Bureau of Justice Statistics Working Paper Series

Federal Sentencing Disparity: 2005–2012

William Rhodes, Ph.D.

Ryan Kling, M.A.

Jeremy Luallen, Ph.D.

Christina Dyous, M.A.

Abt Associates, 55 Wheeler St, Cambridge, MA 02138, www.abtassociates.com

WP-2015:01

October 22, 2015

The authors acknowledge the support of the Bureau of Justice Statistics, Award #2013-MU-CX-K057.

Disclaimer: This paper is released to inform interested parties of research and to encourage discussion. 

The views expressed are those of the authors and not necessarily those of the Bureau of Justice 

Statistics or the U.S. Department of Justice. The authors accept responsibility for errors. 
Federal Sentencing Disparity: 2005–2012 i

Abstract: 

Federal Sentencing Disparity, 2005-2012, examines patterns of federal sentencing disparity among white and 

black offenders, by sentence received, and looks at judicial variation in sentencing since Booker vs. United 

States, regardless of race. It summarizes U.S. Sentencing Guidelines, discusses how approaches of other 

researchers to the study of sentencing practices differ from this approach, defines disparity as used in this 

study, and explains the methodology. This working paper was prepared by Abt Associates for BJS in response 

to a request by the Department of Justice’s Racial Disparities Working Group to design a study of federal 

sentencing disparity. Data are from BJS’s Federal Justice Statistics Program, which annually collects federal 

criminal justice processing data from various federal agencies. The analysis uses data mainly from the U.S. 

Sentencing Commission.
Federal Sentencing Disparity: 2005–2012 ii

Table of Contents

Table of Contents.......................................................................................................................................... ii

List of Figures............................................................................................................................................... iv

List of Tables ................................................................................................................................................ vi

Introduction ..................................................................................................................................................1

1.0 Federal Sentencing Guidelines....................................................................................................3

2.0 Recent Studies of Sentencing Disparity .....................................................................................7

3.0 Defining disparity..........................................................................................................................16

3.1 Disparity and the rule of law ...................................................................................................16

3.2 How to define disparity post-Booker......................................................................................18

3.3 Race is bundled with other factors ........................................................................................22

4.0 Statistical methodology: A random effect model .....................................................................27

4.1 Estimation..................................................................................................................................27

4.2 Data and variables ...................................................................................................................33

5.0 Analysis and interpretation..........................................................................................................36

5.1 Operational variables entering the analysis .........................................................................36

5.2 Findings regarding sentencing disparity ...............................................................................38

5.2.1 Converting findings on disparity from standardized units to original units ..............43

5.2.2 Racial disparity across guideline cells ..........................................................................51

5.2.3 Racial disparity across judges........................................................................................51

5.2.4 Increases in disparity: Variance about the guidelines ................................................56

5.3 Evidence of prosecutorial discretion......................................................................................58

5.3.1 Facts surrounding the case ............................................................................................59

5.3.2 Gaming drug amounts near mandatory minimums.....................................................61

6.0 Conclusions...................................................................................................................................66

References ..................................................................................................................................................69

Appendix A: Mechanics of guidelines.........................................................................................................71

Offense level .........................................................................................................................................71

Criminal history category.................................................................................................................73

Departures.........................................................................................................................................73

Appendix B: Detailed findings for sentencing disparity – U.S. citizens.......................................................78

Data partition: Males, no weapons offenses, no sex offenders ....................................................79

Data partition: Females, no weapons offenses, no sex offenders................................................84

Data partition: Weapons offenders, no sex offenders ....................................................................89
Federal Sentencing Disparity: 2005–2012 iii

Data partition: Sex offenders..............................................................................................................94

Appendix C: Detailed findings for sentencing disparity: Non-U.S. citizens.................................................99

Data partition: Males, no weapons offenses, no sex offenders ..................................................101

Data partition: Females, no weapons offenses, no sex offenders..............................................106

Data partition: Weapons offenders, no sex offenders ..................................................................110

Data partition: Sex offenders............................................................................................................114

Appendix D: Detailed findings for prosecutorial discretion......................................................................118
Federal Sentencing Disparity: 2005–2012 iv

List of Figures

Figure 1 – A causal model of how offense and offender facts affect the sentence ...................................13

Figure 2 – Increases in racial disparity over time for four partitions: Males convicted for non-weapons 

violations (overall significance p < 0.01).....................................................................................................45

Figure 3 – Increases in racial disparity over time for four partitions: Males convicted of crimes involving 

weapons violations (overall significance p < 0.05) .....................................................................................47

Figure 4 – Increases in racial disparity over time for four partitions: Alternative specification to figure 2

....................................................................................................................................................................49

Figure 5 – Increases in racial disparity over time for four partitions: Alternative specification to figure 3

....................................................................................................................................................................50

Figure 6 – Variation in racial sentencing disparity across judges for males convicted of non-weapons 

violations.....................................................................................................................................................54

Figure 7 – Variation in racial sentencing disparity across judges for females convicted of nonweapons 

violations.....................................................................................................................................................55

Figure 8 – Distribution of offenders within 100 grams of the 500-gram mandatory minimum threshold, 

by race and ethnicity...................................................................................................................................63

Figure B.1 – Changes over time for three guideline cells: Males................................................................81

Figure B.2 – Predicted and actual sentences across maximum sentence in guideline cells: Males...........82

Figure B.3 – Differences in judge distributions: Males...............................................................................83

Figure B.4 – Changes over time for three guideline cells: Females............................................................86

Figure B.5 – Predicted and actual sentences across maximum sentence in guideline cells: Females.......87

Figure B.6 – Differences in judge distributions: Females............................................................................88

Figure B.7 – Changes over time for three guideline cells: Weapons offenders.........................................91

Figure B.8 – Predicted and actual sentences across maximum sentence in guideline cells: Weapons 

offenders.....................................................................................................................................................92

Figure B.9 – Differences in judge distributions: Weapons offenders.........................................................93

Figure B.10 – Changes over time for three guideline cells: Sex offenders.................................................96

Figure B.11 – Predicted and actual sentences across maximum sentence in guideline cells: Sex offenders

....................................................................................................................................................................97

Figure B.12 – Differences in judge distributions: Sex offenders.................................................................98

Figure C.1 – Changes over time for three guideline cells: Males..............................................................103

Figure C.2 – Predicted and actual sentences across maximum sentence in guideline cells: Males.........104

Figure C.3 – Differences in judge distributions: Males.............................................................................104

Figure C.4 – Changes over time for three guideline cells: Females..........................................................108

Figure C.5 – Predicted and actual sentences across maximum sentence in guideline cells: Females.....108

Figure C.6 – Differences in judge distributions: Females..........................................................................109

Figure C.7 – Changes over time for three guideline cells: Weapons offenders.......................................112

Figure C.8 – Predicted and actual sentences across maximum sentence in guideline cells: Weapons 

offenders...................................................................................................................................................112

Figure C.9 – Differences in judge distributions: Weapons offenders.......................................................113

Figure C.10 – Changes over time for three guideline cells: Sex offenders...............................................116

Figure C.11 – Predicted and actual sentences across maximum sentence in guideline cells: Sex offenders

..................................................................................................................................................................116

Figure C.12 – Differences in judge distributions: Sex offenders...............................................................117

Figure D.1 – Cocaine: 500g Threshold ......................................................................................................118

Figure D.2 – Cocaine: 5000g Threshold ....................................................................................................118
Federal Sentencing Disparity: 2005–2012 v

Figure D.3 – Crack, Pre-2010: 5g Threshold..............................................................................................119

Figure D.4 – Crack, Pre-2010: 50g Threshold............................................................................................119

Figure D.5 – Crack, Post-2010: 28g Threshold..........................................................................................120

Figure D.6 – Crack, Post-2010: 280g Threshold........................................................................................120

Figure D.7 – Heroin: 100g Threshold ........................................................................................................121

Figure D.8 – Heroin: 1000g Threshold ......................................................................................................121

Figure D.9 – Marijuana: 100,000g Threshold............................................................................................122

Figure D.10 – Marijuana: 1,000,000g Threshold.......................................................................................122

Figure D.11 – Methamphetamine (Mixture): 50g Threshold....................................................................123

Figure D.12 – Methamphetamine (Mixture): 500g Threshold .................................................................123

Figure D.13 – Methamphetamine (Pure): 5g Threshold...........................................................................124

Figure D.14 – Methamphetamine (Pure): 50g Threshold.........................................................................124
Federal Sentencing Disparity: 2005–2012 vi

List of Tables

Table 1 – Regression results: Males, no substantial assistance, no weapons or drugs..............................38

Table 2 – An estimated skedastic function based on residuals..................................................................57

Table 3 – Trends in prosecutorial behavior ................................................................................................59

Table 4 – Conditional differences (male and female).................................................................................64

Table B.1 – Number of observations for each guideline cell - Citizens.......................................................78

Table B.2 – Parameter estimates from mixed models: Males....................................................................79

Table B.3 – Parameter estimates from mixed models: Females................................................................84

Table B.4 – Parameter estimates from mixed models: Weapons offenders..............................................89

Table B.5 – Parameter estimates from mixed models: Sex offenders........................................................94

Table C.1 – Number of observations for each guideline cell - Citizens.......................................................99

Table C.2 – Parameter estimates from mixed models: Males..................................................................101

Table C.3 – Parameter Estimates from mixed models: Females, no weapons offenses, no sex offenders

..................................................................................................................................................................106

Table C.4 – Parameter estimates from mixed models: Weapons offenders............................................110

Table C.6 – Parameter estimates from mixed models: Sex offenders......................................................114

Table D.1 – Boundaries chosen around drug threshold amounts based on graphical inspection ...........125

Table D.2 – Percent missing weights, by race and drug ...........................................................................125

Table D.3 – For range check estimation: Conditional differences (males and females) ..........................125

Table D.4 – For logistic estimation: Conditional differences (males and females)...................................125

Table D.5 – For male versus female estimation: Conditional differences (males only) ...........................126

Table D.6 – For Male versus female estimation: Conditional differences (females only)........................126
1

Federal Sentencing Disparity, 2005–2012 

Introduction

As part of a cooperative agreement for the Federal Justice Statistics Program (FJSP), the Bureau of 

Justice Statistics(BJS) instructed Abt Associates to design a study of federal sentencing disparity, as requested 

by the U.S. Department of Justice’s Racial Disparities Working Group. This report responds to those 

instructions by presenting a new methodology for studying sentencing disparity. Although this report is 

principally a discussion of methods, findings are also discussed. For the purposes of this study, the broad 

research question is—

• Do non-Hispanic African American or black (hereafter black) offenders receive prison terms that are 

longer on average than the prison terms received by non-Hispanic white (hereafter white) offenders,

accounting for the apparent facts surrounding the crime and the offender’s criminal record? We call 

observed differences disparity, although based on the evidence we cannot attribute disparate 

decision-making to racial bias.

The principal research question concerns the sentencing disparity between white and black offenders. 

However, using the above measure of disparity, the broad research question is divided into the following 

specific questions:

1. Did the degree of disparity change between 2005 and 2012? As explained later in this report, the 

years are important because a 2005 Supreme Court decision (Booker v. United States) (hereafter 

Booker) rendered the Federal Sentencing Guidelines advisory.

2. Did the degree of disparity change with the seriousness of the offense and the offender’s criminal 

history?

3. To what extent was the disparity systematic and to what extent was it specific to individual judges?

4. Between 2005 and 2012, a period in which the guidelines were advisory rather than mandatory, did 

judges increasingly disagree about the appropriate sentences for offenders?
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Federal Sentencing Disparity, 2005–2012 

The first two questions pertain directly to patterns regarding the differences in sentences received by 

white and black offenders. The third and fourth questions pertain to judicial disagreement about sentences 

without regard to race. Several recent studies have examined how the Booker decision affected disparity by 

giving judges increased latitude to impose sentences. Ourstudy, which uses post-Booker data exclusively, 

does not purport to examine the impact of Booker.1

Data for this study come from the FJSP, sponsored by BJS, which annually assembles federal criminal 

justice processing data from various federal agencies. The analyses rests heavily on data from the U.S. 

Sentencing Commission (USSC) because those data are the richest source of offense and offender 

information, as the USSC is the principal source of data for sentencing. However, this study draws on other 

parts of the FJSP for judicial identity. The data used in this study and the study itself do not identify specific 

judges by name.

 1 Program evaluators recognize that assessing the impact of Booker is an application of program evaluation, which 

is complicated and uncertain outside of randomized experimentation because causation is difficult to establish. At 

the least, a study of Booker’s impact would require the use of pre- and post-Booker sentencing data, but the study 

reported here uses post-Booker data only. Even if it included pre-Booker data, attributing chances to Booker would 

raise validity challenges. The methodology discussed in the study reported here does not deal with methods that 

might be used to overcome those validity challenges.
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Federal Sentencing Disparity, 2005–2012 

1.0 Federal Sentencing Guidelines

Federal Sentencing Guidelines are a set of rules and policy statements for federal judges to use 

when imposing sentences. (See appendix A for more information.) At the time of sentencing, a judge 

considers the facts surrounding the case along with the offender’s criminal history and his or her 

cooperation with the government and then assigns the offender to a cell in a two-dimensional 43x6 

sentencing grid. The grid’s vertical axis corresponds to the facts surrounding the case (e.g., brandishing a 

weapon during a bank robbery). The grid’s horizontal axis corresponds to the offender’s criminal history

(e.g., the offender previously served a prison term in excess of 1 year). If the offender cooperated with 

the government, the sentencing judge can move the offender from one cell to another, according to 

prescribed rules.

The guideline cell stipulates a recommended sentence based on the facts surrounding the case

(e.g., the charge, use of a weapon, and amount of drugs involved), the offender’s criminal record, and 

the offender’s cooperation with the government. Some of the cells allow for probation sentences and 

some allow for a combination of probation and prison. All of the cells identify a lower and upper limit for 

any recommended prison term, each with no more than a 25% difference between the lower and upper 

limit (excluding cells recommending the shortest sentences).

When promulgated in 1987, the guidelines were mandatory and judges were expected to sentence 

within the lower and upper limits, although they could depart from the guidelines with written 

justification subject to appellate review. Since 2005, the guidelines have been advisory and the scope of 

appellate review is limited. Although our study examines the current application of the guidelines, a 

historical perspective is helpful for defining current:

• Mandatory guidelines went into effect for most criminal cases in 1987. The guidelines have 

been revised at the USSC’s discretion, subject to Senate approval.
4

Federal Sentencing Disparity, 2005–2012 

• In 1996, Koon v. United States (hereafter Koon) clarified the role of appellate court review.

Deference was paid to fact findings at the district court level; i.e., an appellate court had to 

accept the facts determined by the sentencing judge. This meant that review was limited to 

mechanical errors in applying the guidelines and the legitimacy of reasons for departure.

• In 2003, Congress passed the PROTECT Act (hereafter PROTECT), which required justification for 

departures, thereby reducing judicial latitude to depart from the guidelines. In exchange for 

cooperation with the government, the Commission strengthened the guidelines consistent with 

PROTECT and formalized some provisions for reducing sentences. Congress specified that higher 

court review would be de novo, meaning that circuit courts no longer had to defer to lower 

court findings of fact. As a result, Koon was nullified.

• In 2005 Booker v. United States (hereafter Booker), the Supreme Court ruled that the guidelines 

were advisory rather than mandatory and reestablished the level of deference to findings of fact 

consistent with Koon. The PROTECT Act retained the features that reward cooperation with the 

government.

• In 2007, the Supreme Court ruled in Gall v. United States (hereafter Gall) that the federal 

appeals courts may not presume that a sentence falling outside the range recommended by the

guidelines is unreasonable. This decision strengthened the authority of district court judges to 

depart from the guidelines.

The USSC identifies four periods in the evolution of the guidelines (Commission, 2012). Ignoring preKoon, the periods are Koon to PROTECT, PROTECT to Booker, Booker to Gall, and post-Gall. The 

Commission’s report shows how disparity has changed over these four periods. However, BJS is

concerned with disparity under current sentencing laws. Our analysis is focused on post-Booker

sentencing, meaning that we examine sentences imposed during the last two periods.
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Federal Sentencing Disparity, 2005–2012 

In Gall, the Supreme Court specified the procedure for post-Booker sentencing. Although the 

guidelines are advisory, a sentencing judge must compute and consider the guideline range and the 

Commission’s policy statements. Thus, although the guidelines are currently advisory, they are not 

irrelevant. An empirical study can still treat the elements entering into guideline computations (as 

reported by the Commission) as representing the facts surrounding the case and the offender’s criminal 

history as established by a preponderance of the evidence (i.e., the evidentiary standard for application 

of the guidelines).2 For our purposes, this means that we can consider the guideline cell as the starting 

point for studying disparity under the guidelines. This is extremely important because otherwise we 

would be unable to distinguish between variation in sentences that are attributed to facts surrounding 

the case or criminal record and systematic unwarranted variation.

The judge must consider the factors set forth in 18 U.S.C. § 3553(a) taken as a whole.

3 There are 

disagreements in circuits and among legal scholars regarding when courts may disregard commission

policy—and even congressional policy—and the permissible grounds for doing so have not been 

resolved. Further, the courts are divided on two important questions: “How much weight should be 

given to guidelines resulting from congressional directives to the Commission?” and “What is the 

appropriate interaction between the proscriptions and limitations on consideration of offender 

characteristics in section 994 of Title 28 and the courts’ consideration of offender characteristics in 

section 3553(a)?”4 Booker has given judges substantial discretion, reinforced by Gall, to impose

sentences using subjective decisions about the adequacy of the sentences recommended by the Federal 

 2 Chapter 6 § 6A1.3 specifies the evidentiary rules: “In resolving any dispute regarding a factor important to the 

sentencing determination, the court may consider relevant information without regard to its admissibility under 

the rules of evidence applicable at trial, provided the information has sufficient indicia of reliability to support its 

probable accuracy.”

3 18 U.S.C. § 3553(a) states the purposes of sentencing, states the role of the guidelines when imposing a sentence, 

and provides justification for sentencing below mandatory minimums and for rewarding offender assistance to the 

government.

4 28 U.S. Code § 994 prescribes duties of the USSC. 
6

Federal Sentencing Disparity, 2005–2012 

Sentencing Guidelines. This observation is important because it provides motivation for studying how 

that discretion is being exercised and whether sentencing disparity is associated with that judicial 

discretion.

A principal difficulty when studying disparity is that the facts surrounding the case cannot be 

known with certainty. Assistant U.S. Attorneys and defense council may manipulate facts to bind the 

judge or to avoid mandatory minimum sentences (Commission, 2011). Even when the facts surrounding 

the case accurately reflect offense behavior and consequences, the judge may observe additional facts 

(relevant for sentencing) that do not appear in the guidelines and, as a result, do not appear in our data.

Fact manipulation and data limitations raise difficult problems with interpretation, which are addressed 

later in this report. (See section 5.3.)
7

Federal Sentencing Disparity, 2005–2012 

2.0 Recent Studies of Sentencing Disparity

Many researchers have examined disparity under the Federal Sentencing Guidelines, but fewer 

researchers have focused their attention on the post-Booker era. We limit this review to selected studies 

that examine post-Booker federal sentencing.

All analyses of sentencing disparity are predicated on a normative position that similarly 

situated offenders who have been convicted of similar crimes should receive similar sentences. The 

exact meaning of this normative position is debatable, but it seems as though most people would agree 

that black and white offenders, convicted of the same crime under the same conditions, should receive 

equivalent sentences. Researchers examining the post-Booker era have taken two approaches to testing 

the null hypothesis of sentencing equality.

One approach has been to start with the facts surrounding the case as relevant to application of 

the Federal Sentencing Guidelines and to determine whether whites and blacks receive comparable 

sentences. Several studies (Motivans & Snyder, 2009; Ulmer, Light, & Kramer, 2011; Commission, 2012)

follow this approach. An alternative approach is to start with the facts surrounding the case at the time 

of prosecution, with the assertion that prosecutors manipulate facts before they are considered for 

guideline application and determine whether offenders accused of the same crime receive the same 

treatment. Other works (Starr & Rehavi, 2013; Rehavi & Starr, 2013; Fishman & Schanzenback, 2012; 

Yang, 2014) are consistent with this alternative approach. These two lines of inquiry answer different 

research questions, although both are framed as studies of sentencing disparity. This section 

summarizes these studies and compares the current study’s approach with extant studies.

Consistent with its role in the federal justice system, the USSC frequently studies federal 

sentencing patterns. Its Report on the Continuing Impact of United States v. Booker on Federal 

Sentencing (2012) is a comprehensive assessment of how the Booker decision affected the application of 

federal sentences. Much of that assessment is tabulation and graphical representation; the descriptive 
8

Federal Sentencing Disparity, 2005–2012 

nature of the analysis appropriately tells a story suitable for the Commission’s audience. Part of the 

Commission’s assessment also includes an empirical analysis that is multivariate and inferential, and is 

similar to the methods presented in our study.

To assess racial disparity at the time of sentencing, the Commission used an ordinary least 

squares (OLS) regression model, with the length of the prison term as the dependent variable, the 

minimum recommended sentence range as the principal covariates, and race and sex as multiplicative 

factors.5 The Commission concluded that “...unwarranted disparities in federal sentencing appear to be 

increasing” (Commission, 2012, p. 3). Summarizing its findings:

“The Commission’s updated multivariate regression analysis showed, among other outcomes, 

that black male offenders have continued to receive longer sentences than similarly situated 

white male offenders.... In addition, female offenders have received shorter sentences than 

similarly situated male offenders.” (Commission, 2012, p. 9)

As with the analysis reported in our study, the Commission used the recommended sentence in the 

Federal Sentencing Guidelines as the starting point for an analysis, asking how sentences for blacks 

differed systematically from sentences for whites. Regarding salient differences between our study and 

the Commission’s study, the Commission used a pre- and post-Booker selection of data, given its 

concern with the impact of Booker, while our analysis is concerned only with post-Booker trends. The 

Commission used what we view as strong assumptions about the underlying sentencing decisions of the 

structural model, while we have used a structural model that is more flexible. The Commission used an 

OLS regression model; our approach uses a linear random effects regression model. Our principal 

analysis excludes noncitizens while the Commission included noncitizens, and our analysis makes a 

 5 The Commission used OLS to regress the logarithm of time served on the logarithm of the minimum sentence and 

a linear combination of variables, including race. This is equivalent to assuming that the race variable has a 

multiplicative effect on the sentence imposed. The specification is cumbersome because sentences and guideline 

minimums are frequently zero and the logarithm of zero is undefined. The Commission set the logarithm of zero to 

a small positive number.
9

Federal Sentencing Disparity, 2005–2012 

somewhat different selection of offenses than was made by the Commission. (This report provides a 

separate analysis of the sentencing of noncitizens.)

Motivans and Snyder (2009) analyzed USSC data for fiscal years 1994 through 2008. Their results 

show that blacks receive mean prison terms that are, in general, longer than whites, and are longer than 

whites after adjusting for offense seriousness and criminal history, both together and separately. Much 

of that disparity disappeared once a regression was used to control for departure type,6 offense type,

and whether there was a weapons charge.

Motivans and Snyder (2009) examined sentences for whites and blacks within each guideline 

cell and then averaged over guideline cells. Their approach to estimating differences within guideline 

cells and then summarizing over the cells is in the spirit of the approach taken in our study. However, we 

adopted a regression model that provides a systematic summary of variation in disparity across the cells 

and over time that often uses stratification instead of covariates and leads to standard statistical testing.

Ulmer, Light, and Kramer (2011) wrote another study as a critique of a 2010 commission report 

(the predecessor of the report cited above). They examined a period that started well before 2005 

through fiscal year 2009. Their findings proved sensitive to the short post-Booker period (Commission, 

2012, pp. 11, part E); based on a reanalysis reported by the Commission (Commission, 2012, pp. 11, part 

E), revised Ulmer, Light, and Kramer findings for the post-Booker period are similar to those reported in 

the Commission’s study. An anonymous reviewer of an earlier draft of this BJS study reports replicating 

the Ulmer, Light, and Kramer approach using data extended through 2012. The reviewer found that 

disparity increases initially and then stops increasing. This BJS study will report similar findings. Ulmer, 

Light, and Kramer made decisions about excluding some cases that are consistent with our decisions, 

and they made decisions about including or not including covariates that are inconsistent with our 

 6 There are many reasons for departures. The most important reasons when studying sentencing disparity are 

departures attributable to the initiative of the assistant U.S. Attorney and departures attributable to judicial 

sentencing discretion.
10

Federal Sentencing Disparity, 2005–2012 

decisions. They used an estimation procedure (a two-step estimator) with which we disagree,7 but we 

still find their results informative and credible.

Starr and Rehavi (2013) are critical of the above tradition that treats the guideline 

recommendations as the starting point for analysis; while they provide a methodological critique, their

harshest criticism is that the above researchers are asking the wrong research question. 8 Ulmer, Light, 

and Kramer were concerned with disparity, conditional on the facts surrounding the case as determined 

at the time of guideline administration. Starr and Rehavi opine that the correct concern is with disparity,

conditional on the original offense. They dismiss answers to the first question because apparent 

disparity at the sentencing stage may merely reflect charging and bargaining decisions by prosecutors.

Another recent study (Johnson, 2014) expands on this line of inquiry by examining racial 

disparities and prosecutorial decision-making in the context of a federal prosecutor’s decision to decline 

prosecution and his or her decision to prosecute an offender under a lesser charge than the arresting 

charge. Johnson’s work uses both fixed and random effects (logit) estimation to study a cohort of 

federal arrestees from 2003 to 2005, and finds at least some evidence to support the argument that

racial disparities exist in prosecutorial decision-making—although disparities tend to favor blacks, not 

whites. It is difficult to conclude from this study whether Johnson’s findings ultimately support or refute

the argument by Starr and Rehavi that disparate sentences are a reaction by judges to bargaining 

decisions by prosecutors. On the one hand, Johnson demonstrates that charge reductions result in 

 7 The approach to two-step models is complicated (Rhodes, 2014). We do not object to estimating the first-stage 

equation of whether the judge imposes a prison term, which is a principal part of the Ulmer, Light, and Kramer 

study. However, consistency of the parameters in the second-stage equation depends on strong assumptions 

regarding independence of the first-stage and second-stage decision or else instrumental variables. When 

independence does not hold, estimated parameters will be biased estimates of their population counterparts. 

Ulmer, Light, and Kramer carefully attempted to counter these problems, but there is no good solution. An 

alternative approach is to use a generalized linear model to estimate the conditional mean instead of underlying 

parameters.

8 We are concerned with the Starr and Rehavi methodology, much of which is described in a second paper (Rehavi 

& Starr, 2012). We are not convinced that the initial charge is a good starting point for a disparity study. Our 

investigation shows that the charges registered by the U.S. Marshals Service are very broad and not good 

descriptions of underlying offense conduct. Also see Rehavi and Starr (2013). 
11

Federal Sentencing Disparity, 2005–2012 

materially lower sentence lengths, but this decrease is not as large as it should have been given the 

decrease in the presumptive sentence that results from moving to a new guideline cell (Johnson, 2014, 

p. 74, table 9). On the other hand, Johnson shows that, even after controlling for the presence of charge 

reduction and the associated presumptive sentence, blacks still receive significantly longer sentences 

(Johnson, 2014, p. 74, table 9). It is difficult to conclude how behavior ultimately affects sentencing 

disparities on average. However, Johnson’s work emphasizes the importance of considering 

prosecutorial practices in studying sentencing disparities.

Fishman and Schanzenbach’s (2012) study is in the spirit of Starr and Rehavi’s (2013) study.

9 It is 

straightforward, examining whether transitions from more to less restrictive guidelines (as a result of 

Supreme Court decisions) caused disparity to increase or decrease. They find that court decisions 

sometimes greatly alter the administration of justice (especially departures and sentencing at the 

statutory minimum), but our interpretation of their work is that the alteration in the administration of 

justice did not have a large impact on racial disparity. Yang (2013) takes a similar approach of basing 

inferences on short-term changes. After accounting for the exercise of prosecutorial discretion with 

regard to charging decision, Yang (2013, p. 2) finds evidence of a 4% increase in racial sentencing 

disparity post-Booker. Our study reports an increase of the same magnitude.10

Our view is that both lines of inquiry pose valid research questions. We agree with Starr and 

Rehavi that it may be impossible to fully discount an explanation that other unobserved variables—

perhaps variables that can be attributed to prosecutorial discretion—account for estimated differences 

 9 Fishman and Schanzenbach introduce the terms endogenous and exogenous, although not necessarily in a way 

that we find helpful. Their argument might be summarized to say that prosecutors make charging and bargaining 

decisions that are endogenous because they take judicial responses into account. Nevertheless, we consider the 

charging and bargaining outcomes as being exogenous to the judge’s decision.

10 Although Yang’s findings are similar to ours, there are large differences in methodology. Yang uses a regression 

model that imposes structural restrictions that are much more restrictive than those adopted for our study; 

includes noncitizens in the analysis while, for reasons explained later, we limit our analysis to citizens; and 

attempts to control for the exercise of prosecutorial discretion, while we examine the exercise of discretion but do 

not build it into our statistical model.
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Federal Sentencing Disparity, 2005–2012 

in the sentences for white and black offenders. However, if we observe trends toward increasing or 

decreasing disparity during a period where those unobserved factors are presumably or demonstrably 

constant, then those trends provide strong evidence of disparity attributable to race.11 We can further 

strengthen the inferences by checking trends in other observed variables. Finding that there are no 

strong trends in observed variables, it seems reasonable to conclude that there are no strong trends in 

unobserved variables. Trend analysis plays an important role in the inferences drawn in our study.

Figure 1 summarizes the arguments. Presumably there is a true set of facts regarding the 

offender and the offense, although offenders attempt to hide their criminal behaviors; as a result, the 

facts may be known imperfectly. The facts are filtered by an assistant U.S. Attorney, who decides what 

to charge and attempts to prove what he or she charges, bargains with defendants and defense 

attorneys, and ultimately presents his or her set of facts to the judge. A probation officer investigates 

the offense conduct according to police reports (e.g., Federal Bureau of Investigation and Drug 

Enforcement Administration), learns about the offender’s criminal history, and studies the offender’s 

background (e.g., employment, and residential and marital status), and prepares and submits a 

presentence investigation report to the judge. Given the convicting charges and the facts surrounding 

the case, the judge imposes a sentence.

 11 Although they are critical of the traditional sentencing guidelines, Starr and Reventi (2013, p. 40) recognize the 

advantage of studies based on changes.
13

Federal Sentencing Disparity, 2005–2012 

Figure 1 – A causal model of how offense and offender facts affect the sentence

The first set of studies examines the causal path that runs from “conviction charges” and “apparent 

facts” through the judge to the sentence. Conditional on the charge and facts that result from 

prosecutorial discretion, the judge imposes the sentence, and one can say that sentencing is disparate,

conditional on those prosecutor-mediated facts. The second set of studies examines the causal path that 

runs from the facts through the sentence. Discretion exercised by prosecutors and judges is cumulative, 

so the disparity is jointly attributable to the prosecutor and judge. Our study shows that the first branch 

of the causal path (which involves the prosecutor) has changed little during the period of our study; that 

is, prosecutorial charging and bargaining practices have remained constant over the study period, or 

when practices have changed, the change has been the same for white and black offenders. In contrast, 

the second path (which involves the judge) has changed considerably; that is, judges have changed their 

behaviors conditional on the facts presented to them. While prosecutorial behaviors have remained 

fairly constant, racial disparity has increased. Although these trends toward greater disparity postdate 

Booker, we cannot say that Booker caused them and we cannot say what would happen if Booker were 

reversed.
14

Federal Sentencing Disparity, 2005–2012 

Another line of enquiry has investigated inter-judge sentencing disparity post-Booker. This work 

has been limited because the USSC has not provided guidelines data matched with judge identifiers. As a 

result, studying inter-judge disparity on a wide scale using data that account for extensive variation in 

offense seriousness and offender criminal records has been restricted. Except for studies done at the 

Commission (Commission, 2012) and a study by Yang (2013) discussed below, researchers have had to 

work with data that have limited geographic (Scott, 2010) or offense (Mason & Bjerk, 2013) coverage, or 

with datasets that have limited detail about offenses and offenders (Hofer, 2012; Yang, 2014), or the 

studies have examined variation across districts rather than judges (Lynch & Omori, 2014). In contrast, 

the data used in this study have judge identifiers for all felonies and serious misdemeanors sentenced in 

federal courts between 2005 and 2012. Having similarly matched judges to guideline cases, Yang (2014)

reports that judges who are appointed to the bench post-Booker are more likely to depart from the 

guidelines, but we could not replicate those findings.12 Using the same data and applying a simple 

analysis of variance technique, Yang (2013) shows that inter-judge disparity has increased from preBooker to post-Gall.

13

As explained in the methodology section (section 4.0), we examine systematic differences across 

judges in the imposition of sentences for white and black offenders. Others have reported intra-judge 

disparity; applying more formality to the problem, similar to an approach used by others (Anderson & 

Spohn, 2010), our statistical model uses a random effect regression to estimate intra-judge disparity.

Intra-judge disparity—as estimated using random effects—is less easily excused as disparate 

prosecutorial decision making or by unobserved factors relevant to sentencing because judges 

 12 Yang faced fundamental limitations because her post-Booker data timeframe was short and judges were Bush

appointees. When using a longer timeframe, we found that judges who were appointed pre-Booker were more 

likely to issue disparate sentences. 13 Yang assumed that cases are randomly assigned to judges within districts, an assumption that seems reasonable 

given the rules used by most districts to assign cases and an assumption that passes diagnostic testing for that 

analysis. Our analysis is based on a similar assumption, but we control for offense and offender characteristics. As 

a result, our findings are less sensitive to whether or not assignment is random.
15

Federal Sentencing Disparity, 2005–2012 

essentially receive a random selection of cases for sentencing. We consider the estimation of random 

effects as a methodological advance.

Finally, our study differs from other studies by examining a longer period of post-Booker

sentencing. Extant studies discussed previously have examined a shorter period. Our study may reveal 

trends that were obscured by a shorter period.
16

Federal Sentencing Disparity, 2005–2012 

3.0 Defining disparity

There is no universally accepted definition of sentencing disparity. We propose a working definition

to support empirical analysis. The working definition is necessarily abstract and readers who are less 

concerned with methodology may wish to skip sections 3.0 and 4.0 after reviewing the following 

summary. This section presents an argument for estimating the following:

• How blacks are disadvantaged compared to whites at the time of sentencing.

• How that disadvantage varies with offense seriousness and criminal record.

• How that disadvantage has varied over time.

• How the dispersion of sentences in general has varied over time.

We specify an operational model where the effect of race can be divided into four components: a 

basic race effect (first bullet), a race effect interacted with the guideline cell (second bullet), a race 

effect interacted with time (third bullet), and a skedastic function (dispersion about the regression line) 

as a function of time (fourth bullet). 

3.1 Disparity and the rule of law

In the abstract, under the rule of law, offenders should know what will happen to them if they 

are convicted of a crime, and offenders convicted of similar crimes under similar circumstances should 

expect to receive similar sentences. In the abstract, then, there should be a function where a sentence S

follows from the facts surrounding case A, the offender’s criminal history B, and concessions made by 

the government in exchange for cooperation C:

[1] S = f (A,B,C)

Throughout this report, we measure the sentence as the length of time sentenced to prison.14

The function represents a normative standard, and any departure from this standard is called disparity.

 14 For less serious crimes, we could examine the decision to impose a prison term. Most federal crimes for which 

the guidelines are relevant result in prison terms. As a result, the decision whether to sentence to prison is of 
17

Federal Sentencing Disparity, 2005–2012 

In the abstract, a study of disparity is straightforward: Given equation [1], a researcher simply needs to 

measure the extent to which sentences depart from this standard.

An immediate problem is determining the standard to which a researcher can identify and 

measure disparity. There are three issues. First, what are the specific components of A, B, and C?

Second, how should those components be weighted by importance? Third, how should the weighted 

components be combined to determine a sentence?

Congress has set broad parameters on the imposition of sentences in the form of statutory 

minimums and maximums. Presumably, sentences that fall outside these parameters are disparate, but 

that standard is not especially helpful because the parameters are wide and few sentences are imposed 

illegally outside these bounds. Within these broad parameters, Congress has delegated to the USSC, 

subject to Congressional veto, the power to determine the standard. The guidelines identify the 

elements of A, B, and C; specify how those elements should be weighted; and instruct how those 

weighted elements should be combined to impose a sentence. Essentially, the guidelines provide

equation [1], subject to major caveats.

One caveat is that the guidelines were never an exact formula for imposing a sentence. The 

guidelines always gave judges latitude to sentence within a 25% range and always allowed judges to 

depart from the range when warranted. The justification is that while the guidelines should apply to 

most cases, the sentencing judge may uncover exceptional cases that require less severe or more severe 

punishment.

Although the guidelines always allowed judicial latitude, the Commission stipulated factors that 

could not be considered—such as race or sex—when departing from the guidelines. Prior to Booker,

disparity might be defined as sentences that were explained by forbidden factors (e.g., race) or that 

 

secondary importance. The analysis of this binary outcome poses a few new analytic problems that are not 

considered when studying the prison sentence. Therefore, this design report does not consider the analysis of 

binary outcomes.
18

Federal Sentencing Disparity, 2005–2012 

departed from the guidelines without acceptable justification. Prior to Booker, sentencing disparity was 

conceptually simple to define.

Post-Booker, existence of a standard is arguable and disparity is more difficult to define. The 

guidelines are advisory but, under Booker, they are still important as a standard that a judge must

consult prior to imposing a sentence. The problem is that a sentence departing from the advisory 

guidelines cannot be identified as disparate because Booker and subsequent court decisions have ceded

judges authority to impose sentences they see as appropriate given the purposes of sentencing. This 

means that after giving due consideration to the guidelines, an individual judge can make his or her own 

determination of equation [1]—the elements that are relevant for sentencing, how they should be 

weighted, and how they should be combined. One might even conclude that post-Booker, there is no 

meaningful standard.

3.2 How to define disparity post-Booker

How, then, should a researcher define and estimate sentencing disparity? The answer requires 

expanding the vocabulary used to describe sentencing disparity. A researcher can always observe how 

the sentence imposed differs from the sentence recommended by the guidelines. A difference cannot 

be declared to be disparate given that judges have discretion to depart from the guidelines.

Nevertheless, some patterns in those differences are suggestive of disparity. To explain, this section 

identifies a model of how sentences are imposed and explains what that model tells or suggests about 

disparity. We start with a relatively simple model and progressively incorporate complexity.

We start with a model of how sentences are imposed within a given guideline cell. Rewrite 

equation [1] as equation [2]. The subscripts identify the i

th offender sentenced by the jth judge in the kth

guideline cell. The ijk e represents the difference between the average sentences imposed within 

guideline cell k and the sentence actually imposed:
19

Federal Sentencing Disparity, 2005–2012 

[2] ijk k ijk S = S + e

k S is the average sentence imposed for offenders sentenced within the kth guideline cell. A researcher

would be concerned with observed patterns of e.

We consider a guideline cell to be an anchor; specifically, we consider the mean sentence within 

the guideline cell as a standard. It is possible that judges, as a collective, have common rules for 

departing from the guidelines. One way to account for a common rule is to introduce additional 

explanatory variables:

[3] ijk k ijk k ijk S = S + X β + e

X is a row vector of variables associated with the i

th offender sentenced by the jth judge in the kth cell. In 

this relatively simple model, the weight assigned to these additional factors (the column vector β) is the 

weighted average over judges. (Weights are proportional to the number of offenders sentenced per 

judge.) To the extent that these variables explain some of the residual variance, sentencing decisions

will be uniform (but different from the guidelines) and the distribution of e will be smaller. Provided it 

excludes clearly inappropriate considerations, such as race, the Xijkβ k term is not disparity; rather, it 

represents a judicial consensus of how the average sentence should vary systematically within a 

guideline cell.

Many A, B, and C variables exist, and it is impractical and arguably unnecessary to include all of 

the variables in a statistical model.15 Because the guidelines already factor most X variables into the 

identification of the guideline cell (e.g., the seriousness of the offense and the danger posed by the 

 15 Some researchers have followed a tradition of introducing a presumably comprehensive set of explanatory 

variables into a regression. A problem with this approach is that it altogether ignores the structure imposed by the 

guidelines and replaces that known structure with a statistical search for the correct model. This is a daunting and 

uncertain exercise that we forego by anchoring our analysis on the guideline cell and then looking for systematic 

departures from that anchor.
20

Federal Sentencing Disparity, 2005–2012 

offender), there is limited variation with which to base inferences.16 Consequently, this study will make 

limited attempts to add X variables to the model, only incorporating them into the analysis when they 

are obviously important. Nevertheless, we know from reviewers’ comments on an earlier draft that the 

decision to include some X variables and exclude others is contentious, and we return to the issue in the 

next subsection.

So far, the discussion has considered residual variance within a guideline cell as variance that is 

unexplained by the legitimate factors (including knowledge of the applicable guideline cell) incorporated 

into the estimation. Unexplained residual variance is not the same as disparity, but it is probative.

Expanding the model specification goes more directly to the issue:

[4] ijk k ij k ijk k ijk S = S + X β + Z γ + e

The Z represents factors that Congress and the Commission recognize as inappropriate considerations 

during sentencing (see appendix A). For our purposes, the important Z variable is race.

Again, currently there is disagreement about the legal standing of the Commission’s policy 

statements, but we doubt that many readers would argue race—the principal focus of this analysis—is 

ever a valid consideration at the time of sentencing. Given the model represented by equation [4], 

interesting aspects of the problem are—

• Does theγ in equation [4] differ from zero? The question is whether there is systematic 

difference across offenders in sentences with regard to race. 

• In equation [4], after accounting for systematic differences in X (common rules used by judges 

for departing from the guidelines) and Z (race and other factors that should not be considered 

 16 For example, for property crimes the dollar value of the loss is a primary determinate of offense seriousness. But 

within a guideline cell, there is likely to be little variation in dollar loss. A regression (the statistical procedure used 

to estimate the parameters in equation [3]) will be uninformative when the independent variable (the X in the 

equation) has small variation.
21

Federal Sentencing Disparity, 2005–2012 

during sentencing), what is the residual variation in e (the average difference between the 

average sentence imposed within the guideline cell and the sentence actually imposed)?

• Has the residual variation in e changed over time?

An extension to [4] almost completes the modeling. Although the β and γ parameters vary across the 

guideline cells, as written in equation [4], the parameters are otherwise fixed as researchers frequently 

use that term with hierarchical linear models. An extension is to write the parameters as being random,

so that [4] is written as [5]:

[5] ijk k ij k ijk ijk ijk S = S + X β + Z γ + e

Note that [4] and [5] are the same, except for the new subscripts that appear on the γ parameter. The 

appearance of the j subscripts allows for the weight that each individual judge assigns to the variable Z

to vary. Some additional structure is required to understand this. Presuming for simplicity that Z is a 

single variable (a dummy variable representing the condition that the offender is black), we might 

express γ as a function of a new vector of variables W .

17

[6] ijk k ijk Wk j γ = γ +W γ + u

Here ijk γ is the effect that being black has on the sentence within the kth cell. The Wij are interesting 

variables that explain systematic patterns in the effects of race (being black) on sentences within the kth

cell. This formulation is often called a hierarchical linear model or a random effect model. It decomposes

the effect of race into three parts. Parameter k γ captures the direct effect that race has on the sentence 

imposed. For example, this parameter might cause us to infer that, on average, black offenders receive 

longer prison terms than do white offenders, taking other factors into account. Parameter Wk γ captures 

the effect of interacting race with some other variable W. For example, if the other variable (W) is the 

 17 Model specifications need to provide additional variables for whites and other races entering the analysis. For 

simplicity, we do not show those additional races.
22

Federal Sentencing Disparity, 2005–2012 

year when the sentence was imposed, this parameter might cause us to infer that, over time, black

offenders receive prison terms that are increasingly longer than the terms received by white offenders,

when taking other factors into account. This is helpful for studying trends. The first two decomposition 

effects are called fixed effects and a third is called a random effect. The random effect uj is attributable 

to the specific judge imposing a sentence. Statisticians might say that judge is nested within race, but 

regardless of the wording, the point is that judges have different reactions to an offender’s race.

18

A final question concerns what to include as X, Z, and W variables. The question has no simple 

answer and we know from reviewers’ comments that the answer is contentious. We explain our 

approach using the concept of bundling, explained in the next subsection.

3.3 Race is bundled with other factors

When studying racial disparity in sentencing, it is necessary to define race and racial disparity. The 

definition may be comparatively simple for a geneticist, who might observe that whites and blacks 

fundamentally share a genetic pool with a few differences that account for skin color; predisposition 

toward certain diseases, such as sickle cell anemia; and other factors. However, when used in the 

context of social responses to race, including criminal sentencing, race seems to mean something other

than genetic variation.

Numerous studies show that blacks have been sociologically and economically disadvantaged; as a 

racial group, they have less education, lower earnings, more serious criminal records, and other factors

distinguishable, on average, from whites. The authors of this report think of genetically defined race as 

being bundled with these social and economic factors.

 18 One reviewer of an earlier draft of this report observed that researchers using hierarchical linear models

typically follow our approach of identifying a variable, such as race, whose effect is allowed to vary with time, 

while other variables are presumed to have fixed effects. The reviewer’s objection is that this is a specification 

error. We grant the validity of this point but assert that justification for using this potentially misspecified model 

comes from the advantage of simplifying a model that otherwise would become so complex as to be 

uninterpretable.
23

Federal Sentencing Disparity, 2005–2012 

When studying racial disparities in sentencing, we must make a decision: Should we seek to 

estimate a pure genetic race effect by controlling for the bundled factors? Or should we treat those 

bundled factors as inseparable from race and not account for them in the analysis? Or should we 

account for some of the bundled factors and ignore others? Reviewers of an earlier draft of this report 

had differing opinions.

We have a preferred approach, although we also attempted to accommodate different opinions.

Overall, we prefer to study the effect of race as a bundle of factors, so that our analysis has a race 

variable but no control variables for education, employment, and other factors associated with race.

With exceptions, identified and justified below, the only control variables are those recognized by the

guidelines.

19

One exception is that we include a covariate that captures nuances in criminal records. To explain, 

the guidelines already identify criminal history categories, derived from collapsing more detailed 

criminal history scores. Because judges potentially see the criminal history scores, because the 

differences between these scores and the criminal history categories may be considered at the time of 

sentencing, and because criminal history is generally considered an appropriate consideration at 

sentencing, we included a transformation of the criminal history scores as covariates. The 

transformation is explained in section 5.1.

In addition to criminal history scores, our preferred model controls for the judicial circuit in the 

regression specification. Empirically, circuits that tend to sentence both white and black offenders 

harshly, compared to other circuits, tend to have a higher proportion of black offenders. Circuits that 

tend to sentence both white and black offenders leniently, compared to other circuits, tend to have a 

 19 One can argue that the Federal Sentencing Guidelines have a built-in, but not necessarily intentional, racial bias. 

The recently changed crack cocaine guidelines illustrate this built-in bias. As another example, blacks may acquire 

lengthier criminal histories than whites for reasons that have nothing to do with inherent criminality, and because 

the guidelines take criminal record into account, blacks may be disadvantaged. This study, which takes the 

guidelines as a normative standard, is not a study of built-in racial disparity.
24

Federal Sentencing Disparity, 2005–2012 

lower proportion of black offenders. Even if blacks suffered no racial disadvantage within every circuit, 

black offenders would appear to be disadvantaged at the national level if the circuit were not taken into 

account. In the case of circuits, we have unbundled circuit as a race attribute. This approach is arguable, 

so we have made accommodations in the form of sensitivity testing. While we focus attention on the 

regression specification with circuit dummy variables, we also report findings from a regression that 

lacks circuits as a control variable and from a regression that substitutes districts for circuits.20

Thus, our preferred model includes a transformed version of criminal history score and circuits as 

the X variables, but at the request of reviewers, we have added education and employment to the 

model to see if these factors account for some of the racial effect. We report findings as a sensitivity test 

of the preferred model.

Despite reviewer recommendations, we do not include covariates that may differentiate offenders 

within guideline cells. For example, the guidelines may place some property offenders and some druglaw violators into the same guideline cell. Despite the fact that these two types of offenders fall into the 

same guideline cell, judges may treat drug offenders more severely than property offenders. If drug 

offenders are more likely to be black, then failing to distinguish between property offenders and drug 

offenders within the same guideline cell may mistakenly associate valid reasons for sentence differences 

to race. From this perspective, the analysis should account for within-guideline differences in crimes.

While giving credit to this argument, we find it difficult to deal with the problem. The differences 

within guideline cells are idiosyncratic and accounting for them would require complicated statistical 

analysis that might obscure more than it explains.21 Furthermore, unless the intra-cell differences 

 20 One review noted that we should use districts to remove regional variations, and while the reviewer’s arguments 

are persuasive, the use of districts instead of circuits does not materially change results. We found that some 

models could not be estimated when district was substituted for circuit.

21 Reviewers have suggested adding dummy variables to account for offense type, but on reflection, this simple 

solution loses its appeal. Depending on the refinement of the offense type variable, certain offenses will appear in 

a limited number of guideline cells, where they will be proxies for those cells. The parameters associated with 
25

Federal Sentencing Disparity, 2005–2012 

uniformly favor whites (or blacks) across all of the cells, the existence of those intra-cell differences will 

not bias estimates of black–white disparity across the cells. Because we have no reason to presume that 

the guideline cells were constructed systematically to disadvantage blacks, we prefer to treat the intracell differences as essentially random across cells. We recognize that this argument will not satisfy all 

readers.22

Although we adopt a simple model with few X variables, based on reading and discussions with 

others, we felt that the structure of equation [5] may differ across settings, an expectation confirmed by 

statistical testing. Evidence shows that females are sentenced less severely than are males. Some 

analysts might deal with this difference by using a dummy variable in a single regression to distinguish 

males from females, but we disagree with that approach. Adding a sex variable as a linear additive effect 

will not account for the fact that the β and γ parameters differ for males and females. (The truth of this 

assertion is demonstrated when discussing empirical results.) Instead of using a dummy variable to 

distinguish sex, we partition the data into 14 strata (see section 4.1) and estimate separate regressions 

for each partition. The β and γ parameters differ demonstrably across these partitions. As a result, we 

cannot simply add dummy variables as control variables.23

The disadvantage of this approach is that with 14 partitions, we have 14 results. However, this is 

only a bookkeeping disadvantage. As explained in the next section, the dependent variable is 

standardized. As a result, the parameters of interest are in the same units and can be averaged across 

 

those dummy variables will not have their usual interpretation as shift parameters. The use of offense variables 

may introduce specification errors that actually mask race effects.

22 Furthermore, considering the bundling argument, the question about intra-cell variation may be unanswerable. 

In the property crime and drug crime example, one could plausibly argue that within a guideline cell, judges 

sentence drug offenders more severely because they are predominately black, while property offenders are 

predominately white.

23 It is possible to specify a model that has interactions between the partitions and the α and β parameters, but 

that is essentially the same as estimating separate models for each partition.
26

Federal Sentencing Disparity, 2005–2012 

partitions, allowing us to make summary statements about disparity in sentencing without reporting the 

results for all 14 partitions.
27

Federal Sentencing Disparity, 2005–2012 

4.0 Statistical methodology: A random effect model

This methodology section has two components. The first section discusses estimation and the 

second section describes the data and variables used in the analysis.

4.1 Estimation

The previous section identified a theoretical model for measuring sentencing disparity. The 

model is potentially useful because it answers questions relevant to this study. Unfortunately, the model 

is not practically useful as written for two reasons: (1) there are too few observations per guideline cell 

to estimate parameters reliably and (2) there is no simple way to summarize results across the 258 

guideline cells. Recognizing these problems, this section provides a model simplification that retains the 

important aspects of modeling already discussed.

We have defined Sijk as the sentenced imposed on the i

th offender by the jth judge in the kth

guideline cell. For reasons to be explained, it will be convenient and useful to rescale the sentence. Let

Nk be the number of sentences imposed within cell k.

k

i j k

ijk

k N

S

M

∑∈ = ,

( )

1

,

2

−

−

=

∑∈

k

i j k

ijk k

k N

S M

SC

The notation i, j ∈k means summation over all i and j in cell k. Mk is the average sentence imposed in 

the kth cell. k SC is the standard deviation for sentences imposed within the kth cell. Then the rescaled 

measure of sentence is—

[7]

k

ijk k

ijk SC

S M

s − =
28

Federal Sentencing Disparity, 2005–2012 

This rescaled measure has two useful properties: (1) within any cell, the average rescaled sentence will 

be zero and (2) within any cell, the standard deviation for the rescaled sentence will be one. Using this 

rescaled version of the sentence, we write the model using all the cells as—

[8]

ij ijk W j

ijk ijk ijk ij ijk

W u

s X Z e

= + +

= + +

γ γ γ

β γ

0

Equation [8] looks similar to equation [5], but there are important differences:

• Equation [5] pertained to a specific guideline cell, while equation [8] applies to all guideline cells.

• In equation [5], the β and γ have k subscripts, implying that those parameters vary from cell to

cell, but the k subscript has been dropped in equation [8], implying that those parameters are 

invariant across the cells. Given 258 guideline cells, this reduces the parameter space by a 

multiple of 258, greatly reducing the estimation problem and providing a useful summary 

measure across cells. This simplification may be an incorrect specification, and we will 

subsequently introduce some model flexibility.

• Although we have retained the β and γ notation, these are not the same parameters as those in 

equation [5]. Rescaling Sijk causes the interpretation of the parameters to change, so parameters 

are now interpreted as changes in standard deviation units. Although this is analytically 

convenient, readers may have trouble interpreting standard deviation units, but we will discuss 

how standard deviation units can be translated back into natural units to facilitate 

interpretation.

The dependent variable now has a mean of zero and a variance of one for every guideline cell, so 

treating the β as the same across the cells is equivalent to saying that a unit change in variable X

increases the sentence by β standard deviations, regardless of the cell. Likewise, treating the γ as the 

same across the cells is equivalent to saying that a unit change in variable Z increases the sentence by γ
29

Federal Sentencing Disparity, 2005–2012 

standard deviations, regardless of the cell. Using standardized scores greatly simplifies interpretation of 

the statistical analysis because a standard deviation change is the same, regardless of the cell.

Although using standardized scores simplifies the model, the simplification may be an incorrect 

specification leading to misleading conclusions. We take two steps to guard against misspecification. The 

first step is to introduce the year when the sentence was imposed as a W variable. This allows us to 

determine whether the severity of sentences is increasing or decreasing over time.24 We also introduce 

the year when the sentences imposed interacted with the variable black as another W variable. This 

allows the proportionality of sentences imposed on white and black offenders to vary systematically 

across time. (For additional flexibility, we use a linear spline with the date of the Gall decision as the join 

point.) The second step is to introduce the maximum of the guideline cell as a W variable. This allows 

the proportionality of sentences imposed on white and black offenders to vary systematically across the 

guideline cells. Think of the statistical model as estimating a smoothed version of the relationship 

between sentences for white and black offenders across the guideline cells and over time.

An attractive feature of building a statistical model capturing variation in sentences for white

and black offenders is that the results from the statistical model are readily expressed using figures.

The analysis will deal with special considerations. For relatively minor crimes committed by 

offenders with minor criminal records, there is a practical lower limit on the sentence imposed: Time

served may be zero for offenders sentenced to probation. For comparatively serious crimes committed 

by offenders with major criminal records, there is a practical upper limit on the sentence imposed, and 

some sentences may be very long (e.g., when a judge imposes consecutive sentences). Researchers have 

struggled with ways to deal with censored variables (as the above problem is known in the econometrics 

literature (Sullivan, McGloin, & Piquero, 2008; Britt, 2009; Ulmer, Light, & Kramer, 2011), but there is a 

 24 More accurately, given the model specification, we are able to determine whether sentence severity for white 

offenders is increasing or decreasing over time. The interaction of time with black offenders tells us how the 

sentences for black offenders relative to white offenders—the measure of racial disparity—has changed over time.
30

Federal Sentencing Disparity, 2005–2012 

special consideration for this study. Many of the solutions do not lend themselves to hierarchical 

modeling, at least not using conventional software. Examining sentences imposed under the guidelines, 

within most guideline cells, shows that most offenders receive jail or prison terms. We can include most 

guideline cells within the study by setting a rule: Include a cell when 85% or more of the offenders 

sentenced within the cell receive some prison time.25 Within each cell, sentences for offenders who 

received non-prison sentences are set to zero. (See the table at the beginning of appendix B.) Within 

each cell, sentences for offenders who received non-prison sentences are set to zero. Adopting this 

allows us to use a linear hierarchical model for the analysis.26

Limiting the analysis to certain cells does not bias the analysis because selection is based on an 

exogenous variable: guideline cell.27 However, we acknowledge that the findings pertain strictly to these 

included cells. We could have relaxed the inclusion rule, but dealing with probation terms requires 

special considerations. In the federal system, terms of probation typically come with onerous behavioral 

restrictions, including house arrest and electronic monitoring. When only a few sentences are to 

probation, we do not set the sentence to zero. However, if a larger number of probation sentences were 

included, we would have to deal with the terms of probation varying in severity.28

 25 This still leaves a lower limit problem, but a linear model will provide a consistent estimate of the average 

sentence when there is a lower limit. Standard errors are corrected using robust standard errors. The upper limits 

are a minor problem. A reviewer of an earlier draft disagreed with this statement, so some clarification is required. 

Using OLS when data are censored will lead to inconsistent estimates of the parameters in an underlying latent 

variable model, a problem discussed extensively in the econometrics literature. However, a correctly specified OLS 

model will be consistent for the conditional mean by definition. This distinction is discussed by Angrist and Pischke

(2009), among others. Our claims about consistency pertain to the conditional mean. 26 With exceptions, guidelines are not required for misdemeanors below class A misdemeanors. Consequently, the 

least serious federal crimes are not sentenced under the guidelines. U.S. Attorneys often employ declination 

standards that limit federal prosecution to serious crimes, and less serious crimes are referred to state courts. 

These two observations may explain why most federal offenders sentenced under the guidelines receive some 

prison time.

27 One might argue that the guideline cell is not exogenous. The argument is that prosecutors wait to determine 

the judge appointed to the case and then manipulate the facts surrounding the case in recognition of judge 

sentencing proclivities. If this happens, the effect does not appear to be large (Yang, 2013), so we treat the 

guideline cell as exogenous.

28 Some reviewers of an earlier version of this report encouraged us to extend the analysis to probation terms, 

suggesting that we estimate separate regressions with binary outcomes (e.g., logistic or probit models). We see 
31

Federal Sentencing Disparity, 2005–2012 

Expecting application of the guidelines to vary across certain offense and offender groups, we 

partition our data into 14 strata.29 Separate analyses are performed within each stratum. The strata are 

defined as follows:

• The USSC makes a useful distinction between upward departures (always attributable to the 

judge), downward departures that are attributable to the judge, and downward departures that 

are attributable to the government.

30 Downward departures attributable to the government are 

legitimate rewards for cooperating with the government to further criminal cases against 

others. It seems best to assume that departures attributable to the government fundamentally 

alter the application of the guidelines. As a result, the analysis described above (and illustrated

below) should be done separately for cases that have departures attributable to the 

government and for cases that do not have departures attributable to the government. We 

make that distinction for this study, so the explanation of sentence variation is found exclusively 

in judicial decision making.

• Federal criminal law always sets an upper limit on the sentence and, for some crimes, federal 

criminal law sets a lower limit greater than zero. Mandatory minimum sentences are especially 

likely for drug violations, and these mandatory minimums are often so severe that Congress has 

provided provisions allowing judges to ignore the mandatory minimums for a class of offenders

(see appendix A). Weapons enhancements, which often trigger mandatory minimum sentences, 

are incorporated into the guidelines. The rules for sentencing drug offenders, those who receive 

 

the required analysis as more difficult than suggested by the reviewers, and resource and time limitations 

precluded taking probation sentences into account.

29 One might argue that there should be more or fewer partitions. In its study of the use of mandatory minimum 

penalties across 13 districts, the USSC partitioned offenses into drug offenses, firearm offenses, and child 

pornography offenses (Commission, 2011, pp. 111-115)—essentially the same partitioning that we have used. The 

Commission also distinguished aggravated identity theft, but we did not make that partition because there are too 

few cases to treat these as a partition.

30 A departure is a sentence that is higher than the upper guidelines limit or lower than the lower guidelines limit.
32

Federal Sentencing Disparity, 2005–2012 

weapons enhancements, and other offenders are so different that we have created a second 

partition determined by four broad offense categories:

o drug violations that do not involve weapons enhancement

o nondrug violations that do not involve weapons enhancements

o drug violations that involve weapons enhancements

o nondrug violations that involve weapons enhancements.

In the federal system, sex offenses are mostly for child pornography, and most of the

convictions for sex offenses are of white offenders. As a result, analyzing disparity among sex 

offenses is of little interest. Nondrug violations account for all nondrug crimes, excluding sex 

offenses. However, when examining sentence variation across judges, where race is not a 

consideration, sex offenses make up their own class.

• Although being male or female is not a legitimate consideration according to guideline policy 

statements, sex has an important effect on sentence imposed. This justifies treating sex as a 

stratifying variable.

Females are rare participants in offenses that involve weapons enhancements. As a result, every 

partition involving females and weapons enhancements is treated as null. Also, females are rarely 

participants in sex violations. In summary, ignoring sex violations, we partition the data into 12 subsets: 

eight subsets for males and four subsets for females. We repeat the same analyses for each of the 12 

subsets. When estimating the skedastic function, we use all 14 cells because race is not a factor for the 

skedastic function.

The principal analysis eliminates noncitizens. The treatment of noncitizens differs from the 

treatment of citizens for at least four reasons. First, the guidelines factors—especially those required to 

construct the criminal history category—are likely to be imprecise for noncitizens. Second, noncitizens 

can be deported, so the stakes at issue are different for citizens and noncitizens. Third, race appears to 
33

Federal Sentencing Disparity, 2005–2012 

be inaccurately reported for noncitizens, who are (according to the data) predominately white 

Hispanics. Fourth, fast-track provision introduces a complication that requires special attention going 

beyond the analysis reported in this study (McClellan & Sands, 2006; Gorman, 2010; Cole, 2012).

Consequently, we drop noncitizens from the principal analysis, but given that noncitizens are a large 

proportion of federal offenders, we report a preliminary analysis of noncitizens in appendix C.

4.2 Data and variables

The USSC maintains a detailed database pertaining to the application of guidelines; this study 

uses an extract of variables from those data. The box below lists the specific variables from the USSC 

database that entered into our analysis. This list allows interested readers to track variables back to the 

USSC’s data.

The box puts variables into three categories. The first category includes stratification variables

that were used to identify the 14 strata and to determine if an offender was a U.S. citizen. The second 

category—the dependent variable—is the sentence. The third category identifies variables used to 

determine independent variables.

Stratification variables

FEMALE A variable coded by the USSC that equals 1 if the offender is female.

REAS* The first, second, etc. reason given by the court for why the sentence imposed was outside the range 

(there are 10 variables, for REAS1 to REAS10). The value indicating substantial assistance is “19” 

((5K 1.1) substantial assistance with government motion). These departures are explained in appendix 

A.

BookerCD An additional variable used to identify a handful of additional substantial assistance cases. The postBooker reporting categories (there are 12 categories) are based on the relationship between the 

sentence and guideline range and the reason(s) given for being outside of the range. The value 

indicating substantial assistance is “5.”

OFFTYPE2 The offense type variable used to determine drug offenders (values “10,” ”11,” and ”12”) and sex 

offenders (values “4,” ”28,” ”42,” ”43,” and “44”).

WEAPON Used to identify weapons offenders. It is a USSC-created variable, where 1 indicates the offender 

received a specific offense characteristics (SOC) weapons enhancement or had an 18:924(C) charge 

present.

NEWCIT Used to identify U.S. citizens. The value “0” indicates a U.S. citizen.
34

Federal Sentencing Disparity, 2005–2012 

Dependent variable

TOTPRISN The total number of months of imprisonment ordered. Sentences of less than 1 month are coded as 

zero. In its analysis, the USSC chose to include alternative sentences (i.e., home confinement, 

community confinement, and intermittent confinement), but these alternatives are not considered to 

be prison terms in our analysis. This variable is top-coded at 470 months, meaning that any sentence 

in excess of 470 months (including life terms and death sentences) are recoded to 

470 months.

Independent variables

XCRHISSR The offender’s final criminal history category (I–VI), as determined by the court. The guidelines 

translate the total criminal history points into the six categories defined by the criminal history 

category.

XFOLSOR The final offense level, as determined by the court. The combination of XCRHISSR and XFOLSOR 

indicates the guideline cell.

MONRACE The race of the offender: white, black, and other race. Race is independent of Hispanic ethnicity. Note 

that while our findings are focused on non-Hispanic whites and non-Hispanic blacks or African

Americans, the analysis uses data representing all races identified by the USSC. We removed any 

offender with an unreported race from the analysis.

HISPORIG An indication of Hispanic ethnicity. We designate an offender as Hispanic if this variable is coded “2” 

(i.e., we consider an offender of Hispanic ethnicity only if there is an indication of Hispanic origin).

XMAXSOR The maximum guidelines range for imprisonment, as determined by the court. When used in the 

analysis, XMAXSOR is recoded to a maximum of 470 (including life terms) and is rescaled by dividing 

by 470. The recoded variable runs from 0 to 1.

SENTYR The year the sentence was imposed. When used in this analysis, SENTYR is recoded from 2005-2012,

to 0- 1 by subtracting 2005 and dividing by 7.

We allow the time trend to break near the Gall v. United States decision. Since it was decided on 

December 10, 2007, we allowed the break for sentences filed beginning on January 1, 2008.

TOTCHPTS The offender’s total criminal history points. To capture the variation of criminal history with each 

criminal history level that may explain differences in sentencing, we use the criminal history points 

interacted with the offender’s criminal history level (XCRHISSR). In particular, for every offender, we 

standardize his or her criminal history points within the offender’s criminal history level. For example, 

if an offender has a criminal history level of III, his or her criminal history points are standardized with 

all other offenders that have a criminal history level of III. Then, we interact the standardized history 

points with the criminal history categories and insert this measure into the statistical models (as six 

variables, for each of the six criminal history categories).

NEWCNVTN Indicates that the adjudication decision was reached by a trial. This variable enters the model as a 

covariate.

MONCIRC Indicates the judicial circuit in which the offender was sentenced. We used fixed effects to indicate 

the judicial circuit, using the 9th judicial circuit as a reference category.

CIRCDIST Indicates the judicial district in which the offender was sentenced.

JUDGE A unique identifier assigned to a judge, used as a random effect in the statistical models.

For the analyses, we use USSC data for all offenders who were sentenced in fiscal years 2005 

through 2012. To distinguish those cases where government-initiated departures were not a factor from 

cases where government-initiated departures were a factor, we inspected the variables REAS1 through 
35

Federal Sentencing Disparity, 2005–2012 

REAS10. If any of these variables reported “(5K 1.1) substantial assistance with government motion,” 

then we assigned the case to the government-initiated departure category. The BookerCD variable 

identified a few additional government-sponsored downward departures.

We identified the guideline cells by interacting the variables XFOLSOR and XCRHISSR. We 

computed the percentage of cases within each cell that resulted in prison and we discarded all cells 

where that rate was lower than 85%. Others (Ulmer, Light, & Kramer, 2011) have considered disparity 

in the imposition of prison terms, and we do not investigate that question.

The dependent variable is a transformation of TOTPRISN. The transformation was described 

earlier using the formula:

k

ijk k

ijk SC

S M

s − =

Substitute TOTPRISN for Sijk .
36

Federal Sentencing Disparity, 2005–2012 

5.0 Analysis and interpretation

Results are presented in two sections. The first section on sentencing disparity is divided into 

four subsections that pertain to the research questions raised in the introduction. Regression results are 

reported in appendices B and D; appendix C reports analyses for noncitizens. The second section 

pertains to prosecutorial discretion; this section tests whether the exercise of prosecutorial discretion 

has changed during the study period. Additional analyses regarding prosecutorial discretion appear in 

appendix D.

Statistical output is voluminous; therefore, to assist the reader, we have taken the following 

steps in this section. First, we interpret the statistical results in detail for the analysis of one partition of 

the data. Interested readers can apply that interpretation to the tables appearing in appendices B and C.

Second, we provide summary statements that appear in bold. These summary statements take 

advantage of the standardization of the dependent variable, which allows parameters to be averaged 

across strata. When we average, we take a simple average across the strata. Third, we report sensitivity 

testing in exhibits 1 to 3.

5.1 Operational variables entering the analysis

Estimation uses a multilevel mixed-effects linear model programmed as procedure mixed in 

version 13 of Stata. (This is xtmixed in earlier versions of Stata.) This section explains the modeling, 

interpretation, and presentation of results. (See appendix B for detailed findings and appendix C for 

results of analysis of noncitizens.)

As described previously, the dependent variable is the rescaled total months of prison imposed.

The fixed effects are:
37

Federal Sentencing Disparity, 2005–2012 

Race/Ethnicity: Black This is a dummy variable that is coded one when the offender is black and coded 

zero otherwise. White offenders are the omitted category. Hispanic and other 

enter into the analysis, but we will not discuss these racial or ethnic categories 

separately because modeling for them is identical to modeling for blacks.

year_pregall Calendar time is modeled with a linear spline. This variable models calendar 

time up to the Gall decision. Calendar time has been recoded to run from 0 at 

the beginning of the observation period to 1 at the end of the observation 

period.

year_postgall This variable models calendar time after the Gall decision.

Black x Year Pre-2008 This is the year_pregall variable interacted with the Race/Ethnicity: Black 

variable.

Black x Year Post-2008 This is the year_postgall variable interacted with the Race/Ethnicity: Black 

variable.

Note that the parameters associated with the last two variables allow us to estimate how the 

sentencing disparity for white and black offenders has changed over time. Interpreting these parameter 

estimates is the principal concern of this study.

Max Sentence in Guideline Cell This is the maximum sentence specified for the guideline cell. It has 

been top coded at 470 months and rescaled to run from 0 to 1.

Black x Max Sentence This is Max Sentence in the guideline cell interacted with the 

Race/Ethnicity: Black variable.

The introduction of these two variables relaxes the restrictive model specification by allowing 

the degree of racial disparity to vary across the guideline cells. Possible disparity is pronounced within

guideline cells that call for relatively short sentences but is insignificant for guideline cells that call for 

comparatively long sentences. The use of the above two variables expands the model’s flexibility, and 

the parameters associated with the last variable estimate how disparity varies across the guideline cells.

newcnvtn This is a dummy variable indicating that the offender was convicted by trial.

c_pts_n There are six of these criminal history point variables distinguished by allowing n to run 

from 1 to 6.

The c_pts_n variable requires comment: Guideline calculations assign criminal history points 

based on the offender’s criminal record and then collapse the criminal history points into six criminal 

history levels that form one dimension of the guideline grid. Because of the collapsing, actual criminal 
38

Federal Sentencing Disparity, 2005–2012 

histories are heterogeneous within guideline cells, and the c_pts_n variables take that heterogeneity 

into account. For example, c_pts_1 is the standardized criminal history points for offenders whose 

criminal history is classified in the first criminal history category. If the typically subtle distinctions in 

criminal history category matter at the time of sentencing, the parameters associated with the c_pts_n 

variables should be positive. Except as control variables, these parameters are of no interest to this 

study.

circ_n There are 11 dummy variables, distinguished by allowing n to run from 1 to 11, that denote the 

circuit. The ninth circuit is the omitted reference category.

Additionally, a sequence number distinguishing judge identity (JUDGE) enters the model as a 

random effect. For every judge, there is a judge random effect for white and black offenders.

5.2 Findings regarding sentencing disparity

Table 1 reports selected regression results31 for the regression using the data partition males, no

drug violations or weapons enhancements, and no government-sponsored departures for substantial 

assistance.32 This partition includes 76,405 offenders who were sentenced by 1,292 judges. An average 

judge sentenced 60 offenders from this partition, but some sentenced only a single offender and at least 

1 judge sentenced 460 offenders. All of the shaded results are statistically significant at p < 0.01.

Table 1 – Regression results: Males, no substantial assistance, no weapons or drugs

Variables Parameter Standard error 95% confidence interval

year_pregall -0.246 0.083 -0.409 -0.083

year_postgall -0.207 0.038 -0.281 -0.133

Trend from 2005 to 2012 -0.222 0.029 -0.278 -0.166

Race/Ethnicity: Black -0.031 0.033 -0.096 0.034

Black x Year Pre-2008 0.446 0.116 0.218 0.673

Black x Year Post-2008 -0.033 0.047 -0.126 0.060

Trend from 2005 to 2012 0.146 0.036 0.075 0.218

 31 The data include Hispanic and other offenders, but they are not of principal interest for this report; therefore, 

results pertaining to Hispanic and others are suppressed. Similarly, we suppress the random effects for these two 

racial and ethnic groups. We also suppress the fixed circuit effects. Complete results appear in appendix B.

32 We only show the parameter estimates that are of interest for estimating racial disparity. The appendix shows 

complete regression results.
39

Federal Sentencing Disparity, 2005–2012 

Variables Parameter Standard error 95% confidence interval

Max sentence in guideline cell -0.054 0.050 -0.152 0.044

Black x Max Sentence -0.213 0.062 -0.334 -0.093

Random effects parameters

Variance (white) 0.075 0.006 0.063 0.087

Variance (black) 0.077 0.007 0.063 0.091

Covariance (white, black) 0.062 0.005 0.052 0.072

Correlation (white, black) 0.808

Var (residual) 0.889 0.020

Observations 76,405

Judges 1,292

The first column in table 1 identifies selected variables that entered the regression. The table 

identifies the parameter in the first column and reports the parameter estimate in the second column, a 

heteroscedastic robust standard error in the third column, and a 95% confidence interval in the last two 

columns. When the confidence interval does not overlap 0, the parameter is deemed statistically 

significant at p < 0.05. The shading denotes parameters that are statistically significant at p < 0.01.

The first two parameter estimates are associated with the variables “year_pregall” and 

“year_postgall.” Collectively, these provide a spline telling us how sentences have changed for white 

offenders between 2005 and 2012. These two parameters tell us roughly that the sentences imposed on 

white offenders have decreased by -(3/8)x0.246-(5/8)x0.207=-0.222 standardized units between 2005 

and 2012. This change is statistically significant at p < 0.01. For white males convicted of crimes other 

than drug violations and weapons offenses, and who did not provide substantial assistance to the 

government, sentences became more lenient between 2005 and 2012.
40

Federal Sentencing Disparity, 2005–2012 

Moreover, based on the results 

reported in appendix B, examining the 

estimated changes over the 8-year period, 

it appears that white males and females

received sentences that decreased in 

severity. When we include sex offenders 

in the analysis, there is an estimated 

reduction in 13 of 14 strata. The change is 

statistically significant at p < 0.01 in six tests and at p < 0.05 in another three tests. Given that the 

dependent variable is measured in standardized units, the changes appear large: The simple average 

change over the 14 strata is -0.22 standardized units, which is significant at p < 0.001. Apparently,

judges have exercised discretion during the post-Booker era to reduce the average length of time that 

offenders serve in prison. Although overall trends in sentences are not the main concern of this report, 

we note that the study is being conducted within an overall context of increasing leniency in federal 

sentencing. Sensitivity testing reported in exhibit 1 indicates that findings are insensitive to model 

specification.

Our interest is principally focused on the parameters associated with Black x Year Pre-2008 and 

Black x Year Post-2008 because these parameters estimate how disparity (the difference between the 

average sentence for blacks and whites) has changed over time. From Booker to Gall, the disparity 

increased (p < 0.01), but it does not appear to have changed any more since Gall. To consider the entire 

period post-Booker, see the parameter associated with Trend from 2005 to 2012. Over the entire postBooker period, the sentences imposed on black offenders have increased by 0.146 standardized units, 

an amount that is statistically significant at p < 0.01. Interestingly, we previously reported that the 

sentences imposed on white offenders decreased by 0.222 standardized units, and now we report that 

Exhibit 1. There has been a trend toward more lenient 

sentences

In the preferred model, sentence severity for white 

offenders decreased by an average of 0.222 standardized 

units between 2005 and 2012 (p < 0.01). When the model 

substitutes district fixed effects for circuit fixed effects, the 

estimated decrease in overall sentence severity is 0.194 

standardized units (p < 0.01). When fixed effects are 

omitted from the model, the decrease is 0.226 (p < 0.01).

Returning to the preferred model and including age and 

education as covariates, we find that sentence severity fell

by 0.215 standardized units (p < 0.01). The decrease in 

sentence severity for white offenders appears robust to 

model specification.
41

Federal Sentencing Disparity, 2005–2012 

racial disparity in sentencing has increased by 0.146 standardized units, implying that blacks did not 

receive harsher sentences between 2005 and 2012; rather, blacks have not benefited as much from the 

increased leniency afforded to whites, and this has widened disparity.

Excluding sex offenses (because there are few black sex offenders) in all eight strata where we 

contrasted the sentences for black males and white males, the trends in sentences for black males

were increasingly longer than the sentences for white males. The contrast was statistically significant 

at p < 0.01 in four of the eight contrasts, and it was significant at p < 0.05 in a fifth. The simple average 

across the eight contrasts showed that at 

the end of 2012, blacks received sentences 

that were 0.173 standardized units higher 

than their white counterparts, a difference 

that was statistically significant at p < 0.01.

Evidence reported in exhibit 2 indicates that 

these findings are robust to model 

specification. We do not find that black 

females are disadvantaged compared with white females.

According to the Black x Max Sentence parameter, the disadvantage suffered by blacks 

decreases as the maximum sentence for a guideline cell increases. This does not mean that blacks are 

disadvantaged for minor crimes and advantaged for serious crimes; rather, the statistics imply that the 

disadvantage between blacks and whites narrows as crimes become more serious.

Table 1 also reports random effects holding the judicial circuit constant.

33 Statistical modeling 

 33 Differences across circuits are large. Averaging across the 14 partitions (including sex offenses), the second 

circuit sentence is an average of 0.46 standard deviation units below the national average and the fifth circuit 

sentences are an average of 0.31 standard deviation units above the national average. That disparity is much larger 

than the racial disparity reported in this study.

Exhibit 2. Sentencing disparity has increased for black 

males

Using the preferred model with circuit fixed effects, 

sentencing disparity has increased by an average of 0.173 

standardized units (p < 0.01). Exchanging districts for 

circuits, we estimate that sentencing disparity has 

increased by an average of 0.161 standardized units (p <

0.01). Dropping both circuits and districts from the model 

specification, sentencing disparity increased by an 

estimated 0.190 standardized units (p < 0.01). Using the 

preferred model, but including age and education in the 

model specification, the increase is 0.168 standardized 

units (p < 0.01). Findings regarding trends in disparity are 

robust to model specification.
42

Federal Sentencing Disparity, 2005–2012 

assumes that judges differ regarding the sentences imposed on white offenders, the sizes of those 

differences are randomly distributed across judges, and that distribution is normal. The variance for that 

distribution is 0.075, which appears to be large in terms of standardized sentences. The confidence 

interval is tight about this estimate. Likewise, judges differ regarding sentences imposed on blacks. The 

variance for that distribution is 0.077, and again, that variance seems large in terms of standardized 

sentences. Observe that the correlation between the random effect across judges for whites and the 

random effect across judges for blacks is very high: 0.808.

Looking across the 14 strata and converting from variances to standard deviations, on average 

the standard deviation for the random judge effect is 0.36 for whites and 0.40 for blacks (see exhibit 

3). This is evidence of high disparity in general: Judges who impose above average prison terms on black 

offenders tend to impose above average prison terms on white offenders, and judges who impose 

below average prison terms on white offenders tend to impose below average prison terms on black 

offenders. In this regard, sentences are disparate in the sense that similarly situated offenders who have 

committed similar crimes receive sentences that differ depending on the judge who imposes the 

sentence.34 In standard deviation units, the random effects are 15% to 20% larger for females than for 

males, implying that judges disagree more about the sentences to impose on females than the 

 34 Generalizing this statement is difficult because we could only estimate covariances for four of the regressions. 

This is a practical limitation of working with random effect models. The correlation was close to 0.85 in three 

regressions and closer to 0.6 in one regression.
43

Federal Sentencing Disparity, 2005–2012 

sentences to be imposed on males.

Although the analysis reported in 

table 1 pertains to a regression using the 

standardized scores for sentences, estimates

based on these results are readily translated 

back into the original metric of months 

sentenced by reversing the transformation 

represented by equation [7]. We have 

applied this reverse transformation when 

producing the figures reported below.

5.2.1 Converting findings on disparity 

from standardized units to original units

Statistical testing shows that the table 1 parameters associated with time interacted with blacks 

(Black x Year Pre-2008 and Black x Year Post-2008) imply positive, statistically significant trends.

Apparently, blacks have been increasingly disadvantaged over time. The parameters are difficult to 

interpret, but they can be translated into natural units (months) and their implications can be graphed.

Graphing also allows us to extend findings to other partitions of the data.

Figure 2 represents trends in racial disparity for the first four partitions of data: Males convicted 

of crimes that do not involve weapons violations, both with and without substantial assistance to the 

government. The horizontal axis in each panel is the year that the sentence was imposed. When we 

translate backwards from standardized units to original units, we have to make the translation for 

specific guideline cells. (The translation first multiplies by the standard deviation of sentences within a 

cell and then adds the mean for that cell.) The translation is reported for maximum guideline sentences 

at the break for the first quartile of cells used in the analysis, for the mean, and at the break for the third 

quartile. For example, in the first panel (males, no drugs or weapons, and no substantial assistance), a 

Exhibit 3. Judges disagree about sentences

According to the preferred model, when sentencing 

whites, the distribution of judge random effects has a 

standard deviation of 0.36 on average across 12 data 

partitions. When sentencing blacks, the standard 

deviation is 0.40. (There is no change when age and 

education are added to the model.) As expected, when 

district is substituted for circuit, the standard deviations 

for the random effects fall to 0.23 for whites and 0.30 for 

blacks because the districts account for more residual

variance than do the circuits. Likewise, when neither 

district nor circuit enters the model, the standard 

deviations for judge random effects increase to 0.44 for 

whites and 0.50 for blacks. These patterns are expected 

because circuit fixed effects account for some of the 

residual variance otherwise attributed to judges and 

district fixed effects account for even more of the residual.
44

Federal Sentencing Disparity, 2005–2012 

quarter of offenders were sentenced under guidelines calling for maximum sentences of 33 months or 

less, half were sentenced under guidelines calling for maximum sentences of 46 months or less, and a 

quarter were sentenced under guidelines calling for maximum sentences of 87 months or more. The 

quartile breaks differ across the data partitions.
45

Federal Sentencing Disparity, 2005–2012 

Figure 2 – Increases in racial disparity over time for four partitions: Males convicted for non-weapons violations (overall significance p < 0.01)

Changes over time: Males

No drugs, no substantial assistance No drugs, substantial assistance

Drugs, no substantial assistance Drugs, substantial assistance

-1

0

1

2

3

Difference in months

2005 2006 2007 2008 2009 2010 2011 2012

Year

33 Months 46 Months 87 Months

-2

-1

0

1

2

3

Difference in months

2005 2006 2007 2008 2009 2010 2011 2012

Year

37 Months 57 Months 96 Months

0

2

4

6

8

10

2005 2006 2007 2008 2009 2010 2011 2012

Difference in months

Year

57 Months 87 Months 151 Months

0

1

2

3

4

5

6

2005 2006 2007 2008 2009 2010 2011 2012

Difference in months

Year

71 Months 108 Months 188 Months
46

Federal Sentencing Disparity, 2005–2012

The first two panels appear to show a sharp break at the Gall decision. (We reference panels from left to 

right and then from top to bottom.) We are not inclined to take the break seriously, as it could result 

from our decision to place the knot for the spline at the time of Gall. A different placement might show 

a different pattern, but our principal concern is with the level of disparity at the end of 2012, and the 

estimates at the end of the period should be relatively insensitive to the placement of the knot. All four 

panels agree that disparity increased from 2005 to 2012, although the change is not statistically 

significant in the fourth panel. If we consider all panels jointly, giving each an equal weight in the 

calculations, we find they are jointly significant at p < 0.01.

The next set of four partitions (figure 3) pertains to males convicted of crimes that involve 

weapons enhancements. Some of these crimes are drug-related and others are not. Again, we 

distinguish between cases where the offender was rewarded for substantial assistance to the 

government and cases where there was no reward for substantial assistance.
47

Federal Sentencing Disparity, 2005–2012

Figure 3 – Increases in racial disparity over time for four partitions: Males convicted of crimes involving weapons violations (overall significance p <

0.05)

Changes over time: Weapons

No drugs, no substantial assistance No drugs, substantial assistance

Drugs, no substantial assistance Drugs, substantial assistance

0

5

10

15

20

25

30

2005 2006 2007 2008 2009 2010 2011 2012

Difference in months

Year

51 Months 87 Months 151 Months

-10

-5

0

5

10

15

2005 2006 2007 2008 2009 2010 2011 2012

Difference in months

Year

57 Months 96 Months 175 Months

-2

0

2

4

6

8

2005 2006 2007 2008 2009 2010 2011 2012

Difference in months

Year

87 Months 151 Months 235 Months

0

1

2

3

4

5

2005 2006 2007 2008 2009 2010 2011 2012

Difference in months

Year

108 Months 168 Months 262 Months
48

Federal Sentencing Disparity, 2005–2012

The figure shows patterns of increasing racial disparity for offenses that involve weapons enhancement.

The increases are not statistically significant when offenders receive reductions for substantial 

assistance to the government, but the increases are always positive. If we consider the four trends 

jointly, they are statistically significant at p < 0.05.

Results for females are different. There are too few cases involving females with weapons 

violations to allow testing. Considering the four offenses without weapons enhancements, one partition 

shows a statistically significant (p < 0.05) trend while the other three do not, and the joint effect is not 

statistically significant. We do not graph the results. Increasing racial disparity in sentencing appears to 

be limited to males.

Although other factors may have been changing during this same 8-year period, a subsection on 

“evidence of prosecutorial discretion” (see section 5.3) does not find trends in prosecutorial behavior, 

causing us to discount prosecutorial behavior as the cause of increasing disparity. Other explanations 

are plausible, but it seems reasonable to conclude these trends could be attributed to judicially induced 

disparity in the treatment of black offenders, compared to white offenders.

Some reviewers of an earlier draft were concerned that findings might be sensitive to the choice 

of a linear spline and suggested replacing the linear spline with an alternative approach. The data 

definitely suggest that the trend is nonlinear, so using a simple linear trend would be a misspecification.

(One of the reviewers performed a reanalysis using the methodology of Ulmer, Light, & Kramer (2011), 

reporting that the trend was positive post-Booker and then appears to have reached a plateau, 

consistent with the spline.) We tried using a polynomial but—as often happens with polynomials—the 

end points seem uninformative and perhaps misleading about the trend as it nears 2012. A 

nonparametric alternative is to substitute dummy variables for every post-Booker year. Figures 4 and 5 

are the exact counterparts to figures 2 and 3, with dummy year variables substituted for the spline.
49

Federal Sentencing Disparity, 2005–2012

Figure 4 – Increases in racial disparity over time for four partitions: Alternative specification to figure 2

Changes over time: Males

No drugs, no substantial assistance No drugs, substantial assistance

Drugs, no substantial assistance Drugs, substantial assistance

-1

-0.5

0

0.5

1

1.5

2

2.5

2005 2006 2007 2008 2009 2010 2011 2012

Difference in Months

Year

33 Months 46 Months 87 Months

-2

-1

0

1

2

3

4

5

2005 2006 2007 2008 2009 2010 2011 2012

Difference in Months

Year

37 Months 57 Months 96 Months

0

2

4

6

8

10

2005 2006 2007 2008 2009 2010 2011 2012

Difference in Months

Year

57 Months 87 Months 151 Months

0

2

4

6

8

2005 2006 2007 2008 2009 2010 2011 2012

Difference in Months

Year

71 Months 108 Months 188 Months
50

Federal Sentencing Disparity, 2005–2012

Figure 5 – Increases in racial disparity over time for four partitions: Alternative specification to figure 3

Changes over time: Males

No drugs, no substantial assistance No drugs, substantial assistance

Drugs, no substantial assistance Drugs, substantial assistance

-10

0

10

20

30

40

2005 2006 2007 2008 2009 2010 2011 2012

Difference in Months

Year

51 Months 87 Months 151 Months

-20

-10

0

10

20

30

2005 2006 2007 2008 2009 2010 2011 2012

Difference in Months

Year

57 Months 96 Months 175 Months

-5

0

5

10

15

20

2005 2006 2007 2008 2009 2010 2011 2012

Difference in Months

Year

87 Months 151 Months 235 Months

-2

0

2

4

6

8

10

2005 2006 2007 2008 2009 2010 2011 2012

Difference in Months

Year

108 Months 168 Months 262 Months
51

Federal Sentencing Disparity, 2005–2012 

Readers can bring their own interpretations to figures 4 and 5. There is considerable random fluctuation 

from year to year, which is why we employed a smoothing technique—linear splines—to provide a 

summary. (We discourage readers from making much of year-to-year changes.) Some of the figures 

suggest why using polynomials can be misleading: There are apparently random spikes in the latter 

years. Our interpretation is that the general trend toward increasing racial disparity seems to reach a 

rough plateau sometime after the Gall decision. The linear splines appear to be reasonably consistent 

with this interpretation.

5.2.2 Racial disparity across guideline cells

Allowing the sentences to vary across the guideline cells is of some importance for model 

specification (significant in 5 of 14 partitions), but this finding is not of substantive interest.35 Racial 

disparity is statistically significant at p < 0.01 in 3 of 12 comparisons. We do not consider this to be an 

important finding. The signs of coefficients associated with the race effect vary, and the coefficients are 

statistically significant in only 3 of 12 comparisons. The results are sensitive to model specification.

Evidence is that standardizing the sentences has been useful for model specification.

5.2.3 Racial disparity across judges

Table 1 also reports random-effects parameters. We have already discussed those findings by 

presenting variance estimates in standardized units, and this subsection provides a visual impression 

after converting back to original units. Random effects may be difficult to interpret, so some intuition 

may be useful. The fixed effects (i.e., all of the parameters except the random effects) provide an 

estimate of the average sentence imposed on white and black offenders, conditional on the facts 

surrounding the case. Given that average, we can estimate the amount by which an individual judge 

differs from the average when sentencing black offenders and when sentencing white offenders. These 

estimated differences are the random effects. Subtracting the random effect for a judge when 

 35 By construction, the mean sentence is zero across the guideline cells. Given the regression specification, the 

statement pertains to the variation in average sentences for whites across the guideline cells.
52

Federal Sentencing Disparity, 2005–2012 

sentencing a white offender from the random effect for a judge when sentencing a black offender 

translates the random effects into a difference score—how much a judge sentences blacks more 

severely than whites.

The statistical model assumes that the random effects are distributed as bivariate normal. This is 

probably not exactly true, but we assume it is sufficiently approximate that we can graph the implied 

difference scores. By construction, the difference scores are themselves distributed as normal, 

explaining why the graph in figure 6 has the familiar shape of a normal distribution.

This discussion is focused on three parameters: the variance in judge effects for whites( ) 2 σ w , 

the variance in judge effects for blacks( ) 2 σ b , and the correlation in the judge effects for whites and 

blacks( ) σ wb . The variance for the distribution of differences in effects for whites and blacks is

( ) σ w σ b σ wb 2 2 2 + − . Because the analysis was done using standardized sentences, the disagreement 

across judges in sentences for blacks is large,36 but then so too is the disagreement across judges in 

sentences for whites. Furthermore, when we were able to compute the correlation in the effects for 

blacks and whites, that correlation is high. The story is that some judges typically apply relatively harsh 

sentences to both blacks and whites, while other judges typically apply relatively lenient sentences to 

both blacks and whites. This is disparity but it is not necessarily racial disparity.

When we performed the analysis with all of the data (as reported previously), we discovered 

that the covariance estimate was unstable. We could improve the estimates by limiting the data to 

judges who sentenced at least five offenders. The results we present below pertain to the random 

effects after imposing that data limitation. Even with this data restriction, we could not always estimate 

a covariance reliably. We only present figures when a covariance estimate was available. Figure 6

 36 The analysis reported in table 1 was based on transformed sentences, where the distribution of sentences within 

a guideline cell had a mean of zero and a standard deviation of one. The judge random effects are scaled according 

to these unitary standardized deviations, suggesting that the random effects are large.
53

Federal Sentencing Disparity, 2005–2012 

represents the variance for males convicted of non-weapons violations. Figure 7 is similar but pertains 

to females.

Figures 6 and 7 aid in interpreting regression results. For reasons already discussed, we draw 

the distribution of the difference scores for three levels of guideline cells. These levels are at the 25th, 

median, and 75th percentiles of the maximum sentence lengths of the guideline cells. For each judge, we 

compute the difference in predicted sentences for blacks and whites for the three sentence lengths.

The two figures depict the extent of disagreement across judges regarding the sentencing of white and 

black offenders. The horizontal axis reports the difference in months of the predicted difference in 

sentence lengths for black and white offenders for each judge. The vertical axis reports the density of 

the distribution. The estimates are highly inferential and intended to approximate and illustrate the

extent to which federal judges disagree about sentences by race.

By construction, the judge random effects are centered on zero. The differences in random 

effects will also be centered on zero. However, for purposes of data visualization, we have centered 

them on the mean differences in sentence for black and white offenders.

Thus, for males, we observe that the centers of the distributions are all above zero. Blacks receive longer 

sentences than whites for the average judge; for females, the distributions are centered near zero 

because female white and black offenders receive similar terms. The distributions are approximations,

but if we took them literally, we would conclude that judges tend to sentence blacks more severely than 

they sentence whites. For some judges, the sentencing disparity seems especially large, while for others 

it seems substantively insignificant. For a few judges, blacks appeared to be advantaged compared to 

whites, and while this may be true, the advantage typically appears to be small, and it may occur 

because we have used the bivariate normal as a useful approximation of reality.
54

Federal Sentencing Disparity, 2005–2012 

Figure 6 – Variation in racial sentencing disparity across judges for males convicted of non-weapons violations

Differences in judge distributions: Males

No drugs, no substantial assistance No drugs, substantial assistance

Drugs, no substantial assistance Drugs, substantial assistance
55

Federal Sentencing Disparity, 2005–2012 

Figure 7 – Variation in racial sentencing disparity across judges for females convicted of nonweapons violations

Differences in judge distributions: Females

No drugs, no substantial assistance No drugs, substantial assistance

Drugs, no substantial assistance Drugs, substantial assistance
56

Federal Sentencing Disparity, 2005–2012 

If judges sentenced blacks and whites to equivalent terms, conditional on the facts surrounding 

the case, the distributions of the difference in sentences for blacks and whites would collapse to zero.

This does not happen. (Table 1 provides a test of the null hypothesis that these distributions have a 

variance of zero, meaning that they collapse to zero. The test rejects the null, although we recognize 

that the estimated variance has a large confidence interval, so there is some uncertainty about the 

spread of these distributions.) It seems likely that black and white offenders differ systematically in ways 

that cause judges to sentence them differently and, if we could observe those differences, the 

sentencing differences might be appropriate under the rule of law. However, that does not explain why 

some judges sentence blacks especially severely compared to whites. Unobserved, systematic 

differences between whites and blacks cannot account for the fact that the average difference in 

sentences for black and white offenders varies across judges. 

5.2.4 Increases in disparity: Variance about the guidelines

We re-estimated the regression discussed previously without the judge random effects. From 

the regression, we estimated the squared residual, equal to 2

ijk e in the notation used earlier.37 Then we 

regressed the squared residual on the linear splines representing post-Booker trends and onto the 

maximum sentence specified by the guidelines. Table 2 shows the results of repeating this exercise for

the 12 partitions of the data.

 37 Our intent is to examine changes in the variance of the regression.
57

Federal Sentencing Disparity, 2005–2012 

Table 2 – An estimated skedastic function based on residuals

Males, no weapons, no sex offenders

No drug, no SA No drug, SA Drug, no SA Drug, SA

Estimate Std err p-value Estimate Std err p-value Estimate Std err p-value Estimate Std err p-value

Skedastic function

year_pregall 0.358 0.187 0.055 0.330 0.177 0.063 0.182 0.156 0.242 0.401 0.143 0.005

year_postgall 0.300 0.076 0.000 0.134 0.070 0.054 0.400 0.063 0.000 0.113 0.060 0.059

Observations 76405 10829 62650 25380

Increase 2005–2012 0.322 0.059 <0.001 0.208 0.056 <0.001 0.318 0.049 <0.001 0.221 0.045 <0.001

Females, no weapons, no sex offenders

No drug, no SA No drug, SA Drug, no SA Drug, SA

Estimate Std err p-value Estimate Std err p-value Estimate Std err p-value Estimate Std err p-value

Skedastic function

year_pregall 0.512 0.450 0.256 0.348 0.262 0.184 -0.040 0.231 0.863 0.263 0.149 0.079

year_postgall 0.293 0.169 0.083 0.157 0.100 0.118 0.359 0.090 0.000 0.060 0.061 0.326

Observations 9001 1818 9501 5737

Increase 2005–2012 0.375 0.142 0.008 0.228 0.082 0.005 0.209 0.071 0.003 0.136 0.047 0.004

Weapons offenders

No drug, no SA No drug, SA Drug, no SA Drug, SA

Estimate Std err p-value Estimate Std err p-value Estimate Std err p-value Estimate Std err p-value

Skedastic function

year_pregall -0.282 0.256 0.271 -0.526 0.349 0.132 -0.522 0.219 0.017 -0.070 0.178 0.694

year_postgall 0.161 0.102 0.114 0.205 0.141 0.145 0.053 0.094 0.571 0.091 0.076 0.231

Observations 15035 3462 14500 6771

Increase 2005–2012 -0.005 0.082 0.952 -0.069 0.112 0.539 -0.162 0.070 0.021 0.031 0.058 0.597
58

Federal Sentencing Disparity, 2005–2012 

As noted previously, we can estimate how dispersion has increased about the average as of 

2012 by weighting and summing year_pregall and year_postgall parameters. Standard error calculations 

are provided in the table. Except for the weapons violations, the trends are toward higher dispersion 

and all trends are statistically significant at p < 0.05 or better. Post-Booker, we previously saw that 

sentencing has become more lenient. We now see that it has become more disparate. Excluding 

weapons violations, similarly situated offenders convicted of similar crimes are increasingly sentenced

differently. As a robustness check, we find that the qualitative patterns (and tests of statistical 

significance) do not change when district fixed effects are included in the model.

5.3 Evidence of prosecutorial discretion

Because prosecutors exercise wide discretion to charge and bargain with offenders, 

prosecutorial discretion may be exercised to disadvantage blacks. That possibility is difficult to discount 

using FJSP data because FJSP data do not provide a rich description of offenses and offenders at the 

time prosecution is initiated. The full story may not emerge before a federal probation officer writes a 

presentence investigation report based on a narrative of the crime provided by a law enforcement 

source, a criminal record check, and interviews with the offender and his or her associates.

Furthermore, the current version of FJSP data provides limited means to link data from the Executive 

Office of U.S. Attorneys with sentenced offenders, so any study using Executive Office data necessarily 

works with a selected dataset.

Even if U.S. Attorneys treat blacks differently than whites, it is nevertheless difficult to discount 

the findings reported in the previous section. If federal prosecutors discriminate against blacks, and if 

judges could somehow recognize that differential treatment,38 we might expect federal judges to 

 38 The federal probation officer prepares a presentence investigation report for the judge. The report includes a 

description of the crime according to case files, the offender’s criminal history according to a records check, and 

interviews with the offender and his or her associates. In theory, then, the judge could form an opinion about the 

case that is independent of the rendition communicated by the prosecution and defense. However, others have 

reported that judges are typically deferential (Commission, 2011; Commission, 2012).
59

Federal Sentencing Disparity, 2005–2012 

partially rectify the injustice by being more lenient with black offenders than with white offenders,

conditional on the guideline cell. That relative leniency is the opposite of what we find. Rather, if federal 

prosecutors discriminate against blacks, federal judges appear to reinforce discrimination by disparate 

sentences. It is possible that federal prosecutors discriminate in favor of black offenders and we are 

simply estimating corrective action by federal judges (although we cannot prove otherwise, this 

explanation seems unlikely and we do not pursue it).

Figure 2 shows trends toward increasing disparity. If prosecutorial behavior explained those 

trends, we would expect to see coincident trends in prosecutorial behavior. Evidence reported in the 

following subsections suggests otherwise.

5.3.1 Facts surrounding the case

Table 3 shows summary statistics reflecting changes in prosecutorial behavior. It is possible that 

prosecutors have increasingly manipulated offenders’ criminal history scores. If so, we should be able to 

observe changes over time, and we are especially interested in determining whether blacks are 

increasingly advantaged or disadvantaged, as this may explain what we are observing about trends in 

sentencing disparity. Table 3 shows seven indicators of prosecutorial behavior. We are interested in 

whether those indicators change materially over time.

Table 3 – Trends in prosecutorial behavior

Year 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

Criminal history (mean by race and year)

Black 3.00 3.08 3.15 3.20 3.22 3.21 3.22 3.21 3.13 3.11

White 2.19 2.29 2.26 2.24 2.28 2.26 2.28 2.27 2.22 2.23

Offense level (mean by race and year)

Black 20.57 20.46 21.21 21.30 21.43 21.44 21.37 21.18 20.93 21.30

White 17.79 17.86 18.61 18.81 18.92 18.93 19.08 19.32 19.67 20.16

Acceptance of responsibility (average level reduction by race and year)

Black -2.40 -2.39 -2.41 -2.44 -2.48 -2.49 -2.49 -2.49 -2.52 -2.54

White -2.42 -2.42 -2.44 -2.47 -2.49 -2.51 -2.53 -2.54 -2.55 -2.60

Substantial assistance (proportion by race and year)

Black 0.19 0.19 0.19 0.19 0.19 0.19 0.19 0.18 0.19 0.19

White 0.21 0.2 0.2 0.2 0.19 0.18 0.18 0.18 0.18 0.18
60

Federal Sentencing Disparity, 2005–2012 

Year 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

Government-sponsored reductions (proportion by race and year)

Black - - 0.02 0.02 0.02 0.03 0.03 0.05 0.05 0.06

White - - 0.03 0.03 0.04 0.04 0.04 0.05 0.06 0.07

Conviction by trial (proportion by race and year)

Black 0.07 0.07 0.08 0.07 0.07 0.06 0.06 0.07 0.06 0.06

White 0.05 0.04 0.06 0.05 0.05 0.04 0.04 0.04 0.04 0.04

Imposition of a mandatory minimum (proportion by race and year)

Black 0.257 0.277 0.299 0.299 0.294 0.282 0.263 0.263

White 0.157 0.153 0.143 0.145 0.149 0.149 0.150 0.157

Evidence shows that blacks have higher criminal history scores than do whites, but we do not 

observe a strong difference in the trends for whites and blacks (table 3). Blacks tend to have higher 

offense level scores. We see some narrowing in the difference in the scores for whites and blacks, but 

overall we do not see large trends in the offense severity score and certainly no trends that 

disadvantage blacks.

The original commission considered acceptance-of-responsibility adjustments as a substitute for 

plea bargaining. As table 3 shows, blacks receive slightly smaller acceptance-of-responsibility 

adjustments. (The numbers reflect the average number of reductions in the offense level, so the more 

negative the reduction, the greater the benefit to the offender.) There has been a modest increase in 

the size of acceptance-of-responsibility adjustments, but the increase has not been large and both 

whites and blacks have benefited to the same degree.

Prosecutors exercise choice over petitioning the court for substantial assistance departures. As 

shown in table 3, blacks and whites receive substantial assistance departures at about the same rate.

Over time, the rate has been constant for blacks and has decreased for whites. However, these changes 

have not been large. Prosecutors also exercise choice over petitioning the court for other downward 

departures. We see modest trends in other government-sponsored departures, and blacks and whites 

receive other government-sponsored departures at about the same rates. Data for governmentsponsored departures below the guideline range are only available for cases sentenced since the Booker
61

Federal Sentencing Disparity, 2005–2012 

v. United States decision. Therefore, no data appear for 2003 and 2004. Continuing this logic, table 3 

also shows the proportion of cases involving the imposition of a mandatory minimum, regardless of the 

offense associated with the minimum (i.e., for a drug offense or a weapons offense).

39 It shows that 

blacks are more likely to receive mandatory minimums, and it apparently shows random fluctuations.

Overall, the proportion of cases where a mandatory minimum was imposed has not changed 

significantly over time for either blacks or whites.

Few offenders demand a trial, but blacks may be more likely to demand trials if they are 

disadvantaged by plea agreements. Blacks are convicted at trial rather than by plea more frequently 

than are whites, but the differences are not large (because trials are infrequent) and there is no 

evidence that the decreasing frequency of trials is disadvantaging black offenders.

The evidence does not show that prosecutorial behavior changed from 2003 through 2012. The 

relative constancy of prosecutorial practices cannot explain the trends reported in figure 2.

5.3.2 Gaming drug amounts near mandatory minimums

The evidence presented in the previous subsection pertained to trends in indicators of 

prosecutorial discretion. In this subsection, we examine charging decisions with respect to drug 

amounts. This is not based on trend analysis, but it is nevertheless informative about prosecutorial 

decision-making.

Drug offenses provide one venue for finding evidence of whether prosecutors have exercised 

discretion to the disadvantage of blacks. Mandatory minimums for drug violators are triggered by the 

amount of drugs that were trafficked. For example, when an offender is convicted of trafficking 500 or 

more grams of cocaine, he or she is subject to a mandatory minimum sentence, absent some mitigating 

considerations. If there were evidence of discretion favoring one group over others around a statutory 

 39 We used the USSC variables MAND1 to MAND6 to determine whether any mandatory minimum sentence was 

imposed in the case. These variables are only available since 2005.
62

Federal Sentencing Disparity, 2005–2012 

mandatory minimum, we would expect to observe larger percentages of favored groups having drug 

amounts just shy of the minimum, compared to the other groups. Our analysis suggests that this is not 

happening.

We look for evidence of prosecutorial manipulation in recorded drug weights for drug trafficking 

cases. Specifically, we look to see whether blacks are more likely than whites to be above a mandatory 

minimum threshold for drug cases, with amounts near a threshold that triggers the application of 

mandatory minimum sentencing laws. If blacks are systematically disadvantaged, then blacks should be 

more likely than whites to be above a mandatory minimum threshold. We limit this investigation to the 

six major drugs that make up the overwhelming majority of sentenced cases: cocaine, crack, heroin, 

marijuana, mixture methamphetamine, and pure methamphetamine.

Figure 8 provides an example based on powder cocaine. We have included Hispanics in the 

figure, so the categories are non-Hispanic whites (white), non-Hispanic blacks or African Americans

(black), and Hispanics. This figure shows three distributions of drug amounts for offenders in a broadly

defined range (+/- 100 grams) around the lower mandatory minimum threshold amount for cocaine 

(500 grams). For this figure, offenders have been grouped into discrete bins spanning approximately 10 

grams (i.e., 480 to 489.99, 490 to 499.99, 500 to 509.99). The horizontal axis shows the grams of cocaine 

associated with the offense, and the vertical axis shows the percentages of offenders within each 

grouping that fall into each bin. The bins themselves have been mapped to a smoothed line to aid in 

visualization.
63

Federal Sentencing Disparity, 2005–2012 

Figure 8 – Distribution of offenders within 100 grams of the 500-gram mandatory minimum threshold, by 

race and ethnicity

Five hundred grams of cocaine is one-half kilogram, and perhaps this is a standard unit of transaction, 

explaining the concentration around 500 grams. A more likely explanation is that prosecutors are most 

interested in establishing that offenders have transacted at least 500 grams, which triggers a mandatory 

minimum, and that prosecutors have little incentive to demonstrate that offenders have transacted 

somewhat more than this amount until the transaction reaches about 5 kilograms, which triggers the 

next application of a mandatory minimum. 

This figure depicts a divergence between the three racial or ethnic groups on the interval 

between 480 and 500 grams and suggests that, relative to whites, blacks and Hispanics are more likely 

to fall just below the 500-gram cutoff. The differences are not large, however, implying that during the 

post-Booker period, prosecutors have not discriminated against blacks when establishing that a case 

meets the mandatory minimum threshold.

To formally test for differences by race, we estimate a linear regression that models the 

probability of falling above a threshold amount, controlling for offender criminal history, education, sex, 

substantial assistance to the prosecution, sentencing year, whether the case went to trial, and circuit 

0%

5%

10%

15%

20%

25%

30%

35%

Proportion of offenders (+/

400 420 440 460 480 500 520 540 560 580 600

-) 100 

gms. of the threshold 

Grams of cocaine

Whites Blacks Hispanics
64

Federal Sentencing Disparity, 2005–2012 

fixed effects. We estimate separate models for each drug and each mandatory minimum threshold 

amount. In addition, the sample is restricted to cases where the safety valve provision was not applied.

Based on drug statute 21 U.S.C. § 841, we identify two thresholds for each drug—low and high—defined 

in table D1 in appendix D. Overall, we do not find strong evidence to support the argument that blacks 

face systematic prosecutorial discrimination. Rather, racial inequities around minimum thresholds 

appear more idiosyncratic or drug-specific. Table 4 shows the result of our estimation.

Table 4 – Conditional differences (male and female)

Differences in probability of being above the cutoff, relative to whites

White Black Hispanic White Black Hispanic

Lower Upper

Cocaine - -10.0 ** -14.3 *** - 6.4 -8.7 **

Crack - 4.7 12.0 ** - -4.1 -3.0

Heroin - -7.1 -13.3 - -14.3 -11.3

Marijuana - 24.1 *** 5.1 - -9.9 -8.7

Meth (mix) - 7.3 0.2 - 17.8 4.3

Meth (pure) - -25.2 -0.1 - -3.7 -9.6

Notes: ** p < 0.01, *** p < 0.001

This table shows the estimated difference in the probability of being just above a threshold amount by 

race, drug, and threshold. For cocaine, it shows that blacks have a probability that is 0.10 lower than 

whites to be above the 500-gram threshold, but not statistically more or less likely to be above the 

5,000-gram threshold (i.e., the next step in the mandatory minimum gradient). Hispanics are also less 

likely than whites to be above either the 500- or 5,000-gram threshold. For crack, heroin, and 

methamphetamine, no strong differences emerge. For marijuana, blacks are more likely to be above the 

lower (1,000 kilogram) threshold, with no detectable differences for Hispanics. Based on these results, 

there is no obvious pattern of preference that favors or disadvantages blacks.

In addition to the results presented here, there are other aspects of the data that warrant 

further discussion and from which we conduct additional sensitivity analysis. The first is that drug 

amounts are not always recorded as exact weights or amounts in the sentencing data. Instead, amounts 
65

Federal Sentencing Disparity, 2005–2012 

are often recorded as ranges. We find that this occurs roughly 25% of the time for drug trafficking cases 

overall, although this percentage varies depending on the drug type. Table D2 in appendix D shows the 

percentage of cases in which no exact drug amount is reported, stratified by drug type and race 

category. Given the sizeable number of such cases, we would not want to exclude them from analysis. 

However, because the reported ranges themselves are relatively wide, we cannot identify offenders as 

being close to the thresholds. Our solution is to analyze these cases as a separate group. 

For this group, we find that reported ranges generally (1) do not overlap thresholds and (2) 

often use threshold amounts as range boundaries. Given this, we select and analyze offenders with 

recorded ranges bounded by an amount that is also a threshold cutoff (e.g., as in a range of cocaine 

amount [from > 0 to 500 grams or from 500 to 1,500 grams]) and test whether black offenders are more 

likely to be strictly at or above the threshold, relative to whites. The specification for this test is identical 

to the estimation performed using the exact weights discussed earlier (i.e., estimating a linear 

probability model using covariates, such as criminal history, sex, race and circuit, and separate models 

for each drug). Table D3 in appendix D reports the results of these estimations. This table shows

estimates that are largely consistent with our earlier findings. And while there are some differences 

from our earlier results, some of these differences may simply be due to chance. We find no discernable 

evidence of systematic bias in prosecutorial practice.
66

Federal Sentencing Disparity, 2005–2012 

6.0 Conclusions

At least since Marvin Frankel’s 1973 book, Criminal Sentences; Law without Order, was 

published, sentencing disparity has been a concern of federal justice administration. That concern led 

Congress to pass the Comprehensive Crime Control Act in 1984, which created the USSC. The duly 

appointed commission crafted the first Federal Sentencing Guidelines in 1987. For decades, scholars 

have debated whether the guidelines have reduced disparity; with the Booker decision, which rendered 

the guidelines advisory, scholars have argued whether disparity has subsequently increased or 

decreased, and they have debated whether a return to some form of mandatory guidelines would

benefit or harm justice administration.

Our study does not attempt to answer the question of whether the guidelines increased or 

decreased disparity, whether the Booker decision increased or decreased disparity, and whether a new 

mandatory guideline system that passed Supreme Court scrutiny would improve justice administration.

Commissioned by BJS, our study has proposed a way of studying sentencing disparity that helps answer 

questions about the level of disparity and post-Booker trends. The methodology could be extended to 

study the causal effects of Booker, although the grounds for making causal statements in a nonexperimental setting are treacherous.

Like earlier studies, our study treats the guideline cell as the anchor point for any further 

analysis of sentencing patterns. Using data transformations that standardize sentences within each 

guideline cell, we have introduced a regression-based methodology that allows us to make summary 

statements about how racial disparity varies across guideline cells and over time. By using a linear 

random effects regression model, we are able to make summary statements about how racial disparity 

varies across judges. We do not claim this is the only valid methodology for studying disparity, and for 

some research questions it may not even be the best; however, for the questions posed by BJS, this 

methodology has strong appeal.
67

Federal Sentencing Disparity, 2005–2012 

The methodology is solidly within the tradition of studying disparity, given the facts known at 

the time of sentencing, but some researchers claim that locating a study of disparity this late in the 

judicial process ignores disparity in prosecutorial decision-making. While we do not necessarily find this 

counterargument compelling, we have dealt with the critique indirectly by showing that prosecutorial 

discretion does not appear to have changed much since 2005 (the beginning of our study), although we 

find trends toward increased racial disparity between 2005 and 2012. These trends are likely 

attributable to judicial behavior, not prosecutorial behavior. This conclusion is strengthened by evidence 

from the estimated random effects of considerable inter-judge differences in the sentences for white 

and black offenders.

What we find is that black males receive harsher sentences than white males after accounting 

for the facts surrounding the case, and we also find that the sentencing disparity has grown over the 8

years since Booker. We find that females receive sentences that are less harsh than their male 

counterparts, but curiously we find that black and white females receive similar sentences. Something 

other than skin color and racial prejudice per se is driving these results.

We find it difficult to attribute racial disparity to skin color alone. While it is an obvious 

distinction, in the United States race is bundled with a large number of unobserved characteristics. We 

have observed that blacks are more concentrated within circuits that impose harsh sentences compared 

with more lenient circuits. It is possible that blacks receive the same sentences as whites within every 

circuit, but that blacks receive harsher sentences than whites nationally. After we account for these 

circuit differences, racial disparity remains, but the point is that race is correlated with other 

characteristics that may account for different sentences among whites and blacks. For example, we 

know that blacks sentenced in the federal justice system are, on average, less educated than are whites 

sentenced in the federal justice system. Therefore, if judges take education into account (along with

correlates such as earnings and demeanor), then racial disparity could be explained by factors that 
68

Federal Sentencing Disparity, 2005–2012 

might be deemed to be reasonable desiderata when imposing sentences. A study of disparity is not a 

study of bias. Our study cannot get at the ultimate reasons why black males receive harsher sentences 

than do white males, after accounting for the facts surrounding the case.

We are concerned that racial disparity has increased over time since Booker. Perhaps judges, 

who feel increasingly emancipated from their guidelines restrictions, are improving justice 

administration by incorporating relevant but previously ignored factors into their sentencing calculus,

even if this improvement disadvantages black males as a class. But in a society that sees intentional and 

unintentional racial bias in many areas of social and economic activity, these trends are a warning sign.

It is further distressing that judges disagree about the relative sentences for white and black males

because those disagreements cannot be so easily explained by sentencing-relevant factors that vary 

systematically between black and white males. (The judge-specific effects take random variation into 

account.) We take the random effect as strong evidence of disparity in the imposition of sentences for 

white and black males. 
69

Federal Sentencing Disparity, 2005–2012 

References

Anderson, A. L., & Spohn, C. (2010). Lawlessness in the federal sentencing process: A test for uniformity 

and consistency in sentence outcomes. Justice Quarterly : JQ, 27(3), 362. Retrieved from: 

http://search.proquest.com.libproxy.highpoint.edu/docview/228169004?accountid=11411

Booker v. United States. 543 US 220. Supreme Court of the United States. 2005.

Britt, C. L. (2009). Modeling the distribution of sentence length decisions under a guidelines system: An 

application of quantile regression models. Journal of Quantitative Criminology, 25(4), 341-370. 

doi:http://dx.doi.org.libproxy.highpoint.edu/10.1007/s10940-009-9066-x 

Cole, J. M. (2012). DOJ Memo to Prosecutors: Department Policy on Early Disposition or “Fast- Track” 

Programs. Federal Sentencing Reporter, 25(1), 53-56.

Commission, U. S. (2011). U.S. Sentencing Commission Report on Mandatory Minimum Penalties in 

Federal Sentencing. Washington, D.C.: U.S. Sentencing Commission.

Commission, U. S. (2012). Report on the Continuing Impact of United States v. Booker on Federal 

Sentencing. Washington,D.C.: U.S. Sentencing Commission.

Federal Sentencing Reporter, Vol. 25 No. 5, June 2013; (pp. 327-333) DOI: 10.1525/fsr.2013.25.5.327

Fishman, J., & Schanzenback, M. (2012). Racial Disparities under the Federal Sentencing Guidelines: The 

Role of Judicial Discretion and Mandatory Minimums. Journal of Empirical Legal Studies vol 9 (4).

Frankel, M. E. (1973). Criminal sentences: Law without order.

Gall v. United States. 552 US 38. Supreme Court of the United States. 2007.

Gorman, T. E. (2010). Fast-Track Sentencing Disparity: Rereading Congressional Intent to Resolve the 

Circuit Split. University of Chicago Law Review, 77, 479.

Hofer, P. J. (2012). Data, disparity, and sentencing debates: Lessons from the TRAC report on interjudge disparity. Federal Sentencing Reporter, 25(1), 37-45. 

doi:http://dx.doi.org.libproxy.highpoint.edu/10.1525/fsr.2012.25.1.37

Johnson, B. (2012). The missing link: Examining prosecutorial decision-making across Federal District 

Courts. In ACJS 2012 conference, New York, NY.

Koon v. United States. 518 US 81. Supreme Court of the United States. 1996.

Lynch, M., & Omori, M. (2014). Legal change and sentencing norms in the wake of booker: The impact of 

time and place on drug trafficking cases in federal court. Law & Society Review, 48(2), 411-445. 

Retrieved from: 

http://search.proquest.com.libproxy.highpoint.edu/docview/1553397580?accountid=1141
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Mason, C., & Bjerk, D. (2013). Inter-judge sentencing disparity on the federal bench: A examination of 

drug smuggling cases in the southern district of california. Federal Sentencing Reporter, 25(3), 190. 

Retrieved from: 

http://search.proquest.com.libproxy.highpoint.edu/docview/1354453416?accountid=11411 

McClellan, J. L., & Sands, J. M. (2006). Federal Sentencing Guidelines and the Policy Paradox of Early

Disposition Programs: A Primer on Fast-Track Sentences. Ariz. St. LJ, 38, 517.

Prosecutorial Remedies and Other Tools to End the Exploitation of Children Today (PROTECT) Act of 

2003, Pub. L. No. 108-21, 117 Stat. 650 § 151 (2003-2004)

Starr, S. B., & Rehavi, M. M. ( 2013). Mandatory sentencing and racial disparity: Assessing the role of 

prosecutors and the effects of booker. Yale Law Journal, 123, 1, 2-80.

Scott, R. (2010). Inter-Judge Sentencing Disparity After Booker: A First Look. Stanford Law Review vol 63 

(2).

Starr, S. B., & Rehavi, M. M. (2013). On Estimating Disparity and Inferring Causation: Sur-Reply to the US 

Sentencing Commission Staff. Yale LJ Online, 123, 273-2559.

Sullivan, C. J., Mcgloin, J. M., & Piquero, A. R. (2008). Modeling the deviant Y in criminology: An 

examination of the assumptions of censored normal regression and potential alternatives. Journal of 

Quantitative Criminology, 24(4), 399-421. doi:http://dx.doi.org.libproxy.highpoint.edu/10.1007/s10940-

008-9051-9

Ulmer, J., Light, M. T., & Kramer, J. (2011). The “Liberation” of Federal Judges’ Discretion in the Wake of 

the Booker/Fanfan Decision: Is There Increased Disparity and Divergence between Courts?. Justice 

Quarterly, 28, 6, 799-837. doi:10.1080/07418825.2011.553726

United States Sentencing Commission, Guidelines Manual, §3E1.1 (Nov. 2013)

Yang, C. (2013). Free at Last? Judicial Discretion and Racial Disparities in Federal Sentencing. Chicago: 

Coase-Sandor Institute for Law and Economics Working Paper No. 661: The University of Chicago 

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Yang, C. (2014). Have Inter-Judge Sentencing Disparities Increased in an Advisory Guideline Regime? 

Evidence from Booker. Coase-Sandor Institute for Law and Economics: Research Paper No. 662.
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Appendix A: Mechanics of guidelines

The United States Sentencing Commission Guidelines Manual (2013) provides instructions for 

applying the guidelines. These instructions are detailed, and interested readers should consult them in 

the original. Our current intention is to provide an overview.

The guidelines stipulate a sentencing table that has 43 rows and 6 columns defining 258 cells.

The applicable row is determined by the offense seriousness and the applicable column is determined 

by the offender’s criminal history. Calculations required to identify the row and column are described

below. The cells are clustered into four zones. A probation term is authorized in zones A and B, but a 

probation term in zone B must be accompanied by an alternative to confinement, such as home 

detention. A prison term is required in zones C and D.

The sentencing table cell specifies the length of the prison term. For example, an offense level of 

16 and a criminal history category of IV require a prison term between 33 and 41 months. Even when 

the guidelines were mandatory, a judge could depart upward or downward from the stipulated range. 

Now that the guidelines are advisory, there is no obligation to adhere to the range. We discuss 

departure reasons later in this appendix; first we review how the guidelines establish the offense level.

Offense level

Determination of offense level begins with the basic offense. For example, chapter 2 in the 

guidelines defines an aggravated assault. A judge who is sentencing an offender convicted of an 

aggravated assault starts with a baseline offense level of 14 and considers other aspects of the case.

Instructions are—

• If the crime involved more than minimal planning, add 2 points, increasing the offense level 

from 14 to 16.

• Add 3 to 5 points depending on the nature of the weapon (if any) and how it was used.

• Add 3 to 10 points depending on the extent of injury.
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• Add 2 points if the crime was motivated by profit.

• Add 2 points if certain statutory provisions are met.

The guidelines provide detailed instructions and definitions.

Other offenses have different baseline offense levels and recognize case elements that 

distinguish cases based on severity within an offense type. Points for property crimes are determined by 

the dollar loss. Points for drug crimes are determined by the type and amount of drugs bought or sold.

Offense categories sometimes overlap, and the guidelines provide cross-references to resolve 

ambiguities.

Some elements of criminal cases are common to multiple types of cases. These elements are 

identified in chapter 3, where they are called adjustments, and consist of five categories:

• Victim adjustments (e.g., an enhancement for a vulnerable victim, as defined by the guidelines).

• The offender’s role in the offense (e.g., points are added if the offender leads a criminal 

enterprise, and points are subtracted if the offender was a minimal participant).

• Points are added if the offender obstructed or impeded the administration of justice.

• Offenders are often convicted of multiple counts for the same type of offense or for different 

offenses. The guidelines provide rules for imposing a sentence given multiple counts of 

conviction.

• The guidelines apply what they call “acceptance of responsibility provisions.” If the offender

clearly demonstrates acceptance of responsibility for his or her offense, the offense level is 

decreased by 2 levels. Under some conditions, on motion of the government stating that the 

offender has assisted authorities in the investigation or prosecution of his or her misconduct by 

timely notifying authorities of an intention to enter a guilty plea, the offense level is decreased 

by 1 additional level.
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Criminal history category

Chapter 4 provides rules for determining the criminal history category. This chapter applies 

points to the offender’s criminal record, taking into account prior sentences and whether the instant 

crime was done while the offender was under community supervision. The criminal history score makes 

special provisions for career criminals and criminal livelihoods.

Departures

Using the offense level from chapter 3 and the criminal history category from chapter 4, 

calculations identify the guideline cell. The guidelines sometimes use the term heartland to mean the 

guidelines capture most of the elements of the offense and offender. As a result, most sentences should 

be imposed consistent with the guideline cell. The guidelines prohibit departures under some conditions 

and allow departures for others. In fact, because the guidelines are now voluntary, there is great 

latitude for departures. Some latitude for departures is built into the guidelines, and its presence needs 

to be recognized by the study of disparity—a point made below.

Mandatory minimum sentences

Federal criminal codes specify maximum sentences for all crimes. For example, a code might 

specify that an offender can serve 0 to 5 years if convicted for a count of larceny. There is no minimum 

prison term. Other federal criminal codes—especially for drug violations—specify both a minimum and a 

maximum. For example, if someone is convicted of distributing X grams of cocaine, the code may specify 

that the sentence is between 2 and 5 years. The guidelines might then require a sentence between 2 

and 21⁄2 years. The minimum sentence sets a lower limit on the guidelines and on any legitimate 

sentence.

However, federal law (18 U.S.C. 3553(f)(1)-(5)) allows the court to sentence below the mandatory 

minimum when the following hold:

• The offender has no more than 1 criminal history point.

• He or she did not use violence or credible threats.
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Federal Sentencing Disparity, 2005–2012 

• There was neither death nor serious bodily injury.

• The offender was neither an organizer, leader, manager, or supervisor of a criminal enterprise.

• The offender revealed all known information about the crime.

Provided the minimum sentence is 5 years or more, the minimum guidelines range may be reduced, but 

no lower than level 17.

Substantial assistance

The sentencing judge is able to depart downward on a motion by the government that the 

offender “...has provided substantial assistance in the investigation or prosecution of another person 

who has committed an offense...” Commentary in the guidelines instructs: “Substantial weight should be 

given to the government’s evaluation of the extent of the defendant’s assistance, particularly where the 

extent and value of the assistance are difficult to ascertain.” Government-initiated downward 

departures are frequent.

Warranted departures

While the guidelines are intended to cover most circumstances, the Commission indicates that the 

sentencing judge may confront situations where the circumstances faced by the court are so unusual 

that applying the guidelines would be an injustice. In those cases, the sentencing judge can depart from 

the guidelines provided he or she provides an explanation. The guidelines also provide policy statements 

identifying special circumstances when a departure would apply. For example, if a victim or victims 

suffered psychological injury much more serious than that normally resulting from commission of the 

offense, the court may increase the sentence above the authorized guidelines range. In addition, the 

guidelines offer numerous examples of when a departure would be appropriate.

Prohibited departures

The guidelines identify factors that cannot be taken into account when departing from the 

guidelines range. A judge cannot base a sentence on race, sex, national origin, religion, and 
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Federal Sentencing Disparity, 2005–2012 

socioeconomic circumstances. A judge cannot reconsider the weighting of factors, such as acceptance of 

responsibility and role in the offense, that are already incorporated into the guidelines.

Characteristics of the offender

Chapter 5, part H, discusses some specific characteristics of offenders that may not be taken 

into account at the time of sentencing. Referring to the Sentencing Reform Act, according to the 

guidelines manual:

First, the act directs the Commission to ensure that the guidelines and policy statements "are 

entirely neutral" as to five characteristics—race, sex, national origin, creed, and socioeconomic 

status. See 28 U.S.C. § 994(d).

Second, the act directs the Commission to consider whether 11 specific offender characteristics, 

"among others," have any relevance to the nature, extent, place of service, or other aspects of an 

appropriate sentence, and to take them into account in the guidelines and policy statements, only 

to the extent that they do have relevance. See 28 U.S.C. § 994(d).

Third, the act directs the Commission to ensure that the guidelines and policy statements, in 

recommending a term of imprisonment or length of a term of imprisonment, reflect the "general 

inappropriateness" of considering five of those characteristics—education, vocational skills,

employment record, family ties and responsibilities, and community ties. See 28 U.S.C. § 994(e).

Fourth, the act also directs the sentencing court, in determining the particular sentence to be 

imposed, to consider, among other factors, "the history and characteristics of the defendant." See 

18 U.S.C. § 3553(a)(1).
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Federal Sentencing Disparity, 2005–2012 

According to the Commission: 

The Supreme Court has emphasized that the advisory guideline system should "continue to move 

sentencing in Congress’ preferred direction, helping to avoid excessive sentencing disparities 

while maintaining flexibility sufficient to individualize sentences where necessary. See United 

States v. Booker, 543 U.S. 220, 264-65 (2005). Although the court must consider "the history and 

characteristics of the defendant" among other factors, see 18 U.S.C. § 3553(a), in order to avoid 

unwarranted sentencing disparities the court should not give them excessive weight. Generally, 

the most appropriate use of specific offender characteristics is to consider them not as a reason 

for a sentence outside the applicable guideline range but for other reasons, such as in determining 

the sentence within the applicable guideline range, the type of sentence (e.g., probation or 

imprisonment) within the sentencing options available for the applicable Zone on the Sentencing 

Table, and various other aspects of an appropriate sentence. To avoid unwarranted sentencing 

disparities among defendants with similar records who have been found guilty of similar conduct,

see 18 U.S.C. § 3553(a)(6), 28 U.S.C. § 991(b)(1)(B), the guideline range, which reflects the 

defendant’s criminal conduct and the defendant’s criminal history, should continue to be "the 

starting point and the initial benchmark." Gall v. United States, 552 U.S. 38, 49 (2007).

Accordingly, the purpose of this part is to provide sentencing courts with a framework for 

addressing specific offender characteristics in a reasonably consistent manner. Using such a framework 

in a uniform manner will help "secure nationwide consistency" (see Gall v. United States, 552 U.S. 38, 49 

(2007)), "avoid unwarranted sentencing disparities" (see 28 U.S.C. § 991(b)(1)(B), 18 U.S.C. § 3553(a)(6)), 

"provide certainty and fairness" (see 28 U.S.C. § 991(b)(1)(B)), and "promote respect for the law" (see 18 

U.S.C. § 3553(a)(2)(A)).

The Commission identified several offender characteristics regarding which sentencing judges 

may have dissenting views. The Commission deemed that age may be relevant but considered the 
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situation where the frail may not require prison. Education and vocational skills are considered 

irrelevant, unless they are pertinent to the crime. Mental and emotional conditions may be relevant but 

only in extreme circumstances. Similar to age, physical condition may be relevant. Drug and alcohol 

dependence is ordinarily not a reason for a departure, unless it accomplishes a specific treatment 

purpose. Employment is ordinarily irrelevant. Family ties and responsibilities are not ordinarily relevant,

although the Commission makes exceptions for loss of caretaking and financial support.
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Appendix B: Detailed findings for sentencing disparity – U.S. citizens

This appendix includes tables and figures pertaining to the sentencing of U.S. citizens. Some of these 

tables and figures appear in the main text with summaries.

Table B.1 – Number of observations for each guideline cell - Citizens

Criminal history category

Offense level I II III IV V VI

1

2

3 10

4

5 151

6 491

7 448 669

8 339 486

9 252 180 287

10 2,233 1,070 704 998

11 374 282 498

12 2,934 1,827 1,232 1,600

13 2,474 3,075 1,839 1,110 1,732

14 582 648 369 230 827

15 2,310 2,783 1,530 984 1,326

16 582 666 368 208 300

17 2,147 3,753 2,800 1,784 2,144

18 3,388 541 618 333 224 313

19 7,085 1,784 2,571 1,662 1,068 1,405

20 3,045 627 776 506 275 334

21 10,350 1,961 3,198 2,609 1,886 2,979

22 2,961 510 680 468 280 463

23 8,497 3,373 4,827 2,948 1,916 2,246

24 3,432 594 740 493 321 587

25 6,213 2,430 3,126 1,917 1,182 1,553

26 2,862 725 875 482 288 506

27 7,616 1,648 2,215 1,349 833 970

28 2,761 577 656 337 221 298

29 5,245 2,481 3,467 1,868 1,058 5,138

30 2,402 424 495 774 546 1,696

31 3,674 1,680 2,210 1,283 767 6,292

32 1,425 381 495 228 163 745

33 2,818 934 1,215 824 459 866

34 1,473 373 452 215 159 5,433

35 1,566 710 929 438 296 866

36 700 209 267 158 86 156

37 1,427 361 411 217 140 1,046

38 602 187 229 142 83 219

39 501 127 145 74 40 118

40 462 113 179 111 85 199

41 287 71 98 69 34 102

42 316 79 107 47 47 96

43 742 161 225 148 116 258
79

Federal Sentencing Disparity, 2005–2012 

Data partition: Males, no weapons offenses, no sex offenders

Table B.2 – Parameter estimates from mixed models: Males

No drugs, no substantial 

assistance

No drugs, substantial 

assistance

Drugs, no substantial 

assistance Drugs, substantial assistance

Variable Est Std err p Est Std err p Est Std err p Est Std err p

Year x Pre-Gall -0.246 0.083 0.003 0.005 0.179 0.978 0.179 0.105 0.089 0.255 0.125 0.041

Year x Post-Gall -0.207 0.038 <0.001 -0.140 0.075 0.061 -0.496 0.051 <0.001 -0.330 0.058 <0.001

Race/Ethnicity: Non-Hispanic black -0.031 0.033 0.354 -0.139 0.090 0.122 0.039 0.043 0.360 0.088 0.055 0.112

Race/Ethnicity: Hispanic 0.028 0.044 0.523 0.044 0.143 0.761 0.151 0.041 <0.001 0.282 0.059 <0.001

Race/Ethnicity: Non-Hispanic other 0.011 0.103 0.914 -0.190 0.213 0.374 0.229 0.102 0.025 0.130 0.114 0.256

Black x Year x Pre-Gall 0.446 0.111 <0.001 0.675 0.289 0.020 0.164 0.130 0.205 0.077 0.167 0.645

Hispanic x Year x Pre-Gall -0.065 0.152 0.669 0.095 0.455 0.834 -0.246 0.132 0.062 -0.190 0.195 0.329

Other x Year x Pre-Gall 0.090 0.331 0.785 0.869 0.709 0.220 -0.459 0.319 0.151 -0.154 0.344 0.655

Black x Year x Post-Gall -0.033 0.047 0.480 0.035 0.114 0.760 0.143 0.058 0.013 0.080 0.076 0.296

Hispanic x Year x Post-Gall 0.176 0.065 0.007 -0.071 0.160 0.659 0.250 0.068 <0.001 0.060 0.084 0.477

Other x Year x Post-Gall -0.028 0.135 0.837 -0.292 0.276 0.289 0.139 0.153 0.363 0.111 0.206 0.590

Max Sentence in Guideline Cell -0.054 0.050 0.278 0.154 0.093 0.098 -0.301 0.054 <0.001 0.046 0.059 0.432

Black x Max Sentence -0.213 0.062 0.001 -0.080 0.139 0.563 0.044 0.061 0.474 -0.110 0.075 0.140

Hispanic x Max Sentence -0.156 0.091 0.089 -0.005 0.185 0.979 -0.039 0.070 0.573 -0.223 0.085 0.009

Other x Max Sentence 0.493 0.140 <0.001 0.255 0.290 0.380 -0.348 0.182 0.056 0.033 0.223 0.882

Sentence is a new conviction 0.158 0.019 <0.001 0.308 0.192 0.108 0.270 0.023 <0.001 0.448 0.167 0.007

CH Points: Category 1 0.078 0.011 <0.001 0.051 0.017 0.003 0.045 0.007 <0.001 0.055 0.010 <0.001

CH Points: Category 2 0.035 0.011 0.002 0.031 0.031 0.323 0.039 0.011 <0.001 0.070 0.013 <0.001

CH Points: Category 3 0.045 0.012 <0.001 0.043 0.027 0.120 0.051 0.016 0.001 0.046 0.013 0.001

CH Points: Category 4 0.024 0.008 0.003 0.064 0.024 0.008 0.019 0.011 0.090 0.050 0.018 0.006

CH Points: Category 5 0.033 0.011 0.003 -0.029 0.046 0.526 0.013 0.017 0.439 0.033 0.029 0.263

CH Points: Category 6 0.108 0.009 <0.001 0.124 0.023 <0.001 0.102 0.010 <0.001 0.113 0.012 <0.001

Circuit: DC 0.077 0.071 0.278 -0.489 0.104 <0.001 0.010 0.072 0.886 -1.455 0.093 <0.001

Circuit: 1 0.089 0.062 0.151 0.038 0.111 0.731 0.240 0.068 <0.001 -0.212 0.108 0.050

Circuit: 2 -0.088 0.037 0.018 -0.757 0.072 <0.001 -0.166 0.047 <0.001 -0.974 0.088 <0.001

Circuit: 3 0.149 0.035 <0.001 -0.184 0.065 0.005 0.204 0.046 <0.001 -0.359 0.065 <0.001

Circuit: 4 0.357 0.038 <0.001 0.212 0.064 0.001 0.505 0.043 <0.001 0.204 0.064 0.001

Circuit: 5 0.407 0.037 <0.001 0.349 0.061 <0.001 0.524 0.039 <0.001 0.436 0.059 <0.001

Circuit: 6 0.147 0.036 <0.001 0.243 0.061 <0.001 0.380 0.044 <0.001 0.274 0.067 <0.001

Circuit: 7 0.182 0.042 <0.001 0.243 0.073 0.001 0.344 0.064 <0.001 0.434 0.063 <0.001

Circuit: 8 0.132 0.040 0.001 -0.099 0.071 0.167 0.348 0.042 <0.001 0.008 0.072 0.907
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Federal Sentencing Disparity, 2005–2012 

No drugs, no substantial 

assistance

No drugs, substantial 

assistance

Drugs, no substantial 

assistance Drugs, substantial assistance

Variable Est Std err p Est Std err p Est Std err p Est Std err p

Circuit: 10 0.092 0.040 0.020 0.093 0.070 0.183 0.182 0.045 <0.001 0.025 0.062 0.687

Circuit: 11 0.294 0.031 <0.001 0.398 0.055 <0.001 0.548 0.046 <0.001 0.497 0.056 <0.001

Intercept -0.127 0.032 <0.001 -0.101 0.067 0.129 -0.320 0.044 <0.001 -0.259 0.057 <0.001

Random effects

Var (white) 0.075 0.006 0.141 0.014 0.131 0.012 0.210 0.015

Var (black) 0.077 0.007 0.176 0.020 0.119 0.010 0.230 0.016

Var (Hispanic) 0.020 0.008 0.067 0.047 0.026 0.009 0.013 0.010

Var (other) 0.206 0.049 0.137 0.046 0.268 0.072 0.334 0.116

Cov (white, black) 0.062 0.005 0.103 0.009 0.197 0.013

Cov (white, Hispanic) -0.015 0.005 -0.044 0.008 -0.029 0.011

Cov (white, other) 0.056 0.009 0.111 0.021 0.183 0.031

Cov (black, Hispanic) -0.008 0.006 -0.026 0.007 -0.024 0.010

Cov (black, other) 0.036 0.010 0.094 0.015 0.203 0.037

Cov (Hispanic, other) -0.021 0.013 -0.035 0.017 -0.032 0.017

Var (residual) 0.889 0.020 0.722 0.021 0.823 0.027 0.646 0.016

obs 76405 10829 62650 25380

groups 1292 1020 1181 1064

ln L -105157 -14282 -84030 -31563
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Federal Sentencing Disparity, 2005–2012 

Figure B.1 – Changes over time for three guideline cells: Males

No drugs, no substantial assistance No drugs, substantial assistance

Drugs, no substantial assistance Drugs, substantial assistance

-1

0

1

2

3

Difference in months

2005 2006 2007 2008 2009 2010 2011 2012

Year

33 Months 46 Months 87 Months

-2

-1

0

1

2

3

Difference in months

2005 2006 2007 2008 2009 2010 2011 2012

Year

37 Months 57 Months 96 Months

0

2

4

6

8

10

2005 2006 2007 2008 2009 2010 2011 2012

Difference in months

Year

57 Months 87 Months 151 Months

0

1

2

3

4

5

6

2005 2006 2007 2008 2009 2010 2011 2012

Difference in months

Year

71 Months 108 Months 188 Months
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Federal Sentencing Disparity, 2005–2012 

Figure B.2 – Predicted and actual sentences across maximum sentence in guideline cells: Males

No drugs, no substantial assistance No drugs, substantial assistance

Drugs, no substantial assistance Drugs, substantial assistance

Note. Dashed line is a quadratic trend fit to the predicted difference.

-20

0

20

40

Difference in months

Maximum sentence for the guideline cell (470 

maximum)

Actual_Difference Predicted_Difference

-20

0

20

40

60

80

Difference in months

Maximum sentence for the guideline cell (470 

maximum)

Actual_Difference Predicted_Difference

-10

0

10

20

30

40

Difference in months

Maximum sentence for the guideline cell (470 

maximum)

Actual_Difference Predicted_Difference

-20

-10

0

10

20

Difference in months

Maximum sentence for the guideline cell (470 

maximum)

Actual_Difference Predicted_Difference
83

Federal Sentencing Disparity, 2005–2012 

Figure B.3 – Differences in judge distributions: Males

No drugs, no substantial assistance No drugs, substantial assistance

Drugs, no substantial assistance Drugs, substantial assistance
84

Federal Sentencing Disparity, 2005–2012 

Data partition: Females, no weapons offenses, no sex offenders

Table B.3 – Parameter estimates from mixed models: Females

No drugs, no substantial 

assistance

No drugs, substantial 

assistance

Drugs, no substantial 

assistance Drugs, substantial assistance

Variable Est Std err p Est Std err p Est Std err p Est Std err p

Year x Pre-Gall -0.125 0.209 0.550 0.988 0.387 0.011 -0.061 0.236 0.795 0.344 0.234 0.141

Year x Post-Gall -0.281 0.098 0.004 -0.343 0.184 0.063 -0.565 0.100 <0.001 -0.333 0.093 <0.001

Race/Ethnicity: Non-Hispanic black -0.113 0.094 0.231 0.269 0.188 0.153 0.098 0.119 0.409 -0.065 0.119 0.585

Race/Ethnicity: Hispanic -0.002 0.125 0.990 0.057 0.308 0.854 0.179 0.086 0.038 0.055 0.151 0.715

Race/Ethnicity: Non-Hispanic other -0.010 0.173 0.952 -0.191 0.470 0.685 -0.092 0.179 0.605 0.049 0.188 0.795

Black x Year x Pre-Gall 0.561 0.323 0.082 -0.854 0.616 0.166 -0.207 0.400 0.604 -0.305 0.404 0.450

Hispanic x Year x Pre-Gall -0.149 0.380 0.695 -0.084 0.919 0.927 -0.218 0.277 0.431 -0.191 0.483 0.692

Other x Year x Pre-Gall 0.292 0.592 0.622 1.158 1.942 0.551 0.809 0.516 0.117 -0.121 0.658 0.855

Black x Year x Post-Gall 0.140 0.140 0.318 0.416 0.264 0.115 0.112 0.182 0.540 0.224 0.223 0.314

Hispanic x Year x Post-Gall -0.001 0.153 0.996 0.109 0.294 0.711 0.105 0.130 0.419 0.298 0.178 0.095

Other x Year x Post-Gall 0.264 0.264 0.316 -0.423 0.824 0.608 0.143 0.208 0.491 0.106 0.321 0.742

Max Sentence in Guideline Cell -0.062 0.158 0.696 -0.144 0.270 0.594 -0.186 0.126 0.139 -0.313 0.128 0.014

Black x Max Sentence -0.422 0.249 0.090 -0.267 0.472 0.572 0.022 0.195 0.910 0.309 0.237 0.192

Hispanic x Max Sentence 0.661 0.368 0.072 0.029 0.678 0.966 -0.195 0.183 0.286 -0.003 0.222 0.989

Other x Max Sentence 0.130 0.353 0.713 0.486 0.590 0.410 -0.596 0.321 0.064 0.282 0.315 0.371

Sentence is a new conviction 0.111 0.043 0.009 0.458 1.019 0.654 0.254 0.059 <0.001 0.118 0.202 0.557

CH Points: Category 1 0.040 0.022 0.063 0.074 0.038 0.052 0.061 0.013 <0.001 0.082 0.015 <0.001

CH Points: Category 2 0.019 0.026 0.479 -0.019 0.049 0.701 0.087 0.025 0.001 0.036 0.033 0.269

CH Points: Category 3 0.020 0.022 0.380 0.048 0.046 0.301 0.059 0.023 0.009 0.090 0.029 0.002

CH Points: Category 4 0.107 0.043 0.014 -0.058 0.112 0.603 0.034 0.037 0.358 -0.044 0.063 0.486

CH Points: Category 5 -0.016 0.058 0.787 0.006 0.158 0.970 -0.088 0.061 0.146 -0.051 0.085 0.550

CH Points: Category 6 0.145 0.029 <0.001 0.090 0.070 0.198 0.153 0.037 <0.001 0.042 0.029 0.155

Circuit: DC 0.402 0.103 <0.001 0.141 0.219 0.521 -0.656 0.191 0.001 -1.260 0.140 <0.001

Circuit: 1 0.047 0.092 0.609 -0.201 0.179 0.259 0.160 0.123 0.194 -0.336 0.169 0.047

Circuit: 2 -0.246 0.085 0.004 -0.564 0.107 <0.001 -0.647 0.087 <0.001 -0.925 0.102 <0.001

Circuit: 3 0.138 0.067 0.039 -0.123 0.092 0.179 0.061 0.102 0.550 -0.555 0.101 <0.001

Circuit: 4 0.425 0.056 <0.001 0.515 0.105 <0.001 0.466 0.056 <0.001 0.030 0.092 0.741

Circuit: 5 0.412 0.051 <0.001 0.442 0.097 <0.001 0.531 0.060 <0.001 0.219 0.086 0.011

Circuit: 6 0.148 0.058 0.011 0.134 0.097 0.167 0.365 0.085 <0.001 0.130 0.089 0.146

Circuit: 7 0.081 0.072 0.266 0.419 0.134 0.002 0.156 0.120 0.193 0.138 0.113 0.222

Circuit: 8 0.193 0.064 0.003 -0.003 0.117 0.983 0.298 0.071 <0.001 -0.161 0.099 0.105
85

Federal Sentencing Disparity, 2005–2012 

No drugs, no substantial 

assistance

No drugs, substantial 

assistance

Drugs, no substantial 

assistance Drugs, substantial assistance

Variable Est Std err p Est Std err p Est Std err p Est Std err p

Circuit: 10 0.245 0.069 <0.001 0.081 0.130 0.532 0.111 0.083 0.182 -0.186 0.095 0.051

Circuit: 11 0.422 0.055 <0.001 0.393 0.093 <0.001 0.371 0.067 <0.001 0.257 0.082 0.002

Intercept -0.166 0.073 0.023 -0.435 0.127 0.001 -0.171 0.083 0.039 0.014 0.096 0.887

Random effects

Var (white) 0.128 0.018 0.145 0.035 0.147 0.020 0.238 0.023

Var (black) 0.091 0.021 0.164 0.041 0.285 0.042 0.220 0.037

Var (Hispanic) 0.060 0.038 0.028 0.052 0.000 0.000 0.052 0.024

Var (other) 0.195 0.063 0.293 0.170 0.303 0.109 0.303 0.087

Cov (white, black) 0.063 0.013

Cov (white, Hispanic) -0.059 0.024

Cov (white, other) 0.054 0.031

Cov (black, Hispanic) -0.013 0.021

Cov (black, other) 0.001 0.046

Cov (Hispanic, other) 0.005 0.049

Var (residual) 0.824 0.040 0.688 0.034 0.704 0.030 0.612 0.021

obs 9001 2124 9501 5737

groups 1031 709 931 863

ln L -12307 -2810 -12393 -7277
86

Federal Sentencing Disparity, 2005–2012 

Figure B.4 – Changes over time for three guideline cells: Females

No drugs, no substantial assistance No drugs, substantial assistance

Drugs, no substantial assistance Drugs, substantial assistance

-3

-2

-1

0

1

2

3

4

2005 2006 2007 2008 2009 2010 2011 2012

Difference in months

Year

27 Months 37 Months 57 Months

-2

-1

0

1

2

3

4

2005 2006 2007 2008 2009 2010 2011 2012

Difference in months

Year

33 Months 41 Months 63 Months

0

0.5

1

1.5

2

2.5

3

2005 2006 2007 2008 2009 2010 2011 2012

Difference in months

Year

46 Months 63 Months 105 Months

0

0.5

1

1.5

2

2.5

3

2005 2006 2007 2008 2009 2010 2011 2012

Difference in months

Year

46 Months 63 Months 105 Months
87

Federal Sentencing Disparity, 2005–2012 

Figure B.5 – Predicted and actual sentences across maximum sentence in guideline cells: Females

No drugs, no substantial assistance No drugs, substantial assistance

Drugs, No Substantial Assistance Drugs, Substantial Assistance

Note. Dashed line is a quadratic trend fit to the predicted difference.

-100

-50

0

50

100

Difference in months

Maximum sentence for the guideline cell ...

Actual_Difference Predicted_Difference

-30

-10

10

30

50

Difference in months

Maximum sentence for the guideline cell (188 ...

Actual_Difference Predicted_Difference

-50

0

50

100

Difference in months

Maximum sentence for the guideline cell (470 

maximum)

Actual_Difference Predicted_Difference

-40

-20

0

20

Difference in months

Maximum sentence for the guideline cell (365 

maximum)

Actual_Difference Predicted_Difference
88

Federal Sentencing Disparity, 2005–2012 

Figure B.6 – Differences in judge distributions: Females

No drugs, no substantial assistance No drugs, substantial assistance

Drugs, no substantial assistance Drugs, substantial assistance
89

Federal Sentencing Disparity, 2005–2012 

Data partition: Weapons offenders, no sex offenders

Table B.4 – Parameter estimates from mixed models: Weapons offenders

No drugs, no substantial 

assistance

No drugs, substantial 

assistance

Drugs, no substantial 

assistance Drugs, substantial assistance

Variable Est Std err p Est Std err p Est Std err p Est Std err P

Year x Pre-Gall -0.460 0.222 0.039 -0.733 0.420 0.081 -0.640 0.202 0.002 -0.176 0.267 0.509

Year x Post-Gall -0.013 0.089 0.879 -0.013 0.195 0.949 -0.509 0.083 <0.001 -0.191 0.106 0.072

Race/Ethnicity: Non-Hispanic black 0.022 0.082 0.790 0.021 0.177 0.908 -0.035 0.084 0.676 0.118 0.113 0.296

Race/Ethnicity: Hispanic 0.209 0.135 0.121 -0.004 0.233 0.986 0.014 0.112 0.900 0.346 0.161 0.032

Race/Ethnicity: Non-Hispanic other -0.425 0.093 <0.001 0.133 0.409 0.745 -0.400 0.168 0.017 0.106 0.208 0.611

Black x Year x Pre-Gall 0.741 0.262 0.005 0.632 0.522 0.226 0.578 0.246 0.019 0.116 0.326 0.722

Hispanic x Year x Pre-Gall -0.231 0.394 0.558 0.525 0.688 0.445 -0.021 0.324 0.948 -0.697 0.473 0.140

Other x Year x Pre-Gall 0.433 0.298 0.146 -1.291 1.263 0.307 1.166 0.592 0.049 -0.451 0.631 0.475

Black x Year x Post-Gall 0.033 0.111 0.767 -0.048 0.228 0.833 -0.028 0.102 0.782 -0.023 0.141 0.869

Hispanic x Year x Post-Gall -0.015 0.129 0.906 -0.320 0.315 0.310 0.230 0.118 0.052 0.044 0.166 0.793

Other x Year x Post-Gall -0.033 0.134 0.805 0.616 0.498 0.216 -0.036 0.369 0.922 0.238 0.366 0.516

Max Sentence in Guideline Cell -0.289 0.076 <0.001 0.581 0.174 0.001 -0.213 0.084 0.011 0.098 0.098 0.316

Black x Max Sentence -0.317 0.083 <0.001 -0.456 0.200 0.022 -0.126 0.094 0.181 -0.189 0.120 0.115

Hispanic x Max Sentence -0.200 0.122 0.100 -0.380 0.246 0.122 -0.019 0.112 0.866 -0.202 0.153 0.186

Other x Max Sentence 0.533 0.140 <0.001 0.662 0.499 0.184 0.060 0.234 0.798 -0.012 0.280 0.967

Sentence is a new conviction 0.751 0.038 <0.001 0.530 0.312 0.089 0.425 0.032 <0.001 0.203 0.233 0.383

CH Points: Category 1 0.004 0.013 0.769 0.024 0.018 0.172 0.037 0.013 0.004 0.025 0.017 0.127

CH Points: Category 2 0.024 0.019 0.218 -0.028 0.040 0.491 0.042 0.025 0.089 0.009 0.014 0.521

CH Points: Category 3 0.018 0.017 0.306 0.027 0.039 0.487 0.048 0.018 0.007 0.014 0.024 0.568

CH Points: Category 4 -0.047 0.017 0.007 0.015 0.040 0.704 0.021 0.025 0.394 -0.007 0.039 0.851

CH Points: Category 5 -0.051 0.030 0.093 -0.139 0.087 0.111 -0.006 0.033 0.862 0.018 0.018 0.329

CH Points: Category 6 0.012 0.017 0.480 0.077 0.033 0.021 0.109 0.018 <0.001 0.064 0.023 0.006

Circuit: DC -0.210 0.133 0.115 -0.563 0.170 0.001 -0.252 0.097 0.009 -1.464 0.113 <0.001

Circuit: 1 0.085 0.080 0.289 0.202 0.109 0.064 0.188 0.065 0.004 -0.156 0.147 0.288

Circuit: 2 -0.186 0.051 <0.001 -0.498 0.085 <0.001 -0.045 0.072 0.535 -1.022 0.114 <0.001

Circuit: 3 0.167 0.056 0.003 0.025 0.087 0.777 0.116 0.074 0.119 -0.193 0.100 0.052

Circuit: 4 0.370 0.048 <0.001 0.417 0.091 <0.001 0.420 0.052 <0.001 0.302 0.090 0.001

Circuit: 5 0.135 0.048 0.005 0.320 0.086 <0.001 0.425 0.060 <0.001 0.327 0.086 <0.001

Circuit: 6 0.246 0.045 <0.001 0.494 0.080 <0.001 0.246 0.059 <0.001 0.234 0.092 0.011

Circuit: 7 0.164 0.053 0.002 0.389 0.102 <0.001 0.269 0.074 <0.001 0.345 0.094 <0.001

Circuit: 8 0.053 0.043 0.219 0.082 0.086 0.336 0.209 0.054 <0.001 0.100 0.102 0.326
90

Federal Sentencing Disparity, 2005–2012 

No drugs, no substantial 

assistance

No drugs, substantial 

assistance

Drugs, no substantial 

assistance Drugs, substantial assistance

Variable Est Std err p Est Std err p Est Std err p Est Std err P

Circuit: 10 0.043 0.045 0.347 0.007 0.096 0.939 0.108 0.060 0.071 -0.077 0.093 0.404

Circuit: 11 0.361 0.051 <0.001 0.648 0.090 <0.001 0.511 0.060 <0.001 0.438 0.092 <0.001

Intercept -0.121 0.078 0.119 -0.207 0.152 0.173 -0.015 0.078 0.849 -0.102 0.113 0.369

Random effects

Var (white) 0.043 0.009 0.063 0.030 0.081 0.013 0.164 0.021

Var (black) 0.073 0.010 0.158 0.029 0.149 0.022 0.205 0.028

Var (Hispanic) 0.044 0.031 0.004 0.070 0.000 0.000 0.000 0.000

Var (other) 0.001 0.006 0.035 0.072 0.075 0.059 0.187 0.083

Cov (white, black)

Cov (white, Hispanic)

Cov (white, other)

Cov (black, Hispanic)

Cov (black, other)

Cov (Hispanic, other)

Var (residual) 0.677 0.023 0.724 0.035 0.809 0.026 0.633 0.020

obs 15035 3462 14500 6771

groups 1039 749 1026 878

ln L -19937 -4285 -19604 -8578
91

Federal Sentencing Disparity, 2005–2012 

Figure B.7 – Changes over time for three guideline cells: Weapons offenders

No drugs, no substantial assistance No drugs, substantial assistance

Drugs, no substantial assistance Drugs, substantial assistance

0

10

20

30

Difference in months

2005 2006 2007 2008 2009 2010 2011 2012

Year

51 Months 87 Months 151 Months

-10

-5

0

5

10

15

Difference in months

2005 2006 2007 2008 2009 2010 2011 2012

Year

57 Months 96 Months 175 Months

-2

0

2

4

6

8

2005 2006 2007 2008 2009 2010 2011 2012

Difference in months

Year

87 Months 151 Months 235 Months

0

1

2

3

4

5

2005 2006 2007 2008 2009 2010 2011 2012

Difference in months

Year

108 Months 168 Months 262 Months
92

Federal Sentencing Disparity, 2005–2012 

Figure B.8 – Predicted and actual sentences across maximum sentence in guideline cells: Weapons offenders

No drugs, no substantial assistance No drugs, substantial assistance

Drugs, no substantial assistance Drugs, substantial assistance

Note. Dashed line is a quadratic trend fit to the predicted difference.

-10

0

10

20

30

40

50

16 27 37 51 71 96 108125150168210293405

Difference in months

Maximum sentence for the guideline cell (470 

maximum)

Actual_Difference Predicted_Difference

-80

-60

-40

-20

0

20

40

60

16 27 37 51 71 96 108125150168210293405

Difference in months

Maximum sentence for the guideline cell (470 

maximum)

Actual_Difference Predicted_Difference

-20

-10

0

10

20

30

16 27 37 51 71 96 108125150168210293405

Difference in months

Maximum sentence for the guideline cell (470 

maximum)

Actual_Difference Predicted_Difference

-30

-20

-10

0

10

20

30

21 30 41 57 78 97 115 135 151 175 235 327 470

Difference in months

Maximum sentence for the guideline cell (470 

maximum)

Actual_Difference Predicted_Difference
93

Federal Sentencing Disparity, 2005–2012 

Figure B.9 – Differences in judge distributions: Weapons offenders

No drugs, no substantial assistance No drugs, substantial assistance

Drugs, no substantial assistance Drugs, substantial assistance
94

Federal Sentencing Disparity, 2005–2012 

Data partition: Sex offenders

Table B.5 – Parameter estimates from mixed models: Sex offenders

No substantial assistance Substantial assistance

Variable Est Std err p Est Std err p

Year x Pre-Gall -0.404 0.147 0.006 -0.362 0.720 0.615

Year x Post-Gall -0.658 0.055 <0.001 0.020 0.270 0.942

Race/Ethnicity: Non-Hispanic black 0.616 0.385 0.110 2.751 0.638 <0.001

Race/Ethnicity: Hispanic 0.076 0.242 0.753 0.427 0.774 0.581

Race/Ethnicity: Non-Hispanic other 0.050 0.118 0.672 1.197 0.785 0.127

Black x Year x Pre-Gall -1.955 1.136 0.085 -9.122 2.351 <0.001

Hispanic x Year x Pre-Gall -0.574 0.737 0.436 0.039 2.388 0.987

Other x Year x Pre-Gall -0.541 0.403 0.180 -5.341 2.159 0.013

Black x Year x Post-Gall 0.238 0.227 0.294 1.144 0.699 0.102

Hispanic x Year x Post-Gall 0.172 0.196 0.381 -1.071 0.963 0.266

Other x Year x Post-Gall 0.519 0.184 0.005 3.116 1.547 0.044

Max Sentence in Guidelines Cell -0.043 0.047 0.367 0.001 0.198 0.997

Black x Max Sentence -0.082 0.158 0.601 -0.044 0.604 0.941

Hispanic x Max Sentence 0.088 0.173 0.612 -0.527 0.724 0.467

Other x Max Sentence -0.235 0.127 0.065 -1.079 0.975 0.269

Sentence is a new conviction 0.303 0.039 <0.001

CH Points: Category 1 0.079 0.012 <0.001 0.053 0.033 0.106

CH Points: Category 2 0.060 0.037 0.108 0.160 0.140 0.253

CH Points: Category 3 0.132 0.034 <0.001 -0.093 0.177 0.599

CH Points: Category 4 -0.002 0.053 0.970 0.197 0.166 0.237

CH Points: Category 5 -0.029 0.013 0.028 0.014 0.050 0.776

CH Points: Category 6 -0.052 0.081 0.521 -0.964 0.495 0.051

Circuit: DC 0.002 0.085 0.982 -0.489 0.380 0.199

Circuit: 1 0.149 0.089 0.093 0.448 0.581 0.440

Circuit: 2 -0.156 0.062 0.012 -0.147 0.209 0.484

Circuit: 3 0.076 0.054 0.162 -0.214 0.148 0.149

Circuit: 4 0.307 0.056 <0.001 -0.045 0.162 0.778

Circuit: 5 0.481 0.057 <0.001 0.316 0.316 0.318

Circuit: 6 0.198 0.052 <0.001 0.004 0.146 0.979

Circuit: 7 0.364 0.064 <0.001 0.367 0.137 0.007

Circuit: 8 0.161 0.049 0.001 -0.030 0.172 0.863

Circuit: 10 0.111 0.049 0.023 0.434 0.208 0.037
95

Federal Sentencing Disparity, 2005–2012 

No substantial assistance Substantial assistance

Variable Est Std err p Est Std err p

Circuit: 11 0.309 0.052 <0.001 -0.039 0.164 0.814

Intercept 0.113 0.055 0.039 0.126 0.231 0.587

Random effects

Var (white) 0.090 0.008 0.105 0.077

Var (black) 0.243 0.088 0.000 .

Var (Hispanic) 0.118 0.091 0.268 0.377

Var (other) 0.136 0.038 0.243 0.273

Cov (white, black)

Cov (white, Hispanic)

Cov (white, other)

Cov (black, Hispanic)

Cov (black, other)

Cov (Hispanic, other)

Var (residual) 0.819 0.024 0.683 0.075

obs 15011 504

groups 1067 287

ln L -20369 -652
96

Federal Sentencing Disparity, 2005–2012 

Figure B.10 – Changes over time for three guideline cells: Sex offenders

No substantial assistance Substantial assistance

-10

-5

0

5

10

15

20

2005 2006 2007 2008 2009 2010 2011 2012

Difference in months

Year

71 Months 108 Months 188 Months

-40

-20

0

20

40

60

80

100

2005 2006 2007 2008 2009 2010 2011 2012

Difference in months

Year

87 Months 262 Months
97

Federal Sentencing Disparity, 2005–2012 

Figure B.11 – Predicted and actual sentences across maximum sentence in guideline cells: Sex offenders

No Substantial Assistance Substantial Assistance

Note. Dashed line is a quadratic trend fit to the predicted difference.

-40

-20

0

20

40

16 27 37 51 71 96 108 125 150 175 235 327 470

Difference in months

Maximum sentence for the guideline cell (470 

maximum)

Actual_Difference Predicted_Difference

-100

-50

0

50

57 78 87 108 121 135 151 210 262 293

Difference in months

Maximum sentence for the guideline cell (293 

maximum)

Actual_Difference Predicted_Difference
98

Federal Sentencing Disparity, 2005–2012 

Figure B.12 – Differences in judge distributions: Sex offenders

No substantial assistance Substantial assistance
99

Federal Sentencing Disparity, 2005–2012 

Appendix C: Detailed findings for sentencing disparity: Non-U.S. citizens

Tables and figures appearing in this appendix are the counterparts to the tables and figures appearing in appendix B. The sentencing of 

noncitizens is discussed here.

Table C.1 – Number of observations for each guideline cell - Citizens

Criminal history category

Offense level I II III IV V VI

1

2

3

4

5

6 254

7 5 12

8 80 76

9 26 9 12

10 10,540 7,624 4,118 2,823

11 42 40 54

12 454 203 92 75

13 2,400 3,508 2,756 1,835 2,154

14 213 240 124 84 98

15 754 555 231 95 86

16 111 121 47 45 47

17 2,116 2,856 1,494 652 426

18 855 162 171 68 33 28

19 3,487 271 257 116 48 30

20 642 92 91 40 24 9

21 6,734 6,922 11,625 7,826 4,428 3,891

22 958 317 464 285 186 160

23 4,584 726 641 196 110 48

24 1,724 120 140 85 72 78

25 2,447 517 345 112 45 39

26 1,175 127 113 40 19 19

27 4,771 288 243 68 26 19
100

Federal Sentencing Disparity, 2005–2012 

Criminal history category

Offense level I II III IV V VI

28 617 104 80 30 11 5

29 3,192 524 419 110 44 126

30 493 84 84 21 16 18

31 2,231 459 367 105 36 149

32 532 75 68 24 2 23

33 2,432 269 235 55 26 23

34 497 80 88 23 3 220

35 1,216 235 182 51 19 65

36 384 63 40 23 6

37 533 96 66 19 4 54

38 425 68 41 9 2 19

39 312 38 42 3 3 7

40 239 43 38 6 6 6

41 116 31 17 3 3

42 119 21 18 3 3 2

43 259 49 38 18 46
101

Federal Sentencing Disparity, 2005–2012 

Data partition: Males, no weapons offenses, no sex offenders

Table C.2 – Parameter estimates from mixed models: Males

No drugs, no substantial 

assistance

No drugs, substantial 

assistance

Drugs, no substantial 

assistance Drugs, substantial assistance

Variable Est Std err p Est Std err p Est Std err p Est Std err p

Year x Pre-Gall -0.180 0.257 0.483 -0.203 0.680 0.765 0.251 0.244 0.304 0.493 0.415 0.235

Year x Post-Gall -0.285 0.124 0.021 0.138 0.256 0.589 -0.833 0.106 <0.001 -0.324 0.171 0.059

Race/Ethnicity: Non-Hispanic black 0.109 0.113 0.335 -0.111 0.303 0.715 -0.057 0.083 0.493 0.032 0.105 0.765

Race/Ethnicity: Hispanic -0.189 0.091 0.037 0.262 0.248 0.291 0.262 0.086 0.002 0.323 0.123 0.009

Race/Ethnicity: Non-Hispanic other 0.051 0.222 0.819 -0.039 0.337 0.907 0.147 0.205 0.473 -0.050 0.206 0.808

Black x Year x Pre-Gall 0.322 0.356 0.365 0.714 0.981 0.466 0.172 0.261 0.511 0.212 0.345 0.538

Hispanic x Year x Pre-Gall 0.258 0.257 0.315 -0.072 0.764 0.925 -0.491 0.251 0.050 -0.296 0.410 0.470

Other x Year x Pre-Gall -0.179 0.753 0.812 0.574 1.048 0.584 -0.621 0.629 0.323 0.163 0.689 0.813

Black x Year x Post-Gall -0.522 0.167 0.002 -0.138 0.369 0.708 -0.058 0.144 0.687 -0.246 0.195 0.207

Hispanic x Year x Post-Gall -0.025 0.128 0.847 -0.230 0.297 0.438 0.633 0.119 <0.001 0.193 0.175 0.269

Other x Year x Post-Gall -0.159 0.312 0.610 -0.605 0.357 0.090 -0.020 0.311 0.949 -0.144 0.326 0.659

Max Sentence in Guideline Cell -0.638 0.159 <0.001 0.731 0.397 0.065 -0.397 0.134 0.003 0.220 0.143 0.123

Black x Max Sentence 0.284 0.263 0.280 0.155 0.491 0.753 0.314 0.153 0.040 -0.080 0.161 0.620

Hispanic x Max Sentence 1.432 0.229 <0.001 -0.773 0.403 0.055 -0.167 0.134 0.211 -0.168 0.148 0.256

Other x Max Sentence 0.738 0.339 0.030 0.161 0.619 0.795 -0.084 0.271 0.756 -0.521 0.377 0.167

Sentence is a new conviction 0.229 0.045 <0.001 0.285 0.267 0.286 0.232 0.032 <0.001 0.122 0.155 0.433

CH Points: Category 1 0.029 0.011 0.008 0.070 0.038 0.071 0.063 0.008 <0.001 0.011 0.014 0.421

CH Points: Category 2 0.055 0.011 <0.001 0.041 0.065 0.525 0.033 0.022 0.141 0.010 0.028 0.721

CH Points: Category 3 0.069 0.008 <0.001 -0.079 0.055 0.154 0.046 0.020 0.019 0.066 0.034 0.058

CH Points: Category 4 0.061 0.009 <0.001 -0.067 0.079 0.393 0.051 0.035 0.151 0.070 0.083 0.397

CH Points: Category 5 0.052 0.010 <0.001 -0.030 0.137 0.825 -0.006 0.029 0.826 0.049 0.162 0.763

CH Points: Category 6 0.138 0.019 <0.001 0.047 0.128 0.715 0.014 0.038 0.708 -0.001 0.067 0.993

Circuit: DC 0.520 0.119 <0.001 -0.461 0.188 0.014 -0.439 0.150 0.003 -1.328 0.138 <0.001

Circuit: 1 0.285 0.100 0.004 -0.154 0.176 0.381 0.223 0.078 0.004 -0.130 0.141 0.357

Circuit: 2 0.168 0.062 0.007 -0.797 0.097 <0.001 -0.175 0.060 0.004 -1.248 0.092 <0.001

Circuit: 3 0.279 0.068 <0.001 -0.244 0.092 0.008 0.317 0.062 <0.001 -0.390 0.071 <0.001

Circuit: 4 0.725 0.073 <0.001 0.316 0.111 0.005 0.573 0.054 <0.001 0.067 0.076 0.376

Circuit: 5 0.892 0.054 <0.001 0.173 0.075 0.022 0.531 0.044 <0.001 0.227 0.065 <0.001

Circuit: 6 0.542 0.067 <0.001 0.169 0.118 0.151 0.334 0.066 <0.001 0.096 0.070 0.170

Circuit: 7 0.546 0.061 <0.001 0.206 0.152 0.174 0.356 0.059 <0.001 0.335 0.070 <0.001

Circuit: 8 0.518 0.065 <0.001 -0.169 0.191 0.377 0.426 0.044 <0.001 0.004 0.093 0.964
102

Federal Sentencing Disparity, 2005–2012 

No drugs, no substantial 

assistance

No drugs, substantial 

assistance

Drugs, no substantial 

assistance Drugs, substantial assistance

Variable Est Std err p Est Std err p Est Std err p Est Std err p

Circuit: 10 0.203 0.067 0.002 -0.076 0.106 0.476 0.218 0.055 <0.001 -0.008 0.080 0.919

Circuit: 11 0.686 0.056 <0.001 0.317 0.075 <0.001 0.556 0.045 <0.001 0.332 0.057 <0.001

Intercept -0.148 0.092 0.107 -0.078 0.223 0.726 -0.197 0.090 0.029 -0.222 0.131 0.089

Random effects

Var (white) 0.161 0.016 0.085 0.028 0.089 0.010 0.130 0.019

Var (black) 0.444 0.098 0.123 0.112 0.134 0.033 0.274 0.077

Var (Hispanic) 0.113 0.017 0.000 0.000 0.019 0.008 0.043 0.018

Var (other) 0.651 0.195 0.185 0.089 0.523 0.129 0.336 0.077

Var (residual) 0.726 0.033 0.714 0.038 0.739 0.034 0.513 0.019

obs 87399 1918 29042 6609

groups 1141 597 1062 893

ln L -111812 -2510 -37639 -7761
Federal Sentencing Disparity, 2005–2012 103

Figure C.1 – Changes over time for three guideline cells: Males

No drugs, no substantial assistance No drugs, substantial assistance

Drugs, no substantial assistance Drugs, substantial assistance

-1

0

1

2

3

4

2005 2006 2007 2008 2009 2010 2011 2012

Difference in months

Year

24 Months 41 Months 57 Months

-1

0

1

2

3

4

2005 2006 2007 2008 2009 2010 2011 2012

Difference in months

Year

37 Months 57 Months 71 Months

-0.5

0

0.5

1

1.5

2

Difference in months

2005 2006 2007 2008 2009 2010 2011 2012

Year

46 Months 71 Months 108 Months

-4

-2

0

2

4

Difference in months

2005 2006 2007 2008 2009 2010 2011 2012

Year

63 Months 108 Months 168 Months
Federal Sentencing Disparity, 2005–2012 104

Figure C.2 – Predicted and actual sentences across maximum sentence in guideline cells: Males

No drugs, no substantial assistance No drugs, substantial assistance

Drugs, no substantial assistance Drugs, substantial assistance

Note. Dashed line is a quadratic trend fit to the predicted difference.

-150

-100

-50

0

50

100

Difference in months

Maximum sentence for the guideline cell (470 

maximum)

Actual_Difference Predicted_Difference

-20

0

20

40

60

Difference in months

Maximum sentence for the guideline cell (188 

maximum)

Actual_Difference Predicted_Difference

-20

0

20

40

60

Difference in months

Maximum sentence for the guideline cell (470 

maximum)

Actual_Difference Predicted_Difference

-80

-60

-40

-20

0

20

Difference in months

Maximum sentence for the guideline cell (365 

maximum)

Actual_Difference Predicted_Difference
Federal Sentencing Disparity, 2005–2012 105

Figure C.3 – Differences in judge distributions: Males

No drugs, no substantial assistance No drugs, substantial assistance

Drugs, no substantial assistance Drugs, substantial assistance
Federal Sentencing Disparity, 2005–2012 106

Data partition: Females, no weapons offenses, no sex offenders

Table C.3 – Parameter Estimates from mixed models: Females, no weapons offenses, no sex offenders

No drugs Drugs

Variable Est Std err p Est Std err p

Year x Pre-Gall -0.829 1.303 0.525 -1.170 0.716 0.102

Year x Post-Gall -0.658 0.341 0.054 0.059 0.211 0.780

Race/Ethnicity: Non-Hispanic black -0.039 0.512 0.939 -0.265 0.272 0.330

Race/Ethnicity: Hispanic -0.154 0.462 0.739 0.291 0.260 0.262

Race/Ethnicity: Non-Hispanic other -0.350 0.674 0.604 -0.735 0.353 0.037

Black x Year x Pre-Gall 0.002 1.649 0.999 1.386 0.865 0.109

Hispanic x Year x Pre-Gall 0.671 1.331 0.614 0.328 0.762 0.667

Other x Year x Pre-Gall 1.441 2.060 0.484 2.624 1.049 0.012

Black x Year x Post-Gall 0.523 0.604 0.386 -0.472 0.337 0.162

Hispanic x Year x Post-Gall 0.275 0.353 0.436 -0.321 0.241 0.183

Other x Year x Post-Gall 0.618 0.552 0.264 -1.400 0.482 0.004

Max Sentence in Guideline Cell 0.452 0.699 0.517 0.392 0.539 0.467

Black x Max Sentence 0.553 0.975 0.571 0.522 0.634 0.410

Hispanic x Max Sentence -0.683 0.770 0.375 -0.663 0.554 0.231

Other x Max Sentence -2.502 1.440 0.082 0.305 0.714 0.669

Sentence is a new conviction 0.428 0.105 <0.001 0.438 0.085 <0.001

CH Points: Category 1 0.034 0.046 0.462 0.031 0.036 0.397

CH Points: Category 2 0.028 0.052 0.584 0.033 0.096 0.733

CH Points: Category 3 0.104 0.034 0.002 0.029 0.103 0.779

CH Points: Category 4 0.071 0.063 0.259 0.587 0.220 0.008

CH Points: Category 5 0.060 0.074 0.417 0.345 0.715 0.629

CH Points: Category 6 0.152 0.105 0.149 0.080 0.147 0.588

Circuit: DC 0.131 0.312 0.674 -1.088 0.208 <0.001

Circuit: 1 0.105 0.167 0.530 -0.008 0.212 0.971

Circuit: 2 -0.306 0.093 0.001 -0.654 0.084 <0.001

Circuit: 3 0.095 0.143 0.505 -0.313 0.115 0.006

Circuit: 4 0.426 0.113 <0.001 0.384 0.126 0.002

Circuit: 5 0.541 0.090 <0.001 0.632 0.075 <0.001

Circuit: 6 0.188 0.212 0.375 -0.126 0.144 0.382

Circuit: 7 0.278 0.146 0.056 0.124 0.100 0.215

Circuit: 8 0.114 0.184 0.536 0.378 0.118 0.001

Circuit: 10 0.108 0.121 0.370 0.105 0.110 0.339
Federal Sentencing Disparity, 2005–2012 107

Circuit: 11 0.524 0.079 <0.001 0.553 0.081 <0.001

Intercept 0.096 0.454 0.833 -0.032 0.254 0.901

Random effects

Var (white) 0.118 0.057 0.051 0.034

Var (black) 0.570 0.188 0.224 0.061

Var (Hispanic) 0.064 0.054 0.078 0.044

Var (other) 0.325 0.143 0.296 0.120

Var (residual) 0.704 0.037 0.620 0.037

obs 2847 2833

groups 593 615

ln L -3759 -3531
Federal Sentencing Disparity, 2005–2012 108

Figure C.4 – Changes over time for three guideline cells: Females

Figure C.5 – Predicted and actual sentences across maximum sentence in guideline cells: Females

No drugs Drugs

Note. Dashed line is a quadratic trend fit to the predicted difference.

-20

0

20

40

Difference in months

Maximum sentence for the guideline cell (108 

maximum)

Actual_Difference Predicted_Difference

-100

-50

0

50

Difference in months

Maximum sentence for the guideline cell (235 

maximum)

Actual_Difference Predicted_Difference

No drugs Drugs

-1

0

1

2

3

4

5

6

Difference in months

2005 2006 2007 2008 2009 2010 2011 2012

Year

24 Months 41 Months 57 Months

-5

0

5

10

15

Difference in months

2005 2006 2007 2008 2009 2010 2011 2012

Year

51 Months 63 Months 97 Months
Federal Sentencing Disparity, 2005–2012 109

Figure C.6 – Differences in judge distributions: Females

No drugs Drugs
Federal Sentencing Disparity, 2005–2012 110

Data partition: Weapons offenders, no sex offenders

Table C.4 – Parameter estimates from mixed models: Weapons offenders

No drugs Drugs

Variable Est Std err p Est Std err p

Year x Pre-Gall 0.987 0.897 0.271 -2.801 1.116 0.012

Year x Post-Gall -0.220 0.367 0.550 0.440 0.298 0.140

Race/Ethnicity: Non-Hispanic black 0.493 0.362 0.173 -0.071 0.368 0.847

Race/Ethnicity: Hispanic 0.521 0.290 0.072 -0.551 0.412 0.181

Race/Ethnicity: Non-Hispanic other 0.671 0.544 0.218 -1.503 0.514 0.003

Black x Year x Pre-Gall -0.212 1.147 0.854 0.861 0.953 0.366

Hispanic x Year x Pre-Gall -1.281 0.918 0.163 2.264 1.104 0.040

Other x Year x Pre-Gall -2.101 1.569 0.181 4.105 1.376 0.003

Black x Year x Post-Gall -0.549 0.405 0.176 -0.663 0.318 0.037

Hispanic x Year x Post-Gall 0.308 0.361 0.393 -0.650 0.299 0.030

Other x Year x Post-Gall -0.074 0.503 0.882 -0.884 0.453 0.051

Max Sentence in Guidelines Cell 0.126 0.235 0.591 0.050 0.277 0.858

Black x Max Sentence -0.364 0.257 0.158 -0.242 0.278 0.384

Hispanic x Max Sentence -0.429 0.230 0.062 -0.172 0.271 0.526

Other x Max Sentence -0.160 0.358 0.654 0.454 0.377 0.229

Sentence is a new conviction 0.572 0.078 <0.001 0.441 0.063 <0.001

CH Points: Category 1 0.049 0.031 0.118 0.055 0.020 0.007

CH Points: Category 2 -0.039 0.071 0.582 0.087 0.043 0.043

CH Points: Category 3 0.086 0.050 0.083 -0.025 0.039 0.522

CH Points: Category 4 -0.011 0.060 0.857 0.078 0.084 0.351

CH Points: Category 5 0.012 0.047 0.805 0.026 0.087 0.760

CH Points: Category 6 0.063 0.063 0.316 0.010 0.074 0.888

Circuit: DC -0.078 0.152 0.606 -0.103 0.181 0.570

Circuit: 1 0.563 0.151 <0.001 0.085 0.160 0.596

Circuit: 2 -0.185 0.084 0.028 -0.812 0.101 <0.001

Circuit: 3 0.319 0.127 0.012 -0.237 0.130 0.067

Circuit: 4 0.515 0.100 <0.001 0.393 0.072 <0.001

Circuit: 5 0.096 0.099 0.331 0.203 0.066 0.002

Circuit: 6 0.115 0.136 0.399 0.050 0.098 0.607

Circuit: 7 0.165 0.124 0.183 0.214 0.092 0.020

Circuit: 8 0.008 0.151 0.956 0.218 0.064 0.001

Circuit: 10 0.140 0.124 0.259 0.012 0.073 0.867
Federal Sentencing Disparity, 2005–2012 111

No drugs Drugs

Variable Est Std err p Est Std err p

Circuit: 11 0.567 0.103 <0.001 0.412 0.071 <0.001

Intercept -0.565 0.282 0.045 0.682 0.418 0.103

Random effects

Var (white) 0.139 0.039 0.099

Var (black) 0.112 0.084 0.167

Var (Hispanic) 0.055 0.041 0.000

Var (other) 0.036 0.088 0.000

Var (residual) 0.646 0.043 0.756

Obs 2256 4408

Groups 564 749

ln L -2886 -5831
Federal Sentencing Disparity, 2005–2012 112

Figure C.7 – Changes over time for three guideline cells: Weapons offenders

Figure C.8 – Predicted and actual sentences across maximum sentence in guideline cells: Weapons offenders

No drugs Drugs

Note. Dashed line is a quadratic trend fit to the predicted difference.

-100

-50

0

50

100

Difference in months

Maximum sentence for the guideline cell (470 

maximum)

Actual_Difference Predicted_Difference

-60

-40

-20

0

20

40

Difference in months

Maximum sentence for the guideline cell (470 

maximum)

Actual_Difference Predicted_Difference

No drugs Drugs

-10

0

10

20

30

40

Difference in months

2005 2006 2007 2008 2009 2010 2011 2012

Year

51 Months 78 Months 168 Months

-20

-10

0

10

Difference in months

2005 2006 2007 2008 2009 2010 2011 2012

Year

97 Months 151 Months 235 Months
Federal Sentencing Disparity, 2005–2012 113

Figure C.9 – Differences in judge distributions: Weapons offenders

No drugs Drugs
Federal Sentencing Disparity, 2005–2012 114

Data partition: Sex offenders

Table C.6 – Parameter estimates from mixed models: Sex offenders

Variable Est Std err p

Year x Pre-Gall -1.171 0.921 0.203

Year x Post-Gall 0.017 0.390 0.965

Race/Ethnicity: Non-Hispanic black 0.219 0.844 0.795

Race/Ethnicity: Hispanic -0.117 0.540 0.829

Race/Ethnicity: Non-Hispanic other -0.940 0.603 0.119

Black x Year x Pre-Gall -1.958 2.657 0.461

Hispanic x Year x Pre-Gall 0.887 1.717 0.605

Other x Year x Pre-Gall 2.846 1.943 0.143

Black x Year x Post-Gall -0.057 0.734 0.938

Hispanic x Year x Post-Gall -0.400 0.468 0.392

Other x Year x Post-Gall -0.823 0.761 0.279

Max Sentence in Guidelines Cell -0.156 0.332 0.637

Black x Max Sentence 0.374 0.893 0.675

Hispanic x Max Sentence 0.220 0.440 0.616

Other x Max Sentence 0.103 0.472 0.827

Sentence is a new conviction 0.145 0.150 0.333

CH Points: Category 1 0.128 0.088 0.146

CH Points: Category 2 -0.210 0.172 0.222

CH Points: Category 3 -0.181 0.270 0.504

CH Points: Category 4 n/a n/a n/a

CH Points: Category 5 n/a n/a n/a

CH Points: Category 6 n/a n/a n/a

Circuit: DC -0.554 0.223 0.013

Circuit: 1 -0.167 0.385 0.665

Circuit: 2 -0.129 0.188 0.491

Circuit: 3 -0.041 0.196 0.835

Circuit: 4 0.327 0.164 0.045

Circuit: 5 0.145 0.177 0.412

Circuit: 6 0.210 0.177 0.234

Circuit: 7 0.628 0.340 0.065

Circuit: 8 0.171 0.154 0.267

Circuit: 10 -0.049 0.298 0.869

Circuit: 11 0.195 0.134 0.145
Federal Sentencing Disparity, 2005–2012 115

Variable Est Std err p

Intercept 0.356 0.263 0.177

Random effects

Var (white) 0.109 0.101

Var (black) n/a n/a

Var (Hispanic) 0.127 0.136

Var (other) 0.519 0.282

Var (residual) 0.637 0.106

obs 541

groups 327

ln L -721
Federal Sentencing Disparity, 2005–2012 116

Figure C.10 – Changes over time for three guideline cells: Sex offenders

Figure C.11 – Predicted and actual sentences across maximum sentence in guideline cells: Sex offenders

Note. Dashed line is a quadratic trend fit to the predicted difference.

-150

-100

-50

0

50

Difference in months

Maximum sentence for the guideline cell (293 maximum)

Actual_Difference Predicted_Difference

-12

-10

-8

-6

-4

-2

0

2

2005 2006 2007 2008 2009 2010 2011 2012

Difference in months

Year

60 Months 97 Months
Federal Sentencing Disparity, 2005–2012 117

Figure C.12 – Differences in judge distributions: Sex offenders
Federal Sentencing Disparity, 2005–2012 118

Appendix D: Detailed findings for prosecutorial discretion

This appendix presents tables and figures pertaining to prosecutorial discretion.

Figure D.1 – Cocaine: 500g Threshold

Figure D.2 – Cocaine: 5000g Threshold

0%

5%

10%

15%

20%

25%

30%

35%

400420440460480500520540560580600

Proportion of offenders (+/-) 100 gms. of 

the threshold 

Grams of cocaine

Whites Blacks Hispanics

-10%

0%

10%

20%

30%

40%

50%

60%

70%

80%

4,5004,6004,7004,8004,9005,0005,1005,2005,3005,4005,500

Proportion of offenders (+/-) 500 gms. of 

the threshold 

Grams of cocaine

Whites Blacks Hispanics
Federal Sentencing Disparity, 2005–2012 119

Figure D.3 – Crack, Pre-2010: 5g Threshold

Figure D.4 – Crack, Pre-2010: 50g Threshold

0%

5%

10%

15%

20%

25%

Proportion of offenders (+/

2345678

-) 3 gms. 

of the threshold 

Grams of Crack

Whites Blacks Hispanics

0%

10%

20%

30%

40%

50%

4042444648505254565860

Proportion of offenders (+/-) 10 gms. 

of the threshold 

Grams of Crack

Whites Blacks Hispanics
Federal Sentencing Disparity, 2005–2012 120

Figure D.5 – Crack, Post-2010: 28g Threshold

Figure D.6 – Crack, Post-2010: 280g Threshold

0%

5%

10%

15%

20%

25%

30%

202224262830323436

Proportion of offenders (+/-) 8 gms. of 

the threshold 

Grams of Crack

Whites Blacks Hispanics

0%

5%

10%

15%

20%

25%

Proportion of offenders + 120 & 

200220240260280300320340360380400400

- 80 

gms. of the threshold 

Grams of Crack

Whites Blacks Hispanics
Federal Sentencing Disparity, 2005–2012 121

Figure D.7 – Heroin: 100g Threshold

Figure D.8 – Heroin: 1000g Threshold

-5%

0%

5%

10%

15%

20%

25%

50556065707580859095

100105110115120125130135140145150

Proportion of offenders (+/-) 50 gms. of 

the threshold 

Grams of Heroin

Whites Blacks Hispanics

-10%

0%

10%

20%

30%

40%

50%

800820840860880900920940960980

1,0001,0201,0401,0601,0801,1001,1201,1401,1601,1801,200

Proportion of offenders (+/-) 200 gms. of 

the threshold 

Grams of Heroin

Whites Blacks Hispanics
Federal Sentencing Disparity, 2005–2012 122

Figure D.9 – Marijuana: 100,000g Threshold

Figure D.10 – Marijuana: 1,000,000g Threshold

0%

5%

10%

15%

20%

25%

80,00084,00088,00092,00096,000

100,000104,000108,000112,000116,000120,000

Proportion of offenders 

(+/-) 20,000 gms. of the threshold 

Grams of Marijuana

Whites Blacks Hispanics

0%

5%

10%

15%

20%

25%

30%

35%

800,000840,000880,000920,000960,000

1,000,0001,040,0001,080,0001,120,0001,160,0001,200,000

Proportion of offenders (+/-) 200,000 

gms. of the threshold 

Grams of Marijuana

Whites Blacks Hispanics
Federal Sentencing Disparity, 2005–2012 123

Figure D.11 – Methamphetamine (Mixture): 50g Threshold

Figure D.12 – Methamphetamine (Mixture): 500g Threshold

0%

5%

10%

15%

20%

25%

2530354045505560657075

Proportion of offenders (+/-) 25 gms. 

of the threshold 

Grams of Methamphetamine

Whites Blacks Hispanics

-5%

0%

5%

10%

15%

20%

25%

30%

35%

400420440460480500520540560580600

Proportion of offenders (+/-) 100 gms. of 

the threshold 

Grams of Methamphetamine

Whites Blacks Hispanics
Federal Sentencing Disparity, 2005–2012 124

Figure D.13 – Methamphetamine (Pure): 5g Threshold

Figure D.14 – Methamphetamine (Pure): 50g Threshold

0%

5%

10%

15%

20%

25%

30%

2345678

Proportion of offenders 

(+/-) 3 gms. of the threshold 

Grams of Methamphetamine

Whites Blacks Hispanics

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

2530354045505560657075

Proportion of offenders 

(+/-) 25 gms. of the threshold 

Grams of Methamphetamine

Whites Blacks Hispanics
Federal Sentencing Disparity, 2005–2012 125

Table D.1 – Boundaries chosen around drug threshold amounts based on graphical inspection

*For cocaine: lower cutoff (500) = +/- 20 g; upper cutoff (5,000) = +/- 100 g

*For crack (pre 2010): lower cutoff (5) = +/- 1 g; upper cutoff (50) = +/- 5 g

*For crack (post 2010): lower cutoff (28) = +/- 4 g; upper cutoff (280) = +/- 40 g

*For heroin: lower cutoff (100) = +/- 10 g; upper cutoff (1,000) = +/- 50 g

*For marijuana:lower cutoff (100,000) = +/- 4,000 g; upper cutoff (1,000,000) = +/-40,000 g

*For meth (mix): lower cutoff (50) = +/- 5 g; upper cutoff (500) = +/- 20 g

*For meth (pure): lower cutoff (5) = +/- 1 g; upper cutoff (50) = +/- 5 g

Table D.2 – Percent missing weights, by race and drug

Any Cocaine Crack Heroin Marijuana Meth (mix) Meth (pure)

White 28.7% 26.6% 23.8% 39.4% 18.4% 34.7% 16.6%

Black 23.1% 22.1% 17.6% 35.6% 12.8% 22.9% 8.0%

Hispanic 24.8% 32.2% 35.8% 35.3% 9.1% 24.6% 8.0%

Overall 25.1% 25.9% 19.5% 36.1% 13.1% 32.4% 13.7%

Table D.3 – For range check estimation: Conditional differences (males and females)

White Black Hispanic White Black Hispanic

Lower Upper

Cocaine - -8.1 *** -5.4 - 5.2 -8.0 ***

Crack - 3.2 -0.5 - 3.6 -18.4 ***

Heroin - -1.6 -11.1 ** - -0.6 -3.0

Marijuana - 2.1 -4.4 - 15.7 *** 13.7 ***

Meth (mix) - 3.3 5.3 - -20.0 *** 6.1

Meth (pure) - 9.8 -10.7 - 8.9 1.3

Notes. **p < .01; ***p < .001

Table D.4 – For logistic estimation: Conditional differences (males and females)

Differences in probability of being above the cutoff, relative to whites

White Black Hispanic White Black Hispanic

Lower Upper

Cocaine - 13.6 ** -21.2 - 6.0 ** -9.2 **

Crack - 5.3 ** 6.7 - -5.2 ** -1.0

Heroin - -9.9 -12.6 - -1.2 -8.1

Marijuana - 44.4 -1.3 - 5.4 -14.9

Meth (mix) - 6.1 -7.4 - <0.00 -0.3

Meth (pure) - -33.0 -3.6 - -6.5 -14.5

Notes. **p < .01; ***p < .001
Federal Sentencing Disparity, 2005–2012 126

Table D.5 – For male versus female estimation: Conditional differences (males only)

Differences in probability of being above the cutoff, relative to whites

White Black Hispanic White Black Hispanic

Lower Upper

Cocaine - -10.3 ** -17.6 *** - 7.8 ** -12.1 ***

Crack - 7.2 9.9 - -4.5 0.8

Heroin - -13.6 *** -19.8 ** - 3.5 -4.4

Marijuana - 29.5 -3.0 - 4.3 -12.4

Meth (mix) - -3.3 -5.3 - 18.8 3.3

Meth (pure) - -27.4 -7.0 - -2.5 -10.3

Notes. **p < .01; ***p < .001

Table D.6 – For Male versus female estimation: Conditional differences (females only)

Differences in probability of being above the cutoff, relative to whites

White Black Hispanic White Black Hispanic

Lower Upper

Cocaine - -21.5 -21.7 - -18.8 -26.6

Crack - 5.8 -28.3 - -6.4 -19.9

Heroin - -6.1 12.3 - -53.8 36.5

Marijuana - 63.7 -3.4 - <0.00 <0.00

Meth (mix) - 150.9 ** -28.0 - <0.00 -48.3

Meth (pure) - <0.00 7.6 - -88.6 -59.1 ***

Notes. **p < .01; ***p < .001