David Abrams (University of Pennsylvania) has posted Estimating the Deterrent Effect of Incarceration Using Sentencing Enhancements on SSRN. Here is the abstract:
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Increasing criminal sanctions may reduce crime through two primary mechanisms: deterrence and incapacitation. Disentangling their effects is crucial, since each mechanism has different implications for optimal policy setting. I use the introduction of state add-on gun laws, which enhance sentences for defendants possessing a firearm during the commission of a felony, to isolate the deterrent effect of incarceration. Defendants subject to add-ons would be incarcerated in the absence of the law change, so any short-term impact on crime can be attributed solely to deterrence. Using cross-state variation in the timing of law passage dates, I find that the average add-on gun law results in a roughly 5 percent decline in gun robberies within the first three years. This result is robust to a number of specification tests and does not appear to be associated with large spillovers to other types of crime.