Does Visitation in Prison Reduce Recidivism?
Yuki Otsu∗†
Center for Spatial Information Science,
The University of Tokyo
May 17, 2023

Abstract
Visitation in prison is associated with a low recidivism rate after release, but thecausality is not clear. This paper tries to estimate the effect of visitation experience on the recidivism outcome of state prisoners in Missouri, using an instrumental variable approach. The instrumental variable used for identification is the
distance from a prison to an address before incarceration. The results support
that visitation has a causal effect on recidivism in the short run. Further analysis
shows that employment is an important channel of the visitation effect. However,no discernible effect on housing stability is found.
JEL classification: C26, J68, K42, R23
Keywords: recidivism, reentry, visitation, causal inference, instrumental variable∗ Center for Spatial Information Science, The University of Tokyo.

5-1-5 Kashiwanoha, Kashiwa,
Chiba 277-8568, Japan. Email: y.otsu@csis.u-tokyo.ac.jp† I appreciate the staff of the Missouri Department of Correction for providing the dataset for the research project. I sincerely thank my supervisor Ian Fillmore for his support, comments, and suggestions.
I would also like to thank Marcus Berliant, George Gayle, and Robert Pollak, John MacDonald, and threeanonymous refrees for beneficial discussions, comments, and advice. I also thank seminar participants
at internal seminars and the Olin Brown Bag Seminar at Washington University in St. Louis, the Happy
Hour Seminar, the UGOD seminar, and the International Trade and Urban Economics Workshop. The
views expressed in this paper are those of the author and do not necessarily reflect the view of the Missouri Department of Corrections. This project is approved by the IRB board at Washington University
in St. Louis: IRB ID 201904050.

1

Introduction

Since 1976, the prison population in the United States has grown rapidly such that by2008 there were 2.3 million prisoners. Although the number of prisoners has gradually
declined since then, it has remained near peak levels over the last forty years (Bronson
and Carson, 2019), and the U.S. has one of the highest incarceration rates in the world(Walmsley, 2015). Since most prisoners are eventually released, a high prison population implies a high rate of people with a criminal record in society. Indeed, Kaeble andGlaze (2016) estimated that in 2015, about 7 million individuals were either in prison,in jail, or on parole or probation, and 4.9 million people had experienced incarcerationin their past. However, it is not easy for offenders to overcome recidivism. According
to Alper et al. (2018), 68% of prisoners released in 2005 from correctional facilities in 30
states were arrested within three years of release and 83% were arrested within nine
years.
This high recidivism rate could be attributed to social disadvantages. For example,
prisoners are less formally educated (Motivans, 2017) and less healthy (Maruschak
et al., 2015) than those without a criminal record. Since these disadvantages are associated with race, there are more black prisoners than white (Bronson and Carson,2019). However, the high rate of recidivism is partially due to the collateral consequences of incarceration. Incarceration experience and criminal records cause many
problems such as discrimination in the labor market (Pager, 2003) and low employment probability (Bhuller et al., 2018; Mueller-Smith, 2015) and is associated with unstable housing (Harding et al., 2013). Hence, removing these obstacles could be a way
to reduce the recidivism rate, and it is important to know what policies can help thereentry of prisoners into normal life.
Strong social bonds are considered as mitigating these obstacles for ex-offenders.
A social bond here means a good relationship with family, friends, and neighbors.
Family and friends can provide employment opportunities through their networks,
stable housing, and emotional support.1 Strong social bonds increase the chance of
1 Visher and Travis (2003) surveyed literature focusing on prisoner transition back to the community.

1

getting this support, which is useful to overcome the obstacles. Hence, the support byfamily and friends is helpful for the successful reentry of prisoners into society andreduction of recidivism.2
However, since imprisonment physically separates prisoners from family and friends,
they have a hard time maintaining social ties. Correctional facilities offer several ways
for prisoners to keep in communication with those who are out of prison: letters,
phone calls, and visitation. In particular, as seen in the literature on social bonds
and recidivism, prison visitation is considered to be an important way for prisoners
to keep in communication with family and friends (Laub et al., 1998; Rocque et al.,2013).3 The relationship between visitation and recidivism are analyzed in the literature (Visher and Travis, 2003; Brunton-Smith and McCarthy, 2017; Bales and Mears,
2008; Mears et al., 2012; Cochran and Mears, 2013; Derkzen et al., 2009; Mitchell et al.,2016; Cochran, 2019; Lee, 2019; Cochran et al., 2020).4 The literature, for example
Visher and Travis (2003), finds that visitation experiences in prison are associated witha low recidivism rate and claims that this effect is through social ties maintained or
improved by prison visitation. Hence, it is claimed prisons should adopt policies thatencourage visitation, relying on the idea that there is a causal effect of visitation on
the reduction of recidivism. However, most of these papers claim causality under theassumption that there is no omitted variable bias, which is unlikely true.
Although visitation seems to be an important tool to maintain and improve social
They pointed out the importance of family ties for successful reentry, in particular, through housing
security and emotional support.
2 Social bonds may encourage recidivism if it implies, for example, bonding with other offenders.
Hereafter, I describe social bonds as something helpful for reentry.
3 In criminology, several theories are provided to explain the link between visitation and recidivism:(1) the social bond theory, (2) the social capital theory, (3) the general strain theory, and so on. For
example, social bond theory, provided by Hirschi (1969), argues that strong social bonds with family,
friends, and community help to form norms and values that deter recidivism. The social capital theory
puts more emphasis on the support provided through strong family ties, such as money, housing, andemployment opportunities.
Although there are many theories, the focus of this paper is not to test each theory but to provide
solid evidence for those theories; these theories rely on a causal relationship existing between visitation
and recidivism, but the causality has not yet been formally investigated.
4 Since visitation can be defined in various ways, many aspects have been investigated with a recidivism outcome: relationship with visitors (Bales and Mears, 2008), frequency (Mears et al., 2012), timing(Cochran and Mears, 2013; Bales and Mears, 2008), and length of visit (Derkzen et al., 2009). Recently,
using UK data, Brunton-Smith and McCarthy (2017) concluded visitation by parents improves familyties and lowers reoffending of inmates.

2

ties and hence reduce reoffending, it is not easy to identify a causal effect of visitation
on recidivism due to endogeneity issues. Many papers have mentioned that the relationship may be causal, but most of the papers do not have a strong identification
strategy to estimate the causal effect of visitation on recidivism. We cannot conclude
that visitation has a causal effect on lower recidivism rates only from the fact that
visited prisoners have a lower recidivism rate than non-visited prisoners. It may bestrong social ties that increase prison visitation experience and reduce the recidivism
rate of ex-offenders through housing, employment, and other channels. If there is nocausal relationship, visitation experiences work as a good predictor of recidivism, but
a marginal increase in visitation may not affect the recidivism rate.
Providing physical visitation opportunities would require the management of contraband (Siennick et al., 2013) and additional staff, which are costly. Virtual visitation
may be desirable because it reduces such costs, and prisons may charge a fee for its
use. However, visitation may benefit many other aspects of the post-release situation,
including the prevention of recidivism and its effect on family members and acquaintances. Therefore, whether physical visitation opportunities should be provided needs
to be judged comprehensively, but if there is a recidivism prevention benefit, it needs
to be taken into account. Specifically, this paper will identify how one visit reduces
recidivism and estimate the monetary costs saved by possible policies.
This paper investigates the causal effect of visitation on recidivism. To check thecausal effect and to investigate the channels of the effect, this paper uses data fromstate prisoners in Missouri released between 2012 and 2015. For the identification of
the causal effect, the regression analysis is based on an instrumental variable approach.
In particular, the instrumental variable (IV) is the distance of the incarcerated prison
from the home address of the prisoner. Individuals are likely to have a social networkin their community. Hence, when prisoners are assigned to a prison that is far fromtheir home, they are less likely to be visited by family members or friends, simply
because the prison is far from the community; in other words, the opportunity cost ofvisitation for visitors is high.

3The regression results show that a negative and statistically significant effect ofvisitation on recidivism: one visit per month reduces the reincarceration rate by 8
percent points. In particular, the short-run effects are robust under different samples,
control variables, and specifications.
Using the same IV approach, I also investigate the two potential channels of theeffect of visitation: employment and housing stability. A strong social bond is considered to provide better employment opportunities and a labor-market opportunity
is a key deterrence factor. The results indicate that visitation increases employment
probability and reduces the time to get the first job. Similarly, housing stability is considered as another important factor since homelessness and frequent movement areassociated with a higher recidivism rate. However, the estimation results do not show
any effect on housing stability. Hence, the employment channel is more important
than the housing channel to explain the visitation effect. Finally, as a result of a backof-the-envelope calculation, the state government can save the expenditure per inmate
by 813 dollars at the median if every prisoner were assigned to the closest prison.
This paper advances the literature in two ways. First, this paper provides empirical support for the literature about visitation and recidivism. An official report by the
Minnesota Department of Corrections (Minnesota Department of Corrections, 2011)concludes one visitation reduces the risk of recidivism by 13% for felony convictions
and 25% for technical violation revocation. However, the report is based on a simple
Cox hazard model and hence, as mentioned in the report, the estimator shows a correlation rather than causality. Most other papers show a correlation between visitation
and recidivism. Cochran et al. (2020) and Lee (2019) are two recent papers that use asimilar IV approach to check the causal effect of visitation on recidivism using state
prisoners in Florida and Iowa, respectively.5 They cast doubt on the causality because
they did not find a causal effect on recidivism. However, they measured a recidivism
outcome only at three years from release. Using administrative data in Missouri, this5 Cochran et al. (2020) used the distance to the first prison assigned to as an IV to predict visitation

experiences, and Lee (2019) checked several measures of distance from the prison. In both papers, theresult of the instrumental variable regression shows an insignificant effect of visitation on recidivism
within three years, and hence they are skeptical of any causality.

4paper supports that visitation has a causal effect and helps successful reentry. The
results suggest that the key differences are the time when the recidivism outcome ismeasured.
Second, this paper contributes to the literature on the channels of the visitation
effect: specifically employment and housing. The literature shows that better employment opportunity decreases recidivism rate (Yang, 2017; Schnepel, 2018). Higher
wages (Yang, 2017) and more vacancies (Schnepel, 2018) in local labor markets reduce
the recidivism rate. Unstable housing is associated with higher recidivism outcomes(Geller and Curtis, 2011). However, the visitation literature mainly focuses its effecton recidivism, but the channels of the effect are not well-investigated (Cochran, 2019).
This paper fills this gap by investigating the effect on employment and housing outcomes. The results provide evidence that visitation improves employment outcomesbut no evidence of improvement in housing stability.

2

TheoryFigure 1 summarizes the conceptual framework of why visitation improves the recidivism outcome. Prisoners are sent to a prison with an initial level of social ties. Social
ties in this context mean connections with families, friends, and communities. During
the imprisonment, the level changes through visitation experiences.
Although there are other ways to interact with outsiders, such as letters and phone
calls, visitation is one of the few opportunities for inmates to interact face-to-face withoutsiders. Though one visit may only have a negligible effect, regular visitation could
have larger and long-lasting effects on maintaining and improving social ties.
The visitation experiences are affected by the initial level of social ties as well as
the distance to prisoners’ homes from the prison. The initial level of social ties andvisitation experiences determine the social ties at release, and the social ties affect postrelease behavior. Social ties affect the recidivism outcome both directly and indirectly
through employment and housing situation.

5

Incarceration

ReleaseEmployment

Distance

Initial Social Ties

Visitation

Crime

Social Ties
Housing

Figure 1: Conceptual framework
Strong social ties increase opportunities to get job offers after release. Having
more and reliable connections with others increases job opportunities through their
networks. Employment has been considered as a desistance tool. Chalfin and McCrary (2017) surveyed the literature on crime and employment and concluded that
employment is a tool to reduce crime. One reason is that legal income becomes theopportunity cost of crime (Becker, 1968). Another reason is time allocation: engaging
in a legal job as an occupation reduces the time spent on illegal activities. This relationship holds for ex-prisoners. Schnepel (2018) found that released prisoners are lesslikely to recidivate when local labor markets are strong: that is, more vacancies. Yang(2017) also reached a similar conclusion using different data.
Social ties are also considered an essential factor for the stability of the housing situation (Visher and Travis, 2003). Geller and Curtis (2011) summarized why housing
security is important for ex-prisoners.6 Stable housing helps ex-prisoners to become
employed, to access social services such as healthcare, and to keep in contact with parole officers. Moreover, loitering or homelessness increases contact with police officers,which increases the probability of reincarceration.
The relationship between the housing situation and crime relates to housing policies. Housing support could be helpful to get a job, and employment eventually re6 Frequent movement or homelessness is considered as a bad signal for recidivism.

Harding et al.
(2013) found a low rate of homelessness but high residential mobility among former prisoners, partially
due to discrimination in the housing market.

6duces crime through the opportunity cost. For example, low-income housing developments reduce violent crimes in poor neighborhoods (Freedman and Owens, 2011),
and an emergency financial assistance for those who cannot pay the rent for the current month reduces crime (Palmer et al., 2019).7
There are other channels through which social bonds affect recidivism. A line ofliterature in criminology emphasizes the importance of support from others. In particular, family support is considered an important factor in reducing recidivism. Using survey data, Naser and La Vigne (2006) found that prisoners rely on family forboth material and emotional support. For example, material support, such as social
welfare, health care, and transportation, could affect recidivism. Another importantchannel is the emotional channel, which could directly affect criminal behavior. For
example, peer effects of criminal behavior have been analyzed in network literaturein economics. Depending on the peers, the peer effect could improve or worsen postrelease behavior (Corno, 2017). Moreover, social ties construct social norms that emotionally deter criminal behavior as described by the general strain theory.
Even though I have explained these channels separately, they are interrelated. Stable housing helps to have a job, and a job helps to have stable housing, since it makes
the rent payment more likely. Family support helps stable housing, since ex-prisoners
can live together with their family or receive help to rent an apartment. Also, family
and friends’ support can introduce job opportunities through their existing networks.
Hence, it is important to note that this paper aims to estimate the overall effect ofvisitation on a recidivism outcome.
Note that in this section I describe strong social ties from the perspective of crime
reduction and distinguish them from criminal ties. For example, Kirk (2009) finds
forced migration due to Hurricane Katrina reduced recidivism. Moving farther awayfrom home makes it harder for released prisoners to maintain the former criminal
networks in the community. Hence, losing criminal ties may effectively reduce recidivism. However, losing social ties would increase recidivism through loss of support
7 Since the financial assistance could be used for another purpose, the result may represent an income

effect.

7

from others.
In summary, visitation improves social ties, and improved social ties change postrelease criminal behavior through employment, housing stability, and other channels.
Following the argument in this section, visitation reduces recidivism, increases employment probability, and improves housing stability through stronger social ties.

3

Data

3.1

Summary Statistics

The data used for this paper are administrative data obtained from the Missouri Department of Corrections. The sample for the analysis consists of parolees and probationers in Missouri released between 2012 and 2015. Although the analysis in this paper is limited to parolees and probationers, they account for more than 90 % of released
prisoners. Each observation is based on a cycle defined by the admission date and therelease date. For each observation, the data contain residential and employment information during supervision and recidivism outcomes until 2019 August; hence thedata contain complete information on recidivism for at least three years. It is important to note that the recidivism results are based on records in Missouri. Therefore,
incarceration in other states is not included in the data.
A recidivism measure in the paper is defined as a return to incarceration. By definition, it contains a supervision condition violation.
Visitation could be measured in several ways. In particular, this paper uses the following two measures: visit dummy and visit frequency over the entire sentence period.
Visit dummy is a binary measure of visitation experience that takes one if someone(family, friends, etc.) visits the offender while incarcerated, and zero otherwise. Visit
frequency is the number of total visitations over incarcerated months.
Among all released prisoners on parole or probation, the sample used for the analysis satisfies the following conditions: (1) male, (2) at working age, (3) living only in
Missouri during supervision, and (4) serving an original sentence. Given that most8

prisoners are male, it is reasonable to focus on the male sample for the analysis. Moreover, gender might have correlated with the distance between home and prisons, sincemost of the prisons are for males. The sample is limited to those of working age (20–65)
at release to focus on the employment channel. An out-of-state sample is excluded to
avoid a selection problem.8 Lastly, this paper focuses on an initial cycle for a sentence:in other words, not a cycle for parole revocation. Some observations are dropped during the data cleaning process, such as missing values. Finally, 33,971 observations areused for the analysis. Note that since each observation consists of one cycle from incarceration to release, one person could have multiple observations when the person isreleased, incarcerated, and released again between January 2012 and December 2015.
Basic demographics are summarized in Table 1. The mean age at release is 35.1,
and 70% of observations are below the age of 40. Non-Hispanic whites and blacks
account for almost all observations and other ethnic groups such as Hispanics, Asians,
and Native Americans are rare.
Table 2 compares demographics by visitation experience. The visited group is prisoners who experienced visitations at least once while in prison. The visited group has
similar characteristics with the non-visited group, but the sentence length is longer.
This is likely because the more time they spend in prison, the more chances they will
be visited.

3.2

Post Release Outcomes

Figure 2 summarizes the recidivism rate for up to three years since release. At six
months from release, 8.6% of the visited group returns, while 11.5% of the non-visitedgroup returns. The difference remains stable over time. At three years since release,
48.2% of visited prisoners return, while 51.3% of non-visited prisoners return. Overall, as seen on the graph, visitation experience is associated with a relatively lower
recidivism rate by about 3 percentage points.
8 Out-of-state sample has a lower recidivism rate because of the following two reasons. One is that re-turn to prisons in other states is not recorded in the Missouri database. Another reason is that prisoners
have to behave well to get approval for the interstate supervision.

9

Table 1: Summary statistics
N=33,971
Mean
Distance (mile)
114.31
Visitation (Dummy)
0.48
Visitation (Freq. per month)
0.43
Age at Release
35.09
Race/Ethnicity
White (Non-Hispanic)
0.66
Black (Non-Hispanic)
0.24
Other Race
0.10
Sentence Length
5.58
Parole0.70
Primary Crime Type
Property
0.29
Violent
0.13
Drug
0.28
Other Crime
0.30
Felony ClassA (10-30 year)
0.02
B (5-15 year)
0.17
C (3-10 year)
0.65
D (-7 year)
0.15
Custody Level
Low
0.39
Medium
0.39
High
0.22
Reincarceration
within 6 month
0.10
within 1 year
0.24
within 2 year
0.42
within 3 year
0.50
Supervision Completion
0.35
Employment
ever since release0.47
at 3 month from release
0.23
at 6 month from release
0.29
Fulltime (ever since release) 0.39
Movement (Dummy)
0.55
Movement (Freq. per month)
0.07

S.D. Min
68.79 .706
0.50
0
0.88
0
10.18 20

Max
385
1
17
64.9

0.47
0.43
0.29
3.06
0.46

0
0
0
0
0

1
1
1
50
1

0.46
0.34
0.45
0.46

0
0
0
0

1
1
1
1

0.15
0.38
0.48
0.36

0
0
0
0

1
1
1
1

0.49
0.49
0.41

0
0
0

1
1
1

0.30
0.43
0.49
0.50
0.48

0
0
0
0
0

1
1
1
1
1

0.50
0.42
0.45
0.49
0.50
0.16

0
0
0
0
0
0

1
1
1
1
1
15

Notes: Supervision completion is defined as a share of “Discharge” over sum of “Abscond”, “Revoke”,
and “Discharge”. The other outcome “Death”, which account for 6.7% of overall sample, is not included.

10

Table 2: Mean by visitation experience

Distance (mile)
Age at Release
Race/Ethnicity
White (Non-Hispanic)
Black (Non-Hispanic)
Other Race
Sentence Length
ParolePrimary Crime Type
Property
Violent
Drug
Other Crime
Felony ClassA (10-30 year)
B (5-15 year)C (3-10 year)
D (-7 year)
Custody Level
Low
MediumHigh
Reincarceration
within 6 monthwithin 1 year
within 2 year
within 3 year
Supervision Completion
Employment
ever since releaseat 3 month from releaseat 6 month from release
Fulltime (ever since release)
Movement (Dummy)
Movement (Freq. per month)

Not Visited
Visited
N=17,784
N=16,187
Mean
S.D.
Mean
125.7
70.9
101.8
35.7
10.6
34.5

S.D.
64.1
9.71

0.64
0.26
0.098
5.16
0.63

0.48
0.44
0.30
2.81
0.48

0.68
0.23
0.093
6.04
0.77

0.47
0.42
0.29
3.26
0.42

0.29
0.10
0.30
0.31

0.45
0.30
0.46
0.46

0.30
0.16
0.25
0.29

0.46
0.37
0.44
0.45

0.012
0.14
0.68
0.17

0.11
0.35
0.47
0.37

0.038
0.21
0.62
0.13

0.19
0.41
0.49
0.34

0.46
0.30
0.24

0.50
0.46
0.43

0.32
0.49
0.19

0.47
0.50
0.39

0.11
0.26
0.44
0.51
0.32

0.32
0.44
0.50
0.50
0.47

0.086
0.23
0.41
0.48
0.39

0.28
0.42
0.49
0.50
0.49

0.40
0.19
0.24
0.32
0.54
0.079

0.49
0.39
0.43
0.47
0.50
0.19

0.54
0.28
0.33
0.47
0.56
0.070

0.50
0.45
0.47
0.50
0.50
0.12

11

51.3

50.0
48.2

43.7

40.0

41.1

30.0
26.0

22.7

20.0
11.5

10.0
8.6

Not Visited
Visited

0.0
6 month

1 year
2 yearTime from Release

3 yearNotes: The lines show the recidivism rate of male prisoners over timewith the confidence interval (CI). The CI is at 95% level.

Figure 2: Reincarceration rate over time
As seen in Table 2, the visited group has a higher supervision completion rate andare more likely to have employment since release. More than half of the released prisoners experienced at least one movement (change of the address) during supervision.

3.3

Visitation

Figure 3 shows the visitation timing over the sentence period. The fraction of people
who have ever been visited increases over time. However, the total counts of visits
peak in the middle and then decrease as the release date approaches.
Figure 4 summarizes the visitation experience by the relationship between prisoners and visitors. The fractions indicate those who have been visited by the visitor typeat least once during incarceration. The category Others contains persons such as attorneys and clergy. The number does not sum up to one, since visitation by multiple
types of people is possible. The figure indicates that 48% of the sample has an experience of visitation by someone at least once. 38.7% of the sample is visited by relatives
and 25.4% is visited by friends. Visitation by relatives is more common than friends
12

50

15000

40

12000

20
30
% Ever Visited

Total Counts
6000
9000

10

3000
Enter

.25

CDF

0

0

Counts.5.75
Visitation Timing over Cycle

Release47.6

Ever Visited by the group (%)
10
20
30
40

50

Figure 3: Visitation timing

38.7

26.3

25.4
23.1

15.0
10.1

9.2
6.2

O

th

er
s

s

n

nd
Fr
ie

re
ld

C
hi

th
er

an
tO

ou
se
Si
g

ni

fic

Sp

Fa
th
er

ot

he
r

s
M

es

Pa
re
nt

iv

R
el

at

An
y

0

2.3

Notes: This graph shows the fraction of prisoners visited by the category during incarceration. Relatives
and parents are aggregated categories. Relatives include parents, spouses, children, and other relatives,and parents contain mother and father. The sum of the fractions of mother and father is not equal to thefraction of parents, since some prisoners experience visitation by both.

Figure 4: Visitation by relationship13

or others. Among relatives, mothers are the most common as a single category, and
1 in 5 observations experienced a mother’s visitation. Only 6.2% of prisoners experience visitation by a spouse, but since 20% of the sample reported being married at theinitial classification, 1 in 4 married observations experienced spousal visitation.

3.4

Prison environment in Missouri

3.4.1

Prison assignment process

Before the regression analysis, this section summarizes the prison assignment processin Missouri. Once the sentence is determined, prisoners are sent to one of the Diagnostic Intake Centers for initial classification. Based on gender, special needs, andthe custody level determined by the classification, an offender is assigned to an initial prison.9 During incarceration, the custody level is updated periodically. Typically,
the first reclassification of the custody level happens about six months from the initialassessment, and after that, reclassification is completed every 12 months.
Each prisoner is assigned one of three levels of custody: minimum, medium, andmaximum. In principle, the custody level is determined by the maximum of twoscores: institutional score (I score) and public risk score (P score).10 The I score is
calculated by certain variables: age, most serious offense, mental health, education,
vocational skill, and conduct violations (for both the initial and reassessment), employment status, marital status, revocations, incarceration history (only for an initialassignment), and program failure (only for reassessment). The P score is based on theseriousness of the pending charge, remaining sentence, program completion, conduct
violation, and prior escape. As of June 30, 2015, 36.4% of male prisoners are assigned
the lowest risk and 35.9% and 27.7% are assigned medium and maximum level, respectively (Nixon and Lombardi, 2015).
9 See Missouri Department of Corrections (2013) for a complete description of the classification pro-cess.
10 This rule may not be so strict in practice because some are assigned a lower custody level than their
P score. However, the number of such observations is only 552, which accounts for only about 1.6% of
the total sample, so the problem is not severe.

14

M
in
im
u
m
M
ed
iu
m
M
ax
im
u
m

1
0
1-1
,0
0
0
1
,0
0
0-3
0
,0
0
0
3
0
,0
0
0-1
7
9
,5
3
3

K
a
n
sa
sC
ity
S
t.L
o
u
is

0

2
5

5
0

1
0
0M
iles

Notes: There are 19 correctional facilities for male prisoners in Missouri and each facility has its security
levels. Prisons with small, medium, and large circles indicate minimum, medium, maximum security
levels, respectively. There are only 16 points in the map, since 3 facilities are adjacent to other facilities.
The gradation of red color is based on total crime counts over 4 years (2012–2015).

Figure 5: Missouri state prisons for male
3.4.2

Prison locations

In Missouri, there were 22 correctional facilities as of the end of 2015. Since two prisons among them were for females11 and another one had switched from a community
release center to a prison in late 2015, the analysis focuses on 19 correctional facilities. Figure 5 shows the locations of the facilities. Prisons are roughly concentrated
along a line from northwest to southeast, and the southwest region has a few prisonsonly. Missouri has two major cities: St. Louis and Kansas City. There are multiple maximum-security facilities near St. Louis but not many near Kansas City. Eachfacility has its security level: Minimum, Medium, and Maximum. Some facilities accommodate offenders of multiple security levels. Six prisons have all security levels
and two facilities that have medium and maximum levels locate next to other levels ofprisons.12
11 There are only two facilities for female prisoners, which are located in the north of Missouri(Audrain County and Livingston County). Both can accommodate prisoners of any custody level. Since
the possible variation of distance is limited, the main section of this paper focuses on male prisoners.
The analysis of female prisoners is in Section 5.2.1.
12 Most prisons were open during the entire sample period (2003–2015), except ERDCC and JCCC,
which opened in 2003 and 2004, respectively. Some inmates were assigned to facilities other than the 19

15

Figure 5 also shows the number of reported crimes by county from 2012 to 2015.
The number is high in large cities such as St. Louis City and County, Kansas City, andColumbia. Prison locations are not concentrated in high crime rate counties, however.

3.4.3

Visitation process

In order to receive visitation, Missouri prisoners have to submit a list of potential visitors, and the list can have at most 20 persons. Prisoners can update the list at most
twice a year.13 Generally, prisons accept visitors from 9:30 to 13:30 and 14:30 to 18:30
on Friday, Saturday, and Sunday, although there are slight differences across facilities.
It’s worth mentioning that conjugal visits are not permitted in Missouri prisons.
Additionally, visitation privileges can be restricted as a disciplinary measure, andthere may be additional restrictions imposed from the visitors’ side as well.
Prisoners have the opportunity to receive multiple visits in a single day. A person can visit the same prisoner on two consecutive days, or they can opt to visit theprisoner in both the morning and evening on the same day.

4

Approach

4.1

Regression model

The regression is based on the following specification:
yitpc = α + β visit visitit + β X Xit + ηt + η p + ∑ ηcj 1(custody = j) + eitpc .

(1)

j∈ J

An outcome variable yitpc is a binary indicator of outcome after the release of aperson i who is from a county c, incarcerated in a prison p,14 and released at time
discussed above. For example, two prisons existed for a short time in the sample period: the Missouri
State Penitentiary (MSP), which closed in 2004, and the Kansas City Reentry Center (KCRC), whichswitched from the Kansas City Community Release Center in 2015. Moreover, inmates could also be
assigned to community release centers during incarceration. However, this paper does not use thesecycles for the analysis because they are rare.
13 For more information about the regulations, see Precy and Greitens (2018).
14 Offenders can be assigned to multiple prisons over one sentence. p is defined as the initial prison

16

t. Visitit is a measure of visitation experience while imprisoned. Xit is a vector ofcontrol variables at the time of release.15 ηt and ηcj are time and county fixed effects,
respectively. The county fixed effects ηcj are defined separately for each custody levelj ∈ J = { Min, Med, Max }. The prison fixed effects η p capture the prison-specific factor
such as job training and an education program. Following Lee (2019), standard errors
are clustered at county level.16 The regression coefficient of interest is β visit and thecoefficient measures the effect of visitation experience on recidivism.
The regression is based on a linear probability model (LPM). Since visitations arecount data, Poisson and negative binomial models are standard, especially in the literature in criminology. However, this paper uses LPM rather than nonlinear models
because LPM is superior when interpreting the marginal effect. Since the objective is
to check the effect of an additional visit on recidivism, and this paper uses different
measures of visitation including continuous measures, LPM is better than other nonlinear models such as Logit and Probit. The coefficient under the LPM captures the
local average treatment effect (LATE).
As claimed in the literature, the expected sign of β visit is negative. However, the
OLS regression may suffer an omitted variable bias. Possibly the bias stems fromthe strength of social bonds. When strong social bonds increase visitation as well as
decrease reoffending behavior, the OLS estimator could overestimate the negative impact of visitation in magnitude. Alternatively, the OLS estimator could underestimate
the negative impact if criminal bonds are strengthened through visitation. Hence, thispaper uses an instrumental variable approach to check a causal effect.
where a prisoner is assigned after the initial risk assessment.
15 The list and details of the control variables are in the appendix A.
16 Following the literature and due to the sample size, I cluster standard errors at the county level.
It is ideal for clustering standard errors at the county level and at the prison level. This change, however, increases the standard errors in most specifications but preserves the short-run effects in the main
results.

17

4.2

Explanatory variables

Control variables are demographics (age at release, race/ethnicity, and number of dependents), crime information (felony class, the primary type of crime, sentence length)
and the initial custody level.17 The complete list and detailed information of control
variables are in the Appendix. Three fixed effects are included in the model: prison,time, and county by custody level fixed effects.18 Prison fixed effects capture the difference across prisons such as a rehabilitation program offered in a specific prison.
Time fixed effects are to capture the effect by economic conditions, since, as Schnepel(2018) and Yang (2017) pointed out, better economic conditions at the time of releaseprovide better employment opportunities and better opportunities in legal sectors of
the economy eventually decrease criminal behavior. County by custody level fixed
effects capture time-invariant county characteristics. Hence, the county by custodylevel fixed effects control a consistently higher crime rate in big cities such as St. Louisand Kansas City. Most importantly, the fundamental distance to correctional facilities
is captured by the county by custody level fixed effects.19 As Bedard and Helland(2004) found, criminals may commit a crime taking less visitation into account when
their home is far from any prison. By including the county by custody level fixed effects, the distance term in the first stage regression captures the unexpected variationof distance. It is worth noting that the county by custody level fixed effects are definedfor each custody level (Min, Med, Max) to capture the unexpected distance, which is
discussed more in detail in the next section.
17 Lee (2019) used LSI-R score to control existing family factors.

However, MDOC uses the Salient
Factor Score instead of LSI-R to calculate the risk of recidivism. Moreover, incarceration history is notavailable. The Salient Factor (SF) score is an index based on some demographic variables, criminal
history, and behavior while incarcerated. Since visitation could affect the SF score through misconduct,
the score is not included as a control variable in the main regression. The regression results with the SF
score are in Section 5.2.1.
18 In other words, estimation uses the variation of recidivism rates net of mean differences acrossprisons, times, and county-custody pairs.
19 Mcclellan et al. (1994) used a distance to the hospital as the instrumental variable to check theeffect of intensive treatment on mortality. They also conditioned on the distance to the closest hospital
to avoid potential confounders such as urban-rural differences. Cochran et al. (2020) and Lee (2019)
controlled the average distance by county fixed effects.

18

4.3

Instrumental variable

The identification of the causal effect relies on an instrumental variable approach. An
instrumental variable for visitation is the distance from prisoners’ home to the prison
they were in.20 The reason why distance could be correlated with the visitation experience is that people have social ties locally based on the residential location, andfamilies and friends likely live in the neighborhood. Hence, when prisoners are assigned to a prison that is far from their home, they are less likely to be visited by theirfamily members or friends. The literature found a correlation between more distantprisons and less visitation (Mears et al., 2012; Cochran et al., 2020).
Since the data do not have the exact address of each prisoner before incarceration,
the county of conviction is used as a proxy of an initial address before incarceration
following Schnepel (2018) and Cochran et al. (2020).21 The measure of distance usedin the analysis is the linear distance from the geometric center of counties to prisons.22
Since there are 115 county-equivalent areas23 and 19 state correctional facilities formale prisoners in Missouri, there are 2185 pairs of a county and a prison.
The prison used to compute the distance is set to the first prison assigned after the
initial risk assessment. Sometimes prisoners experience a transfer from the first facility
to another correctional facility. In the data, 38% of the observations experience morethan one transfer. However, this paper does not use the distance to the second or later
prisons since the transfer decisions take into consideration some factors potentiallyproblematic to the validity of the instrumental variable (Precy and Greitens, 2018).24
20 Physical distance has been used as an instrumental variable in other papers (Mcclellan et al., 1994;

Baiocchi et al., 2010; Cochran et al., 2020; Lee, 2019).
21 County of conviction is determined by the place of the offense. This may not be a good proxy ofresidential address when people commit crimes at a place far from their homes. However, crime is alocal phenomenon; Bernasco (2010) showed that 75% of burglaries are committed within five kilometers
and about 90% is committed within ten kilometers from home in the Hague, Netherlands.
22 Road distance could be the best proxy. However, since location data is county level and travel timewithin a county could be large, this paper does not use the travel time.
23 Missouri state has 114 counties and one independent city (St. Louis City).
24 Cochran et al. (2018) note that the pattern of visitation frequency experienced during incarceration
may vary from person to person. In addition, since distance and visitation are correlated, changes in
distance due to transfers may affect visitation frequency. The initial distance is used as the instrumental
variable in this study since there is an endogeneity problem if the estimation uses the distance affectedby transfers, such as the weighted average. However, the estimator in this study using initial distanceas the manipulated variable is an estimate of the effect of initial distance on the overall duration of in-

19

.008
.006
Density
.004
.002
0
0

100

200
Distance (mile)

300

400

Notes: The vertical line is at the mean. Home address is based on counties of conviction.

Figure 6: Distance from home
For example, to keep good institutional conduct is one of the factors but this may
generate a correlation between the distance and family ties, since the distance may
affect institutional misconduct through visitation as showed in Mears et al. (2012).
Another problematic factor is the request from prisoners to be assigned to a facility
close to their families. The request could also generate a correlation between distanceand family ties. Hence, this paper uses the distance to the first facility after the initialrisk assessment. The distribution of the distance is in Figure 6.

4.3.1

Identification assumptions

This paper uses a distance from prisoners’ homes to their prison as an instrument.
With the instrumental variable approach and some conditions, the estimated coefficient β visit in the equation (1) is the local average treatment effect (LATE) of visitation
carceration, and the effect through transfers is also included in the estimated effect. Suppose there is alarge group of inmates for whom initial distance has a significant effect on initial visitation frequency.
In that case, the effect of distance may be overestimated or underestimated through its effect on subsequent transfers. However, as shown in Figure 3, visitation frequency during incarceration is stable
except immediately after incarceration and just before release, so the effect on the estimates is likely tobe small.

20

(Imbens and Angrist, 1994): the average treatment effect among the compliers. In thiscontext, a complier is someone who can experience visitation if assigned to a nearby
prison but not if assigned to a distant prison. For the estimation of the LATE, thispaper assumes the following conditions: (1) the distance correlates with the visitation variable (relevance), (2) the distance is correlated with an outcome variable only
through the visitation variable (exclusion restriction), and (3) visitation decreases with
distance (monotonicity).
Relevance and monotonicity are confirmed in Figure 7. Figure 7 plots visitation
experience and distance. Both figures show that the longer the distance, the lower
the fraction of prisoners that experienced visitation. The extensive margins of visitation seem to have a linear relationship. However, the means of the intensive margins
drop more at a lower distance. The non-linear relationship for intensive margins was
also found in Lee (2019). Hence, the figures support the relevance and monotonicity
conditions of the instrumental variable.
The exclusion restriction is related to the assignment process. The assignment is
influenced by two factors: the custody level and county of origin. As I discussed
in Section 3.4.1, the custody level is an important factor in the assignment process
because it determines a possible set of prisons a prisoner can be assigned.
Moreover, the assigned prison tends to be closer to the county of origin. Figure
8 shows the origin of prisoners at each correctional facility. The figure indicates thateach facility accommodated more prisoners from the neighborhoods.
However, the assignment is not deterministic: people from the same county andcustody level are assigned to different facilities. The source of variation is capacity
constraints. Since the sample period is during the period of mass incarceration, thecorrectional facilities in Missouri have chronically faced a shortage of available beds
for prisoners, which generates randomness in the assignment process. Hence, conditional on the two key factors, the custody level and county of conviction, the assignment can be regarded as random, and the identification of visitation effects relies on
the unexpected variation of the distance. To control for the custody level and county

21

.8
Visitation Experience
.4
.6
.2
0
0

50

100
150
Distance (mile)

200

250

200

250

0

.2

Visitation Frequency per month
.4
.6
.8
1
1.2

1.4

(a) Extensive margin

0

50

100
150
Distance (mile)(b) Intensive margin
Notes: The point at the longest distance in the figure is the mean of all observations that exceed 250
miles.

Figure 7: Visitation experience by distance22Notes: A circle in each graph represents the location of the facility. The color of each county is basedon the share of prisoners from the county relative to the state average. A red (blue) color in a graphmeans the share of prisoners from the county is higher (lower) than the share of prisoners in the entire
sample.

Figure 8: Origin of prisoners by prison compared to the statewide meanof origin, the explanatory variables in the regression include the county fixed effects
for each custody level.
Table 3 confirms the correlation of distance with observable variables by the OLS
regression. The result shows that distance correlates with some variables, but not in an
unexpected way. The positive correlations with sentence length and the violent crime
indicator are because of the severity of the crime. Longer sentence length and violent crime tend to assign a higher custody level. Since high-security level prisons are
relatively rare, a higher custody level correlates with longer distances. The negative
correlation with drug crime was also confirmed by Lee (2019), although it was insignificant in Lee (2019). Lastly, among those who experience visitation only, non-Hispanic
blacks tend to have longer distance than non-Hispanic white, since blacks concentratein particular counties.25 In the sample, 59% of non-Hispanic blacks come from the top
three counties (St. Louis City, St. Louis County, Jackson County), and these counties
25 Appendix B checks the racial heterogeneity of the effect.

23

are relatively close to facilities. However, only 15% of non-Hispanic whites are fromthe top three counties (St. Louis, St. Charles, and Greene counties) and are dispersed
throughout each county. Hence, even if the fixed effects are included in the model,
they do not fully capture the racial difference.
In summary, the key factors in deciding the assignment are the custody level andthe origin of prisoners. Conditional on the same custody level and the same sentencing
county, the assignment could be considered as random.

5

Main results

5.1

First stage

The first stage regression results confirm the distance has a strong correlation with visitation in Table 4. For the estimation shown in Table 4, all control variables and fixed
effects are used as explanatory variables. The estimated coefficients show that an increase in the distance by 100 miles reduces the chance of visitation by 7.4 percentage
points and the monthly frequency by 17.8 percentage points. The large first-stage F
statistics indicate that the distance is a strong instrumental variable for the two measures of visitation (Stock and Yogo, 2005). Hence, the first-stage results support thatthe distance is a valid instrumental variable in terms of the strength of the correlation.

5.2

The effect on recidivism

The regression results are summarized in Table 5 and 6. The first column shows the
OLS results and the second column shows the IV regression results. Each row shows
the result of recidivism outcomes at four points (6, 12, 24, and 36 months from release).
Visitation is measured by a dummy variable in Table 5, and by frequency per monthin Table 6.
In the OLS, the estimated coefficients show a negative correlation between visitation and recidivism. Visitation experience is associated with 3–6% point lower re-24

Table 3: Correlation with distance(2)
Not Visited(3)
Visited-0.0520**(0.0245)
Sentence Length
0.667***(0.195)
Non-Hispanic Black
1.555(1.105)
Other Race
-1.537*(0.926)
Dependents-0.280*(0.161)Violent Crime
3.607***(1.005)
Drug Crime-2.301***(0.866)
Other Crime
0.173(1.137)
Felony Class B-2.626(5.849)Felony Class C-3.383(6.732)Felony Class D-4.723(6.960)
Custody Level (Medium) -19.39***(5.791)
Custody Level (High)15.33***(3.133)-0.0493(0.0363)0.804***(0.237)-1.699(1.144)-1.185(1.274)-0.286(0.238)4.886***(1.248)-2.814**(1.131)
0.0923(1.432)-3.778(8.382)-5.541(9.783)-7.866(10.04)-15.95***(5.677)12.71***(3.140)-0.191***(0.0393)0.691***(0.221)3.330**(1.281)-3.000**(1.285)0.0272(0.193)3.313**(1.328)-2.263**(1.037)0.310(1.230)-1.308(4.382)-2.103(4.940)-1.890(5.322)-19.57***(5.078)20.39***(3.834)Controls
Fixed effects
ObservationsYY
17,784YY
16,187Distance(1)All

Age at ReleaseYY
33,971

Standard errors are clustered at county level. *** p<0.01, ** p<0.05, * p<0.1.

25

Table 4: First stage
Visitation
Distance (100 miles)
Controls
Fixed effects
ObservationsFirst-Stage F Statistic

(1)
Dummy

(2)
Frequency-0.0740***(0.00685)
YY
33,971116.9-0.178***(0.0172)
YY
33,971
107.6

cidivism rates, and one visitation per month is associated with a 1–3% point lower
recidivism rate.
The IV results have larger negative effects than the OLS results.26 Based on the estimators in Table 5, those who are visited while in prison are about 18 to 19 percentage
points less likely to return to prisons. At six months from release, the visited group
has a 19.6% point lower recidivism rate, but the magnitude is stable over time. At
three years from release, the visitation effect is 19.8 percentage points.27 The result inTable 6 indicates that a marginal increase in visits per month decreases reincarceration
within six months by 8.2 percentage points, and hence additional one visit per year
decreases reincarceration by 0.68 percentage points (−0.082/12 = −0.0068). Similarly,
the marginal increase in visitation reduces recidivism by 0.65, 0.65, 0.69 percentage
points and 1, 2, and 3 years from release, respectively. The coefficients up to one year
from the release show a statistically significant effect of visitation experience. Similar
to a binary case, the magnitude of the negative effect declines gradually over time, andthe standard errors increase.
Under the IV regression, the visitation effect is confirmed at each point for up to 3
years. However, decreasing the magnitude and increasing standard errors over timesuggest the long-run outcomes may be affected by other factors and may not be appropriate to measure the visitation effect.
26 In Cochran et al. (2020), the point estimate under the IV regression is larger than the OLS estimate,

but neither is statistically different from zero.
27 Assuming that the marginal effect does not decrease with the number of visits, five visits per monthwould be sufficient to prevent recidivism. Thus, regular weekly visits over the entire period of incarceration may be sufficient, and no further visitation opportunities may be necessary.

26

Table 5: Main results: visitation measured by a binary variable
(1)
OLS

(2)
IV

β
S.E.

-0.038***(0.005)-0.196***(0.054)βS.E.

-0.051***(0.008)-0.187***(0.064)βS.E.

-0.054***(0.008)-0.188**(0.080)β
S.E.

-0.062***(0.009)YY
33,971-0.198**(0.083)YY
33,971

Visitation (Dummy)
6 month

1 year

2 year

3 yearControls
Fixed effects
Observations

Standard errors in parentheses are clustered at county level. *** p<0.01, ** p<0.05, * p<0.1.
Notes: Each row uses different outcome variables. Each pair of coefficient and the standard error isfrom different regression.

Table 6: Main results: visitation measured by frequency per month
(1)
OLS

(2)
IV

β
S.E.

-0.016***(0.002)-0.082***(0.024)βS.E.

-0.021***(0.004)-0.078***(0.028)βS.E.

-0.029***(0.003)-0.078**(0.035)βS.E.

-0.032***(0.004)YY
33,971-0.083**(0.037)
YY
33,971

Visitation (Frequency)
6 month

1 year

2 year

3 yearControls
Fixed effects
Observations

Standard errors in parentheses are clustered at county level. *** p<0.01, ** p<0.05, * p<0.1.
Notes: Each row uses different outcome variables. Each pair of coefficients and the standard errors arefrom different regressions. Frequency is defined as the total number of visits over incarcerated month.

27

5.2.1

Sensitivity checks

The main results confirm the negative effect of visitation on recidivism. To check therobustness of the effect, I check the sensitivity of the results with three different specifications and samples.
Tables 7 and 8 check the results with different control variables. The first column
uses actual imprisonment length as a substitute for the sentence length. The magnitude of the visitation effects becomes smaller in the short run, and hence the shortrun negative effect is partially mediated by a shorter incarceration length. However,shorter incarceration may be harmful in the long run, since the magnitude of the visitation effect is larger compared to Table 5 and Table 6. The second column includes arecidivist dummy variable as an additional control. It is worth noting that the recidivist dummy variable is an imperfect measure. The recidivist dummy variable takes avalue of one from the second or more time a prisoner appears in the data. Since thedata period is limited, some prisoners might not be counted as a recidivist when theprevious incarceration cycle ends before the sample period. The result shows a significant effect only at six months and one year from release. The point estimates indicatethat the magnitude declines and the standard errors increase over time.28 Lastly, thethird column uses dummy variables for each SF score. The SF score is used as another imperfect measure of crime records, since the score reflects crime history as wellas other factors (conviction history, incarceration history, age, education, vocational
skills, drug history, treatment completion, and behavior in prison). The results are
similar to those with a recidivist dummy variable. The negative effect of visitation is
confirmed in the short run, but it loses statistical significance after 1 year from release.
The main sample is restricted to residents in Missouri only. However, the estimation results may underestimate the effect of visitation due to sample selection, and so
Tables 9 and 10 show additional analysis with different samples. The first and second
28 Since prisoners with a record would be more likely to have a greater distance, the model withouta prior record may, in an absolute sense, overestimate the effect of distance on visitation. Although
the estimated effects are statistically significant in the short run, the second columns in Tables 7 and 8
confirm that the visitation effect becomes smaller when the recidivist dummy is added.

28

Table 7: Different control variables: dummy
Visitation (Dummy)
6 month

(1)
Days

(2)
Recidivist

(3)
SF

β
-0.185***
S.E. (0.048)-0.167***(0.052)-0.165***(0.048)β-0.185***
S.E. (0.059)-0.126**(0.060)-0.143**(0.062)β-0.196***
S.E. (0.072)-0.111(0.075)-0.136*(0.080)β-0.213***
S.E. (0.075)
Y
N
N
Y
Y
33,971-0.127(0.078)NYNYY
33,971-0.152*(0.081)NN
Y
YY
33,971

1 year

2 year

3 yearIncarcerated days
Recidivist
SF scoreControls
Fixed effects
Observations

Standard errors in parentheses are clustered at county level. *** p<0.01, ** p<0.05, * p<0.1.
Notes: The same control variables are used except sentence length in the first column. Instead of sentence length, actual incarcerated length is used.

29

Table 8: Different control variables: frequency
(1)
Days

(2)
Recidivist

(3)
SF

β
S.E.

-0.080***(0.023)-0.069***(0.022)-0.070***(0.022)βS.E.

-0.080***(0.027)-0.052**(0.025)-0.061**(0.027)βS.E.

-0.085**(0.033)-0.046(0.031)-0.058*(0.035)βS.E.

-0.093***(0.035)YNN
YY
33,971-0.052(0.033)NY
N
Y
Y
33,971-0.064*(0.037)NN
Y
YY
33,971

Visitation (Frequency)
6 month

1 year

2 year

3 yearIncarcerated days
Recidivist
SF scoreControls
Fixed effects
Observations

Standard errors in parentheses are clustered at county level. *** p<0.01, ** p<0.05, * p<0.1.
Notes: The same control variables are used except sentence length in the first column. Instead of sentence length, actual incarcerated length is used.

columns include observations with an out-of-state address. In Missouri, St. Louis andKansas City are the two biggest cities and are on the border with other states. In thefirst column, the sample contains residents in the Kansas City and St. Louis metropolitan areas as well as residents just in Missouri. They have a much lower reincarceration
rate for two reasons. One is that the reincarceration rate for them may be underestimated, since recidivism outcomes are measured in Missouri only. Another reason is
selecting a better sample, since prisoners must have a reason to be out of state: having
families or relatives who support the released prisoners or good behavior in the short
run in Missouri. The regression results for long-run outcomes show a significantly
negative effect now but this may be due to the measurement problem. The second column expands samples for all out-of-Missouri observations. The estimated visitation
effects are similar but smaller in the short run compared to the first column because
those who live outside of Missouri after release are less likely to be visited during
incarceration and return to prison in Missouri.

30In the main specification, I use the county of conviction as a proxy of the residential address. One concern of this proxy is that a particular county-prison pair mightcause the main result. For example, a gang member may sustain the gang ties throughvisitation in a prison where other members had been incarcerated. Since gang crimes
are more popular in big cities like St. Louis or Kansas City, the problem seems serious
in those areas. In the third column, I perform the estimation without the prisoners
coming from St. Louis and Kansas City. However, the estimation results are similar to
the main results and still show a statistically significant effect of visitation. Therefore,
the estimated impact is unlikely driven by a particular county-prison pair.
When the cycle of technical violations is included in the sample of regressions, themagnitude of the negative effect is smaller in the long-run.29 In other words, the effectof visitation on parole or probation violators is likely to be small.
Finally, the last column shows the results using female prisoners. There are only
two prisons for females, and the sample size is smaller than the male case. Due to thesmall sample size, the estimated coefficients have high standard errors, so most are notstatistically significant. However, the results show that visitation reduces reoffendingat six months from release.

5.2.2

Discussion

This paper found a negative effect of visitation on recidivism, while Cochran et al.
(2020) and Lee (2019) found no effect taking a similar approach like mine. Here thispaper presents a list of potential reasons why these results are different.
The first reason is the state difference. The recidivism rate in Missouri is higher
than that of Florida (Cochran et al., 2020) and Iowa (Lee, 2019). The recidivism rate
is not directly comparable between states since each state is different in various dimensions: demographics, the legal system, and so on. Hence, these differences may
generate different results. One possibility is that, given that the difference between
OLS and IV results is large, the initial criminal ties of prisoners in Missouri are very
29 Since the actual incarcerated length is used in the regression, the comparison is based on the firstcolumn in Table 7 and 8.

31

Table 9: Different sample: visitation measured by a binary variable(1)
MSA

Visitation (Dummy)
6 month

(2)
(3)
(4)
Out of Missouri Not MSA Tech. violation(5)
FemaleβS.E.

-0.196***(0.053)-0.176***(0.049)-0.178**(0.076)-0.196***(0.053)-0.145**(0.062)βS.E.

-0.193***(0.064)-0.179***(0.054)-0.212***(0.081)-0.162***(0.061)-0.149*(0.089)βS.E.

-0.193**(0.078)-0.190***(0.070)-0.169**(0.068)-0.185***(0.072)0.048(0.142)βS.E.

-0.202**(0.080)YY
34,476-0.204***(0.076)YY
37,480-0.180**(0.075)
YY
23,702-0.206***(0.071)YY
41,641

0.234(0.162)YY
7,830

1 year

2 year

3 yearControls
Fixed effects
Observations

Standard errors in parentheses are clustered at county level. *** p<0.01, ** p<0.05, * p<0.1.
Notes: Each row uses different outcome variables. Each pair of coefficients and the standard errors isfrom a unique regression. The MSA column uses the baseline sample and the sample released to the
St. Louis MSA and Kansas City MSA. The St. Louis MSA includes Bond, Calhoun, Clinton, Jersey,
Macoupin, Madison, Monroe, and St. Clair counties in Illinois state. The Kansas City MSA includes
Johnson, Leavenworth, Linn, Miami, and Wyandotte counties in Kansas state. The ”Out of Missouri”
column uses all samples regardless of the location after release. The ”Not MSA” column excludes theprisoners from the St. Louis MSA and Kansas City MSA. The technical violation column uses actual
incarceration days in place of sentence length for all observations, since sentence length is not applicableto the technical violation served.

32

Table 10: Different sample: visitation measured by frequency per month
(1)
MSA

(2)
Out of Missouri(3)
Not MSA(4)
Tech. violation(5)
FemaleβS.E.

-0.082***(0.024)-0.077***(0.023)-0.073**(0.036)-0.083***(0.025)-0.110**(0.053)βS.E.

-0.081***(0.028)-0.078***(0.024)-0.087**(0.037)-0.069**(0.028)-0.113(0.070)β
S.E.

-0.081**(0.035)-0.083***(0.032)-0.069**(0.030)-0.078**(0.033)0.036(0.108)βS.E.

-0.084**(0.036)YY
34,476-0.089**(0.036)YY
37,480-0.074**(0.034)YY
23,702-0.087**(0.035)YY
41,641

0.176(0.128)YY
7,830

Visitation (Frequency)
6 month

1 year

2 year

3 yearControls
Fixed effects
Observations

Standard errors in parentheses are clustered at county level. *** p<0.01, ** p<0.05, * p<0.1.
Notes: Each row uses different outcome variables. Each pair of coefficients and the standard errors isfrom a unique regression. Frequency is defined as the total number of visits over incarcerated month.
The MSA column uses the baseline sample and the sample released to the St. Louis MSA and Kansas
City MSA. The St. Louis MSA includes Bond, Calhoun, Clinton, Jersey, Macoupin, Madison, Monroe,
and St. Clair counties in Illinois state. The Kansas City MSA includes Johnson, Leavenworth, Linn,
Miami, and Wyandotte counties in Kansas state. The ”Out of Missouri” column uses all samples regardless of the location after release. The ”Not MSA” column excludes the prisoners from the St. LouisMSA and Kansas City MSA. The technical violation column uses actual incarceration days in place ofsentence length for all observations, since sentence length is not applicable to the technical violation
served.

33different compared to other states. Visitation may be effective for the particular groupof prisoners with criminal ties and so the LATE estimators are much larger than theprevious studies.
The second difference is the outcome measures. Their papers use a recidivism
measure at three years from release. However, three years may be too long and noisy
to measure the effect of visitation. The main estimation results suggest that visitation
seems to have an effect at least within one year, but the standard errors increase overtime. Hence the outcome measure may be a key difference from the two papers.
The third difference is that they include both females and males for regression. This
paper focuses only on male prisoners, but they include females and males and control
the difference by a binary variable in the regression. However, since not many facilities
are for female prisoners, they would have a longer distance to their homes than maleprisoners. In this case, the distance correlates with a gender indicator variable andviolates the assumption as an instrumental variable.
The fourth difference is the reason for incarceration. The sample used for the analyses is either on parole or probation, but they account for 90% of released prisoners in
Missouri. Moreover, for those who are under supervision, a technical violation could
be a reason for reincarceration. Tables 9 and 10 shows the results including the cycles
for technical violations. It shows a similar negative effect of visitation at each point intime.
Lastly, although Cochran et al. (2020) and Lee (2019) use crime history in theirregression, this paper does not use criminal history information in the main results
due to data limitations. I check the sensitivity to crime history in Tables 7 and 8 using
two measures of crime history (a recidivist dummy, and the SF score).30 The resultswith a recidivist dummy show negative effects in the short run. However, although
the coefficients are negative, the long-run effects become insignificant. Similar results
are obtained when the SF score is included. Hence, the short-run effect is robust to the
30 Note that both are an imperfect measure of crime history. The recidivist dummy only captures therecidivists during the sample period, and the SF score is based on crime history as well as other factors
such as employment history.

34

inclusion of crime history measures.
To clarify the points discussed above, I replicate the results in the two papers using the Missouri data. Table 11 shows the replication results. Although I could not
replicate the same regression,31 both specifications show a negative but statisticallyinsignificant effect only. However, in the fourth column where the outcome variable isreincarceration within six months and the sample is male only, I confirm the significant
visitation effect, at least, for Lee (2019). 32
In summary, the visitation effect within a year is quite robust, but the effect becomes unclear as the time from release becomes longer. Hence, compared to Cochranet al. (2020) and Lee (2019), this paper reaches a similar conclusion about the causal
effect at three years from release. Although the causal effect may be from state-specificfactors, it is fair to say that visitation has a causal impact in the short run but it does
not have a persistent effect in the long run.

5.3

The effect on supervision outcome and employment

Although I provide evidence for the causal effect of visitation on reducing recidivism,
it is not clear how visitation affects recidivism (Cochran, 2019). To investigate thepotential channels, I examine the effects on other outcomes: specifically, supervision,and employment.
The first analysis is about if visitation helps offenders to complete supervision. In
the first column in Table 12, the outcome variable is supervision completion. Possiblesupervision outcomes are discharge, revocation, interstate, and death. Supervisioncompletion is defined as discharge over the entire sample excluding death or interstate supervision.33 Under the IV regression, a visited person has a 20.2% point higher
31 Some variables are not available in Missouri. The details of the difference are described in the notes

in Table 11.
32 Another difference is non-linearity of distance. The distance measure in Cochran et al. (2020) is a setof dummies representing each distance category while the measure in Lee (2019) contains a quadratic
term. However, from Figure 7, a linear form seems appropriate for the analysis of a binary visitation
measure. A quadratic form may be more suitable for frequency analysis. However, the replication
results in Table 11 show a statistically significant effect. In addition, the main regression results in Table
6 hold with the quadratic distance as an additional instrumental variable.
33 Although the sample consists of the prisoners released on supervision, it may not be the case when35

Table 11: Replication results
Lee (2019)
Visitation (Frequency)

Observations
Cochran et al. (2020)
Visitation (Dummy)

Observations
Outcome
Gender

(1)

(2)

(3)

(4)

-0.00510(0.0163)-0.00988(0.0185)-0.0226*(0.0120)-0.0290**(0.0138)

55,57945,95655,57945,956-0.0531(0.0402)-0.0691(0.0471)-0.0143(0.0296)-0.0156(0.0350)

55,579New Conv. 3yBoth45,956
New Conv. 3yMale55,579Any Ret. 6m
Both45,956
Any Ret. 6m
MaleStandard errors are in parentheses.
Notes: Each coefficient is from separate regression. The first column is based on the original specification in each paper: the sample contains both males and females and the dependent variable isreincarceration within 3 years by a new conviction. Instead, the fourth column uses male prisoners andthe dependent variable is reincarceration within 6 months for any reason.
For Lee (2019), both linear and quadratic distance measures are used as instruments. The control
variables are a gender dummy, the number of dependents, a recidivist dummy, category dummies (byage groups, racial groups, and crime types), crime rate at the county of conviction, and fixed effects(year, prison, and county). Since LSI-R and total crimes committed are not in the data, they are notcontrolled. Age is grouped by the deciles and racial groups are divided into four (non-Hispanic white,
non-Hispanic black, Hispanic, other). Quarter fixed effects are substituted by year fixed effects.
For Cochran et al. (2020), the distance is discretized every 50 miles and there are 7 distance groups intotal: from 0–50 miles to 300 or above. The control variables are a gender dummy, a recidivist dummy,
age at the admission date for the sentence, category dummies (by racial groups, and crime types),
sentence length, actual time served, and county by custody level fixed effects. Age is as of the admission
date. Prior prison conviction, misconduct, and prison commitment are not available in my dataset:
instead, the recidivist dummy is used. As crime type, sex offense is categorized into ”other” category.
Sentence length is the original sentence for those who served for technical violations. Time served andmonths remained are substituted by actual time served. In Missouri, most offenders are assigned todiagnostic centers for initial classification, so the number of visits was taken as the number of visits
over the entire period, not just the visits at the initial facility.

36

Table 12: Supervision and employment outcomes
VARIABLES(1)
Supervision completion

Visitation (Dummy)(2)(3)
Emp (ever) Emp (3 month)(4)
Emp (6 month)

Controls
Fixed effects
Observations

0.202***(0.0590)YY
33,3690.324***(0.0656)
YY
33,9710.164**(0.0787)YY
32,1830.164**(0.0824)
YY
28,944

VARIABLES(1)
Supervision completion(2)
Emp (ever)(3)
Emp (3 month)(4)
Emp (6 month)

0.0842***(0.0291)YY
33,3690.135***(0.0332)
YY
33,971

0.0693*(0.0370)YY
32,1830.0649*(0.0345)
YY
28,944

Visitation (Frequency)
Controls
Fixed effects
Observations

Standard errors in parentheses are clustered at county level. *** p<0.01, ** p<0.05, * p<0.1.
Notes: Frequency is defined as the total number of visits over incarcerated month. “Supervision completion” excludes those who died during supervision and who were assigned interstate supervision.
“Emp (ever)” is whether prisoners are employed since the release. “Emp (3 month)” and “Emp (6month)” are based on the employment status at 3 months and 6 months from release, conditional on
not incarcerated at the time.

chance of successful completion and one visit per month increases the completion rateby 8.4 percentage points. Hence, visitation plays a crucial role in the successful completion of supervision.
Second, I run a regression analysis using employment status as the outcome tosee if visitation changes post-release employment opportunities. Similar to the supervision completion, visitation has a positive effect on employment.34 It increases the
chance of being employed after release by 32.4 percentage points. I also use a measureof employment status at three months and six months from release. Excluding those
who are caught by the time, visitation increases the chance of being employed at both
points in time. Conditional on not being incarcerated, visited prisoners are 16.4 percentage points more likely to be working at three and six months from release. Hence,
the results support a positive effect of visitation on employment status.
the cycle is for parole revocation. Hence, only the cycles for the original sentence are used for the
regression.
34 See Appendix A for the definition of employment outcomes.

37

5.4

The effect on the housing situation

Finally, this section checks whether visitation has any effect on the housing situation.
One of the difficulties after release from prison is finding stable housing. Therefore,
I first check to see if visitation is effective in finding stable housing. In Table 13, thevisitation does not significantly increase movement when movement is measured bya dummy variable. However, this could be because the non-visited return to prison
faster than the visited. When the frequency is used as another measure of movement,
the coefficients are negative but are still insignificant.
Although visitation does not improve the number or frequency of relocations, it
may have encouraged released inmates to relocate to better neighborhoods. I define ameasure of neighborhood difference across movements based on comparing the median wage in the location before and after the first movement. The definition of the
upward movement is the movement to a neighborhood where the median wage ishigher than the previous location and vice versa. However, it is also possible that visited prisoners live in a good place as the first location. Hence, as the last measure of
movement, I compare the log of the median income of the first address.
Table 13 shows the results. Against the initial expectations, visitation changes theprobability of the upward movement. The downward movement might increase but
this is because the visited prisoners live in a relatively better neighborhood as their initial address after release. Hence, since it does not change the probability or frequency
of movements, visitation does not improve housing stability.
In Appendix C, I also check if these findings hold under the model by Cochranet al. (2020) and Lee (2019). The results show similar patterns and hence the effects on
employment and housing are not unique to the model employed in this paper.
In summary, visitation has a negative impact on recidivism and a positive impact
on labor market outcomes, but no effect is found on housing stability.

38

Table 13: Movement outcomes(1)(2)
Move (Dummy) Move (Dummy)

VARIABLES
Visitation (Dummy)

0.107(0.0675)

VARIABLES
Visitation (Dummy)-0.0183(0.0556)

Visitation (Frequency)
Controls
Fixed effects
Observations

0.0443*(0.0264)
YY
33,971

YY
33,971(1)(2)
Move up Move up

YY
32,624YY
33,867(3)(4)
Move down Move down
0.111**(0.0526)-0.00734(0.0221)YY
32,624(4)
Move (Freq.)-0.0246(0.0290)

Visitation (Frequency)
Controls
Fixed effects
Observations(3)
Move (Freq.)YY32,624(5)ln(income)-0.0103(0.0128)YY
33,867(6)ln(income)

0.137***(0.0277)0.0445*(0.0229)
YY
32,624YY
31,996

0.0548***(0.0124)YY
31,996

Standard errors in parentheses are clustered at county level. *** p<0.01, ** p<0.05, * p<0.1.
Notes: Movement frequency is defined as the total number of movements over the months under supervision. A total of 104 observations are dropped for the frequency regression since the supervision
end date is missing. “Move up” and “Move down” are based on the comparison of the median income
between the initial address and the second address at the zip code level. Non-movers are treated aszero. ln(income) is the log of the median income at the initial address at the zip code level. The sample
size difference is due to an invalid address or addresses without median income information.

39

0.50
0.40
0.30
0.20
0.10
0.00

Short distance & No visitation
Short distance & Visitation
Long distance & No visitation
Long distance & Visitation
0

200

400
600
Days from Release

800

1000

Notes: The sample is divided into four groups by the distance and visitation experience. The classification of the distance groups is based on the raw distance from the assigned prison to the county ofconviction.

Figure 9: Kaplan-Meier estimates for reincarceration

5.5

Duration analysis

The linear probability model focuses on the outcome at an arbitrary point in time fromthe release date. However, we are also interested in the duration until the reincarceration happens. Figure 9 shows the Kaplan-Meier plot of the cumulative probability ofreincarceration for four groups. The visited groups have a lower reincarceration rate
than the no visitation groups. In addition, prisoners assigned a distant prison tend tohave a higher reincarceration rate.
However, these differences may be due to other variables. Hence, for the formal
analysis, I also perform a duration analysis based on the Cox proportional hazard
model. As is the case in the linear probability model, it is necessary to control theendogeneity of visitation. Hence, the Cox model also uses the distance as an IV for
visitation. Since the Cox model is non-linear, the estimation is based on a control function approach. The method is based on two-stage residual inclusion (2SRI), introduced
by Terza et al. (2008), and details of the method are in Appendix D.1. Similar to theprevious sections, I perform the basic analysis to confirm the effects on recidivism,
employment, and housing situation, and the results are in Appendix D.2. Specifically,40

the outcome variables are the time to be incarcerated again, time to get the first job,
and time to change the address. The estimation results in Appendix D.2 are consistent
with the linear probability model: visitation reduces the hazard rate of recidivism,
increases the hazard rate of getting a job, and has no effect on movement.

6

Instrument validity

The instrumental variable approach employed in the analysis has provided insights
into the impact of visitation on recidivism, employment, and housing stability. However, it is crucial to assess the validity of using distance as an instrumental variable
and consider potential issues with the obtained results.
First, to check the instrument validity, I predict the recidivism outcomes using observable variables and then regress the predicted values on distance. The results show
that, for the recidivism rate one year after release, the predicted recidivism rate did notcorrelate with distance. However, I still find a correlation for results six months, twoyears, and three years after release. Although the correlation is not systematic, I cannot rule out the possibility that distance correlates with recidivism outcomes throughother pathways.
Next, it may be questionable whether the assignment process is truly random, since
the assignment may be based on something unobservable for researchers. Therefore,
I also check to see if the coefficients in the first-stage coefficient is sensitive to the inclusion of the recidivist dummy and SF score. A recidivist dummy is included since
the MDOC can observe the criminal record of prisoners. Also, the SF score is included
since it is a summary measure of crime history and other characteristics that are unobservable for researchers. By adding the two variables, the first stage coefficient on
visitation frequency changes from -0.178 (Table 4) to -0.176. The stability of the firststage estimator supports the validity of the instrument.
This paper does not separate the effect of transfer since the distance at the first facility is used for the analysis. However, a transfer would change the visitation experience41

by changing the distance from home. In Table 22, I run the main regression separatelyby transfer experience to check if there is any difference by transfer experience. The
results show that the crime-reducing effect is larger for those who experience transfer,
although the short-run effects are confirmed in both samples. Since prisoners must
behave well in prison to experience transfers, the difference is partially due to theselection caused by factors such as strong social bonds at the time of incarceration.
Transfer experience may correlate with other variables. For example, in the data,prisoners incarcerated in more distant prisons are more likely to experience transfers,
which is unsurprising since the Department of Corrections intentionally transfers prisoners to facilities closer to their homes. However, transfer experience does not correlate with the probability of returning home after release, so the transfer is unlikely
affect the post-release outcome directly.
Additionally, in the exclusion restrictions, I could not examine the impact of peer
connections in this paper due to data limitations. If offenders are incarcerated in neighboring prisons, it is likely that acquaintances are incarcerated in the same prison. In
such cases, the distance may correlate with peer connections, which influence recidivism. If such peer connection effects are large, then the assumption of the exclusion
restrictions may not have been met and the estimator may be biased. However, thedirection of the bias is unclear since, depending on the peer type, the connection could
be both beneficial and detrimental for recidivism.

7

Counterfactual analysis

The main results confirm that visitation reduces reincarceration. This section considers
two counterfactual policies. One is a policy that every prisoner is assigned to theclosest prison from home. Another is the location of a new prison that minimizes therecidivism rate.
In the main sample, prisoners are assigned 114.3 miles away from their home, on
average. If everyone were assigned to the closest prison conditional on the initial42

custody level, it would be 43.1 miles.35 The reduction by 71.2 miles increases the meantime to reincarceration by 48.8 days.36 37 38
In the fiscal year of 2016, 12,874 male offenders were released on supervision. According to the 2016 annual report by the Missouri Board of Probation and Parole, thedaily cost of incarceration is 57.25 dollars. A total of 16.67 out of the 57.25 dollars are
the direct cost of incarceration, which includes health care, wage, discharge costs, foodcosts, and operational expenses and equipment. The rest of the total cost is the costto keep the institution such as labor and maintenance costs. Hence, 48.8 days longer
time to be incarcerated would decrease the direct cost per inmate by 813 dollars.39
Given the assignment policy, we can identify where is the best location for a new
prison to minimize recidivism. Given the distribution of prisoners in the sample, St.
Louis County is the county for a prison location that minimizes the weighted distance to prison with the minimum security level. Although St. Louis County is not
far from prison with the minimum security, a high population of prisoners from theneighborhood makes St. Louis County the best location. However, for the mediumand maximum-security levels, the best location is Greene County, where Springfield
is located, since the southwest area in Missouri is far from prison with higher security
levels and a new prison in the area reduces the weighted distance.
35 The calculation does not consider the capacity constraint of each facility.
36 To estimate the mean time, we need to fix the baseline hazard. Here, the Weibull model is assumed,

and the number is from the estimated model.
37 The linear model is used in the main results. The LATE derived from the IV regression tells that therecidivism rate at six months from the release decreases by 1 percentage points under the policy. Alternatively, we can estimate the policy-relevant treatment effect (PRTE) based on the marginal treatment
effect (MTE) (Heckman and Vytlacil, 2005; Andresen, 2018). The PRTE estimator of the visitation effectis −19.5% points, and a reduction by 71.2 miles increases the propensity score by 5.3 percentage points.
Hence, the recidivism rate, for example, at six months from release decreases by 1% points.
38 Weber (2020) reaches an opposite conclusion. She has found that the unexpectedly longer distanceto the assigned prison has an overall negative impact on recidivism. Admitting the importance ofsocial ties, she interprets the results as the impact from the deteriorated criminal ties dominates theimpact from social ties. This different conclusion might be due to the state difference since she uses theassignment data from Florida and Oklahoma in the first stage regression.
39 By an additional assumption that the cost saving is uniform for all prisoners, the annual direct costof incarceration decreases by about 10 million dollars. Similarly, the total daily cost of incarceration
would decrease by about 36 million dollars.

43

8

Conclusion

This paper investigates the effect of the visitation on post-release outcomes and thechannels of the effect. The results show that visitation has a large negative effect onrecidivism. The results also confirm that visitation improves employment outcomes.
However, visitation does not change the probability nor frequency of movement, andhence it has no impact on housing stability. Note that this study uses distance-induced
visitation to identify the visitation effects. Visitation differences induced by other factors may show different impacts on recidivism and other outcomes.
This paper has two limitations. Although this paper focuses on in-person visitation, most prisons provide other opportunities to communicate with the outside. Somestates have recently started to permit video visitation instead of in-person visitation,and video visitation is replacing actual visitation because of lower costs (Rabuy and
Wagner, 2015). Besides, phone calls and letters could also be substitutes for prison
visitation. This paper could not compare other communication tools, but they could
be a more cost-effective approach to reduce recidivism.
Another limitation is that since this paper focuses on the prisoner’s side, the visitors’ decisions are ignored. For example, new public transportation for better access tothe prisons might change the effect of distance on visitation decisions. However, thereaction for the new transportation will be different by wealth status. For example,
some people may have a car and others not. Moreover, high-income earners may facea higher opportunity cost of visitation. Since visitation is the endogenous choice ofvisitors, it would help better policy design to know the decisions of visitors. Hence,
further analysis of the visitation decision from a visitor’s side is necessary for the better visitation policy design.
Lastly, although visitation is mostly associated with a lower recidivism rate, Bedardand Helland (2004) pointed out another possibility that encouraging visitation could
be harmful to the overall crime rate. They investigate the effect of distance to thenearest prison on the female crime rate of counties and find that an increase in the
distance caused by prison closure decreases the local crime rate. They claim that this is
44

likely because the expectation of lower visitation works as an emotional cost of crimeand decreases the crime rate. Although Bedard and Helland (2004) focused on theeffect of visitation on recidivism, we have to consider the side effects of visitation
policy for evaluation.

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50

AppendicesA

Variables

The list of control variables is summarized in Table 14.
Table 14: Control variables
Variable nameAge at release
Sentence length (year)
Dependents
Race and Ethnicity
CountyPrisonTime
Crime type
Felony classInitial custody level

Type
Numeric
Numeric integer
Numeric
Categorical
Categorical
Categorical
Categorical
Categorical
Categorical
Categorical

Category

White (NH), Black (NH), Other
114 counties and St. Louis City
19 correctional facilities
Quarterly (2012q1–2015q4)
Property, Violent, Drug, Other
A, B, C, D
Minimum, Medium, High

Notes: Each category in the categorical variables is put in the regression as a binary variable and the firstcategory is used as the base. White and Black are non-Hispanic (NH), and Hispanic is in the ”Other”
category.

Employment records in the dataset has both the start and end dates for each job.
A prisoner could have multiple jobs on the same day: for example, multiple part-timejobs. The definition of employment at a particular date (3 months and 6 months) is
whether a prisoner has at least one job on that date. Employment (ever) takes one if aprisoner has been employed since release.
For some prisoners, the start date on the record is before the release date. Oneof the reasons is that having a job is sometimes a condition of parole. Since visitation
might be helpful in finding a job before release, the analysis uses these samples as well.
Moreover, it is worth noting that, I found a similar effect on employment outcomeseven without those sample.

51

B

Heterogenous effects

So far, the visitation effect is treated as uniform across individual characteristics, butthere may be the heterogeneity of the effect. This section investigates the heterogeneity of the visitation effect by racial groups, crime types, and age groups. To check theheterogenous effects, I run the IV regression using the interaction terms. The instrumental variables are the distance measures interacted with each group dummy. Thenthe second-stage regression uses the predicted visitation measures for each group.
Table 15 and 16 show the results for different racial groups (Non-Hispanic white,
Non-Hispanic black, and Other). The estimated impact for non-Hispanic whites isnegative and persistent. Since the majority of the sample consists of non-Hispanic
whites, the baseline results are similar to the white group. However, the effects aredifferent for other two groups. Although the short-run effect is confirmed, the effectfor non-Hispanic blacks disappears over time. The coefficients for the other racial
group show larger impacts compared to the non-Hispanic white. Hence, the visitation
effect may be less important for non-Hispanic blacks and more important for otherracial groups.
Next, Table 17 and 18 confirm the heterogeneity by the primary offense type. Regardless of offense type, the visitation effect is significant in the short run. However,
the effect for drug crime offenders becomes statistically insignificant after one year.
Moreover, the long-run effect for property-crime offenders is persistent with the binary
measure of visitation but the effect disappears with the frequency measure. Hence, thevisitation appears to be more effective against offenders of violent and other crimes.
Lastly, Table 19 and 20 check the heterogeneity by three age groups since the importance of social ties may vary by age. For the age groups below 40, the negative effectis confirmed in the short run but not obvious in the long run. However, the other twogroups have negative effects up to 3 years from release. These results suggest that
visitation experience is more effective for decreasing criminal behavior after youth.
The heterogeneity analyses show additional implications of the main results. The
estimated results show that the visitation effect may vary by racial and age groups and52

Table 15: Heterogeneity by race: visitation measured by dummy(1)
6 month(2)
1 year(3)
2 year(4)
3 yearvisitation × Non-Hispanic White -0.188***(0.0530)
visitation × Non-Hispanic Black -0.217***(0.0809)
visitation × Other-0.239***(0.0926)
Non-Hispanic Black-0.0148(0.0284)
Other-0.0116(0.0342)-0.181***(0.0686)-0.135*(0.0769)-0.274***(0.0920)-0.0690**(0.0337)-0.0294(0.0384)-0.183**(0.0775)-0.108(0.119)-0.289**(0.116)-0.0954***(0.0348)-0.0685*(0.0379)-0.199**(0.0776)-0.0437(0.124)-0.321**(0.137)-0.138***(0.0360)-0.0589(0.0415)

Observations

33,971

33,971

33,971

Recidivism

33,971

Standard errors in parentheses are clustered at county level. *** p<0.01, ** p<0.05, * p<0.1.
Notes: Each column uses a different dependent variable. The regressions use the same control variables
and fixed effects (prison, county, time). The italicized variables (the visitation measure interacted withgroup dummies) are instrumented by the distance measure interacted with group dummies.

crime types.

53

Table 16: Heterogeneity by race: visitation measured by frequency per month
Recidivism(1)
6 monthvisitation × Non-Hispanic White -0.0733***(0.0230)
visitation × Non-Hispanic Black-0.108**(0.0511)
visitation × Other-0.144**(0.0667)
Non-Hispanic Black-0.00470(0.0145)
Other-0.00190(0.0251)
Observations

33,971(2)
1 year(3)
2 year(4)
3 year

-0.0734**(0.0303)-0.0618(0.0420)-0.181***(0.0682)-0.0440***(0.0162)-0.0244(0.0298)-0.0752**(0.0322)-0.0458(0.0637)-0.195**(0.0828)-0.0642***(0.0222)-0.0646**(0.0311)-0.0845**(0.0331)-0.00784(0.0726)-0.225**(0.100)-0.0893***(0.0247)-0.0539(0.0333)

33,971

33,971

33,971

Standard errors in parentheses are clustered at county level. *** p<0.01, ** p<0.05, * p<0.1.
Notes: Each column uses a different dependent variable. The regressions use the same control variables
and fixed effects (prison, county, time). The italicized variables (the visitation measure interacted withgroup dummies) are instrumented by the distance measure interacted with group dummies.

54

Table 17: Heterogeneity by crime type: visitation measured by dummy
Recidivism(1)
6 month(2)
1 yearvisitation × Property Crime -0.161***(0.0543)
visitation × Violent Crime-0.209***(0.0746)
visitation × Drug Crime-0.215***(0.0686)
visitation × Other Crime-0.213***(0.0672)
Violent Crime
0.0200(0.0351)
Drug Crime-0.00260(0.0264)
Other Crime
0.0149(0.0214)-0.140**(0.0679)-0.223**(0.0894)-0.123(0.0774)-0.314***(0.0755)-0.000353(0.0445)-0.0454(0.0319)0.0416(0.0377)

Observations

33,971

33,971(3)
2 year(4)
3 year

-0.182**-0.198**(0.0854)(0.101)-0.202**-0.231**(0.103)(0.0960)-0.0541-0.0399(0.0943)(0.0909)-0.362*** -0.387***(0.0853)(0.0890)-0.0521-0.0501(0.0443)(0.0418)-0.0968*** -0.112***(0.0349)(0.0385)0.02520.0204(0.0349)(0.0395)
33,971

33,971

Standard errors in parentheses are clustered at county level. *** p<0.01, ** p<0.05, * p<0.1.
Notes: Each column uses a different dependent variable. The regressions use the same control variables
and fixed effects (prison, county, time). The italicized variables (the visitation measure interacted withgroup dummies) are instrumented by the distance measure interacted with group dummies.

55

Table 18: Heterogeneity by crime type: visitation measured by frequency per month
Recidivism(1)
6 month(2)
1 year(3)
2 year(4)
3 yearvisitation × Property Crime -0.0628*** -0.0491-0.0702*-0.0770(0.0243)(0.0327)(0.0384)(0.0470)
visitation × Violent Crime-0.0785** -0.0847**-0.0729-0.0859**(0.0314)(0.0383)(0.0445)(0.0422)
visitation × Drug Crime-0.0995**-0.0437-0.00117
0.00913(0.0416)(0.0419)(0.0483)(0.0471)
visitation × Other Crime-0.0867*** -0.135*** -0.158*** -0.169***(0.0289)(0.0334)(0.0399)(0.0420)
Violent Crime-0.00787-0.0366 -0.0706*** -0.0736***(0.0172)(0.0227)(0.0223)(0.0211)
Drug Crime-0.00840 -0.0376** -0.0644*** -0.0724***(0.0144)(0.0189)(0.0198)(0.0207)
Other Crime-0.00220 -0.00667-0.0249-0.0323*(0.00977) (0.0193)(0.0183)(0.0187)
Observations

33,971

33,971

33,971

33,971

Standard errors in parentheses are clustered at county level. *** p<0.01, ** p<0.05, * p<0.1.
Notes: Each column uses a different dependent variable. The regressions use the same control variables
and fixed effects (prison, county, time). The italicized variables (the visitation measure interacted withgroup dummies) are instrumented by the distance measure interacted with group dummies.

56

Table 19: Heterogeneity by age: visitation measured by dummy(1)
6 month(2)
1 year(3)
2 year(4)
3 yearvisitation × age (20–30) -0.193***(0.0736)
visitation × age (30–40) -0.203***(0.0547)
visitation × age (40–65) -0.191***(0.0520)age (30–40)-0.00520(0.0262)age (40–65)-0.0279(0.0259)-0.170*(0.0915)-0.218***(0.0686)-0.166**(0.0689)0.0185(0.0444)-0.0272(0.0387)-0.137(0.107)-0.163**(0.0749)-0.273***(0.0955)
0.0306(0.0386)
0.0678(0.0445)-0.167(0.110)-0.186**(0.0753)-0.250**(0.0972)
0.0380(0.0406)
0.0574(0.0458)

Observations

33,971

33,971

33,971

Recidivism

33,971

Standard errors in parentheses are clustered at county level. *** p<0.01, ** p<0.05, * p<0.1.
Notes: Each column uses a different dependent variable. The regressions use the same control variables
and fixed effects (prison, county, time). The italicized variables (the visitation measure interacted withgroup dummies) are instrumented by the distance measure interacted with group dummies.

Table 20: Heterogeneity by age: visitation measured by frequency per month
Recidivism(1)
6 monthvisitation × age (20–30)-0.0701**(0.0313)
visitation × age (30–40) -0.0834***(0.0236)
visitation × age (40–65) -0.0949***(0.0276)age(30–40)-0.00463(0.0119)age (40–65)-0.0135(0.0166)
Observations

33,971(2)
1 year(3)
2 year(4)
3 year

-0.0609(0.0389)-0.0928***(0.0295)-0.0810**(0.0365)
0.00906(0.0206)-0.0138(0.0236)-0.0432(0.0452)-0.0629**(0.0318)-0.148***(0.0500)
0.0265(0.0182)
0.0487*(0.0282)-0.0567(0.0474)-0.0738**(0.0316)-0.131**(0.0538)
0.0361*(0.0201)
0.0519*(0.0290)

33,971

33,971

33,971

Standard errors in parentheses are clustered at county level. *** p<0.01, ** p<0.05, * p<0.1.
Notes: Each column uses a different dependent variable. The regressions use the same control variables
and fixed effects (prison, county, time). The italicized variables (the visitation measure interacted withgroup dummies) are instrumented by the distance measure interacted with group dummies.

57

C

Supplementary tables
Table 21: Employment and housing outcomes
(1)

(2)

(3)

Emp (ever) Emp (3 month) Emp (6 month)

(4)

(5)

Move (Dummy)Move (Freq.)

Lee (2019)
Visitation (Frequency)

0.0893***0.0461**

0.0425**0.0395*0.00536(0.0210)(0.0189)(0.0202)(0.0228)(0.0301)

45,956

41,73837,04445,95645,7570.111**

0.0894*0.04280.08470.0859(0.0530)(0.0465)(0.0528)(0.0576)(0.0760)

Observations

45,956

41,73837,04445,95645,757

Gender

Male

Male

Male

Male

Male

Observations

Cochran et al. (2020)
Visitation (Dummy)Standard errors in parentheses are clustered at county level. *** p<0.01, ** p<0.05, * p<0.1.
Notes: See Table 11 for model specifications.

58

Table 22: By transfer experience
(1)

(2)

(3)

(4)

Transfer experience

N

Y

N

Y

Visitation (Dummy)-0.142**-0.248***(0.0610)(0.0812)-0.0600**-0.0992***(0.0270)(0.0313)

Visitation (Frequency)

Controls

Y

Y

Y

Y

Fixed effects

Y

Y

Y

Y

Observations

21,00912,96221,00912,962Standard errors in parentheses are clustered at county level. *** p<0.01, ** p<0.05, * p<0.1.
Notes: The outcome variable is the recidivism outcome at 6 month from release. Since a typical prisoner
is assigned to a prison for initial classification, transfer experience is defined by more than one transfer.

59

D

Duration analysis

D.1

MethodI run a regression on the time by reincarceration, getting first job, and the first movement. The estimation is based on the Cox proportional hazard model using the same
IV. The Cox proportional hazard model is defined by the following hazard function:h(t|Vi , Xi , Ui ) = λ0 (t)exp( β V Vi + β X Xi + βU Ui )(2)

where t, V, X, and U are time, treatment (visitation), observable characteristics, andunobservable characteristics. Our coefficient of interest is β V . However, since we do
not observe U, we cannot run the regression directly. It seems natural to use 2SLS,
but the 2SLS estimator is not consistent under non-linear models. To estimate β V consistently under non-linear setting, this paper uses a control function approach: thetwo stage residual inclusion (2SRI) proposed by Terza et al. (2008). The first step is toestimate Vi using the distance as an instrument Zi .

Vi = α X Xi + α Z Zi + ei

(3)

From the results, we obtain the residual as Ûi = Vi − V̂i . The second stage is to estimate
the hazard function using the residual.

h(t|Vi , Xi , Ui ) = λ0 (t)exp( β V Vi + β X Xi + βU Ûi )(4)The equation gives a consistent estimator of β V .

D.2

Results

The results are in Table 23. The numbers in the table show the ratio of the hazard
rates of recidivism. Visitation decreases the hazard rate of reincarceration. When the
instrumental variable is used, the estimator shows a larger effect on the hazard rate.
60

Table 23: Duration analysis (recidivism)
Recidivism
Visitation (Dummy)

(1)
Cox

(2)
2SRI

0.826***(0.0214)0.520**(0.143)

Visitation (Frequency)
Residuals

Controls
Fixed effects
ObservationsYY
33,971

(3)
Cox

(4)
2SRI

1.591*(0.427)0.899*** 0.775**(0.0112) (0.0897)
1.163(0.133)YY
33,971

YY
33,971

YY
33,971

Standard errors in parentheses are clustered at county level. *** p<0.01, ** p<0.05,* p<0.1.
Notes: The estimated hazard ratios are in the table.

The estimator implies that the hazard rate of recidivism is 48 percentage points less for
those who are visited. As for employment outcomes in Table 24, visitation increases
the hazard rate of having the first job. Without an instrument, the effect is positive
but the magnitude is amplified when the IV is used. Both a visitation dummy andvisitation frequency show significantly positive effects. The visited have 144% higher
the hazard rate of getting the first job. Hence, visitation makes released prisoners geta job faster in expectation.
The Cox regression in Table 25 shows a negative effect of the days until the firstmovement for both a visitation dummy and visitation frequency. However, once theomitted variable bias is controlled by an instrumental variable approach, visitation
does not have a significant effect on the time to first move.
In summary, both linear probability models and duration analysis show similareffects of visitation post-release outcomes. Visitation improves recidivism and employment outcomes but does not improve the housing situation. The robustness ofthe main results and the duration analysis are in the appendix section.

61

Table 24: Duration analysis (first job)
First Job
Visitation (Dummy)

(1)
Cox

(2)
2SRI

1.341***(0.0250)

2.438***(0.462)Visitation (Frequency)
Residuals

(3)
Cox

(4)
2SRI

1.102***(0.0102)1.427***(0.118)0.770***(0.0651)

YY
32,905YY
32,9050.548***(0.103)Controls
Fixed effects
Observations

YY
32,905YY
32,905

Standard errors in parentheses are clustered at county level. *** p<0.01, ** p<0.05,* p<0.1.
Notes: The estimated hazard ratios are in the table.

Table 25: Duration analysis (first move)First Move
Visitation (Dummy)

(1)
Cox

(2)
2SRI

(4)
2SRI

0.901***(0.00920)

0.997(0.118)0.902(0.110)YY
31,988YY
31,9880.835*** 0.960(0.0158) (0.256)

Visitation (Frequency)
Residuals

Controls
Fixed effects
Observations

(3)
Cox

0.869
(0.237)YY
31,988YY
31,988

Standard errors in parentheses are clustered at county level. *** p<0.01, ** p<0.05, * p<0.1.
Notes: The estimated hazard ratios are in the table.

62