Costly Rehabilitation and Deterrence

Transcription

1 Costly Rehabilitation and Deterrence Siddhartha Bandyopadhyay a and Nigar Hashimzade b,c a University of Birmingham; b Durham University; c CESifo 26 June 2017 SB & NH (Birmingham&Durham&CESifo) Rehabilitation 26 June / 16

2 Motivation Does rehabilitation deter recidivism? The history of the research in criminology: Nothing works (Martinson 1974) Focus on justice, not crime prevention; Principles of e ective correctional treatment (Andrews and Bonta 1996) Meta-studies: mixed evidence (various, 2000-s) ntegrity issues Types: CBT, non-cognitive, vocational, reentry, bootcamps, etc. Targeting issues Cost-bene t analysis: taxpayers/victims Research questions: 1 Under what conditions will a young convict choose to participate in a voluntary rehab programme? 2 When is mandatory rehab participation socially more desirable than voluntary? SB & NH (Birmingham&Durham&CESifo) Rehabilitation 26 June / 16

3 Rehabilitation Conceptual framework Robinson 2008: rehabilitation as a right of the o ender (welfarist rationale) was politically unattractive; new focus on victims right for protection. A new approach: Utilitarian rehabilitation A good that bene ts the broader society Focus on reduction in reconvictions F Reducing re-o ending by ex-prisoners (2002 report by the Social Exclusion Unit) Managerial rehabilitation A means of risk management Focus in reducing risk and danger to public Expressive rehabilitation Rehabilitative intervention is allied with punitiveness Focus on hybrid sanctions: enforcement; discipline F o ender manager ; ntensive Supervision and Surveillance/ntensive Control and Change programmes SB & NH (Birmingham&Durham&CESifo) Rehabilitation 26 June / 16

4 Theoretical model Rational choice This framework is translated into an economic model: A potential o ender compares net gains from a criminal activity and a legal occupation A young convict can participate in a rehabilitation programme Trade-o : participation is costly (utility loss: expressive e ect ) but leads to higher future legal earnings Corrective intervention: combination of treatment and external controls (Palmer, 1992) Higher legal earnings make re-o ence less attractive We model a decision to re-o end as a rational economic choice. Participation in a rehab programme can be mandatory or voluntary Mandatory participation can be blanket or targeted This allows a comparison of di erent policies SB & NH (Birmingham&Durham&CESifo) Rehabilitation 26 June / 16

5 Model assumptions Dynamic framework We focus on an individual choice of a convicted young o ender. Three periods: young, adult, old; Beta-delta time preferences; A young o ender may or may not participate in a rehab programme: f participates incurs an additional utility loss (expressive e ect) v (r + ); F r 2 [0, R] is the intensity of the rehab programme. An o ender is released when adult; Two (mutually exclusive) sources of income when adult: Legal occupation: net earnings w i ; utility u (w i ); Criminal activity: gain θ a i, cost c i ; utility u θ a+ i ; c i + ; An adult recidivist is caught with probability q: No rehab opportunity: utility loss v (0) from incapacitation; Loses criminal gains and pays ne f θ a+ i : utility u 0; c i + f + (θ a i ) ; Released when old and retires: utility eu i o ; Otherwise, retires with utility u o i > eu o i. SB & NH (Birmingham&Durham&CESifo) Rehabilitation 26 June / 16

6 Model assumptions E ect of rehabilitation Let wi a denote maximal potential earnings in legal occupation for individual i when adult. A released ex-convict earns w i = ew i a (): ncapacitation partly destroys human capital; Not all jobs are available to ex-convicts; Rehab improves earning opportunities: ew i a (0) < ew i a r + < w a i Recidivism condition: (1 q) (u (θ a i ; c i ) + βδui o ) + q u (0; c i f (θ a i )) v (0) + βδui o1 u ( ew i a (r) ; 0) + βδui o. Rewrite this as (1 q) u (θ a i ; c i ) + qu (0; c i f (θ a i )) u ( ew i a (r) ; 0) + q [v (0) + βδ (ui o eu i o )]. SB & NH (Birmingham&Durham&CESifo) Rehabilitation 26 June / 16

7 Recidivism Threshold type Consider a released adult ex-convict of type c i facing a criminal gain opportunity (crime shock) of θ a i. (1 q) u (θ a i ; c i ) + qu (0; c i f (θ a i )) u ( ew i a (r) ; 0) + q [v (0) + βδ (ui o eu i o )]. There is a threshold crime cost, c i, such that the individuals with c i < c i become recidivists; The threshold decreases as ew a i (r) (legal earnings when adult), v (0) (utility loss from incapacitation), and/or u o i eu o i (retirement di erential) increase; The e ect of θ a i (crime shock) is ambiguous: Higher shock brings higher gains from crime but also raises penalty. SB & NH (Birmingham&Durham&CESifo) Rehabilitation 26 June / 16

8 Deterrence e ect Mandatory participation We are interested in the e ect of rehabilitation on recidivism. No e ect on o enders with low crime cost: c i < c m i () where (1 q) u (θ a i ; c m i ) + qu (0; c m i f (θ a i )) = u ( ew i a (r) ; 0) + q [v (0) + βδ (ui o eu i o )]. However, those with high crime cost will not re-o end even without rehab: c i > c i () where (1 q) u (θ a i ; c m i ) + qu (0; c m i f (θ a i )) = u ( ew a i (0) ; 0) + q [v (0) + βδ (u o i eu o i )]. Note that c m i < c m i as long as ew i a (r) > ew i a (0) for r 2 (0, R). Thus, a mandatory rehab programme helps prevent recidivism for c i 2 [c m i, c m i ]. Observe that d c m i du( ew a i (r )) dr < 0, since dr = u 0 ( ew i a (r) ; 0) ew i 0a (r) > 0. A higher rehab intensity pushes down the lower threshold and thus prevents recidivism by criminals with lower crime cost. SB & NH (Birmingham&Durham&CESifo) Rehabilitation 26 June / 16

9 Deterrence e ect Voluntary participation To evaluate the e ect of voluntary participation on recidivism we need to evaluate and compare (expected) utilities from criminal and legal activities: V L i (x) = v (x) + βδ (u ( ew a i (x) ; 0) + βu o i ) V C i (x) = v (x) + βδe θ [(1 q) (u (θ a i ; c i ) + βu o i ) +q (u (0; c i f (θ a i )) v (0) + βeu o i )] x 2 f0, rg. Since Vi C (r) < Vi C (0) we can ignore Vi C (r). Choice = NOT participate if either n o Vi C (0) > max Vi L (r), Vi L (0) : recidivism; or n o Vi L (0) > max Vi L (r), Vi L (0) : no recidivism. Choice = participate if Vi L (r) > max Vi C (0), Vi L (0) if Vi C (0) < Vi L (0) < Vi L (r): no e ect; would not re-o end without rehab; if V L (0) < V C (0) < V L (r): rehab reduces recidivism. i i i SB & NH (Birmingham&Durham&CESifo) Rehabilitation 26 June / 16

10 Deterrence e ect Voluntary participation The deterrence e ect depends on the criminal type. Case 1. High cost of crime. Convicts with c i c v i participate but ex ante they would not re-o end in any case. E θ [(1 q) u (θ a i ; c v i ) + qu (0; c v i f (θ a i ))] = u ( ew a i (0)) + βq (u o i eu o i ) + qv (0) Case 2. ntermediate cost of crime. Convicts with c i 2 [c v i, cv i ] participate AND rehab has deterrent e ect E θ [(1 q) u (θ a i ; c v i ) + qu (0; c v i f (θ a i ))] = u ( ew i a v (r) (1 βδq) v (0) (r)) βq (ui o eu i o ). βδ Case 3. Low cost of crime. Convicts with c i < c v i do not participate and become recidivists. SB & NH (Birmingham&Durham&CESifo) Rehabilitation 26 June / 16

11 E ect of rehab intensity Comparison Both mandatory and voluntary participation can deter recidivism and can also be redundant. Recidivism is deterred: For c i > c m i under mandatory participation; d c m i dr < 0: higher intensity increases reduction in recidivism. For c i 2 [c v i, cv i ] under voluntary participation; c v i does not depend on r; c v i may be increasing or decreasing in r F Higher intensity may overturn reduction in recidivism if d c v i dr > 0. We show that for d c v i dr < 0 to hold the earnings e ect must be su ciently strong: ew a0 i (r) > ε a w v 0 (r) βδu 0 ( ew i a 8r 2 (0, R), (r)) r ew a0 i (r) ew i a (r) > 1 rv 0 (r) βδ ew i a (r) u 0 ( ew i a 8r 2 (0, R). (r)) SB & NH (Birmingham&Durham&CESifo) Rehabilitation 26 June / 16

12 E ect of rehab intensity Comparison As long as an individual chooses to participate, a small increase in rehab intensity up from zero always reduces recidivism: ew i a0 v (0) > 0 (0) βδu 0 ( ew i a (0)) ) dcv i dr < 0. r =0 We show that if for some r 2 (0, R) then dc v i dr ew a0 i (r ) = r <r v 0 (r ) βδu 0 ( ew a i (r )) < 0 and dcv i dr > 0. r >r The e ciency threshold, r, is unique (under standard assumptions on the utilities); Largest reduction in recidivism. Earnings in legal occupation depend on innate abilities, availability of jobs, etc. To analyse the e ciency threshold we make further assumptions. SB & NH (Birmingham&Durham&CESifo) Rehabilitation 26 June / 16

13 E ect of rehab intensity E ciency threshold and abilities Assume ew i a (r) = ew i a (0) φ (r), φ 0 (r) > 0, φ 00 (r) 0, ew i a (0) = γwi a < ew a i (R) < w a i, γ 2 (0, 1) Maximal wage wi a is determined by individual i s innate abilities, education or training, available job opportunities, etc. Adult individual i earns wi a if was not convicted when young. Across population, wi a 2 wl a, w H a, with some distribution. We show that ε r w i a dr 1 σ r dwi a =. eε v + eε φ + σε φ where σ ε φ r φ 0 (r ) φ (r ) u2 00 ( ew i a ; 0) ew i a u2 0 ( ew i a ; 0) > 0,eε v r v 00 (r ) v 0 (r ) > 0,eε φ r φ 00 (r ) φ 0 (r ) > 0. > 0, SB & NH (Birmingham&Durham&CESifo) Rehabilitation 26 June / 16

14 E ect of rehab intensity E ciency threshold and abilities Depending on the degree of risk aversion (σ) ε r can be positive or negative. t is plausible to assume low risk aversion among young o enders: σ 0. 1 ε r > 0. eε v + eε φ What does this mean for the optimal choice of the rehab intensity under voluntary participation? Setting r at r (wi a ) maximises reduction in recidivism for o enders with earning ability w a i : Released adults with crime cost at or above c v i (r (w a i )) choose legal occupation; Those with crime cost c i > c v i (r (wi a )) and earning ability above wi a also prefer legal occupation. SB & NH (Birmingham&Durham&CESifo) Rehabilitation 26 June / 16

15 E ect of rehab intensity E ciency threshold Optimal r is the lowest for those with the lowest earning ability, min [w a L,w a H] r (w a i ) = r (w a L ): Thus, setting rehab intensity at r (wl a ) gives the maximal ex ante reduction in recidivism among the lowest earning ability individuals This also ex ante will reduce recidivism among those with wi a 2 (wl a, w H a ] and c i 2 [c v i (r (wi a )), c i (wi a )] where c i (wi a ) solves E θ a [(1 q) u (θ a i c i ) + qu ( c i f (θ a i ))] = u (γw a i ) + βδ u o1 A higher level of rehab intensity will tend to reduce further recidivism among higher abilities but have opposite e ect on lower ability types. The net e ect may well be higher rate of recidivism, especially if the distribution of abilities among young o enders is su ciently right-skewed. qu o SB & NH (Birmingham&Durham&CESifo) Rehabilitation 26 June / 16

16 Further research Recidivism and welfare This part of work has focussed on the reduction in recidivism. Correctional programmes (MacKenzie 1997): ncapacitation & Deterrence & Community Restraints (no transforming e ect) Rehabilitation & Structure/Discipline/Challenge (transforming e ect) Combined Rehabilitation and Restraint Welfare e ect of rehabilitation: how to de ne? Social welfare: fewer crimes; lower losses from crime (= lower criminal gains); ndividual welfare: higher earning ability; lower utility loss; Deterrence of crime more generally: Reduction in the rst-time o ences-rehab may lower this Cost-bene t analysis Welsh & Farrington (2000); Aos et al. (2001); Duwe (2015) F F Perspective of the public; Economic e ciency vs non-economic criteria; distribution/fairness. SB & NH (Birmingham&Durham&CESifo) Rehabilitation 26 June / 16