Modeling the Distribution of Sentence Length Decisions Under a Guidelines System: An Application of Quantile Regression Models

How should sentencing disparity be assessed when decisions are constrained under a sentencing guidelines system? Much of the debate over the measurement of sentence disparity under a guidelines system has focused primarily on using specific values from within the sentencing grid (e.g., minimum recommended sentence) or on using interaction terms in regression models to capture the non-additive effects of offense severity and prior record on length of sentence. In this paper, I propose an alternative method for assessing sentencing disparity that uses quantile regression models. These models offer several advantages over traditional OLS analyses (and related linear models) of sentence length, by allowing for an examination of the effects of case and offender characteristics across the full distribution of sentence lengths for a given sample of offenders. The analysis of the distribution of sentence lengths with quantile regression models allows for an examination of questions such as: Do offender characteristics, such as race or offense severity, have the same effect on sentence length for the 10% of offenders who receive the shortest sentences as they do for the 10% of offenders who receive the longest sentences? I illustrate the application and interpretation of these models using 1998 sentencing data from Pennsylvania. Key findings show that the effects of case and offender characteristics are variable across the distribution of sentence lengths, meaning that traditional linear models assuming a constant effect fail to capture important differences in how case and offender characteristics affect punishment decisions. I discuss the implications of these findings for understanding sentencing disparitites, as well as other possible applications of quantile regression models in the study of crime and the criminal justice system.