American Economic Journal: Economic Policy 2021, 13(2): 408–438
https://doi.org/10.1257/pol.20170474

Impacts of Private Prison Contracting on Inmate Time
Served and Recidivism†
By Anita Mukherjee*
This paper examines the impact of private prison contracting by
exploiting staggered prison capacity shocks in Mississippi. Motivated
by a model based on the typical private prison contract that pays a
per diem for each occupied bed, the empirical analysis shows that
private prison inmates serve 90 additional days. This is alternatively
estimated as 4.8 percent of the average sentence. The delayed release
erodes half of the cost savings offered by private contracting and is
linked to the greater likelihood of conduct violations in private prisons. The additional days served do not lead to apparent changes in
inmate recidivism. (JEL H76, K42)

T

he United States contains 5 percent of the world’s population but 25 percent
of its prisoners, and spends more than $80 billion each year managing these
inmates (BJS 2015, 2016; Liptak 2008). The size of the prisoner population has
increased more than ­six-fold since 1980, creating concerns about excessive costs
and prison overcrowding that have fueled a trend toward private contracting.
Currently, about 10 percent of all prisoners in the United States are in private facilities. This allocation is much higher in federal prisons: for example, 73 percent of
immigration detention centers are privately operated (Homeland Security Advisory
Council 2016). Private prison contracting is also becoming more common globally,
especially in the United Kingdom, Australia, and New Zealand. Advocacy groups,
governments, and scholars have voiced numerous concerns about this $5 billion
industry ranging from human rights violations to the lack of evidence on promised cost savings, but to date there has been little analysis to verify or dispel these
concerns.
The economic tension is that public and private companies are unlikely to maximize the same objective function. Private prison companies are typically paid a
per diem for each occupied bed with few other conditions, creating a potentially

* University of Wisconsin-Madison, 975 University Ave., Madison, WI, 53706 (email: anita.mukherjee@wisc.
edu). Matthew Notowidigdo was coeditor for this article. I am indebted to David S. Abrams, Fernando Ferreira,
Olivia S. Mitchell, and Jeremy Tobacman for their guidance and support on this paper. I thank Hessam Bavafa,
Kerwin Charles, Anthony DeFusco, John DiIulio, Mark Duggan, Steven Durlauf, Jean-Françcois Houde, Judd
Kessler, John MacDonald, Emily Owens, Daniel Sacks, Jesse Shapiro, and Justin Sydnor for helpful comments.
I gratefully acknowledge financial assistance from the Wisconsin Alumni Research Foundation and the University
of Pennsylvania’s Pension Research Council and the Population Studies Center.
†
Go to https://doi.org/10.1257/pol.20170474 to visit the article page for additional materials and author
disclosure statement(s) or to comment in the online discussion forum.
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perverse incentive for them to maximize the number of occupied beds. The extent
to which these incentives can be powerful is highlighted by cases of corruption:
for example, a private prison company paid two judges over $2.6 million to inflate
offender sentences and assign them to its juvenile facility (Chen 2009). In another
case relevant to the current study, the Commissioner of the Mississippi Department
of Corrections and a h­ igh-ranking colleague recently had to step down from their
posts and were sentenced to nearly 20 years in prison for accepting bribes to promote private contracting (Amy 2017).
Despite evidence that private prison operators respond to contract incentives, little empirical work to date has examined whether inmates in private prison serve
more time than those in public prison. Time served in prison is an important outcome because it is the primary punishment that society imposes on offenders. This
punishment is carried out unfairly, however, if it varies systematically with whether
an inmate is assigned to a private or public prison. Beyond the fairness aspect, the
number of days a prisoner is incarcerated directly erodes the cost savings offered
by private contracting. Yet, private contracting may still be appealing if competition
improves quality, for example, through reductions in recidivism. Hence, I also study
this outcome.
This paper exploits the staggered entry and exit of private prisons in Mississippi
between 1996 and 2004 to contribute instrumental variable (IV) estimates of the
impact of private prison on inmate time served and recidivism. The rich set of
inmate data available make it possible to control for a wide range of characteristics
that are known to predict these outcomes. The striking differences across inmates
in public and private prison raise concerns about selection on unobservable characteristics, however. Private prison inmates have longer sentences and have different
racial, age, and marital status composition. They also serve a greater fraction of their
sentences (73 percent versus 70 percent). If prison assignment is based on characteristics unobservable to the researcher, a credible empirical strategy requires a source
of experimental or q­ uasi-experimental variation to draw valid conclusions about the
effect of private prisons on inmate outcomes. The large capacity shocks from private
prison openings, expansions, and closings provide this needed variation by serving
as instruments for prison assignment.
Figure 1 shows the daily inmate population across all private prisons: the state
filled each private prison within two weeks of their opening or expanding, and then
operated them at nearly full capacity. This pattern suggests that the probability with
which an inmate was assigned to private prison is an increasing function of private
prison bed capacity, a relationship that persists in a formal regression analysis. This
finding enables an IV estimation in which the identifying assumption is that the
sharp shocks to private prison bed capacity did not independently affect inmate time
served or recidivism, an assumption that is plausible given that ­cost-cutting is typically the main motivation for private contracting.
Prior research on comparing inmate outcomes in public versus private prisons
has been limited to observational studies that do not address potentially ­nonrandom
selection of inmates to private prison. They also focus mostly on recidivism, though
an important exception is a working paper by Lindqvist (2008), which examines
residential treatment centers for youth in Sweden. The paper finds that those in

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Public prison

12,000

9,000
3,000

Private
prison
6,000

2,000

3,000

1,000

0

Private prison daily population

Public prison daily population

4,000

0
1996

1998

2000

2002

2004

2006

2008

2010

2012

Figure 1. Daily Prison Population by Facility, 1­ 996–2012
Notes: Daily inmate population in Mississippi for public and private prisons for all adult male inmates admitted
between May 1, 1996 and May 1, 2012. The spikes (indicated by the vertical lines) correspond to shocks in the
private prison capacity either through private prison entry, closure, or bed expansion. The dip in the private prison
population in March 2001 corresponds to the opening of a juvenile private prison facility, where many inmates aged
18 to 20 were transferred upon its opening. The shaded region indicates data post July 31, 2004, which is not used
in estimation (except in robustness checks) and is reserved for observing the conclusion of sentences served and
recidivism.

privately owned centers spent more days in treatment compared to those in p­ ublic
centers. Some previous studies have found increases in recidivism for private prison
inmates (Bayer and Pozen 2005, Spivak and Sharp 2008), while others have found no
differences in this outcome (Bales et al. 2005; L
­ anza-Kaduce, Parker, and Thomas
1999).1 The empirical models in these papers do not attempt to deal with inmate
selection to private prison. Additionally, these prior studies do not typically use
information on an inmate’s location throughout his sentence and instead limit the
definition of private prison exposure to whether the inmate began or finished his
sentence in such a location. This simplification causes mismeasurement in the extent
of private prison exposure, a limitation that the present study addresses.
I begin by constructing a model to help motivate the empirical analysis. As noted,
the standard private prison contract pays a per diem for each occupied bed with
­limited additional contingencies; similar contracts are common in health care.2
1
Bayer and Pozen (2005) find that juvenile offenders released from private prisons have 5 to 8 percent higher
rates of o­ ne-year recidivism; they study the role of ­nonprofit private prisons, which are more prevalent in the
juvenile prison system. Bales et al. (2005) and ­Lanza-Kaduce, Parker, and Thomas (1999), however, use similar
data and find no effect of private prison assignment on recidivism rates for male, female, or juvenile offenders in
Florida. Spivak and Sharp (2008) estimate a 16 percent greater recidivism rate using data on adult male offenders
in Oklahoma.
2
Per diem reimbursement is a key form of prospective payment method in health care (Casto and Forrestal
2013). These contracts are common in settings ranging from Medicaid nursing home reimbursements in the
United States (Intrator et al. 2007) to hospital reimbursements in Asian countries (Jian and Guo 2009, Rodwin
and Okamoto 2000).

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The theoretical prediction given this type of contract is that private operators may
increase recidivism because they ignore the benefits of n­ oncontractible quality, for
example, in the form of rehabilitation programs (Hart, Shleifer, and Vishny 1997). In
the model, the private operator selects whether to distort release decisions based on
the marginal profit and the level of government monitoring. The model also yields
implications for recidivism based on the assumption that recidivism risk declines
with time since offense, as in Kuziemko (2013).
I study inmate time served using primarily a set of IV regressions. The instrument measures the capacity shock in private prisons experienced by each inmate;
it equals the net number of private prison bed openings over the assigned sentence.
The IV estimate shows that private prison inmates serve about 90 extra days, alternatively measured as 4.8 additional percent of their sentences. The OLS estimates
are similar to the IV results, which suggests that the main controls used in these
models are sufficient to address the most important sources of selection bias. I then
explore a mechanism to explain the observed difference in inmate time served and
establish that the widespread use of infractions (prison conduct violations) in private
prisons is the likely reason for delayed release. Baseline infraction rates in public
and private prisons are 18 and 46 percent, respectively. Even after controlling for all
covariates, I find that an inmate in private prison is 9 to 14 percent more likely to be
cited with an infraction over the course of his sentence.
The final step in the analysis examines recidivism, defined as an inmate’s probability of r­ e-offending with a new felony within three years of release. The IV estimate of the impact of private prison on this outcome is not statistically significant;
the 95 percent confidence interval includes effects ranging from −5.7 to 9.1 percent. The literature examines mostly the impact of time served on recidivism and
offers a range of possible effects. For example, M
­ ueller-Smith (2017) finds that 90
additional days in prison (the results in the present paper) would translate to a 1 to
1.8 percent increase in quarterly recidivism. By contrast, estimates in Kuziemko
(2013), Bhuller et al. (2018), and Zapryanova (2014) suggest a 3 percent reduction
in recidivism risk for 90 additional days. (Part of the reason for the conflicting evidence is because the marginal impact of incarceration depends on the incarceration
rate itself, as noted in Raphael and Stoll 2014.)
The rest of this paper is organized as follows. Section I provides institutional background on private prison contracting and the parole system in Mississippi. Section II
provides a model of release policies in private versus public prisons. Section III
describes the data. Section IV details the empirical strategy. Section V discusses
the results on time served and infractions, a mechanism for the delayed release.
Section VI revisits the model and discusses the recidivism results. Section VII provides robustness checks, and Section VIII concludes.
I. Institutional Background

The correctional facilities in Mississippi include four private prisons and three
state prisons, along with several county jails (all public) approved for holding
­long-term inmates. About 40 percent of all the state’s prison beds are private. The
private and public prisons are comparable on most dimensions. For example, they

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offer ­
state-mandated resources including drug rehabilitation programs and are
accredited by the American Correctional Association. Private companies exert
control over a wide range of management decisions, however, ranging from meal
choices to employee contracts. Over the time period studied, private prison guards
in Mississippi earned $35,000 (compared to $50,000 for public prison guards) annually and had fewer employee benefits (MDOC 2012).
A. Private Prison Contracts
States contract with private prison operators to save costs and expand bed capacity.3 When selecting a contractor, the state solicits proposals for private prison beds
and these “per diem” beds are required to provide at least a 10 percent cost savings compared to the public prison.4 The per diem payments depend only on the
type of bed supplied (i.e., a ­high-security bed is provided a larger ­per diem than a
­medium-security bed), with some additional transfers for inmate health expenses.
All private prisons in Mississippi were paid per bed occupied until May 2001. At
that time, two private prisons were promised a guaranteed payment for 90 percent
of the beds with a p­ er diem for the remaining beds. The guarantee was inoperative,
however, since the prisons typically operated above 90 percent occupancy.5
B. Prison Assignment and Parole Processes
Prisons in Mississippi are reserved for inmates who commit felonies and have
sentences of at least one year. Once an offender is convicted of a felony, he is transferred to a public prison for classification. I detail the variables related to classification in Section III. The state then places the inmate in a private prison bed if
one is available; because private prisons are mandated to be less expensive on a
­per-prisoner, ­per-day basis, the state mandates that these beds are filled first. If no
private bed is available, the inmate goes to public prison but may later be moved.
The data show that 90 percent of inmates who go to private prison remain there
until release. Generally, inmates who are moved are done so by the state. Inmaterequested moves are rare because they must pay for the vehicle and security during
the transport.
Most inmates are released by a parole board prior to completion of their sentences.
Factors influencing release are the amount of time already served (at least 25 ­percent
3
A quote from former Mississippi Department of Corrections Commissioner S.W. Pickett to Mississippi’s
Governor and State Legislature in 1996 (the year the state began private prison contracting) illustrates these
core goals: “The end of the Fiscal Year 1995 was essentially the middle of the largest expansion program in the
Mississippi Department of Corrections’ history. Included in this expansion was the initiation of institutional privatization. This approach will minimize construction expenditure obligated by the state to relieve overcrowding,
and must show at least a 10 percent cost savings in operational expenses. Our current expansion program will help
ensure that Mississippi has an adequate number of prison beds to house those offenders sentenced to the Agency”
(MDOC 1996, 2).
4
The Mississippi Senate Bill ​#​2005 states: “No contract for private incarceration shall be entered into unless
the cost of the private operation, including the state’s cost for monitoring the private operators, offers a cost savings
of at least 10 percent to the Department of Corrections for at least the same level and quality of service offered by
the Department of Corrections.” https://www.peer.ms.gov/Reports/reports/458.html.
5
I show that there is no heterogeneity by contract structure in online Appendix Table A.1.

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of the original sentence is required), severity of the main offense, ­community ­support
or opposition to the inmate’s release, prior criminal records, crimes committed
while incarcerated, behavior in prison, and participation in rehabilitative programs.
Importantly, whether the inmate spent time in private or public prison is not a factor,
and the parole process is the same for inmates regardless of their prison placement.
Parole in Mississippi requires a unanimous vote from an appointed board, which
always consists of five state employees who serve on a rotating basis.6
II. A Model of Prisoner Release Decisions

I develop a model of prisoner release decisions to illustrate the distortion that
can result from private contracting. The model borrows elements from Kuziemko
(2013), which studied the costs and benefits of discretionary parole regimes. The
setup also incorporates an important aspect of the incomplete contracting model in
Hart, Shleifer, and Vishny (1997), which argued that private prison operators may
undertake excessive cost cutting because they ignore the impact of these cost reductions on ­noncontractible quality. Both of these models, and hence the present model,
also draw elements from Shavell (1987), which provides a framework for studying
optimal prisoner release policies.
A. Baseline Model without Private Contracting
I posit that a state chooses an optimal release policy based on the t­rade-off
between incarceration costs and the cost of ­severity-weighted recidivism risk. As
in Kuziemko (2013), incarcerating a prisoner for an additional day costs the government some amount, but society benefits from a reduction in crime due to both
an incapacitation effect (i.e., the prisoner cannot commit crime while incarcerated,
and may even “age” out of crime while incarcerated) and a specific deterrence effect
(i.e., a prisoner’s recidivism risk declines with time since the original offense as a
result of punishment).7
Let prisoner ​i​pose a ­severity-weighted cost of recidivism ​​r​i​​​that is a function
of his ­individual-specific risk, R​
​​ i​​​, and a parameter ​​βi​​​  > 0​that captures the rate
at which his recidivism risk decreases with the number of days since his offense:
​​ gov​​, and the pris​​r​i​​​(t)​  = ​Ri​​​  − ​β​i​​  t​. If the daily cost of incarceration to the state is C​​ 
oner time served is ​​s​i​​​, the state’s cost minimization problem is given by
Recidivism ccsts
Incarceration
costs

∞
⏞
(1)	​​min​​ ​ ​ ​​C​​  gov​ ​si​​​​​​ ​+ ​ ​ ​ ​s​i​ ​​ ​​​ri​​​​(t)​𝑑t ​​​ ​.​
​si​​​

∫

6

The full set of official parole guidelines for Mississippi is provided in online Appendix C.
Prior research indicates that the incapacitation effect can be large: for example, Barbarino and Mastrobuoni
(2014) estimates that the elasticity of total crime to incapacitation is between −17 and −30 percent, and related
work finds that increases in time served can reduce subsequent recidivism (Maurin and Ouss 2009). Buonanno
and Raphael (2013) also finds strong incapacitation effects using evidence from a large and collective Italian pardon. Owens (2009) finds that the incapacitation effect can be strong enough to justify longer sentences for at least
juvenile offenders. There may also be a general deterrence effect as in Becker (1968), by which criminals decide
to engage in less crime because of an increase in the expected incarceration length, but the empirical evidence for
this channel is mixed.
7  

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In this cost minimization problem, the first-order condition is C​​ 
​​ gov​  − ​r​i​​​(​s​  ⁎i​  ​)​  = 0​,
⁎
and the optimal policy for the state is to release prisoner ​i​ at ​​s​  i​  ​​, the point at which
​​ gov​​, the marginal
the prisoner’s expected risk r​
​​ i​​​, or marginal social benefit, equals C​​ 
social cost. Rewriting and rearranging this equality in terms of the components of r​
​​ i​​​
yields
​Ri​​​  − ​C​​  gov​
(2)	​​s​  ⁎i​  ​  = ​ _
 ​
.​
​βi​​​
Accordingly, the optimal time served in prison is an increasing function of the pris​​ i​​​.
oner’s initial risk R​
​​ i​​​and a decreasing function of the rehabilitation rate β​
Figure 2 shows the recidivism cost and daily incarceration curves. The optimal
number of days served, ​​s​  ⁎i​  ​​, has a legislative upper bound at the ­court-ordered sentence. In this setup, the state pays ​​C​​  gov​ ​s​  ⁎i​  ​​in incarceration costs in exchange for
⁎
social benefit ​​∫0​s​  ​  i​  ​​​​ri​​​​(t)​  dt​from incapacitation. At this optimum, the state still faces an
​​​ t)​  dt​in s­ everity-weighted potential recidivism resulting from
expected cost of ∫​​ ​s∞
​  ⁎i​  ​​  ​​​ri​(
prisoner ​i​’s release.
It is important to note that even without the private prison’s profit motive, there
is a likely mismatch between the objective functions of private and public prisons that produce distortions in inmate outcomes. This is because the counterfactual to private prison is not a social planner, but a public prison operated by
fallible humans with their own inefficient objective functions. For example, public prisons and their employees may also seek to maximize the number of beds
filled each day as inmate populations are a primary determinant of prison budgets and thereby the basis of all prison employees’ job security. To the extent
that profit motives and such other considerations are at play, both private and
public prisons will keep inmates for a different amount of time compared to a
social planner.
B. Distortion of the Release Decision by the Private Operator
As established in Section I, private prison operators must provide cost savings to
be hired. Let the private operator charge a ­per diem P
​ < ​C​​  gov​​for each day that a
bed is occupied. Friction arises because the private contractor faces ​P​as its marginal
revenue; it does not internalize the social benefit of minimizing recidivism risk.
Since P
​ ​is the negotiated payment made by the state to the private operator for each
bed occupied, the private operator incurs cost ​​C​​  priv​  < P​, else it would not generate
profit. The private operator’s marginal cost, ​​C​​  priv​​, need not be constant, although it
is useful to think of C​​ 
​​ priv​​as a fixed marginal cost for the first s​ ​​ ⁎i​  ​​number of days, i.e.,
the case with no distortion in days served.
When a private operator holds a prisoner beyond the number of days expected by
the state, it must exert effort. This effort could take the form of distributing excessive infractions that delay an inmate’s release. This effort could also take the form
of broader cost reductions that unintentionally affect infractions or delay release,
such as hiring fewer guards than required or shirking on required prison conditions
such as poor heating or cooling; these are examples of complaints lodged against

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MUKHERJEE: IMPACTS OF PRIVATE PRISON CONTRACTING

Recidivism risk =

415

R − βt

Cost

Cpriv

Private prison’s
marginal cost of
incarceration

Cgov

State’s marginal
cost of incarceration

P

Per diem payment
to private prison

Expected cost saving

s* + dˆ

s*

Days since offense (t)

Distortion

Figure 2. Theoretical Framework
Notes: The figure shows the distortion in release policy arising from differences in objectives of the state and private
operators. The state minimizes ­severity-weighted recidivism subject to cost ​​C​​  gov​​, but the private operator maximizes
profit given its p­ er diem payment ​P​and marginal cost ​​C​​  priv​​. The parameter ​R​represents prisoner i​ ​’s recidivism risk,
and ​β​is the rate at which recidivism risk declines with days since offense. The state chooses to hold inmates for s​​ ​​ ⁎​​
days and the private prison chooses to hold inmates for an additional ​​dˆ ​​ days.

the private prison operators in Mississippi (MDOC 2012). Formally, let the private
prison’s daily cost of incarcerating an inmate be
κ
if  ​d​i​​  ≤ 0
(3)	​​C​​  priv​  = ​ ​  
​ 
​ 
​​​​
{κ + M​d​  2i​  ​ if  ​di​​​  > 0,
​ ​is a scalar capturing the cost of
where ​​d​i​​​is the amount of distortion (in days) and M
distorting an inmate’s length of stay. This distortion allows the private prison operator to realize profit on each prisoner ​i​in the amount ​​(P − ​C​​  priv)​ ​​(​s​  ⁎i​  ​  + ​d​i​​)​  − M​d​  2i​  ​​.
Figure 2 illustrates how equation (3) affects the equilibrium outcomes in this
framework. The optimal level of distortion based on the first-order condition is
​​​dˆ​i ​ ​​  = ​(P − ​C​​  priv)​ ​/(2M)​. As expected, this quantity decreases with the cost of distortion. The distortion in the number of prisoner days served is positive as long as
the marginal revenue, ​P​, exceeds the marginal cost to the private operator, ​​C​​  priv​​.
C. Assessing Welfare
Distortion of the release decision has direct implications regarding the fairness
of the criminal justice system. Conditional on all available information, the state,
acting as the social planner, does not seek differential punishment of inmates by
assigning them to private prison. Therefore, the primary welfare loss from release
policy distortion is unfair treatment, but society may also care about the eroded

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cost savings—both in direct prison costs and future crime—and the prisoner’s value
ˆi ​P
​​  ​ in
of freedom. Regarding the incarceration costs alone, the state pays an extra ​​​d​
incarceration costs for each prisoner i​,​ and loses all the expected cost savings from
gov
⁎
ˆi ​P
​​  > ​
private contracting if ​​​d​
(​C​​  ​  − P)​ ​s​  i​  ​​. If the cost savings offered by private
operators is (​1 − γ​) percent per occupied bed (by Mississippi state law, ​​(1 − γ)​  ≥​
10 percent), then the inequality becomes d​
​​​ˆi ​ ​​  γ ​C​​  gov​  > ​(1 − γ)​​C​​  gov​ ​s​  ⁎i​  ​​, which simpli⁎
ˆ
ˆ
fies to ​​​di​ ​/​​  (​​di​ ​ ​​  + ​s​  i​  ​) > 1 − γ​. Thus, any distortion in time served directly erodes the
cost savings expected from private contracting.8
III. Mississippi Prisoner Data and Sample Definition

The empirical analysis uses Mississippi inmates sentenced to prison between
May 1, 1996 and July 31, 2013.9 Administrative records were obtained directly from
the Mississippi Department of Corrections (MDOC), which manages an inmate
data file that covers every inmate who served time in a state prison since 1981.
Some variables, such as the dates of inmate transfers between facilities, are available only from May 1, 1996. The data contain standard criminal justice information
on each offender’s demographics, current offense, offense history, and infractions
while incarcerated. A special feature of this data is information on the movement of
inmates between facilities over the course of their sentences, which permits measurement of whether an inmate ever served time in a private facility. This transfer
information is difficult to obtain (and not available for current or recently released
inmates) because the MDOC uses protected algorithms to move inmates between
beds in the same facility, or between facilities, so that they do not develop excessive
familiarity with guards or other inmates.
Demographic variables available in the MDOC dataset include the offender’s age
and gender, along with s­ elf-reported inmate information on race, education level,
and marital status. While inmate hometown is not available, the MDOC records the
county of conviction for each inmate. The classification data include information
on the offender’s custody designation level (A to D, where A is minimum custody
and D is maximum custody) as well as two medical designations that determine the
extent to which the inmate will work while in prison: medical class, which focuses
on physical health (and ranges from values A, excellent physical condition, to E,
poor physical condition and severely limited physical capacity or stamina), and
level of care, which focuses on mental health (and ranges from A, no mental health
problems, to E, inpatient health treatment). I use the initial classification variables
in all analyses. The MDOC Inmate Handbook (2011, 7) states that “all privileges, to
include level of supervision within and outside of the institution, access to programs,
activities, jobs, canteen, visits, and telephone, are based on the inmate’s custody
[designation] level.” Additionally, the Handbook (p. 8) states that “the classification
system is also used to determine which facility inmates will be housed in and places
them in housing units which are appropriate for their custody ­assignment.” The
8
An extension to this model that allows the state to ­reoptimize release policies based on the cost savings offered
by private contracting is in online Appendix B.
9
The data and analysis files are available in Mukherjee (2020).

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c­ lassification variables are determined by a classification hearing officer (always
in a public prison) and are based on a variety of factors (e.g., a personal interview,
expert recommendations, and prior escape history, in addition to factors such as the
inmate’s age, education, and offense(s) committed), as well as medical and psychological evaluations of the inmate.10
The data also include information on the crime(s) committed, ­court-ordered sentence length, and the number of days served while the case was under trial. Using
this information, I construct two key variables of interest: whether an inmate ever
served time in a private prison, and whether he recidivated with a new felony within
three years of release. Note that I only observe felonies in Mississippi, so prior or
future crimes may be underestimated. This is a common censoring problem, but
most offenders have convictions in only one state (Durose, Cooper, and Snyder
2014). I also use the available information to generate controls for criminal history.
The primary analysis sample begins with 40,195 felonies committed by 34,571
adult male inmates between May 1, 1996 and July 31, 2004. Sentences that occur
after July 31, 2004 were omitted to allow for the observation of time served and
­three-year recidivism for the analysis sample. Between August 1, 2004 and July 31,
2013, I observe an additional 39,059 sentences for 34,620 adult male inmates to
examine recidivism.
The sample is then restricted to bookings with sentence length between one and
six years, bringing the number of i­nmate sentences to 32,614 (2,607 are dropped
because of sentence lengths less than one year; 6,793 are dropped because of sentence lengths greater than six years). The sentences with less than one year are
dropped because one year is the minimum sentence required to be eligible for
prison (versus jail or county corrections) placement. Additionally, these sentences
are anomalies because the MDOC states that all felonies must carry a minimum
sentence of one year. In rare cases, however, the judge may award u­ p-front meritorious time to reduce the sentence. The sentences greater than six years are dropped to
enable the observation of time served and ­three-year recidivism.
Next, the sample is restricted to inmates who served at least 25 percent of their
sentences for the given booking as this was the s­ tate-mandated minimum over the
time period studied. This step removes 5,748 inmates. Finally, I drop 273 bookings
due to missing covariates (239 for missing county and 34 for missing level of care).
Together, these restrictions result in the primary sample of 26,593 bookings used in
the analysis. Note that the robustness checks in Section VII present estimates of the
main coefficients by relaxing some of the sampling restrictions.
A. Summary Statistics
Table 1 shows summary statistics for the sample of inmates by whether they
served time in private prison. The sample consists of 26,593 inmates, about
19 percent of whom went to private prison over the time period examined. The
descriptive ­statistics in Table 1 foreshadow the main results. As mentioned in the
10
I refer the reader to the MDOC’s Inmate Handbook (MDOC 2011) for further details on the classification
process and the c­ lassification-related variables.

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Table 1—Summary Statistics
Sample:

All
(1)

Public
(2)

Private
(3)

1.98
0.71
0.25
0.24

1.82
0.70
0.25
0.18

2.65
0.73
0.26
0.47

0.68
0.31
0.57
0.54

0.67
0.32
0.55
0.53

0.71
0.28
0.67
0.56

0.04
0.18
0.20
0.14
0.09
0.06
0.04
0.10
0.16

0.03
0.17
0.22
0.13
0.10
0.06
0.03
0.10
0.16

0.07
0.21
0.14
0.15
0.03
0.04
0.09
0.10
0.18

2.93
1.17
0.27

2.75
1.15
0.27

3.68
1.23
0.27

Custody designation ( proportions)
A
B
C
D
Unclassified

0.34
0.54
0.02
0.00
0.10

0.37
0.50
0.01
0.00
0.12

0.25
0.70
0.04
0.00
0.01

Medical class ( proportions)
A
B
C
D
E

0.83
0.05
0.09
0.01
0.02

0.84
0.05
0.09
0.01
0.01

0.80
0.06
0.09
0.02
0.03

Level of care ( proportions)
A
B
C
D
E

0.09
0.70
0.12
0.07
0.02

0.10
0.68
0.12
0.07
0.02

0.01
0.78
0.12
0.08
0.01

0.24

0.22

0.36

26,593

21,449

5,144

Outcomes
Years served
Fraction of sentence served
Recidivism (­36-month)
Any infraction?a
Demographics
Black
Age/100
Single
Education <
​ ​ HS
Offenses ( proportions)
Aggravated assault
Burglary
Drug possession
Drug selling
Felony DUI
Fraud
Robbery
Theft
Other
Offenses
Sentence length
Number of offenses
Prior incarcerations (5 years)

Instrument
​CapacityShock​ (​/​1,000)
Observations

Notes: Table shows summary statistics by whether the inmate ever went to private prison during his sentence. Each
observation is an i­nmate-sentence between May 1, 1996 and July 31, 2004. The sample consists of male inmates
with original sentences of 1 to 6 years that serve at least 25 percent of their sentences; see Section III in the text for
further details.
a Infractions data are available ­post-2000.

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i­ntroduction, ­private prison inmates serve a greater fraction of their sentences (73
versus 70 percent); this difference is statistically significant. Recidivism rates are
similar for the two groups (25 versus 26 percent), and they mirror the national average of 24 percent over this time period (Langan and Levin 2013). The higher average sentence length among ­privately incarcerated inmates reflects both the state’s
preferences in prison assignment and that inmates with longer sentences experience
more private prison openings and bed expansions.11
Table 1 also reveals a considerable degree of difference along observed characteristics between inmates in public versus private prison. Echoing the anecdotal evidence
of Spivak and Sharp (2008), I find that inmates in private prison are more likely to be
Black (71 versus 67 percent), single (67 versus 55 percent), young (mean age of 28
versus 32), and less educated (56 versus 53 percent do not have a high school degree).
Due to the detailed data available, much of the selection of inmates into private prison
is observed and can be accounted for in the empirical analysis. The differences in these
observables—all of which are statistically significant—raise concerns about selection
on unobservables, which the IV analysis will address.
The other variables shown in Table 1 relate to the breakdown of inmate offenses
by private prison assignment. There are some differences by offense category in the
types of inmates assigned to private prison; for example, fewer have drug possession
and felony DUI charges, and more have robbery and assault charges. For each sentence, the average inmate in private prison had 1.23 offenses, versus 1.15 for those
in public prison. The number of prior incarcerations (felonies) in the past five years
is 0.27 for both groups.
Table 1 also shows the distribution of the classification variables and the value
of the instrument across these inmate groups. We observe that in terms of custody
designation, a higher proportion of inmates in private prison (70 versus 50 percent)
belong to the medium designation of B, with fewer being in the lowest designation
of A (25 versus 37 percent). This difference helps explain the apparent negative
selection of private prison inmates, for example, by sentence length and offense
type. Both custody designations of C and D are rare, and about 12 percent of inmates
in public prison remain unclassified in the data (unclassified inmates receive a custody designation of D until there is a change). In terms of medical class, slightly
fewer private prison inmates belong to the lowest class of A (80 versus 84 percent),
but all class levels are represented in both types of prison. Similarly, for the level of
care, all levels are represented in both types of prison, but private prison inmates are
more likely to have a level of B, indicating that some mental health interventions
may be needed, versus a level of A, indicating no mental health concerns.
It is worth noting that even though Mississippi has the fourth highest incarceration rate in the country (as of 2004), the state’s inmates are generally representative of state prison inmates in the United States based on nationwide summary
statistics provided in Harrison and Beck (2005). The average sentence length and
demographic characteristics of inmates are similar to other states, especially in the
11
Panel A of Figure A.1 in the online Appendix illustrates that inmates with longer sentence lengths are more
likely to go to private prison. Panel B of the same figure shows that the instrument, explained in Section ­IVB, is
similarly higher for inmates with greater sentence lengths.

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southern United States. The percent of inmates in private prison is also not atypical:
the state prison systems in Vermont, Oklahoma, Tennessee, and Idaho also held
about 20 percent of inmates in private prison over this time period.
IV. Empirical Strategy

I begin with OLS analysis to show association between serving any time in private prison on inmate outcomes, and then introduce an IV strategy to deal with
potential n­ onrandom selection into private prison.
A. OLS Analysis
I estimate the impact of private prison on inmate outcome ​​Y​i​​​ using
(4)	​​Y​i​​  = βPrivat​ei​​​  + θ​X​i​​  + ​ϵ​i​​,​
where P
​ rivat​e​i​​​is a binary variable indicating whether the inmate served any time in
private prison.12 I estimate two outcomes for time served: the number of days served
and the fraction of sentence served.
The vector X​
​​i​​​ captures demographic, offense (including criminal history),
classification-related variables, admission time, and geographic information.
­
Demographic information includes prisoner age at admission date, race, marital status, and education level; these variables are included because prior literature indicates they may be correlated with the outcomes studied. (For example, Lochner
and Moretti 2004 finds that education reduces the probabilities of both incarceration
and arrest.) For o­ ffense-related information, the controls include sentence length
incorporated as dummies for each rounded sentence year, offense type for up to
three offenses related to each ­inmate-sentence (included separately as primary, second, and third offenses), and criminal history.13 This latter set of variables includes
controls for the number of felonies in the five years prior to the admission date,
along with controls for the types of prior offenses when relevant. Classification
variables include dummies for the inmate’s custody designation, medical class, and
level of care. Admission time trends are linear (calculated as days since January 1,
1990) and interacted with the sentence length dummies to control for policies that
may be changing over time. Finally, the geographic information contains dummies
for the county of conviction related to the ­inmate-sentence.
B. Instrumental Variable Analysis
The IV approach uses capacity shocks in private prisons to generate variation
in prison assignment. The openings of private prisons over the timespan studied
12
Online Appendix Figure A.2 shows the extent of treatment, i.e., the distributions of time served in private
prison.
13
Note that 92.15 percent of sentences are within 30 days of an exact round year. The rounding process is standard: e.g., if an inmate’s sentence length is 2.49 years, his rounded sentence length is 2 years; if the sentence length
is 2.51 years, it is rounded to 3 years.

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p­ rovide most of the variation, and similar instruments have been used in prior work.
For example, Atkin (2016) uses the openings of manufacturing plants in Mexico to
instrument for the returns to education in the study of high school dropout rates. In
a more closely related setting, Chirakijja (2018) uses prison openings over a long
timespan to examine their impact on local labor market conditions.
The capacity shocks in Figure 1 are converted into an instrument by calculating
the net number of private bed openings over the inmate’s assigned sentence. There
is a small adjustment made to ensure that the capacity shock could have affected
the inmate’s probability of going to private prison: it had to occur at least 90 days
after his admission and at least 90 days before the sentence end date. The reason for
the first cutoff is because the MDOC does not move inmates to private prison until
inmate classification (which takes up to 45 days) and orientation (which could take
up to 90 days) are complete. Consistent with this policy, I do not observe any inmate
transfers to private prison until at least 90 days have been served (the minimum is
109 days). The MDOC also has a policy of not transferring inmates to a new prison
if they have less than 90 days left to serve, which I observe to be true in the data.
The instrumental variable ​CapacityShoc​ki​​​  = ​∑Jj=1​​​  capacityshoc​k​ij​​​, where
​Cj​​​ if ​ai​​​  ≤ ​t​j​​  − 90 and  ​v​i​​  ≥ ​t​j​​  + 90
(5)    ​
​capacityshoc​k​ij​​  = ​    
​ ​  ​ 
 ​​​​
{0 otherwise.
The variable a​
​​ i​​​is the prisoner’s admission date, ​​v​i​​​is his ­court-ordered release date
(i.e., the prisoner’s admission date plus his assigned sentence), ​​tj​​​​is the date of the
private prison bed capacity shock, and ​​C​j​​​is the number of private prison beds opening or closing.
Estimating the first-stage equation requires care because the endogenous variable
is binary. I adopt the ­two-stage least squares (2SLS) with probit correction method
outlined in Wooldridge (2002) and discussed in Angrist and Krueger (2001).14 This
method uses a probit model to estimate the probability of treatment, and the predicted
probabilities are used as instruments in a standard 2SLS framework. Intuitively, the
method works because any nonlinear function of an instrument is also a valid instrument. The key advantage is efficiency; while both the traditional 2SLS and 2SLS
with probit correction methods yield estimates that are asymptotically unbiased,
the latter method produces estimates more tightly centered around the true coefficient when the first stage is better approximated by a nonlinear function. Additional
advantages of the procedure are that it is robust to misspecification of the probit
model, and the standard errors are estimated in the same manner as in a traditional
2SLS framework. A disadvantage is potential identification from nonlinearity, but
this is overcome by the use of a valid instrument—in this setting, C
​ apacityShock​—
in estimating the “​0th​” stage probit model from which the fitted values are obtained
as instruments.15
14
Prior studies using this 2SLS with probit correction method in a variety of settings include Dubin
and McFadden (1984) (one of the first applications); Norton and Staiger (1994); Cameron et al. (1988); Adams,
Almeida, and Ferreira (2009); Berger and Roman (2017); and Allen, Chandrasekaran, and Basuroy (2018).
15
In online Appendix Section D, I show the probit versus linear model fits of the first stage, and demonstrate
via Monte Carlo simulation the relative efficiency of the 2SLS with probit correction method in the presence of

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The probit model is given by P​
​​ i​​  = Φ(γ​  CapacityShock​​i​​   +​​​  θ​Xi​​​)​, where ​​Xi​​​​ is the
same as in the OLS specification. The predicted probabilities ​​Pˆ ​​are used as instruments in the first-stage equation, which is given by
(6)	​​Private​i​​  = α + β​​Pˆ ​ ​i​​  + δ​Xi​​​  + ​η​i​​.​
The second-stage equation is given by
​ ​​  + ​β​IVˆ
​​​ rivate​i​​​  + ​δ​IV​​ ​Xi​​​  + ​ϵ​i​​.​
​P
(7)	​​Y​i​​  = ​αIV
In estimation, the standard errors are clustered by admission m
­ onth-year and sentence length (rounded to the nearest year) to account for parole guidelines over time
that may have affected inmates differently depending on their sentence length. For
example, Mississippi overhauled its parole guidelines by sentence length in 1995,
before the start of the sample analyzed in this paper.16
Identification in the IV analysis requires three assumptions. First, CapacityShock
must be a good predictor of prison assignment, and I show this in the regression
analysis. Figure 3 also shows a visual representation of this first-stage relationship.
Second, there should be instrument monotonicity. Following Dobbie, Goldin,
and Yang (2018), I demonstrate this by showing that the first-stage relationships
are strongly statistically significant and stable across subsegments of the inmate
population by race, marital status, education, and age.17 Note that monotonicity in
this setting means that the capacity shock can only increase an inmate’s likelihood
of being assigned to private prison—in other words, no inmate can become more
likely to go to public prison as a result of the increase private prison bed capacity
(these would be defiers). Defined in this way, the estimation yields a local average
treatment effect (LATE) interpretation, where the causal effect of private prison
is estimated for the compliers who are assigned to private prison because of the
capacity shock, but who would otherwise have been assigned to public prison in the
absence of the capacity shock.
Third, the exclusion restriction should be satisfied—the instrument should be
otherwise unrelated to prisoner outcomes. In Section VII, I show a test of instrument exogeneity following Altonji, Elder, and Taber (2005). I also show that the
instrument is not strongly correlated with any variable used in the analysis.18 While
one can never “prove” the exclusion restriction, the sharp changes in private prison
capacity are plausibly unrelated to patterns in the variables studied. This is not surprising given research showing that judges do not adjust sentences even in light

varying levels of treatment and endogeneity. The results for all key outcomes using a traditional 2SLS method are
in online Appendix Table A.2.
16
The results that follow are robust to clustering by admission ­month-year, as shown in online Appendix
Table A.3. Their direction and statistical significance are also robust to more flexible time trends in the form of year
fixed effects interacted with sentence length dummies. These results are in online Appendix Table A.4.
17
These results are in online Appendix Table A.5. The implied ​F​-statistic of the instrument in each subsample
exceeds 300.
18
These results are in online Appendix Table A.6.

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Coefficient on private

1

0.5

0

−0.5

−500

0

500

1,000

1,500

2,000

2,500

Instrument (CapacityShock)

Figure 3. Private Prison Treatment by Instrument Value
Notes: The figure shows coefficients from a single probit regression on categories of the C
​ apacityShock​ instrument
(the reference category is CapacityShock = −1,000 beds). The dependent variable in the regression is ​Private​, i.e.,
whether the inmate ever went to private prison, and the other covariates include the controls in Table 2.

of policies such as t­ruth-in-sentencing that increase time served more sharply and
directly (Owens 2011).19
V. Results

A. Time Served
Table 2 presents results on the effect of private prison assignment on inmate time
served. Columns 1 and 3 report the saturated OLS regression estimates on the number of days and fraction of sentence served, respectively, with all the controls discussed in Section IV. These results show that private prison inmates serve 85 more
days, alternatively estimated as 6.2 percent of their sentences, than inmates in public
prison. These estimates are consistent with each other, because 6.2 percent translates to about 83 additional days in prison based on the average sentence length for
inmates in private prison.20
The other covariates shown in Table 2 have the expected sign across specifications:
for example, each prior incarceration increases the fraction of sentence served by
about 1 percent. Even after controlling for all covariates, I find that older, Black, and
19
Note that Dippel and Poyker (2019) finds that private prisons appear to increase sentence length for all
inmates through a channel in which the state ­reoptimizes release policies as discussed in online Appendix Section
B. The time served outcome in this analysis controls flexibly for sentence length and accounts for this possibility.
20
Table 1 shows that the average sentence length for inmates in private prison is 3.68 years. Thus, a 6.2 percent
increase in fraction of sentence served translates to ​3.68 × 365 × 0.062 = 83.28​additional days.

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Table 2—Impact of Private Prison on Time Served
Dependent variable:

Private
Prior incarcerations
Age/100
Black
Single
Education <
​ ​ HS
​CapacityShock​ (​/​1,000)

Days served
OLS
(1)

85.250
(4.375)
11.907
(6.756)
198.121
(17.969)
16.585
(3.377)
29.741
(3.015)
−4.823
(2.796)

IV
(2)

89.627
(26.414)
11.921
(6.732)
199.981
(19.129)
16.601
(3.355)
29.612
(3.119)
−4.852
(2.780)

Fraction served
OLS
(3)

0.062
(0.003)
0.009
(0.005)
0.170
(0.014)
0.015
(0.003)
0.025
(0.002)
−0.001
(0.002)

IV
(4)

0.048
(0.019)
0.009
(0.005)
0.164
(0.015)
0.014
(0.003)
0.025
(0.002)
−0.001
(0.002)

Instrument (predicted
probit)
Dependent variable mean
­2
R
​F​-statistic
Observations
Offense variables
Classification
Time trends
County fixed effects

722.7
0.737
—
26,593
Yes
Yes
Yes
Yes

722.7
0.737
—
26,593
Yes
Yes
Yes
Yes

0.71
0.280
—
26,593
Yes
Yes
Yes
Yes

0.71
0.279
—
26,593
Yes
Yes
Yes
Yes

Private

Private

Probit eqn.
(5)

First stage
(6)

−0.002
(0.013)
−0.456
(0.029)
−0.007
(0.006)
0.023
(0.005)
0.008
(0.005)
0.034
(0.003)

−0.002
(0.013)
0.059
(0.029)
0.002
(0.005)
−0.005
(0.004)
−0.001
(0.005)

0.19
—
—
26,593
Yes
Yes
Yes
Yes

0.19
0.177
887
26,593
Yes
Yes
Yes
Yes

1.155
(0.039)

Notes: The table shows regression estimates of the impact of private prison (​Private​) on inmate outcomes. “Fraction
served” is the fraction of the inmate’s sentenced days that were served. “Private” is a binary variable for whether the
inmate served any time in a private prison. Offense variables include sentence length dummies (rounded to the nearest year) and dummies for offense type for up to three offenses related to each i­nmate-sentence. They also include
controls for the number of prior incarcerations in the five years before the admission date, along with controls for
the offense type(s) of prior incarceration(s). Classification variables include the custody designation level, medical
class, and level of care. Time trends include a linear time trend and its interaction with sentence length dummies.
County fixed effects are for the county of conviction. Column 5 shows the mean marginal effects of the “​0th​” stage
probit equation; the instrument ​CapacityShock​has a ­t-statistic of 11.22. Column 6 shows the first-stage estimates
using the predicted probit probabilities from column 5 as an instrument. Standard errors in parentheses are robust
and clustered by admission ­month-year and sentence length.

single inmates each serve significantly larger fractions of their sentences. For example, column 3 shows that Black and single inmates serve 1.5 and 2.5 percent larger
fractions of their sentences, respectively. Some of these differences may be due to
­in-prison behavior, which I explore in the next section.
Figure 4 provides a visual of these results: it plots the time until release for
inmates in private versus public prison. We observe that inmates in private prison
have a lower likelihood of release (as estimated by ­Kaplan-Meier failure estimates)
at every level of time served. There are spikes in the probability of release for inmates
in both prison types at exact years, which are both common sentence lengths and
common levels of time served.21
21
For improved comparison of inmates in public and private prison, this figure uses the matched and restricted
sample of inmates (described in Section ­VIIC) eligible for private prison assignment during the capacity shocks.

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1

Proportion released

0.75

0.5

0.25

0
0

1

2

3

4

5

6

Time served (years)
Figure 4. Proportion of Inmates Released by Time Served and Prison Type
Notes: The figure shows the K
­ aplan-Meier failure estimates of time (years) until release for the sample of inmates
eligible for private prison assignment during the capacity shocks; this is the restricted sample used in the matching
analysis described in Section ­VIIC. The solid line shows the proportion of private prison inmates released at each
level of time served. The dashed line shows the analog for public prison inmates.

The IV estimates are in columns 2 and 4 of Table 2. The estimates indicate that
private prison inmates serve 90 additional days, alternatively estimated as an additional 4.8 percent in fraction of sentence served. The standard errors on the IV
­estimates contain the OLS estimates for both measures of time served. All covariates
have similar magnitudes and signs as in the OLS regressions. Column 5 reports the
marginal effects of the “​0th​” stage probit regressions discussed in Section IV. The
coefficient of 0.034 on the instrument in column 5 indicates a 3.4 percent higher
likelihood of private prison assignment for every 1,000 net private prison beds that
opened over the inmate’s sentence. The CapacityShock instrument is strongly statistically significant; its ­t-statistic is 11.22. In implementing the ­two-step procedure,
I use the predicted probit instrument shown in column 6; the coefficient of 1.155
implies that a 1 percentage point change in the inmate’s predicted probability leads
to a change in likelihood that he goes to private prison by 1.155 percentage points.
The ​t​-statistic on this instrument is 29.62, translating to an ​F​-statistic of 877.06 as
shown in column 6.
B. Infractions as a Mechanism for Delayed Release
Having established that private prison assignment increases time served, I explore
a mechanism that explains these results. Infractions are prison conduct violations
given to inmates for behaviors ranging from disobeying a guard to ­possessing

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Table 3—Infractions by Inmate Characteristics
Public
(1)

Private
(2)

Demographics
Black
White
Age ­18–24
Age ­25–34
Age ­35–49
Age 50+

0.19
0.16
0.22
0.19
0.15
0.11

0.51
0.38
0.54
0.46
0.33
0.22

Offenses
Aggravated assault
Burglary
Drug possession
Drug selling
Felony DUI
Fraud
Robbery
Theft
Other

0.20
0.25
0.14
0.22
0.09
0.16
0.30
0.18
0.19

0.45
0.53
0.40
0.51
0.16
0.33
0.60
0.47
0.46

Sentence length
1
2
3
4
5
6

0.05
0.11
0.18
0.31
0.39
0.43

0.14
0.24
0.37
0.55
0.68
0.76

Overall

0.18

0.46

Notes: The table shows the proportion of inmates receiving an infraction by prison type and
selected characteristics. For example, 19 percent of Black inmates received an infraction in
public prison versus 51 percent in private prison. All differences are statistically significant
( ​p <​  0.05). The sample contains 12,551 inmates in public prison and 3,203 in private prison.
The sample includes inmates with admission dates between January 1, 2000 and July 31, 2004,
because the infractions data are available ­post-2000.

c­ ontraband.22 They are a critical component of release decisions by the parole
board. Infractions are imperfect measures of behavior, however, because they can
be affected by factors such as harsher prison conditions in private prisons—a problem relevant in Mississippi (Williams 2016). On the other hand, private prisons may
have a better technology for monitoring infractions, or may be more likely to report
them due to contract renewal incentives. A difference in infraction rates between
inmates in public and private prison could also stem from shirking by public prison
employees who ­underreport such violations.
Table 3 shows summary statistics on infractions given to inmates by whether
they were in private prison. They provide a leading explanation for why inmates
serve more time in private prison: 46 percent of private prison inmates receive at
least one infraction, versus 18 percent for those in public prison. Private prison

22
A new crime such as an assault on a fellow inmate is also processed as a crime with a sentence to be served
concurrently or consecutively, and is accounted for in the calculation of sentence length.

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Table 4—Impact of Private Prison on Infractions
Dependent variable: Any infraction?

Private
Prior incarcerations
Age/100
Black
Single
Education <
​ ​ HS
Dependent variable mean
­R2
Observations
Offense variables
Classification
Time trends
County fixed effects

Probit
(1)

OLS
(2)

0.090
(0.006)
0.040
(0.012)
−0.431
(0.036)
0.023
(0.007)
0.030
(0.006)
0.009
(0.006)

0.142
(0.010)
0.051
(0.015)
−0.415
(0.040)
0.027
(0.007)
0.032
(0.006)
0.016
(0.006)

0.24
—
15,754
Yes
Yes
Yes
Yes

0.24
0.317
15,754
Yes
Yes
Yes
Yes

Notes: The table shows regression estimates of the impact of private prison (​Private​) on
whether the inmate had any infraction during his sentence. Sample includes inmates with
admission dates between January 1, 2000 and July 31, 2004 since the infractions data are available p­ ost-2000. See notes for Table 2 for a list of the detailed controls. Mean marginal effects
are reported for the probit model in column 1. Standard errors in parentheses are robust and
clustered by admission ­month-year and sentence length.

inmates in every demographic, offense, and sentence length category accumulate
more infractions.
Table 4 shows the difference in the probability of receiving an infraction by
whether a prisoner is assigned to private prison after controlling for the available covariates, using both probit and linear probability specifications. (The
IV approach is unavailable for the infractions analysis since these data are
available p­ost-2000, which is after the period in which most of the private
prison bed capacity shocks occurred.) The estimating equation used to generate column 1 is a probit model with ​​Infractions​i​​​as a binary variable indicating
whether the prisoner received any infractions over the course of his sentence:
​​Infractions​i​​  = Φ​(β ​Private​i​​  + δ​X​i​​)​.​The estimating equation for column 2 is the
analogous linear probability model: Infractions​
​​
i​​  = β​Private​i​​ + δ​X​i​​  + ​ϵ​i​​.​ The probit and linear probability model estimates suggest that a private prison inmate is 9
or 14.2 percent more likely to obtain an infraction over the course of his sentence,
respectively. These effects are high given that the baseline rates of any infraction. In
both specifications, inmates with more prior incarcerations and less education are
more likely to obtain an infraction. Inmates who are young, Black, or single all also
show higher infraction rates.

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Panel A

R

Cost

Recidivism risk =

R − βt
Cpriv

Private prison’s
marginal cost of
incarceration

Cgov

State’s marginal
cost of incarceration

Expected recidivism
benefit from extra days

Per diem payment
to private prison
Expected loss from
extra days

P

s* + dˆ

s*

Distortion

Days since offense (t)

Panel B

R

Recidivism risk =

R − β govt

Recidivism risk =

R − β privt

Cpriv

Private prison’s
marginal cost of
incarceration

Cgov

State’s marginal
cost of incarceration

P

Per diem payment
to private prison

Cost

s*

s* + dˆ
Distortion

Days since offense (t)

Figure 5. Theoretical Framework with Recidivism
Notes: Figure illustrates hypotheses related to the effect of private prison exposure on inmate recidivism. See
Figure 2 notes for notation. Panel A shows that recidivism risk is expected to decrease for private prison inmates due
to the additional time served. Panel B shows that this effect could be undone if private prisons alter the rate at which
recidivism risk falls with time served, i.e., if ​β​is indexed by whether the inmate is in private prison.

VI. Recidivism Analysis

A. Assessing Welfare Impacts Considering Recidivism
The results so far establish that private prison inmates serve more time. If these
additional days decrease recidivism, then private prisons may not harm social welfare. Panel A of Figure 5 depicts this t­rade-off: distortions of increased time served
are socially beneficial if they are sufficiently small and the recidivism risk curve is
sufficiently flat.

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To consider the welfare impacts of private contracting, we calculate the
social costs of incarceration with and without it. Without private contracting, the social costs of incarcerating an individual are (​​​C​​  gov​  − ​R​i​​)​​s​  ⁎i​  ​  +
, where Δ
​ = ​R​i​​  t − ​(​β​i​​/2) ​t​​  2​​ ​​​t=∞​​​. With private contracting,
(​β​i​​/2)​​(​s​  ⁎i​  ​)​​​  2​  + Δ​
ˆi ​​,​​  the amount of distortion, and ​P​, the ­per diem payment:
these costs depend on ​​​d​
2
⁎
ˆ
​​(P − ​R​i​​)​​(​s​  i​  ​  + ​​d​i ​​​ )​  + (​β​i​​/2)​​(​s​  ⁎i​  ​  + ​​dˆ​i ​​​ )​​​  ​  + Δ.​
A few observations are in order. First, absent distortion (i.e., ​​​dˆ​i ​ ​​  = 0​), social
welfare is guaranteed to improve under private contracting by (​​ ​C​​  gov​  − P)​​s​  ⁎i​  ​​ due to
the cost savings. Second, if recidivism risk does not respond to time elapsed since
offense (i.e., ​​β​i​​  = 0​), the increase in social welfare from private prison contracting
is (​​ ​C​​  gov​  − P)​ ​s​  ⁎i​  ​  − ​(P − ​R​i​​)​​​dˆ​i ​​.​​  In this case, social welfare is an increasing function
of distortions, assuming that the criminal justice system incarcerates individuals
with recidivism risk exceeding the marginal cost of incarceration. Based on these
assumptions, private prisons increase social welfare by holding inmates longer if

|

___________________________

gov
2
​​(​C​​  gov​  − P)​​​  2​  + 2​(​C​​  gov​  − P)​​(​Ri​​​  − ​C​​  gov​)​ ​
(​​ ​C​​  ​  − P)​​​  ​  + ​√    
ˆi ​ ​​  ≤ ​ ______________________________________________
     
   ​.​
(8)	​​​d​
​βi​​​

The intuition from equation (8) is as follows. If the distortion from private prison
contracting is sufficiently small, then social welfare improves. If β​
​​ i​​  = 0​, the condition requires only that d​
​​​ˆi ​ ​​  < ∞​, which is always the case since the private prison
cannot hold a prisoner beyond his ­court-ordered sentence length. If private prisons
offer no cost saving, i.e., if C​​ 
​​ gov​  = P​, then equation (8) shows that social welfare is
unchanged only if there is no distortion.
Two testable implications emerge from this framework given the time served
results. First, if recidivism risk falls with time since offense, and if private prisons
have no other impact on recidivism risk, then recidivism risk should be lower for
inmates who go to private prison. Using prisoner data from Georgia and an IV analysis based on parole guidelines, along with the same definition of recidivism used
in this paper, Kuziemko (2013) estimated that each additional month in prison was
associated with a 1.4 percent reduction in recidivism. Applied to Mississippi, this
estimate implies a 2.8 to 4.2 reduction in recidivism rates for inmates who go to
private prison. (As noted in the introduction, however, there is conflicting evidence
on the impact of time served on recidivism.)
Second, if there is no reduction in recidivism for inmates that go to private prison
(as is true in the empirical analysis that follows), this result could be consistent with
two interpretations. Either the marginal social benefit of incarceration, ​β​, is close to
zero (Abrams 2012), or, as illustrated in panel B of Figure 5, private prisons affect
the slope of the recidivism risk curve. In the model, this implies that ​β​is indexed
by whether the inmate is in private or public prison, with ​​β​​  priv​  < ​β​​  gov​​ (recall that
we assume ​β > 0​). This latter effect could occur through several channels. Harsher
conditions in private prison, which might result from c­ost-cutting incentives,
could increase recidivism risk as evidenced in prior literature (Chen and Shapiro
2007; Drago, Galbiati, and Vertova 2011). Or, worse peer effects in private prison
could lead them to be a “school of crime” (Bayer, Hjalmarsson, and Pozen 2009).

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Table 5—Impact of Private Prison on Recidivism
Dependent variable: Recidivism (­36-month)

Private
Prior incarcerations
Age/100
Black
Single
Education <
​ ​ HS
Dependent variable mean
­R2
Observations
Offense variables
Classification
Time trends
County fixed effects

OLS
(1)

Probit
(2)

IV
(3)

0.014
(0.007)
0.062
(0.016)
−0.311
(0.031)
0.023
(0.006)
0.067
(0.006)
−0.011
(0.005)

0.015
(0.007)
0.052
(0.013)
−0.336
(0.033)
0.024
(0.006)
0.067
(0.006)
−0.010
(0.005)

0.017
(0.038)
0.062
(0.016)
−0.310
(0.035)
0.023
(0.006)
0.067
(0.006)
−0.011
(0.005)

0.25
0.084
26,593
Yes
Yes
Yes
Yes

0.25
—
26,593
Yes
Yes
Yes
Yes

0.25
0.084
26,593
Yes
Yes
Yes
Yes

Notes: Table shows regression estimates of the impact of private prison (​Private​) on ­36-month
recidivism (binary). See notes for Table 2 for a list of the detailed controls and the first-stage
estimates related to column 3. Mean marginal effects are reported for the probit model in column 2. Standard errors in parentheses are robust and clustered by admission ­month-year and
sentence length.

B. Recidivism Results
The present analysis does not provide consistent evidence that private prison
assignment impacts recidivism. The OLS effect of private prison assignment on
recidivism in column 1 of Table 5 indicates a 1.4 percent increase in reoffending
with a felony within three years, and the probit model estimate in column 2 is similar at 1.5 percent. Both these estimates are statistically significant ( ​p < 0.05​
).
The IV estimate in column 3, however, has a similar point estimate of 1.7 percent
but is not statistically significant. The base rate of recidivism in this sample is
about 25 percent, so the OLS and probit estimates imply effect sizes of about 6
percent.
The coefficients on the covariates are similar across columns and mostly behave
as shown in the literature. Inmates with a felony history recidivate at greater rates,
and each prior incarceration is associated with a 5 to 6 percent increase in recidivism. Older inmates recidivate less, and each additional year of age lowers recidivism by 3 to 4 percent (close to the 5 percent estimate in Ganong 2012). Third,
compared to married inmates, single inmates recidivate at about a 7 percent higher
rate. The coefficient on education is the least expected, as it suggests that inmates
with less than high school education recidivate at a 1 percent lower rate. It is not
clear why this would be the case, though possibly such inmates receive their General

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431

Educational Development degrees (GEDs) in prison which reduces their propensity
for future crime.
Given the imprecision of the IV estimate, it is difficult to rule out the potential
theories raised in the previous section. The 95 percent confidence interval on the IV
estimate is wide and includes effects from −5.7 to 9.1 percent. The OLS and probit estimates both indicate increases in recidivism for private prison inmates, suggesting that private prisons may undo the reduction in reoffending rates we would
expect from the additional time served. I refrain from interpretation of these results,
however, as they are not robust to the IV or other specifications. They also do not
change with different model specifications, including the addition of r­ elease-period
controls.23
VII. Robustness

The main results are robust to a variety of sampling methods, variable definitions,
and estimation strategies. Here, I present a selection of tests that deal with potential
concerns.
A. Instrument Exogeneity: Sensitivity to Controls
I show in Table 6 that the estimated impacts of private prison on inmate days
served, fraction served, and recidivism are stable to the addition of layered controls.24 The controls are added in eight steps. The first column contains no controls
and is included for consistency with prior papers; the second column only controls
for sentence length and the custody designation component of the classification
variables. Given that there are other strong predictors of the outcomes studied (e.g.,
time trends), it is not surprising that these first two columns produce estimates that
are too large or of incorrect sign. The coefficients stabilize in columns 4 through
8, even as informative covariates related to the inmate’s offense, criminal history,
medical class and level of care, demographics, and prior incarcerations are added in
a stepwise fashion. (Note that the coefficients in column 8 replicate columns 2 and
4 of Table 2, and column 3 of Table 5.) The stability of the coefficients across these
columns provides evidence for the exogeneity of the ​CapacityShock​ instrument.

23
I do not include r­elease-period controls in the main analysis because the number of days served (and,
hence, the release date) is endogenous to whether an inmate is in private prison. In a separate analysis, I include
Mississippi’s unemployment and crime rates (violent crime, murder/manslaughter, rape, robbery, aggravated
assault, property crime, burglary, larceny/theft, motor vehicle theft) in the year of the inmate’s release. These
results are in online Appendix Table A.7. The OLS result is similar to that in Table 5; there is a 1.3 percent increase
in recidivism for private prison inmates (​  p < 0.10​). The probit and IV specifications yield similar magnitudes but
are not statistically significant.
24
This test of instrument exogeneity was proposed in Altonji, Elder, and Taber (2005). ­Pettersson-Lidbom
(2010, 170), which also uses this test, writes: “For this test to be useful in practice, the number of controls must be
sufficiently large, they must have significant explanatory power, and they must be representative of the full range of
factors that determine the outcome as discussed by Altonji, Elder, and Taber (2005).” These conditions are met in
my setting, as there are a large number of controls known to be predictive of inmate outcomes from prior literature;
also, the ​F​-statistics show that each layer of controls has substantial explanatory power.

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Table 6—Sensitivity to Controls: IV Estimates of Private Prison Impact on Inmate Outcomes
(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Panel A. Dependent variable: Days served (mean: 722.7)
Private
953.144 226.369 85.423 100.033
(340.162) (62.172) (34.062) (31.400)

116.592 81.809 90.322 89.627
(30.091) (26.170) (26.167) (26.414)

Wald test of joint significance of the control
variables ( ​p​-value in parentheses)

­R2

−0.288

0.687

0.715

0.717

0.732

0.734

10,591
(0.000)

725
(0.000)

149
(0.000)

582
(0.000)

118
(0.000)

137
91
(0.000) (0.000)

Panel B. Dependent variable: Fraction served (mean: 0.71)
Private
0.115
−0.724
(0.109) (0.040)

0.069
(0.024)

0.078
(0.022)

0.055
(0.021)

0.043
(0.019)

0.053
0.048
(0.019) (0.019)

Wald test of joint significance of the control
variables ( ​p​-value in parentheses)

944
(0.000)

219
(0.000)

818
(0.000)

135
(0.000)

121
109
(0.000) (0.000)

Panel C. Dependent variable: Recidivism (­36-month) (mean: 0.25)
Private
0.068
−0.186 −0.022
(0.098) (0.065) (0.044)

0.051
(0.040)

0.077
(0.040)

0.034
(0.038)

0.044
0.017
(0.038) (0.038)

Wald test of joint significance of the control
variables ( ​p​-value in parentheses)

­R2

­R2

First stage F
​ ​-statistic (cluster robust)
Observations
Sentenced years
Custody designation
County fixed effects
Time trends
Medical class and level of care
Offense
Age and race
Prior incarcerations
Single and education

—
—

−2.228
—
—

−0.030

0.175

3,272
(0.000)

0.216

0.223

0.055

0.268

0.064

0.272

0.073

0.736

0.276

0.078

0.737

0.279

0.020

0.043

—
—

455
(0.000)

933
(0.000)

250
(0.000)

256
(0.000)

165
(0.000)

138
133
(0.000) (0.000)

0.084

57
26,593

202
26,593

565
26,593

666
26,593

706
26,593

902
26,593

900
26,593

887
26,593

No
No
No
No
No
No
No
No
No

Yes
Yes
No
No
No
No
No
No
No

Yes
Yes
Yes
Yes
No
No
No
No
No

Yes
Yes
Yes
Yes
Yes
No
No
No
No

Yes
Yes
Yes
Yes
Yes
Yes
No
No
No

Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
No

Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No

Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes

Notes: The table shows regression estimates of the impact of private prison (​Private​) on inmate time served in panels
A (days served) and B (fraction of sentence served) and ­36-month recidivism (binary) in panel C. Column 1 includes
no controls; column 2 adds controls for sentence length dummies and custody designation; column 3 adds controls for
the county of conviction, linear time trends, and the linear time trend interacted with sentence length dummies; column
4 adds dummies for medical class and level of care; column 5 adds indicators (if any) for the primary offense type and
up to two additional offenses related to the i­nmate-sentence; column 6 adds controls for the inmate’s age at admission
and his race (whether Black); column 7 adds a set of detailed controls for criminal history, i.e., the number of felonies
in the five years prior to admission as well as binary indicators for the offense types of any such felonies; and column 8
adds controls for inmate marital status (whether single) and education (whether less than high school). The Wald tests
of joint significance and their respective p​ ​-values show that the control variables added at each step have significant
explanatory power. The first stage ​F​-statistics indicate the strength of the ​CapacityShock​instrument in each column.
Standard errors in parentheses are robust and clustered by admission ­month-year and sentence length.

B. Alternate Variable Definitions and Sampling Strategies
Fraction Served in Private Prison.—The main analysis treats private prison exposure as binary. I also estimate models using the fraction of sentence served in private
prison.25 I find that the coefficient on FractionPrivate is 292 for the number of days
served and to 0.21 for the fraction of sentence served. Since the mean fraction of
sentence served in private prison is about 30 percent, these estimates corroborate
the main results, which are roughly o­ ne-third the size of these estimates. This result

25

These results are in online Appendix Table A.8.

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suggests that the amount of delayed release increases linearly with time served in
private prison. The recidivism results remain imprecise.
Expanding the Inmate Sample.—The main analysis makes two key sample restrictions. It includes only inmates with sentences less than or equal to six years, so that
there are sufficient windows to observe time served and t­hree-year recidivism. It
also includes only inmates who served at least 25 percent of their sentences because
this is the c­ ourt-ordered minimum amount, and deviations occur for extenuating circumstances, e.g., compassionate release due to poor health. I demonstrate that these
restrictions do not affect the main results. First, I include inmates with sentence
lengths between 1 and 11 years and show that the time served results are stable for
this group.26 Next, I include those inmates who served less than 25 percent of their
sentences. The sample increases to 32,275 and mostly adds inmates with shorter
sentence lengths and in public prison. Since these inmates are likely to be of lower
recidivism risk—else they would not have received an early release exception—it
is not surprising their inclusion increases the effect of private prison exposure on all
outcomes.27
C. Alternate Estimation Strategies
­Leave-One-Out IV Analysis.—I estimate the main results using an alternative
l­eave-one-out instrument that equals the fraction of other inmates with the same
admission month and year who are assigned to private prison.28 This instrument
obtains predictive power from admission date, as inmates who enter in the same
­month-year have correlated exposure to the shocks to private prison capacity. (By
contrast, ​CapacityShock​uses variation from both admission date and sentence
length.) L
­ eave-one-out instruments are generally reserved for random examiner
settings such as those involving judging leniency as in Dobbie and Song (2015),
but is also strong in this setting: the ­first-stage ​F​-statistic is 935 after implementing the 2SLS with probit correction method. The estimates on both measures of
time served are consistent with the ­capacity-based IV estimates (90 more days and
4.4 percent more fraction served for private prison inmates), and the recidivism estimate remains imprecise.
Matching Analysis on a Restricted Sample.—The shocks in private prison capacity lead to private prison assignment because the new beds are filled quickly, so
eligible inmates have a higher likelihood of transfer. I restrict to those inmates who
were eligible for each private prison opening or expansion by keeping only those
inmates admitted within 90 days of a private prison opening or expansion (the closing is not used in this analysis). Then, I match each one inmate who went to private
26
OLS and IV results are presented in online Appendix Figure A.3. I do not observe the ­three-year recidivism
­follow-up window for all of these inmates, so I do not examine that outcome.
27
OLS results in online Appendix Table A.9. Since the IV estimate may be unreliable with the inclusion of these
inmates (they are not observed being sent to private prison), I estimate OLS regressions and find that the effect of
private prison increases to 242 for the number of days served and to 16.3 percent for the fraction of sentence served.
The OLS and probit estimates of private prison on recidivism produce statistically significant coefficients of about
2 percent, similar to the results in Table 5.
28
These results are in online Appendix Table A.10.

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prison with an inmate who stayed in public prison for improved estimates of the
impact of private prison on the outcomes studied.29 In total, 1,009 inmates go to
private prison during the opening or expansion periods, and the matching method
achieves its goal of generating comparable inmates among this restricted sample:
the matched pairs are balanced on nearly all covariates. The estimates show that
private prison inmates serve 71.2 more days, alternatively estimated as 5.2 more
percent of fraction served. There is no statistically significant result on recidivism.30
VIII. Conclusion

Despite the continued increase in private prison contracting, there has been little
research on how they impact inmates and whether they provide cost savings. This
paper contributes a key set of initial evidence on this question, taking care to address
concerns about unobservable selection of inmates to private prison.
Evaluating private prisons is challenging because prison assignment may depend
on unobservable prisoner traits. I address this problem by leveraging prison capacity shocks to generate ­quasi-random assignment. The analysis shows that inmates
in private prison serve about 4 to 7 percent larger fractions of their sentences, or
85 to 90 extra days for the average prisoner. The increased time served for inmates
in private prison constitutes a distortion in the delivery of justice. Broadly, these
bed capacity shocks also illustrate how c­ apacity-based constraints can have large
impacts within criminal justice. For example, Yang (2016) finds that judge vacancies led to 1.5 percent fewer inmates in the prison system due to increased plea
bargaining and reduced prison sentences.
The estimates on the impact of private prisons on recidivism are not consistently
statistically significant, so I focus my attention on the results related to time served.
Based on this metric, the analysis shows that private prisons are indeed ­cost-saving
but may not be as attractive a choice as claimed by their proponents. The results
imply that about 48 percent of the cost savings are eroded by the additional time
served, leaving about 52 percent in cost savings. To put a number on this in 2016
dollars, consider an average inmate in the sample studied, with sentence length of
about three years. Assuming that each year in private prison costs about $45,000
(versus about $50,000 for public prison), the cost savings offered by private prison
would be approximately $7,800 (52 percent of the upper bound of three years ×
​ ​
$5,000/year = $15,000 in savings) over that inmate’s sentence.31
There are, of course, other costs that are difficult to quantify—e.g., the cost of
injustice to society (if private prison inmates systematically serve more time), the
inmate’s individual value of freedom, and impacts of the additional incarceration
on future employment. Abrams and Rohlfs (2011) estimates a prisoner’s value of
29
The matching analysis requires inmates to be exactly matched on sentence length (rounded to the nearest
year), primary offense type, number of offenses, and classification variables. Additionally, inmates are matched on
the second and third offense types, if any; number and offense type(s) of prior felonies in the past five years; age;
race (whether Black); marital status (whether single); and education (whether less than high school).
30
The summary statistics for the matched sample pairs are in online Appendix Table A.11. The matching on
restricted sample results are in online Appendix Table A.12.
31
The cost estimates are broadly taken from Hyland (2019).

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freedom for 90 days at about $1,100 using experimental variation in bail setting.
­Mueller-Smith (2017) estimates that 90 days of marginal incarceration costs about
$15,000 in reduced wages and increased reliance on welfare. If these social costs
were to exceed $7,800 in the example stated, private prisons would no longer offer
a bargain in terms of ­welfare-adjusted cost savings.
Another contribution of this paper is to show that the mechanism by which private prison inmates experience delayed release is via the greater accumulation of
infractions or prison conduct violations. Infractions are used by the state parole
board to assess whether prisoners should be granted early release, and inmates in
private prison are 9 to 14 percent more likely to receive an infraction over the course
of their sentences. This finding suggests that release policy distortions could be curtailed by greater monitoring. For example, states could appoint committees to evaluate whether infractions are correctly imposed. States could also establish tighter
guidelines regarding infractions to address the widespread differences between public and private prisons.
These findings point to several avenues for future work. Quantifying specific
deterrence—the effect of time served in prison on future reoffending—has been a
longstanding question to which researchers have uncovered conflicting evidence.
This paper provides a unique experiment in which certain inmates receive two treatments: both additional time in prison and serving time in a private rather than public
prison. The point estimate of these combined effects in my analysis is about 1.5 percent, which is about a 6 percent effect size. It is possible that all of this effect comes
from the additional time served in prison. Or, it could be that private prisons increase
criminal reoffending; separating the effects in future work would be valuable in
assessing the policy impacts of private contracting. E
­ x ante, the answer is not clear:
on the one hand, factors such as the harsher conditions that have been documented
in private prisons may increase future criminal behavior as in Chen and Shapiro
(2007). On the other hand, factors such as more disciplining in private prison could
reduce future criminal behavior.
Future related research on private contracting may also find inspiration from
health care, a setting that has been studied more thoroughly in this context (e.g.,
Duggan, Gruber, and Vabson 2017). For example, states worry that private prison
contractors may “cream skim” the lowest cost inmates in the same way that insurers
can attempt to select lowest risk patients (Brown et al. 2014; Kuziemko, Meckel,
and ­Rossin-Slater 2013). As another example, the Hospital Readmissions Reduction
Program was introduced in 2013 by the Center for Medicare and Medicaid Services
to penalize hospitals for excessive readmission rates, which are akin to recidivism
rates; Gupta (2017) and Batt, Bavafa, and Soltani (2020) analyze this program,
focusing on contract incentives. Similar studies in the prison context would be
useful.
REFERENCES
Abrams, David S. 2012. “Estimating the Deterrent Effect of Incarceration Using Sentencing Enhance-

ments.” American Economic Journal: Applied Economics 4 (4): 32–56.

Abrams, David S., and Chris Rohlfs. 2011. “Optimal Bail and the Value of Freedom: Evidence from

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