The Effects of Male Incarceration Dynamics on AIDS Infection Rates among
African-American Women and Men
Rucker C. Johnson
Goldman School of Public Policy
University of California, Berkeley
Tel: (510) 643-0169
E-mail: ruckerj@berkeley.edu

Steven Raphael
Goldman School of Public Policy
University of California, Berkeley
Tel: (510) 643-0536
E-mail: stevenraphael@berkeley.edu

July 2005

We are grateful to Shawn Bushway, William Dow, John Ellwood, Theodore Hammett, and
Eugene Smolensky for their valuable input. We also wish to thank Harry Holzer, Steven Levitt,
and Kevin Reitz for sharing their data on state prison sentencing reform and prison overcrowding
litigation; Peter Bacchetti for sharing data on the AIDS incubation period distribution; and
Matthew McKenna of the CDC for providing useful information about the data collection
process of AIDS cases. We thank the Russell Sage Foundation for their financial support of this
project.

The Effects of Male Incarceration Dynamics on AIDS Infection Rates
among African-American Women and Men

Abstract
In this paper, we investigate the potential connection between incarceration dynamics and AIDS
infection rates, with a particular emphasis on the black-white AIDS rate disparity. Using caselevel data from the U.S. Centers for Disease Control and Prevention, we construct a panel data
set of AIDS infection rates covering the period 1982 to 2001 that vary by year of onset, mode of
transmission, state of residence, age, gender, and race/ethnicity. Using data from the U.S.
Census, we construct a conforming panel of male and female incarceration rates. We use this
panel data to model the dynamic relationship between the male and female AIDS infection rates
and the proportion of men in the age/state/race-matched cohort that are incarcerated. We find
very strong effects of male incarceration rates on both male and female AIDS infection rates.
The dynamic structure of this relationship—i.e., the lagged effects of the proportion of
incarcerated males—parallels the distribution of the incubation time between HIV infection and
the onset of full-blown AIDS documented in the medical and epidemiological literature. These
results are robust to explicit controls for (race-specific) year fixed effects and a fully interacted
set of age/race/state fixed effects. Our results reveal that the higher incarceration rates among
black males over this period explain a substantial share of the racial disparity in AIDS infection
between black women and women of other racial and ethnic groups. In a separate analysis, we
estimate a two-stage-least-squares (TSLS) model of AIDS infection rates employing a set of
variables describing intra-state changes in sentencing regimes as instruments for variation in
incarceration rates. We find TSLS effects of incarceration rates on AIDS infection rates that are
significant and comparable in magnitude to the corresponding OLS estimates.

1

I. Introduction
Coincident with the large increase in black male incarceration rates is a pronounced
increase in the AIDS infection rate among African-American women and men. Between 1970
and 2000, the proportion of black men incarcerated on any given day increased from 0.03 to
0.08, with a much larger increase in the proportion that has ever been to prison. There is no
comparable increase among non-Hispanic white men. Concurrently, the HIV/AIDS infection
rate among African-American women went from zero during the pre-epidemic period to an
annual rate of 55 per 100,000 between 2000 and 2003 (an infection rate nearly nineteen times
higher than that for non-Hispanic white women). For African-American men, this rate exceeds
100 per 100,000 (in contrast to less than 15 per 100,000 among non-Hispanic white men).
Moreover, African-Americans accounted for half of the AIDS cases reported in 2002, despite
accounting for only 12 percent of the overall population. The sources of racial differences in
HIV/AIDS infection rates are not well understood.
In this paper, we investigate the potential connection between incarceration dynamics and
AIDS infection rates. Our analysis considers the role of the relatively high levels of black male
incarceration as a potential explanation for the black-white AIDS rate disparity. This research
represents the first systematic analysis of the relationship between incarceration and AIDS
infection rates using nationally representative population data from the U.S.. Has the trend of
increased incarceration, most pronounced among African-Americans, produced the deleterious
effects of accelerated AIDS infection rates among affected communities? Our task is to sort out
how much, if any, of the observed correlations in these aggregate trends represent causal
relationships of incarceration on subsequent AIDS infection rate trajectories.
An increase in male incarceration rates may affect HIV/AIDS infection rates among
inmates and members of the community at large through several channels. First, the relatively
high concentration of HIV-positive people in prison (Hammett et. al. 2002) coupled with risky

behavior among inmates (Krebs 2002, Swartz et. al. 2004) may accelerate the transmission rate
of the disease among the incarcerated and among non-incarcerated members of the sexual
networks of former inmates. Second, the temporal dynamics of incarceration, characterized by
brief incarceration spells and the cycling in and out of institutions, may increase the degree of
concurrent sexual relationships (sexual relationships that overlap in time) among inmates and
their non-institutionalized partners (Adimora and Schoenbach 2005). This is a factor known to
augment the risk of contracting and spreading sexually transmitted diseases. In addition, spells
of incarceration may hasten the dissolution of sexual relationships, enlarging the total lifetime
number of sex partners among inmates and their partners.
An increase in incarceration rates may be viewed as an exogenous shock to an affected
individual or group’s sexual-relationship market (in much the same way economists traditionally
conceive of marriage markets (Becker 1981)). In particular, male incarceration lowers the sex
ratio (male-to-female), abruptly disrupts the continuity of heterosexual relationships, and
increases exposure to homosexual activity for incarcerated males—all of which may have farreaching implications for an individual or group’s AIDS infection risk. Given the relatively high
rate of incarceration among black men, all these avenues of HIV/AIDS transmission are likely to
have disproportionate effects on the AIDS infection rates of black women and men.
An alternative explanation for an apparent relationship between a community’s AIDS
prevalence and the proportion that has ever served time in prison is that it is spurious and stems
from rates of participation in risky behaviors that affect both AIDS and incarceration rates, such
as drug use. We attempt to distinguish between these competing explanations, which is the
principle challenge of the empirical work.
Our empirical strategy exploits the fact that the overwhelming majority of sexual
relationships as well as marriages occur between women and men in relationship markets
defined by the interaction of race, age, and state of residence (Charles and Luoh 2005, Laumann
2

et. al. 1994). We exploit this stratification of sexual relationships and the tremendous variation
in the incarceration trends over the past two decades within these groups, to identify the effect of
incarceration on AIDS infection rates. Accordingly, we define sexual relationship markets by
age/state/race groupings, since sexually-transmitted AIDS infection is the hypothesized chief
mechanism linking incarceration and AIDS.
Using case-level data from the U.S. Centers for Disease Control and Prevention, we
construct a panel data set of AIDS infection rates covering the period 1982 to 2001. Our
tabulated infection rates vary by year of onset, mode of transmission, state of residence, age,
gender, and race/ethnicity. Using data from the U.S. Census, we construct a conforming panel of
male and female incarceration rates. We use this panel data to model the dynamic relationship
between the male and female AIDS infection rates and the proportion of men in the
age/state/race-matched cohort that are incarcerated. The impact of incarceration is identified
from variation within sexual relationship markets over time. We estimate 13-year (constrained)
distributed lag models separately by gender and mode of transmission to gain greater
understanding of the underlying pathways through which incarceration dynamics may affect
HIV/AIDS infection rates.
To preview the results, we find very strong effects of male incarceration rates on both
male and female AIDS infection rates. The dynamic structure of this relationship—i.e., the
lagged effects of the proportion of incarcerated males—parallels the distribution of the
incubation time between HIV infection and the onset of full-blown AIDS documented in the
medical and epidemiological literature. These results are robust to explicit controls for (racespecific) year fixed effects and a fully interacted set of age/race/state fixed effects. Our results
reveal that the higher incarceration rates among black males over this period explain a large
share of the racial disparity in AIDS infection between black women and women of other racial
and ethnic groups. During the decade of the 1990s, the largest component of the growth in the
3

racial disparity in female AIDS infection rates resulted from infection occurring through
heterosexual sex (as opposed to intravenous drug use), while homosexually-contracted AIDS
was a growing component of the black-white AIDS gap among men. These results taken
together suggest that high black male incarceration rates is a principal explanation for the
relatively high rate of infection among black women. The strong link between incarceration and
AIDS is further evidenced in our findings that the black-white gap in homosexually-contracted
AIDS infection rates among males can be fully accounted for by black’s higher incarceration
rates.
In a separate analysis, we assess whether the effect of incarceration on AIDS infection
rates are causal by re-estimating a modified model specification using instrumental variables.
Specifically, we estimate a two-stage-least-squares (TSLS) model employing a set of variables
describing intra-state changes in sentencing regimes as instruments for variation in incarceration
rates. We find TSLS effects of incarceration rates on AIDS infection rates that are significant
and comparable in magnitude to the corresponding OLS estimates.
The remainder of the paper is organized as follows. Section II provides a brief overview
of the conceptual framework of plausible mechanisms linking incarceration and AIDS infection
rates. This section also provides a literature review of the state of knowledge on HIV
transmission risk (and AIDS prevalence) in and out of prison, related characteristics and
behaviors of individuals who serve time in prison, and a brief discussion of factors that affect the
spread of the AIDS epidemic in a community more generally.
identification strategy and econometric model.

Section III lays out our

Section IV describes the data sources and

provides descriptive analysis. Sections V and VI present the results from the dynamic regression
models and the instrumental variables approach, respectively.

Section VII concludes with

discussion of the implications of the results for public health and criminal justice policy.

4

II. Incarceration and HIV/AIDS Transmission Among Inmates and the Community
Our paper builds upon and extends two strands of literature. The first is the analysis of
previously unexplored dimensions of the intended and unintended consequences of incarceration
policy. The second contributes to our understanding of the sources of racial/ethnic differences in
HIV/AIDS infection rates and the divergent patterns that have emerged over the past two
decades. At the nexus of these two literatures, this paper explores the connection between AIDS
and the number of men relative to women in the sexual-relationship market and, of these men,
the proportion who have ever served time in prison or who are at high risk of imprisonment in
the future.
The general epidemiological assumption that behavior is exogenous to environment can
lead to erroneous conclusions about the cause of disease patterns, and consequently, to
misguided public health policy decisions. This was emphasized as a cautionary note in Kremer’s
(1996) work on AIDS. For example, an economic model of the spread of infectious diseases
hypothesizes that individuals will alter their demand for risky activities as risk increases, holding
all else constant (Philipson and Posner 1993). Ahituv, Hotz, and Philipson’s (1996) results
suggest there has been an increase in the demand for safer sex, such as the use of condoms, in
response to the increase in the prevalence of AIDS. They find that while there was no difference
in condom demand among U.S. census regions in 1984 (before AIDS cases were very prevalent),
the incidence of condom usage became geographically heterogeneous as the AIDS epidemic
progressed, with higher rates of utilization in states with higher AIDS prevalence rates, and more
rapid growth in condom utilization among black men, single men, those in urban areas, and those
who are more sexually active. Based on their estimates, they conclude that more than half of the
rise in condom use among young adults that occurred during the second half of the 1980s can be
explained solely by the increases in local prevalence of AIDS cases that occurred during this
decade. However, it must be borne in mind that the imperfect information of transmission risk
5

possessed by an individual, due to delays in onset and awareness of HIV prevalence, is likely to
significantly limit the efficacy of this behavioral response in slowing the speed of the AIDS
epidemic in a community.
How, then, would a large exogenous increase in incarceration rates affect the rate at
which HIV/AIDS propagates through a given population? Perhaps the most mechanical effect
may occur through the incapacitation of a group of individuals who are likely to engage in risky
behaviors while not incarcerated. To the extent that prisons remove from society individuals
whose behavior accelerate the spread of infectious diseases, an increase in incarceration may
actually reduce the overall incidence of HIV/AIDS. Even if offenders are eventually returned to
society, their time in prison reduces the total exposure of the non-incarcerated public to high-risk
individuals, holding all else constant.
However, there are likely to be countervailing effects of incarceration that may accelerate
the spread of HIV/AIDS. For example, the concentration of high-risk individuals behind bars
coupled with the behavioral responses (sexual and otherwise) to being incarcerated may elevate
the rate at which inmates transmit the disease to each other. Thus, while reducing the aggregate
exposure time of the non-incarcerated to the incarcerated, imprisonment may raise the AIDS
incidence among those who are currently serving or have served time. Furthermore, as most
inmates are returned to society after a relatively short prison spell, an accelerated transmission
rate among inmates may spillover to the non-institutionalized population post-release.
A less obvious transmission mechanism may occur through the effect of incarceration
on the process by which sexual partners match with another.

Given that inmates are

overwhelmingly male and minority, a disproportionately large increase in incarceration among
minority men differentially reduces the ratio of minority men to minority women. This relative
scarcity of minority men improves the bargaining position of non-institutionalized minority men
in negotiating personal relationships. The relative shortage of men may translate into men
6

having to display less commitment or loyalty in seeking sexual relations, a factor that is likely to
increase the average lifetime number of partners among both sexes and perhaps even the
incidence of concurrent sexual relationships (both known risk factors for the spread of sexually
transmitted diseases). Moreover, independently of these effects, the disruptive effects of men
cycling in and out of institutions may further increase the risk of HIV transmission through the
disruption of existing heterosexual relationships (and by extension, the creation of new
relationships) and the increase in the average lifetime number of sex partners.
The net effect of an increase in incarceration rates on AIDS transmission is thus
theoretically ambiguous.1 While this net effect is essentially the main empirical question that we
address below, here we discuss existing research pertaining to these questions.
Evidence of incapacitation and enhanced transmission behind bars
The relatively high prevalence of various infectious diseases among the imprisoned is
well documented in the U.S. and abroad. Between 2 and 3 percent of prison inmates in the U.S.
have HIV/AIDS, a figure that is nearly 5 times the infection rates for the general population
(Hammett et. al. 2002). The World Health Organization documents comparably high infection
rates among prisoners in Western and Eastern Europe (WHO 2001). U.S. prisoners also account
for disproportionately large shares of those infected with the hepatitis B virus (Macalino et. al.
2004) and the hepatitis C virus (Hammett et. al. 2002, Macalino et. al. 2004), and have been
linked to several tuberculosis outbreaks within prisons and within communities receiving
released inmates (Freudenberg 2001).
The relatively high HIV/AIDS infection rates among U.S. prison inmates may reflect
either a selected population at high risk of infection regardless of incarceration, an elevated risk
of infection while incarcerated, or some combination of the two. To the extent that the high rate
simply reflects pre-incarceration behavior, imprisonment may simply isolate a high risk
1

In future work, we plan to develop a formal model of the supply and demand dynamics of sexual behavior, with
emphasis on the role of incarceration and implications for HIV epidemics, which nest these ideas.

7

population from the general public and thus reduce transmission, holding all else equal. To be
sure, the profile of the average inmate clearly indicates that the incarcerated population is drawn
from a sub-population at high risk of having HIV/AIDS. The typical inmate in the United States
is relatively young, poor, minority, with very low levels of educational attainment (Raphael and
Stoll 2005), and is likely to engage in risky sexual activity and drug abuse prior to becoming
incarcerated (Swartz et. al. 2004). Thus, part of the higher infection rate among inmates is
certainly attributable to the pre-prison behaviors and characteristics of inmates themselves.
Whether the incarceration of these high-risk individuals epidemiologically incapacitates
them and reduces HIV/AIDS transmission is an unanswered question. However, there is ample
evidence of an incapacitation effect of incarceration on crime (Levitt 1996, Raphael and Stoll
2005), and thus the proposition that similar effects exist for the transmission of infectious
diseases is not implausible.
Any incapacitation effect of incarceration on overall transmission rates, however, may be
offset by an instrumentally higher transmission rate while incarcerated. Concentrating high-risk
individuals behind bars may accelerate the transmission of HIV/AIDS among inmates (and
ultimately the general community) due to behaviors that are specific to prison as well as risks
that are faced specifically by inmates. Researchers have identified a number of behaviors that
are common in correctional settings that may facilitate transmission of blood-borne illnesses,
such as tattooing, drug use, and high-risk sexual activity. Tattooing is a common practice in
prison culture, and prisoners often receive tattoos while incarcerated under unsanitary conditions
(Krebs 2002). While intravenous drug use is likely to be suppressed while incarcerated, some
prisoners do indeed abuse drugs, and many argue that intravenous drug use in prison is more
likely to involve risky sharing of needles among users (Hammett 2004).
Research pertaining to consensual sexual activity among inmates provides a fairly
imprecise portrait of the extent to which prisoners have sex behind bars. Most research indicates
8

that between 20 percent (Tewksbury 1989) and 65 percent (Wooden and Parker 1982) engage in
sexual activity while incarcerated (although at least one study cited in Krebs (2002) provides an
estimate as low as 2 percent). There is even greater uncertainty regarding the likelihood of being
sexually assaulted while incarcerated, although there is consensus that the risk for males of being
sexually assaulted while incarcerated exceeds the comparable risk while not incarcerated.2
Nonetheless, it seems safe to assume that sex among inmates is not infrequent and that the sexual
activity that occurs is particularly high risk. The risk of transmission is greatest for men who
have sex with other men, and the overwhelming majority of prisons and jails (95 percent) in the
United States do not provide condoms to inmates (Hammett 2004).
The results from inmate surveys suggest that many of these high-risk behaviors are
associated with prison sub-culture and the material and emotional deprivation of being
institutionalized. Krebs’ (2004) survey of prison inmates in a southern state of the U.S. reveals
that many prisoners believe that tattooing is an activity that often commences behind bars and
occurs with increasing frequency while incarcerated. Inmates also indicated that they believed
that at least half of inmates engage in homosexual sex while incarcerated, and that most who do
had no prior homosexual intercourse before entering prison. Thus, while prisoners in general are
likely to be drawn from sub-segments of the population with high HIV/AIDS infection rates,
behaviors that are common behind bars are likely to independently elevate the rate of
transmission.
There are a handful of studies that attempt to measure the rate at which HIV is
transmitted within prisons. This research typically follows one of two strategies: (1) estimating

2

The Bureau of Justice Statistics recently completed the first-ever national survey of administrative records on
sexual violence in adult and juvenile correctional facilities. This data collection effort to estimate the incidence and
prevalence of sexual violence in prison was mandated by the Prison Rape Elimination Act of 2003. Administrative
records alone, however, cannot provide reliable estimates of sexual violence because victims are often reluctant to
report incidents to correctional authorities due to fear of retaliation from perpetrators. During 2004, an estimated
8,210 allegations of sexual violence were reported by correctional authorities—the equivalent of 3.2 allegations per
1,000 inmates and youths incarcerated in 2004. See http://www.ojp.usdoj.gov/bjs/abstract/svrca04.htm for details of
the BJS report, the survey instrument and methods for data collection.

9

the rate at which new inmates seroconvert (test negative upon entering prison and positive at a
follow up date) while incarcerated (Brewer et. al. 1988, Horsburgh et. al. 1990, Castro et. al.
1994, Macalino et. al. 2004), or (2) assessing the degree to which long-term prisoners that had
been incarcerated since before the start of the AIDS epidemic become infected with the HIV
virus (Mutter et. al. 1994, Krebs and Simmons 2002). While not all of these studies tabulate
annual transmission rates (thus limiting comparability),3 those that do suggest transmission rates
per year served on the order of 0.1 to 0.5 percent. By comparison, the CDC estimates that there
were 40,000 new HIV cases in 2001, giving an overall transmission rate for the general
population of 0.014 percent. Thus, the extant research suggests that the rate of transmission in
prison is between 7 and 35 times the rate of transmission for the nation overall. However, this
relatively high transmission rate behind bars may occur at a similarly high rate among the
comparable non-incarcerated population.
This evidence does not address the relevant questions pertaining to the group’s
counterfactual HIV transmission rate that would have prevailed in the absence of their
imprisonment, nor does it resolve the related question of what the community’s HIV incidence
rate would have been in the short- and long-run had these individuals not been incarcerated. It is
possible for the short- and long-run impacts of an increase in incarceration on a community’s
HIV infection rates to move in opposite directions. For example, an increase in incarceration
may result in a short-run decline in HIV incidence due to an incapacitation effect followed by a
subsequent long-run increase post-release due to inmates’ elevated risks of acquiring HIV while
previously incarcerated.

The attempt to construct appropriate counterfactual estimates of

HIV/AIDS rates under different scenarios, and identifying exogenous sources of variation in
incarceration rates to do so, is the chief challenge empirically.

3

For example, Krebs and Simmon (2002) tabulate the proportion of long term inmates in a southern state that test
positive before leaving prison but do not normalize for time served. See Hammett (2004) for a thorough discussion
of this research.

10

The effect of incarceration on concurrency and the lifetime number of sexual partners
The rate at which a sexually transmitted disease spreads through a population depends
critically on the initial prevalence of the disease in the population, the rates at which new sexual
relationships form and dissolve, the riskiness of the sexual activity involved, and the degree to
which members of the population engage in concurrent sexual relationships. An increase in
incarceration rates may alter the sexual behaviors of the non-incarcerated in ways that increase
the risk of transmission. Of particular importance are the effects of incarceration on the total
lifetime number of sex partners and the likelihood of concurrent sexual relationships. The rates
at which new relationships form and dissolve impacts the lifetime number of sexual partners at
any given age, which affects the risk of sexual contact with an infected person.
Concurrent sexual relationships increase transmission rates through a number of
channels. Morris and Kretzchmar (1995, 1996) note that when an individual who is engaged in
concurrent sexual relationships becomes infected, a subsequent transmission is likely to occur
more rapidly. Subsequent transmissions do not depend on the dissolution of the relationship
generating the initial infection. In addition, for serially monogamous relationships, prior partners
are protected from a newly infected current partner. For concurrent relationships, however, there
is no comparable sequential break between the sexual networks of an individual’s various sex
partners.
Incarceration may impact the number of sex partners and the likelihood of concurrency
through two specific avenues: through a destabilizing effect on existing relationships and through
a general equilibrium effect on sexual relationship markets. The dynamics of prison entry and
exit, coupled with a large increase in incarceration rates for men, are likely to impact the rate at
which existing sexual relationships dissolve and form. The majority of men that enter U.S.
prisons will serve relatively short spells (a median of 2 years) followed by even shorter spells
(for roughly two thirds of releases) usually triggered by a parole violation (Raphael and Stoll
11

2005).4 In addition to time actually served in prison, spells outside of prison are likely to be
punctuated by jail time while awaiting trial or while attempting to make bail. These periodic
absences from non-incarcerated partners are likely to result in the formation of new relationships
by the partners left behind, as well as new sexual relationships formed by the inmate while
incarcerated, thus increasing the total lifetime number of partners. To the extent that these
ancillary relationships continue after an inmate is released and returns to previous partners, the
churning in and out of prison may augment the extent of concurrency.
A more subtle pathway through which a large increase in incarceration may affect the
formation of new relationships and concurrency operates through the impact of incarceration on
the ratio of non-incarcerated men-to-women. The model of social exchange applied to the
formation of sexual relationships in Baumeister and Vohs (2005) serves to illustrate this point.
In this model, the social interactions at the beginning of heterosexual relationships are akin to a
bargaining process, where the relationship will form if both parties can agree on the terms.
Factors that will influence whether the relationship forms may include the degree of commitment
and loyalty displayed by members of either sex, the perceived trustworthiness of the potential
partner, potential promises of economic security, etc.
The value of what is gained and exchanged in a relationship market is determined in part
by preferences and in part by broader market conditions. Market forces tend to stabilize the rate
of exchange within a community (but not necessarily across communities). For example, a
decline in the relative supply of men (driven by an increase in incarceration) may lead women to
lower their standards and match with less reliable and less stable men. Accordingly, with a
lower sex ratio, non-incarcerated men may lower the degree to which they make perceived costly
commitments to ensure the formation of a new sexual relationship, and may display less loyalty.
4

In an analysis of 18 to 25 year olds entering the California state prison system in 1990, Raphael (2005) finds that
over the subsequent decade, the typical inmate served 2.8 years behind bars with roughly 5 years elapsing between
the date of the initial admission and the final release. For black inmates, the comparable figures were 3 years served
over a 6.2 year period.

12

In the aggregate, the degree of concurrency may increase, as well as the total number of sex
partners at a given age. While there is little direct evidence of an effect of incarceration on
relationship formations and concurrency operating through this channel, Charles and Louh
(2005) show that higher male imprisonment has lowered the likelihood that women marry,
reduced the quality of their spouses when they do, and caused a shift in the gains from marriage
away from women and towards men. In addition, low sex ratios have been shown to be
associated with higher rates of teen pregnancy (Sampson 1995), syphilis (Kilmarx et. al. 1997)
and gonorrhea (Thomas et. al. 2003).
Incarceration trends and racial differences in AIDS infection rates
The mechanisms noted above – incapacitation effects operating through the temporary
isolation of high-risk individuals, elevated transmission rates while incarcerated, and effects of
incarceration dynamics on the formation of new sexual relationships and concurrency – should
disproportionately impact the African-American community in the United States. Roughly onefifth of black adult males in the U.S. have served time (Raphael 2005), and many of these men
have cycled in and out of correctional institutions for fairly long periods of their early adult lives.
The ratio of men to women among the non-institutionalized is markedly lower for non-Hispanic
blacks than for non-Hispanic whites (Adimora and Schoenbach 2005). Moreover, black women
are nearly twice as likely to have recently had concurrent partnerships relative to white women
(Adimora and Schoenbach 2005), and, on average, they have higher lifetime numbers of partners
holding age constant (all factors that may result theoretically from high black male incarceration
rates).5

Whether these factors translate into greater AIDS infection rates among African-

Americans is the question to which we now turn.

5

Our own tabulations of the 2001-2002 National Health and Nutrition Examination Survey Sexual Behavior
Component revealed that black women on average have greater lifetime numbers of sexual partners relative to white
women. These differences are on the order of 20 percent and disappear for women over 50. It is notable that these
race differences in the lifetime number of sexual partners are specific to only younger cohorts and emerged
coincident with the trends of increasing incarceration rates of the past several decades. These differences did not
exist (or are not detected) among older generations, suggesting cohort effects.

13

III. Our Empirical Strategy
The empirical strategy taken in this paper builds on the observation that the
overwhelming majority of marriages occur within demographic groups defined by the interaction
of race, age, socioeconomic markers such as education, and earnings, and state of residence
(Charles and Luoh 2005). Moreover, high inter-marriage rates within these demographic and
socioeconomic sub-groups mirror the stratification of sexual relationships along these lines, thus
creating sharp and distinct sexual relationship markets (Laumann et. al. 1994).
To identify the effect of incarceration rates on AIDS infection rates, we exploit this
empirical regularity and the substantial variation in the incarceration trends over this period
occurring within these demographic groups. Accordingly, we define sexual relationship markets
by the interaction of race, age, and state of residence. We use standard panel data methods to
estimate the partial effect of incarceration rates on infection rates using variation in both series
occurring within the defined sexual relationship markets after purging the data of race-, age-, and
state-specific time trends.

The strategy presumes that the remaining variation in the male

incarceration trends within sexual relationship markets is akin to differential shocks to the sexual
relationship markets driven by disparate male incarceration patterns over the past two decades.
By focusing the analysis on AIDS cases (i.e., advanced-stage HIV) rather than earlystage HIV (which is often asymptomatic), we minimize differences in reported rates that are
simply an artifact of differential interaction with the health care system, which result in
differences in rates of early detection. Since our principal dependent variable of analysis is the
rate at which demographic subgroups develop full blown AIDS, the relationship between
incarceration and new AIDS infection is inherently dynamic. Several factors will induce a
delayed response between the male incarceration rate and AIDS infection rates for both men and
women. For both genders, variance in the AIDS incubation distribution – where incubation is
14

defined as the time between HIV infection and the development of a measurably suppressed
immune system – will induce a lag between any incarceration-induced infections and newly
diagnosed AIDS cases. Estimates of the cumulative distribution function (CDF) of incubation
for the pre-1996 period6 reveal sharp increases in the proportion developing full blown AIDS
starting three years post seroconversion and a flattening of the CDF at around ten years post
infection (Bacchetti 1990, Brookmeyer 1991, U.K. Register of HIV Seroconverters Steering
Committee 1998). These estimates suggest that roughly one-quarter of HIV-positive individuals
develop AIDS within six years, one-half within nine years, and three-quarters within twelve
years.
For women who are at risk of infection via heterosexual relationships with former
inmates, time served will also induce a lag between men becoming infected while incarcerated
and the ultimate infection of female partners. Moreover, conditional on having sex with an
infected person, the probability of acquiring HIV depends on a number of factors, including
whether the sex is unprotected and the specific act.
To account for the likely lagged effect of incarceration rates on infection rates, we
estimate a dynamic panel data model where we allow incarceration to impact AIDS infection
rates over a thirteen-year period. Specifically, our principal estimates come from estimation of
the regression equation
13

13

τ =0

τ =0

AIDSRate rsat = ∑ ω mτ IM rsa ,t −τ + ∑ ω fτ IFrsa ,t −τ + δ rsa + λ rt + φ st + π at + ε Rsat ,

(1)

where r indexes racial/ethnic groups, s indexes state of residence, a indexes age groups, and t
indexes year of infection. The variable AIDSRatersat measures the number of new AIDS cases
diagnosed per 100,000 individuals from race group r, age group a, in state s, during year t;

6

The AIDS incubation period was altered considerably by the introduction of antiretroviral drugs in 1996, with the
variance increasing considerably along with the median and mean time to the development of symptoms. For this
reason, the empirical tests below will focus on the pre-1996 period.

15

IM rsa ,t − c provides the male incarceration rate (defined as the proportion incarcerated at a point in

time for the given year) for the demographic group rsa for the contemporaneous year of infection
and for thirteen lagged years; IFrsa ,t −c provides the comparable incarceration rates for
women; δ rsa denote a complete set of sexual-relationship market fixed effects defined by the
interaction of race, age, and state of residence; λrt denote a complete set of race-specific year
effects; φ st denote a complete set of state-specific year effects; π at provides a complete set of
age-specific year effects; and ε rsat is the random error term. Finally, the parameters ωmτ and

ω fτ provide the coefficients on the contemporaneous and lagged incarceration rates and provide
the principal parameters of interest.
Before discussing the details of the dynamic structure of the model, a brief discussion of
the variation being used to identify the incarceration effects is needed. Equation (1) includes
both sexual relationship market fixed effects and allows race-specific, age-specific, and statespecific year effects. The sexual relationship market fixed effects allow us to control for (timeinvariant) market-specific characteristics, such as drug use prevalence or behavioral norms, that
are otherwise difficult to quantify. Allowing for race-specific, age-specific, and state-specific
individual year effects controls for race- and age-specific trends that might exist in AIDS
incidence at the national level, and overall trends that may vary by state. Factors that may create
such trends include changes in sexual awareness and AIDS prevention (AIDS-preventative risk
behaviors), innovations in medical treatments that delay the onset of advanced stage HIV/AIDS,
changes in drug use technologies and prevalence (e.g., crack cocaine epidemic began in 1985),
and changes in guidelines for reporting cases.
Collectively, the inclusion of the sexual market effects and the various time effects means
that we are identifying the effect of incarceration on AIDS infection rates using variation in both
series occurring within sexual relationship networks after accounting for race, age, and state
16

level time trends in both variables. That is, the effect of incarceration is estimated off of the
differential variation in the incarceration rate in a market over time, relative to overall (racespecific, age-specific, state-specific) trends. We estimate equation (1) using weighted least
squares, where we weight by the population size of each group defined by race, state, age, and
year. Finally, to ensure that our statistical inferences are robust to serial correlation in the error
term, we estimate the standard errors of the model by bootstrapping.
We estimate equation (1) separately by gender.

Since sexually-transmitted AIDS

infection is the hypothesized chief mechanism linking incarceration and AIDS, we also estimate
the equation separately for new AIDS infections contracted through heterosexual sex (for
women), homosexual sex (for men), in addition to estimating models for overall AIDS infection
rates. In each model, we control for the contemporaneous and lagged incarceration rates for both
genders. Given the high degree of correlation between current and lagged incarceration rates, we
use a third-order polynomial distributed (Almon) lag for both male and female incarceration
rates to reduce multicollinearity problems and yet allow a fairly flexible structure on the shape of
the lag distribution.

Our modeling of the lag structure is guided by the medical and

epidemiological evidence regarding the pre-1996 incubation period (which suggests no more
than two inflections in the incubation probability distribution function). We tested alternative lag
lengths and higher-order polynomials, but none significantly improved the fit of the model.
We further constrain the lag coefficients to equal zero for those whose transmission
effects correspond with time periods that predate the AIDS epidemic (i.e., before 1980). For
example, for AIDS rates in 1985 we constrain all coefficients on lagged incarceration rates in
excess of five years to zero; for AIDS rates in 1986 we constrain all coefficients on lagged
incarceration rates in excess of six years to zero, and so on. Thus, given that our panel begins in
1982, the matrix of the lag coefficients (W) on the male incarceration rates for the first twelve
years of the panel is given by
17

W=

0
0
M
ωm13

0
0
M
ωm12

0
0
M
ωm11

0
0
M
ωm10

0
0
0
0
0
0
M
M
M
ωm9 ωm8 ωm7

0
0
M
ωm6

0
0
M
ωm5

0
0
M
ωm4

0
ωm3
M
ωm3

ωm2
ωm2
M
ωm2

ωm1
ωm1
M
ωm1

ωm0
ωm0
M
ωm0

where the columns dimension of the matrix pertains to the lag length (with the first column the
13th lag and the final column the contemporaneous effect) and the row dimension to the panel
corresponds to year. This constraint essentially means that later lags are being identified by
variation occurring later in the panel. This specification of the distributed-lag model parallels
that of Pakes and Griliches (1984) and Andrews and Fair (1992) in other applications.
The model in Equation (1) measures the effects of incarceration on AIDS transmission
using variation within sexual relationship markets after netting out race-, age-, and state-specific
time trends in both variables. Thus, any unobserved determinants of the incidence of AIDS that
vary across but not within sexual relationship markets, or that drive year-to-year changes for
specific racial groups, age groups, or states, are accounted for in this model specification.
Nonetheless, there may be omitted variables that vary within the remaining slice of variation that
we are using to identify the incarceration lag coefficients, such as changes in high risk behavior.
Perhaps the strongest contender for a contaminating omitted variable is crack cocaine usage.
There is plenty of speculation that the use of crack cocaine during the late 1980s and early 1990s
increased the degree of concurrent sexual relationships, both due to pharmacological effects of
the drug as well as users prostituting themselves for money to support their habits (Levenson
2004). Moreover, the surge in the use of crack cocaine has been linked to increase in crime as
well as increases in various other adverse social trends (Grogger and Willis 2000, Fryer et. al.
2005).
To address this issue, we would need to identify instrumental variables that would cause
exogenous variation in incarceration rates across groups defined by the four dimensions of our
panel. Unfortunately, we were unable to identify such instruments.
18

Nonetheless, there is

substantial cross- and within-state variation in various gauges of sentencing and parole reforms
that have differentially affected prison growth rates (Reitz 2005). Following the discussion of
our dynamic model estimation results, we employ these sentencing reforms to re-estimate a
modified version of Equation (1) using a two-stage-least-squares estimator. We discuss this
additional estimation strategy in greater detail along with the presentation of the results.
IV. Description of the Panel Data Set and Descriptive Statistics
To estimate the model discussed in the previous section, we construct a panel data set
covering the period 1982 to 1996 that measures the rate of advanced-stage HIV infection7 for
sub-populations of the United States as well as a host of same- and cross-gender incarceration
rates. The dimensions of the panel are defined by the interactions between the year of diagnosis,
the state of residence at the time of diagnosis, age group, racial/ethnic group, and gender. We
calculate AIDS infection rates using data from the 2001 CDC AIDS Public Information Data Set
(PIDS) as well as the 1980, 1990, and 2000 five percent Public Use Microdata Samples (PUMS)
from the U.S. Census of Population and Housing. We calculate incarceration rates using the
census data. In this section, we discuss the construction of these variables and the details of our
panel data set.
Calculating the AIDS infection rate
The AIDS Public Information Data Set provides case-level information on all known
AIDS cases measured by the national AIDS surveillance system. Since 1985, all states require
health service providers to report diagnosed AIDS cases to state and local health departments. In
turn, these departments voluntarily report the details of such cases to the CDC.8
Since the onset of the AIDS epidemic, the definition of a case has changed several times.
Prior to the ability to identify the HIV antibody, AIDS cases were defined by the presence of a
7

Advanced-stage HIV is commonly referred to as a full-blown AIDS case.
Evaluation studies of the completeness of the reporting of AIDS cases has been estimated to be more than 85
percent complete, with the level of reporting completeness varying by geographic area. For a complete discussion,
see Rosenblum et. al. (1992).
8

19

disease indicative of a suppressed immune system, such as pneumocystis carinii pneumonia,
Kaposi’s sarcoma, and other opportunistic infections. The definition was changed in 1985,
reflecting the discovery of HIV as a causative agent of AIDS. The 1985 change was restricted to
those with HIV infections and included additional medical conditions.

The number of

admissible conditions for an AIDS diagnosis was expanded again in 1987 and 1993. The
definition of AIDS was expanded to more generally reflect those with HIV infections and
measurably-suppressed immune systems. These redefinitions also expanded the number of
medical conditions that lead to an AIDS diagnosis for an HIV positive individual.
The three redefinitions of an AIDS case increased the likelihood of an AIDS diagnosis
independent of actual incidence. The CDC reports that the 1985 redefinition added 3 to 4
percent to total annual new diagnoses, while the 1987 change augmented cases by nearly 25
percent. Similarly, the expanded definition based on a gauge of a suppressed immune system
caused a discrete change in reported cases. Moreover, there is evidence that the redefinitions had
larger effects on reporting for racial and ethnic minorities and on AIDS cases that were not
contracted through male homosexual activity. To control for the effects of these case reporting
redefinitions and any other common temporal changes, we include complete controls for year of
diagnosis as well as complete sets of race-, age-, and state-specific year effects.
Using the AIDS PIDS database, we first tabulate the total number of newly diagnosed
AIDS cases by the state of residence, race, age, gender and year of diagnosis for individuals with
advanced-stage HIV. We then use data from the 1980, 1990, and 2000 Census PUMS to
estimate the national population corresponding to each state/race/age/gender/year cell.

For

census years, we directly calculate the population with the sample data by summing the provided
sample weights within cells. For inter-census years, we linearly interpolate the population using
the population estimates for the respective cell for the two census year bracketing the year in

20

question. With these population estimates, we tabulate an AIDS diagnosis rate expressed per
100,000 individuals. This variable is the principal dependent variable of our analysis.
An individual’s race/ethnicity is defined by four mutually-exclusive categories nonHispanic white, non-Hispanic black, non-Hispanic Asian, and Hispanic. We use nine of the ten
age groupings used to characterize new diagnoses in the AIDS PIDS data, effectively limiting
the analysis to AIDS cases among individuals between 20 and 65 years of age.9 The introduction
and widespread use of medical therapies, particularly antiretroviral drugs introduced in 1996,
have slowed the HIV progression to AIDS. These medical advances since 1996 may have
altered and elongated the lagged structure of the relationship between incarceration and AIDS
incidence. In light of this fact, our analysis focuses on the period from 1982 to 1996.
One problem with the AIDS PIDS data concerns the ability to identify the state of
residence at the time of diagnosis for each demographic sub-group of our analysis. Because of
confidentiality restrictions due to small cell sizes within some dimensions of our panel (state,
race, age, gender, and mode of transmission), roughly 15 percent of AIDS cases observed over
this period lack state identifiers. For the levels of disaggregation of AIDS cases required by our
analysis, the PIDS identifies the metropolitan area of residence for those individuals residing in
large metropolitan areas. This accounts for 85 percent of documented AIDS cases, and includes
AIDS cases from 38 states plus Washington, D.C..10

For the remaining 15 percent of

documented AIDS cases, the only geographic identifier is the region of residence (defined as
west, south, midwest and northeast). Thus, the infection rates in our panel data set are estimated
using only 85 percent of the total number of AIDS cases recorded in the U.S. To make use of all
cases, we also estimated the models below using the four-category region of residence to define
9

The age ranges describing each infected individual refer to age at infection and are 20 to 24, 25 to 29, 30 to 34, 35
to 39, 40 to 44, 45 to 49, 50 to 54, 55 to 59, 60 to 64, and 65 plus. We drop the 65 plus category since many of those
65 plus in the census defined as institutionalized are in nursing homes.
10
The twelve states with missing disaggregated AIDS case-level information (due to confidentiality restrictions
because of small cell sizes) are: Alaska, Iowa, Idaho, Maine, Mississippi, Montana, North Dakota, New Hampshire,
South Dakota, Vermont, West Virginia, Wyoming. There are also missing state identifiers for some AIDS cases in
small rural areas, disproportionately in the South.

21

geographic location rather than state of residence. The results are qualitatively and numerically
similar to what we present below and are available from the authors upon request.
Given that the panel spans fifteen years (1982 to 1996) and covers 38 states plus
Washington, D.C., the dimensions of the panel define 21,060 individual demographic groups for
each gender.11
Figures 1 and 2 present our estimates of the annual newly-diagnosed AIDS cases
(expressed per 100,000) for men and women for 1982 through 2000.12 The figure for men
reveals that the incidence rate for black men is between three and nine times the comparable rate
for white men (with the larger figures pertaining to the latter periods). The rate of new AIDS
cases for black women is between 12 and 24 times the annual rate of new diagnoses for white
women. For all racial/ethnic groups, the AIDS infection rates for men are generally many times
greater than the comparable rates for women.
Figures 3 through 6 decompose newly diagnosed AIDS cases per 100,000 by the reported
mechanism of transmission for men and for each of the racial/ethnic groups in the panel. Figures
7 through 10 present the comparable decompositions for women. Among white men with AIDS,
the large majority of new cases are attributable to transmission through sexual contact (with the
lion’s share of this subset attributable to homosexual activity).

Intravenous drug use is a

significant contributor to infection rates among black men, especially for cases diagnosed during
the early 1990s. At the same time, sexual contact is also an important transmission mechanism
for black men, and towards the end of the 1990s, it is the dominant mode of transmission.
Comparable patterns are observed for Hispanic men.

11

For cells with a positive population estimate and zero new AIDS cases, we set the AIDS infection rate to zero.
After omitting those cells where the population estimates from the census are zero, there are 21,018 observations for
men and women.
12
For the descriptive statistics in Figures 1 through 10, we use all AIDS cases recorded in the AIDS PIDS data set,
since the analysis is at the national level. The model estimates that follow are based on the 85 percent of cases
where we can identify the state of residence.

22

For women, transmission through intravenous drug use is consistently a proportionately
greater contributor to AIDS infections than it is for men. Nonetheless, a significant proportion of
AIDS cases among women are attributable to infections through sexual contact. For both black
and white women, roughly twenty percent of cases during the early 1980s are attributable to
sexual transmission. This figure increases to over 40 percent during the 1990s. For Hispanic
women, sexual transmission accounts for over half of new AIDS cases for several years during
the early and mid-1990s. Moreover, closer investigation reveal that during the decade of the
1990s, the largest component of the growth in the disparity in female AIDS infection rates
between whites and minorities resulted from infection occurring through heterosexual sex.
Calculating Incarceration Rates from the PUMS
Estimating Equation (1) requires data on current and lagged incarceration rates for both
men and women. Here we first describe how we estimate incarceration rates with data from the
U.S. Census. We then describe the lagged structure of our panel data set and the manner in
which we calculated the lagged incarceration rates.
To estimate the proportion incarcerated for each sub-group of our panel, we make use of
the group-quarters identifier included in the PUMS data. The decennial Census enumerates both
the institutionalized as well as the non-institutionalized population. The PUMS data for each
census includes a flag for the institutionalized as well as micro-level information on age,
education, race and all other information available for other non-institutionalized long-form
respondents. The group-quarters variable allows one to identify those individuals residing in
non-military institutions, a category that includes inmates of federal and state prisons, local jail
inmates, residents of inpatient mental hospitals, and residents of other non-aged institutions. We
use this variable as our principal indicator of incarceration.13

Raphael (2005) presents a

comparison of incarceration estimates from the census to those tabulated by the Bureau of Justice
13

See Butcher and Piehl (1998) for an analysis of incarceration among immigrant men that also uses the group
quarter variable to identify the incarcerated.

23

Statistics using alternative data sources and shows that the institutionalized in the decennial
census provide a good proxy for the incarcerated population.
For the census years 1980, 1990 and 2000, we measure the contemporary incarceration
rate for each demographic group defined by state of residence, age group, racial/ethnic group,
and gender as the proportion of the members of the demographic cell that is institutionalized.
For non-census years, we linearly interpolate the incarceration rate using the estimated rates for
the two years bracketing the year in question.
Our model requires that we estimate lagged incarceration rates for each demographic
group defined by our panel data set. We assume that the AIDS epidemic begins in 1980 and
allow for up to 13 lags of the incarceration rate.14 We calculate the lagged incarceration rates in
the following manner. First, we redefine the age groupings of our panel to reflect the effect of a
time lag. For example, for black women 30 to 34 in New Jersey who are infected in 1990, the
one-year lagged incarceration rate should correspond to New Jersey black women that are 29 to
33 in 1989, the two-year lagged incarceration rate should correspond to New Jersey black
women that are 28 to 32 in 1988, and so on. Given that the maximum number of lags in our
panel is 13 years, we must adjust the age structure 13 times.
Next, for each of these 13 additional age structures interacted with the other dimensions
of our panel, we estimate the contemporary incarceration rate for each year from 1980 to 2000
using the PUMS. This essentially creates 13 ancillary panel data sets using 13 alternative age
groupings.
Finally, we match observations from our original panel to the corresponding observations
from each of the 13 ancillary panels that gauge the appropriate time lags. For example, using the
ancillary panel where the age structure is lagged one year, the 1995 incarceration rates provide
the one-year lag for 1996, the 1994 incarceration rate provides the one-year lag for 1995 and so
14

Recall from our methodological discussion above, for any year where lags one through thirteen occur prior to
1980, we constrain the coefficient on that lag for that year to zero.

24

on. Using the ancillary panel where the age structure is lagged two years, the 1994 observations
provide the two-year lag for 1996, the 1993 observation provides the two-year lag for 1995, and
so on.
Each observation in our final data set is matched to 13 lags of the own-gender
incarceration rate, where observations with infection years between 1982 and 1992 will have
missing values for lags that date prior to 1980. In addition, each observation is matched by year
of infection, state of residence, race/ethnicity, and age to the contemporary and lagged
incarceration rates for individuals of the opposite gender.
Figure 11 presents our estimated incarceration rates for men by race and ethnicity for the
period 1982 to 2000. Figure 12 presents the comparable figure for women. There are notable
and large differences in incarceration rates between our four mutually exclusive racial/ethnic
groups. Over this time period, the incarceration rate for black men increases from roughly 4
percent in 1982 to nearly 9 percent in 2000. Tabulating these figures separately by age reveals
even larger increases for younger black men. For black men 20 to 29 years of age, the fraction
incarcerated increases from 5.8 to 12.3 percent. For black men 30 to 39 year of age, the
comparable figures are 4.4 and 11.1 percent.
The increase in incarceration for white men is markedly smaller.

Overall, the

incarceration rate increases from 0.8 to 1.3 percent between 1982 and 2000. Again, we observe
the largest increases for young white men, although the changes are small compared to those for
blacks. For white men 20 to 29, the incarceration rate increases from 1.0 to 1.9 percent. The
increases for all other age groups are considerably smaller. Changes in incarceration rates for
Hispanics are slightly larger than those for whites, though considerably smaller than the change
observed for black men. The incarceration rates for men in the “non-Hispanic other” category
parallel the results for white men.

25

Incarceration rates are markedly lower for women relative to men for all racial/ethnic
groups. The overall racial differences in incarceration parallel those observed for men (black
women have the highest rate, followed by Hispanic women and white women), though the
magnitude of these differences are very small. Moreover, the increases in incarceration rates for
women are minuscule compared to those for men. For example, the proportion of black women
incarcerated on any given day increases from 0.5 percent to 0.9 percent over the time period.
The incarceration rates among white women and other women actually decline.
V. Empirical Results from the Dynamic Regression Models
In this section we present various estimates of the dynamic model of AIDS transmission
presented in Equation (1). Our goals are two-fold. First, we aim to estimate the overall dynamic
relationship between incarceration rates and AIDS infection rates among men and women, for all
AIDS cases as well as the special case of AIDS cases transmitted through sexual contact. We
focus on the special case of sexually-transmitted HIV/AIDS infections to ensure that the patterns
that we observe are not being driven by intravenous drug use alone. Second, we wish to use
these results to provide a statistical accounting of the fraction of the racial differences in AIDS
infection rates attributable to differences in incarceration rates.
Here, we discuss three sets of results that permit an assessment of these two questions.
First, we discuss the results from a set of somewhat restrictive specifications that permit
assessing the effect of controlling for incarceration on the overall estimate of the racial/ethnic
differentials in infection rates. We then present the estimated lag effects of male incarceration
from more liberal specifications that allow for sexual relationship market fixed effects and other
effects geared at netting out common time trends. Finally, we use the full specification from this
second set of regression results to simulate the effect of incarceration on the time-path of blackwhite differences in infection as well as how infection rates would have differed had
incarceration rates remained at their 1980 levels.
26

Controlling for incarceration and the overall race/ethnic differences in infection
Tables 1 and 2 present some preliminary estimates of the lagged effects of incarceration
on AIDS incidence per 100,000 for men and women using a rather restrictive version of the
model in Equation (1).

Table 1 models the AIDS infection rate for men for both AIDS

transmission from any source, and homosexually-contracted AIDS cases. For each dependent
variable, the table presents two specifications: (1) a model including race, year, state, and age
effects, and (2) a model with all of these fixed effects plus the contemporaneous and thirteen
years of lags of the incarceration rate for men and the comparable incarcerations rates for
women. To assess the effects of controlling for incarceration on the racial/ethnic differentials in
AIDS infection, the table displays the estimated race effects in each model.

The female

incarceration coefficients are suppressed to conserve space.
Regression (1) indicates that over the course of the panel annual black male infection
rates exceed annual white male infection rates by over 87 incidents per 100,000 people.
Hispanic male infection rates exceed white male rates by 21 per 100,000, while other male
infection rates are roughly 35 per 100,000 lower than white male infection rates. Adding the
incarceration rates in regression (2) substantially reduces the black-white difference, eliminates
the Hispanic-white differences, and slightly widens the other-white difference in infection rates.
Concerning the effects of incarceration, the estimates reveal no measurable effects of
contemporaneous incarceration rates and lagged effects that are increasing with the time lag. In
particular, the lagged incarceration effects become significant at lag year four, reach a maximum
at lag year 10, and remain significant through lag year 13.
Regressions (3) and (4) reproduce these models where the dependent variable is restricted
to homosexually-contracted AIDS incidence. The race effects presented in regression (3) are
considerably smaller than the effects presented in regression (1). This is consistent with the fact
(revealed in Figure 3 and 4) that transmission through homosexual contact is a proportionally
27

less important avenue of transmission for black men relative to white men. Nonetheless, the
average annual infection rates for black men are considerably higher than those for white men
(by roughly 29 per 100,000) while the transmission rates for Hispanic men are slightly lower.
For the black-white difference, controlling for incarceration reduces the coefficient on the black
dummy from roughly 29 to -14, while for the Hispanic-white difference adding incarceration
rates widens the negative differential.
The lag coefficients on the male incarceration rates parallel those in regression (2) with
two important differences. First, the magnitudes of the lag coefficients are considerably smaller
(a pattern which is not surprising given our focus on one source of transmission). Second, the
contemporaneous incarceration effect is positive. Given that only a small fraction of those who
contract HIV develop AIDS within the same year of being infected, any contemporaneous effects
are likely to be driven by something other than transmission while incarcerated. For example, a
contemporaneous effect may be indicative of an effect of wide-scale testing of the incarcerated
on the number of new diagnoses.
Table 2 presents comparable regression results for women. Again, the first specification
includes race, age, year, and state effects only, while the second specification includes these
fixed effects along with the male and female incarceration rate variables. For AIDS cases
transmitted by any source, there are large average racial/ethnic differentials in the annual average
infection rate. The black-white difference for women is on the order of 31 cases per 100,000, the
Hispanic-white differential is approximately 10 per 100,000, while the other-white differential is
approximately -3 per 100,000. These absolute differentials are smaller than those observed for
men, resulting from the relatively lower infection rates among women. The inclusion of the
incarceration rate variables completely eliminates the positive black-white and Hispanic-white
differentials in infection rates, while not affecting the other-white differential. Concerning the
lag coefficients on male incarceration rates, there is no measurable effect of the
28

contemporaneous incarceration rate and lagged effects that increase monotonically with the lag
length.
Regressions (3) and (4) present comparable results where the dependent variable is
annual AIDS infections contracted through heterosexual sex. Here, the average differentials
relative to whites in infection rates are roughly one-third the differentials observed for the
models of all AIDS cases. Nonetheless, these differentials are large and significant, with a
difference between black and white women of 11 cases per 100,000 and a Hispanic-white
difference of 5 per 100,000.
Adding the incarceration variables to the specification again eliminates the black-white
differential and the Hispanic-white differentials in these variables. In fact, the black-white
differential becomes negative and significant, suggesting that holding incarceration rates
constant, black women are infected at a lower rate than white women. The shape of the lag
function is similar to that observed for the model using the overall AIDS infection rate, although
the coefficients are smaller.
Allowing for sexual relationship market fixed effects
Tables 3 and 4 present estimates of the lagged effects of male incarceration rate on AIDS
infection rates using more flexible specifications than those employed in Tables 1 and 2. Table 3
displays estimation results for men and Table 4 presents results for women. The first three
models pertain to AIDS infection through any source, while the second three models pertain
specifically to sexually-contracted AIDS infection rates (via homosexual contact for men and
heterosexual contact for women). For each group of regressions, we present the results from
three alternative specifications: (1) a model including the male and female contemporary and
lagged incarceration rates, a complete set of fixed effects for race/state/age groups (which we
refer to as the sexual relationship market fixed effects), and year effects, (2) a model with the
incarceration rate variables, the relationship market fixed effects, and race-specific year effects,
29

and (3) a model with the incarceration rate variables, the relationship market fixed effects, and
race-specific, age-specific, and state-specific year effects. We report only the coefficients on the
contemporaneous and lagged male incarceration rates.
For the overall AIDS infection rate models for men, the parameter estimates of the lag
coefficients look very similar to the parameter estimates from the lag coefficients using the
somewhat restrictive model in Table 1. There is little evidence of a positive contemporaneous
effect of incarceration on male AIDS infections, or of effects of the first three lags. The lag
coefficients become positive and significant at the 4th lag, increase through the 10th year (the 11th
in the third specification), and decline thereafter. Adding the race-, age-, and state-specific year
effects diminishes the magnitude of the coefficients only slightly.
The results are similar for homosexually-contracted AIDS infections. Like the results
from the restricted models presented in Table 1, we observe a statistically significant
contemporaneous incarceration effect, and small or insignificant effects for the first four lags.
The lagged effects become somewhat larger and significant for the 5th lag and increase in
magnitude through the 10th year. Here, adding the race-, age-, and state-specific year effects
reduce the lag coefficients somewhat, although many remain significant and the temporal pattern
of the lag function remains the same.

The robustness of these results for homosexually-

contracted AIDS is particularly suggestive of a link between male incarceration and AIDS, since
potential omitted variables such as changes in drug use within relationship markets are not
typically associated with increases in homosexual activity.
Table 4 presents the comparable results modeling the AIDS infection rates for women.
The first three models pertain to overall AIDS infections, while the second three columns pertain
to AIDS infection rates where transmission occurs through sexual contact. Again, the models
controlling for sexual relationship market fixed effects and the various year effects yield a lag
structure that is nearly identical to those from the restrictive models estimated in Table 2. The
30

results from the full specification in regression (3) reveals no significant contemporaneous male
incarceration rate effects and lagged effects that increase monotonically in the lag length. The
results for heterosexually-contracted infections are qualitatively similar, although the coefficients
are smaller in magnitude reflecting the fact that infection through heterosexual sex accounts for
at most half of infection among women in any given year.
The lag structures revealed in Tables 3 and 4 suggest that the effects of male
incarceration on AIDS incidence do not surface for several years and increase considerably over
a ten-year period for men and over at least a thirteen-year period for women. Several factors
may be driving these delayed responses. For men infected while in prison, infection may not
occur immediately inducing a delay between incarceration and the transmission of HIV. In
addition, the incubation delay following seroconversion will further add to the lag. For women
infected through contact with former inmates, the transmission of the disease must await the
release of the inmate and the formation of a heterosexual relationship. Thus, for both men and
women, the expected patterns of the lagged effects of incarceration would parallel the incubation
distribution of the disease, but with additional delays. In other words, the lag structure should
peak later than the peak in the incubation distribution due to factors that cause delay between an
increase in incarceration rates and a new HIV infection.
To assess whether this is the case, Figures 13 and 14 plot the lagged coefficients from the
third specifications of Tables 3 and 4 (the lag effects for the overall AIDS rates from the most
complete specification) along with two alternative estimates of the probability distribution
functions of the incubation period between seroconversion and the onset of AIDS. The first
incubation distribution is calculated using the United Kingdom AIDS registry and pertains to
HIV infections in the U.K. occurring prior to 1996 (U.K. Register of Seroconverters Steering

31

Committee 1998).15 The second incubation distribution estimate comes from an analysis of the
incubation period among homosexual men in San Francisco during the pre-1996 period (Bachetti
1990). Based on both incubation period distribution estimates, the probability of becoming
advanced-stage HIV (following seroconversion) increases in each of years one through seven,
reaching a peak likelihood in the seventh year, and declining thereafter. By comparison, the
lagged effects of male incarceration on overall AIDS infections for men follow a similar shape,
though delayed an additional four years (with a peak at the 11th lag). For women, the delay
appears to be greater, as the lag coefficients increase through the thirteen-year period suggesting
a maximum effect beyond the lag length allowed in our panel regressions.
Simulating the effect of racial differences in incarceration and the post 1980 increase
To summarize the results thus far, for both men and women we find significant effects of
the time path of male incarceration rates on the rate at which men and women become infected
with AIDS. The lagged effects of incarceration increase with time, suggesting significant delays
between the incarceration of men and the onset of AIDS for both genders. The temporal pattern
of these lagged effects parallel the pre-1996 incubation distribution for the disease with an
additional time lag: very small effects early on followed by increasingly larger effects that peak
later than previously-estimated peaks in the pre-1996 incubation distribution.
The results in Tables 1 and 2 indicate that racial differences in incarceration rates largely
explain the sizable overall black-white differential in annual AIDS infection rates. However,
there are additional questions to explore that require further analysis and probing of the dynamic
model estimates presented in Tables 3 and 4.

First, to what extent does adjusting for

incarceration rates explain the time path of the racial difference in incarceration rates? Second,
to what extent is the increase in incarceration rates since 1980 responsible for the subsequently
higher infection rates among African-Americans?
15

The figure in the graph smooths the raw estimate of the pdf reported by the U.K. Register of Seroconverters
Steering Committee using a third-order polynomial regression of the infection probability on the time since
seroconversion.

32

Answering the first question provides a more detailed decomposition of the racial
differentials in infection rates accounting for the changes in incarceration rates over time and the
lagged effects of incarceration on AIDS infection rates. In effect, the question asks how the
black-white AIDS infection rate differential would have changed over time had the incarceration
rates for these two groups been equal. Using the most complete specifications for overall
infection rates in Tables 3 and 4 (regression 3 in each table), we calculate the counterfactual
black-white difference in AIDS infection rate that would have occurred had black male
incarceration rates equaled white male incarceration rates. We do so by subtracting the predicted
AIDS differential caused by male differences in incarceration rates from the overall black-white
difference in AIDS infection rates.16
Figure 15 displays the actual black-white differential in overall AIDS incidence among
men along with the predicted black-white differentials after accounting for black-white
differences in male incarceration rates. Figure 16 presents the comparable series for women.
Figure 15 reveals that racial differentials in incarceration rates explains little of the racial
differentials early on in the epidemic but account for a proportionally increasing share as we
progress through the time period of the panel. In the latter years of the panel, racial differences

16

To illustrate this decomposition, here we present a simplified version of Equation (1). Suppose that the AIDS
infection rates depends on a set of sexual relationship market fixed effects, and race-, age-, and state-specific year
effects, and the contemporaneous incarceration for males only (the decomposition can be easily extended to the
dynamic model we estimate in Tables 1 through 4). In other words, we would estimate the equation
AIDS rast = α ras + γ rt + δ at + θ st + β MI rast + ε rast . Taking expectations of this equation conditional on

race=B and t=t0 and allowing the subscript, Bt0, to denote this conditional expectation gives the expression
AIDS Bt0 = α Bt0 + γ Bt0 + δ Bt0 + θ Bt0 + βMI Bt0 , where the first fixed effect is the average network effect for
blacks, the second effect is the black time effect for the given year, the following fixed effect is the average age-time
effect for blacks, and the remaining provides the average state effect for blacks. If we take a similar expectation for
whites and subtract this expectation from that for blacks, we get the final expression

AIDS Bt0 − AIDSWt0 = (α Bt0 − α Wt0 ) + (γ Bt0 − γ Wt0 ) + (δ Bt0 − δ Wt0 ) + (θ Bt0 − θ Wt0 )

+ β ( MI Bt0 − MI Wt0 ). The first term in the decomposition provides the average black-white differential for the
whole panel, the second difference provides the additional period specific difference, the third term provide the
differential attributable to difference in the age distribution, while the next term provides the portion of the
differential attributable to difference in the geographic distribution. The final term provides the portion of the
difference in AIDS infection rates attributable to racial difference in incarceration rates. The tabulations in figures
13 through 16 show the overall unadjusted differential (the left hand side of this equation) as well as the overall
differential less the final component of the decomposition due to incarceration.

33

in incarceration rates account for between 70 and 100 percent of the black-white differences in
AIDS infection rates. For women, Figure 16 reveals that accounting for the effect of racial
differences in male incarceration rates yields negative black-white differentials in overall AIDS
infection rates. In other words, the model predicts that if black male incarceration rates had been
at the lower level experienced by whites, black women would have been infected with AIDS at a
rate that fell short of that for white women between 1982 and 1996.
The second question that we ask of our model is somewhat more subtle, and is an attempt
to estimate the magnitude of a potential externality of the post-1980 increase in incarceration
rates. The substance of this question is best illustrated by the following counterfactual scenario.
Suppose, for the moment, that the post-1980 increases in incarceration rates were driven by statelevel policy choices regarding sentencing and parole policy (we discuss these reforms in greater
detail below). Had individual states chosen not to implement these reforms (i.e., had held
incarceration rates at their 1980 levels), our models would still predict racial differentials in
infection rates that would have increased over the first thirteen years of the AIDS epidemic. This
counterfactual increase in incarceration rates would be driven by two factors. First, there are
substantial racial differences in incarceration rates in 1980, likely reflecting racial differences in
the propensity to offend as well as racial discrimination in the criminal justice system (Raphael
and Sills 2005). Second, the positive and increasing lagged effects of incarceration on AIDS
infections should translate this initial incarceration differential into increasing racial infection
differentials. Thus, the introduction of an infectious disease in an environment where blacks are
disproportionately incarcerated will generate increasing racial differentials in infection, even in
the absence of “tough-on-crime” reforms to the criminal justice system. To the extent that the
actual differentials exceed those of this counterfactual scenario, one can infer the extent to which
post-1980 policy choices exacerbated racial differentials in AIDS infection rates.

34

We use our models to simulate two sets of black-white differentials in AIDS infection
rates. First, we predict the path of the racial differences in AIDS infection rates based on the
actual incarceration rates observed between 1982 and 1996.

Second, we simulate the

counterfactual path in these differentials that would have resulted had incarceration remained at
its pre-AIDS epidemic levels (for our purposes as of 1980). We interpret the difference between
these two series as the unintended consequences of the increase in incarceration rates on racial
inequality in AIDS infections.
Figure 17 presents these simulations for men using the most complete specification of the
dynamic model of overall AIDS infection rates (model 3 in Table 3). Figure 18 presents the
comparable simulations for women. The results for men reveal that the lion’s share of the
increase in the black-white differential in AIDS infection rates attributable to incarceration
would have occurred in the absence of a post-1980 increase in incarceration. However, the
differential would have been lower had incarceration rates not increased. Moreover, the gap
between the black-white differential predicted using the actual incarceration rates and the
differential predicted holding incarceration constant at 1980 levels increases considerably with
time, reaching nearly 60 incidents per 100,000 by the end of the panel.
The results for women are comparable.

The two simulations yield fairly similar

incarceration-induced infection rates during the 1980s. In every year between 1982 and 1996,
the predicted black-white differential using 1980 male incarceration rates is less than the
predicted differential using historical incarceration rates. However, the disparity between these
two series widens significantly over the period, reaching a peak of nearly 33 incidents per
100,000 by 1996.
VI. Are These Effects Causal?

Thus far, we have documented strong partial correlations between the rate at which men
and women become infected with full blown AIDS and lagged values of the incarceration rate
35

for males in one’s demographic group defined by age, race, year, and state of residence. These
correlations persist when we focus only on variation occurring within sexual relationship markets
over time and after removing race-, age-, and state-specific year-to-year changes in both AIDS
infection and incarceration rates. These partial correlations are highly significant and the implied
lagged effects of incarceration parallel estimates of the pre-1996 AIDS incubation period
distribution. Moreover, the effect sizes suggest that much of the racial differential in AIDS
infection rates are attributable to historical differences in the rates at which black men are
incarcerated.
There are three key additional econometric modeling issues this analysis confronts: (1)
the (non-)stationarity of AIDS and prison population data; (2) the stability of the relationship
between incarceration and AIDS infection rates over the analysis period (structural change); and
(3) unobserved determinants of AIDS infection rates that are correlated with incarceration rates
(resulting in omitted variable bias). We consider and discuss aspects of each in turn.
We use the annual state-level data to test for unit roots in both the AIDS incidence and
incarceration rate time series.

It is well known that OLS regressions performed on non-

stationary data series can yield spurious results unless the trend is removed by direct subtraction
or by differencing. The unit root tests, which include state-specific time trends, show that these
series appear to be stationary or I(0) processes.
For completeness and as a further check of the robustness of the results, however, we also
transform the model and re-estimate it in first-difference form. The first-difference form of the
model estimates the annual change in the state’s AIDS incidence rate on 13-year distributed lags
of annual changes in the state’s incarceration rate—in other words, the model estimates the
effects of an increase in incarceration on the acceleration in the growth of AIDS cases distributed
over the subsequent 13-year period. Our first-difference specifications include state fixed effects
and use prison data from the Bureau of Justice Statistics. The first-difference results show that
36

an increase in incarceration rate accelerates the growth rate of AIDS infection cases, reaching
peak acceleration in years 7 and 8 following the incarceration rate increase. This dynamic
structure mirrors with a two-year lag the corresponding growth path of the estimated incubation
period distribution of HIV infection to AIDS (in this case, the first derivative of the probability
density function or the second derivative of the cumulative density function of the incubation
period distribution). The close resemblance of the implied effects of incarceration on AIDS from
this alternative model specification lends further support of the hypothesized relationship.
(These results are available from the authors upon request).
Another potential threat to uncovering unbiased estimates of the effects of incarceration
dynamics on AIDS infection rates stems from the fact that the strength of any underlying
relationship between the probability of acquiring HIV and the proportion who has ever served
time in prison may change as the AIDS epidemic progresses. In particular, we expect any
relationship between HIV incidence and prison population size to grow stronger over time, as the
prevalence of HIV increases in the population. This resulting lack of stability in the strength of
the relationship could lead to biased estimates of the dynamic structure linking incarceration
rates and AIDS, since the later lagged incarceration coefficients are identified disproportionately
from the most recent observation years on AIDS incidence. We examined the sensitivity of the
results to modest changes in the choice of the analysis period and lag length. The results from
these checks were not fundamentally altered from the qualitative patterns of results reported in
the paper. However, we are more limited in the robustness checks we can perform in this regard.
Perhaps the most important caveat to the results above concerns whether we have
adequately controlled for all important determinants of AIDS infection rates in our models.
Clearly, variation in sexual behavior, as well as variation in the type and/or frequency of drug
use, will cause variation in infection rates. While between-group differentials in these behaviors
should be captured by our sexual relationship market fixed effects, any changes in behavior that
37

occur over time and within these relationship markets may contaminate the coefficient estimates
presented in the previous section.
A factor that we do not control for that some have argued helped propagate the AIDS
epidemic throughout the black community is the introduction of crack cocaine. Emergency room
admission statistics suggests that the use of crack cocaine in American cities began in earnest
between 1984 and 1987 (Grogger and Willis 2000); the precise time when HIV infections were
on the rise in African-American communities. In his ethnography of the AIDS epidemic in the
black community, Levenson (2004) intimates that promiscuity and unprotected sex are integrally
related to the crack cocaine trade, as users trade sex for crack or sex for money to buy crack and
through a psycho pharmacological effect of the drug itself. Moreover, the introduction of crack
cocaine has been linked to a number of negative outcomes, including homicide rates, and infant
mortality (see Blumstein 1995, Fryer et. al. 2005).
To assess whether the results presented thus far reflect a causal effect of incarceration, we
need to identify a source of exogenous variation in prison incarceration rates and then use this
variation to identify the causal effect (if any) of incarceration on AIDS infection rates. Towards
this end, in this section we present results from TSLS estimates of the effect of incarceration on
AIDS infection rates using within-state variation in sentencing policy as instruments for the
prison population.
We use a set of instrumental variables that characterizes the legal regimes governing
criminal sentencing in state courts.

Reitz (2004, 2005) has assembled a set of variables

characterizing the legal structure within which judges in state courts sentence convicted
offenders.

Reitz characterizes state sentencing systems as being governed by presumptive

guidelines, voluntary guidelines, or traditional indeterminate sentencing systems. Presumptive
sentencing guidelines provide a set of predetermined sentencing ranges (a minimum and a
maximum) that vary with the severity of criminal offense and the criminal history record of the
38

offender.

Judges generally sentence within these guidelines, and judicial departures from

presumptive sentencing guidelines must be justified in writing. Voluntary guidelines are, by
definition, voluntary and are generally perceived to not constrain judicial discretion in
sentencing. Traditional indeterminate sentencing was the dominant sentencing regime in nearly
all states prior to the 1970s and remains an important sentencing regime in over half of states
today. Indeterminate sentencing regimes are often characterized by complete judicial discretion
at the front end of a prison sentence and a fair degree of release discretion afforded to parole
boards for early release at the back end of the prison term.
In addition to the sentencing regimes governing judicial behavior, Reitz has also
assembled data on whether the state has abolished the release authority of parole boards. The
abolition of parole boards is generally presumed to increase incarceration rates (see Petersilia
2003), as it constrains a release mechanism that may be used in the event of prisoner
overcrowding or to release those who are unlikely to pose a further danger to society. However,
Reitz (2004) challenges this presumption based on the reasoning that time off for good behavior
or rehabilitative activities can and is incorporated into administrative rules governing parole in
mandatory parole states that afford little discretion to a centralized parole board. In the estimates
below, we use the two indicators for sentencing regimes (a presumptive guidelines dummy and a
voluntary guidelines dummy) interacted with whether the state has abolished parole as
instruments for the state prison population in TSLS models of various state-level AIDS infection
rates.
Unfortunately, these instruments do not vary by all of the dimensions of the panel data set
that we use to estimate the models above – i.e., by race, age, year, and state of residence. Adult
offenders of all age, race, and gender groups are subject to the same sentencing regime for a
given state and year. Moreover, we observe within-state variation in these variables for only
thirteen states and for a relatively small number of state-year observations, a fact that makes it
39

difficult to identify the full 13-year lag structure that we estimated above. In light of these
constraints, we use a simplified model specification exploiting long differences in cumulative
AIDS infections to roughly identify a lagged effect of incarceration on AIDS infection rates.
Specifically, we estimate the structural second stage equation,
7

(2)

∑ AIDS
i=0

st − i

= α s + λ t + β Incarcerat ion st − 7 + χ Admissions

st − 7

+ δ Re leases st − 7

+ ϕ X st − 7 + γ ∆ X st − 7 , st + ε st − 7 ,

where the dependant variable is the sum of new AIDS cases per 100,000 for each state occurring
between years t-7 and t, Incarcerationst-7 is the incarceration rate in state s and year t-7 expressed
per 100,000 residents, Admissionsst-7 and Releasesst-7 are the number of prisoner admissions and
releases per 100,000 in state s in year t-7, Xst-7 is a vector of demographic control variables for
the state in year t-7, and ∆Xst-7,st represents the changes in these variables. We instrument the
incarceration rate, prisoner admissions, and prisoner releases using dummy variables indicating
presumptive guidelines, voluntary guidelines, and interaction terms between a dummy indicating
whether the state has abolished its parole release authority with the two guideline dummy
variables. We do not include a base “abolish parole” term, since there are no states that abolish
parole without implementing either presumptive or voluntary guidelines. Since we include both
state and year effects in the TSLS model, we are identifying the effect of incarceration using
within-state variation in the sentencing variables after netting out common year effects.
Since we measure incarceration at the state-year level, here we employ state-level prison
counts produced by the Bureau of Justice Statistics. Moreover, since data on prison admissions
and releases are available at this level of aggregation, we add these flow rates to the specification
to test for an independent effect of correlates of prison turnover on AIDS infection rates holding
the overall incarceration rate constant.17 These data are also available from the Bureau of Justice
Statistics. By lagging the incarceration rate seven years and constructing a dependent variable
17

The results below regarding incarceration are not sensitive to the inclusion of these additional flow variables.

40

equal to the seven-year change in the cumulative number of AIDS cases per 100,000, the
coefficient on the incarceration rate reflects the cumulative of the lagged effects through lag year
seven of this variable (as well as capturing the effects of previous lags through the correlation
between lag year seven incarceration and more distant lagged incarceration rates). Concerning
the state-level AIDS infection rates, the AIDS PIDS data set provides a separate set of state-level
tabulations of the total number of AIDS cases in each state by year. These state-level totals are
provided for all AIDS cases, all AIDS cases by gender, and all AIDS cases by race.18
Before proceeding to the results, we discuss the underlying identification assumption
made herein. To identify a causal effect of incarceration on AIDS infection rates, the sentencing
variables must influence incarceration rates (be correlated with the incarceration variable) yet
influence AIDS rates only through the effect of sentencing reform on incarceration. The latter
condition implies that the sentencing reforms must be uncorrelated with any of the unobservable
determinants of AIDS infection rates that are swept into the error term of the second-stage
equation articulated above. To the extent that the introduction of these sentencing guidelines are
driven by changes in sexual behavior or behavior related to drug use, or by the crack epidemic,
then our instrumental variables fail the test for exogeneity.
While it is difficult to identify the precise motivation behind these sentencing reforms,
the extant literature on sentencing guidelines suggests a number of possibilities that have little to
do with the crack epidemic. For example, many state efforts to reform their sentencing structure
are in response to the “truth-in-sentencing” movement beginning during the mid-1970s devoted
to ensuring that sentenced felons ultimately serve an amount of time that reflects the original
sentence meted out by the trial judge. In fact, many states had to alter their sentencing regimes
to comply with a federal mandate that inmates serve 85 percent of their original sentence, or lose
federal funds (Petersilia 2003, Tonry 1998). More generally, the introduction of guidelines and
18

Recall, our AIDS infection rates used above are tabulated with the 85 percent of microdata observations where we
can observe the metropolitan area of residence and infer a state of residence. In the TSLS models presented in this
section, we are using all AIDS cases to construct the long difference.

41

abolishing of parole release authority can be viewed as attempts to increase the transparency in
sentencing and to concentrate the power of the amount of time served into the hands of state
sentencing commissions and judges (Reitz 2004). Moreover, these reforms have also been
characterized as state efforts to rationalize the state department of corrections and prevent
excessive growth in the prison population (Sorensen and Stemen 2002). To the extent that the
variation we observe reflects inter-state policy experimentation in response to a common
motivation (increase transparency, response to a federal mandate), then the variation in
incarceration rates predicted by our instruments should be exogenous.

To be sure, future

research on this question that employs alternative identification strategies is needed.19
Table 5 presents the first-stage regression results. Since there are three endogenous
explanatory variables, there are three first-stage models. Concerning the first-stage results for
the incarceration rates, each of the four sentencing reform variables is statistically significant
with an F-statistic of the joint significance of these variables equal to 10.0.

Presumptive

guidelines exert a significant negative effect on incarceration rates, a pattern consistent with
previous research (Reitz 2004, Sorensen and Stemen 2002). However, when combined with the
abolition of parole release authority, the incarceration rate is predicted to be slightly higher than

19

In addition to employing the sentencing variables as instruments, we also experimented with the prisonerovercrowding law suit variables used by Levitt (1996) in his study of the effect of incarceration rates on crime.
Levitt uses state-level law suits and court decisions pertaining to prisoner overcrowding to identify exogenous
variation in the prison population and, in turn, identify the crime-prison elasticity. In an alternative model
specification, we estimated the second-stage model above where we regressed the long difference in cumulative
AIDS cases on the seven-year lag in prison releases (since the Levitt instruments primarily impact the release of
prisoners to relieve, under court mandate, overcrowding in prison). In both OLS and TSLS models, we find
positive and significant effects of lagged prisoner releases on the long difference in cumulative AIDS cases.
Moreover, the magnitude of the effects is comparable in OLS and TSLS. However, it is difficult to interpret these
results relative to the primary questions that we seek to answer in this study. We are primarily interested in the
effect of the overall incarceration rate on the AIDS infection rate, operating through differential transmission rates in
prison, general equilibrium effects on sexual relation networks, and through any other channel. The Levitt
instruments permit us to assess the causal effect of releasing inmates a little earlier than they would otherwise be
released on overall AIDS infection rates. A positive impact of early release on AIDS infection rates is consistent
with both prison increasing the overall AIDS infection rate (by higher transmission behind bars which eventually
raises transmission rates when inmates reenter the community) and prison decreasing the overall AIDS infection rate
(no higher transmission rate behind bars but prison incapacitates high risk offenders, temporarily preventing them
from spreading the disease among members of the non-institutionalized community). Nonetheless, the positive
effect of releases on AIDS infection rates using this alternative IV strategy does document the transmission of
HIV/AIDS from ex-prisoners to the general community. These additional results are available upon request.

42

that for indeterminate states. Voluntary guidelines independently exert a positive significant
effect on incarceration rates. One explanation consistent with these findings is that in voluntary
guideline states where the guidelines are essentially non-binding on judicial behavior, judges
may face an incentive to exceed the guidelines to establish a record for being tough. However,
the abolition of parole release authority appears to moderate prison growth in these states. This
may be consistent with judges exercising greater restraint when the back-end release valve
operating through a parole board is constrained.

The first-stage effects of the sentencing

variables on prison admissions and releases are comparable.

This is not too surprising

considering that the flow into, and out of, prison are strongly correlated with the overall
incarceration rate.
Table 6 presents OLS and TSLS estimates of Equation (2) for four separate AIDS
dependent variables: the change in the cumulative AIDS infection rate among all state residents,
all men, all women, and African-Americans. For all models, we generally find positive and
significant effects of overall prison population size (per 100,000 residents) in both the OLS and
TSLS models and no measurable effects of the admission and release rates. For the overall
AIDS infection rate, the predicted marginal effect of an increase in prison population size (per
100,000 residents) is 0.7 compared to the TSLS estimate of 1.4. Both are statistically significant
at the one percent level of confidence.
The estimated effects of prison population size for the overall AIDS models among males
are somewhat larger, with an OLS estimate of 1.1 and a TSLS estimate of 2.22. The comparable
estimates for women are 0.3 and 0.6, while the comparable effects for the AIDS infection rates
for African-Americans are 0.7 and 2.3. In all models, the positive effects of prison population
size are statistically significant at the one percent level of confidence with the exception of the
TSLS estimate for black infection rates (the coefficient has a p-value of 0.052).

43

VII. Conclusion

The findings of this study are several. We demonstrate a strong positive correlation
between increases in incarceration rates occurring among men within narrowly defined
demographic groups and corresponding increases in the incidence of new AIDS infection among
both men and women. This relationship survives detailed controls for sexual relationship market
fixed effects, overall national time trends, and time trends that are specific to age, racial, and
state groups.

The estimated dynamic relationship between male incarceration and AIDS

infections resembles estimates of the probability distribution of the incubation period between
seroconversion and the onset of symptomatic AIDS. For men, the lagged effects of incarceration
peak two years after the estimated peak in the incubation distribution. For women, the added
delay is larger. This is a sensible pattern considering the greater transaction delays that are likely
to influence the effect of male incarceration rates on female AIDS infections relative to male
infections.
Moreover, given the sizable racial differentials in incarceration rates at the beginning of
the AIDS epidemic and the increases in these differentials thereafter, our model estimates
suggest that the lion’s share of the racial differentials in AIDS infections rates for both men and
women are attributable to racial differences in incarceration trends. While our models predict
that much of the post-1982 increases in the racial differential in AIDS infection rates would have
occurred had incarceration rates remained at the their 1980 levels, increasing relative
incarceration rates contributed significantly to the relatively high AIDS infection rates of
African-Americans, especially during the 1990s.
In a separate analysis, we re-estimate the relationship between male incarceration and
AIDS infection rates using within-state variation in sentencing regimes as instruments for statelevel incarceration rates. We find a strong first-stage relationship between our instruments and
incarceration rates, and TSLS estimates of the prison-AIDS effects that are positive, statistically
44

significant, and comparable in magnitude to the OLS estimates.

While we are unable to

reproduce exactly the dynamic specification providing us with our principal model estimate (due
to constraints on the dimensions of variation in our instruments), these TSLS results provide
evidence that buttress our principal analysis.

Exploring the causality of this relationship

employing alternative instrumental variables strategies provides a fruitful avenue for future
inquiry.
While we have focused explicitly on the transmission of HIV/AIDS, the theoretical story
being told here as well as the empirical analysis can easily be extended to other communicable
diseases that are thought to be transmitted among prisoners. For example, we have cited existing
evidence of higher than usual inter-personal transmission of the Hepatitis-B and Hepatitis-C
viruses as well as tuberculosis among inmates. In the recent past, there have been media reports
of the spread of a streptococcal skin infection from prisoners released from the California state
prison system to members of the non-institutionalized public. Given the large numbers of
individuals cycling through corrections systems in the United States, the more general issue of
how prison is impacting the transmission of communicable diseases broadly defined is clearly an
issue in need of further research as well as attention from policy makers.
What do these results imply for national and state-level policy debates regarding the
optimal level of incarceration? Existing research clearly documents the benefits of prison in
terms of crime reduction that extend beyond society’s desire to punish those who transgress the
law. However, imprisonment is costly, and some of the costs come in the form of unintended
consequences. To assess whether we are at, below, or beyond the optimal level of incarceration,
one would need to put a monetary value on the benefits to society in terms of the crime reduction
of incarcerating the last offender and compare these benefits to the costs. Donohue (2005)
estimates that we are currently incarcerating people at a rate beyond the point where the benefits

45

exceed the costs. Based on an annual per-inmate cost of $46,000 per year, Donohue argues that
the optimal incarceration level is roughly 300,000 persons less than the current level.
The findings of our study suggest that there are additional costs to society of
imprisonment that extend beyond the per-inmate per-year costs of incarceration.

These

additional costs include the additional medical expenditure for post-release treatment of
offenders and the treatment of others who are infected as a result of incarceration, as well as the
loss of health and happiness among those affected. While it is difficult to place a monetary value
on these factors, they certainly add to overall costs of incarceration, and their incorporation into
cost-benefit accounting would certainly lower the optimal incarceration point even further than
that estimated by Donohue.
Our results suggest that there are large and important unintended health consequences for
former offenders and for non-incarcerated members of the communities that disproportionately
send young men into the state and federal prison systems. A comprehensive assessment of
criminal justice policy in the United States should clearly be taking these considerations into
account.

46

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50

Figure 1
Annual Newly-Diagnosed AIDS Cases Per 100,000 Men Age 20t to 64 by Race/Ethnicity, 1982
to 2001
300

AIDS Cases per 100,000

250

200
Non-Hispanic White
Non-Hispanic Black
150

Hispanic
Non-Hispanic Other

100

50

0
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Figure 2
Annual Newly-Diagnosed AIDS Case Per 100,000 Women Age 20 to 64 by Race/Ethnicity, 1982
to 2001
100

90

80

AIDS Cases per 100,000

70

60

Non-Hispanic White
Non-Hispanic Black

50

Hispanic
Non-Hispanic Other

40

30

20

10

0
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

51

Figure 3
Distribution of Newly-Diagnosed AIDS Cases Per 100,000 White Men Age 20 to 64 by
Transmission Mechanism, 1982 to 2001
70

60

AIDS Cases per 100,000

50

Cause Unreported

40

Medical Procedure
Intravenious Drug Use
Sexual Contact

30

20

10

0
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Figure 4
Distribution of Newly-Diagnosed AIDS Cases Per 100,000 Black Men Age 20 to 64 by
Transmission Mechanism, 1982 to 2001
300

AIDS Cases per 100,000

250

200
Cause Unreported
Medical Procedure
150

Intravenious Drug Use
Sexual Contact

100

50

0
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

52

Figure 5
Distribution of Newly Diagnosed AIDS Cases Per 100,000 Hispanic Men Age 20 to 64 by
Transmission Mechanism, 1982 to 2001
180

160

AIDS Cases per 100,000

140

120
Cause Unreported
100

Medical Procedure
Intravenious Drug Use
Sexual Contact

80

60

40

20

0
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Figure 6
Distribution of Newly Diagnosed AIDS Cases Per 100,000 Non-Hispanic Other Men Age 20 to
64 by Transmission Mechanism, 1982 to 2001
30

AIDS Cases per 100,000

25

20
Cause Unreported
Medical Procedure
15

Intravenious Drug Use
Sexual Contact

10

5

0
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

53

Figure 7
Distribution of Newly-Diagnosed AIDS Cases Per 100,000 White Women Age 20 to 64 by
Transmission Mechanism, 1982 to 2001
6

AIDS Cases per 100,000

5

4
Cause Unreported
Medical Procedure
3

Intravenious Drug Use
Sexual Contact

2

1

0
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Figure 8
Distribution of Newly-Diagnosed AIDS Cases Per 100,000 Black Women Age 20 to 64 by
Transmission Mechanism, 1982 to 2001
100

90

80

AIDS Cases per 100,000

70

60

Cause Unreported
Medical Procedure

50

Intravenious Drug Use
Sexual Contact

40

30

20

10

0
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

54

Figure 9
Distribution of Newly-Diagnosed AIDS Cases Per 100,000 Hispanic Women Age 20 to 64 by
Transmission Mechanism, 1982 to 2001
45

40

AIDS Cases per 100,000

35

30
Cause Unreported
25

Medical Procedure
Intravenious Drug Use
Sexual Contact

20

15

10

5

0
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Figure 10
Distribution of Newly-Diagnosed AIDS Cases Per 100,000 Non-Hispanic Other Women Age 20
to 64 by Transmission Mechanism, 1982 to 2001
3.5

3

AIDS Cases per 100,000

2.5

Cause Unreported

2

Medical Procedure
Intravenious Drug Use
Sexual Contact

1.5

1

0.5

0
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

55

Figure 11
Overall Male Incarceration Rates by Race/Ethnicity, 1982 to 2001
0.100

0.090

0.080

Proportion Incarcerated

0.070

0.060

Non-Hispanic White
Non-Hispanic Black

0.050

Non-Hispanic Other
Hispanic

0.040

0.030

0.020

0.010

0.000
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Figure 12
Overall Female Incarceration Rates by Race/Ethnicity, 1982 to 2001
0.090

0.080

0.070

Proportion Incarcerated

0.060
Non-Hispanic White

0.050

Non-Hispanic Black
Non-Hispanic Other
Hispanic

0.040

0.030

0.020

0.010

0.000
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

56

Figure 13
Impact of Male Incarceration on AIDS among Males
0
2
4
6
8
% Become Advanced-stage AIDS
(Based on Incubation Dist Estimates)

Annual Male AIDS cases per 100,000
Dist Lag Incarc Efx on AIDS
0
2
4
6

Based on 13-yr Distributed Lag Model w/Sex Mkt Fixed Effects(1982-1996)

1

2

3

4

5

6

7
t...

8

9

10

11

12

13

# of Years after Male Incarceration-induced shock to Sex Market
Dist Lag Incarc Efx on AIDS
predicted Incubation_Dist_pdf_UK

Incubation Dist-pdf (SF)

Figure 14
Impact of Male Incarceration on AIDS among Females
0
2
4
6
8
% Become Advanced-stage AIDS
(Based on Incubation Dist Estimates)

Annual Female AIDS cases per 100,000
Dist Lag Incarc Efx on AIDS
.5
1
1.5
2
2.5

Based on 13-yr Distributed Lag Model w/Sex Mkt Fixed Effects(1982-1996)

1

2

3

4

5

6

7
t...

8

9

10

11

12

13

# of Years after Male Incarceration-induced shock to Sex Market
Dist Lag Incarc Efx on AIDS
predicted Incubation_Dist_pdf_UK

57

Incubation Dist-pdf (SF)

Figure 15
Actual Black-White Differences in Overall AIDS Infection Rates for Men and the Black-White
Difference After Accounting for Male Incarceration Rates
200

Black-White Difference in AIDS Incidence per 100,000

180

160

140

120
Actual Differential
100

Differential after accounting for differences in
male incarceration rates

80

60

40

20

0
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996

Figure 16
Actual Black-White Difference in Overall AIDS Infection Rates for Women and the Black-White
Difference After Accounting for Male Incarceration Rates
80

Black-White Difference in AIDS Incidence per 100,000

70

60
50

40

30

Actual differential

20

Differential after accounting for differences in
male incarceration rates

10

0
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996
-10

-20

-30

58

Figure 17
Simulated Black-White Differentials in Overall AIDS Infection Rates for Men, Allowing
Incarceration to Pursue its Historical Path and Constraining Incarceration Rates to 1980
Levels
180

Black-White Difference in AIDS Incidence per 100,000

160

140

120

100
Predicted difference, actual incaceration rate
Predicted differential, 1980 incarceration rate
80

60

40

20

0
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996

Figure 18
Simulated Black-White Differential in Overall AIDS Infection Rates for Women, Allowing Male
Incarceration to Pursue its Historical Path and Constraining Incarceration Rates to 1980
Levels
100

Black-White Differences in AIDS Incidence per 100,000

90

80

70

60
Predicted difference, actual incaceration rate

50

Predicted differential, 1980 incarceration rate

40

30

20

10

0
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996

59

Table 1: Regression Models Examining the Role of Male Incarceration Rates and Overall
Racial/Ethnic Differences in AIDS Infection Rates Among Men
AIDSrsat (any source)
Variables
Black (ref cat. White)
Hispanic
Asian

(1)

(2)

87.3739***
(2.8102)
20.9899***
(2.8613)
-35.0814***
(1.5153)

10.9101***
(3.2807)
0.4095
(2.6441)
-35.4066***
(1.3630)

Homosexually-contracted
AIDSrsat
(3)
(4)
28.8359***
(1.1620)
-3.4704**
(1.6813)
-31.3973***
(1.2082)

-14.7595***
(1.3481)
-13.9691***
(1.5089)
-30.3543***
(1.1359)

Male Incarceration Ratersat

-0.8050
(0.7792)

2.1212***
(0.2124)

Male Incarceration Ratersat-1

-0.8211***
(0.2546)

0.7073***
(0.0937)

Male Incarceration Ratersat-2

-0.3940
(0.3885)

-0.0088
(0.1070)

Male Incarceration Ratersat-3

0.3732
(0.4850)

-0.1660
(0.1229)

Male Incarceration Ratersat-4

1.3770***
(0.4303)

0.0969
(0.1102)

Male Incarceration Ratersat-5

2.5143***
(0.3045)

0.6407***
(0.0906)

Male Incarceration Ratersat-6

3.6818***
(0.2855)

1.3266***
(0.1016)

Male Incarceration Ratersat-7

4.7762***
(0.4393)

2.0156***
(0.1410)

Male Incarceration Ratersat-8

5.6942***
(0.5940)

2.5686***
(0.1762)

Male Incarceration Ratersat-9

6.3326***
(0.6453)

2.8468***
(0.1842)

Male Incarceration Ratersat-10

6.5881***
(0.5419)

2.7112***
(0.1526)

Male Incarceration Ratersat-11

6.3573***
(0.3933)

2.0228***
(0.1091)

Male Incarceration Ratersat-12

5.5372***
(0.8447)

0.6426***
(0.2222)

Male Incarceration Ratersat-13

4.0243**
-1.5683***
(1.8953)
(0.4960)
Year controls?
yes
Yes
yes
yes
State controls?
yes
Yes
yes
yes
Age group controls?
yes
Yes
yes
yes
Observations
21,060
21,018
21,060
21,018
Bootstrapped standard errors in parentheses; * significant at 10%; ** significant at 5%; *** significant at 1%
Columns 2 and 4 estimate constrained 13-yr distributed lag models, using a third-order polynomial to represent
the lag weights. These models include the same series of lagged female incarceration rates as shown for men-coefficient estimates on these variables are suppressed in the Table. All regressions are weighted by cell
frequency.

60

Table 2: Regression Models Examining the Role of Male Incarceration Rates and Overall
Racial/Ethnic Differences in AIDS Infection Rates Among Women
Variables
Black (ref cat. White)
Hispanic
Asian

AIDSrsat (any source)
(1)
(2)
31.0285***
(1.5282)
10.1768***
(1.0101)
-2.5483***
(0.3482)

-5.1316***
(1.1888)
0.4197
(0.7569)
-2.4078***
(0.4415)

Heterosexually-contracted AIDSrsat
(3)
(4)
10.9711***
(0.5100)
4.6943***
(0.3480)
-0.8652***
(0.1101)

-4.0420***
(0.5189)
0.8141**
(0.4014)
-0.6524***
(0.1497)

Male Incarceration Ratersat

-0.0907
(0.3371)

0.2204**
(0.1094)

Male Incarceration Ratersat-1

0.2442***
(0.0883)

0.2734***
(0.0372)

Male Incarceration Ratersat-2

0.5367***
(0.1334)

0.3136***
(0.0463)

Male Incarceration Ratersat-3

0.7912***
(0.1867)

0.3446***
(0.0618)

Male Incarceration Ratersat-4

1.0123***
(0.1762)

0.3696***
(0.0600)

Male Incarceration Ratersat-5

1.2047***
(0.1297)

0.3922***
(0.0484)

Male Incarceration Ratersat-6

1.3731***
(0.1036)

0.4159***
(0.0426)

Male Incarceration Ratersat-7

1.5219***
(0.1460)

0.4440***
(0.0536)

Male Incarceration Ratersat-8

1.6558***
(0.2021)

0.4800***
(0.0700)

Male Incarceration Ratersat-9

1.7795***
(0.2267)

0.5274***
(0.0785)

Male Incarceration Ratersat-10

1.8975***
(0.2069)

0.5896***
(0.0734)

Male Incarceration Ratersat-11

2.0145***
(0.2071)

0.6702***
(0.0660)

Male Incarceration Ratersat-12

2.1351***
(0.3995)

0.7724***
(0.1078)

Male Incarceration Ratersat-13

2.2638***
0.8999***
(0.7970)
(0.2174)
Year controls?
yes
Yes
yes
yes
State controls?
yes
Yes
yes
yes
Age group controls?
yes
Yes
yes
yes
Observations
21,051
21,018
21,051
21,018
Bootstrapped standard errors in parentheses; * significant at 10%; ** significant at 5%; *** significant at 1%
Columns 2 and 4 estimate constrained 13-yr distributed lag models, using a third-order polynomial to represent the
lag weights. These models include the same series of lagged female incarceration rates as shown for men-coefficient estimates on these variables are suppressed in the Table. All regressions are weighted by cell frequency.

61

Table 3: Regression Models Estimating the Effect of Male Incarceration Rates on AIDS
Infection Rates Among Men, Complete Specification
AIDSrsat (any source)
Variables

(1)

(2)

Homosexually-contracted AIDSrsat
(3)

(4)

(5)

(6)

Male Incarceration Ratersat

-2.2868*** -3.6826*** 0.7772 1.2361*** 1.6494***
(0.6770)
(0.7475) (0.6464) (0.3920)
(0.4357)

1.7982***
(0.3220)

Male Incarceration Ratersat-1

-1.9605*** -2.8746*** 0.0689
(0.3329)
(0.3606) (0.3124)

0.3691*
(0.2102)

0.8659***
(0.1556)

Male Incarceration Ratersat-2

-1.2239*** -1.8544*** -0.1575 -0.4241***
(0.2020)
(0.2412) (0.2114) (0.1170)

-0.2148
(0.1406)

0.3816***
(0.1053)

-0.2466
(0.1618)

0.2551**
(0.1203)

0.1294
(0.1678)

0.3961***
(0.1235)

0.0793
(0.1928)

Male Incarceration Ratersat-3

-0.1876
(0.2223)

Male Incarceration Ratersat-4

1.0382***
(0.2352)

Male Incarceration Ratersat-5

2.3430*** 1.7876*** 1.2128*** 0.6218*** 0.7690***
(0.2096)
(0.2501) (0.2136) (0.1214)
(0.1457)

0.7143***
(0.1064)

Male Incarceration Ratersat-6

3.6165*** 2.9645*** 2.0720*** 1.3673*** 1.5278***
(0.1695)
(0.1973) (0.1701) (0.0981)
(0.1150)

1.1194***
(0.0847)

Male Incarceration Ratersat-7

4.7483*** 4.0075*** 2.9922*** 2.0839*** 2.2617***
(0.1578)
(0.1855) (0.1663) (0.0914)
(0.1081)

1.5211***
(0.0829)

Male Incarceration Ratersat-8

5.6279*** 4.8474*** 3.8891*** 2.6349*** 2.8264***
(0.1870)
(0.2266) (0.2060) (0.1083)
(0.1321)

1.8292***
(0.1026)

Male Incarceration Ratersat-9

6.1450*** 5.4149*** 4.6785*** 2.8839*** 3.0776***
(0.2166)
(0.2652) (0.2393) (0.1254)
(0.1546)

1.9532***
(0.1192)

Male Incarceration Ratersat-10

6.1892*** 5.6407*** 5.2763*** 2.6944*** 2.8710***
(0.2098)
(0.2569) (0.2301) (0.1215)
(0.1497)

1.8029***
(0.1147)

Male Incarceration Ratersat-11

5.6502*** 5.4557*** 5.5983*** 1.9298*** 2.0625***
(0.1654)
(0.2006) (0.1848) (0.0958)
(0.1169)

1.2880***
(0.0920)

Male Incarceration Ratersat-12

4.4174*** 4.7905*** 5.5602*** 0.4537*** 0.5077***
(0.2241)
(0.2702) (0.2640) (0.1298)
(0.1575)

0.3182**
(0.1315)

Male Incarceration Ratersat-13

2.3805*** 3.5760*** 5.0778*** -1.8704*** -1.9376***
(0.5145)
(0.6252) (0.5896) (0.2979)
(0.3644)
yes
yes
yes
yes
yes

-1.1968***
(0.2937)
yes

Year controls?

-0.6911** 0.0138 -0.4104***
(0.2776) (0.2414) (0.1287)
0.5459*
(0.2879)

0.4986**
(0.2478)

-0.0163
(0.1362)

Sex Market Fixed Effect:
Race*State*AgeGroup

yes

yes

yes

yes

yes

yes

Race-specific Year Effect:
Year*Race

no

yes

yes

no

yes

yes

Age group-specific Year Effect:
Year*AgeGroup
State-specific Year Effect:
Year*State
Observations

no

no

yes

no

no

yes

no

no

yes

no

no

yes

21,018

21,018

21,018

21,018

21,018

21,018

Standard errors in parentheses; * significant at 10%; ** significant at 5%; *** significant at 1%
Columns 1-6 estimate constrained 13-yr distributed lag models, using a third-order polynomial to represent the
lag weights. These models include the same series of lagged female incarceration rates as shown for men-coefficient estimates on these variables are suppressed in the Table. All regressions are weighted by cell
frequency.

62

Table 4: Regression Models Estimating the Effect of Male Incarceration Rates on AIDS
Infection Rates Among Women, Complete Specification
AIDSrsat (any source)
Variables

(1)

(2)

Heterosexually-contracted AIDSrsat
(3)

(4)

(5)

(6)

0.0703
(0.2600)

0.0162
(0.1023)

-0.9686***
(0.1124)

-0.0182
(0.1090)

Male Incarceration Ratersat

-0.9744*** -2.4443***
(0.2436)
(0.2710)

Male Incarceration Ratersat-1

-0.2524**
(0.1202)

-0.8958*** 0.5001***
(0.1307)
(0.1256)

0.2173***
(0.0504)

-0.2536***
(0.0542)

0.2664***
(0.0527)

Male Incarceration Ratersat-2

0.3178***
(0.0720)

0.2354***
(0.0865)

0.8317***
(0.0842)

0.3522***
(0.0302)

0.2494***
(0.0359)

0.4659***
(0.0353)

Male Incarceration Ratersat-3

0.7553***
(0.0787)

1.0077***
(0.0995)

1.0802***
(0.0961)

0.4329***
(0.0331)

0.5705***
(0.0413)

0.5926***
(0.0403)

Male Incarceration Ratersat-4

1.0795***
(0.0836)

1.4795***
(0.1035)

1.2611***
(0.0990)

0.4717***
(0.0351)

0.7399***
(0.0429)

0.6585***
(0.0415)

Male Incarceration Ratersat-5

1.3096***
(0.0748)

1.7092***
(0.0901)

1.3894***
(0.0856)

0.4807***
(0.0314)

0.7876***
(0.0374)

0.6755***
(0.0359)

Male Incarceration Ratersat-6

1.4650***
(0.0606)

1.7553***
(0.0711)

1.4804***
(0.0681)

0.4722***
(0.0254)

0.7437***
(0.0295)

0.6558***
(0.0286)

Male Incarceration Ratersat-7

1.5650***
(0.0560)

1.6762***
(0.0665)

1.5494***
(0.0662)

0.4582***
(0.0235)

0.6383***
(0.0276)

0.6114***
(0.0277)

Male Incarceration Ratersat-8

1.6289***
(0.0659)

1.5303***
(0.0810)

1.6116***
(0.0817)

0.4511***
(0.0277)

0.5016***
(0.0336)

0.5543***
(0.0342)

Male Incarceration Ratersat-9

1.6760***
(0.0763)

1.3760***
(0.0949)

1.6824***
(0.0949)

0.4629***
(0.0320)

0.3636***
(0.0393)

0.4966***
(0.0398)

Male Incarceration Ratersat-10

1.7255***
(0.0741)

1.2718***
(0.0920)

1.7768***
(0.0915)

0.5058***
(0.0311)

0.2543***
(0.0382)

0.4504***
(0.0384)

Male Incarceration Ratersat-11

1.7968***
(0.0585)

1.2761***
(0.0720)

1.9103***
(0.0736)

0.5920***
(0.0246)

0.2040***
(0.0298)

0.4276***
(0.0308)

Male Incarceration Ratersat-12

1.9092***
(0.0790)

1.4474***
(0.0967)

2.0979***
(0.1046)

0.7337***
(0.0332)

0.2427***
(0.0401)

0.4404***
(0.0439)

Male Incarceration Ratersat-13

2.0819***
(0.1813)
yes

1.8439***
(0.2237)
yes

2.3551***
(0.2336)
yes

0.9431***
(0.0761)
yes

0.4004***
(0.0928)
yes

0.5007***
(0.0979)
yes

Year controls?

Sex Market Fixed Effect:
yes
yes
yes
yes
yes
Race*State*AgeGroup
Race-specific Year Effect:
no
yes
yes
no
yes
Year*Race
Age group-specific Year Effect:
no
no
yes
no
no
Year*AgeGroup
State-specific Year Effect:
no
no
yes
no
no
Year*State
Observations
21,018
21,018
21,018
21,018
21,018
Standard errors in parentheses; * significant at 10%; ** significant at 5%; *** significant at 1%

yes
yes
yes
yes
21,018

Columns 1-6 estimate constrained 13-yr distributed lag models, using a third-order polynomial to represent the lag
weights. These models include the same series of lagged female incarceration rates as shown for men--coefficient
estimates on these variables are suppressed in the Table. All regressions are weighted by cell frequency.

63

Table 5: First-Stage Results from Regressions of Prison Incarceration Rates, Prison
Admission Rates, and Prison Release Rates on State Sentencing Reform Variables and
Other Controls
Prison Incarceration Prisoner Admission
Prisoner Release
Rate
Rate
Rate
Presumptive Guidelines
-73.358***
-46.471***
-49.083***
(19.303)
(14.912)
(15.474)
Presumptive Guidelines
87.624***
56.408***
64.814***
*Abolished Parole
(23.937)
(18.493)
(19.190)
Voluntary Guidelines
98.032***
16.023
21.130
(20.643)
(15.949)
(16.550)
Voluntary Guidelines
-99.722***
-56.032***
-50.712***
*Abolished Parole
(26.821)
(20.736)
(21.518)
a
10.00
4.56
4.37
F-Statistic
(P-value)
(<0.0001)
(0.0012)
(0.0017)
N
896
896
896
*. Significant at 10%; ** significant at 5%; *** significant at 1%.
Standard errors are in parentheses. Each regression includes a complete set of state and time fixed
effects, controls for the percent black, the percent of the population between 18 to 24, 25 to 44, 45 to 64
and 65 and over, the proportion residing in metropolitan areas, and the proportion in poverty. The
regression also include controls for the seven year changes in these variables between the year
corresponding to the incarceration rate and the final year of the long difference in the cumulative AIDS
infection rates. The sample is restricted to the incarceration rates in the years 1977 to 1994. This
corresponds to long differences in the AIDS infection rates with an end year ranging from 1984 through
2001.
a. This provides the F-statistics from a test of the joint significance of the four sentencing variables in
each regression.

64

Table 6: OLS and Two-Stage Least Squares Estimates of the Effect of Incarceration Rates
and New AIDS Infections
Explanatory Variables
Prison Incarceration
Prison Admission
Prison Release Rate
Dependent
Rate
Rate
Variable and
Estimation Method
Total AIDS
Infection Rate
OLS
0.689***
0.087
-0.180*
(0.034)
(0.106)
(0.095)
TSLS
1.418***
-1.481
0.017
(0.389)
(2.048)
(2.343)
Male AIDS
Infection Rate
OLS
1.106***
0.065
-0.387**
(0.057)
(0.173)
(0.155)
TSLS
2.222***
-2.759
0.334
(0.617)
(3.246)
(3.715)
Female AIDS
Infection Rate
OLS
0.275***
0.105**
0.029
(0.015)
(0.046)
(0.042)
TSLS
0.607***
-0.268
-0.217
(0.177)
(0.931)
(1.066)
Black AIDS
Infection Rate
OLS
0.676***
0.447**
-0.205
(0.065)
(0.199)
(0.178)
TSLS
2.314*
-10.095
6.060
(1.193)
(6.278)
(7.185)
*. Significant at 10%; ** significant at 5%; *** significant at 1%.
Standard errors are in parentheses. The figures reported in the table are the coefficients on the prison
incarceration rate, prisoner admission rate, and prisoner release rate from either OLS or TSLS regressions
of each of the listed AIDS infection rates on these explanatory variables. In the TSLS models, the four
sentencing reform instruments listed in Table 5 are used as instruments for each of the endogenous
variables. All of the models include the complete set of control variables used in the first-stage models
presented in Table 5.

65