Skip to main content
SpringerLink
Log in

Race and Women’s Imprisonment: Poverty, African American Presence, and Social Welfare

  • Original Paper
  • Published:
Journal of Quantitative Criminology Aims and scope Submit manuscript

Abstract

Female imprisonment rates have increased proportionately more than male imprisonment rates over recent decades. There are substantial race differences in women’s rates, as is the case for men. Yet, there has been little quantitative research on the correlates of women’s imprisonment using data over time, or on potential race differences in those correlates. The present research analyzes data on black and nonblack female imprisonment rates in the 50 states for the period 1981–2003. The analyses are guided substantively by existing research on race, social threat and criminal punishment, and theory and research on the penal-welfare hypothesis. The study uses bivariate-response multilevel modeling to simultaneously examine the factors associated with black and nonblack women’s imprisonment rates. The results show that black female imprisonment rates increase when the concentration of African Americans in metropolitan areas and poverty rates grow, whereas nonblack female imprisonment rates are unaffected by poverty rates and actually decrease when African American populations become more concentrated in metro areas. Both black and nonblack women’s imprisonment rates increase when welfare spending declines. The results are consistent with social threat perspectives and the penal-welfare hypotheses.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Notes

  1. At midyear 2010, the male imprisonment rate was 14 times higher than the female rate, and females comprised about 7.2% of all inmates housed in state prisons whereas males comprised close to 93% (West 2010).

  2. In our empirical analyses, we refer to the categories of black and nonblack, as we determined that we could not differentiate whites from Latinos reliably for all of our state-years with our data source, the National Prisoner Statistics data. We discuss this issue further in our data section.

  3. Because male rates of imprisonment far exceed those of females, research on non-disaggregated imprisonment rates speaks mainly to patterns of male imprisonment.

  4. However, the association between unemployment rates and incarceration has received mixed support in the literature (see Chiricos and Delone 1992).

  5. Bridges and Crutchfield (1988) also found that the traditional measure of minority presence—the percentage of blacks in the total state population, regardless of their urban residence—was not associated with black imprisonment rates but increased white imprisonment rates.

  6. Yates (1997) extended the Bridges and Crutchfield analysis in a research note reporting a cross-sectional analysis of pooled data for 1990–1992, and also found that the rate ratio of black-to-white imprisonment was increased when states’ black populations were more concentrated in urban areas than was the case for whites.

  7. Research also suggests that as the size of the welfare safety net decreases, crime increases (Messner and Rosenfeld 1997; DeFronzo 1997). Generally, the argument is that generous welfare benefits show state support for poor and marginalized populations, which in turn reduces the impetus of these groups to commit crime, and thus should lead to less perceived need for imprisonment. Although the theoretical argument is somewhat different than that offered by the penal-welfare hypothesis, the prediction is similar: When states invest less in welfare, the use of imprisonment should increase.

  8. Annual sample data from the Current Population Surveys does not allow reliable estimates of race-specific poverty and female-headship for many of the state-years in our study, particularly for states with smaller black populations.

  9. Because official measures of unemployment ignore work in the home, they are questionable measures of women’s “idleness.” However, we estimated subsequent models that included race-specific as well as overall unemployment rates, and found no effects of unemployment and no meaningful departures from our reported findings. This is consistent with the mixed evidence regarding unemployment in previous research (see Chiricos and Delone 1992).

  10. As with many variables that have a large range of positive values (e.g. dollar amounts), percent changes are often more meaningful than unit changes. For example, consider increasing welfare spending (dollars per capita) in one state from 2.50 to 5.00 and from 50.00 to 52.50 in another state. The unit changes are identical (2.50 dollars) but the percent changes are quite different (100% vs. 5%). Arguably, the percent change is a better gauge of qualitative change in welfare spending. When an untransformed covariate is included in a linear model, a Δ UNIT increase in the covariate is associated with the same change in the response regardless of the level of the covariate. In contrast, when the log transformed version of the covariate, say log(covariate), is included in a linear model, a Δ PERCENT increase in the covariate is associated with the same change in response at any level of the covariate.

  11. Arrest rates reflect both male and female arrests by race, as the available data cannot be disaggregated by race and sex simultaneously.

  12. Although imprisonment rates are small, they are based on relatively large sample sizes so Normal approximations are likely reasonable. To improve the Normal approximations, we use the log transformation to mitigate boundary and skewness effects. By taking the log of the rates, we also can interpret more directly covariate effects on the rate ratios, rather than the less meaningful rate differences.

  13. Note that the random effect \( U_{it}^{*} \) is a first difference between independent random effects. Specifically, \( U_{it}^{*} \equiv U_{it} - U_{it - 1} \), where the U it are independent and identically distributed. This implies that the \( U_{it}^{*} \)’s are not independent; in fact, they have a Toeplitz correlation structure. In symbols, \( \text{cov} (U_{it}^{*} ,U_{is}^{*} ) = 2\text{var} (U_{it} ),\, - \text{var} (U_{it} ),\,{\text{or}}\,0, \) as |t − s| = 0, 1, or >1. This is precisely the Toeplitz(2) variance-covariance structure.

  14. Two percentage points is approximately the average of the within-state standard deviations in our data.

  15. The approximate average concentration of state black populations in metro areas across states and over time in our data was 80%.

  16. We re-estimated our models and determined that the effect of percent of blacks in metro areas does not depend on the percentage of blacks in the state population. (In other words, there is no concentration of blacks in metro areas * % black state population interaction.) Our diagnostics also reveal that there are no detectable issues concerning multicollinearity among these variables and/or any of our variables.

  17. The across-state and over-time average in AFDC/TANF spending per capita in our data is approximately $50.

  18. Other analyses showed that the effects of welfare spending were not dependent on the black population or poverty rate variables; these interaction effects were not statistically significant.

  19. Here, “sizable” means large relative to the within-state 23-year average of Latino percent (i.e. 5 percentage points above the within-state average).

  20. Although the assessment of race-specific male imprisonment is important, including males in our analysis would detract from our goal of focusing attention on women’s incarceration, which has received much less research attention than men’s incarceration. Not surprisingly, our preliminary analyses suggest the need for different covariates and explanations for male imprisonment rates by race.

  21. Again, incorrectly treating the two regressions as independent—that is fitting the two regressions separately—would lead to incorrect standard errors associated with the cross-equation differences between effect estimates.

References

  • Asen R (2003) Women, work and welfare: a rhetorical history of images of poor women in welfare policy debates. Rhetoric Public Aff 6:285–312

    Article  Google Scholar 

  • Baumer E, Messner S, Rosenfeld R (2003) Explaining spatial variation in support for capital punishment: a multilevel analysis. Am J Sociol 108:844–875

    Article  Google Scholar 

  • Beck A, Harrison P (2001) Prisoners in 2000. Bureau of Justice Statistics, Washington, DC

    Google Scholar 

  • Beckett K, Sasson T (2004) The politics of injustice: crime and punishment in America, 2nd edn. Pine Forge Press, Thousand Oaks, CA

    Google Scholar 

  • Beckett K, Western B (2001) Governing social marginality: welfare, incarceration, and the transformation of state policy. Punish Soc 3:43–59

    Article  Google Scholar 

  • Blalock H (1967) Toward a theory of minority-group relations. Wiley, New York

    Google Scholar 

  • Blumstein A, Beck A (1999) Population growth in U.S. prisons, 1980-1996. Crime Justice Rev Res 26:17–61

    Article  Google Scholar 

  • Bobo L, Hutchings V (1996) Perceptions of racial group competition. Am Soc Rev 61:951–972

    Article  Google Scholar 

  • Bridges G, Crutchfield R (1988) Law, social standing and racial disparities in imprisonment. Social Forces 66:699–724

    Google Scholar 

  • Carbone-Lopez KC, Kruttschnitt C (2003) Assessing the racial climate in women’s institutions in the context of penal reform. Women Crim Justice 15:55–79

    Article  Google Scholar 

  • Chesney-Lind M (2002) Imprisoning women: the unintended consequences of mass imprisonment. In: Mauer M, Chesney-Lind M (eds) Invisible punishment: the collateral consequences of mass imprisonment. The Free Press, New York, pp 79–94

    Google Scholar 

  • Chiricos T, Crawford C (1995) Race and imprisonment: a contextual assessment of the evidence In Hawkins D (ed) Ethnicity, race and crime, SUNY Press Albany, New York, pp 281–309

  • Chiricos T, Delone M (1992) Labor surplus and punishment: a review and assessment of theory and evidence. Soc Prob 39:421–446

    Article  Google Scholar 

  • Chiricos T, Eschholz S (2002) The racial and ethnic typification of crime and the criminal typification of race and ethnicity in local television news. J Res Crime Delinq 39:400–420

    Article  Google Scholar 

  • Chiricos T, Hogan M, Gertz M (1997) Racial composition of neighborhood and fear of crime. Criminology 35:107–132

    Article  Google Scholar 

  • Corcoran M, Danziger S, Kalil A, Seefeldt K (2000) How welfare reform is affecting women’s work. Ann Rev Soc 26:241–269

    Article  Google Scholar 

  • Covington J, Taylor R (1991) Fear of crime in urban residential neighborhoods: Implications of between- and within-neighborhood sources for current models. Soc Quart 32:231–249

    Article  Google Scholar 

  • D’Alessio S, Eitle D, Stolzenberg L (2005) The impact of serious crime, racial threat and economic inequality on private police size. Soc Sci Res 34:267–282

    Article  Google Scholar 

  • Daly K (1994) Gender, crime and punishment. Yale University Press, New Haven, CT

    Google Scholar 

  • DeFronzo J (1997) Welfare and homicide. J Res Crime Delinq 34:395–406

    Article  Google Scholar 

  • Dixon T, Linz D (2000) Overrepresentation and underrepresentation of African Americans and Latinos as lawbreakers on television news. J Commun 50:131–154

    Article  Google Scholar 

  • Dixon T, Linz D (2002) Television news, prejudicial pretrial publicity and the depiction of race. J Broadcast Electron Media 46:112–136

    Article  Google Scholar 

  • Eitle D, D’Alessio S, Stolzenberg L (2002) Racial threat and social control: a test of the political, economic, and threat of black crime hypotheses. Soc Forces 81:557–576

    Article  Google Scholar 

  • Enos S (1998) Managing motherhood in prison: the impact of race and ethnicity on child placements. Women Therapy 20:57–73

    Article  Google Scholar 

  • Entman R (1992) Blacks in the news: television, modern, racism and cultural change. J Quart 69:341–361

    Article  Google Scholar 

  • Ferraro K, Moe A (2003) Mothering, crime, and incarceration. J Contemp Ethnograph 32:9–40

    Article  Google Scholar 

  • Frees E (2004) Longitudinal and panel data: analysis and applications in the social sciences. Cambridge University Press, New York

    Book  Google Scholar 

  • Frost N, Greene J, Pranis K (2006) Hard hit: the growth in the imprisonment of women, 1977–2004. Institute on Women and Criminal Justice, Women’s Prison Association

  • Garland D (1985) Punishment and welfare: a history of penal strategies. Gower Publishing, Brookfield, VT

    Google Scholar 

  • Garland D (2001) The culture of control: crime and social order in contemporary society. University of Chicago Press, Chicago

    Google Scholar 

  • Gartner R, Kruttschnitt C (2004) A brief history of doing time: the California Institution for Women in the 1960s and 1990s. Law Soc Rev 38:267–304

    Article  Google Scholar 

  • Greenberg D, West V (2001) State prison populations and their growth, 1971–1991. Criminology 39:615–653

    Article  Google Scholar 

  • Hamilton J (1994) Time series analysis. Princeton University Press, Princeton, NJ

    Google Scholar 

  • Haney L (2004) Gender, welfare and states of punishment. Soc Politics Int Stud Gender State Soc 11:333–362

    Article  Google Scholar 

  • Hawkins D, Hardy K (1989) Black-white imprisonment rates: a state by state analysis. Soc Jus 16:75–94

    Google Scholar 

  • Jackson P (1989) Minority group threat, crime, and policing: social context and social control. Praeger, New York, NY

    Google Scholar 

  • Jacobs D, Carmichael J (2001) The politics of punishment across time and space: a pooled time-series analysis of imprisonment rates. Soc Forces 80:61–91

    Article  Google Scholar 

  • Jacobs D, Carmichael J (2002) The political sociology of the death penalty: a pooled time-series analysis. Am Soc Rev 67:109–131

    Article  Google Scholar 

  • Jacobs D, Carmichael J (2004) Ideology, social threat, and the death sentence: capital sentences across time and space. Soc Forces 83:249–278

    Article  Google Scholar 

  • Jacobs D, Helms R (1996) Toward a political model of incarceration: a time-series examination of multiple explanations for prison admission rates. Am J Sociol 102:323–357

    Article  Google Scholar 

  • Jacobs D, Helms R (1999) Collective outbursts, politics, and punitive resources: toward a political sociology of spending on social control. Soc Forces 77:1497–1523.

    Google Scholar 

  • Kauermann G, Carroll R (2001) A note on the efficiency of sandwich covariance matrix estimation. J Am Stat Assoc 96:1387–1396

    Article  Google Scholar 

  • Keen B, Jacobs D (2009) Racial threat, partisan politics and racial disparities in prison admissions: a panel analysis. Criminology 47:209–237

    Article  Google Scholar 

  • King RD, Wheelock D (2007) Group threat and social control: race, perceptions of minorities and the desire to punish. Soc Forces 85:1255–1280

    Article  Google Scholar 

  • Kruttschnitt C, Gartner R (2003) Women’s imprisonment. Crime Justice 30:1–81

    Google Scholar 

  • Kruttschnitt C, Gartner R (2005) Marking time in the golden state: women’s imprisonment in California. Cambridge University Press, New York, NY

    Google Scholar 

  • Liska A, Lawrence J, Benson M (1981) Perspectives on the legal order: the capacity for social control. Am J Sociol 87:413–426

    Article  Google Scholar 

  • Liska A, Lawrence J, Sanchirico A (1982) Fear of crime as social fact. Soc Forces 60:760–771

    Google Scholar 

  • Mauer M (1999) Race to incarcerate. The New Press, New York, NY

    Google Scholar 

  • Mauer M, Potler C, Wolf R (1999) Gender and justice: women, drugs and sentencing policy. The Sentencing Project, Washington DC

    Google Scholar 

  • McCorkel J (2004) Criminally dependent? Gender, punishment and the rhetoric of welfare reform. Soc Politics Int Stud Gender State Soc 11:386–410

    Article  Google Scholar 

  • Messner S, Rosenfeld R (1997) Political restraint of the market and levels of criminal homicide: a cross-national application of institutional anomie theory. Soc Forces 75:1393–1413

    Google Scholar 

  • Michalowski R, Pearson M (1990) Punishment and social structure at the state level: a cross-sectional comparison of 1970 and 1980. J Res Crime Delinq 27:52–78

    Article  Google Scholar 

  • Monnat SM (2010) The Color of welfare sanctioning: exploring the individual and contextual roles of race on TANF case closures and benefit reductions. Sociol Quart 51:678–707

    Article  Google Scholar 

  • Owen B (1998) “In the Mix”: struggle and survival in a women’s prison. SUNY Press, Albany, NY

  • Patillo M (1999) Black picket fences: privilege and peril among the black middle class. University of Chicago Press, Chicago, IL

  • Pfaff JF (2005) The continued vitality of structured sentencing following Blakely: the effectiveness of voluntary guidelines. UCLA Law Rev 54:235–307

    Google Scholar 

  • Quillian L (1996) Group threat and regional change in attitudes toward African Americans. Am J Sociol 102:816–860

    Article  Google Scholar 

  • Raudenbush S, Bryk A (2002) Hierarchical linear models: applications and data analysis methods. Sage Publications Inc, Thousand Oaks, CA

    Google Scholar 

  • Rusche G, Kirschheimer O (1939/1968) Punishment and social structure. Russell and Russell, New York

  • Sabol WJ, Rosich K, Mallik-Kane K, Kirk DP, Dubin G (2002) The influences of truth-in-sentencing reforms on changes in states’ sentencing practices and prison populations. The Urban Institute, Washington, DC

    Google Scholar 

  • Schram S (2005) Contextualizing racial disparities in American welfare reform. Perspect Politics 3:253–368

    Google Scholar 

  • Sokoloff N (2005) Women prisoners at the dawn of the 21st century. Women Crim Justice 16:127–137

    Article  Google Scholar 

  • Sorensen J, Stemen D (2002) The effect of state sentencing policies on incarceration rates. Crime Delinq 48:456–475

    Google Scholar 

  • Spelman W (2008) Specifying the relationship between crime and prisons. J Quant Criminol 24:149–178

    Article  Google Scholar 

  • Stemen DS, Rengifo AF (2006) Of fragmentation and ferment: State sentencing policies 1975–2002. A final report to the National Institute of Justice for Grant # 2002-IJ-CX-0027

  • Stemen DS, Rengifo AF (2011) Policies and imprisonment: the impact of structured sentencing and determinate sentencing on state incarceration rates, 1978–2004. Just Quart 28:174–201

    Article  Google Scholar 

  • Stucky TD, Heimer K, Lang JB (2005) Partisan politics, electoral competition, and imprisonment: an analysis of states over time. Criminology 43:211–248

    Article  Google Scholar 

  • Stucky TD, Heimer K, Lang JB (2007) A bigger piece of the pie? State corrections spending and the politics of social order. J Res Crime Delinq 44:1–33

    Article  Google Scholar 

  • Stults B, Baumer E (2007) Racial threat and police force size: evaluating the empirical validity of the minority threat perspective. Am J Sociol 113:507–546

    Article  Google Scholar 

  • Tonry M (1995) Race, crime, and punishment in America. Oxford, New York, NY

    Google Scholar 

  • Wacquant L (2000) Deadly symbiosis: when ghetto and prison meet and mesh. Punish Soc 3:95–134

    Article  Google Scholar 

  • Watts J (1997) The personal responsibility and work opportunity reconciliation act of 1996: the end of work and the end of welfare. Contemp Sociol 26:409–415

    Article  Google Scholar 

  • West HC, Sabol WJ, Greenman SJ (2010) Prisoners in 2009. Bureau of Justice Statistics, Washington, DC. http://bjs.ojp.usdoj.gov/content/pub/pdf/p09.pdf.

  • Western B (2006) Punishment and inequality in America. Russell Sage, New York, NY

    Google Scholar 

  • White H (1980) A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48:817–838

    Article  Google Scholar 

  • Yates J (1997) Racial incarceration disparity among states. Soc Sci Quart 78:1000–1010

    Google Scholar 

  • Yates J, Fording R (2005) Politics and state punitiveness in black and white. J Politics 67:1099–1121

    Article  Google Scholar 

  • Zellner A (1962) An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias. J Am Stat Assoc 57:348–368

    Google Scholar 

Download references

Acknowledgments

The authors thank the reviewers for their helpful comments and Paige Harrison at the Bureau of Justice Statistics for making data available to us. This research benefited from the institutional support of the Public Policy Center at the University of Iowa.

Author information

Authors and Affiliations

  1. University of Iowa, Iowa City, IA, USA

    Karen Heimer & Joseph B. Lang

  2. University at Albany, State University of New York, Albany, NY, USA

    Kecia R. Johnson

  3. Rutgers University, Newark, NJ, USA

    Andres F. Rengifo

  4. Loyola University Chicago, Chicago, IL, USA

    Don Stemen

Authors
  1. Karen Heimer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kecia R. Johnson
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Joseph B. Lang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Andres F. Rengifo
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Don Stemen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Karen Heimer.

Appendices

Appendix 1: Variable Descriptions and Sources

All variables are computed for every state-year in the data set.

Female Imprisonment Rate by Race = total numbers of adult female inmates under jurisdiction by race (black, nonblack) divided by the adult female population (black, nonblack). Sources: U.S. Bureau of Justice Statistics: Prisoners in State and Federal Institutions, Correctional Populations in the United States and unpublished agency data. Adult female populations by race were obtained from unpublished data for 1981–1989 furnished by the U.S. Census Bureau, and data downloaded from the U.S. Census Bureau website (“Annual Time Series of County Population Estimates by Age, Sex, Race, and Hispanic Origin”) for subsequent years.

Percent Black = total number of black state residents divided by the total population, and multiplied by 100. Source: Data for 1981–1989 are unpublished data furnished by the U.S. Census Bureau. Data from 1990 onward were downloaded from U.S. Census Bureau website, “Annual Time Series of County Population Estimates by Age, Sex, Race, and Hispanic Origin.”

Percent Black in Metropolitan Areas = total number of black residents in metropolitan counties divided by the total state black population, and multiplied by 100. Source: Data for 1981–1989 are unpublished data furnished by the U.S. Census Bureau. Data from 1990 onward were downloaded from U.S. Census Bureau website, “Annual Time Series of County Population Estimates by Age, Sex, Race, and Hispanic Origin.”

Percent Latino = total number of Latino or Hispanic state residents, divided by total population, and multiplied by 100. Source: 1981–1989 comes from an interpolation using the 1980 and 1990 Decennial Census Data, because annual state-level estimates are unavailable. Data from 1990 onward were downloaded from U.S. Census Bureau website, “Annual Time Series of County Population Estimates by Age, Sex, Race, and Hispanic Origin.”

Poverty Rate = total number of state residents living below the poverty line, divided by the total population and multiplied by 100. Source: Statistical Abstracts of the United States, 1981–2003.

Percent Female-Headship = total number of families in state that are headed by females, divided by total number of families and multiplied by 100. Source: Statistical Abstracts of the United States, 1981–2003.

AFDC/TANF per Capita = total AFDC or TANF payments in dollars per state-year divided by the state population and adjusted to 1983 dollars by the Consumer Price Index. Source: U.S. Administration for Children and Public Assistance, taken from the Statistical Abstract of the United States, 1981–2003.

Reported Crime Rates = the number of UCR crimes known to the police committed per 100 persons. Aggregated across Part I index offenses of murder, rape, robbery, aggravated assault, burglary, larceny, and auto theft. Source: Uniform Crime Reports collected by the Federal Bureau of Investigation, as reported in the Statistical Abstract of the United States.

Arrests for Index Crimes by Race = the number of UCR arrests of adult blacks and nonblacks (all other races combined) per 100 black and nonblack adults, respectively. Aggregated across Part I index offenses of murder, rape, robbery, aggravated assault, burglary, larceny, and auto theft. Source: Uniform Crime Reports collected by the Federal Bureau of Investigation, made available on the National Consortium of Violence Research Data Center http://www.ncovr.heinz.cmu.edu/Docs/datacenter.htm.

Presumptive Sentencing Laws = binary variable coded 1 if a state were operating under presumptive sentencing guidelines in a given year and 0 otherwise. Source: Stemen and Rengifo (2006).

Determinate Sentencing = binary variable coded 1 if a state had determinate sentencing in a given year and 0 otherwise. Source: Stemen and Rengifo (2006).

State Population = number of state residents (in millions). Source: Data for 1981–1989 are unpublished data furnished by the U.S. Census Bureau. Data from 1990 onward were downloaded from Census website “Annual Time Series of County Population Estimates by Age, Sex, Race, and Hispanic Origin.”

Gross State Product = total Gross State Product (GSP) in thousands of dollars, divided by the state population and adjusted to 1983 dollars by the Consumer Price Index. Source: Bureau of Economic Analysis, http://www.bea.gov/regional/.

State sentencing policies = (used in supplemental analyses only).

  • Minimum sentence for heroin/cocaine offenses = Statutory minimum prison sentence (in months) for possession of 1 oz (28 grams) of heroin or cocaine. Source: Stemen and Rengifo (2006).

  • Minimum sentence for marihuana = Statutory minimum prison sentence (in months) for possession of 1 pound (453 grams) of marihuana. Source: Stemen and Rengifo (2006).

  • Sentencing enhancements for marihuana, heroin or cocaine sales = Additive scale reflecting the presence/absence of up to eight different sentencing enhancements applicable to sales of marihuana, heroin or cocaine. These enhancements are tied to the attributes of the offense (large quantity), or location (near a park) among others. Source: Stemen and Rengifo (2006).

  • Mandatory sentencing of drug offenses = binary variable coded 1 if a state required judges to alter statutory sentences for drug offenses involving an underage victim and 0 otherwise. Source: Stemen and Rengifo (2006).

Appendix 2: Model Fit Assessment and Analysis of Residuals

Our final model fit well. In Fig. 3, we show the observed and fitted percent changes in black female imprisonment. In states with a greater proportion of the population that is African-American, and hence higher signal-to-noise ratios, the fitted values track the observed values reasonably well. In states with smaller black populations, and hence lower signal-to-noise ratios, the fitted values are smoothed toward the observed average. Similar patterns were observed for nonblack female imprisonment, but are not included here in the interest of space. The pseudo-R2, defined as the square of the weighted correlation coefficient between the observed and fitted response values, is R2 = 0.35. Thus the variability in the covariates can account for a significant part of the variability in the responses. Our final model showed no signs of problematic multicollinearity.

Fig. 3
figure 3

Observed vs. fitted percent changes in black female imprisonment for select states

Full size image

Residual analyses did not indicate significant model lack of fit, nor did they lead to the deletion of any observations. There were several residuals that were relatively large in absolute value. We checked the corresponding observations to assess their influence on coefficient estimates and qualitative conclusions (see the influence analysis below). Based on the results of the influence analyses, we decided to leave these observations in to avoid artificially deflating the variability. To accommodate the possibility of incorrect specification of the error structure, we computed the empirically-adjusted variance matrix (cf. White 1980) and compared it to the model-based variance matrix. Both the empirically-adjusted and model-based variances led to the same conclusions of statistical significance/non-significance. We used the model-based variance estimate because the empirically-adjusted variance estimators may be of questionable validity in this setting where there are relatively few independent contributions, n = 50 states, and many observations per state (see Kauermann and Carroll, 2001.)

We assessed the estimation influence of each of the 50 states and each of the 2,107 individual observations. The states that had the most influence on the estimation of coefficients, as measured by Cook’s D, were California (D = 0.4), Illinois (D = 0.21), Texas (D = 0.23), and New York (D = 0.10). We checked the influence of these states on the estimation of individual coefficients: The coefficient on black metropolitan proportion in the black regression model becomes more significant when Illinois is dropped from the model. None of the other coefficient estimates change by more than one standard error when any of these states are dropped, and their statistical significances do not change. The most influential individual observations were those corresponding to the black and nonblack responses in Illinois 1983 (D = 0.282, 0.260) and 1984 (D = 0.225, 0.15), and the black response in Illinois 1991 (D = 0.13). The coefficient on black metropolitan proportion in the black regression model becomes more significant when Illinois 1991 is dropped from the model. None of the other coefficient estimates change by more than one standard error when any of these observations are dropped, and their statistical significance does not change. In summary, the influence analyses showed that our conclusions about the statistical significance and direction of the effects are not unduly influenced by any particular state or any particular observation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Heimer, K., Johnson, K.R., Lang, J.B. et al. Race and Women’s Imprisonment: Poverty, African American Presence, and Social Welfare. J Quant Criminol 28, 219–244 (2012). https://doi.org/10.1007/s10940-011-9144-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10940-011-9144-8

Keywords

Search

Navigation