An Examination of Prison-Based Programming and Recommitment to Prison

Abstract

Policy makers and correctional leaders continue to rely on research to identify how best to improve the outcomes of incarcerated populations. Prison-based programming is one way to address the needs of individuals and improve public safety. We draw from research on correctional programming to examine the impact of different types of correctional programs on returns to prison. Administrative panel data from the Arizona Department of Corrections Rehabilitation and Reentry is used to estimate the impact of cognitive thinking, substance abuse treatment, and education-based programs on reincarceration outcomes. To account for observable selection bias, we use propensity score matching to create comparable treatment and comparison groups. In addition, we use survival curves to compare three-year reincarceration survival rates of individuals in the treatment and comparison groups. Findings indicate that program participants have lower reincarceration rates than program non-participants. Further, correctional program completion plays an important role in this process, as program completers exhibit consistently lower predicted reincarceration rates compared to program non-completers. In addition, the survival curves show that program non-completers maintain highest reincarceration risk than program completers. We discuss the implications for studies of recidivism and for correctional programming.

Keywords:

• Correctional programming
• recidivism
• reincarceration

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 Another estimate shows that approximately half of incarcerated persons have not completed their high school education nor attained GED certification (Petersilia, 2005; Visher, Debus, and Yahner, 2008). It should be noted that the estimates may differ across studies because sample composition and survey years are different.

2 https://crimesolutions.ojp.gov/

3 The source is a meta-analysis and includes studies that evaluate the impact of education-based programs that led to a degree, license, or certification. The treatment group includes participants or completers (meaning individuals who earned a degree/license/certification).

4 We examine the impact of the programs that serve the largest population in the context of ADCRR. An examination of programs serving a small number of persons would be ideally suited for mix-methods or qualitative methods, which is beyond the scope of this study.

5 New felony – violent offense is based on the FBI’s definition of a violent offense. FBI broadly defines violent offenses as those offenses which involve force or threat of force. As per the FBI’s definition, a violent offense is composed of four offenses: murder and nonnegligent manslaughter, forcible rape, robbery, or aggravated assault.

6 Survival analyses are used to analyze the timing of recidivism. A recent report from the PA DOC highlights the importance of timing of recidivism in illustrating the department’s recidivism rates (See Bucklen et al. (2022)).

7 To avoid issues of spillover effects of programming from multiple incarceration spells, we only include the first incarceration spell of individuals. Participation for all programs was need-specific and was identified by the prison staff during individual’s intake or classification process. Due to the constraint of resources, some individuals were eligible to participate but did not participate in the programming. Among program participants, some individuals did not complete a program due to multiple reasons, including but not limited to discontinuation of a program, disqualification from a program, or lack of motivation to complete the program.

8 Risk score is calculated based on the seriousness of current and prior offenses, escape history, disciplinary violation history, gang affiliation status, and current age. The calculated AUC for the risk score variable is 0.6475. The risk score variable plays a role in program participation and therefore, the inclusion of this measure controls for unobservable differences between the treatment and comparison groups, thereby strengthening our model.

9 Table A.1 in Appendix A shows sample mean of the control variables for the treatment and comparison groups of all programs.

10 One caveat of our analysis is that the data set does not provide information on activities or programs individuals participated in their communities, before coming to prison.

11 Standardized difference in percent is the mean difference as a percentage of standard deviation and is given as: $\left({\overline{x}}_1-{\overline{x}}_{0R}\right)/{\left[\frac{{\overline{s}}_1^2+{\overline{s}}_{0R }^2}{2}\right]}^{\frac{1}{2}},$ where ${\overline{x}}_1$ and ${\overline{x}}_{0R}$ are the sample means of covariates for individuals in the treated and comparison groups, while ${\overline{s}}_1^2+{\overline{s}}_{0R }^2$ are the corresponding sample variances of covariates. Each sub-figure presents standardized mean differences in treatment and comparison groups covariates on the x-axis, and the corresponding covariate is indicated on the y-axis. The rule of thumb for the standardized bias is 20, i.e., bias values over 20% (or 0.2 in absolute terms) are considered imbalanced (Rosenbaum and Rubin, 1985). The “rule of thumb” threshold is indicated by two dotted red lines in each sub-figure. Light green dots in each of the sub-figures represent standardized mean differences between unmatched treatment and comparison groups, while dark green dots in each of the sub-figures represent standardized mean differences between matched treatment and comparison groups.

12 In addition to the ATE, we also report predicted probabilities of all outcome measures of reincarceration for treatment and comparison groups of each program.

13 All computations related to matching, ATE, and standard errors are conducted using ‘teffects nnmatch’ program in STATA. The standard errors that we compute using ‘teffects nnmatch’ are also referred as AI robust standard errors and are derived from (Abadie and Imbens, 2006).

14 Survival functions estimate the proportion of the sample with the time to event value more than an arbitrary time t. Mathematically, for a given time $t,$ survival function is given as ${\int }_t^{\infty }f(x)dx$ or $1-{\int }_0^{t}f(x)dx$

15 The key advantage of constructing survival curves is that it allows examining reincarceration risk across the pooled time interval rather than a single cut-off point, which is not possible with binary outcomes.

16 We adopt the following conventional approach to impute potential outcomes for individuals in the treatment and comparison groups. First, the observed outcome for the matched individual in the comparison group serves as the imputed potential outcome under control for each matched treated individual. Conversely, the observed outcome for the matched individual in the treatment group serves as the imputed potential outcome under treatment for each matched individual in the comparison group. With imputed potential outcomes and observed outcomes for each individual in the treatment and comparison group, we then use the Kaplan-Meier method to estimate survival function for treatment and comparison groups.

17 All computations related to matching are conducted using ‘teffects nnmatch’ program in STATA. Survival curves are constructed in Python using KMF functions.

18 Statistical significance at 10% level is indicated by *, at 5% is indicated by **, and at 1% is indicated by ***.

19 The initial sample comprised of 27,548 individuals out of which 4,309 individuals were excluded at the matching stage due to lack of matches. Importantly, the matching with replacement methodology that we use allows us to retain a higher number of matches and also lowers the bias compared to matching without replacement

20 While the control variables in our model account for unobservable factors that can potentially bias our estimates, we further test the robustness of our estimates by controlling for participation in multiple programs. Most of our estimates remain stable and statistically significant after its inclusion.

21 We also estimated our models by restricting the comparison group to only those individuals who did not participate in any program. The general pattern of findings reveals that program participants for all programs fare better than individuals who do not participate in any program during their incarceration.

22 Supplementary analysis based on Cox regression reinforce our findings related to covariate-adjusted survival analysis. The findings show that program participants have significantly lower hazard of re-incarceration than program non-participants for all programs except functional literacy and GED program. Similarly, the results also show that program completers have significantly lower hazard of re-incarceration than program non-completers.