Recent Innovations in Multiple Regression Studies of Federal Sentencing Decisions

Paul J. Hofer, U.S. Sentencing Commission
Kevin R. Blackwell, U.S. Sentencing Commission

Empirical investigation of disparity in sentencing has a long history. It was recognized early on that simple comparisons among racial or ethnic groups (either in the proportion of each group receiving prison, or in their average sentence lengths) might not reveal discrimination but instead reflect differences in the types of crimes committed or the extent of group members= criminal history. This led to the use of multivariate techniques, particularly multiple regression analysis, to control for the variation in sentences that might be attributed to legally-relevant factors (Hagan 1974).

Multiple regression models of this type have been used for decades to study discrimination in federal sentencing, including at least 13 studies conducted following the introduction of federal sentencing guidelines in 1987 (Hofer & Blackwell, 1999). Four of these studies have appeared in peer-reviewed journals (Albonetti, 1997; Herbert, 1997; Steffensmeier & Demuth, 2000; Mustard, 2001) and several appeared in the popular press (Frank, 1995; Flaherty & Casey,1996). These studies have reported that offenders= race and ethnicity continue to have a significant effect on sentences, even after controlling for the most important legally relevant factors.

Hofer and Blackwell (1997) argued that methodological problems with the multiple regression analyses used in these studies made it likely that the racial discrimination they reported was exaggerated. The prevailing modelsCwhich used direct measures of legally-relevant factors such as use of a gun, or used the guidelines= own offense level or criminal history scores as global measures of the legally relevant factorsCfailed to specify properly the known relationships among the control variables and sentences. For example, mandatory minimum penalty statutes linked to certain facts can Atrump@ the guidelines and force judges to impose specific penalties above the minimum of the guideline range. Under 18 U.S.C. '924(c), offenders who possess a gun during a drug or violent crime must receive a five-year consecutive sentence in addition to the guideline sentence for the underlying crime. Simply adding a control variable for a conviction under '924(c) does not guarantee that the model will properly specify this effect. Further, because these mandatory minimums disproportionately affect minority offenders, failure to correctly specify them leads to exaggerated race and ethnic effects.

Similarly, judges may legitimately depart from the guidelines if they identity, on the record, an aggravating or mitigating factor present in the case that was not adequately taken into account by the guidelines. Given the known disproportionate rates of departure among different racial and ethnic groups (Kramer and Maxfield, 1998; Adams, 1998) failure to include departure status as a control variable leads to race and ethnic effects that may be due to legally important differences among the groups. Indeed, much of the Adisparity@ that has been reported in the literature (Steffensmeier & Demuth, 2000; Mustard 2001) is due to differences in departures.

Other researchers noted additional problems with the standard multiple regression approach. Mustard (2001) described one problem---a lack of linearity between offense level, criminal history score, and sentence lengthCand avoided it by using dummy variables representing each cell of the sentencing table rather than offense level and criminal history as linear control variables.

Engen and Gainey (2001), in a study of sentencing under the Washington State guideline system, refined this approach further by representing all legally relevant factors with a single independent variable, the Apresumptive sentence,@ which was defined as the mid-point of the range of imprisonment recommended by the guidelines applicable to each case. As predicted, this approach reduced the effects for race, ethnicity, and gender and in some cases eliminated the effects altogether.

Hofer and Blackwell (2001) showed how use of the presumptive sentence as a control variable might also avoid one of the problems with previous studies of federal guideline system---the trumping of the guideline range by mandatory minimum penalties. By defining the presumptive sentence as the minimum sentence required by the applicable guidelines or by any applicable statutory penalty the presumptive sentence provides a precise method for specifying the legally-defined relationships among the statutes and the guidelines. By adding variables for the various types of departures, researchers could specify more precisely both the legally relevant factors on which we have data and the known legal effects of these factors on each other and on the final sentence.

In a comment on Engen and Gainey=s article, Ulmer (2001) pointed out a circumstance in which models that include particular legal factors---such as offense level, prior record, or use of a gun----might outperform the presumptive sentence model in terms of variance explained. This could happen if the guidelines are Aloose@Cif they afford judges significant discretion within the guideline rangeCand if the weight judges attach to the particular factors differ from the weight given them by the guidelines themselves. If judges think that the presence of a firearm is more important than its effect on the presumptive sentence, a regression model including firearm as a separate factor could represent judges= reasoning better than the presumptive sentence. Thus, it is necessary to carefully consider the particular guideline system being studied, and to compare the fit of the presumptive sentence model with that of reasonable alternatives.

Bushway and Piehl (2001), in a study of sentencing under the Maryland guidelines, pointed to possible confusion surrounding interpretation of the presumptive sentence model proposed by Engen and Gainey. If the presumptive sentence is included as a normal predictor variable in a multiple regression analysis, it will receive a coefficient conditioning its effect on predicted sentences. (The magnitude and direction of this coefficient is determined by the analysis=s model-fitting procedures. Ordinarily, predictor variables are assigned the coefficients that minimize the squared errors of prediction of the outcome variable.) Once this coefficient is included in the model, the presumptive sentence no longer represents how the legal system itself (i.e. the guidelines and statutory rules) says that the considerations reflected in the presumptive sentence should affect sentences, but instead how those factors are actually used by judges. A coefficient different than 1 indicates that judges weight the considerations represented by the presumptive sentences somewhat differently than the rules themselves, in ways that the analysis leaves obscure.

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Updated 05/20/2006