Theoretical and Empirical Linkages Between Incarceration and Health: Inside the Prison and After Incarceration

Multiple research traditions are suggestive of a significant association between exposure to the penal system, for instance, incarceration, and later health. These include the literature on exposure to stress, research in the social gradient tradition, work on stratification and health, and life course studies.

Racial Differences in Health and the Penal System

In light of racial differences in incarceration rates, an explicit consideration of whether the incarceration system contributes to racial disparities in health is warranted. By almost any objective standard, the health of blacks is disadvantaged relative to whites (Reference SmajeSmaje 2000; Reference Hayward and HeronHayward & Heron 1999). While specific estimates vary slightly, whites can expect to live approximately six years longer than African Americans, with the gap being greater for males than females (Reference VenturaVentura et al. 1997; Reference Williams and CollinsWilliams & Collins 1995; Reference Rubio, Williams, Beech and GoodmanRubio & Williams 2004; Reference HoyertHoyert et al. 2006).

In addition, blacks are likely to live a greater portion of their lives with chronic health conditions (Reference Hayward and HeronHayward & Heron 1999; Reference HaywardHayward et al. 2000). Blacks can thus expect to live shorter lives, while dealing with more chronic pain and illness than whites. Efforts to explain racial differences in health focus on factors ranging from structural conditions to employment and lifestyle choices to psychological factors (Reference BirdBird et al. 2000). While Reference Schnittker and JohnSchnittker and John (2007) find the incarceration system is unrelated to racial differences in severe health problems, to date no research has assessed whether the penal system impacts racial differences in general health functioning.

As discussed, the rapid expansion of the penal system has not affected all racial groups equally. While specific estimates vary by subgroup (e.g., high school degree or not), minority males are five to eight times more likely to be incarcerated than comparably educated whites (Reference Pettit and WesternPettit & Western 2004). While health disparities were evident well before the expansion of the penal system, Reference Link and PhelanLink and Phelan (1995) argue that the cause of these health disparities likely changes over time. In light of evidence suggesting that the health status of blacks, relative to whites, has worsened in the same time period that roughly corresponds to the implementation of punitive incarceration initiatives (Reference CooperCooper 1993; Reference Williams and CollinsWilliams & Collins 1995; National Center for Health Statistics 2001; Reference FreemanFreeman 1996), it may be that incarceration serves as an important and under-researched factor in the study of race and health. Consistent with the theoretical notion of Reference Link and PhelanLink and Phelan (1995), the penal system may have emerged as a system of health inequality. Such findings call for an investigation into the potential contribution of incarceration to racial differences in health outcomes. The following sections of the article outline the logic, data, and methods used to examine the impact of exposure to incarceration on health, and the contribution of the penal system to racial disparities in health. While a number of theoretical and empirical linkages are evident, it is important to craft the analysis while mindful of the potential for spuriousness. It may be that some individuals engage in behavior—for instance, illicit drug use or repeated violence—that increases both the likelihood that they are unhealthy or injured and the likelihood that they will be incarcerated.

Data, Logic of Analysis, and Methods

As with related research on the life course consequences of incarceration (Reference Lopoo and WesternLopoo & Western 2005; Reference WesternWestern 2002) data from the National Longitudinal Survey of Youth 1979 (NLSY79) is used for analysis. The NLSY79 allows for an assessment of the lasting relationship between incarceration and health using a number of factors that predict incarceration and are associated with health. Moreover, the analysis can speak to specific theoretical frameworks previously introduced. For instance, the NLSY79 includes factors such as employment and poverty, which address Marmot's theoretical notions of “social gradient” (2004). Moreover, while direct measures of stress are rare in social science research, the analysis includes measures of mental health that help speak to factors such as anxiety and stress levels. Finally, measures such as marriage or education level are consistent with prior empirical and theoretical treatments of the life course determinates of health. Complete descriptions of the data and variables are presented in Table 1.

Table 1. Descriptive Statistics

In conjunction with the Bureau of Labor Statistics, data collection began in 1979, when the respondents were between ages 14 and 22 (respondents were drawn from a nationally representative sample and were incarcerated at any point over the survey period). As part of the NLSY79 collection protocol, a comprehensive health questionnaire was given to respondents during the survey period immediately after they turned age 40. As of 2002, approximately 5,500 respondents had turned 40 and answered the health 40 module of the survey.Footnote ² This group serves as the analytic sample for analysis. Respondents answered the health 40 module only once, and those who were not 40 by 2002 were omitted from analysis because they had not answered the module.Footnote ³

The health 40 module employs the physical health component of the Short Form 12 (SF-12) to ask a series of questions on the physical and mental health functioning of respondents. The SF-12 serves as the dependent variable in this analysis and is an established indicator of health functioning (Reference McDowell and NewellMcDowell & Newell 1996) that probes the degree to which health problems affect the respondent's lifestyle.

The Bureau of Labor Statistics and NLSY79 standardize these multiple responses into a single, normally distributed, variable of self-reported physical health functioning with a theoretical range of 0–100 and a mean of 50 (sample range is 29–72, sample mean is 51.11).Footnote ⁴ This indicator of self-reported physical health serves as the main dependent variable for this analysis. Self-reported health is the subject of considerable scholarly attention (Reference BoundBound 1991; Reference Browning and CagneyBrowning & Cagney 2002; Reference Hayward and HeronHayward & Heron 1999; Reference Ross and WuRoss & Wu 1996; Reference Ferraro and FarmerFerraro & Farmer 1996, Reference Ferraro and Farmer1999; Reference Idler and BenyaminiIdler & Benyamini 1997).

Focal Independent Variable and Lagged Measure of Health

The focal independent variable is incarceration. The data collection protocol is structured so that shorter incarceration spells, those less than one year, may be missed, but spells greater than one year will not be missed (Reference WesternWestern 2002). The average length of incarceration is slightly more than three years.Footnote ⁶ Accordingly, the incarceration indicator depicts invasive and prolonged exposure to a correctional setting rather than more fleeting involvement in the justice system—for instance, a short stay in jail resulting from a drunken driving arrest. Approximately 5 percent of the sample has been incarcerated, and these individuals are disproportionately members of racial minority groups. More specifically, during the time period under investigation, 270 individuals (182 minorities) were incarcerated.

As a key control variable, a lagged measure of problematic health is included in all models. Respondents are asked to report whether they have a health problem that prevents them from performing social or work functions. The data are arrayed to ensure that the measurement of prior health problems precedes risk of incarceration. Prior to incarceration, slightly more than 6 percent of the sample report having health problems. Including a lagged measure of health helps attenuate bias introduced from unmeasured heterogeneity in the sample.

While incarceration is measured each year, this analysis considers only those who were incarcerated after 1979 and prior to 1996. This is done to maintain the temporal sequence underlying the model predicting health. In addition, the models include a lagged indicator of health functioning. Formally, the final models can be expressed as:

Formula 1:

$Healt{h}_{40}=a+X_1{\beta }_1\left(bg\right)+X_2{\beta }_2\left(prison\right)+X_3{\beta }_3\left(ls\right)+X_4{\beta }_4\left(lc\right)+\varepsilon$

where X ₁β ₁(bg) is a vector of background variables, including prior health and accompanying parameter estimates, and X ₂β ₂(prison) represents incarceration history (0 for those never incarcerated, and 1 for those who were incarcerated) and associated parameter estimates of incarceration on health. Finally, X ₃β ₃(ls) and X ₄β ₄(lc) represent vectors of lifestyle and life course markers and their accompanying parameter estimates. Finally, in the regression models, the data are weighted to make the sample nationally representative.Footnote ⁷

Treatment Effects and Propensity Score Models

The estimation of treatment effects is dependent upon a counterfactual. As noted by others (Reference Winship and MorganWinship & Morgan 1999; Reference MorganMorgan 2001), it is impossible for any individual to be in both the treated and untreated state (both ever incarcerated and never incarcerated). As such, the problem can be seen as one of missing data.

Propensity score methods attempt to address this problem by using relevant background characteristics and behavioral indicators to match individuals on the basis of their likelihood to experience a treatment, in this case their likelihood of experiencing prison (Reference Rosenbaum and RubinRosenbaum & Rubin 1983; Reference Winship and MorganWinship & Morgan 1999; Reference MorganMorgan 2001; Reference HardingHarding 2003). The propensity score, which represents the conditional probability of incarceration, can be written as (Reference Rosenbaum and RubinRosenbaum & Rubin 1983):

Formula 2:

$\text{Formula}\hspace{0.17em}\text{2}:\hspace{0.17em}p\left(incarceration\right)=Pr(T_i=1|X_i)$

Where T _i=1 if individual i has ever been incarcerated, and X _i is a vector of covariates, often including multiple interaction terms, for individual i that predict incarceration or are potential confounding variables in the association between incarceration and health.Footnote ⁸

After the propensity scores and matched sample have been created, the analysis then utilizes nonparametric procedures to estimate the treatment effect of incarceration on later health. This analysis generates treatment effects using four different matching algorithms to pair incarcerated individuals (treated) with similar non-incarcerated individuals (controls) on the basis of their likelihood to experience incarceration.

This analysis uses four different matching procedures to assess the effect of incarceration on health: neighbor matching, radius matching, kernel matching, and stratification matching. As each matching procedure has potential strengths and weaknesses, the results from all four matching estimators are presented. While variants are evident across different matching procedures, the guiding principle behind each method is to create homogeneous samples by matching individuals based on their propensity scores, allowing incarceration to be treated as though it has occurred at random; the ignorable treatment assumption (Reference Rosenbaum and RubinRosenbaum & Rubin 1983; Reference Morgan and HardingMorgan & Harding 2005). Under conditions where the treated and untreated samples have identical scores across relevant variables (the covariates), the samples are considered to be balanced (Reference RubinRubin 1985; Reference MorganMorgan 2001; Reference HardingHarding 2003).Footnote ⁹ It is important to note that the analysis specifically models prior health problems as a risk factor for exposure to incarceration. This helps address concerns of spuriousness and selection. See the Appendix for more detailed information on the matching methods and sensitivity analysis.

To further ensure the homogeneity of the matched sample and confidence in the estimates, all analysis is restricted to regions of common support. In practice, restricting analysis to regions of common support excludes outliers, identified on the basis of their propensity score, from analysis. Finally, no distributional assumptions are imposed in analysis, ensuring that the estimates are derived from the actual distribution of the data (Reference MorganMorgan 2001; Reference HardingHarding 2003). The potential advantages of propensity estimators over traditional regression are discussed in more detail in Reference Joffe and RosenbaumJoffe and Rosenbaum (1999), Reference MorganMorgan (2001), and Reference Morgan and HardingMorgan and Harding (2005).

Findings

Table 2 presents the results from a series of regression equations predicting general health functioning at age 40. Model 1 shows the effect of a series of background and demographic variables on health. The results are consistent with prior research; those whose family receives public assistance, those who feel that they have less control over the direction of their lives, and those with prior health problems have poorer midlife health. Not surprisingly, prior health problems are the strongest predictor of later health. Growing up in an intact family, drug use, and self-reported crime in youth are unrelated to health at age 40.

Table 2. Background, Lifestyle, Life Course, Social Location, and Incarceration Effects on Physical Health Functioning at Age 40: Regression Results

^* p<0.05; nonsignificant 98-00-02 cohort dummies not reported.

Consistent with prior research, Model 1 indicates that whites have significantly better health functioning than minorities. Model 2 both attempts to explain racial differences in health functioning with a number of lifestyle variables and establishes a baseline model for the introduction of the incarceration indicator. Again, the results are generally consistent with prior research; for instance, those who exercise more frequently and have health insurance report better health, while cigarette smoking and increased weight have detrimental effects on health. Despite the introduction of these relevant lifestyle factors, whites still have significantly better health functioning than minorities. In fact, racial differences in health are slightly stronger in magnitude after incorporating these factors (0.769).

Model 3 introduces incarceration. The magnitude of the incarceration effect (−3.553) exceeds other factors commonly used to explain health functioning—for instance, access to insurance. This indicates that incarceration has a lasting and significant impact on physical health. Moreover, with one notable exception, the direction and significance of all other processes in Model 3 are similar to those presented in Model 2. The notable exception is race: the introduction of incarceration attenuates racial difference in health by almost 70 percent and renders racial differences nonsignificant. In addition to having a significant effect on later health functioning, this suggests that incarceration contributes to persistent racial differences in midlife health functioning.

Model 4 in Table 2 presents results using the full model specification presented in Formula 1. That is, the effect of incarceration on health is estimated when controlling for demographic, background, and health indicators prior to incarceration, and lifestyle and life course processes after incarceration. This model specification tests whether the relationship between incarceration and health is explained by other contemporaneous life course processes.

The results presented in Model 4 are again consistent with much prior work: smoking and increased weight are negatively associated with health, as is poverty status. Conversely, education, exercise, and mental health all positively affect physical health. In addition, those who are married and are in the labor force have increased health functioning.Footnote ¹⁰

In the full models, incarceration continues to exert a significantly negative effect on health. Introducing the final block of life course variables reduces the incarceration effect approximately 40 percent, from −3.553 to −2.208.Footnote ¹¹ These results indicate that, in part and in a manner predicted by prior research, incarceration works through life course processes to affect health by lowering marriage, employment, and educational prospects.

To provide additional evidence of the health-incarceration relationship, the matching methods previously described are used to further assess the relationship between incarceration and later health functioning. Given the apparent significance of incarceration in explaining racial differences in health, these methods further test the robustness and magnitude of the incarceration effect (−2.208) reported in the final model of Table 2. All indicators used to create the matching equation are measured prior to the period of risk of incarceration, and earlier regression analysis informs the selection of variables for the propensity models.

A few notes warrant discussion before moving to a consideration of the propensity models. First, in contrast to the average treatment effects estimated with regression models, the propensity estimates are derived from a sample matched on their likelihood to experience incarceration. As such, the estimates represent the average treatment effect among the treated (ATT). In addition, the matched sample is significantly more disadvantaged—both in terms of health and other social indicators—than the general population. Thus while both estimators speak to the impact of incarceration on health, the specific inferences and generalizations drawn from the estimators vary based on the analytic sample. As such, it is perhaps most informative to view the propensity models as a further, yet complementary, test of the relationship between incarceration and health.

Depending on the specific matching procedure, almost all incarcerated individuals have appropriate control matches. After the matching procedure, the sample size of the treatment groups ranges from 214 to 242 (approximately 87–98 percent of the incarcerated sample, depending on the matching procedure), and the remaining individuals in the control group are homogeneous given the covariates in the models. In all cases the balancing property is satisfied.

As reported in Table 3, incarceration significantly lowers later health functioning. While there is some variation in the magnitude of the effect based on the matching procedure, ranging from −1.505 to −2.011, the consistency of the results is striking. This demonstrates the robustness of the incarceration-health relationship even when controlling for the likelihood of experiencing incarceration with multiple matching techniques. Moreover, because nonparametric methods are utilized, the relationship is not dependent on any distributional assumptions for either the matching estimator or the incarceration effect.

Table 3. Propensity Estimators With Multiple Matching Procedures: The Treatment Effect of Incarceration on Physical Health

Notes:

^* p<0.05. Numbers in parentheses represent treated individuals with matched controls for each estimator. All analysis restricted to regions of common support.

^# Radius width set to 0.001.

From the first part of the analysis, two significant findings emerge. First, regardless of the analytic procedure and controls imposed, a significant relationship between incarceration and later health is evident. Second, using multiple methods, the effect of incarceration on health is similar or greater in magnitude to many factors traditionally associated with health, such as marital and employment status.

This analysis now moves to an explicit consideration of incarceration and racial differences in health. As shown in Table 2, racial differences in health are mediated by approximately 70 percent and become nonsignificant when exposure to incarceration is considered. Two plausible scenarios could explain this finding. First, minorities are significantly more likely to be incarcerated. As a function of this differential exposure, even if the effect of incarceration on later health is the same across races, the impact will be greater on the aggregate health of minorities because minorities are considerably more likely to be exposed to the detrimental health effects of incarceration. Essentially, this is a consideration of racial variation in aggregate exposure to the penal system. Alternatively, the impact of exposure to the penal system may be worse for minorities, a finding consistent with other work on the justice system (Reference PagerPager 2003). This suggests an interaction between incarceration exposure and minority status.

Figure 1 explores the relationship between incarceration and racial disparities in general health functioning in more detail by considering aggregate exposure to the penal system. Moreover, Figure 1 places incarceration along other systems of stratification and disadvantage. Attempts to examine racial health disparities often focus on employment and education, arguing in part that the labor market and education are systems of stratification that place minorities in a disadvantaged position relative to whites. Figure 1 locates incarceration next to these other systems of health stratification.

Notes: Disadvantage is characterized by failure to graduate college, unemployment, or having been incarcerated. The baseline represents average health differences between whites and blacks. To help assess the general impact of disadvantage across these social domains, the average health score of individuals disadvantaged in each domain is graphed next to the health status of whites and blacks who are not disadvantaged in those social domains. Accounting for disadvantage in any of these social domains has a similar impact on racial health inequalities. In addition, this shows the importance of incarceration relative to education and employment in perpetuating racial health inequalities.

Figure 1. Short form 12 reported physical health values-racial differences

For illustrative purposes, in addition to showing baseline health differences for whites and minorities, Figure 1 graphs physical health values (higher scores indicate better health) and shows the impact of disadvantage across three different social arenas. Those labeled as disadvantaged in Figure 1 are those without a college diploma, without a job, or those who have been incarcerated. Controlling for gender, Figure 1 shows significant baseline differences in health between whites and minorities. Consistent with other work, accounting for socioeconomic status such as education or employment minimizes general differences in health (Reference Williams and CollinsWilliams & Collins 1995; Reference RobertRobert 1999). In part, this is because minorities disproportionately carry the weight of disadvantage in these areas. For instance, while comprising only 36 percent of the overall sample, nonwhites represent more than half (52 percent) of those without jobs and approximately 77 percent of those without a college degree.

Figure 1 shows that incarceration works in a manner consistent with other systems of stratification; after separating those who have been incarcerated, the health profiles of whites are similar to those of minorities. As with disadvantage in educational and occupational domains, this is because minorities disproportionately face disadvantage in the penal system. With incarceration rates five to eight times higher than those of comparable whites, the aggregate health impact of incarceration is greater for the minority community. Clearly these systems of stratification are not independent of one another. Figure 1 suggests, however, that incarceration is likely another system of inequality that produces variation in health functioning.

Finally, the main effect reported in Table 2 (Model 4) and further assessed by the propensity models reported in Table 3 is decomposed. To examine a possible differential impact of incarceration, an interaction term for minorities and prison was constructed. Such a term examines if the impact of incarceration is more detrimental to the general health functioning of minorities. Consistent with other research (Reference Schnittker and JohnSchnittker & John 2007), the magnitude of the coefficient (−0.249) does not reach conventional levels of statistical significance.

The evidence then is equivocal when linking incarceration to racial disparities in health. Less clear is whether the individual-level impact of incarceration on health varies by race; the available evidence from the NLSY79 does not suggest that it does (see also Reference Schnittker and JohnSchnittker & John 2007). What is clear, however, is the strong negative effect of incarceration on health, and the disproportionate likelihood that minorities will be in the penal system. Figure 1 suggests that this disproportionate probability of incarceration has implications for racial differences in general health status.

Discussion

The penal and legal system has reached the point where the pervasive use of prison as a mechanism of social control has touched almost every aspect of contemporary American society. More than 600,000 individuals are released from prisons yearly (Reference MauerMauer 2006). As these individuals are released, the burden of their problems is shifted from the penal and legal system to general society. The health problems revealed in this analysis present yet further barriers to the successful reintegration of ex-offenders. As the number of individuals released from correctional institutions increases, so too do the social, economic, and legal implications of offender reintegration.

A developed literature on the consequences of incarceration explains part of the relationship between incarceration and physical health. Incarceration negatively impacts a number of factors, such as wages (Reference WesternWestern 2002), that are associated with health functioning. Still, even after accounting for these processes, the analysis shows incarceration to be a strong predictor of health. In so doing, this article adds to an emerging literature that finds the consequences of contact with the penal system extend into areas well outside the legal system that have not been fully appreciated in other work.

That is not to suggest this analysis is not without limitations. While the NLSY79 has many strengths, it was not specifically designed for an investigation of health and incarceration. As such, there are some data limitations. First, the dependent variable is measured at only one point in time. While propensity estimators help alleviate this concern through randomization, future work would be well served to collect repeated measures and incorporate models focusing on change in health status. Along similar lines, more specific health measures emphasized in other work, such as low birth weight (Reference Johnson and SchoeniJohnson & Schoeni 2003, Reference Johnson and Schoeni2007), would further refine an understanding of the prison-health relationship. Future work in the area would benefit from data collection designed specifically to examine the health-incarceration relationship.

In addition, both the regression and propensity models are sensitive to bias from unmeasured processes. While sensitivity analysis suggests that the problem is not a significant contaminant (see Appendix), with social science data it is virtually impossible to definitively rule out unmeasured heterogeneity. Future work might consider if the impact of incarceration on health varies by years since release. Indeed, there is rationale to suggest both that the negative effects may lessen over time and that the negative effects may worsen over time. Along similar lines, it is plausible that the incarceration spell itself—perhaps as a function of increased access to health care, daily meals, or even removal from an abusive relationship—provides some immediate health benefits to some inmates. The impact of incarceration may well be conditioned by a host of socioeconomic or other contextual factors. Finally, while this analysis considers only the United States, there may be cross-national variation in the impact of the penal system on health. Given these many possible contingencies, this analysis should be seen as but an initial step in specifying the complexities in the penal state-health relationship.

This relationship between the penal state and health is partially explained by the concept of “exposure.” Incarceration exposes individuals to a number of infectious diseases including HIV, hepatitis B, hepatitis C, and tuberculosis (Reference Farmer, Mauer and Chesney-LindFarmer 2002; Reference Talvi, Herivel and WrightTalvi 2003; Reference MassogliaMassoglia 2008; National Commission on Correctional Health Care 2002).Footnote ¹² Even short prison sentences may provide ample exposure to infectious disease and alter the potential social and medical consequences of contact with the penal system.

Research on social epidemiology, stress, and the social hierarchy suggests that the relationship between health and punishment may be driven by mechanisms beyond life course processes and infectious disease; the status of ex-con itself signals a lower position on the social hierarchy. As public awareness and concerns have risen, few labels are as stigmatizing as ex-con. Felons are viewed as the “underclass” of society (Reference IrwinIrwin 1985).

This lower standing has implications for health (Reference MarmotMarmot 2004). Moreover, the processes by which social standing impacts health—the inability of individuals to exercise control over their lives and participate fully in society—appear particularly relevant for understanding the strong association between incarceration and health. Both while inmates are incarcerated and upon their release, legislative initiatives and legal mechanisms assure that inmates face both significant public stigma and legal regulation over their lives. In explaining the relationship between incarceration and health, there is perhaps no clearer relationship than the restrictive capacity of incarceration and the justice system to prevent individuals from participating fully in society. To be sure, some of these legal restrictions are rooted in public safety, but the public good, legislative goals, and legal aims of many post-release legal sanctions—for instance, bans on voting and many government subsidy programs, as well recent initiatives to place identification markers on license plates—appear less clear.

From Reference MarmotMarmot's (2004) perspective, such restrictions could have negative implications for health by restricting individuals' societal participation and control over their life. As has been noted in other places (Reference Mauer and Chesney-LindMauer & Chesney-Lind 2002), at a minimum the cost and value of these collateral consequences—and indeed the cost and value of the widespread use of incarceration—should become a greater part of the ongoing debate about the penal and legal systems in contemporary American society.

Incarceration and Racial Inequalities in Physical Health

The second major thrust of this research assesses whether the penal system plays a role in average health differences between whites and nonwhites. Given the makeup of the NLSY79, this analysis speaks best to differences in health between blacks and whites.Footnote ¹³

Attempts to explain racial disparities in health often focus on socioeconomic indicators such as education and employment. Figure 1 indicates that incarceration effects parallel those of other classic markers of socioeconomic status and suggests that the penal system merits consideration as one of the fundamental systems of stratification that contributes to racial health disparities in general health functioning. It is noteworthy that this finding is in contrast to other work on incarceration and severe health problems (Reference Schnittker and JohnSchnittker & John 2007). Similar to earlier suggestions to further examine the contingencies in the incarceration-health relationship, further research is needed to definitively examine the conditions or measures of health status where the penal state perpetrates racial differences in health. The significant contribution of the penal state to racial differences in general health functioning may not extend to all health outcomes or specific ailments.

That said, a number of mechanisms help explain the importance of the penal system in explaining the racial differences in general health functioning found in this analysis. First, in the labor and marriage market—two key tenets of adult health—blacks appear disproportionately impacted by incarceration or contact with the legal system (Reference PagerPager 2003; Reference StaplesStaples 1987; Reference WilsonWilson 1987). Accordingly, as compared to whites, two key venues to partially overcome the detrimental health effects of incarceration are more likely to be closed for black ex-inmates. Second, as compared to whites, the application of the law is such that blacks have a much greater likelihood of contact with the penal system (Reference Pettit and WesternPettit & Western 2004). As a percentage of the overall population, many more blacks are incarcerated, which this analysis suggests has implications for aggregate minority general health functioning.

While blacks are disproportionately incarcerated, the analysis suggests that the penal system produces significant stratification in physical health for all incarcerated individuals. The penal system has expanded so tremendously that its scope and stratifying impact appear similar to that of other systems of health stratification. Recent estimates indicate that the legal and penal systems have grown to the point where there are roughly as many felons and ex-felons as college students, and there are as many inmates and ex-inmates as men in college (Reference UggenUggen et al. 2006; United States Department of Education 2003). As the footprint of the penal system takes an ever larger place in the landscape of American society, debates about the scope, goals, costs, and benefits of the penal system are needed. This research seeks to inform and contribute to those debates. To that end, it reaches two basic conclusions about the long-term consequences of incarceration. Incarceration has significant long-term effects on physical health, and incarceration plays a role in perpetuating racial inequalities in health. The effect on health appears so robust and the incarceration disparities so great, that the penal system likely warrants consideration alongside other systems of health stratification.

Appendix: Matching Models and Sensitivity Analysis

This Appendix briefly discusses each of the four matching procedures used in the analysis, beginning with neighbor matching.Footnote ¹⁴ Neighbor matching is a relatively straightforward and parsimonious way to create a matched sample for subsequent analysis. A propensity score is estimated for every individual in the sample, independent of incarceration history. The nearest neighbor matching procedure identifies the propensity score of all incarcerated individuals and then selects a non-incarcerated individual whose propensity score is closest to each incarcerated individual. In its simplest form, and using a 1–1 match, nearest neighbor matching pairs each incarcerated individual to the closest non-incarcerated unit on the basis of the estimated propensity score. Analysis is then done on the matched sample to determine the treatment effect of incarceration.

In many respects, stratification matching operates similarly to neighbor matching. However, it divides the range of variation of propensity scores into strata, or intervals, such that within each strata the treated and control units have, on average, the same propensity score. The estimated treatment effect is the average difference in health across treated and nontreated individuals in each stratum.

While neighbor and stratification matching are straightforward and conceptually simple, they are not without potential problems. In particular, if no restrictions are imposed, nearest neighbor matching, by design, selects the nontreated individuals closest to the treated individuals, independent of the actual differences in propensity scores. That is, neighbor matching takes the closest match to any treated individual, even if the closest individual is, in fact, relatively dissimilar in terms of propensity score. This problem is conceptually similar to that of outliers in traditional regression models in that individuals with poor matches (meaning a significant difference between the propensity score of the two individuals) contribute the same to the calculation of the treatment effect as individuals with identical matches. Radius and kernel matching offer solutions to this potential problem.

Radius matching allows the user to define the radius, or neighborhood, around each treated individual from which matches can be drawn. The user sets a radius, for example, 0.001 in this analysis, and all nontreated individuals whose propensity score is within 0.001 of a treated individual will be selected for analysis.Footnote ¹⁵ Finally, kernel matching invokes a matching procedure where all treated individuals are matched with a weighted average of all untreated controls that is inversely proportional to the distance between the propensity scores of the treated and the controls. Substantively, this procedure uses weights to balance the contribution of each individual in the control group. This ensures that the contribution of an individual in the control group to the calculation of the treatment effect is based on how closely the individual is matched to an individual who has experienced incarceration.

The equation used to generate the matched sample is formally presented in Formula 2. As presented in the body of the article, one key component of the equation is the vector of covariates, X _i, used to create the propensity scores.

In this article, the matching equation includes measures of race, gender, whether the respondents came from an intact family, whether the respondents' family received public assistance, high school degree completion, employment status, juvenile involvement with the justice system, self-reported drug use, acts of violence, and a series of gender and race interactions. Because individuals with unhealthy lifestyles may be disproportionately incarcerated, propensity equations used to generate the results in Table 3 also include prior health problems. In so doing, the estimates specifically account for and control whether individuals with health problems are more likely to be “selected” into incarceration.Footnote ¹⁶

The inclusion of indicators of crime and involvement with the justice system has multiple functions. First, they help ensure that the treatment effect reported in Table 3 represents an effect of incarceration as opposed to an effect of criminal behavior or more fleeting contact with the justice system, such as arrest. Moreover, including factors such as arrest, drug use, and self-reported crime has another important function: it helps create a matching equation well-suited to place individuals in the treatment state of incarceration. Indicators of criminal behavior and correctional intervention are highly predictive of incarceration status. Moreover, the specific criminal behavior indicators included, violence and drug use, are particularly predictive of incarceration (Reference Blumstein, Beck, Tonry and PetersiliaBlumstein & Beck 1999). In conjunction with socio-demographic indicators, the matching equation includes many factors that prior research indicates are key predictors of incarceration. Depending on the matching algorithm, 87–98 percent of incarcerated individuals are matched with appropriate nonincarcerated controls, with a slight variation in the number of matched individuals based on the specific matching procedure employed. While left-skewed, estimated propensity scores range from 0.001 to approximately 0.7. Important to note, the range of propensity scores is consistent across both treated and nontreated groups. Even after restricting the analysis to regions of common support, the majority of incarcerated individuals are matched with appropriate controls.

The radius matching procedure finds suitable matches for the lowest number of incarcerated individuals, 214. In part, this is a function of the highly restrictive conditions placed on how individuals are selected as controls. The radius width is set to 0.001, indicating that for an individual to be selected as a control, that individual's propensity score has to be within 0.001 of an incarcerated individual. This highly restrictive criterion further ensures the homogeneity of the sample, but it comes at the expense of the number of paired individuals. The less restrictive the radius bandwidth, the more individuals matched. In subsequent analysis, with the bandwidth increased to 0.005 and 0.01, 229 and 240 individuals respectively are matched. The substantive results do not change when these different radius bandwidths are used for analysis.

One potential weakness of propensity models is bias from unobservables. As noted by others (Reference Caliendo and KopeinigCaliendo & Kopeinig 2005; Reference Becker and CaliendoBecker & Caliendo 2007), there are a number of procedures that help assess the role of unobservables, speak to the quality of the matching procedure, and test the robustness of the treatment effect. Following the lead of Reference Caliendo and KopeinigCaliendo and Kopeinig (2005:23) multiple steps were undertaken to ensure the adequacy of the matching procedure. First, as noted earlier, in all cases the balancing property was tested for and satisfied. Moreover, tests for standardized bias indicated that the bias reduction was below the 3–5 percent generally accepted as sufficient (Reference SianesiSianesi 2004; Reference Caliendo and KopeinigCaliendo and Kopening 2005:15). Finally, t-tests were utilized to examine mean differences between the treated and the control group, and in all cases the tests failed to reach conventional levels of statistical significance. The results of all tests point to an adequate matched and control sample.

With regard to the calculation of the treatment effect(s) shown in Table 3, one sensitivity check is to estimate the parameter using multiple matching methods (e.g., kernel, neighbor) and using bootstrapped standard errors. Both were done for all the analysis presented in Table 3. Moreover, as outlined in Reference RosenbaumRosenbaum (2002), Reference DiPrete and GanglDiPrete and Gangl (2004), and Reference Becker and CaliendoBecker and Caliendo (2007), estimates were derived using the complimentary psmatch2 method, and the Rosenbaum bounds were calculated. This sensitivity analysis specifically addresses the potential role of unobservable processes in the estimation of the treatment effects presented in Table 3. It examines the departure from an analysis free of hidden bias to empirically assess how much bias from unobservables would have to be introduced to significantly alter the inferences drawn from the parameter estimates. The results indicate that the estimates in Table 3 are not overly sensitive to potential bias from unobservables. More specifically, the odds that any matched pair differs in their probability of receiving treatment due to unobservables (γ or Γ) would have to exceed 30 percent (Γ=1.3) to alter the substantive conclusions here. As such, the estimates appear robust. All sensitivity analyses are available upon request. In addition, as noted in footnote 11, the regression results remain significant even when restricting the analysis to the sibling data. Thus while almost no social science models can rule out the possibility of some unmeasured heterogeneity impacting the statistical results or substantive inferences, the available evidence—gathered through a series of sensitivity analyses—suggests that the findings presented herein are robust.