Prevalence of Imprisonment in the U.S. Population, 1974-2001

by Thomas P. Bonczar

4. The number of living persons at each age who had ever gone to prison was then calculated by summing the number going to prison for the first time during that year of age (column 5) plus the number of members of the 1980 birth cohort who previously went to prison and survived until the next year of age (column 6 times the survival rate, not shown).

* Of the 1,132 persons who had gone to prison and reached age 20, 1,131 survived to reach age 21. An additional 343 persons were expected to be incarcerated for the first time before reaching age 22 (for a cumulative total of 1,474).

5. The percent of persons at each specific age who had ever gone to prison (column 7) was then calculated by dividing the number of persons who had ever gone to prison and were still alive (column 6) by all persons who were still alive (including persons never incarcerated plus ever incarcerated).

* Among persons age 21, the prevalence rate was 1.510%, obtained by dividing 1,474 (column 6) by 97,646 (column 1 minus columns 3 and 5, plus 1,474), times 100%.

Prevalence rates for other birth cohorts were calculated using similar procedures. For example, to estimate the percent of persons age 31 in 2001 who had ever gone to prison, the calculations were applied to the 1970 birth cohort. However, the rates of first incarceration (column 4) and mortality (column 2) used in the calculations were unique to the birth cohort. (Note the differences between Appendix tables 2 and 3.)

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+Appendix table 2. Estimating the prevalence of imprisonment in the
U.S. population for persons born in 1980+
Population of 100,000 births, 1980, reduced by mortality and
incarceration in each successive year of age
Number alive
and not Rate of first Surviving
incarcerated admission to Expected cumulative
at beginning Number Expected State or number of number of
Age at of age dying per number of Federal prison first first Prevalence
first interval 100,000 deaths[a] per 100,000 admissions admissions[c] percent[d]
admission Year (1) (2) (3) (4) (5) (6) (7)
0-13 1980-93 100,000 ... 1,732 0 0 0 0.000%
14 1994 98,268 44 43 1 1 1 0.001
15 1995 98,224 57 56 5 5 6 0.006
16 1996 98,163 73 72 39 38 44 0.045
17 1997 98,053 84 83 135 132 176 0.180
18 1998 97,838 93 91 283 277 453 0.462
19 1999 97,470 93 91 346 337 789 0.806
20 2000 97,043 94 91 355 344 1132 1.158
21 2001 96,607 96 92 356 343 1474 1.510
Note: Calculations for ages 0 to 13 were based on data for each
single year of age and then grouped for presentation.
... Not shown, because calculations were based on rates for single
years of age.
[a] To estimate the number expected to die at each year of age,
age-specific mortality rates(column 2) were multiplied by the number
of persons alive and not previously incarcerated (column 1).
To estimate the number expected to go to prison at each year of
age, age-specific first admission rates (column 4) were multiplied
by the number of persons surviving (column 1 minus column 3).
[c] To estimate the surviving number of first admissions, the number
of first admissions from the x-th year of age (column 5) were added
to the number of surviving first admissions from the x-1 year of age.
Mortality rates for ex-prisoners by age were based on mortality rates
in the general population and adjusted to reflect higher ex-prisoner
mortality.
[d]To estimate the prevalence percent, this procedure was followed.
The surviving number of persons ever incarcerated (column 6) was
divided by the total number of surviving persons never incarcerated
(column 1 minus both columns 3 and 5) and persons ever incarcerated
(column 6), times 100%.
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Appendix table 3. Estimating the prevalence of imprisonment in the
U.S. population for persons born in 1970
Population of 100,000 births, 1970, reduced by mortality and
incarceration in each successive year of age
Number alive Rate of first
and not admission Surviving
incarcerated to State Expected cumulative
at beginning Number Expected or Federal number of number of
of age dying per number of prison per first first Prevalence
Age at first interval 100,000 deaths[a] 100,000 admissions admissions[c] percent[d]
admission Year (1) (2) (3) (4) (5) (6) (7)
0-13 1970-83 100,000 ... 2,099 0 0 0 0.000%
14 1984 97,901 49 48 1 1 1 0.001
15 1985 97,852 62 61 0 0 1 0.001
16 1986 97,791 73 71 24 23 24 0.025
17 1987 97,697 86 84 74 73 97 0.099
18 1988 97,539 96 94 186 181 278 0.285
19 1989 97,265 102 99 265 258 535 0.549
20 1990 96,907 107 103 331 320 855 0.878
21 1991 96,484 110 107 266 257 1,110 1.142
22 1992 96,121 113 109 305 293 1,402 1.444
23 1993 95,719 111 106 272 260 1,660 1.711
24 1994 95,353 108 103 279 266 1,924 1.985
25 1995 94,984 104 99 230 218 2,139 2.210
26 1996 94,668 100 94 232 219 2,356 2.436
27 1997 94,354 100 94 217 205 2,558 2.648
28 1998 94,055 97 92 257 241 2,796 2.897
29 1999 93,722 102 95 218 204 2,997 3.108
30 2000 93,422 104 97 275 257 3,250 3.374
31 2001 93,068 110 102 218 203 3,448 3.584
Note: Calculations for ages 0 to 13 were based on data for each
single year of age and then grouped for presentation.
... Not shown, because calculations were based on rates for
single years of age.
[a] To estimate the number expected to die at each year of age,
age-specific mortality rates(column 2) were multiplied by the number
of persons alive and not previously incarcerated (column 1).
To estimate the number expected to go to prison at each year of
age, age-specific first admission rates (column 4) were multiplied
by the number of persons surviving (column 1 minus column 3).
[c] To estimate the surviving number of first admissions, the number
of first admissions from the x-th year of age (column 5) were added
to the number of surviving first admissions from the x-1 year of age.
Mortality rates for ex-prisoners by age were based on mortality rates
in the general population and adjusted to reflect higher ex-prisoner
mortality.
[d] To estimate the prevalence percent, this procedure was followed.
The surviving number of persons ever incarcerated (column 6) was
divided by the total number of surviving persons never incarcerated
(column 1 minus both columns 3 and 5) and persons ever incarcerated
(column 6), times 100%.
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Limitations

1. The data in this report are restricted to incarcerations in State or Federal prison. Excluded are prior incarcerations in local jails and juvenile facilities because of the lack of data needed to estimate the number of first admissions to these forms of correctional supervision.

2. Estimates of the number of first admissions are subject to sampling and nonsampling errors. Because the numbers of first admissions are based on a sample rather than a complete enumeration, the estimated number of first admissions may vary depending on the size of the estimate and the base population for each demographic group.