people, he’ll find a way. How many of the victims had guns?

          1. 2slugbaits

            Why don’t you try and refute the statistical evidence presented by Menzie. And by “refute” I don’t mean coming up with half-baked theories and screwball claims. You like to tell us that you’ve been trained in graduate level economics. So go for it. Let’s see your econometric skills in action.

          2. PeakTrader

            2slugbaits – hello, are you awake yet?

            Mass shootings are too rare to make a determination – see article I posted above.

            “Looking only at frequency of attacks…the U.S…0.078 per million people.”

            Also, only one event can skew fatalities tremendously (see Norway).

          3. PeakTrader

            Looking only at frequency of attacks…(compared to European countries)…while still adjusting for population, the U.S. came in 12th, with 0.078 per million people.

        2. CoRev

          Ugh! 2lugs wrong again. The Norwegian shooter had almost 1.5 hours to complete his killings, because they were on an island. Weapon choice was incidental for that time frame.

          1. 2slugbaits

            CoRev. It takes time to reload, during which a shooter is vulnerable. It’s also a lot more difficult to carry loose ammunition than it is ammo already in a magazine or drum. That’s exactly why semi-automatic weapons with large magazines is the weapon of choice for mass murderers. In this case he owned other weapons, but they weren’t a good choice for someone hell bent on killing a bunch of people. That’s why he went to great effort to get a Mini-14. Weapon choice was critical to the shooter, not incidental.

          2. Moses Herzog

            CoRev has seen many many Arnold Schwarzenegger and Sylvester Stallone movies, in addition to ALL of the Jason Bourne film series. In ALL of these movies, the hero has only re-loaded twice with a very high kill rate. And the reload was in scenes where the hero had forgotten to double up on his testosterone supplement with a side of viagra. The only way for any hero to get out of that predicament would have been to put “just a pinch” of chewing tobacco between their cheek and gum, which wasn’t handy at that particular moment.

            On top of that, everyone knows all the biggest mass shootings have been done with single-action guns. That’s a well established fact that any law enforcement officer will tell you. That or a water gun. Bean bags also strike fear into the heart of most SWAT teams. That’s why cornhole has been banned on most islands

            Be that as it may, I’m afraid CoRev has the preponderance of evidence, not to mention movie history, on his side.

            This blog comment certified as “Genius” status, as verified by “PeakIgnorance Social Media Consultants LLC”

        3. Moses Herzog

          I generally agree with your comment, but I take issue with this part: “The killer also passed all of the standard background checks”

          Although factually true, that sentence is another standard vacuous Republican argument: Find single examples of shooters who can pass the background check and that means “All background checks are useless”. This is the equivalent in logic of finding a bad apple in your workplace who is a predator of women, molests 30 women and saying “See, John Doe molested 30 girls in our office, I told you doing job interviews accomplishes nothing”. Because you found one bad apple at work who got through quality control procedures (job interview) does not mean the process is useless. First, you do not know how many MORE molesters would have been at your office, had the interviews not been conducted. SECONDLY, the better question to ask is “What questions were we not asking, or information did we not research about this guy that made it possible for him to enter our company workforce??”

          You can find how many people dying from non-functioning parachutes every year?? Does that mean the company that makes the parachutes should stop their quality control procedures or testing of the product before selling them—because some senile idiot like Senator James Inhofe or supreme b*stard like Senator John Cornyn can give examples of two skydivers who died as a result of non-functioning parachutes in the last year??

    2. pgl

      Why did you not admit upfront that John Lott wrote this? Oh yea he is the Master of abusing statistics to mislead and you are just his Minnie Me. Never mind.

  1. Moses Herzog

    I think the standard Republican argument in relation to more reporting on backgrounds for gun checks (the number of “red flags” used), intercommunication between agencies, and limits on the type of guns sold to the general public is “Well it wouldn’t change anything anyway”. So what are they afraid of??

    Here is the deal, lets say you had a list of students who had been expelled from public school for violence or threat of violence —–similar to Nikolas Cruz. Now Republicans say “Well everyone acts up when they’re young.” OK, let’s put a 5 year “probationary period” from the point of the official charge of violence and/or threat of violence. If that public school student who either committed violence to get expelled from school or made a serious threat (say, for example, a long-winded “screed” or gameplan of violence found on their possession or in their own writing) to commit violence kept their nose clean for 5 years minimum, they can get their name taken off the “banned sell” list, for say a $10 processing fee. So around age 23, (if they committed the act or threat as a “minor”) they could purchase a gun again, after having a clean record and paying the processing fee. The person committing the act of violence (and/or serious threat) adds extra bureaucratic cost to the government. So the violator should have responsibility for that cost. The fee could be raised or lowered based on the added cost of that particular “red flag” to the national “banned sale” list registry.

  2. 2slugbaits

    These time series regression results, albeit suggestive, are probably fragile

    I’ll admit that I’m too lazy to formally test for it, but just based on visual inspection of the event data one possible source of fragility might be overdispersion resulting in a “zero inflate” risk. Just looking at the chart it appears that with 427 total observations there are probably a lot of zeros in the count data. A zero inflated Poisson (ZIP) regression model might make the results less fragile.

  3. Bruce Hall

    Given the low total number of incidents and an r-squared that is very low, I’m not sure that much significance can be assumed. Perhaps there is a tendency of the unstable minds to copy-cat something that is argued extensively in the media (clustering).

    1. 2slugbaits

      Bruce Hall I wouldn’t put too much emphasis on the low R-square, especially with regard to the Poisson regression event model. In fact, the R-square is not usually even reported for the Poission regression in many statistical packages. Typically goodness of fit measures for models like the ones Menzie used are reported as a Pearson’s statistic.

      The fact that the data fit a Poisson distribution up until 2011 suggests (but does not prove) an interesting interpretation. It suggests that mass shootings up through 2011 are independent and not serially correlated, but after 2011 that is no longer true. Let’s think of an analogy. Suppose you’re Frederick the Great and ask some bright mathematician to describe the probability of a horse throwing one of your cavalrymen during training. It turns out that you can estimate that with a Poisson distribution. But that assumes that a cavalryman falling from his horse doesn’t cause another cavalryman to fall from his horse; i.e., they are independent events. But suppose you change the physical scenario so that the horses are all bunched together in a full throated cavalry charge against an Austrian Habsburg army. Would you expect horses to throw their riders following a Poisson distribution? Probably not. One rider falls and so do several other riders near him. I think we have a similar dynamic with mass shootings. Something has changed in the physical environment so that shootings are no longer independent events.

  4. D

    Your memo variable is coded wrong: Obama’s law was never fully in effect! How did the assualt weapons ban effect crime when it only changed the appearance of how some guns were made and not their mechanical operation? Why don’t you report on all the literature, including from the National Research Council, that shows not effect from the assualt weapons ban?

  5. Steven Kopits

    The problem with this regression is, of course, that a mental health ban would not have stopped the five events with greatest fatalities:

    Paddock had no mental health priors, to the best of my knowledge: Fatalities: 64

    Cruz’s guns were under lock and key at his foster home, but somehow, he managed to get a key to them. His foster guardian also had rifles in the same case. Presumably he would have taken one of those, as did Lanza, if he was unable to access his own weapon. Fatalities: 17

    Devin Patrick Kelley, at the Baptist Church massacre, had in fact assaulted his wife, but according to NBC, “the military failed to enter the domestic violence case into a database that would have made it illegal for him to buy a gun, officials said.” Fatalities: 26

    Omar Mateen, of the Orlando shootings, was actually screened. And he passed. According to Wikipedia: “G4S said two screenings of Mateen—one conducted upon hiring and the other in 2013—had raised no red flags.[34] Under Florida state law, for him to work as an armed guard the company was required either to make a full psychiatric evaluation of Mateen, or to administer a “validated written psychological test”.[35] The test administered was the updated Minnesota Multiphasic Personality Inventory (MMPI-2), a test used for job screenings and court cases requiring those subjected to it to agree or disagree with statements such as “My soul sometimes leaves my body” and “Once in a while I think of things too bad to talk about.”[35] Carol Nudelman, the psychologist listed on the character certification submitted by G4S to the state said she stopped working for the company in 2005. After the shooting, Nudelman, who was said to have evaluated and cleared Mateen for his firearms license in 2007, according to the records of the security company G4S, denied ever meeting him or having lived in Florida at the time, and said she had stopped her practice in Florida in January 2006. G4S said Mateen was not actually interviewed by a psychologist, but rather, a psychologist evaluated the results of a standard test used in job screenings and his test was evaluated by the firm that bought Nudelman’s practice, Headquarters for Psychological Evaluation, owned by Dr. Joanne Bauling.[36][37]

    “On September 10, 2016, the Florida Department of Agriculture and Consumer Services fined G4S $151,400 for providing inaccurate psychological testing information after it found the psychologist whose opinion was necessary to permit Mateen to carry a weapon was not practicing as a screener. Between 2006 and 2016, 1,514 forms were submitted erroneously listing Nudelman’s name.”

    Florida fatalities: 49.

    And of course, Adam Lanza stole his gun from his mother, who was not a mental health risk of herself. Fatalities: 27.

    Thus, 173 deaths from the five most fatal mass shootings of recent years, would not have been prevented by mental health checks. In the case of Paddock, there were no visible mental health issues. In the case of Lanza and Cruz, both either sourced or likely would have sourced the weapons from family members. Kelly failed an effective test in the military, but it was not reported. And Mateen passed a test, even though there were lots of warning signs.

    I think there may be cause to tighten up mental health requirements, but it is not clear that HJ Res 40 would have prevented these events.

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