Estimating the effects of a California gun control program with Multitask Gaussian Processes

Authors: Eli Ben-Michael, David Arbour, Avi Feller, Alex Franks, Steven Raphael

License: CC BY 4.0

Results of the summarizing process for the arXiv paper: 2110.07006v2

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Gun violence is a major public safety concern in the United States, and California implemented a unique firearm monitoring program called the Armed and Prohibited Persons System (APPS) in 2006 to address this issue. The APPS program identifies firearm owners who become prohibited from owning one due to federal or state law and confiscates their firearms. This study aims to assess the effect of APPS on California murder rates using annual, state-level crime data across the US for years before and after the introduction of the program. To do so, researchers adapted a non-parametric Bayesian approach called multitask Gaussian Processes (MTGPs) to estimate the causal effect of APPS. The MTGP framework allows for flexible and parsimonious panel data models that nest many existing approaches while allowing direct control over both dependence across time and units, as well as natural uncertainty quantification. The approach was extended to incorporate non-Normal outcomes, auxiliary covariates, and multiple outcome series, which are all important in this application. Applying this approach revealed that increased monitoring and enforcement from the APPS program substantially decreased homicides in California. The study found that the effect on murder was driven entirely by declines in gun-related murder with no measurable effect on non-gun murder. Estimated cost per murder avoided was substantially lower than conventional estimates of the value of a statistical life, suggesting a very high benefit-cost ratio for this enforcement effort. Methodologically, researchers believe that the MTGP framework is a promising approach for estimating causal effects with panel data more broadly. The Bayesian approach yields coherent uncertainty quantification while producing uncertainty intervals that grow over time post-treatment. This study is one of few papers specifically using GPs to estimate causal effects in panel data settings. While there are other relevant proposals such as Modi and Seljak's GP approach for estimating causal effects in frequency domain or Carlson's GP approach without exploiting multitask structure, researchers view their model as complementary to these approaches. Overall, this study provides a detailed analysis of the impact of APPS on California murder rates and demonstrates the potential of MTGPs for estimating causal effects with panel data.
AI-generated keywords: Gun violence Armed and Prohibited Persons System (APPS) Multitask Gaussian Processes (MTGPs) California murder rates Value of a Statistical Life

AI-generated Key Points

  • Gun violence is a major public safety concern in the United States
  • California implemented a firearm monitoring program called the Armed and Prohibited Persons System (APPS) in 2006 to address this issue
  • The APPS program identifies firearm owners who become prohibited from owning one due to federal or state law and confiscates their firearms
  • A study was conducted to assess the effect of APPS on California murder rates using annual, state-level crime data across the US for years before and after the introduction of the program
  • Researchers adapted a non-parametric Bayesian approach called multitask Gaussian Processes (MTGPs) to estimate the causal effect of APPS
  • Increased monitoring and enforcement from the APPS program substantially decreased homicides in California, with no measurable effect on non-gun murder
  • Estimated cost per murder avoided was substantially lower than conventional estimates of the value of a statistical life, suggesting a very high benefit-cost ratio for this enforcement effort
  • The MTGP framework is a promising approach for estimating causal effects with panel data more broadly, yielding coherent uncertainty quantification while producing uncertainty intervals that grow over time post-treatment.
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Abstract: Gun violence is a critical public safety concern in the United States. In 2006 California implemented a unique firearm monitoring program, the Armed and Prohibited Persons System (APPS), to address gun violence in the state. The APPS program first identifies those firearm owners who become prohibited from owning one due to federal or state law, then confiscates their firearms. Our goal is to assess the effect of APPS on California murder rates using annual, state-level crime data across the US for the years before and after the introduction of the program. To do so, we adapt a non-parametric Bayesian approach, multitask Gaussian Processes (MTGPs), to the panel data setting. MTGPs allow for flexible and parsimonious panel data models that nest many existing approaches and allow for direct control over both dependence across time and dependence across units, as well as natural uncertainty quantification. We extend this approach to incorporate non-Normal outcomes, auxiliary covariates, and multiple outcome series, which are all important in our application. We also show that this approach has attractive Frequentist properties, including a representation as a weighting estimator with separate weights over units and time periods. Applying this approach, we find that the increased monitoring and enforcement from the APPS program substantially decreased homicides in California. We also find that the effect on murder is driven entirely by declines in gun-related murder with no measurable effect on non-gun murder. Estimated cost per murder avoided are substantially lower than conventional estimates of the value of a statistical life, suggesting a very high benefit-cost ratio for this enforcement effort.

Submitted to arXiv on 13 Oct. 2021

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