Optimal Unconditional Parole David Scoones Department of Economics University of Victoria December 2009
Motivation Each time an offender on parole release commits a crime, calls for parole reform are widespread. “Truth in sentencing” reforms requires serving a full sentence In Canada much attention has been drawn to “statutory release” where offenders are released on parole at a pre-determined point, (almost) independently of evidence of rehabilitation.
Not much work in the Economics of Crime literature has examined parole. One exception is Bernhardt, Mongrain and Roberts (2006) which considers informed release. This paper ask what might be the rationale for automatic early release I find that statutory release may indeed be optimal in some contexts.
Preview of results When sentences are long, criminals discount the future sufficiently that the extra deterrence of prison versus parole is minimal. In addition, parolees on statutory release face a significantly higher likelihood of arrest should they commit crimes, and so are more likely to be deterred from crime than are similar individuals in the community who are not on parole. However, when statutory release periods increase, the discounted value of eventual release becomes small, at least at the beginning of parole, and parolees are more likely to return to offending. Provided that they avoid arrest, the incentive to not engage in crime rises as the end of the parole period draws near. Thus the model predicts that statutory release parolees are less likely to re-offend as their time on parole passes. When sentences are short, increasing the portion of the sentence served on parole reduces the deterrence of punishment. In this case, society may be better of without statutory release.
This suggests that far from a trade off, as implicitly assumed by the arguments for "truth-in-sentencing", statutory release and long sentences might be complementary. Provided that sentences exceed a certain length, some short period of statutory release is welfare improving. With long sentences, longer periods of statutory release become optimal.
Among what I ignore The dominant explanations for parole, and these too might be used to justify statutory release. The most common argument for statutory release is that releasing prisoners without restriction or community support greatly increases the chance they will re-offend. Another argument is that people change, and jailing the no longer criminally-minded is unduly costly. (This is the focus of Bernhardt, Mongrain and Roberts (2006)) In the present model types are fixed and there is no prospect of reform. Trying to learn these types is still potentially useful. To explain statutory release on this basis, it must be that some aspect of offenders' types is better measured on parole than in prison. Finally, a little noted value of parole is how it allows local law enforcement officials (including parole officers) with the modus operandi, family contacts and likely whereabouts of a town’s criminal class.
The Canadian Federal Parole System All persons sentenced to two years or longer enter the Federal Corrections system All parolees are monitored by regular contact with a parole officer, and possible others. Restrictions are set by the Federal Parole Board at the time of release. Day parole : release into a “community residential facility” – halfway house Full parole : allowed to live independently
Opportunities for parole: ♦ Accelerated Parole Review. First time non-violent offenders are eligible for day parole at six months regardless of sentence length. The onus is on the parole officer to demonstrate that there is an uncontrollable risk to re-offend. If Day Parole is granted, Full Parole is automatic six months later. ♦ Full Parole eligibility is at 1/3 the sentence. Day Parole is Full Parole less 6 months. ♦ Statutory Release is at 2/3 the sentence. ♦ IF a parolee is suspended and (eventually) revoked, the process restarts at the date the warrant is executed. ♦ Section 810 Orders are sought by a local police force to impose parole-like conditions on inmates for one year at the end of their sentence. Can be renewed. ♦ Long Term Supervision Orders
Some Federal Numbers (Corrections and Conditional Release Statistical Overview 2008) Cost per annum (2006-7) Men Women Prison $90,744 $166,830 Parole $23,076 Population Compared to European countries Canada has a high incarceration rate: 108 per 100K population. Germany is 91 and Denmark 63. Canada’s rate has fallen in recent years. The US is 762, and rising. Men Women Total 13,500 495 57.7% were under age 40 in 2007-08. The population is aging. (Aboriginals are greatly overrepresented: in 2007-08 17.3% of federal offenders were Aboriginal compared with 4.0% of the population)
Parole outcomes Men Women Day parole Granted 69% (3K) 89% (283) Success 83.5% Revoked 13% New offence 4% Full Parole Granted 41% (14K) 71% (168) Success 72% Revoked 19% New offence 8% Statutory release Detained 266 Success 59% (3348) Revoked 30.5% (1739) New offence 10% (606 – 110 violent)
The model ♦ A unit population of infinitely lived, potentially criminal citizens. ♦ Time is discrete. At the start of each period every agent is in one of the following: a free non-criminal, a free criminal, in jail, or on parole. ♦ Free citizens and parolees must choose between engaging in criminal activity and working in the legal sector. The environment is stationary. ♦ All criminals are subject to arrest and conviction, leading to a prison term of length J followed by P periods of parole. ♦ Each agent is characterised by a type, ψ , distributed according to F , that affects his return from crime. All other parameters are assumed to be identical for every agent. ♦ The higher is an agent's ψ -coefficients the greater is ψ his benefit from crime, c ♦ > > . w p j
= Jail time only: . P 0 Value functions Value for non-criminals NC = + δ V w V i i The value of a crime is given by = ψ + δ λ + − λ C A V c [ V ( 1 ) V ] i i i i The value of a prison term of length followed by J release − δ = ∑ = J j ( 1 ) J − δ = + δ A t 1 J V j V − δ i i t 1 1 Thus ψ + δλ − δ − δ − J 1 c j ( 1 )( 1 ) = j C V + − δ + λ δ − δ i J 1 1 ( )
The marginal criminal for P=0 Characterised by the ψ -coefficient for which = NC C V V i i The marginal criminal is then − λ δ − δ + J 1 w ( w j ) ( ) ψ = + * . − δ c c ( 1 ) The population is partition: ψ > ψ , agent i is a criminal 1. if * i ψ < ψ , agent i is not a criminal 2. if * i λ = Notice that if there is no chance of arrest, , then 0 ψ c = . * w
Comparative Statics ∂ ψ ∂ < 1. * j 0 ∂ ψ ∂ > 2. * w 0 ∂ ψ − δ − δ + J 1 * ( w j )( ) 3. = > 0 ∂ λ − δ c ( 1 ) ∂ ψ − − λδ + δ J 1 * ( w j ) ln 4. = > 0 ∂ − δ J c ( 1 ) + ∂ ψ − − λδ δ 2 J 1 2 * ( w j ) (ln ) 5. = < 0 − δ ∂ 2 J c ( 1 )
Parole γ > λ On parole the arrest rate is higher: + The population partitions into groups: P 2 ♦ the λ -deterred never commit crimes (non- criminals) ♦ the = + deterred for . γ − t 1 ... P 1 i The deterred commit crimes when free and on γ − t = P + parole up to the period. When the criminals th t 1 t are never deterred. Depending on the parameters of the model, each of these partitions can range from empty to containing the entire population.
Value functions For non-criminals life is as before. The value of arrest for a γ − deterred agent is A , V D t t which depends on type as well as the parole period in which the agent is deterred. V is the value at the first period of parole. This is P 1 D t defined recursively by: If < P + t 1 = + δ P C V p V P D D t t t < If , in the penultimate period P = + δ = + δ + δ P P 2 C − V p V ( 1 ) p V P 1 P D D D t t t And so on until period , at which point t = + δ + − P P 1 t C V pF V t D D D t t t where − δ + − P 1 t 1 = F − δ D t 1
Prior to this the agent is not deterred and earns the higher payoff from crime, but faces the possibility of arrest: = ψ + δ γ + − γ = ψ + δγ + δ − γ + δ + − P A P A P 1 t C V − c ( V ( 1 ) V ) c V ( 1 )( pF V ) t 1 t D D D D D D t t t t t t . This continues until = ψ + δγ + δ − − γ − + δ + − P A t 1 t 1 P 1 t C V Q ( c V ) ( 1 ) ( pF V ) 1 D D D D D t t t t t . where − − − δ − γ t 1 t 1 1 ( 1 ) = . Q − δ − γ D t 1 ( 1 )
The value at arrest = + δ A J P V K V 1 D D t t where − δ J j ( 1 ) = . K − δ 1 Hence + − − + − δ ψ + + δ − γ + δ J J t 1 t 1 P 1 t C Q c K ( 1 ) ( pF V ) = D D D A V t t t − δ + γ D J 1 1 Q t D t
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