Here’s an interesting paper by Benjamin Hansen on punishment severity and deterrence.
I exploit discrete thresholds that determine both the current as well potential future punishments for first-time and repeat offenders. Specifically, in WA a blood alcohol content (BAC) measured above 0.08 is considered a DUI while a BAC above 0.15 is considered an aggravated DUI, or a DUI that results in higher fines, increased jail time, and a longer license suspension period. Importantly, the potential future penalties increase for each DUI received, regardless of whether the previous offense was an ordinary DUI or aggravated DUI.
The estimated effects suggest that having BAC above the DUI threshold reduces recidivism for both first-time and repeat offenders, consistent with a rational economic model of criminal behavior due to the increase in the expected cost of future punishments. However, receipt of an aggravated DUI offense also reduces recidivism. This is in contrast to the predictions of a fully rational model of criminal behavior, as a fully informed criminal would realize the enhanced punishment for their current offense would have no bearing on the expected cost of punishment for future crimes. Rather, this is consistent with models of bounded rationality, wherein criminals update their beliefs about the cost of future expected penalties based on the last punishment they received.
Having a BAC above the DUI threshold decreases the likelihood of recidivism, consistent with the predictions of a rational model of criminality as a DUI increases the expected cost of future criminality. However, aggravated DUI receipt also decreases the likelihood of recidivism. If an offender were fully rationally, they would consider the marginal BAC over the aggravated BAC threshold bad luck and realize that higher penalty was higher on this occasion is a sunk cost. However, the significant decrease in recidivism evident in drunk drivers with BAC over the .15 threshold is consistent with a model where criminals update their beliefs about expected punishment for future crimes based on the last punishment they received. […]
Importantly,one implication of this type of behavior or learning in offenders is that changes in punishments may require long durations in order to reaching their full deterring potential. So while well publicized changes in punishments such as three-strikes laws or easily understood sentence enhancements may deter crime significantly (see Helland and Tabborak, 1997 and Abrams, 2011), less well known changes in punishments such as increases in fines or minor shifts or complicated changes in sentencing may have limited deterring effects in the short-run.
For researchers, this suggests that interrupted time-series approaches or difference-in-difference models which take advantage of discrete changes in laws may underestimate the long-run impact of increased punishments. From a policy perspective, utilizing increases in punishments or fines to offset temporary reductions in police may work well in theory, but in the short run may fail in practice.