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THE ENCYCLOPEDIA OF CORRECTIONS: Desistance and aging out Haas
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Desistance and “Aging Out” of Offending after Punishment
Henriette S. Haas
Entry in:
THE ENCYCLOPEDIA OF CORRECTIONS
Brent Kerley (Ed), Wiley (2017)
Full version
(including the Blumstein model, statistics and formula with permission of Jusletter)
Abstract
The decline of criminal energy with growing age in the general offender population is
replicated in a similar pattern for the active and serious criminals. Predictions of their
dangerousness can be made more accurate by using longitudinal statistics on reoffending
according to age, crime type, and previous convictions as base rates. For this purpose
Blumstein and Larson conceived a model of the interactions between offenders and the
criminal justice system. It can be used to calculate the average number of offenses committed
by a given type of offender, such as street criminals or sex offenders, after release from long
prison sentences. As a consequence of the aging-out effect the number of offenses will be
considerably reduced after several years behind bars, even for those ex-convicts who were not
able or not willing to benefit from rehabilitation programs.
Keywords: antisocial behavior; crime prevention; criminal justice system; deterrence;
incapacitation; persistent offenders; punishment.
Abstract
A key topic of penology is the effect of punishment on multi-recidivists and criminals with
long sentences. It is also a political issue that provokes heated debates. All statistics show a
gradual decline in offending with growing age – for males as well as for females. The older
they get, the more offenders tend to desist from criminal activities. Eventually, almost all will
settle down. This is called the aging-out effect. Most criminologists agree that criminal
recidivism is a failure to mature, a delayed transition into adulthood, but they differ about the
variance or invariance of this effect across the life span. These opinions are addressed in the
criminal career debate. The psychological school, represented by Moffitt (1993, 1994), for
example, claims the existence of two types of antisocial trajectories: adolescence-limited
offenders (ALO) and persistent offenders (PO). The latters’ antisocial behavior goes back to
their childhood and their crimes tend to be more frequent and more serious than those of the
former. POs also show more psychopathology than ALOs, whereas the ALOs resemble much
more the nondelinquent population (abstainers) – in every respect. This concept falls in line
with the results of cross-sectional studies, beginning with Wolfgang, Figlio, and Sellin (1972),
who showed that a small number of persistent offenders do enormous damage as they account
THE ENCYCLOPEDIA OF CORRECTIONS: Desistance and aging out Haas
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for the biggest share of offenses and especially for almost all of the severe violent crimes
committed by the members of a birth cohort. Moffitt (2002) showed with prospective
longitudinal data that boys with severe childhood antisocial symptoms practically never
recover. Even cases that seemed to have disappeared from the official records for a certain
time span unfortunately resurfaced in the justice system later.
The sociological school (represented by Hirschi and Gottfredson 1983, later with their
General Theory of Crime 1990) claims the invariance of aging out: they see gradual
desistance in all offenders. Statistical evidence for the aging out process shown as curves of
recidivism depending on age as well as on the number of previous convictions is difficult to
find, but we did find data from Denmark (Statbank) and from the United Kingdom (Lloyd et
al. 1995). These show a distinct, but slower decline in recidivism for the more active
offenders compared to the rest.
Figure 1. Number of re-convictions of males according to age and previous convictions
(StatBank Denmark, last visited on Jan. 20th 2014)
Longitudinal studies on complete biographies of (former) offenders now shed a new
light on the criminal career debate (Sampson and Laub 2003). These authors have collected
the follow-up data on the Glueck sample (1957) of 480 delinquent boys. They found a
universal pattern of desistance, varying for different types of crimes committed by the same
group. Property crime peaks sharply during adolescence, becoming quite insignificant after
age 25. For violent crime there is a rather flat inverted U-curve, beginning shortly before the
20s and lasting into the mid-30s for men. The curve of violence is overlaid by a much higher
and wider inverted U-shape concerning alcohol- and drug-related crime, lasting from the early
20s until the beginning of the 50s for the men. One-fourth of the men who survived to age 50
seemed to have stopped crimes of violence and property after age 17 (no arrests), half of them
stopped after age 25, and 80% had no arrests for predatory crime after age 40. Their data
THE ENCYCLOPEDIA OF CORRECTIONS: Desistance and aging out Haas
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suggest that the age–crime decline in the general population is replicated, almost in the same
fractal fashion – for the active serious offenders. Thus the data mitigate theoretical
controversies.
There is also the very problematic group of the most severe criminals, such as leading
organized crime figures and persistent sexual and violent predators. Even though they
represent only a tiny fraction of the population, they attract the most media attention. For
central Europe (FSO 1997) the prevalence of truly dangerous violent and sex offenders is
about 1 out of 10,000 inhabitants (judged by the severity of prison sentences). Even if in more
crime-ridden countries this figure could be doubled, no prospective study can ever contain a
sufficient number of those rare cases so as to evaluate their offending pattern, not even those
composed of juvenile delinquents. Considering the length of their sentences and the
impossibility of releasing them when they are in their late 30s without risking further victims
and major scandals, there is a gradual buildup of the stock of inmates in maximum security
correctional facilities all over the world. Finding appropriate aging-out limits for them
depends very much on the collection of longitudinal data as base rates. Only they allow the
application of the so-called Bayes’s theorem in the actuarial prediction of dangerousness
(Wollert 2006), considering correctly all possible outcomes.
Both psychological and sociological schools have a point in that desistance is
universal; however, there seem to be personality-related clusters according to the severity of
the antisocial behavior. A growing body of neurological studies (e.g., Raine et al. 2005)
provides insights into probable causes for the occurrence of clusters. Adolescence-limited
offending seems to be heavily mediated by the teenage brain’s reorganization under the
hormonal surge, whereas persistent offenders suffer from frontal-executive dysfunctions from
childhood, causing psychiatric symptoms of ADHD, addictions, or personality disorders. This
being said, social and psychological influences do also play a role since they can create,
reinforce, or contain neurological deficits. Cluster patterns stem from the neuronal network’s
capacity to compensate deficits to a certain degree. With an accumulation of too many risks
and when the load becomes too heavy, the brain organizes itself on a lower level of overall
functioning. Then again, this explanation remains incomplete as long as base rates of similar
neurological deficits in the general population are unknown, that is, if there are any such
neurologically affected individuals without antisocial tendencies (what is called
counterfactuals).
Considering Aging Out after Punishment
It is widely recognized that noncustodial and custodial sanctions are quite effective for two-
thirds of all first-time offenders. Controversies about the efficiency of punishment focus most
on the question of how to deal with multi-recidivists and with severe felons. The high
recidivism rate of former prisoners is one frequently heard argument for a supposed
inefficiency of incarceration (with finite sentences). There is also an implicit belief that
deterrence by sanctions must totally prevent any new offense or else it would not be working
at all. This fallacy originates from the confusion between reconviction rates of individuals (in
Figure 1) and the number of offenses committed or prevented. It also results from not
considering the aging out effect on recidivism in the later stages of a criminal career. Thus the
real issue for public security is not the percentage of reconvictions, but the number of
committed offenses and the increase or decrease in their severity of them. The very existence
of criminal justice puts a constant pressure on offenders – forcing them to be much more
cautious than they would be otherwise. This greatly reduces their opportunities to commit
crimes.
THE ENCYCLOPEDIA OF CORRECTIONS: Desistance and aging out Haas
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Unfortunately, the number of prevented offenses is difficult to estimate while rearrest and
reconviction figures are easily available. Blumstein and Larson (1971) created a so-called
Markov chain (Figure 2), modeling the interactions between offenders and criminal justice.
With this model, consisting of four states, we can estimate the number of offenses by
inserting well-known statistical parameters.
1. state 1 (transient) = active offending
2. state 2 (transient) = apprehension by the police
3. state 3 (transient) = conviction by the court
4. state 4 (absorbing) = desistance from further offending.
The number of offenses (the expectation E) is a function of the offender’s proneness to crime
and the possibilities to thwart crime by prosecution. The conditional probabilities between
those states are (o = offending, a = apprehended, c = convicted):
pa = p(a|o) the probability that an offender be (apprehended) arrested by the police
after an offense
pc = p(c|a) the probability that a police suspect be convicted after being apprehended
for the offense
p1 = p(o|o) an offender’s proneness to re-offend under uncontrolled circumstances
p2 = p(o|a) an offender’s proneness to re-offend after having been contacted by the police
p3 = p(o|c) an offender’s proneness to re-offend after having been convicted
The transition probabilities within the model, the paths between the states, are unconditional
probabilities. So the offender’s return to state 1 is his individual proneness to offend
multiplied by the probability of not being arrested (1–pa), etc.
Figure 2. Interactions between offenders and Criminal Justice (Blumstein & Larson 1971)
Let P be the transition-probabilities of the Markov-model with the elements Pij as transition-
probabilities from one state i to the state j, then:
THE ENCYCLOPEDIA OF CORRECTIONS: Desistance and aging out Haas
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(1)
P
=
€
(1 −pa)p1pa0 (1 −pa)(1 −p1)
(1 −pc)p20pc(1 −pc)(1 −p2)
p30 0 1 −p3
0 0 0 1
#
$
%
%
%
%
&
'
(
(
(
(
Note that the certainty C of punishment (Beccaria) is the product C = papc. Let δ be the unity
matrix (δij = 0 for i≠j and δii=1 for all i). The expectation matrix E covers the average number
of visits to the different states before the system reaches its absorbing state:
(2)
E(P)
=
€
pk
k=0
∞
∑
=
€
δ
δ
−P
=
€
(
δ
−P)−1
We need only the first diagonal element E11 here, i.e. the number of expected offenses after
the first one. The others, namely E22, the number of police contacts and E33, the number of
Court convictions, could be relevant for other computations.
(3)
E11
=
€
1
1−p1+pa(p1−p2)+papc(p2−p3)
Among the variables in P we do know pc from the comparison of Police and Court statistics.
Under the assumption that we are dealing with persistent offender of the worst kind: those
who remain unimpressed by the criminal justice system, the formula for E (expected offenses
after the first one) can be simplified. For such offenders we have p1 = p2 = p3 which simplifies
the denominator of all elements and contains only one unknown:
(4)
E11
=
€
1
1−p1
Figure 3 shows that the expectation of offenses relates the offender’s proneness to commit an
offense in a non-linear way. Under the assumption that we are dealing with persistent
offenders of the worst kind – those who remain unimpressed by the criminal justice system –
most parameters can be simplified to one single variable p which stands for the offender’s
probability to commit an offense during a given time period. Then it is quite easy to calculate
the expected number of offenses per time period: E = 1/ (1-p). E is a non-linear function, a
hyperbola. For as long as p remains below the value of 0.8 (i.e., an 80% chance to commit an
offense per time period), there are not too many offenses to be expected. For p = 0.8 we
expect an average of five offenses per time period. However, the more p approaches the value
of 1 (which stands for the condition of remaining unpunished and leaving the offenders a
100% chance to commit crimes) the steeper the expectation curve mounts. For p = 0.95 the
offenses average on E = 20, whereas for p = 0.98 there are E = 50 and for p = 0.99 there are
even E = 100 offenses expected by the same person.
THE ENCYCLOPEDIA OF CORRECTIONS: Desistance and aging out Haas
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Figure 3. Hyperbolic function of the expectation of the number of offenses
The hyperbolic nature of this curve explains why a total absence of sanctions leads to
a disproportionate increase in crime. In fact, deterrence is a mathematical function and not a
constant. Countless times, history has proven the asymptotic increase of crime under
conditions of anarchy, for example after Hurricane Katrina in New Orleans in 2005 or after
the conquest of Baghdad by US troops in 2003. The political experiment with an open drug
market in Switzerland during the 1980s and 1990s, the so-called needle park, provided yet
another window to observe the total failure of a policy of laxness. Furthermore, there is not a
single society known to live peacefully without laws and sanctions. At the same time, the
curve shows that absolute deterrence is not necessary at all. It suffices that chances to succeed
with offending be significantly reduced by a reasonably high certainty of punishment. From
the perspective of the offender the existence of the criminal justice system considerably
reduces his opportunities. It forces him to be much more cautious. Because of the non-linear
shape of the expectation a small percentage of reduction in the probability to offend can be
quite effective in reducing the total number of offenses committed by recidivists.
Next, we want to explore the impact of a prison sentence on the expectancy of
offenses with regard to the age decline of offending with the help of the Blumstein model. We
still ignore pa, p1, p2, and p3 because their values fall under the dark figure of undetected
crime. Hence we need a middle step to calculate those probabilities from other known
statistical parameters, such as the re-conviction probability after a first conviction (in Figure
4).
THE ENCYCLOPEDIA OF CORRECTIONS: Desistance and aging out Haas
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Figure 4. Recidivism according to age and number of previous convictions
(Lloyd, Mair & Hough, Home Office 1995, table B.1 appendix, p.77)
Let the matrix H be defined as the probability that a state i from the chain be ever re-visited
from another state j in a finite number of steps (across all states that the system assumes
stochastically until it stops in the absorbing position). To obtain the formula for H we can
relate it to the expectation matrix E. It is the expectation of visits minus 1, divided by its
diagonal.
(5)
H
=
(E –
δ
)(
δ
E)-1
Obviously H11 is the same as p1, the proneness to reoffend for a recidivist, and S = 1 – H33 is
the survival rate after release from a sentence. To calculate p1 we need police statistics H22
(probability for a re-arrest of former police suspects) and court statistics H33 (probability for a
reconviction of ex-convicts):
(6)
H22
=
€
pap2+papc(p3−p2)
1−p1(1 −pa)
(7)
H33
=
€
papcp3
1−p1+pa(p1−p2)+papcp2
THE ENCYCLOPEDIA OF CORRECTIONS: Desistance and aging out Haas
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Knowing the values of H22, H33 and pc from official statistics, and assuming the worst case
scenario of p1 = p2 = p3 for simplicity, we now have a system of two equations with only two
remaining unknowns p1 and pa, which is solvable (in theory).
For an evaluation of the efficiency of prison terms for career criminals, we will take the
example of a violent drug dealer at age 24, convicted for the sixth time to several years behind
bars.
(8)
H33
=
€
papcp1
1−p1+papcp1
Let us assume that this fictive street criminal will be released shortly after his thirtieth
birthday. His probability of arrest by the police after reoffending and being convicted
thereafter is higher than for other offenders because he is on the radar of the police. We can
calculate the expectation of offenses E for him before, during, and after his six-year prison
term. As there was no complete set of longitudinal crime statistics available containing H22,
H33 and pc we have to estimate certain parameters. Let us estimate pa = 0.3 and pc = 0.7. This
assumption seems reasonable in the light of all the registered offender data available about
him (photographs, DNA, fingerprints, whereabouts, contacts, etc. from the probation office).
Then we can insert the values for H33 from Figure 4 and calculate the expectation of offenses
before, during, and after his six-year prison term:
Before incarceration (curve with squares):
H33 = 69%
E(69%)
= 11.6 offenses
During incarceration (6 years)
(assuming that within walls offending is greatly
reduced but not eliminated)
-
E
< 3.0 offenses
After liberation (curve with circles):
H33 = 43%
E(43%)
= 4.6 offenses
As a consequence of incapacitation during the critical years, prison prevented dozens of
offenses (estimated 67 offenses). After liberation society gets back an older, less active ex-
convict, whose criminal energy has been considerably reduced. Even if this person is not
rehabilitated in the least, he will commit less than half of his former total offenses per time
period. The chance that he will be caught again are still 45%. If such cases seem to be a
failure of the system, the impression is false–what counts is the number of prevented offenses.
Using this example, we can read two tendencies. First, except in cases of the severest
violence and offenders with high PCL-R scores, lifelong incapacitation, such as the “three
strikes” laws, are not needed to protect the public from the deeds of persistent offenders.
These solutions are costly for taxpayers without providing additional security. Second, it does
indeed make sense to imprison rehabilitation-resistant multi-recidivists during their most risky
years in order to protect society. Any legislation seeking a reasonable compromise between
the interests of society, victims, and offenders should beware of excesses in both directions:
neither too much leniency nor too much severity makes sense.
SEE ALSO: Beccaria, Cesare; Deterrence; Habitual Offender Laws; Incapacitation;
Incarceration Rates; Recidivism; Rehabilitation; Three Strikes Laws
THE ENCYCLOPEDIA OF CORRECTIONS: Desistance and aging out Haas
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References
Blumstein, A., and Larson, R. 1971. “Problems in Modelling and Measuring Recidivism.”
Journal of Research on Crime and Delinquency, 8 (2): 124–132.
DOI:10.1177/002242787100800202.
FSO (Swiss Federal Statistics Office). 1997. Convictions and Recidivism. Order numbers:
217-9600 and 216-9601. Berne, Switzerland. Accessed October 12, 2016.
http://www.bfs.admin.ch/bfs/portal/en/index.html.
Glueck, S., and Glueck, E. 1957. Unraveling Juvenile Delinquency. Cambridge, MA: Harvard
University Press.
Gottfredson, M. R., & Hirschi, T. 1990. A General Theory of Crime. Stanford, CA: Stanford
University Press.
Hirschi, T., and Gottfredson, M. 1983. “Age and the Explanation of Crime.” American
Journal of Sociology, 89(3): 552–584. DOI:10.1086/227905.
Lloyd, C., Mair, G., and Hough, M. 1995. Explaining Reconviction Rates: A Critical
Analysis. Home Office Research Study No. 136. London, UK: Her Majesty’s
Stationery Office.
Moffitt, T. E. 1993. “Adolescence-Limited and Life-Course-Persistent Antisocial Behaviour:
A Developmental Taxonomy.” Psychological Review, 100 (4): 674–701.
DOI:10.1037/0033-295X.100.4.674.
Moffitt, T. E. 1994. “Natural Histories of Delinquency. In Cross-national Longitudinal
Research on Human Development and Criminal Behavior”. In: E. Weitekamp and H.-
J. Kerner (eds.) Cross-National Longitudinal Research on Human Development and
Criminal Behavior (pp. 3-61). Netherlands: Springer.
Moffitt, T. E. 2002. “Males on the Life-Course-Persistent and Adolescence-Limited
Antisocial Pathways: Follow-Up at Age 26 Years.” Development and
Psychopathology, 14: 179–207. DOI:10.1017/S0954579402001104.
Raine, A., Moffitt, T. E., Caspi, A., Loeber, R., Stouthamer-Loeber, M., and Lynam, D. 2005.
“Neurocognitive Impairments in Boys on the Life-Course Persistent Antisocial Path.”
Journal of Abnormal Psychology, 114: 38–49. DOI:10.1037/0021-843X.114.1.38.
Sampson, R. J., and Laub, J. H. 2003. “Life-Course Desisters? Trajectories of Crime among
Delinquent Boys Followed to Age 70.” Criminology, 41: 319–339.
DOI:10.1111/j.1745-9125.2003.tb00997.x.
StatBank Denmark. 2014. “Number of Re-convictions of Males According to Age and
Previous Convictions.” Accessed January 20, 2014. http://www.statbank.dk.
Wolfgang, M. E., Figlio, R., and Sellin, T. 1972. Delinquency in a Birth Cohort. Chicago, IL:
University of Chicago Press.
Wollert, R. 2006. “Low Base Rates Limit Expert Certainty When Current Actuarials Are
Used to Identify Sexually Violent Predators: An Application of Bayes’s Theorem.”
Psychology, Public Policy, and Law, 12: 56–85. DOI:10.1037/1076-8971.12.1.56.
Further reading
Belkin, J., Blumstein, A., and Glass, W. 1973. “Recidivism as a Feedback Process: An
Analytical Model and Empirical Validation.” Journal of Criminal Justice, 1 (1): 7–26.
DOI:10.1016/0047-2352(73)90003-2.
THE ENCYCLOPEDIA OF CORRECTIONS: Desistance and aging out Haas
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Farrington, D. P., Auty, K. M., Coid, J. W., and Turner, R. E. 2013. “Self-Reported and
Official Offending from Age 10 to Age 56.” European Journal of Criminal Policy and
Research, 19 (2): 135–151. DOI:10.1007/s10610-012-9195-x.
Haas, H., and Killias, M. 2003. “The Versatility vs. Specialization Debate: Different Theories
of Crime in the Light of a Swiss Birth Cohort.” In C. Britt and M. Gottfredson (eds.),
Control Theories of Crime and Delinquency (Advances in Criminological Theory,
Vol. 12). New Brunswick, NJ: Transaction Publishers.
Maltz, M. 1975. “Crime Statistics: A Mathematical Perspective.” Journal of Criminal Justice,
3 (1): 177–194. DOI:10.1016/0047-2352(75)90064-1.
Author Biography
Henriette S. Haas is adjunct professor of forensic psychology at University of Zürich. She has
worked as a psychotherapist at a maximum security corrections facility for men from 1991 to
1996. She is also the main author of the Swiss recruits’ 1997 study (e.g. Haas and Cusson
2015).
Haas, H., and Cusson, M. 2015. “Comparing Theories’ Performance in Predicting Violence.”
International Journal of Law and Psychiatry. 38, 75-83.
DOI:10.1016/j.ijlp.2015.01.010
Haas, H. 2001. Agressions et victimisation: une enquête sur les délinquants violents et sexuels
non détectés. Sauerländer Verlag Aarau. ISBN 3-7941-4915-7. Postdoctoral Thesis
(Habilitation) at the Faculty of Philosophies I, University of Zurich. (Engl. Violence
and Victimization: A Study on Violent and Sexual Offenders Undetected by the
Police).
Haas, H., Tönz, P., Gubser-Ernst, J., and Pisarzewska Fuerst, M. 2015. “Analyzing the
Psychological and Social Contents of Evidence – Experimental Comparison between
Guessing, Naturalistic Observation and Systematic Analysis.” Journal of Forensic
Science. 60(3), 659-668. DOI:10.1111/155 6-4029.12703.
Killias, M., and Haas, H. 2002. “The Role of Weapons in Violent Acts: Some Results of a
Swiss National Cohort Study”. Journal of Interpersonal Violence Vol. 171N: 14-32.
DOI:10.1177/0886260502017001002.
Haas, H. 2008. “Evaluation der spezialpräventiven Effekte der Strafverfolgung mit Hilfe der
neuen Kriminalstatistik.” (Engl. Evaluation of crime prevention by Law Enforcement
based on the new federal criminal statistics). Jusletter. Online:
http://jusletter.weblaw.ch/juslissues/2008/477.html
