Studying the Effects of Incarceration on Offending Trajectories
An Information-Theoretic Approach
Document date: July 01, 2006
Released online: March 02, 2007
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Dated arrest histories of a sample of prisoners released from state prisons in 1994, collected by the Bureau of Justice Statistics, were used to model re-offending trajectories and study their deflection. A semi-parametric method was used to develop plausible counterfactual trajectories and compare them with actual postrelease offending patterns. Analysis suggests that most individuals were either deterred from future offending (40 percent) or reverted back to projected offending patterns (56 percent) as a result of their incarceration. About 4 percent had a criminogenic effect.
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BACKGROUND AND OBJECTIVES
Imprisonment, for any length of time, is a life-interrupting event. The process of reentry
into society after a period of incarceration is ridden with questions of individual sustainability,
vulnerability, and fear of failure. Therefore, identifying and understanding the effects
that incarceration can have on different types of offenders under different contexts is crucial
to developing strategies that minimize any criminogenic harm, and maximize any deterrent
benefits, that result from it. This report describes an analytical framework designed to aid
practitioners, analysts, and researchers in investigating these issues.
It builds on one of the well established and widely accepted empirical regularities in
criminology: the link between an individual's past and future crime. Criminologists are not
in complete agreement with regard to explanations of this link. However, none deny that
such continuity in offending is a very real phenomenon. To the extent that such links exist,
studying prior involvement in crime should provide useful insights into future offending
patterns. This notion is validated in almost all studies of criminal recidivism—that prior
criminal history is one of the best and most consistent predictors of recidivism.
It is also a well established fact in criminology that the rate of offending increases
as youthful offenders age but that, at some point, the rate begins to decline. Hence, this
non-monotonic shape (first increasing then decreasing)—termed the "age-crime curve"—is a very predictable aspect of offending over the life course. Given this second fact, it is
not at all surprising that individuals' past involvement in crime predicts recidivism well.
The total amount of crime accumulated by any individual at the time of release captures
one aspect of the "age-crime curve." However, the second aspect of this relationship—the process by which individuals were accumulating their criminal histories—is seldom
utilized in recidivism research in general, or for understanding the effects of incarceration
in particular. Since it can be anticipated that individuals' involvement in criminal activities
over the life course can be characterized (probabilistically) by a trajectory, then it should
be helpful to study how incarceration deflects an individual's trajectory.
With this goal in mind, the objective of this research effort is to develop, and demonstrate
the utility of an analytical framework that can aid practitioners, analysts, and researchers
- Model the pre-release criminal history accumulation process in order to characterize,
as trajectories, the process by which these individuals had been accumulating their
respective criminal histories;
- Use this knowledge as a way to project into the future what could reasonably have
been expected of these individuals given their past—i.e., project a counterfactual
- Use this counterfactual trajectory as a backdrop against which to assess the actual
post-release offending patterns.
The framework has the potential to help researchers answer a very basic question:
How does incarceration affect individuals? This report describes one way of addressing
this important question in terms of whether, and to what extent, incarceration is able to
deflect the trajectory a particular offender is on. In order for any analytical framework
to provide meaningful insights into this question it must confront three related problems.
First, it needs to be able to model individuals' trajectories using knowledge of their past
offending patterns. Second, it needs to be capable of projecting trajectories into the future.
Finally, it needs to have a mechanism by which to compare actual and counterfactual
trajectories for each and every individual so that their incarceration can be appropriately
classified as having had a deterrent, a criminogenic, or an incapacitative effect on them.
The information-theoretic approach described in this report is one approach that offers
each of these capabilities. It only requires that detailed dated arrest histories, both
before incarceration and after prison release, be available to the analyst. Moreover, it
provides the usual statistical inferential apparatus whereby analysts can gauge the sensitivity
of their results to sampling variation—i.e., how different their estimates would be
had a slightly different sample been used. The report provides detailed derivations of the
analytical framework and points readers to appropriate sources in the related econometrics/statistics literatures.
The developed framework is tested using a real world data set. In early 2002, the Bureau of
Justice Statistics issued a report titled Recidivism of prisoners released in 1994 that reported
on criminal re-involvement of a sample of roughly 38,000 prisoners who were released in
1994 from prisons in 15 states (Langan and Levin, 2002). The data used to support their
findings were subsequently archived at the National Archive of Criminal Justice Data at
the Inter-University Consortium of Political and Social Research (study # 3355). These
data contain detailed information on up to 99 arrest events for each of the individuals in the
sample. This includes their pre-incarceration arrest events as well as arrest events within
a period of three years after release. In addition, the data provide standard demographic
information on each of the individuals as well as some limited information on their 1994
To show how the developed framework may fruitfully be applied by researchers, analysts,
and practitioners having access to such detailed data the BJS recidivism data were
used as a test bed. The report describes in detail how the data were restructured, what
predictable patterns were found in the data, and provides detailed estimates of the models.
Once modeled, the counterfactual trajectories of each individual in the sample were
compared with the actual post-release offending patterns in order to classify the effect that
incarceration had in deflecting these trajectories. Finally, the limited set of explanatory information
available in these data were used to model and study what factors, if any, helped
explain the kinds of experiences people were expected to have. Unfortunately, this source
provides insufficient data to make sound policy recommendations about what factors (or
policy options) can be expected to maximize the deterrent benefits (or minimize criminogenic
harm) of incarceration. The results presented in this report, for this part of the
analysis, are intended primarily to showcase the capabilities of the developed framework.
Despite the emphasis of this research effort being on the development of the framework,
some interesting findings are summarized below.
- There was a fair amount of consistency among all the pre-prison based models of
the criminal history accumulation processes across the 15 states analyzed. For example,
being further along in the criminal career (i.e., being at risk of a higher arrest
number) and starting the career later (i.e., having a higher age at first arrest) are consistently
associated with lowered hazard trajectories. Similarly, all else being equal,
being closer to past arrest clusters is consistently associated with an increased hazard
trajectory. There was less consistency among states when modeling the deviation
between the counterfactual and actual rearrest trajectories after release. Being later
in the criminal career was found to exert an upward pressure on the offending trajectory
relative to the counterfactual. Similarly, being closer to past cluster was found
to exert a downward pressure on the trajectory relative to the counterfactual.
- The criminal history accumulation process contained valuable information about the
long-term trends in individuals' offending patterns over the life course. The counterfactual
trajectories, based on estimated models of the pre-prison based criminal
history accumulation process and projected for the post-release period, perform remarkably
well in predicting rearrests within three years of release. On the other hand,
these same counterfactuals do not perform as well when used for making short-term
projections. The false-positive rates are at very high levels throughout the follow-up
period. When updated with models of the post-release behavior, the models perform
Figure A: A counterfactual trajectory compared with three hypothetical post-release trajectories showing criminogenic, incapacitative, and deterrent effects of incarceration.
- Information-theoretic measures were developed to quantify and classify the divergence
between the counterfactual and the actual post-release micro-trajectories. Figure
A displays three hypothetical post-release trajectories compared to a counterfactual
and how each would be classified. Based on those computations, and in this
analysis, large portions of the released cohort were classified as having had an incapacitative
(56 percent) or a deterrent (40 percent) experience. A small proportion of
the sample (4 percent) experienced criminogenic effects as a result of this incarceration.
- Using these classifications as the criterion outcome, being older at release and being
closer to past clusters were consistently found to increase the likelihood of a releasee
being deterred. Having more prior accumulated arrests and having a later age at first
arrest were both found to significantly decrease the likelihood of a deterrent effect.
Being released to supervision was found not to deter releasees substantially.
- Using the average log divergence between the counterfactual and the actual trajectories
as the criterion some conflicting findings emerged. However, the effects of
age at first arrest and age at release were qualitatively similar to what were found in
the categorical analysis. Additionally, females experienced larger deterrent effects
compared to similar males.
This research effort has important substantive, methodological, and practical implications.
- Substantive implications. Substantively, the analytical framework developed here
has the potential to shed light on a very important question: How does incarceration
affect individuals? The framework allows researchers to determine, or at the very
least investigate, the types of individuals likely to be deterred by incarceration. In a
similar way, it allows them to better understand how incarceration can have diering
impacts on the same people at various stages in their life and/or criminal careers.
- Methodological implications. When the detailed dated arrest histories of a sample
of releasees is available to researchers, utilizing only one source of variation in the
data—the total amount of criminal history accumulated prior to prison admission—when modeling the risk of future recidivism forces analysts to waste valuable information
and thereby forgo learning opportunities. A second source of variation
available in these pre-prison arrest histories—the process by which individuals were
accumulating these histories—contains immense amount of information about future
offending patterns. The information-theoretic event-history models, developed
in this research effort, show how this knowledge can be introduced into the modeling
strategy in a very effective way. The process by which individuals accumulate
their pre-prison arrest histories, typically, have very predictable patterns that can be
modeled. These models allow projection of person-specific micro-trajectories that
trace out the evolution of rearrest risk had the individual not been incarcerated. As
such, they are perfect counterfactuals against which to assess post-release offending
- Practical Implications. Although much of the software needed for the analysis conducted
here needed to be programmed from scratch, the availability of standard software
allowing researchers to utilize information and entropy based methods is increasing
rapidly. For example, SAS has introduced an experimental procedure under
its ETS module called PROC ENTROPY that is designed for the estimation of linear
and non-linear models using the Generalized Maximum Entropy (GME) approach
introduced by Golan, Judge, and Miller (1996). Additionally, LIMDEP—another
popular econometrics software—has recently added the GME methods for estimating
binary and multinomial logit models.
Software needed to estimate generalized hazard models using the framework described
in this report here is far from being developed. In the interim, researchers
and practitioners will need to rely on routines and macros developed and made available
to the public. An Appendix to this report provides a sample SAS program that
was developed to estimate the models presented in this report.
As a result of this research effort, and based on the findings reported in this report, some
recommendations for future research can be enumerated.
- The emphasis in this research effort was on development of the analytical framework
and demonstration with an application. Comparison of the developed framework to
existing and related approaches remains to be done as does the work of assessing
the framework's performance using artificially generated data. Such simulation exercises
are crucial to establish the credibility of the modeling approach as well as its
performance relative to others.
- The framework can also be fruitfully extended to study the trajectories of multiple
types of repeatable events such as offending and drug use over the life-course, or
offending and employment, etc. Such analyses have the potential of shedding light
on how incarceration can interrupt the co-evolution of these interrelated behaviors.
- The framework can also be extended to study how other interventions, not just incarceration,
may deflect the trajectories of offending. For example, the effects of
participation in various treatment programs may be quantified in terms of the program's
ability to deflect individuals' offending trajectories.
The complete paper is available in PDF format.
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