How Mandatory are Mandatory Minimum Sentencing Laws and to
What Extent do they Impact Sentence Length? Evidence from United
States Federal Drug Convictions*
David Bjerk
Department of Economics
Claremont McKenna College
500 East Ninth St, Claremont CA 91711
[email protected]
August 2014
Abstract: Despite the name, less than half of those eligible for sentencing under the U.S.
mandatory minimum sentencing laws for drug trafficking actually receive sentences consistent with
the mandated minimums. Mandatory minimum eligible defendants who are female, white, and/or
charged with drugs other than crack are more likely to receive sentences short of the mandated
minimums than eligible male, non-white, and/or crack defendants. Much of these differentials are
explained by differences in criminal history. However, surprisingly, the impact of exceeding the
mandatory minimum quantity cutoffs on sentence lengths is positive and significant for everyone
except black defendants and crack defendants. JEL codes: J15, K14, K40
* Thanks to Eric Helland Shawn Bushway, numerous other members of my department, and
participants at the Institute for Research on Poverty Summer Workshop for helpful suggestions.
Also, special thanks to Caleb Mason for helping to germinate this project.
I - Introduction
One of the most prominent and controversial components of the United States federal
judicial system is U.S. Federal law 21 U.S.C § 841, which prescribes mandatory minimum
sentences for defendants convicted for trafficking quantities of illegal drugs over certain thresholds.
This law is prominent and controversial for two reasons. First, it potentially applies to a very large
population of defendants. Indeed, in fiscal year 2010, drug offenses made up almost 30 percent of
all federal offenses (second only to immigration offenses), with almost 25,000 offenders convicted
for a federal drug offense (U.S.S.C., 2011). Second, the mandatory minimums can be quite long
(10 years) even for non-violent first time offenders. Moreover, different drugs are treated quite
differently. Most notably, under the initial mandatory minimum law, the amount of crack cocaine
required to trigger a mandatory minimum was one hundred times less than the amount of powder
cocaine required to trigger a mandatory minimum. This differential treatment of crack cocaine
relative to powder cocaine has been so controversial, and many indeed claiming racist, that the U.S.
congress eradicated some of this differential treatment with the Fair Sentencing Act of 2010.
Advocates for presumptive sentencing laws have argued that mandated minimums add
greater uniformity to the justice system, ensuring that similar crimes garner similar sentences by
removing much of the individual judicial discretion with respect to sentencing, as well as provide a
means of lowering crime by through strong deterrence and incapacitation of law-breakers. At the
same time, critics argue that these laws often impose unfair and unduly harsh sentences on lower
level offenders, and most notably, are much of the reason behind the massive incarceration rates in
the United States, especially for black Americans.
While the law as written is quite straightforward, the ways in which it has been
implemented and/or is circumvented are less so. The purpose of this paper is to analyze the degree
to which these mandatory minimum sentences really are mandatory, and how much they actually
1 impact sentence lengths. In particular, I use federal sentencing data to answer the following: (i)
How often do individuals technically eligible for mandatory minimum drug sentences actually
receive sentences shorter than the prescribed mandatory minimum? (ii) Conditional on being
eligible, are particular types of defendants more or less likely to actually receive a sentence
consistent with the mandatory minimum? (iii) Finally, to what extent does exceeding the drug
quantity thresholds that ostensibly trigger mandatory minimum sentences actually impact sentence
lengths, and does this differ by type of defendant?
The answers to these questions turn out to be arguably quite surprising. On average, during
the 2011 and 2012 fiscal years, less than 40 percent of the individuals ostensibly eligible for
sentencing under 21 U.S.C § 841 based on the drug type and amount they were convicted for
trafficking actually receive a sentence consistent with the prescribed mandatory minimum. For
reasons described later in the paper, I argue that even this number provides an upper bound on the
likelihood that an eligible drug defendant actually receives a sentence consistent with the relevant
mandatory minimum. Moreover, whether an eligible defendant actually receives a sentence
consistent with the mandatory minimum is highly heterogeneous with respect to which court
district the defendant's case is adjudicated in, the type of drugs the defendant was convicted for
trafficking, as well as the defendant's race, gender, citizenship, and criminal history.
For example, with respect to the race and gender of the defendant, at the low end, only 16
percent of Hispanic females eligible for mandatory minimum drug sentencing actually receive a
sentence consistent with the mandated minimum, while at the high end, almost 65 percent of
eligible black males receive a sentence consistent with the mandatory minimum (which was almost
twice the rate for eligible non-black males). Similarly, whether an eligible defendant actually
receives a sentence consistent with the mandatory minimum is correlated with the type of drug the
defendant is convicted of trafficking. Defendants convicted for trafficking mandatory minimum
2 eligible amounts of crack cocaine are almost twice as likely to actually receive a sentence
consistent with the relevant mandatory minimum than defendants convicted for trafficking
mandatory minimum eligible amounts of other drugs.
Not surprisingly, many of these relationships are highly interconnected, and moreover are
strongly related to criminal history. In particular, differences in criminal history explain all of the
difference in mandatory minimum consistent sentencing between eligible defendants across drug
types, and the vast majority of the differences across genders and races. This is not surprising as
one of the primary ways mandatory eligible defendants can avoid mandatory minimum sentencing
is by being determined to be eligible for the federal "safety-valve" provision, which requires the
defendant to have a minimal criminal history, and criminal history turns out to be strongly
correlated with drug type, race, and gender.
The latter part of this paper then looks at the extent to which expected sentence length
appears to be affected by being convicted for drug amounts that trigger eligibility for a federal
mandatory minimum sentence, and evaluating whether this impact differs by defendant
characteristics.
Using a regression discontinuity estimation design, I find that on average, conviction for a
quantity that just triggers eligibility for a 10-year mandatory minimum increases expected sentence
length by a little over 1.7 years relative to those defendants convicted for quantities just under the
relevant 10-year mandatory minimum threshold. Interestingly, the analogous impact of conviction
for quantities just in excess of 5-year mandatory minimum thresholds on sentence length is also
about 1.7 years. Both of these impacts are highly statistically significant.
As stated previously, eligible females are much more likely than eligible males to avoid the
mandated minimum. Not surprisingly, this causes the average impact of the mandated minimum
sentence law on the expected sentence length of a marginally eligible offender to be much smaller
3 for females than males. However, while eligible white defendants are much more likely than
eligible black defendants to avoid the mandated minimum, and eligible powder cocaine defendants
are much more likely than eligible crack cocaine defendants to avoid the mandated minimum, the
actual impact of the law on expected sentence length for a marginally eligible defendant is higher
for whites than blacks, and higher for powder cocaine defendants than crack cocaine defendants. In
fact, being convicted for a quantity just exceeding the eligibility cutoffs for a 5- or 10-year
mandatory minimum sentence has a significant impact on expected sentence for everyone except
black defendants and crack defendants.
The explanation for this finding appears to be the following. Black and crack defendants not
eligible for mandatory minimums are much more likely to receive sentences close to or exceeding
the mandated minimums than not eligible white defendants and powder cocaine defendants (again,
often due to more substantial criminal histories). So even though eligible black and crack
defendants are less able to avoid a mandated minimum sentence than eligible white defendants or
powder cocaine defendants, among those who cannot avoid the mandated minimum, the marginal
impact of being just eligible for a mandated sentence on sentence length is substantially less severe
for black defendants and crack defendants than it is for white defendants or powder cocaine
defendants. In other words, black and crack defendants are generally sentenced sufficiently harshly
via the underlying sentencing system such that the mandatory minimums are not actually binding
on average for these types of defendants.
II - Background
Via the Anti-Drug Abuse of 1986, the U.S. Congress prescribed mandatory minimum
sentences for drug trafficking based on drug type and quantity cutoff thresholds (21 U.S.C. §841).
Table 1 summarizes the basic information regarding these federal mandatory minimum sentences.
As can be seen, according to the law, defendants convicted for their first drug trafficking offense
4 over a certain quantity of a given type of drug should receive a prison sentence of 5 years or more,
or 10 years or more, depending on the drug type and quantity. For example, if convicted for 100
kilos of marijuana, a defendant is ostensibly required to be given a sentence of 5 years or more.
Similarly, if convicted for trafficking 5 kilos of powder cocaine or more, a defendant is ostensibly
required to be given a sentence of 10 years or more. But controversially, even after the Fair
Sentencing Act of 2010, a defendant convicted for trafficking only 0.28 kilos of crack cocaine is
also ostensibly required to be given a sentence of 10 years or more. These mandated minimums are
then extended for second or third drug trafficking offenses, or if the offense also led to a death or
serious bodily injury. There are also additional extensions applied if a gun was used in the
commission of the crime.
The law is written such that judges have very little discretion of their own regarding
whether to impose the mandated minimum sentence given a conviction for requisite amounts of
given drugs. However, there are three basic ways in which a defendant ostensibly eligible for a
mandatory minimum drug sentence can get a shorter sentence than the mandated minimum. The
first is during the plea process, where prosecutors may agree to lessen the quantity they actually
charge the defendant with trafficking and thereby drop an otherwise eligible defendant below the
quantity cutoff threshold. While the data used here cannot speak conclusively to this practice, as it
only captures the quantity officially charged by the prosecutor in court not the original amount the
defendant may have been arrested with, I will give some evidence regarding this issue later in the
paper. But, if anything, because of this issue the results below provide an upper bound on how
often defendants ostensibly eligible for a mandatory minimum drug sentence actually get a
sentence consistent with that mandated minimum.
After a federal drug defendant has been convicted for trafficking a drug amount at or in
excess of the mandatory minimum cutoff---either by trial or via plea bargain---there still exist two
5 ways in which he or she can avoid the mandated minimum sentence. First, the defendant may be
determined to qualify for the federal “safety valve." Congress enacted the safety valve statute (18
U.S.C. §3553(f)) in 1994 to provide relief from the federal mandatory minimum drug sentences for
defendants that were determined by the presiding judge to have met five basic criteria: (i) the
defendant has little or no prior criminal history (category 1 criminal history), (ii) the defendant did
not use violence or possess a firearm in connection with the offense, (iii), the offense did not result
in death or serious injury to anyone, (iv) the defendant was determined not to be an organizer or
leader, and (v) the defendant was determined to fully cooperate with investigators regarding his or
her role in the offense.
The second way in which a federal drug defendant who has been convicted for trafficking a
drug amount at or in excess of the mandatory minimum cutoff can still avoid the mandated
minimum is if the prosecutor files a motion seeking a lower sentence because the defendant
provided “substantial assistance.” In particular, a judge may only go below the mandated minimum
if the prosecutor invokes 18 U.S.SC § 3553(e) in the motion (Human Rights Watch 2013).
How often and for whom these later two loop holes are applied is one of the primary
questions of this paper.
While to my knowledge there have not been papers looking at the particular questions
examined in this paper with respect to the federal mandatory minimums for drug trafficking, there
have been numerous papers looking at how different actors in the judicial system attempt to avoid
or manipulate presumptive sentence guidelines. For example, Miethe (1987), Ulmer, Kurlychek,
and Kramer (2007), Bushway and Piehl (2007), Piehl and Bushway (2007) look at how state
prosecutors manipulate charges and/or decline to pursue a mandatory minimum sentencing policy
to circumvent specific state presumptive sentencing guidelines.
6 Somewhat relatedly, while there have been few papers explicitly looking at the extent to
which defendants of different races or genders are more or less subject to federal drug mandatory
minimum sentences, a variety of papers have looked at how defendants of different races and
genders are or are not treated differently by the courts, especially with respect to the federal
sentencing guidelines (Bushway and Piehl 2001; Mustard 2001; Johnson 2003; Everett and
Wojtkiweicz 2002; Schlesinger 2005; Steffensmeier, Ulmer, and. Kramer 1998; Steffensmeier and
Demuth 2001; Abrams, Bertrand, and Mullainathan 2012; to name just a few). Generally these
papers find that after controlling for a variety of defendant and crime characteristics, black
defendants are sentenced more harshly than white defendants, and male defendants are sentenced
more harshly than female defendants. Relatedly, several more recent papers have examined
whether sentencing disparity across races and/or genders has increased subsequent to the 2005
Booker decision that made the sentencing guidelines advisory rather than mandatory (United States
Sentencing Commission 2010; Ulmer et al. 2011; Fischman and Schanzenbach 2012; Nowacki
2013; Nutting 2013, Starr and Rehavi 2013).
The most comprehensive study to date specifically looking at federal mandatory minimum
sentencing laws, and particularly the federal drug laws, is the United States Sentencing
Commission Report to Congress (United States Sentencing Commission 2011). Using data from
the 2010 fiscal year, and similar to the analysis below, they find that mandatory minimum eligible
federal drug defendants appear to receive sentences consistent with the mandated minimums less
than half of the time. Also similar to the findings below, they find eligible black defendants are
more likely to receive a sentence consistent with the mandated sentence than white or Hispanic
defendants. While the U.S.S.C. study did suggest that part of the reason black defendants were
more likely than defendants of other races to receive a sentence consistent with the mandatory
minimum might be because they were more likely to have substantial criminal records making
7 them ineligible for safety valve relief, they did not explicitly analyze this issue as done below.
Moreover, the U.S.S.C. study did not look explicitly at the direct impact of the mandatory
minimum sentences on sentence length as done below. One of the most interesting things to come
out of the U.S.S.C. study, however, was that drug amount had little correlation with offender
function (i.e. role played by the offender). In other words, drug amount appears to be a very poor
proxy for what level the defendant played in the overall operation, even though one of the
motivations for the quantity cutoffs in the mandated minimum sentence regulations was to target
higher level offenders. But, it should also be noted that the U.S.S.C. study found that relief from
mandated minimums was more likely for those who did indeed perform less serious functions.
Finally, in an important recent study, Starr and Rehavi (2014) show that while much of the
racial gap in sentence length at the federal level can be explained by racial differences in crime type
and criminal history, a substantial portion also appears to be due to differences across races at the
charging stage. Most notably, even conditional on initial charge, federal prosecutors are more likely
to charge black defendants with a mandatory minimum sentence eligible crime than white
defendants, which has substantial explanatory power regarding the resulting differences in
sentencing across races. An important distinction between Starr and Rehavi’s (2014) study and this
one is that they focus almost exclusively on non-drug offenses, while this study focuses exclusively
on drug offenses. In this way, this paper is complementary to their work, and as will be seen below,
there are both similarities and differences in the role played by mandatory minimums regarding
drug crimes versus the crimes they examine.
III - Description of the Data
The data used for this paper come from Monitoring of Federal Criminal Sentences for the
fiscal years 2011 and 2012. These data sets are collected and organized by the United States
Sentencing Commission, and contain information on all cases sentenced under the federal court
8 system between October 2010 and September 2012. These data contain a wealth of defendant
information, including conviction charge---and for drug convictions, drug type and quantity---as
well as adjudication district, and demographic and criminal history category for each defendant.
Moreover, sentencing information is provided for each case.
From this data, I extract only cases where the defendant was charged with only one type of
drug, where the drug was powder cocaine, crack cocaine, methamphetamine, marijuana, or heroin.
I also limit the sample to only those with valid data on drug amount and sentence length, and who
had no additional firearm charge.1 Then, using the quantity cutoffs in column 1 of Table 1
(corresponding to first time drug offenders), I determine which cases should be eligible for 5- or
10-year mandatory minimum sentences based on the drug type and quantity. Overall I find that of
the 23,325 observations for trafficking or possession of powder cocaine, crack cocaine,
methamphetamine, marijuana, and heroin with valid data on quantity and sentencing and no
firearm charge, about 60 percent were ostensibly eligible for a mandatory minimum sentence based
on their drug type and quantity.
At this point, it should be emphasized that the way I define eligibility for a 5- or 10-year
mandatory minimum is very conservative, and will mean that my results will, if anything, overstate
the extent to which a defendant eligible for a mandated minimum receives a sentence consistent
with that mandated minimum for two reasons. First, as stated above, the drug quantity amounts in
this data are likely to be sometimes misreported downward from the amounts the defendants may
have originally been arrested for, as during the plea bargaining process the Assistant US Attorneys
sometimes may lower the charged amount of the drug significantly from the actual amount found.
Second, as can be seen in Table 1, mandated minimums increase for defendants with past drug
1
Also, all cases adjudicated in non‐US districts such as Puerto Rico, Guam, and the Virgin Islands are excluded. The subsample used for this analysis constituted about 50 percent of all drug cases over the time period covered, and over 60 percent of the powder cocaine, crack, methamphetamine, marijuana, and heroin cases. 9 convictions (additional enhancements for violence and firearms is not an issue since such
individuals are excluded from the sample). The U.S.S.C. data does not provide information on
whether bodily injury occurred in the years analyzed here, and while the data includes each
defendant's criminal history category, it does not tell us whether any prior convictions were for
drug trafficking. Therefore, I cannot directly determine whether any defendant is eligible for an
enhanced mandatory minimum.2
So, in general, what the analysis below is really looking at is the extent to which being
convicted for drug amounts at or in excess of a mandatory minimum quantity cutoff actually leads
to a sentence at or in excess of the minimum possible mandatory sentence associated with that
quantity cutoff, and how much do sentences increase for being convicted for a drug amount just
over a mandatory minimum quantity cutoff relative to being convicted for a drug amount just under
the cutoff?
IV - Data Analysis
The first bar in Figure 1 shows the fraction of federal drug trafficking defendants who are
eligible for a 5- or 10-year mandatory minimum sentence (based on the drug type and quantity they
were convicted for) who actually receive a sentence consistent with the relevant mandatory
minimum. As can be seen, these sentences are far from mandatory, with less than half of those
eligible actually receiving a sentence consistent with the mandatory minimum. The second and
third bars in Figure 1 show the analogous results for those eligible for 5- and 10-year mandatory
minimums separately. As can be seen, results are quite consistent across these two categories, with
2
The U.S.S.C. data does have a variable reporting any mandatory minimum a defendant is ostensibly eligible for, but this variable is missing for more than half the defendants in the sample. Among those in the data set for whom this variable is not missing and are ostensibly eligible for a 5‐ or 10‐year mandatory minimum based on drug type and quantity, about 10 percent appear to be eligible for an enhanced mandatory minimum, as the mandatory minimum as listed in the U.S.S.C. data exceeds the 5‐ or 10‐year mandatory sentences we calculated using drug and quantity thresholds.
10 43 percent of those eligible for a 5-year mandatory minimum sentence actually receiving a sentence
of 5 years or more, and only 33 percent of those eligible for a 10-year mandatory minimum
sentence actually receiving a sentence of 10 years or more.
Figure 2 shows how these rates differ by race and gender (those eligible for 5- and 10-year
mandatory minimums are analyzed together). The first set of bars show the results for males, while
the second set of bars show the results for females. As can be seen, while 64 percent of black males
eligible for a mandatory minimum receive a sentence at or above the mandatory minimum
sentence, only 33 percent of mandatory minimum eligible white males and 35 percent of
mandatory minimum eligible Hispanic males actually receive a sentence consistent with the
mandated minimum.3 For all races, these rates are even lower for females, with mandatory
minimum eligible black females receiving a sentence consistent with the mandatory minimum only
29 percent of the time, and mandatory minimum eligible white and Hispanic females only
receiving sentences consistent with the mandatory minimum 20 percent and 16 percent of the time
respectively.
Moreover, even conditional on being eligible for mandatory minimum sentencing, the
likelihood of actually receiving a sentence consistent with the mandatory minimum law depends on
drug type. Figure 3 shows that while less than 35 percent of those eligible for mandatory minimum
sentencing who were convicted for powder cocaine, heroin, and marijuana actually received
sentences consistent with the mandatory minimum, 41 percent of those convicted for trafficking
mandatory minimum eligible amounts of methamphetamine received a sentence consistent with
such mandatory minimums. Most notably however, 68 percent of those convicted for trafficking
eligible amounts of crack cocaine ended up receiving sentences at or above the relevant mandatory
3
Here and throughout the paper, "white defendants" refers to non‐black non‐Hispanic defendants (therefore, would include Asian, Native American, and Pacific Islander in addition to "white" defendants.) 11 minimum. Finally, Figure 4 shows that almost 50 percent of eligible defendants who were U.S.
citizens received sentences consistent with the mandatory minimums, while only 25 percent of
eligible non-citizens did.
As described in Section II above, one of the primary ways in which defendants who appear
to be eligible to receive a mandatory minimum actually end up with a sentence less than the
mandated minimum is that they are deemed to be eligible for the "safety valve" statute. The dataset
used here actually contains an indicator revealing whether or not “safety valve” sentencing was
invoked. In 79 percent of the cases where a defendant’s drug type and listed quantity made him or
her eligible for a mandatory minimum sentence but received a sentence less than the mandated
minimum, the “safety valve” was invoked (this was almost identical for 5- and 10- year mandatory
minimum eligibility cases). As also discussed above, one of the primary criteria for being eligible
for safety valve relief was a minimal criminal history. Therefore, to what extent do differences in
criminal history, and therefore eligibility for safety-valve relief, help us understand the patterns in
Figures 2, 3(a), and 3(b)?
Figure 5 shows that indeed criminal history is strongly related to whether an eligible
defendant actually receives a sentence consistent with the mandated minimum. In particular, while
62 percent or more of eligible defendants with more substantial criminal histories (criminal history
categories 2 or higher) do end up receiving sentences consistent with the mandated minimums,
only 14 percent of those with minimal criminal histories (category 1) do. Figures 6(a) through 6(c)
show the relative presence of minimal criminal histories (by race/citizenship, drug type, and gender
among eligible defendants. As can be seen in Figure 6(a), while the fraction of eligible white
defendants with a category 1 criminal history (the minimal criminal history category that is
necessary for safety-valve eligibility) is 0.57, the analogous fraction for eligible black defendants is
only half that at 0.28. Similarly, while 80 percent of eligible Hispanic non-U.S. citizens had a
12 minimal criminal history, only 55 percent of eligible Hispanic U.S. citizens had a minimal criminal
history.
With respect to drug type, Figure 6(b) shows that while over 45 percent of eligible
defendants convicted for powder cocaine, meth, heroin, and marijuana actually had minimal
criminal histories, only 18 percent of eligible crack cocaine defendants had the minimal criminal
history necessary for safety-valve eligibility. Finally, figure 6(c) shows that the fraction of
mandatory minimum eligible males who had the minimal criminal history necessary for safetyvalve eligibility was almost 50 percent lower than the analogous fraction for eligible females.
Given many of the previously discussed covariates are highly correlated with each other
and with criminal history, which as stated above is necessary for eligibility for safety-valve relief
from a mandated minimum sentence, it is useful to look at these issues within a multivariate
regression context. Table 2 shows the results of this analysis, where the sample is limited to only
those ostensibly eligible for a 5- or 10-year mandatory minimum sentence and the dependant
variable is 1 if the defendant received a sentence consistent with the mandatory minimum and zero
otherwise. Specification (1) shows the results controlling for only gender, race, and age.
Specification (2) shows what happens when we further control for citizenship, an interaction
between citizenship and Hispanic ethnicity, and defendant education. Specification (3) shows the
results when we further control for drug type, while specification (4) further controls for criminal
history via dummies for each criminal history category. Finally, specification (5) further controls
for court district via district dummies.4
Looking first at the results with respect to race, by comparing the coefficient on the black
indicator variable across specifications, we can see that much of the racial difference in receiving a
4
All specifications are simple OLS linear probability models. Results are essentially identical if probit specifications are run instead. 13 sentence consistent with the mandatory minimum conditional on being eligible is explained by
education (specification (2)), type of drug (specification (3)), and especially criminal history
(specification (4)). This is certainly consistent with the notion that one of the primary reasons
eligible black defendants are more likely than eligible white defendants to receive a sentence
consistent with the mandated minimum is because their criminal history precludes them from
safety-valve eligibility. However, it should be noted that even after further controlling for district of
adjudication, we can see from the coefficient on the black indicator variable in specification (5) that
eligible black defendants still are significantly more likely than similarly eligible white defendants
to receive a sentence consistent with the mandatory minimum. These results are in many ways
consistent with much of the previous literature on racial disparities in sentencing in other contexts
that was cited in Section II.
Hispanic ethnicity has a somewhat complicated role. In specification (1), we see that
conditioning on only race and age, the coefficient on the Hispanic indicator variable is statistically
indistinguishable from zero, implying that eligible Hispanic defendants are no more or less likely
than eligible whites to actually receive a sentence consistent with the mandatory minimum.
However, looking at specifications (3)-(5), where I control for citizenship, type of drug and
criminal history, the positive coefficients on the two Hispanic indicator variables (one for U.S.
citizens, the other for non-citizens) suggest that eligible Hispanic defendants are actually more
likely than similar eligible white defendants to receive a mandatory minimum consistent sentence.
Indeed, once everything is controlled for in specification (5), eligible Hispanic defendants, both
U.S. citizens and non-U.S. citizens, fare similarly on this dimension to black defendants.
Table 2 is also informative with respect to the role of drug type. The coefficients on the
crack cocaine and meth indicators in specification (3) are both positive and significant (the
excluded category is marijuana). However, once we further control for criminal history
14 (specification (4)) and judicial district (specification (5)), the coefficients on these variables fall
dramatically and indeed become statistically indistinguishable from zero. Therefore, again this is
consistent with the notion that one of the primary reasons why eligible defendants convicted for
crack cocaine are so much more likely to receive a sentence consistent with the mandated minimum
than eligible marijuana or powder cocaine defendants is because they are more likely to have a
criminal history that precludes them from safety-valve relief.
Something that is also notable is that among those who are eligible for mandatory minimum
sentencing, but get a sentence less than the relevant mandatory minimum, the sentence is often well
less. For example, for those eligible for a 5 year mandatory minimum but received less, the median
sentence was only just over 2.5 years. Similarly, for those eligible for a 10 year mandatory
minimum but received less, the median sentence was only just under 4.33 years. So, for those
eligible for a mandatory minimum but who receive a sentence less than the mandatory minimum,
about fifty percent receive sentences less than half the length of the relevant mandatory minimum.
This leads us to the next section, which explicitly analyzes the impact of eligibility for a mandatory
minimum on sentence length.
V – Impact of 5- and 10-year Mandatory Minimums on Sentence Length
The previous section showed that the federal mandatory minimum sentence laws regarding
drug trafficking are actually far from mandatory, with a substantial fraction of individuals
ostensibly eligible 5- or 10-year mandatory minimums actually receiving sentences far shorter.
This leads to another important question, namely, to what extent does being convicted for
trafficking an amount at or just above a 5- or 10-year mandatory minimum quantity cutoff impact
expected sentence length, and moreover, does this impact differ by characteristics of the defendant?
This section examines these questions explicitly.
15 Given eligibility for 5- and 10-year mandatory minimum sentences are defined by strict
drug quantity cutoffs, this provides a natural application for a Regression Discontinuity (RD)
estimation design. In general, the basic RD design is useful for situations where the researcher is
interested in the impact of some treatment on a given outcome of interest, where the treatment is
applied only to individuals for whom a particular "running variable" exceeds some cutoff. The
basic RD design computes a locally weighted kernel regression for the set of individuals for whom
the running variable is just below the cutoff (but within the chosen bandwidth), then computes a
locally weighted kernel regression for the set of individuals for whom the running variable is just
above the relevant cutoff of the running variable (but within the chosen bandwidth). The RD
estimate of the impact of the treatment on the outcome is then computed by comparing the
predicted value of the outcome of interest associated with the cutoff quantity of the running
variable from the under the cutoff sub-sample to the predicted value of the outcome of interest
corresponding to the cutoff quantity of the running variable from the above the cutoff subsample.
The intuition being that the trend in the outcome variable with respect to the running variable for
those just under the cutoff quantity of the running variable acts as a valid absence of treatment
counterfactual for those individuals just above the cutoff quantity of the running variable. More
information about the procedure used can be found in Nichols (2007), and a more general
discussion the RD design can be found in Imbens and Lemieux (2008) and McCrary (2008).
In the context of this paper, the outcome variable here is sentence length, while the running
variable is the raw percentage deviation in quantity from the 5- or 10-year mandatory minimum
cutoff threshold for the relevant drug, with the 5-year and 10-year mandatory minimums analyzed
separately. So, for example, in the 10-year mandatory minimum specifications, the running variable
for a defendant who is convicted for trafficking 4 kilos of cocaine will equal (4-5)/5 = -0.2, since 5
kilos is the quantity of cocaine necessary for the 10-year mandatory minimum sentence. Similarly,
16 for a defendant who is convicted for trafficking 7 kilos of cocaine the running variable will equal
(7-5)/5 = 0.4. This means a defendant is eligible for the "treatment" (i.e., a mandatory minimum
sentence) when this running variable equals or exceeds zero, or in other words, the cutoff quantity
of the running variable is zero.
Figures 7a and 7b show a graphical depiction of the basic RD results over all defendants for
both 10- and 5-year mandatory minimum cutoffs using the “default” bandwidth.5 As can be seen, in
both cases there appears to be a jump up in expected sentence length right where the running
variable equals zero, or right when the amount drugs the defendant was convicted for crosses the
threshold for the mandatory minimum. While these figures are illuminating, more specific point
estimates along with standard errors are discussed below.
Table 3 shows the point estimates from the RD procedure along with standard errors
corresponding to the results in Figures 7a and 7b, as well as for a variety of sub-samples for both
10- and 5-year sentencing cutoffs using the “default” bandwidth. Overall, despite the fact that these
laws seem far from “mandatory,” they do appear to impact sentencing by a reasonably large
amount. Column (1) shows that for those near a 10-year mandatory minimum quantity cutoff, just
exceeding the 10-year mandated minimum cutoff appears to increase expected sentences by 1.7
years, an amount statistically significant at the 1 percent level. Similarly, Column (2) shows that for
those near a 5-year mandatory minimum cutoff, just exceeding the 5-year mandated minimum
cutoff appears to increase sentences also by an average of 1.7 years, an amount again statistically
significant at the 1 percent level. Whether these are large or small effects is a matter of opinion, but
5
In general, it is well known in RD designs, smaller bandwidths tend to produce less bias but also less precision. The "default" bandwidth used here is designed to minimize squared bias plus variance. See Imbens and Kalyanaraman (2012) for particular details. One further note, the default bandwidth changes depending on what subset of the data is used. In order for observations far away from the relevant cutoffs to have little impact on the estimates, I limited the data to observations with quantities less than 100 percent larger than the relevant cutoffs (which is then symmetric with what is observations are used for quantities less than the relevant cutoffs). I feel this is a conservative approach, but indeed not much changes if other trimming procedures are used. As will be seen, I report RD results for a number of different bandwidths besides the "default" bandwidth in the Appendix. 17 I would argue that they are relatively large given those convicted for just slightly lower amounts
(enough to keep them under the cutoff threshold) are on average receiving sentences of about 6
years for those just under the 10-year mandatory minimum thresholds, and just under 3 years for
those just under the 5-year mandatory minimum thresholds. Therefore, despite the fact that a large
fraction of those eligible for a mandatory minimum sentence actually receive a sentence shorter
than the mandated minimum, just exceeding the quantity eligibility thresholds for these laws still
appear to have a significant impact on expected sentence length.6
The lower rows of Table 3 show the RD estimates (again using the “default” bandwidth) of
the impact of just exceeding the 10- and 5-year mandatory minimum sentencing quantity thresholds
on sentencing for different subgroups. There are some somewhat surprising results. For example,
while eligible defendants convicted for crack were shown in the previous section to be substantially
and significantly more likely to receive a sentence consistent with the mandatory minimum
sentencing law than eligible defendants convicted for powder cocaine or marijuana, Table 3 shows
that the average impact of the law on sentencing is much higher for powder cocaine and marijuana
defendants than crack defendants. In fact, the estimates actually suggest that just exceeding either
the 5- or 10-year mandatory minimum cutoffs does not impact expected sentence length for crack
defendants at all.
With regards to defendant race, the previous section showed that 5- and 10-year mandatory
minimum eligible black defendants were significantly more likely to receive sentences consistent
with the mandatory minimums than eligible whites. However, Table 3 shows that the estimated
impact of just exceeding the mandatory minimum quantity thresholds on sentence length is smaller
for black defendants than it is for white or Hispanic defendants. Indeed, the impact of exceeding
6
Note, other than the separate analysis by gender, all estimates presented in Table 3 and related figures pool males and females. However, since males make up more than 85% of the cases in the sample, most of the estimates in Table 3 and the related figures primarily reflect what is happening for males. 18 the 5- or 10-year mandatory minimum quantity thresholds on sentence length is not even
statistically different from zero for black defendants, though it is for white and Hispanic
defendants.
Lastly, the final two panels of Table 3 show the impacts of just exceeding the mandatory
minimum sentence quantity thresholds by gender and citizenship. As can be seen, there are
substantial differences across gender groups, with the point estimates for males being substantially
larger than the point estimates for females. Finally, the impact of exceeding a mandatory minimum
sentence quantity threshold is significantly positive on expected sentencing for both U.S. citizens
and non-citizens, but the point estimates are somewhat higher for citizens than non-citizens at least
for the 10-year mandatory minimum thresholds.
Before discussing how to interpret some of the arguably more counter-intuitive results from
above with respect to drug type and race, it must be acknowledged that it is well known that RD
estimates can vary substantially based on bandwidth. The figures in the Appendix show how the
estimated RD effects of the mandatory minimum sentencing laws vary by bandwidth for each of
the sub-groups analyzed in Table 3 for both 10-year and 5-year mandatory minimums. Specifically,
these figures show point estimates and 95 percent confidence intervals for bandwidths ranging
between 25 percent and 175 percent of the “default” bandwidth (meaning the results for “default”
bandwidth reported in Table 3 correspond to the middle one in each figure).
As can be seen, the point estimates do move around with the chosen bandwidth, but the
basic results described above appear to hold. In general, just surpassing a 10-year mandatory
minimum quantity threshold appears to positively and significantly increase expected sentence
length overall, for all drugs other than crack, and for all defendant races other than black, over a
wide range of bandwidths. The impact of exceeding a 5-year mandatory minimum quantity
threshold also appears to generally be positive, but less robustly so. However, again the results
19 show that regardless of bandwidth, exceeding a 5-year mandatory minimum quantity threshold
does not appear to increase sentences for black defendants or crack defendants.
As a further robustness check, Table 4 shows the results from Regression Discontinuity
estimates associated with "Pseudo" Mandatory Minimum cutoffs. Specifically, column (1) shows
results from supposing the 10-year mandatory minimum quantity cutoffs were 20 percent smaller
than they are in actuality, while column (2) shows the results from supposing the 10-year
mandatory minimum quantity cutoffs were 20 percent longer than they are in actuality. Note, for
the RD methodology to be convincing, applying the RD methodology to these "Pseudo" mandatory
minimum quantity cutoffs should generally find no effects. Looking at Table 4, that is essentially
what we see. Almost all of the point estimates are small (well below a year), and only two of the
twenty-six estimates (less than 10 percent) are statistically significant at the 10 percent level.
Similar results hold if an analogous exercise is done for the 5-year mandatory minimum cutoffs.
Finally, as discussed in Section II, prosecutors potentially may manipulate drug amounts
during the plea bargaining stage. Does this affect our how we interpret the RD results shown in
Table 3? In particular, one might be concerned that prosecutors may be prone to negotiating
quantities down to being just below the mandatory minimum thresholds for some types of
defendants. As a first look at this, Figures 8a and 8b show the distribution of load sizes relative to
the 10- and 5-year quantity cutoffs, from 100 percent below the quantity cutoff to 100 percent
greater than the cutoff. The vertical line in the middle of each figure corresponds to the cutoff
threshold. If there was lots of manipulation of drug quantities to push particular defendants just
below the mandatory minimum quantity thresholds, we should see a noticeable spike in the
distribution just below the vertical line in each figure. As can be seen, with respect to the 5-year
mandatory minimum cutoffs (Figure 8b), there does appear to be slightly more cases with
quantities just below the quantity cutoffs than should be expected. On the other hand, with respect
20 to the 10-year mandatory minimum cutoffs (Figure 8a), there actually appears to be slightly more
cases with quantities just exceeding the thresholds than should be expected. In neither case are
these jumps noticeably substantial however.
As a more rigorous examination of this issue, we can test whether there is a discontinuity in
the distribution at the quantity cutoffs associated with the mandatory minimums in the manner
described by McCrary (2008). Essentially, one can estimate a smoothed version of the density of
the running variable (in our case, percentage difference between the defendant’s conviction amount
and the mandatory minimum quantity cutoff) and test to see if there is a significant discontinuity at
the RD cutoff (i.e., at zero in the case here).7 Table 5 shows the results from this exercise for the
10- and 5-year cutoffs, both overall and separately by drug type and race. As can be seen, while
there often is a significant discontinuity in the density of the estimated quantity distributions at the
mandatory minimum quantity cutoffs, these discontinuities are actually more likely to be positive
than negative.8 In other words, if anything, it is more often the case that there are slightly more
cases than should be “expected” right after the cutoff, than right under the cutoffs. Hence, it doesn’t
appear that prosecutors are particularly prone to negotiating quantities downward to get them just
below the mandatory minimum cutoffs. Rather, since quantities can generally not be increased in
the negotiation stage, it appears that prosecutors may often negotiate quantities downward, but still
staying just above the mandatory minimum quantity thresholds.
So, while one might be concerned that prosecutors negotiate the prosecuted quantity to be
just under the mandatory minimum threshold, which would mean the “seriousness” of the offenders
right below the thresholds might be greater than expected, causing the RD estimate to potentially
understate the true impact of a mandatory minimum on expected sentence length, this doesn’t
7
Thanks to Justin McCrary for providing his code for this procedure on his website. The point estimates show the log difference in height of estimated density function just after cutoff to height of estimated density function just before cutoff. 8
21 appear to be a particularly prevalent issue. Rather, given a greater number of the significant point
estimates in Table 5 are positive rather than negative, the bigger issue appears to be that while
prosecutors may negotiate the prosecuted quantity downward, they generally still keep it just over
the mandatory minimum threshold, which would mean the “seriousness” of the offenders right
above the thresholds might be greater than expected, which in turn suggests the RD estimate may
slightly overstate the true impact of a mandatory minimum on expected sentence length. Given the
RD estimates for both black and crack defendants were already statistically indistinguishable from
zero, and the density discontinuity estimates for both of these groups are never negative (meaning,
if anything, the RD estimates overstate the impact of the mandatory minimums), the basic
interpretation of the results described above arguably still holds.
As a final note, clearly the amount of a given drug a defendant is convicted for depends not
just on negotiations with prosecutors, but also the amount he was actually initially caught and
charged with. While there would seem to be substantial incentive for defendants to traffic in
amounts under the mandatory minimum cutoffs, Figures 8a and 8b (similar figures by race and by
drug are available from the author by request) and the results in Table 5 suggest that there is little
pooling just under the cutoffs. Arguably, the reason for this is that the risk of arrest in any given
transaction is quite small, causing mandatory minimums to not be the primary concern of drug
traffickers at any given time (this may be particularly the case given many defendants are not
sentenced according to the mandatory minimum as shown in the previous section). Relatedly, many
traffickers may be following orders from superiors in the drug operation and therefore not have
much discretion over what they are carrying.
VI - Interpreting the Results
Combining the results from Sections IV and V above, one thing that comes out is that
eligibility for the United States federal drug 5- and 10-year mandatory minimum sentences indeed
22 appears to significantly increase sentence length overall, despite the fact that over half of eligible
drug defendants actually do not receive a sentence consistent with the mandatory minimum
sentence. However, there are also some results that are arguably a bit puzzling. For example,
consistent with much of the public rhetoric, it is indeed the case that black defendants and crack
cocaine defendants ostensibly eligible for 5- or 10-year mandatory minimum sentences are
significantly more likely to receive a sentence consistent with the mandatory minimum than
eligible white defendants or eligible defendants convicted for marijuana or powder cocaine. Given
these findings, simple intuition would suggest that the impact of these laws on sentencing would be
quite a bit larger for black defendants and crack defendants relative to their counterparts. However,
the RD analysis showed that while exceeding a 5- or 10-year mandatory minimum quantity
threshold increased expected sentence length for most types of defendants, it actually appears to
have the smallest impact on the expected sentence length for black defendants and crack cocaine
defendants, indeed the estimated impact of becoming eligible for a mandatory minimum was not
even a statistically significant for these two groups (obviously, there is substantial overlap between
these two groups as well).
In this section I argue that the explanation for these somewhat puzzling results is that black
defendants and crack defendants simply appear to generally be sentenced much more harshly than
other defendants, often to sentences near or in excess of the mandatory minimum even when not
eligible. In other words, while eligible black defendants and eligible crack defendants are more
likely than eligible white defendants or eligible powder cocaine defendants to receive sentences
consistent with the relevant mandatory minimums, non-eligible black defendants and crack
defendants often also get sentenced quite harshly relative to other groups, indeed often at or beyond
the mandatory minimums. Therefore, even though members of these two groups are generally less
able to avoid a sentence consistent with the mandatory minimums, the impact of the law of their
23 actual sentences is muted since they likely would have received a quite severe sentence even if they
were not eligible for the mandatory minimum. In other words, the mandatory minimums often do
not appear to bind for crack defendants and black defendants. By contrast, even though much larger
fraction of eligible white defendants, or eligible powder cocaine and marijuana defendants, are able
to avoid the mandated sentence via the safety valve or substantial assistance, when they cannot, the
mandated sentence represents a substantial increase in sentence length relative to what they would
have gotten if the amount they were convicted for was just enough less so as to be under the
quantity threshold for eligibility.
To provide some evidence for this claim, Figure 9a shows the fraction of drug defendants
not eligible for a mandatory minimum sentence but who none the less receive a sentence at or in
excess of the mandatory minimum sentence, by race, for 10- and 5-year mandatory minimum
thresholds. As can be seen, the fraction of black defendants not eligible for a 10-year mandatory
minimum but who received a sentence of 10 years or longer is over twice the comparable figures
for white and Hispanic defendants not eligible for the 10-year mandatory minimum. Similarly, the
second set of bars in Figure 9a show similar results with respect to those not eligible for a 5-year
mandatory minimum but receive a sentence of 5 years or longer.
Figure 9b shows the results of a similar analysis by drug type. As can be seen, the second
set of bars show that substantial majorities of cocaine, crack, and meth defendants ostensibly not
eligible for 5 year mandatory minimums still receive sentences at or in excess of 5 years. More
notable however, is the first set of bars, which shows that while 10 percent or less of cocaine, meth,
heroin, and marijuana defendants ostensibly not eligible for 10-year mandatory minimums receive
sentences at or in excess of 10 years, almost 25 percent of crack defendants not eligible for the 10year mandatory minimum still receive sentences at or in excess of 10 years.
24 The general harshness in sentencing of crack and black defendants, regardless of mandatory
minimum eligibility, is perhaps most clearly observed via graphical depictions of the RD estimates
of the impact of exceeding a mandatory minimum quantity threshold on sentence length by group.
Figures 10a – 10e show graphical depictions of the RD estimates for exceeding the 10-year
mandatory minimum thresholds by drug type (analogous graphs for the 5-year mandatory
minimum thresholds are very similar so are not shown here due to space constraints, but are
available by request). As can be seen in Figure 10a, the expected sentence for powder cocaine
defendants convicted for quantities just below the 10-year mandatory minimum cutoff is just over 5
years, which jumps up to over 7 years for those just over the cutoff. By contrast, the expected
sentence for crack defendants convicted for quantities just below the 10-year mandatory minimum
cutoff is already around 10 years, which then stays constant for those just over the cutoff.
A similar picture emerges when looking by race. Figure 11a shows that the expected
sentence for white defendants convicted for quantities just below the 10-year mandatory minimum
cutoff is about 6 years, which jumps up to around 8 years for those just over the cutoff. By
comparison, Figure 11b shows the expected sentence for black defendants convicted for quantities
just below the 10-year mandatory minimum cutoff is already around 8 years, which then stays
relatively constant for those just over the cutoff.
The fact that expected sentence appears to drift downward as quantities exceed the
eligibility thresholds for powder cocaine and meth defendants, as well as white and Hispanic
defendants, likely reflects the fact that many defendants in these groups are able to avoid the
mandated minimum sentences via the safety valve or substantial assistance.
As a final note on this issue, it is interesting to compare the mandatory minimum sentences
associated with different quantities of different drugs to the United States Sentencing Guidelines
for drugs. Since 2005 the U.S. Sentencing Guidelines are no longer mandatory, but still are
25 advisory in the time period studied here. The mandatory minimums are actually always within or
below the guideline range, even for those in the most minimal criminal history category (see Table
A1 in Appendix), suggesting that if judges do sentence according the guidelines, the mandatory
minimums would actually not be binding. Hence, it appears that black defendants and crack
defendants are generally given sentences within the guidelines, causing the mandatory minimums
to not really impact sentence length. On the other hand, defendants of other races and convicted for
other drugs appear to often be sentenced below the guideline range, so when they are eligible for a
mandatory minimum and are not able to avoid it, their sentences are substantially increased.
One potential caveat with respect to this interpretation of the results is that one might be
concerned that the reason there is little impact of crossing the 10-year mandatory minimum
quantity thresholds on expected sentence length for black and crack defendants is because many of
black and crack defendants have previous drug convictions. As can be seen in Table 1, this would
mean many of these individuals would still be subject to a 10-year mandatory minimum or more
even if they only were convicted for a quantity in excess of the 5-year mandatory minimum
threshold. Hence, it still may be that the mandatory minimum sentencing laws are impacting black
and crack defendants, but just in different ways than other types of defendants.
While there may be some truth to the above story, it is still notable that to the extent
mandatory minimums are impacting expected sentence length for black drug defendants and crack
defendants, it is through how criminal history interacts with these laws, not the basic laws
themselves. Moreover, I would argue that the above issue is likely to be relatively minor for a few
reasons. First, if I run the RD estimates of the impact of the 10-year law on only the subset of
defendants with minimal criminal history (i.e., category I) who would not be subject to the
mandatory minimum extensions, I still find that crossing the 10-year mandatory minimum quantity
thresholds generally do not have a significant impact on expected sentence length for black and
26 crack defendants. Given the much smaller sample sizes, the RD estimates vary substantially based
on bandwidth. However, for bandwidths ranging from 25% to 175% of the "default" bandwidth, the
RD estimates of crossing the 10-year mandatory minimum quantity threshold on expected sentence
is never significant at the 5 percent level for crack defendants and is never significant even at the
10 percent level for black defendants.
The second reason why I do not think the story described above changes the interpretation
of the results too much is that the second column of numbers in Table 3 showed that the RD
estimates of crossing the 5-year mandatory minimum quantity threshold on expected sentence are
not significant for black or crack defendants either, though they are for all the other types of
defendants. Since there are no mandatory minimums that apply for quantities less than the 5-year
mandatory minimum thresholds, the previously mentioned issues regarding past drug offenses do
not apply.
Finally, as can be seen in Table 1, even if individuals have previous drug convictions,
crossing the 10-year mandatory minimum quantity thresholds (the second quantity threshold under
each drug) should still lead to a substantial bump up in mandatory minimum sentence (from 10
years to 20 years, or 10 year to life). So, one would not necessarily expect the impact of crossing a
10-year mandatory minimum quantity threshold on expected sentence length to be smaller for those
with more substantial criminal drug histories. However, as was shown in Figures 10a – 10e and 11a
– 11c, crossing these 10-year mandatory minimum thresholds impacted sentence length for
everyone except crack defendants and black defendants.
Again, as a final analysis, because many defendant characteristics are inter-related, it is
informative to once again look at some of these issues in a regression context. Table 6a shows the
results of regressing a binary variable equal to one if the defendant receives a sentence of 10 years
or more on a variety of defendant characteristics for only the sub-sample of defendants who are not
27 eligible for a 10-year mandatory minimum sentence. Like previously, specification (1) controls for
defendant gender, race, and age, specification (2) further controls for defendant education and
citizenship, specification (3) further controls for drug type, specification (4) further controls for
defendant criminal history category, and specification (5) further controls for the adjudicating
district.
As can be seen in specifications (1) and (2) of Table 6a, the positive coefficient on the black
indicator variable suggests black defendants not eligible for a 10-year mandatory minimum
sentence are more likely than white defendants to receive a sentence 10 years or longer. However,
as can be seen in specification (4), this coefficient becomes small and economically insignificant
after controlling for criminal history category, suggesting that racial differences in criminal history
primarily explained the racial gap that arose in specification (1).
Similarly, the coefficient on the crack cocaine binary variable in specification (3) of Table
6a shows that defendants convicted for crack cocaine, but in amounts not eligible for a 10-year
mandatory minimum, still were more likely to receive a sentence of 10 years or more than similar
defendants convicted for all of the other drugs. However, as can be seen by moving to specification
(4), again much of this is explained by criminal history.
Table 6b reveals that many of these patterns are similar when looking at defendants not
eligible for a 5-year mandatory minimum. However, conditional on criminal history (specifications
(4) and (5)), crack defendants not eligible for a 5-year mandatory minimum are significantly more
likely than similarly marijuana defendants to receive a sentence of 5 years or more. However,
conditional on criminal history, crack defendants not eligible for a 5-year mandatory minimum do
not appear to be significantly more likely than powder cocaine defendants not eligible for a 5-year
mandatory minimum to receive a sentence of 5 years or more.
28 So again, while it is the case that among defendants not eligible for mandatory minimums,
black defendants and crack defendants are punished more severely than their counterparts, much if
not all of this harsher treatment appears to be associated with more substantial criminal histories.
Finally, at first pass, these results may appear to be somewhat in conflict with Fischman and
Schanzenbach's (2012) interpretation of their results, namely that post-Rita, Gall, and Kimbrough
(a case that clarified the Booker decision that affirmed and expanded district court ability to depart
from federal Guidelines) racial disparity in sentencing went up because of increased relevance of
mandatory minimums. However, at closer inspection, there is not necessarily a conflict. The
primary evidence for their claim comes from looking at how the racial gap in sentencing changed
after Rita, Gall, and Kimbrough for two distinct groups of defendants---(i) those with minimal
criminal history and not arrested for a firearms offense, and (ii) those with a substantial criminal
history or a firearms offense---with the notion being that members of the latter group are ostensibly
more likely to face a binding mandatory minimum. They find that subsequent to Rita, Gall, and
Kimbrough, black defendants with minimal criminal history became no more likely than white
defendants with a minimal criminal record to receive a sentence at the statutory minimum, but
black defendants with more substantial criminal histories or a firearms offense became somewhat
more likely than white defendants with more substantial criminal histories or a firearms offense to
receive a sentence at the statutory minimum. On the other hand, they found that subsequent to Rita,
Gall, and Kimbrough, conditional on base offense level and criminal history, the gap in expected
sentence length between black and white defendants increased for both those defendants with
minimal criminal histories and those defendants with more serious criminal histories or firearms
offenses.
Note that neither of these findings are directly in conflict with the ones shown here. As
discussed above, eligible black defendants are more likely than eligible white defendants to receive
29 sentences consistent with the mandated minimum because black defendants are more likely to have
a substantial criminal history that not only excludes them from safety-valve eligibility, but also
which tends to increase sentence length more broadly. Moreover, the fact that Fischman and
Schanzenbach (2012) find black sentences went up relative to whites after Rita, Gall, and
Kimbrough regardless of criminal history class is certainly not inconsistent with the claim proposed
here that sentences for all black defendants were sufficiently high such that surpassing the quantity
threshold to be eligible for a mandated minimum did not have any marginal impact on expected
sentence length for black defendants. Finally, it should be noted that Fischman and Schanzenbach
(2012) look at all "serious" federal defendants, while this analysis looks only at those convicted for
drug trafficking.
VII - Conclusion
This paper reveals a couple of interesting findings. First, despite the name, United States
federal 5- and 10-year mandatory minimum drug sentences are far from mandatory, with more than
half of those eligible for mandatory minimum sentencing actually receiving sentences well short of
the mandatory minimum. The reason for this is that a large fraction of defendants eligible for a
mandated minimum sentence were able to get relief from the mandated sentence either because
they were determined to be eligible for the safety valve provision or prosecutors determined that
they provided "substantial assistance" to the government.
A variety of defendant characteristics were found to be strongly correlated with whether an
eligible defendant was able to avoid the mandated minimum. For example, male defendants
eligible for a mandatory minimum sentence were far more likely than eligible female defendants to
receive a sentence consistent with the mandated minimum, eligible black defendants were far more
likely than eligible white defendants to receive a sentence consistent with the mandated minimum,
and eligible defendants convicted for crack cocaine were far more likely than eligible defendants
30 convicted for other drugs to receive a sentence consistent with the mandated minimum. However,
much (but not necessarily all) of these cross group differences appear to be explained by the fact
that male defendants (relative to female), black defendants (relative to white), and defendants
convicted for crack (relative to defendants convicted for marijuana or powder cocaine) generally
have more substantial criminal histories, which in turn makes them ineligible for safety valve relief
to avoid the mandated minimum sentence.
Using a regression discontinuity approach, this analysis then looked at the impact 5- and
10-year mandatory sentence eligibility on expected sentence length. The findings showed that
despite the fact that over half of eligible defendants were able to avoid the mandated minimum, the
10-year mandatory minimum sentences increased the sentence lengths of those just over the
quantity cutoffs by an average of 1.7 years, which is substantial given that the average sentence
length for those just under the 10-year cutoffs was a little under 6 years. The analogous impact of
the 5-year mandatory minimums was to increase the expected sentence lengths of those just over
the quantity cutoffs also by about 1.7 years, which would be added to a sentence that average
around 3 years for those just under the 5-year quantity cutoff thresholds. So, overall, it appears that
the federal mandatory minimum drug sentences increase sentence lengths for those just eligible by
30 percent or more.
What is somewhat surprising however, is that while eligible black defendants and eligible
crack defendants are less often able to avoid a mandatory minimum than eligible defendants of
other races or convicted for other drugs, the mandatory minimum cutoffs actually appear to have
very little impact on sentence lengths for black defendants and crack defendants. Why the impact
of being eligible for a 5- or 10-year mandatory minimum on expected sentence length is not
significant for black defendants or for crack defendants appears to be related to the fact that even
non-mandatory minimum eligible black defendants and crack defendants are given quite long
31 sentences, meaning the mandatory minimums simply do not bind for these two (often overlapping)
groups of defendants. Moreover, once again, one reason even non-mandatory minimum eligible
black defendants and crack defendants tend to get longer sentences relative to their counterparts of
other races and drug types appears to be their generally much more extensive criminal histories,
which push up their sentences substantially.
One could argue that these results suggest some odd implications. In particular, despite the
fact that white drug offenders appear to be more able to avoid mandatory minimums than black
drug offenders, the mandatory minimums actually may decrease racial sentencing disparity by
pushing up sentences for at least some white offenders to be closer to the sentences generally given
to black offenders. However, this is probably too strong of a conclusion, as Starr and Revhavi
(2013) make clear, actually eradicating something like the mandatory minimums for drug crimes
would substantially alter numerous parts of the criminal justice system, and there is no way of
knowing how that would play out without a more direct policy experiment.
In general, the strongest conclusion that comes from the analysis presented here is that the
long sentences and large incarceration rates for black and crack defendants has little to do with the
mandatory minimum sentencing laws per se, rather it is primarily how the criminal justice system
treats these types of defendants in general, and particularly the role played by criminal history in
sentencing and relatively high rates of substantial criminal history amongst black and crack
defendants. Therefore, better understanding the processes that lead to black and crack defendants
having such relatively more extensive criminal histories than other types of defendants involved in
the drug trade is certainly a topic of paramount importance for further inquiry.
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34 Table 1 ‐ Federal Mandatory Minimum Drug Sentences, by drug and quantity 2nd Drug 3rd Drug 1st Drug Offense Offense Offense Marijuana 100 kg or more 5 yrs 10 yrs 10 yrs 1000 kg or more 10 yrs 20 yrs Life Methamphetamine 0.05 kg or more 0.5 kg or more 5 yrs 10 yrs 10 yrs 20 yrs 10 yrs Life Heroin 0.1 kg or more 1 kg or more 5 yrs 10 yrs 10 yrs 20 yrs 10 yrs Life 5 yrs 10 yrs 10 yrs 20 yrs 10 yrs Life 5 yrs 10 yrs 10 yrs 20 yrs 10 yrs Life Powder Cocaine 0.5 kg or more 5 kg or more Crack Cocaine 0.028 kg or more 0.280 kg or more 35 Table 2: Likelihood of Receiving a Mandatory Minimum Consistent Sentence
Conditional on being Eligible (Regression Results)
Control Variables
female black Hispanic age Specification
(3)
(1)
(2)
‐0.193*** (0.012) 0.278*** (0.012) 0.015 (0.010) 0.004*** (0.000) ‐0.217*** (0.012) 0.233*** (0.012) 0.005*** (0.000) ‐0.313*** (0.016) 0.027** (0.012) ‐0.135*** (0.012) ‐0.001 (0.009) ‐0.089*** (0.012) ‐0.122*** (0.024) ‐0.214*** (0.012) 0.185*** (0.014) ‐0.082*** (0.010) 0.103*** (0.011) ‐0.070*** (0.010) 0.080*** (0.013) 0.003*** (0.000) ‐0.008 (0.014) 0.104*** (0.011) 0.102*** (0.011) ‐0.006 (0.008) ‐0.028*** (0.010) 0.003 (0.020) 0.009 (0.008) 0.003 (0.013) ‐0.044*** (0.012) 0.019 (0.012) yes no 0.003*** (0.000) 0.031** (0.015) 0.099*** (0.012) 0.092*** (0.012) ‐0.005 (0.007) ‐0.028*** (0.010) 0.001 (0.020) 0.002 (0.009) ‐0.004 (0.014) ‐0.019 (0.013) ‐0.009 (0.013) yes yes 13,901 0.412 13,901 0.441 no no no no 13,901 0.090 13,901 0.133 13,901 0.149 US‐citizen, Hispanic non‐citizen, Hispanic high school degree some college college degree cocaine crack heroin meth Observations R‐squared (5)
0.006*** (0.000) ‐0.250*** (0.017) 0.071*** (0.013) ‐0.084*** (0.012) 0.003 (0.009) ‐0.074*** (0.012) ‐0.099*** (0.024) ‐0.012 (0.010) 0.176*** (0.015) ‐0.033** (0.014) 0.108*** (0.014) no no Non‐citizen, non‐Hispanic criminal history categories district fixed‐effects (4)
Coefficients on dummies for missing race, missing education, and missing criminal history
category not shown. Standard errors in parentheses. *** p < 0.01, ** p < 0.05.
36 Table 3: Regression Discontinuity Estimates of Impact of Mandatory Minimum Sentence Laws on Sentencing ("default" bandwidth) (1) 10 Year Mand Mins (2) 5 year Mand Mins all 1.71*** 1.72*** (.292) (.195) cocaine 1.61*** 0.73* (.419) (.438) crack ‐0.89 0.41 (1.019) (.628) meth 3.89*** 1.50* (1.033) (.914) marijuana 1.46** 1.36*** (.654) (.244) heroin 1.93*** 0.57 (.573) (.612) black 0.86 0.51 (.625) (.442) Hispanic 1.58*** 1.56*** (.297) (.24) White 2.06*** 1.70*** (.737) (.393) male 2.13*** 1.38*** (.389) (.163) female 0.75 1.05*** (.53) (.339) U.S. Citizen 1.79*** 1.28*** (.402) (.205) non‐Citizen 0.92*** 1.24*** (.281) (.214) Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1 37 Table 4: Regression Discontinuity Estimates of Impact of Pseudo Mandatory Minimum Sentence Laws on Sentencing ("default" bandwidth) (1) (2) Pseudo Quantity Cutoff Pseudo Quantity Cutoff 20% shorter than 10‐yr cutoffs 20% longer than 10‐yr cutoffs all ‐0.10 ‐0.23 (.36) (.398) cocaine ‐0.44 0.06 (.529) (.512) crack 1.36 0.44 (.89) (1.813) meth ‐0.52 ‐1.02 (.869) (1.016) marijuana ‐0.47 0.10 (.528) (.694) heroin 0.77 ‐2.00** (.702) (.845) black 0.43 0.25 (.659) (.793) Hispanic 0.42 0.14 (.318) (.331) White 0.06 ‐1.47* (.632) (.886) male ‐0.02 ‐0.34 (.404) (.458) female ‐0.54 0.08 (.509) (.492) U.S. Citizen 0.45 ‐0.34 (.418) (.492) non‐
Citizen ‐0.35 0.18 (.273) (.365) Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1 38 Table 5: Testing Discontinuity of Density of Quantity Distributions at Mandatory Minimum Cutoffs 10‐Year Cutoffs 5‐year Cutoffs Overall 0.32*** ‐0.51*** (0.08) (0.07) Cocaine 0.26*** 0.76*** (0.13) (0.18) Crack 1.14*** 0.24 (0.31) (0.19) Meth 0.23 1.69*** (0.19) (0.46) Marijuana ‐0.10 ‐1.49*** (0.20) (0.11) Heroin ‐0.02 0.86*** (0.17) (0.25) White 0.71*** ‐0.34*** (0.19) (0.15) Black 1.04*** 0.57*** (0.18) (0.16) Hispanic ‐0.19** ‐1.10*** (0.11) (0.11) Discontinuity estimate is log difference in height of estimated density function just after cutoff to height of estimated density function just before cutoff. ** indicates significance at 5% level, *** indicates significance at 1% level. 39 Table 6a: Likelihood of Receiving a 10+ year Sentence Conditional on
Not being Eligible for 10-year Mandatory Minimum (Regression Results)
Control Variables
female black Hispanic age Specification
(3)
(1)
(2)
‐0.053*** (0.006) 0.150*** (0.006) ‐0.032*** (0.005) 0.001*** (0.000) ‐0.064*** (0.006) 0.137*** (0.006) ‐ 0.001*** (0.000) ‐0.101*** (0.010) ‐0.020*** (0.006) ‐0.069*** (0.006) 0.011** (0.005) ‐0.034*** (0.006) ‐0.055*** (0.015) ‐0.063*** (0.005) 0.066*** (0.007) ‐ ‐0.019*** (0.005) 0.022*** (0.006) ‐ ‐0.019*** (0.005) 0.006 (0.006) ‐ 0.000 (0.000) ‐0.004 (0.009) 0.000 (0.005) 0.002 (0.005) 0.007* (0.004) ‐0.005 (0.005) 0.002 (0.013) 0.027*** (0.005) 0.105*** (0.006) 0.014** (0.007) 0.061*** (0.008) yes no 0.000 (0.000) 0.013 (0.009) 0.003 (0.006) 0.002 (0.006) 0.007* (0.004) ‐0.006 (0.005) ‐0.005 (0.013) 0.024*** (0.005) 0.105*** (0.007) 0.028*** (0.007) 0.039*** (0.009) yes yes 17,445 0.324 17,445 0.360 no no no no 17,445 0.097 17,445 0.110 17,445 0.144 US‐citizen, Hispanic non‐citizen, Hispanic high school degree some college college degree cocaine crack heroin meth Observations R‐squared (5)
0.001*** (0.000) ‐0.055*** (0.010) 0.001 (0.006) ‐0.034*** (0.006) 0.012*** (0.004) ‐0.023*** (0.006) ‐0.037** (0.015) 0.036*** (0.005) 0.173*** (0.007) 0.049*** (0.007) 0.102*** (0.009) no no Non‐citizen, non‐Hispanic criminal history categories district fixed‐effects (4)
Coefficients on dummies for missing race, missing age, and district fixed-effects not shown.
Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1
40 Table 6b: Likelihood of Receiving a 5+ year Sentence Conditional on
Not being Eligible for 5-year Mandatory Minimum (Regression Results)
Control Variables
female black Hispanic age Non‐citizen, non‐Hispanic US‐citizen, Hispanic non‐citizen, Hispanic high school degree some college college degree (1)
Specification
(3)
(2)
‐0.107*** ‐0.133*** (0.010) (0.010) 0.243*** 0.216*** (0.011) (0.011) 0.019** ‐ (0.009) 0.008*** 0.008*** (0.000) (0.000) ‐
0.137*** (0.017) 0.065*** (0.011) ‐
0.040*** (0.011) 0.053*** (0.009) 0.005 (0.011) 0.067*** (0.024) 0.005*** (0.000) 0.003*** (0.000) ‐0.132*** (0.015) 0.113*** (0.010) ‐0.058*** (0.015) 0.124*** (0.010) ‐0.006 (0.015) 0.076*** (0.011) 0.123*** (0.010) 0.015** (0.008) 0.008 (0.010) 0.051** (0.021) 0.412*** (0.008) 0.381*** (0.013) 0.300*** (0.012) 0.503*** (0.012) yes no 0.106*** (0.011) 0.008 (0.007) 0.000 (0.010) 0.027 (0.020) 0.354*** (0.008) 0.348*** (0.014) 0.300*** (0.013) 0.407*** (0.013) yes yes 15,304 0.330 15,304 0.401 15,304 0.085 15,304 0.101 15,304 0.286 meth Observations R‐squared 0.005*** (0.000) no no heroin criminal history categories district fixed‐effects ‐0.077*** (0.009) 0.008 (0.012) ‐ no no crack (5)
‐0.130*** ‐0.085*** (0.009) (0.009) 0.112*** 0.059*** (0.012) (0.012) ‐ ‐ 0.064*** (0.010) 0.023*** (0.008) ‐0.015 (0.010) 0.011 (0.021) 0.408*** (0.008) 0.443*** (0.014) 0.319*** (0.013) 0.533*** (0.012) no no cocaine (4)
Coefficients on dummies for missing race, missing age, and district fixed-effects not shown.
Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1
41 Fig 1: Sentence Consistent with Mandatory Minimum for those Eligible
0.50
0.40
0.30
0.20
0.10
0.00
0.43
0.39
0.33
5 and 10 Year Mand Mins
5 Year Mand Mins
10 Year Mand Mins
Fig 2: Sentence Consistent with Mandatory Minimum for those Eligible, by Race and Gender (5 and 10 yr Mand Mins)
1.00
0.50
0.64
white
0.35
0.33
0.20
0.29
black
0.16
hispanic
0.00
males
females
Fig 3: Sentence Consistent with Mandatory Minimum for those Eligible, by Drug Type (5 and 10 yr Mand Mins)
0.80
0.68
0.60
0.40
0.41
0.32
0.30
0.34
Heroin
Marijuana
0.20
0.00
Cocaine
Crack
Meth
42 Fig 4: Sentence Consistent with Mandatory Minimum for those Eligible, by Citizenship
(5 and 10 yr Mand Mins)
0.48
0.50
0.40
0.25
0.30
0.20
0.10
0.00
not U.S. citizen
U.S. Citizen
Fig 5: Sentence Consistent with Mandatory Minimum for those Eligible, by Criminal History Category (5 and 10 yr Mand Mins)
1.00
0.80
0.60
0.40
0.20
0.00
0.62
0.70
0.76
2
3
4
0.93
0.14
1
Criminal History Category
43 0.84
5
6
Fig 6a: Criminal History Category 1 (Minimal History), By Race
1.00
0.80
0.80
0.60
0.57
0.40
white
0.55
black
Hispanic, non‐U.S. citizen
0.28
Hispanic, U.S. citizen
0.20
0.00
Fig 6b: Criminal History Category 1 (Minimal History), By Drug Type
0.80
0.70
0.69
0.66
0.59
0.60
0.48
0.50
crack
0.40
0.30
0.20
cocaine
meth
heroin
0.18
marijuana
0.10
0.00
Fig 6c: Criminal History Category 1 (Minimal History), By Gender
0.80
0.73
0.70
0.60
0.56
0.50
male
0.40
female
0.30
0.20
0.10
0.00
44 Fig 7a: Estimated RD Effect of 10-year Mandatory Minimum
0
Expected Sentence Length (years)
2
4
6
8
10
12
Overall
-1
-.5
0
.5
Percentage difference between defendant's quantity and 10-yr cutoff
1
Fig 7b: Estimated RD Effect of 5-year Mandatory Minimum
0
Expected Sentence Length (years)
2
4
6
8
10
12
Overall
-1
-.5
0
.5
Percentage difference between defendant's quantity and 10-yr cutoff
45 1
Fig 8a: Distribution of Load Sizes Relative to 10‐year Cutoffs (Overall)
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Percentage Deviation from 10‐year Quantity Cutoff
Fig 8b: Distribution of Load Sizes Relative to 5‐year Cutoffs (Overall)
0.4
0.3
0.2
0.1
0
Percentage Deviation from 5‐year Quantity Cutoff
46 Fig 9a: Mandatory Minimum Consistent Sentence for those not Eligible, by Race
0.60
0.50
0.50
0.40
0.30
0.24
0.21
white
0.25
black
0.20
0.10
0.05
hispanic
0.02
0.00
10 yrs + Sentence, not‐eligible 5 yrs + Sentence, not‐eligible for 10‐yr Mand Min
for 5‐yr Mand Min
Fig 9b: Mandatory Minimum Consistent Sentence for those not Eligible, by Drug
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.50
0.57 0.58
Cocaine
0.41
Crack
0.26
0.07
Meth
0.12 0.09
0.07
0.01
Marijuana
10 yrs + Sentence, not‐eligible 5 yrs + Sentence, not‐eligible for 10‐yr Mand Min
for 5‐yr Mand Min
47 Heroin
Fig 10a: Estimated RD Effect of 10-year Mandatory Minimum
10
8
6
4
2
0
Expected Sentence Length (years)
12
Powder Cocaine Defendants
-1
-.5
0
.5
Percentage difference between defendant's quantity and 10-yr cutoff
1
Fig 10b: Estimated RD Effect of 10-year Mandatory Minimum
10
8
6
4
2
0
Expected Sentence Length (years)
12
Crack Cocaine Defendants
-1
-.5
0
.5
Percentage difference between defendant's quantity and 10-yr cutoff
1
Fig 10c: Estimated RD Effect of 10-year Mandatory Minimum
10
8
6
4
2
0
Expected Sentence Length (years)
12
Meth Defendants
-1
-.5
0
.5
Percentage difference between defendant's quantity and 10-yr cutoff
48 1
Fig 10d: Estimated RD Effect of 10-year Mandatory Minimum
0
Expected Sentence Length (years)
2
4
6
8
10
12
Marijuana Defendants
-1
-.5
0
.5
Percentage difference between defendant's quantity and 10-yr cutoff
1
Fig 10e: Estimated RD Effect of 10-year Mandatory Minimum
0
Expected Sentence Length (years)
2
4
6
8
10
12
Heroin Defendants
-1
-.5
0
.5
Percentage difference between defendant's quantity and 10-yr cutoff
49 1
Fig 11a: Estimated RD Effect of 10-year Mandatory Minimum
10
8
6
4
2
0
Expected Sentence Length (years)
12
White Defendants Only
-1
-.5
0
.5
Percentage difference between defendant's quantity and 10-yr cutoff
1
Fig 11b: Estimated RD Effect of 10-year Mandatory Minimum
10
8
6
4
2
0
Expected Sentence Length (years)
12
Black Defendants Only
-1
-.5
0
.5
Percentage difference between defendant's quantity and 10-yr cutoff
1
Fig 11c: Estimated RD Effect of 10-year Mandatory Minimum
10
8
6
4
2
0
Expected Sentence Length (years)
12
Hispanic Defendants Only
-1
-.5
0
.5
Percentage difference between defendant's quantity and 10-yr cutoff
50 1
APPENDIX (For Online Publication)
Table A1: United States Sentencing Guidelines vs Mandatory Minimums (in
months)
Base Criminal History Category Mandatory Minimum I II III IV V VI Marijuana < 0.25 0.25‐1 1 ‐ <2.5k 2.5 ‐ <5k ‐ ‐ ‐ ‐ 0‐6 0‐6 6‐12 10‐16 1‐7 4‐10 8‐14 12‐18 2‐8 6‐12 10‐16 15‐21 6‐12 10‐16 15‐21 21‐27 9‐15 15‐21 21‐27 27‐33 12‐18 18‐24 24‐30 30‐37 5 ‐ <10k ‐ 15 ‐ 21 18 ‐ 24 21 ‐ 27 27 ‐ 33 33 ‐ 41 37 ‐ 46 10 ‐ <20k ‐ 21 ‐ 27 24 ‐ 30 27 ‐ 33 33 ‐ 41 41 ‐ 51 46 ‐ 57 20 ‐ <40k ‐ 27 ‐ 33 30 ‐ 37 33 ‐ 41 41 ‐ 51 51 ‐ 63 57 ‐ 71 40 ‐ <60k ‐ 33 ‐ 41 37 ‐ 46 41 ‐ 51 51 ‐ 63 63 ‐ 78 70 ‐ 87 60 ‐ <80k ‐ 41 ‐ 51 46 ‐ 57 51 ‐ 63 63 ‐ 78 77 ‐ 96 84 ‐ 105 80 ‐ <100k ‐ 51 ‐ 63 57 ‐ 71 63 ‐ 78 77 ‐ 96 92 ‐ 115 100 ‐ 125 100 ‐ <400k 60 63 ‐ 78 70 ‐ 87 78 ‐ 97 92 ‐ 115 110 ‐ 137 120 ‐ 150 400 ‐ <700k 60 78 ‐ 97 87 ‐ 108 97 ‐ 121 110 ‐ 137 130 ‐ 162 140 ‐ 175 700 ‐ <1,000k 60 97 ‐ 121 108 ‐ 135 121 ‐ 151 135 ‐ 168 151 ‐ 188 168 ‐ 210 1,000 ‐ 3,000k 120 121 ‐ 151 135 ‐ 168 151 ‐ 188 168 ‐ 210 188 ‐ 235 210 ‐ 262 3,000 ‐ <10,000k 120 151 ‐ 188 168 ‐ 210 188 ‐ 235 210 ‐ 262 235 ‐ 293 262 ‐ 327 10,000 ‐ <30,000k 120 188 ‐ 235 210 ‐ 262 235 ‐ 293 262 ‐ 327 292 ‐ 365 324 ‐ 405 >=30,000k Meth < 0.0025 0.0025 ‐ 0.005 0.0055 ‐ 0.010 0.01 ‐ 0.02 0.02 ‐ 0.03 0.03 ‐ 0.04 0.04 ‐ 0.050 0.05 ‐ 0.2 0.20 ‐ 0.35 0.35 ‐ 0.50 0.50 ‐ 1.5 1.5 ‐ 5 5‐15 >= 15 Cocaine <0.025 120 235 ‐ 293 262 ‐ 327 292 ‐ 365 324 ‐ 405 360 ‐ life 360 ‐ life ‐ ‐ ‐ ‐ ‐ ‐ ‐ 60 60 60 120 120 120 120 10‐16 15 ‐ 21 21 ‐ 27 27 ‐ 33 33 ‐ 41 41 ‐ 51 51 ‐ 63 63 ‐ 78 78 ‐ 97 97 ‐ 121 121 ‐ 151 151 ‐ 188 188 ‐ 235 235 ‐ 293 12‐18 18 ‐ 24 24 ‐ 30 30 ‐ 37 37 ‐ 46 46 ‐ 57 57 ‐ 71 70 ‐ 87 87 ‐ 108 108 ‐ 135 135 ‐ 168 168 ‐ 210 210 ‐ 262 262 ‐ 327 15‐21 21 ‐ 27 27 ‐ 33 33 ‐ 41 41 ‐ 51 51 ‐ 63 63 ‐ 78 78 ‐ 97 97 ‐ 121 121 ‐ 151 151 ‐ 188 188 ‐ 235 235 ‐ 293 292 ‐ 365 21‐27 27 ‐ 33 33 ‐ 41 41 ‐ 51 51 ‐ 63 63 ‐ 78 77 ‐ 96 92 ‐ 115 110 ‐ 137 135 ‐ 168 168 ‐ 210 210 ‐ 262 262 ‐ 327 324 ‐ 405 27‐33 33 ‐ 41 41 ‐ 51 51 ‐ 63 63 ‐ 78 77 ‐ 96 92 ‐ 115 110 ‐ 137 130 ‐ 162 151 ‐ 188 188 ‐ 235 235 ‐ 293 292 ‐ 365 360 ‐ life 30‐37 37 ‐ 46 46 ‐ 57 57 ‐ 71 70 ‐ 87 84 ‐ 105 100 ‐ 125 120 ‐ 150 140 ‐ 175 168 ‐ 210 210 ‐ 262 262 ‐ 327 324 ‐ 405 360 ‐ life ‐ 10‐16 12‐18 15‐21 21‐27 27‐33 30‐37 51 0.025 ‐ 0.050 0.05 ‐ 0.10 0.1 ‐ 0.2 0.2 ‐ 0.3 0.3 ‐ 0.4 0.4 ‐ 0.5 0.5 ‐ 2 2 ‐ 3.5 3.5 ‐ 5 5‐15 15 ‐ 50 50 ‐ 150 >=150 Crack Cocaine < 0.0014 0.0014‐0.0028 0.0028‐0.0056 0.0056‐0.0112 0.0112‐0.0168 0.0168‐0.0224 0.0224‐0.028 0.028‐0.112 0.112‐0.196 0.196‐0.28 0.280‐0.840 0.84‐2.8 2.8‐8.4 > 8.4 Heroin <0.005 0.005 ‐ 0.010 0.01 ‐ 0.02 0.02 ‐ 0.04 0.04 ‐ 0.06 0.06 ‐ 0.08 0.08 ‐ 0.10 0.1 ‐ 0.4 0.4 ‐ 0.7 0.7 ‐ 1 1‐3 3‐10 10‐30 >30 ‐ ‐ ‐ ‐ ‐ ‐ 60 60 60 120 120 120 120 15 ‐ 21 21 ‐ 27 27 ‐ 33 33 ‐ 41 41 ‐ 51 51 ‐ 63 63 ‐ 78 78 ‐ 97 97 ‐ 121 121 ‐ 151 151 ‐ 188 188 ‐ 235 235 ‐ 293 18 ‐ 24 24 ‐ 30 30 ‐ 37 37 ‐ 46 46 ‐ 57 57 ‐ 71 70 ‐ 87 87 ‐ 108 108 ‐ 135 135 ‐ 168 168 ‐ 210 210 ‐ 262 262 ‐ 327 21 ‐ 27 27 ‐ 33 33 ‐ 41 41 ‐ 51 51 ‐ 63 63 ‐ 78 78 ‐ 97 97 ‐ 121 121 ‐ 151 151 ‐ 188 188 ‐ 235 235 ‐ 293 292 ‐ 365 27 ‐ 33 33 ‐ 41 41 ‐ 51 51 ‐ 63 63 ‐ 78 77 ‐ 96 92 ‐ 115 110 ‐ 137 135 ‐ 168 168 ‐ 210 210 ‐ 262 262 ‐ 327 324 ‐ 405 33 ‐ 41 41 ‐ 51 51 ‐ 63 63 ‐ 78 77 ‐ 96 92 ‐ 115 110 ‐ 137 130 ‐ 162 151 ‐ 188 188 ‐ 235 235 ‐ 293 292 ‐ 365 360 ‐ life 37 ‐ 46 46 ‐ 57 57 ‐ 71 70 ‐ 87 84 ‐ 105 100 ‐ 125 120 ‐ 150 140 ‐ 175 168 ‐ 210 210 ‐ 262 262 ‐ 327 324 ‐ 405 360 ‐ life ‐ ‐ ‐ ‐ ‐ ‐ ‐ 60 60 60 120 120 120 120 10‐16 15 ‐ 21 21 ‐ 27 27 ‐ 33 33 ‐ 41 41 ‐ 51 51 ‐ 63 63 ‐ 78 78 ‐ 97 97 ‐ 121 121 ‐ 151 151 ‐ 188 188 ‐ 235 235 ‐ 293 12‐18 18 ‐ 24 24 ‐ 30 30 ‐ 37 37 ‐ 46 46 ‐ 57 57 ‐ 71 70 ‐ 87 87 ‐ 108 108 ‐ 135 135 ‐ 168 168 ‐ 210 210 ‐ 262 262 ‐ 327 15‐21 21 ‐ 27 27 ‐ 33 33 ‐ 41 41 ‐ 51 51 ‐ 63 63 ‐ 78 78 ‐ 97 97 ‐ 121 121 ‐ 151 151 ‐ 188 188 ‐ 235 235 ‐ 293 292 ‐ 365 21‐27 27 ‐ 33 33 ‐ 41 41 ‐ 51 51 ‐ 63 63 ‐ 78 77 ‐ 96 92 ‐ 115 110 ‐ 137 135 ‐ 168 168 ‐ 210 210 ‐ 262 262 ‐ 327 324 ‐ 405 27‐33 33 ‐ 41 41 ‐ 51 51 ‐ 63 63 ‐ 78 77 ‐ 96 92 ‐ 115 110 ‐ 137 130 ‐ 162 151 ‐ 188 188 ‐ 235 235 ‐ 293 292 ‐ 365 360 ‐ life 30‐37 37 ‐ 46 46 ‐ 57 57 ‐ 71 70 ‐ 87 84 ‐ 105 100 ‐ 125 120 ‐ 150 140 ‐ 175 168 ‐ 210 210 ‐ 262 262 ‐ 327 324 ‐ 405 360 ‐ life ‐ ‐ ‐ ‐ ‐ ‐ ‐ 60 60 60 120 120 120 120 10‐16 15 ‐ 21 21 ‐ 27 27 ‐ 33 33 ‐ 41 41 ‐ 51 51 ‐ 63 63 ‐ 78 78 ‐ 97 97 ‐ 121 121 ‐ 151 151 ‐ 188 188 ‐ 235 235 ‐ 293 12‐18 18 ‐ 24 24 ‐ 30 30 ‐ 37 37 ‐ 46 46 ‐ 57 57 ‐ 71 70 ‐ 87 87 ‐ 108 108 ‐ 135 135 ‐ 168 168 ‐ 210 210 ‐ 262 262 ‐ 327 15‐21 21 ‐ 27 27 ‐ 33 33 ‐ 41 41 ‐ 51 51 ‐ 63 63 ‐ 78 78 ‐ 97 97 ‐ 121 121 ‐ 151 151 ‐ 188 188 ‐ 235 235 ‐ 293 292 ‐ 365 21‐27 27 ‐ 33 33 ‐ 41 41 ‐ 51 51 ‐ 63 63 ‐ 78 77 ‐ 96 92 ‐ 115 110 ‐ 137 135 ‐ 168 168 ‐ 210 210 ‐ 262 262 ‐ 327 324 ‐ 405 27‐33 33 ‐ 41 41 ‐ 51 51 ‐ 63 63 ‐ 78 77 ‐ 96 92 ‐ 115 110 ‐ 137 130 ‐ 162 151 ‐ 188 188 ‐ 235 235 ‐ 293 292 ‐ 365 360 ‐ life 30‐37 37 ‐ 46 46 ‐ 57 57 ‐ 71 70 ‐ 87 84 ‐ 105 100 ‐ 125 120 ‐ 150 140 ‐ 175 168 ‐ 210 210 ‐ 262 262 ‐ 327 324 ‐ 405 360 ‐ life 52 Estimated Impact of 10-yr Mandatory Minimum Eligibility
-2
Estimated effect (sentence years)
0
2
4
6
(by bandwidth)
.18
.37
.55
.74
Bandwidth
CI
.92
1.1
1.3
Est
Estimated Impact of 5-yr Mandatory Minimum Eligibility
-2
Estimated effect (sentence years)
0
2
4
6
(by bandwidth)
9.0e-02
.18
.27
.36
Bandwidth
CI
53 .45
Est
.54
.63
Estimated Impact of 10-yr Mandatory Minimum Eligibility
-8
-6
-4
Estimated effect
-2 0
2
4
6
8
Cocaine Defendants Only (by bandwidth)
.17
.35
.52
.69
Bandwidth
CI
.87
1
1.2
Est
Estimated Impact of 5-yr Mandatory Minimum Eligibility
-8
-6
-4
Estimated effect
-2 0
2
4
6
8
Cocaine Defendants Only (by bandwidth)
.2
.4
.61
.81
Bandwidth
CI
54 1
Est
1.2
1.4
Estimated Impact of 10-yr Mandatory Minimum Eligibility
-8
-6
Estimated effect
-4 -2 0 2 4
6
8
Crack Defendants Only (by bandwidth)
.17
.33
.5
.66
Bandwidth
CI
.83
1
1.2
Est
Estimated Impact of 5-yr Mandatory Minimum Eligibility
-8
-6
-4
Estimated effect
-2 0
2
4
6
8
Crack Defendants Only (by bandwidth)
.17
.35
.52
.7
Bandwidth
CI
55 .87
Est
1
1.2
Estimated Impact of 10-yr Mandatory Minimum Eligibility
-8
-6
-4
Estimated effect
-2 0
2
4
6
8
Meth Defendants Only (by bandwidth)
.13
.27
.4
.54
Bandwidth
CI
.67
.81
.94
Est
Estimated Impact of 5-yr Mandatory Minimum Eligibility
-8
-6
-4
Estimated effect
-2 0
2
4
6
8
Meth Defendants Only (by bandwidth)
.15
.3
.45
.6
Bandwidth
CI
56 .75
Est
.9
1.1
Estimated Impact of 10-yr Mandatory Minimum Eligibility
6
4
2
0
-2
-4
-6
-8
Expected Sentence Length (years)
8
Marijuana Defendants Only (by bandwidth)
.19
.39
.58
.77
.97
1.2
1.4
Percentage difference between defendant's quantity and 10-yr cutoff
CI
Est
Estimated Impact of 5-yr Mandatory Minimum Eligibility
-8
-6
Estimated effect
-4 -2 0
2
4
6
8
Marijuana Defendants Only (by bandwidth)
8.6e-02
.17
.26
.35
Bandwidth
CI
57 .43
Est
.52
.61
Estimated Impact of 10-yr Mandatory Minimum Eligibility
-8
-6
-4
Estimated effect
-2 0
2
4
6
8
Heroin Defendants Only (by bandwidth)
.16
.32
.48
.64
Bandwidth
CI
.79
.95
1.1
Est
Estimated Impact of 5-yr Mandatory Minimum Eligibility
-8
-6
-4
Estimated effect
-2 0
2
4
6
8
Heroin Defendants Only (by bandwidth)
.15
.3
.46
.61
Bandwidth
CI
58 .76
Est
.91
1.1
Estimated Impact of 10-yr Mandatory Minimum Eligibility
-8
-6
-4
Estimated effect
-2 0
2
4
6
8
White Defendants Only (by bandwidth)
.15
.31
.46
.62
Bandwidth
CI
.77
.92
1.1
Est
Estimated Impact of 5-yr Mandatory Minimum Eligibility
-8
-6
-4
Estimated effect
-2 0
2
4
6
8
White Defendants Only (by bandwidth)
.11
.23
.34
.46
Bandwidth
CI
59 .57
Est
.68
.8
Estimated Impact of 10-yr Mandatory Minimum Eligibility
-8
-6
-4
Estimated effect
-2 0
2
4
6
8
Black Defendants Only (by bandwidth)
.2
.39
.59
.79
Bandwidth
CI
.98
1.2
1.4
Est
Estimated Impact of 5-yr Mandatory Minimum Eligibility
-8
-6
-4
Estimated effect
-2 0
2
4
6
8
Black Defendants Only (by bandwidth)
.19
.38
.57
.76
Bandwidth
CI
60 .95
Est
1.1
1.3
Estimated Impact of 10-yr Mandatory Minimum Eligibility
-8
-6
-4
Estimated effect
-2 0
2
4
6
8
Hispanic Defendants Only (by bandwidth)
.2
.39
.59
.79
Bandwidth
CI
.99
1.2
1.4
Est
Estimated Impact of 5-yr Mandatory Minimum Eligibility
-8
-6
-4
Estimated effect
-2 0
2
4
6
8
Hispanic Defendants Only (by bandwidth)
9.1e-02
.18
.27
.36
Bandwidth
CI
61 .45
Est
.54
.64