Evaluating the Role of Race in Sentencing: An Entropy Weighting Analysis

Abstract

The current study builds on prior research examining racial disparities in sentencing. Entropy weighting is introduced as a new method for estimating racial disparities that has several advantages over traditionally used methods. Entropy weighting is compared to regression and propensity score methods in estimating Black-White disparities in incarceration sentences. Although all methods find non-significant racial disparities in incarceration sentences, regression and propensity score methods underestimate disparities in incarceration sentence lengths. Entropy weighting provides comparable estimates to propensity score methods, but assures that the samples are identical on all covariates aside from race. The method offers researchers a useful and flexible approach for estimating racial disparities in criminal justice, and its use may lead to alternative conclusions about the size and presence of racial disparities in sentencing.

Keywords:

• race
• disparity
• sentencing
• entropy weighting
• propensity score

Acknowledgements

The authors thank Chief Justice Leo E. Strine, Jr. for initiating research on the causes of racial disparities in the Delaware criminal justice system in conjunction with the Delaware Access to Justice Commission’s Subcommittee on Fairness in the Adult Criminal Justice System. We acknowledge the special assistance in accessing the Delaware Criminal Justice Information System (DELJIS) and the details of the data from Executive Director Peggy Bell and Operations Manager Lynn Gedney. Special thanks are also due to State Court Administrator Amy Quinlan for coordinating data access and Research and Planning Coordinator Patti Mattson for overseeing research progress and funding. The opinions in this study are those of the authors and do not reflect the official positions of the AOC or Penn. This study was approved by the Penn institutional review board.

Notes

¹ Albeit their estimates of racial disparities are substantially smaller than their previous estimates from a regression model and similar to those reproduced by Berk et al. (2005) using a random forests machine learning algorithm to construct propensity scores.

² Race and ethnicity are coded from reports provided to DELJIS by the arresting police officer. Therefore, it is important to underscore that race and ethnicity are perceived by a law enforcement official and not self-reported by arrested individuals.

³ Approximately one third of the 53,746 individuals arrested between 2012 and 2014 experienced more than one arrest. The range of arrests spans from 1 to 42 contacts with police, and fewer than 5% of arrestees had more than five arrests. Rearrest patterns correspond to criminal processing trends in the State. For instance, a majority of offenders (55.8%) released from Delaware prisons are rearrested within a year. Over 70% of offenders experience an arrest within two years (Delaware Statistical Analysis Delaware Statistical Analysis Center, 2014).

⁴ Delaware has a unified correctional system for jail and prison, meaning that all correctional facilities are operated by the state. Under this structure, individuals receiving incarceration sentences (Level V sentences) are sent to the same correctional institutions regardless of their sentence length. The state does classify an incarceration sentence as a jail sentence when a sentence length is under one year, and a prison sentence when the sentence length is one year or more. Some empirical assessments of sentencing disparities encourage separating these two sanctions because they are substantively distinct (Holleran & Spohn, 2004; Jordan & Freiburger, 2015). Because the sentencing process and supervision of offenders serving time in confinement are the same in Delaware (State of Delaware, 2017), we do not treat jail and prison as substantively distinct sanctions. This methodological choice is similar to that made by others estimating racial disparities sentencing in other states (Bales & Piquero, 2012; Hester & Hartman, 2017; Johnson, 2006).

⁵ Life sentences represent just .2% (n = 16) of the cases.

⁶ When 1:1 nearest neighbor matching is conducted with replacement, only 1 case involving a Black defendant and 26,890 cases involving White defendants were unmatched. In contrast, when this procedure is completed without replacement in the sentencing sample, 6,416 cases involving Blacks and 13,503 cases involving Whites could not be matched. The replacement approach therefore matches and rematches a sizeable subset of White defendants (n = 13,387 or 25% of the White defendant sample). We prefer propensity score matching with replacement because we seek to estimate the treatment-on-the-treated effect (i.e. the influence of minority status on the adjudication of the average Black defendant as compared to a similarly-situated White defendant). In contrast, 1:1 nearest neighbor matching with no replacement identifies a local average treatment effect that only estimates the difference between  Black defendants that are identical on observed variables to single White defendant. In our study, the subgroup of Black defendants who are successfully matched to one White defendant (66% of all Blacks) experienced lower mean probabilities of incarceration than the entire Black defendant sample. As a result, this local average treatment effect underestimates the effect of being Black on sentencing outcomes (treatment-on-the-treated effect). Supplemental tables summarizing the findings of 1:1 matching with and without replacement are available from the authors. Alternative propensity score matching specifications like 3:1 nearest neighbor matching or increases in caliper (e.g. .05) offer similar estimates of race effects in size and direction that do not substantively change conclusions about the presence of sentencing disparities.

⁷ Standardized differences are not shown for ease of exposition. Balance tables that include the means, variances, and skew of covariates by race in both samples are available from the authors.

⁸ Effective sample size is calculated as the sum of weights squared divided by the squared sum of weights. In propensity score matching, unmatched observations are not given any weight.

⁹ The predicted mean probability of incarceration for Black defendants remains the same across methods because these defendants represent the “treatment” group.

Additional information

Notes on contributors

John M. MacDonald

John M. MacDonald is a professor of Criminology and Sociology at the University of Pennsylvania.

Ellen A. Donnelly

Ellen A. Donnelly is an assistant professor of Sociology and Criminal Justice at the University of Delaware.