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Decomposing Racial Disparities in Sentencing Outcomes: Sentencing Guideline versus

Judges’ Discretion

Kenny Lo

May 9, 2016

INTRODUCTION

After the federal courts and various state criminal courts in the U.S adopted sentencing

guidelines during the 1970s and 1980s in large part to address racial disparities that had long

persisted in sentencing outcomes, researchers have set out to determine whether such efforts

have been successful. In doing so, however, many have largely focused on the racial disparity in

sentence length without specifying whether it has occurred when judges followed the guidelines

or when they departed from the guidelines. As a result, the cause of the disparity or lack thereof

has been attributed to the design of the guidelines when it could have actually been the result of

judges’ discretion. The lack of decomposition could have, in turn, misinformed policy and

resulted in its missing the mark at eliminating racial disparities in sentencing outcomes.

Using the Pennsylvania Sentencing Data in 1996 and 1998, the current study looks to

determine whether the racial disparity between Black and White offenders in minimum sentence

length occurred when judges followed the 4th edition Pennsylvania Sentencing Guideline or

when they exercised their discretion by issuing a mitigated sentence, downward departure,

aggravated sentence, or upward departure. Besides the racial disparity in minimum sentence

length, the discrepancy in the likelihood of receiving each of the four deviating sentences versus

a standard guideline sentence by race is also explored. The mean racial difference in both the

minimum sentence length and likelihood of receiving each of the four deviating sentences versus

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a standard guideline sentence is decomposed into a portion that is explained by group differences

in the predictors and a portion that is unexplained.

LITERATURE REVIEW

Insufficient Data & Methodology

The literature on the racial disparity in sentencing is one of back and forth commentary

on methodology and data. Early studies such as that by Meyers (1979) and Unnever et al. (1980)

supported the hypothesis that black defendants receive harsher sentences than white defendants

along with theories that purport to explain why. Conflict theory, for example, argues that groups

with high social standing have an incentive to inflict greater legal constraints on the socially

disadvantaged than on others. In order to engulf the limited resources in society, the powerful is

expected to institutionalize differential treatment of minorities, including that of judicial

sentencing (Schwendinger and Schwendinger, 1970). The labeling perspective provides another

perspective on the matter. It claims that the negative perception of a criminal is more likely to be

applied in court to a minority person than a white person who are otherwise equal (Goode, 1979;

Schur, 1971). Meanwhile, opponents such as Hagan (1975), Hindelang (1969), and Kleck (1981)

emphasized that the methodology and data available were insufficient to conclude racial

disparity in sentencing except for capital offenses in the American South. Failure to control for

relevant legal variables such as offense seriousness, prior record, and quality of the evidence was

especially problematic, as noted by Blumstein et al. (1983) and Garber et al. (1983).

Debate on Sentencing Guidelines

In response, Kempf et al. (1986) used sentencing data on non-capital offenses from a

non-Southern state (Pennsylvania) that included recommended controls and was able to show

significant interaction effects of race with legal variables on sentence length. The data was based

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on 1977, exactly one year before the Pennsylvania Sentencing Commission was created to

develop sentencing guidelines for judges to follow while adjudicating felonies and

misdemeanors. Aimed at eliminating unwarranted disparity and discretion in judicial sentencing,

the implementation of sentencing guidelines has sparked a debate on their effectiveness. Some

researchers like Mieth et al. (1985) and Kramer et al. (1993) agreed that sentencing guidelines

have significantly reduced racial disparities in sentencing outcomes while others like Rothman

(1995) contended the opposite position.

In particular, Gorton et al. (1999) analyzed the pre- and post-guideline effects of race on

felony sentence length in Pennsylvania in 1977, 1983, 1992, and 1993 and found that the

disparity disappeared after the guidelines were instituted. Separate ordinary least squares

regressions were run for all four years while controlling for relevant legal variables, defendant’s

gender, countywide variables, and type of case disposition. The authors concluded that

sentencing guidelines that only constrain minimum sentencing decisions, such as those in

Pennsylvania, are an effective tool in eliminating the racial disparity in sentence length.

Departures from Sentencing Guidelines

Using data from the same source as Gorton et al. (1999) in the years 1996-1998, Johnson

(2003) examined the degree to which the racial disparity in departures from sentencing

guidelines depended on the type of case disposition (i.e. non-negotiated pleas, negotiated pleas,

bench trials and jury trials). By conducting multinomial logistic regressions, the study found that

Black and Hispanic defendants are less likely to receive downward departures and more likely to

receive upward departures than white defendants and the magnitude of the disparity is

conditioned upon the mode of conviction. For example, the effect of being black on the

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likelihood of downward departure is significantly less for defendants who went to trial than for

defendants convicted through non-negotiated guilty pleas.

Unanswered Question

On the surface, the studies by Gorton et al. (1999) and Johnson (2003) seem to present

inconsistent findings; Gorton et al. (1999) concluded that the racial disparity in sentencing length

had been eliminated post-guidelines while Johnson (2003) found that it persisted in the

likelihood of receiving a downward versus upward departure from the guidelines. The discerning

factor is that the dependent variable of Gorton et al.’s study (1999) was sentencing length while

that of Johnson’s study (2003) was the likelihood of receiving a downward versus upward

departure from the guidelines, which relates to a significant problem in the sentencing literature

regarding the effectiveness of guidelines. Researchers have generally focused on racial

disparities in sentencing outcomes without establishing whether they have come from the

departures from the guidelines or the guidelines themselves. Therefore, the question of whether

the racial disparity between Black and White offenders in sentence length has been the result of

judges’ discretion or the design of the guidelines remains unanswered. Similarly, the discrepancy

in the likelihood of judges’ deviating from the guideline versus following the guideline by race is

worth examining. How much of the mean racial difference in both sentence length and likelihood

of receiving a deviating sentence versus a standard guideline sentence can be explained by group

differences in legally relevant characteristics such as offense severity? How much of it cannot be

explained? The current study provides an approach to answer such questions and contributes to

the debate of whether or not guidelines have been effective in addressing racial disparities in

sentencing outcomes.

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DATA AND DEFINITIONS

Description, Restrictions, and Adjustments

The data set used is the 1996 and 1998 Pennsylvania Sentencing Data. It was collected by

the Pennsylvania Commission on Sentencing, a legislative agency of the Commonwealth of

Pennsylvania that develops sentencing guidelines for judges in sentencing felony and

misdemeanor offenses. The 1996 and 1998 Pennsylvania Sentencing Data reflects all the

sentences on felonies and misdemeanors that were reported on Guideline Sentence Forms by

judges to the Commission during the calendar year 1996 and 1998. Part 1, Records Data,

provides information on each offender that includes demographic characteristics such as sex and

race, prior offense history, current supervision status, and type of disposition. Part 2, Offense

Data, provides information on each offense that include the statutory citation for the offense, the

Offense Gravity Score assigned by the Commission, the offender's Prior Record Score, and the

sentence given. The data set is restricted to all offenses committed on or after August 12, 1994,

when the 4th edition guidelines became effective, up until the time that the 5th guidelines

became effective for all offenses committed on or after June 13, 1997. Offenders who were

issued life and death sentences or less than 7 years old at the time of offense are excluded.

Definitions of Offense Gravity Score, Prior Record Score, Standard Guideline Sentence,

Mitigated Sentence, and Aggravated Sentence

All offenses are classified according to the offense gravity score, which measures the

severity of the offense committed ranging from 1 to 13 for each offense categorized in

Pennsylvania statue, and the prior record score, which measures the extent of the offender's

criminal record ranging from 0 to 8 based on the type and number of prior convictions and prior

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juvenile adjudications.1 One of three sentences is recommended based on each combination of

the offense gravity score and prior record score: 1) the standard guideline sentence, when the

judge follows the guideline to issue a sentence that is determined by the two scores, 2) mitigated

sentence, when the judge determines there are mitigating factors present and subtracts a number

of months from the standard guideline sentence that is recommended by the Pennsylvania

Sentencing Commission, and 3) aggravated sentence, when the judge determines there are

aggravating factors present and adds a number of months to the standard guideline sentence that

is recommended by the Pennsylvania Sentencing Commission.2

Definitions of Downward Departure and Upward Departure

In addition, the judge has the discretionary power to issue a downward departure or

upward departure from the standard guideline sentence. A downward departure is defined as

when judges exercise broad discretion to issue a sentence below the standard guideline sentence

and mitigating sentence. An upward departure is defined as when judges exercise broad

discretion to issue a sentence above the standard guideline sentence and aggravating sentence. A

written statement of the reasons for a downward or upward departure must be provided and both

the defendant and the State have the right to appeal.3

Definition of Minimum Sentence Length

Minimum sentence length is defined as the minimum length of incarceration in months,

which is generally the amount of time an offender serves before being considered for parole.

Although each sentence in Pennsylvania is stated as a range between a minimum sentence and a

1 204 Pa. Code § 303.15 and 303.4 2 204 Pa. Code § 303.13 3 204 Pa. Code § 303.1(a)

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maximum sentence in months, the standard guideline sentence only applies to the minimum

sentence.4 Therefore, the measure of sentence length used is that of the minimum sentence for

meaningful comparison of the standard guideline sentence to downward departure, mitigated

sentence, aggravated sentence, and upward departure.

QUESTIONS AND DESCRIPTIVE STATISTICS

Regarding the first question of whether the racial disparity between White and Black

offenders in minimum sentence length occurred when judges followed the 4th edition guideline

or when they exercised their discretion, table 1 provides summary statistics of the minimum

sentence length in months given a downward departure, mitigated sentence, standard guideline

sentence, aggravated sentence, and upward departure by race. It shows that the average and

median minimum sentence length for Black offenders are equal or higher than that of White

offenders across the board, which seems to suggest that racial disparities in minimum sentence

length existed both when judges followed the 4th edition guideline and when they decided to

issue a deviating sentence.

As for the second question of whether there are also racial disparities in the likelihood of

receiving a downward departure, mitigated sentence, aggravated sentence, or upward departure

versus a standard guideline sentence, table 2 offers the absolute and relative frequencies of each

of the five sentencing options at the judges’ disposal by race. Approximately 66.5% of standard

guideline sentences were issued to White offenders while around 33.5% were issued to Black

offenders, close to the racial makeup of the total sentences at 63% and 37%, respectively. In

contrast, 45% of downward departures were issued to White offenders versus 55% to Black

offenders, 45% of mitigated sentences were issued to White offenders versus 55% to Black

4 204 Pa. Code § 303.2, 303.9, and 303.10

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offenders, 69% of aggravated sentences were issued to White offenders versus 31% to Black

offenders, and 60% of upward departures were issued to White offenders versus 40% to Black

offenders. Such variations seem to suggest that Black offenders were more likely to receive a

downward departure, mitigated sentence, and upward departure and less likely to receive an

aggravated sentence than their White counterparts versus a standard guideline sentence.

In order to answer the follow-up questions of how much of the mean racial difference in

both minimum sentence length and likelihood of receiving a deviating sentence versus a standard

guideline sentence can be explained by group differences in characteristics and how much of it

cannot be explained by the same differences, the current study uses two economic models that

are discussed hereafter.

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White Black White Black White Black White Black White Black

Mean 9.64 11.20 9.21 10.36 11.09 12.61 4.74 8.21 18.87 27.99

Median 8.00 11.50 6.00 7.00 6.00 8.00 2.10 3.00 12.00 12.00

Minimum 0.03 0.01 0.00 0.00 0.00 0.00 0.03 0.03 0.16 0.53

Maximum 96.00 120.00 72.30 96.00 120.00 120.00 90.00 120.00 300.00 300.00

Standard Deviation 9.45 9.56 9.58 10.94 14.89 15.79 8.46 12.71 23.22 30.43

Observations 713 981 1,178 1,360 9,243 6,355 5,082 2,416 4,580 3,366

Table 1. Summary Statistics of Minimum Sentence Length in Months Given Each of the Five Sentencing Options by Race

—Source: Pennsylvania Sentencing Data in 1996 and 1998 restricted to all offenses committed on or after August 12, 1994, when the 4th

edition guidelines became effective, up until the time that the 5th guidelines became effective for all offenses committed on or after June 13,

1997. Note: Although each sentence in Pennsylvania is stated as a range between a minimum sentence and a maximum sentence in months, the

standard guideline sentence only applies to the minimum sentence. Therefore, the measure of sentence length used is that of the minimum

sentence for meaningful comparison of the standard guideline sentence to each of the four deviating sentences.

Standard GuidlineMitigated Sentence Aggravated SentenceDownward Departure Upward Departure

Downward Departure Mitigated Sentence Standard Guidline Aggravated Sentence Upward Departure Total

White 1,972 2,511 40,953 5,663 5,349 46,099

3.49 4.45 72.55 10.03 9.48 100.00

45.34 44.99 66.47 68.96 59.87 62.98

Black 2,377 3,070 20,661 2,549 3,585 37,095

737.00 9.52 64.08 7.91 11.12 100.00

54.66 55.01 33.53 31.04 40.13 37.02

Total 4,349 5,581 61,614 8,212 8,934 73,194

4.90 6.29 69.47 9.26 10.07 100.00

100.00 100.00 100.00 100.00 100.00 100.00

Table 2. Absolute and Relative Frequencies of Each of the Five Sentencing Options by Race

—Source: Pennsylvania Sentencing Data in 1996 and 1998 restricted to all offenses committed on or after August 12, 1994, when the 4th

edition guidelines became effective, up until the time that the 5th guidelines became effective for all offenses committed on or after June 13,

1997. Key: Reading from top to bottom are frequency, row percentage, column percentage.

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ECONOMIC MODELS

Ordinary Least Squares and Blinder-Oaxaca Decomposition (Minimum Sentence length)

Following Blinder (1973), Oaxaca (1973), and Jann (2008), ordinary least squares

regressions are estimated based on the linear model:

𝑌ℓ = 𝑋ℓ′𝛽ℓ + ℰℓ, 𝐸(ℰℓ) = 0, ℓ𝜖 (𝐴, 𝐵)

where for group A (White offenders) and group B (Black offenders), Y is the minimum sentence

length, X is a vector that includes the predictors of Y such as prior record score, 𝛽 is a constant

that includes the slope parameters and the intercept, and ℇ is the error term of which the expected

value is assumed to be 0.

The mean difference in minimum sentence length between White and Black offenders is

the difference in the group-specific means predicted by the linear model:

𝑅 = 𝐸(𝑌𝐴) − 𝐸(𝑌𝐵) = 𝐸(𝑋𝐴)′𝛽𝐴 − 𝐸(𝑋𝐵)′𝛽𝐵

where R is the mean racial disparity in minimum sentence length and E(Y) is the expected value

of minimum sentence length, which is reduced as follows:

𝐸(𝑌ℓ) = 𝐸(𝑋ℓ′𝛽ℓ + ℰℓ) = 𝐸(𝑋ℓ′𝛽ℓ) + 𝐸(ℰℓ) = 𝐸(𝑋ℓ)′𝛽ℓ

as 𝐸(𝛽ℓ) = 𝛽ℓ and 𝐸(ℰℓ) = 0 are assumed.

If we let 𝛽* be a coefficient vector that assumes no discrimination, then R is decomposed

as follows:

𝑅 = {𝐸(𝑋𝐴) − 𝐸(𝑋𝐵)}′𝛽∗ + {𝐸(𝑋𝐴)′(𝛽𝐴 − 𝛽∗) + 𝐸(𝑋𝐵)′(𝛽

∗ − 𝛽𝐵)}

where the first portion,

{𝐸(𝑋𝐴) − 𝐸(𝑋𝐵)}′𝛽∗

is the amount of differential that is explained by group differences in the predictors while the

second portion,

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{𝐸(𝑋𝐴)′(𝛽𝐴 − 𝛽∗) + 𝐸(𝑋𝐵)′(𝛽∗ − 𝛽𝐵)}

is the amount of differential that is not explained by the same differences. If we assume that there

was only discrimination against Black offenders and no positive discrimination of White

offenders, then 𝛽* is estimated with 𝛽𝐴 as follows:

�̂� = (�̅�𝐴 − �̅�𝐵)′�̂�𝐴 + �̅�𝐵′(�̂�𝐴 − �̂�𝐵)

On the other hand, if we assume that there was only positive discrimination of White offenders

and no discrimination against Black offenders, then 𝛽* is estimated with 𝛽𝐵 as follows:

�̂� = (�̅�𝐴 − �̅�𝐵)′�̂�𝐵 + �̅�𝐴′(�̂�𝐴 − �̂�𝐵)

Both model specifications are performed to decompose the mean racial disparity in minimum

sentence length given a downward departure, mitigated sentence, standard guideline sentence,

aggravated sentence, and upward departure.

Probit Decomposition (Likelihood of Receiving a Deviating Sentence)

Following Yun (2005), the binary variable of receiving a downward departure, mitigating

sentence, aggravated sentence, or upward departure versus a standard guideline sentence is

modeled as a function of a linear combination of independent variables, but the function itself

may be modeled nonlinearly as follows:

Y = F(Xβ)

where Y is a binary variable of receiving each of the four deviating sentence versus a standard

guideline sentence, X is a vector that includes the predictors of Y, and 𝛽 is a vector that includes

the coefficients.

The mean difference between Black and White offenders in Y is decomposed as follows:

�̅�𝐴 − �̅�𝐵 = [𝐹(𝑋𝐴𝛽𝐴)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅ − 𝐹(𝑋𝐵𝛽𝐴)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅] + [𝐹(𝑋𝐵𝛽𝐴)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅ − 𝐹(𝑋𝐵𝛽𝐵)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅]

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Then, the mean values and first order Taylor expansion are used to weight the contribution of

each variable to the explained and unexplained portion of the racial disparity

�̅�𝐴 − �̅�𝐵 = [𝐹(�̅�𝐴𝛽𝐴) − 𝐹(�̅�𝐵𝛽𝐴)] + [𝐹(�̅�𝐵𝛽𝐴) − 𝐹(�̅�𝐵𝛽𝐵)] + 𝑅𝑀

= [(�̅�𝐴 − �̅�𝐵)′𝛽𝐴]′𝑓(�̅�𝐴𝛽𝐴) + �̅�𝐵′(𝛽𝐴 − 𝛽𝐵)′𝑓(�̅�𝐵𝛽𝐵) + 𝑅𝑀 + 𝑅𝑇

where

𝑅𝑀 = [𝐹(𝑋𝐴𝛽𝐴)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅ − 𝐹(𝑋𝐵𝛽𝐴)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅] + [𝐹(𝑋𝐵𝛽𝐴)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅ − 𝐹(𝑋𝐵𝛽𝐵)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅]

− [𝐹(�̅�𝐴𝛽𝐴) − 𝐹(�̅�𝐵𝛽𝐴)] − [𝐹(�̅�𝐵𝛽𝐴) − 𝐹(�̅�𝐵𝛽𝐵)]

and

𝑅𝑇 = [𝐹(�̅�𝐴𝛽𝐴) − 𝐹(�̅�𝐵𝛽𝐴)] + [𝐹(�̅�𝐵𝛽𝐴) − 𝐹(�̅�𝐵𝛽𝐵)]

− [(�̅�𝐴 − �̅�𝐵)′𝛽𝐴]′𝑓(�̅�𝐴𝛽𝐴) − �̅�𝐵′(𝛽𝐴 − 𝛽𝐵)′𝑓(�̅�𝐵𝛽𝐵)

The scalars 𝑅𝑀 and 𝑅𝑇 are approximation residuals from using the mean values of the function

and first order Taylor expansion. Now the average racial difference in Y is weighted as follows:

�̅�𝐴 − �̅�𝐵 =∑𝑊Δ𝑋𝑖

𝑖=𝐾

𝑖=1

[𝐹(𝑋𝐴𝛽𝐴)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅ − 𝐹(𝑋𝐵𝛽𝐴)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅] +∑𝑊Δ𝛽𝑖

𝑖=𝐾

𝑖=1

[𝐹(𝑋𝐵𝛽𝐴)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅ − 𝐹(𝑋𝐵𝛽𝐵)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅]

where

𝑊Δ𝑋𝑖 =

(�̅�A𝑖 − �̅�B

𝑖 )′𝛽𝐴𝑖 ′𝑓(�̅�𝐴𝛽𝐴)

(�̅�𝐴 − �̅�𝐵)′𝛽𝐴′𝑓(�̅�𝐴𝛽𝐴)=(�̅�A

𝑖 − �̅�B𝑖 )′𝛽𝐴

𝑖

(�̅�𝐴 − �̅�𝐵)′𝛽𝐴

and

𝑊Δ𝛽𝑖 =

�̅�B𝑖 ′(𝛽𝐴

𝑖 − ′𝛽𝐵𝑖 )′𝑓(�̅�𝐵𝛽𝐵)

�̅�𝐵′(𝛽𝐴 − 𝛽𝐵)′𝑓(�̅�𝐵𝛽𝐵)=�̅�B𝑖 ′(𝛽𝐴

𝑖 − ′𝛽𝐵𝑖 )

�̅�𝐵′(𝛽𝐴 − 𝛽𝐵)

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Assuming prob(Y= 1) = Φ(X𝛽), where Φ is a standard normal cumulative distribution

function, the probit decomposition becomes

�̅�𝐴 − �̅�𝐵 =∑𝑊Δ𝑋𝑖

𝑖=𝐾

𝑖=1

[𝜙(𝑋𝐴𝛽𝐴)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅ − 𝜙(𝑋𝐵𝛽𝐴)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅] +∑𝑊Δ𝛽𝑖

𝑖=𝐾

𝑖=1

[𝜙(𝑋𝐵𝛽𝐴)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅ − 𝜙(𝑋𝐵𝛽𝐵)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅]

which is performed to decompose the mean racial disparity in the log likelihood of receiving a

downward departure, mitigated sentence, aggravated sentence, or upward departure versus a

standard guideline sentence.

Variable Name and Description for Both Decompositions

Table 3 provides the variable name and description for each of the variables used in both

the linear decomposition of the mean racial disparity in minimum sentence length and the probit

decomposition of the likelihood of receiving each of the four deviating sentence versus a

standard guideline sentence.

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Name Description

Dependent Variables

Minimum Sentence Length Minimum length of incarceration in months, which is generally the amount of time an offender serves before being

considered for parole. Although each sentence in Pennsylvania is stated as a range between a minimum sentence and

a maximum sentence in months, the standard guideline sentence only applies to the minimum sentence. Therefore, the

measure of sentence length used is that of the minimum sentence for meaningful comparison of the standard guideline

sentence to each of the four deviating sentences defined below.

Downward Departure 1 if an offender was issued a downward departure, 0 otherwise. Downward departure is defined as when judges

exercise broad discretion to issue a sentence below the standard guideline sentence and mitigating sentence. A

written statement of the reasons for downward departure must be provided and both the defendant and the State have

the right to appeal.

Mitigating Sentence 1 if an offender was issued a mitigating sentence, 0 otherwise. Mitigating sentence is defined as when judges

determine there are mitigating factors present and subtracts a number of months from the standard guideline sentence

that is recommended by the Pennsylvania Sentencing Commission.

Standard Guideline Sentence Standard Guideline Sentence is defined as when judges follow the guideline to issue a sentence that is determined by

the offense gravity score, which measures the severity of the offense committed, and the prior record score, which

measures the extant of the offender’s criminal record.

Aggravating Sentence 1 if an offender was issued an aggravating sentence, 0 otherwise. Aggravating sentence is defined as when judges

determine there are aggravating factors present and adds a number of months to the standard guideline sentence that

is recommended by the Pennsylvania Sentencing Commission.

Upward Departure 1 if an offender was issued a upward departure, 0 otherwise. Upward departure is defined as when judges exercise

broad discretion to issue a sentence above the standard guideline sentence and aggravating sentence. A written

statement of the reasons for upward departure must be provided and both the defendant and the State have the right

to appeal.

Independent Variables

A. Main Determinants of Sentencing

Offense Gravity Score Measure of the offense severity ranging from 1 to 13 for each offense categorized in Pennsylvania statue

Prior Record Score Measure of the extent of the offender's criminal record ranging from 0 to 8 based on the type and number of prior

convictions and prior juvenile adjudications

B. Offense Characteristics

Weapon Enhancement 1 if an offender possessed a deadly weapon while committing the offense, 0 otherwise

School Enhancement 1 if an offender trafficked in drugs within 1000 feet of a school, 0 otherwise

Youth Enhancement 1 if an offender invovled youth in drug trafficking, 0 otherwise

Negotiated Guilty Plea 1 if an offender entered into a negotiated guilty plea, 0 otherwise

Non-negotiated Guilty Plea 1 if an offender entered into a non-negotiated guilty plea, 0 otherwise

No Contest 1 if an offender pleaded no contest, 0 otherwise

Bench Trial 1 if an offender went through a bench trial, 0 otherwise

Jury Trial 1 if an offender went through a jury trial, 0 otherwise

Other Disposition 1 if an offender went through a disposition that is not a negotiated/non-negotiated guilty plea, no contest, or

bench/jury trial, 0 otherwise

Presentence Investigation 1 if a presentence investigation was conducted, 0 otherwise

Warrants or Detainers 1 if warrants or detainers were issued, 0 otherwise

Drug and Alcohol Assessment 1 if an offender was dependent, 0 otherwise

C. Offender Characteristics

Sex 1 if an offender was male, 0 otherwise

Age Offender's age at the time of offense

Not Supervised 1 if an offender's supervision status was not supervised, 0 otherwise

State Prison 1 if an offender's supervision status was state prison, 0 otherwise

County Jail 1 if an offender's supervision status was county jail, 0 otherwise

IP Program 1 if an offender's supervision status was intermediate punishment program, 0 otherwise

Probation 1 if an offender's supervision status was probation, 0 otherwise

Parole 1 if an offender's supervision status was parole, 0 otherwise

Federal Incarceration 1 if an offender's supervision status was federal incarceration, 0 otherwise

Other Supervision Status 1 if an offender's supervision status was not state prison, county jail, IP program, probation, parole, federal

incarceration, or not supervised, 0 otherwise

D. County Fixed Effects

County 1 if a sentence was issued in a specific county, 0 otherwise for each of the 67 counties in Pennsylvania

Table 3. Variable Name and Discription

—Source: Pennsylvania Sentencing Data in 1996 and 1998 restricted to all offenses committed on or after August 12, 1994, when the 4th edition guidelines

became effective, up until the time that the 5th guidelines became effective for all offenses committed on or after June 13, 1997.

15

FINDINGS AND ANALYSIS

Table 4 displays the findings from the Blinder-Oaxaca linear decomposition of the

disparity in minimum sentence length between White and Black offenders given a downward

departure, mitigated sentence, standard guideline sentence, aggravated sentence, and upward

departure. Although the average minimum sentence length for Black offenders given a

downward departure was longer than that of White offenders and strongly significant, almost all

the disparity is explained by group differences in predictors while the unexplained portion is not

significant. 5 Therefore, the results suggests that judges did not discriminate against Black

offenders when they issued a downward departure. However, the average minimum sentence

length for Black offenders given a mitigated sentence was longer than that of White offenders

and weakly significant, and around half of the disparity that is strongly significant cannot be

explained by predictors while the explained portion is not significant. Hence, Black offenders

would be expected to receive a shorter sentence than White offenders if they had the White

offenders’ coefficients/treatment given a mitigated sentence, which suggests that judges

potentially discriminated against Black offenders when they issued a mitigated sentence.6 The

average minimum sentence length for Black offenders given a standard guideline sentence was

longer than that of White offenders and strongly significant, but group differences in offense

gravity score and prior record score, the only two predictors of the minimum sentence length

given a standard guideline sentence, explain more than 100% of the mean racial differential at

5 These results assume that there was only positive discrimination of White offenders and no

discrimination against Black offenders (𝛽* = �̂�𝐵). If we assume that there was only discrimination against

Black offenders and no positive discrimination of White offenders (𝛽* = �̂�𝐴), both the explained and

unexplained portions are not significant. 6 These results again assume 𝛽* = �̂�𝐵. If we assume 𝛽* = �̂�𝐴, both the explained and unexplained

portions are not significant.

16

1% significance while the unexplained portion is also strongly significant. In other words, Black

offenders would be expected to receive a shorter minimum sentence length than White offenders

if they had White offenders’ offense gravity scores and prior record scores and a longer sentence

if they had the White offenders’ coefficients/treatment. Surprisingly, the findings are consistent

across both model specifications used and suggest potential discrimination against White

offenders when judges followed the 4th edition guideline. Even though the average minimum

sentence length for Black offenders given an aggravated sentence was longer than that of White

offenders and strongly significant, almost all the disparity is explained by group differences in

predictors while the unexplained portion is not significant. The results are again consistent across

both model specifications used and suggest that judges did not discriminate against Black

offenders when they issued an aggravated sentence. Lastly, the average minimum sentence

length for Black offenders given an upward departure was longer than that of White offenders

and strongly significant, but the findings are substantially different when one model is specified

over the other. If we assume that there was only discrimination against Black offenders and no

positive discrimination of White offenders (𝛽* = �̂�𝐴), group differences in predictors explain

more than 100% of the mean racial differential at 1% significance while the unexplained portion

is not significant. This means that Black offenders would be expected to receive a shorter

minimum sentence length than White offenders if they had White offenders’ predictors,

suggesting that judges potentially discriminated against White offenders when they issued an

upward departure. If we assume that there was only positive discrimination of White offenders

and no discrimination against Black offenders (𝛽* = �̂�𝐵), however, group differences explain

around 70% of the mean racial differential at 1% significance while the unexplained portion is

now weakly significant. The findings now suggest that judges potentially discriminated against

17

Black offenders when they issued a mitigated sentence. Because of such inconsistency across

model specifications, evidence of potential discrimination against Black or White offenders is

ambiguous.

Table 5 displays the results from the probit decomposition of the disparity in the

likelihood of receiving a downward departure, mitigated sentence, aggravated sentence, or

upward departure versus a standard guideline sentence between White and Black offenders. The

average likelihood of receiving a downward departure versus a standard guideline sentence for

Black offenders was higher than that of White offenders and strongly significant, all the disparity

is explained by group differences in predictors while the unexplained portion is not significant.

The findings are consistent across both model specifications and suggest that judges did not

discriminate against White offenders. The average likelihood of receiving a mitigated sentence

versus a standard guideline sentence for Black offenders was higher than that of White offenders

and strongly significant, and both the explained and unexplained portions are strongly

significant. Therefore, Black offenders would be more likely to receive a mitigated sentence than

White offenders if they had White offenders’ predictors and less likely to receive a mitigated

sentence if they had White offenders’ coefficients/treatment. The results are consistent across

model specifications and suggest that judges potentially discriminated against White offenders.

The average likelihood of receiving an aggravated sentence versus a standard guideline sentence

for Black offenders was lower than that of White offenders but not statistically significant.

However, group differences in predictors explain more than 100% of the mean racial differential

at 1% significance while the unexplained portion is also strongly significant. Hence, Black

offenders would be more likely to receive an aggravated sentence than White offenders if they

had White offenders’ predictors and less likely to receive an aggravated sentence if they had

18

White offenders’ coefficients/treatment. The findings are consistent across both model

specifications used and suggest potential discrimination against Black offenders. The average

likelihood of receiving an upward departure versus a standard guideline sentence for Black

offenders was higher than that of White offenders but not statistically significant, and the portion

that is explained by group differences in predictors is not significant, while the portion that

cannot be explained by the same differences is strongly significant. Therefore, Black offenders

would be less likely to receive an upward departure than White offenders if they had White

offenders’ predictors. The results are consistent across model specifications and suggest that

judges potentially discriminated against Black offenders.

19

White 9.62 9.62 9.19 9.19 11.09 11.09 4.73 4.73 18.63 18.63

(0.45) (0.45) (0.43) (0.43) (0.16) (0.16) (0.31) (0.31) (1.18) (1.18)

Black 11.12 11.12 10.32 10.32 12.62 12.62 7.85 7.85 27.87 27.87

(0.61) (0.61) (0.86) (0.86) (0.20) (0.20) (1.13) (1.13) (3.25) (3.25)

Difference -1.50 -1.50 -1.12 -1.12 -1.54 -1.54 -3.12 -3.12 -9.24 -9.24

(0.51) (0.51) (0.65) (0.65) (0.25) (0.25) (1.02) (1.02) (2.98) (2.98)

Explained -0.70 -1.20 -0.60 -0.56 -3.20 -2.85 -2.99 -2.99 -10.54 -6.33

(0.44) (0.46) (0.73) (0.66) (0.21) (0.20) (1.05) (0.94) (2.82) (1.52)

Unexplained -0.89 -0.29 -0.53 -0.56 1.67 1.31 -0.14 -0.14 1.30 -2.91

(0.51) (0.69) (0.37) (0.22) (0.15) (0.15) (0.29) (0.20) (0.99) (1.77)

Offense Gravity Score -0.51 -0.49 1.36 1.32 -1.51 -1.45 -2.73 -2.54 -6.08 -5.60

(0.43) (0.41) (0.82) (0.80) (0.23) (0.22) (0.93) (0.86) (1.88) (1.75)

Prior Record Score -0.19 -0.20 -1.95 -1.87 -1.69 -1.40 -0.38 -0.33 -0.19 -0.19

(0.30) (0.53) (0.49) (0.47) (0.13) (0.11) (0.10) (0.09) (0.18) (0.18)

Offense Characteristics

Offender Characteristics

County Fixed Effects

Observations

Table 4. Blinder-Oaxaca Decomposition of Minimum Sentence Length

Mitigated Sentence Aggravated SentenceDownward Departure Upward DepartureStandard Guideline

—Note: The numbers presented are coefficients and the numbers in paranthesis are standard errors; coefficients with ***, **, and * are

statistically significant at 10%, 5%, and 1%, respectively; standard errors are adjusted for 67 clusters in county when county fixed effects were

included; offense characterisitcs, offender characteristics, and county fixed effects are listed and described in Table 3.

15,5727,329 7,2241,567 7,329

∗∗∗

∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗ ∗∗∗

∗∗∗ ∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗

∗

∗

∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

𝐵 𝐴 �̂�𝐵 𝐵 𝐵 𝐵 𝐵 𝐵 𝐵 𝐵 𝐵𝐵 𝐴 �̂�𝐴 𝐵 𝐴 �̂�𝐴

20

White 0.04 0.04 0.05 0.05 0.12 0.12 0.11 0.11

(0.00) (0.00) (0.01) (0.01) (0.02) (0.02) (0.02) (0.02)

Black 0.10 0.10 0.12 0.12 0.11 0.11 0.15 0.15

(0.01) (0.01) (0.01) (0.01) (0.02) (0.02) (0.03) (0.03)

Difference -0.05 -0.05 -0.07 -0.07 0.01 0.01 -0.03 -0.03

(0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.02) (0.02)

Explained -0.05 -0.05 -0.05 -0.06 0.06 0.03 -0.01 -0.01

(0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.02) (0.02)

Unexplained -0.003 0.01 -0.02 -0.01 -0.05 -0.02 -0.02 -0.02

(0.00) (0.01) (0.00) (0.01) (0.01) (0.00) (0.01) (0.01)

Offense Gravity Score -0.02 -0.02 -0.02 -0.02 0.00 0.01 -0.01 -0.004

(0.01) (0.01) (0.01) (0.01) (0.00) (0.00) (0.00) (0.00)

Prior Record Score -0.02 -0.02 -0.01 -0.01 0.01 0.00 0.01 0.004

(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.01) (0.00)

Offense Characteristics

Offender Characteristics

County Fixed Effects

Observations

—Note: The numbers presented are coefficients and the numbers in paranthesis are standard errors; coefficients with ***, **, and * are

statistically significant at 10%, 5%, and 1%, respectively; standard errors are adjusted for 67 clusters in county when county fixed effects

were included; offense characterisitcs, offender characteristics, and county fixed effects are listed and described in Table 3.

63,560 66,50061,767 66,843

Table 5. Blinder-Oaxaca Decomposition of the Likelihood of Receiving a Deviating Sentence Versus a Standard Guideline Sentence

Mitigated Sentence Aggravated SentenceDownward Departure Upward Departure

∗∗∗

∗∗∗

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∗∗∗

∗∗∗

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∗∗∗

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∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗∗

∗∗

∗∗ ∗∗∗ ∗∗∗

∗

∗∗∗

∗∗∗

∗∗∗ ∗∗∗

∗∗∗

∗∗∗

∗∗

∗∗∗

∗∗∗

𝐵𝐴 𝐵 𝐵�̂�𝐴 𝐵 𝐵 𝐵 𝐴 𝐵 𝐵 𝐵 𝐴 𝐵 𝐵

21

IMPLICATIONS AND CONCLUSION

The first question the current study seeks to answer is whether the racial disparity

between White and Black offenders in minimum sentence length occurred when judges followed

the 4th edition guideline or when they exercised their discretion. Although the average minimum

sentence length for Black offenders given a standard guideline sentence was longer than that of

White offenders and statistically significant at 1%, Black offenders would be expected to receive

a shorter minimum sentence length than the mean racial disparity if they had White offenders’

offense gravity scores and prior record scores and a longer sentence than the mean racial

disparity if they had the White offenders’ coefficients/treatment, suggesting potential

discrimination against White offenders in the design of the 4th edition guideline. However, there

is evidence that Black offenders would be expected to receive a shorter sentence than the mean

racial disparity if they had the White offenders’ coefficients/treatment given a mitigated

sentence, suggesting potential discrimination against Black offenders. Almost all the average

racial disparity in minimum sentence length given an aggravated sentence is explained by group

differences in predictors while the unexplained portion is not significant, as is the story given a

downward departure. There is ambiguous evidence of discrimination against White offenders or

Black offenders given an upward departure because it depends on which model is specified.

The second question the current study seeks to answer is whether there are also racial

disparities in the likelihood of receiving a mitigated sentence, aggravated sentence, downward

departure, or upward departure versus a standard guideline sentence. All the average racial

disparity in the likelihood of receiving a downward departure versus a standard guideline

sentence is explained by group differences in predictors while the unexplained portion is not

significant. However, there is evidence of potential discrimination against White offenders in the

22

likelihood of receiving a mitigated sentence versus a standard guideline sentence, and

discrimination against Black offenders in the likelihood of receiving an aggravated sentence or

upward departure versus a standard guideline sentence.

There is not a very strong policy implication of my findings because the unexplained

portions of both decompositions could capture effects of differences in unobservable variables

rather than discrimination. Due to the limitation of the data to control for potentially important

variables such as the race of the judges, the current study cannot conclude that the unexplained

portion represents the amount of racial discrimination in sentencing. However, it does offer an

approach that can be utilized to discern between the guideline and judges’ discretion as to where

potential racial discrimination occurred, which is essential to answering the question of whether

or not guidelines have been effective in eliminating racial disparities in sentencing outcomes.

23

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