Studying the Effects of Incarceration on Offending Trajectories

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Document date: July 01, 2006
Released online: March 02, 2007

The text below is an excerpt from the complete document. Read the full paper in PDF format.

Executive Summary

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 to:

• 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 trajectory; and
• 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.

DATA USED

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 release mechanism.

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.

FINDINGS

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 much better.

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.

IMPLICATIONS

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 patterns.
• 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.

FUTURE RESEARCH

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.