Relationship Between Prison Length of Stay and Recidivism: A Study Using Regression Discontinuity and Instrumental Variables With Multiple Break Points

• Author: Gerald G. Gaes,William Rhodes,Christopher Cutler,Ryan Kling
• DOI: http://doi.org/10.1111/1745-9133.12382
• Date: 01 August 2018
• Published date: 01 August 2018

RESEARCH ARTICLE

PRISON LENGTH OF STAY AND

RECIDIVISM

Relationship Between Prison Length of Stay

and Recidivism: A Study Using Regression

Discontinuity and Instrumental Variables

With Multiple Break Points

William Rhodes

Consultant

Gerald G. Gaes

Florida State University

Ryan Kling

Christopher Cutler

Abt Associates

Research Summary

In this study, we use both a regression discontinuity design and an instrumental

variable identification strategy to examine the relationship between prison length of

stay and recidivism among a large sample of federal offenders. We capitalize on the

U.S. Sentencing Guidelines structureto apply these strong inference, quasi-experimental

approaches. We find that average length of stay can be reduced by 7.5 months with a

small impact on recidivism. We also examine whether thereis treatment heterogeneity.

We find that length-of-stay effects do not vary by criminal history, offense seriousness,

sex, race, and education level.

Policy Implications

We show that reducing the average length of stay for the federal prison population by

7.5 months could save the Bureau of Prisons 33,203 beds once the inmate population

This article was prepared using federal funding provided by the Bureau of Justice Statistics, Office of Justice

Programs, U.S. Department of Justice, Award 2016-BJ-CX-K04. Direct correspondence to Gerald G. Gaes,

College of Criminology and Criminal Justice, Florida State University, Eppes Hall, 112 S. Copeland Street,

Tallahassee, FL 32306-1273 (e-mail: ggaes@comcast.net). Opinions expressed in this article are those of the

authors and do not necessarily represent the official policy or positions of the U.S. Department of Justice.

DOI:10.1111/1745-9133.12382 C2018 American Society of Criminology 731

Criminology & Public Policy rVolume 17 rIssue 3

Research Article Prison Length of Stay and Recidivism

reaches steady state. This back-of-the-envelope estimate reveals how reductions in time

served can have a much larger impact on prison reductions compared with diverting

low-level offenders from prison to probation. Prisonlength-of-stay reductions can impact

the entire prison population, whereasdiversion typically affects a small subset of offenders

whose consumption of prison beds is a small fraction of the total number of beds. We

also discuss the potential impact of reducing levels of imprisonment on other collateral

consequences.

Keywords

time served, recidivism, length of stay, regression discontinuity, instrumental variable

In this article, we capitalize on the federal sentencing structure to evaluate the effect

of prison length of stay on recidivism. Our findings have policy implications for both

federal and state sentencing reform. In most jurisdictions, sentencing reform has been

designed to divert low-level offenders from prison to probation (La Vigne et al., 2014).

Typically, this policy diverts a small subset of offenders who have short prison lengths of stay.

Placing them on probation has modest effects on levels of imprisonment. Even a modest

reduction in length of stay for all offenders, however, can have a large impact on prison

average daily population and consequently on both capital and operational expenses.

Most scholarship on imprisonment has been aimed at evaluating the impact of the

in/out decision—comparing a term of imprisonment with an alternative sanction (Nagin,

Cullen, and Jonson, 2009; Smith, Gendreau, and Goggin, 2002; Villettaz, Gillieron, and

Killias, 2015). Although a few rigorous studies of the prison in/out decision exist, there are

even fewer rigorous studies on the effect of prison length of stay on recidivism (Nagin et al.,

2009). As of 2009, Nagin et al. identified two experiments and three matching studies. Since

their review, only a few studies with strong counterfactual designs have been published. We

cover these in our literature review.

A second goal of our study is to measure length-of-stay treatment heterogeneity: Does

the effect of modifying the length of stay differ across subgroups of individuals? The federal

sentencing structure once again provides this opportunity. Scholars have argued that the

effect of prison may depend on moderating factors (Mears, Cochran, and Cullen, 2014;

Nagin et al., 2009; National Research Council [NRC],2014). Nagin et al. (2009) proposed

that imprisonment effects may depend on characteristics of the offender, institution, and

sentence. The National Research Council report on the causes and consequences of mass

incarceration included a discussion on the potential variations that depend on characteristics

of individuals, social contexts, and units of analysis (NRC, 2014). As an example, in the

NRC report, the research on the stigma of a criminal record on job seeking (Pager, 2007;

Pager,Bonikowski, and Western, 2009; Pager and Quillian, 2005) is cited as affecting Black

more than White applicants. Incarceration treatment heterogeneity is important because,

as the NRC report indicated, unpacking treatment effect dependence may lead to an

732 Criminology & Public Policy

Rhodes et al.

explanation of why we observe effect size variations across imprisonment studies found in

all the systematic reviews (Nagin et al., 2009; Smith et al., 2002; Villettaz et al., 2015).

Although substantive findings and their policy implications are important, this article

also makes a methodological contribution by using variations on regression discontinuity

design and instrumental variable identification strategies. This methodology transfers to

other states that use guideline sentencing. Therefore, we carefully explain and justify our

approach.

Identifying the Causal Relationship Between Prison Length of Stay and

Reoending

As many researchers have pointed out, estimating the causal relationship between length of

stay and reoffending raises validity challenges (Berube and Green, 2007; Green and Winik,

2010; Loeffler, 2013; Loughran et al., 2009; Nagin et al., 2009). It seems plausible, if

not probable, that offenders receive longer prison terms, in part, because they are likely

to reoffend, potentially inducing a spurious positive correlation between prison length of

stay and recidivism. For example, criminal record is a good predictor of future offending.

Sentencing guidelines (when they are used) and judicial proclivities (when guidelines are

absent) typically take criminal records into account. Offenders with more extensive crimi-

nal histories serve longer terms. Consequently, even if estimated in a regression framework

attempting to control for confounders, a partial correlation of time served and recidivism

may be uninformative. The research provided in this article is aimed at addressing this

methodological concern about identification by employing the logic of a regression dis-

continuity design (hereafter RDD) and an instrumental variable design (hereafter IV) to

rigorously identify the causal relationship between time served and recidivism. The identifi-

cation strategy rests on the structure of guideline sentencing. In the Nagin et al. review, these

scholars anticipated the utility of this approach, “Determinant sentencing grids may provide

a quasi-experiment for constructing the dose-response relationship between sentence length

and reoffending” (Nagin et al., 2009: 184). We find that lengthening a prison term does

not increase recidivism. In fact, increasing the length of a prison term reduces recidivism by

a small amount.

As we explain, the U.S. Sentencing Guidelines provide a structure for an RDD or IV

analysis because by holding constant factors believed to affect recidivism, the guidelines

recommend longer or shorter sentences for similar offenders based on offense factors

that likely have nothing to do with an offender’s risk of recidivism. Many methodologists

consider RDD to be a close second-best alternative to random assignment, and RDDs

have been used in a diverse set of applications (Berk, 2010; Berk, Barnes, Ahlman, and

Kurtz, 2010; Berk and de Leeuw, 1999; Berk and Rauma, 1983; Bloom, 2012; Bor,

Moscoe, Mutevedzi, Newell, and Barnighausem, 2014; Cattaneo, Titiunik, Vazquez-Bare,

and Keele, 2016; Cook, 2008; DiNardo and Lee, 2010; Hahn, Todd, and Klaauw, 2001;

Imbens and Lemieux, 2007; Lee and Card, 2006; Lee and Lemieux, 2010; Rhodes and

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