What Criminal Justice Policies Influence Murder Rates?

International data and other analyses tends to find that gun control does indeed influence murder rates. 

One difficulty may be that the effectiveness of U.S. gun control law is impaired by having a border free zone that makes buying guns where they are legal and transporting them to places where they are banned or restricted a trivial matter.

Overall, I'm skeptical of the statistical methods used, which make a lot of seemingly ad hoc methodological decisions. Moody's publication history shows him to be a conservative hack. But nonetheless, it is a study that deserves mention.

This study investigates the effects of most of the major firearm and crime control policies on murder. We use two-way fixed-effects models based on state-level panel data from 1970-2018. We include a comprehensive list of relevant policy variables to control for their influence in determining the effect of each. We do a specification search using four commonly used econometric methods to estimate three models of the crime equation. A Bonferroni correction is used to control for false rejections. A robustness check using new difference-in-differences estimators confirms the results.

We find that, with the possible exception of constitutional carry laws, no firearm policy can be shown to have a significant long-run effect on murder. However, we find that the traditional policies of prison incarceration and police presence significantly reduce murder in the long run. We also find that executions have no significant long-run effect on murder. Finally, there is considerable evidence that three-strikes laws increase murder in the long run.

Carlisle Moody, "A Comprehensive Analysis of the Effect of Crime-Control Policies on Murder" (September 14, 2023). Available at SSRN: https://ssrn.com/abstract=4574358 or http://dx.doi.org/10.2139/ssrn.4574358