Prisons compared

How do prison sentences compare with alternatives that are neither incapacitative nor criminogenic at different costs of crime?

Prisons could have four possible effects on crime: deterrence, incapacitation, rehabilitation and criminogenic. These are, respectively, that they could dissuade potential criminals from committing crimes by raising the costs of doing so; they could keep away from the public individuals who otherwise would commit crimes in some period of time; they could reform criminals and allow them to reintegrate into society, reducing the incentive for them to commit crimes; or they could encourage criminality among everyone in prison by ensuring that the bulk of individuals the marginal prisoner associated with were criminals. They achieve these four effects at an extremely high cost: £48,000 per prisoner-year in the UK and rising rapidly (average 6.4% per year over the past 5 years).

For the purposes of this blog post, they will be compared to a system with equal deterrence, no incapacitation, no rehabilitation and no criminogenic component and no financial cost excess of court and policing expenses. The no incapacitation assumption is highly conservative due to the low costs and high incapacitation potential of employing say electronic tagging coupled with a curfew for convicted individuals, and the no rehabilitation component would also likely be highly conservative due to the likely public desire for governments to provide such a service. A criminal justice system with zero financial costs beyond the courts and police could be achieved by a massive expansion of community service to allow prisoners to replace existing workers employed by the government for some tasks such as removing litter, plausibly even saving funds on net, or by similar means. The no criminogenic aspect simply relies on the proposed alternative system not forcing individuals convicted of previous offences to live with each other and only each other for years on end, and seems highly plausible. Equal deterrence seems very easy to achieve by frontloading costs, as criminals have much higher discount rates than the already astonishing 20-35% for the general population.¹

Cullen, Jonson and Nagin (2011) reviewed several studies on the effect of prisons on recidivism, with the criminogenic effect dominating the rehabilitative effect. Of the meta-analyses which provided the quantitative estimates necessary for this model, Gendreau, Goggin, Cullen, and Andrews (2000) found a 7% increase; Smith, Goggin, and Gendreau (2002) found an 8% increase, rising to 11% on the highest quality studies; and Jonson (2010) found a 14% increase, falling to 5% on the highest quality studies. An 8.7% effect size will be used here. Implicitly this blog post’s methodology ignores the large numbers of crimes committed within prison or not reported, rendering the benefit estimate conservative. Canada provides a breakdown of recidivism rates by age at release for the 2007-2012 period, which will be used here to estimate total costs of crime over a lifetime for someone convicted of a crime at a given age by punishment system.²

Figure 1: Cost ratio of alternative divided by existing prison system costs by sentence length and crime costs. Interactive version here.

Figure 2: Net benefit from shifting to an alternative system from the present one by crime cost and prison sentence length. Interactive version here.

The resultant cost ratios for a 20-year-old can be seen above.³ The alternative system is better for all crimes and crime costs excluding the very highest sentences for the most costly of crimes - indeed, if interpretted literally the results above imply that only murderers would optimally go to prison as very few crimes even have costs of the minimum $500,000 modelled, let alone the near $10,000,000 required for prison sentences to be better than the alternative.

This method does however have a number of shortcomings. By using data for the average prisoner, this result does not imply the replacement of prison for all offenders, and as recidivism rates may vary by crime does not even necessarily imply that prison is worse than the alternative above for the majority of people in prison for every crime. Additionally, some would argue that the suffering of those who have harmed others is inherently good, which if prisons were worse than the conditions in the alternative could mean that those who held such a belief would place a higher value on prisons relative to the alternatives than the results above. Finally, individuals can commit more than one type of crime over their lifetimes, while the model above only allows individuals to commit crimes of a single cost, albeit permitting them to do so multiple times. This may be problematic because the government could today use the fact that individuals are committing more minor crimes today as a signal that more severe ones will be committted in future, reducing total crime costs, although to the extent that this is a boost in the reoffending rate following crimes this effect will boost both costs and thus have only a small effect on optimal behaviour. These shortcomings will be addressed in a future post.

1. This observation also predicts that variation of prison sentences for most crimes on the margin should have essentially no effect on criminal behaviour - one borne out empirically.

2. Individuals will differ by age at release on many unobservable factors uncontrolled for here.

3. Older individuals both have lower benefits from prison due to increased likelihood to overrun their sentences beyond the age at which committing crimes is feasible but also lower costs due to having fewer years of life remaining to commit crimes in meaning that the criminogenic effect is of lower cost.