Example: Projecting the Juvenile Commitment Population in 2002

The following section presents an example of a projection model using data about the national population of juvenile offenders committed to residential facilities.2 The analysis provides several different projections, each based on a different set of assumptions. The results from each set of assumptions reveal the sensitivity of population projections to changes in policy and practice, including changes in the rate of referral, the rate of adjudication, the number of out-of-home placements, and the average length of those placements. The range of projections based on these varying assumptions helps to set upper and lower bounds on the future size of the national commitment population. The analysis uses data from 1993 to 1997 to project populations through 2002. The results suggest that a major determinant of change in the commitment population originates outside the juvenile court—namely, the number of referrals by law enforcement. The relative rates of adjudication and placement and changes in average lengths of stay also affect the size of commitment populations. (Trends in these components of delinquency case processing between 1993 and 1997 are summarized below.)

Delinquency Case Processing, 1993–97

The number of juveniles in commitment increased from 37,700 in 1993 to 52,500 in 1997. The increase was due to a number of factors—the growth in the number of referrals to juvenile court, changes in the rate of adjudication, changes in the rate of residential placement, and changes in lengths of stay.

Referral

  • The total number of delinquency cases referred to juvenile courts that involved youth ages 10 to 17 increased 19 percent between 1993 and 1997, from approximately 1.4 to nearly 1.7 million.

  • Cases involving property offenses accounted for half of all court referrals in both years.

  • The rate of growth was largest among drug cases, which more than doubled, and for public order offenses, which grew more than 30 percent.

Adjudication

  • Between 1993 and 1997, the number of cases resulting in adjudication increased 26 percent.

  • The number of adjudicated cases increased in every major offense category.

  • The rate of adjudication (the number of adjudications divided by referrals) increased 2 percent. The rate was stable for all major offense categories.

Placement

  • From 1993 to 1997, the percentage of adjudicated cases involving youth ages 10 to 17 that resulted in residential placement was relatively stable at 31 to 32 percent.

  • The use of placement was constant for property and public order offenses. For drug offenses, the use of placement decreased from 32 to 27 percent.

  • For person crimes, the use of residential placement dropped from 35 to 32 percent of adjudications.

Length of Stay

  • The average length of stay for committed juveniles increased 14 percent between 1993 and 1997, from 96 to 109 days.

  • Most of the growth in length of stay was driven by person crime offenders (whose average length of stay increased from 162 to 180 days) and by property crime offenders (89 to 104 days).

  • Length of stay increased from 22 to 49 days for public order offenders and decreased from 148 to 113 days for drug offenders.

Note: These data differ from other published analyses of National Juvenile Court Data Archive data because cases involving youth under age 10 or older than age 17 are excluded, as are technical violation cases. Percent changes were calculated using unrounded numbers.

Source: Urban Institute analysis of data from NCJJ’s National Juvenile Court Data Archive. National estimates of delinquency cases involving youth ages 10 to 17.

According to data collected for OJJDP by the U.S. Bureau of the Census, the daily size of the committed juvenile population in custody for delinquency offenses increased 38 percent between 1993 and 1997, from 52,000 to 71,700 (see table 1). For this example, however, several adjustments to these data are necessary.3 First, the raw data most likely underestimate the number of juveniles in private facilities during the 1993–95 period. Adjusting for this undercount produces slightly higher figures.4 The data are also adjusted to account for the fact that although many youth in the commitment population at any given time are older than 17, very few are older than 17 at the time of their commitment. Adjusting the data for age allows the analysis to compare more directly the data on commitment populations with data on commitment admissions.5 The analysis also limits the commitment population to juveniles who were placed in residential facilities for new offenses. Juveniles committed for technical violations of probation are excluded. After making these adjustments, the analysis suggests that the juvenile commitment population increased 39 percent between 1993 and 1997, from 37,700 to 52,500.

uvenile Offenders in Residential Placement, 1993-97
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To generate estimates of the future commitment population, a statistical flow model is used that analyzes the processing of delinquency cases to the point of placement and models the lengths of stay in placement. The model begins with a starting population and calculates transition rates (or probabilities that cases will move from one stage of the juvenile justice process to the next). The flow model includes the following stages: (1) referral to juvenile court, (2) adjudication, (3) commitment to residential placement, and (4) length of stay for youth in residential placement. Transition probabilities include the adjudication rate (the percentage of referred cases that are adjudicated), the use of residential placement (the percentage of adjudicated cases that are committed to residential facilities), and the average length of stay in facilities (measured as a stock-to-flow ratio; see discussion of length of stay).6 These transition probabilities are shown in table 2.

Referrals to Juvenile Court and Transition Probabilities for Youth in Residential Placement, 1993 and 1997
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Changes in the commitment population can be shaped by a variety of case processing components, including the number of juvenile court referrals, the percentage of those referrals that result in adjudication, the number of those cases that end in residential placement, and the length of those placements. As these components increase or decrease, they exert an influence on the size of the commitment population. It is possible to isolate the changes in each component and determine the share of the total change in the commitment population for which each is responsible (see Methodology). Certain components may contribute to growth, while others may have the opposite effect. For example, if the number of court referrals increases, this will contribute to an expansion of the commitment population. At the same time, other elements of the system could curtail growth. A decrease in the use of placement could offset part or all of the growth generated by increasing referrals. Adding up the “shares” from all components of juvenile justice case processing yields the overall net change in the commitment population.

Change in Number of Juveniles Committed to Residential Placement Between 1993 and 1997, by Category of Offense and Components of Change
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Table 3 and figure 5 show how each component of the system contributed to the amount of overall change in the commitment population between 1993 and 1997. Several factors contributed to the expansion of this population from 37,700 to 52,500 juveniles. Increases in the number of court referrals, the rate of adjudication, and the average length of stay all contributed to the expansion, while the decrease in the use of residential placement had a curtailing effect.

How much did each source of change contribute to the overall change in the population of juveniles in commitment from 1993 to 1997?
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Of the four major offense categories (person, property, drugs, public order), person and property offenses accounted for most (each about one-third) of the total change in the commitment population. Increases in the number of commitments for public order and drug offenses accounted for approximately 27 percent and 9 percent, respectively, of the change in the commitment population.

Increases in length of stay accounted for 80 percent of the growth in the commitment population of offenders charged with public order offenses. For those charged with drug offenses, increases in the number of youth referred—which more than doubled between 1993 and 1997—overrode the generally downward trend of all other transition probabilities (the adjudication rate, the use of placement, and average length of stay) associated with these offenders. Although there were minor offense-specific variations from the overall sources of change, all of the major offense categories contributed to the increase in the number of juveniles committed to residential facilities (table 3).

The commitment population through 2002 is projected in the analysis by using a mathematical flow model based on the approach first developed by Stollmack (1973) to project prison populations (see “A Brief History of Corrections Population Projection Methods”). Future populations are projected by relating flows to stocks by length of stay—the inverse of which represents the turnover rate of the population. The model requires explicit assumptions about the case processing factors that might influence the size of confinement populations. For example, the model must include assumptions about changes in referrals and length of stay. Will the number of court referrals continue to rise through the year 2002, or will it stabilize at the 1997 level? Will average length of stay increase or decrease? Assumptions about how these components will or will not change after 1997 have a significant effect on projections of the juvenile population in facilities. The following analysis considers several possible scenarios to project a range of 2002 commitment populations.

Five projections of the commitment population were developed, each based on a different set of assumptions (figure 6). These projections (referred to as A, B, C, D, and E) yield commitment populations ranging from almost 53,000 to more than 102,000 by the year 2002 (figure 7). For example, if 1997 conditions were to persist for 5 years after 1997 (projection A), the number of juveniles in commitment facilities in 2002 would be expected to remain at the 1997 level (about 53,000 juveniles). In other words, if juvenile courts were to continue to commit juveniles to residential placement at the 1997 rate, to adjudicate cases at the 1997 rate, and to hold juveniles in facilities for an average of 109 days, just as in 1997, the commitment population would remain at the 1997 level.

Five assumptions are used to define alternative projections of the juvenile commitment population, 1998-2002 Conditions in the juvenile justice system rarely remain unchanged for several years at a time. There are specific reasons to doubt that the conditions of 1997 would continue for very long beyond 1997. First, the commitment population was growing at an increasing rate between 1993 and 1997. Second, the number of cases referred to juvenile courts also increased, and this was responsible for a large part of the total increase in the commitment population. In addition, the average length of stay changed between 1993 and 1997, growing from 96 to 109 days. Improbable changes in case processing would have had to occur for admissions and length of stay to have remained constant after 1997. For admissions to stabilize, for example, the increase in the number of referrals to juvenile court between 1993 and 1997 would have had to reverse itself after 1997 or the use of residential placement would have had to decrease sharply. These changes are unlikely, given trends observed between 1993 and 1997.

Projections of the juvenile commitment population vary greatly according to assumptions about future conditions On the other hand, if changes in case-processing practices were incorporated into the projections, the expected population could follow the paths of projection lines B, C, D, or E. These projections show how the juvenile population in residential placement would change based on varying assumptions about admissions and the average length of stay for committed youth. Under projection B (stable length of stay, admission trends continue), the population would increase to almost 69,000 in the year 2002. Under projection C (stable admissions, trends continue in length of stay), the population would grow to about 75,000 by 2002. Projection D shows how the population would change given the assumption that admissions and length of stay each continue the trend observed from 1993 to 1997. It projects that the commitment population would grow at a steep rate, increasing to just more than 98,000 by 2002.

These projections point out the importance of the key policy variables (the rate of referral to court, the rate of adjudication, the use of placement, and the length of stay of youth in residential placement) in anticipating future demand for bedspace. Each of these variables represents important considerations for policy and practice. The number of youth referred to court reflects the volume of delinquent acts in the community, but it also reflects the policies and priorities of the juvenile justice system, the availability of alternatives to secure confinement, and the range of diversion options. The amount of time juveniles spend in residential facilities is a function of offense seriousness, but it also reflects policy decisions about the use of secure confinement and the availability of postrelease supervision. (For a discussion of why length of stay is important and how it is measured, see Length of Stay.)

These relatively simple projection models can also be used to consider different policy and program choices and to simulate their effects. For example, suppose juvenile justice officials know that the average length of stay for youth committed for drug offenses will increase significantly because of plans to administer more drug treatment during confinement. Assume that the new drug treatment programs will increase the average length of stay for drug offenders by 5 percent each year between 1998 and 2002. For all other offenders (nondrug), length of stay will follow the average annual trends seen during the 1993–97 period. Under these assumptions, the commitment population would nearly double from 53,000 in 1997 to about 102,000 in 2002 (projection E). Thus, the addition of drug treatment programs and their effect on length of stay for drug offenders could increase the commitment population by almost 4,000 (the difference between projection D and projection E).

These examples suggest how projection models could be used to anticipate future commitment populations, given varying assumptions about future conditions. The value of these examples is limited by the lack of more detailed data. For instance, the models presented here divide the commitment population into only four categories of offenders—person, property, drug, and public order. Obviously, projections would be even more useful if offenses could be divided into additional categories (e.g., felony or misdemeanor, weapon or weaponless, drug possession or drug sales). Moreover, when agencies wish to apply projection models in actual decisionmaking situations, they would prefer even more data. In addition to dividing the juvenile population by offense, projection models can sometimes be calculated separately for juveniles who are drug dependent, those who are known flight risks, those who have school problems, those with educational deficits, etc. Ideally, projection models should be calculated for any categories or factors that may be involved in actual agency decisions about the use of juvenile bedspace in detention or correctional facilities.

Length of Stay: Why It Is Important and How It Is Measured

Changes in the size of juvenile corrections populations can be understood in relation to the number of people who move into and out of facilities (or “flow”) and the length of time that they stay in facilities (length of stay). Length of stay is a critical ingredient in projections of juvenile custody populations. A corrections or detention population can change dramatically if a facility’s length of stay begins to change, even if admissions are stable. Measuring length of stay, however, can be challenging. There are three commonly used methods of estimating length of stay.

Estimation Methods

Exit Cohort
The most popular measure of length of stay is the average amount of time spent in corrections by a group of youth released during a given period of time. Known as an “exit cohort” estimate, this technique for estimating length of stay is easy to calculate and easy to interpret. However, it can underestimate the length of time individuals actually spend in correctional facilities. By definition, exit cohorts contain a disproportionate number of individuals who had short stays.

Calculating an exit-cohort estimate of length of stay is easy once the necessary data are assembled. The following example shows the data for an exit cohort of five individuals released between April 1 and June 1. By combining their admission dates and release dates and calculating each person’s length of stay, it is possible to determine that this cohort’s average length of stay was 87 days.

Calculating Average Length of Stay With Data
for an Exit Cohort


Cohort
Members
Admission
Date
Release
Date
Length of Stay
(in days)

Person A
Person B
Person C
Person D
Person E
Average
    January 1
    January 1
    February 1
    February 1
    April 1
     April 1
     April 10
     April 23
     May 15
     June 1
             90
           100
             82
           104
             61
             87

Days Since Admission

Another common measure of length of stay is the average number of days that the current population of a detention or correctional facility has been in the facility as of a certain day. This measure is easy to calculate, but it can also involve considerable bias. As with the exit-cohort estimation technique, it involves just one source of data (the current “stock”).

In addition, average “days since admission” can significantly overestimate length of stay because the current population of any facility necessarily contains a disproportionately large number of individuals who have had long stays.* If “days since admission” is the only estimate possible with existing data, however, it can still be useful. The following is an example of a “days since admission” estimate for a population containing five individuals. Using only today’s date and the admission dates for all members of the population, it is possible to determine that the average length of stay for this population is 39 days.

Calculating Average Length of Stay Using “Days Since Admission”

Members
of the
Population
Admission
Date
Today’s Date Days Since
Admission

Person A
Person B
Person C
Person D
Person E
Average
        January 1
        February 1
        March 1
        March 15
        March 31
         April 1
         April 1
         April 1
         April 1
         April 1
            90
            59
            31
            16
              1
            39

Stock/Flow Ratio

A third method of estimating length of stay is to calculate a ratio of “stocks” and “flows,” where stock and flow are defined as follows:

Stock = the number of youth in a population on a given day (or some measure of average daily population).

Flow = the number of youth released from the population over a given period of time, usually monthly or annually. (If data on actual releases are not available, admissions data can be used to estimate “flows,” but this assumes admissions and releases are in equilibrium over the time period of interest.)

A stock/flow ratio can also be a biased estimator for length of stay if the size of the population or the release rate is changing rapidly. The extent of the bias, however, may be less than that of other estimates since stock/flow ratios involve information from two sources (stock and flow). Calculating length-of-stay estimates with stock/flow ratios can be fairly simple once the appropriate information is available. The following two examples present length-of-stay estimates as stock/flow ratios.

Example 1: Assume that a juvenile correctional facility had an average daily population of 300 during the preceding year, and assume that 425 juveniles were released during the year. Using this information, an analyst could estimate the facility’s length of stay by dividing the stock (300) by the flow (425), which would suggest that juveniles stayed in the center for an average of (300/425) years—or 259 days.

Calculating Average Length of Stay as a Stock/Flow Ratio:
Example 1

Stock—average daily population in placement

Flow—juveniles released during previous year

Stock/flow ratio in years (300/425)

Length of stay in days (0.71 X 365)

300

425

     0.71

259


Example 2: Assume that a juvenile detention center has a population of 100 today, and assume that the director of the center considers today’s population typical. If 85 juveniles were released from the center during the previous month, a forecaster could estimate the center’s length of stay by dividing the stock (100) by the flow (85), which would suggest that juveniles stayed in the center for an average of (100/85) months—or 36 days.

Calculating Average Length of Stay as a Stock/Flow Ratio:
Example 2

Stock—average daily population in placement

Flow—juveniles released during previous month

Stock/flow ratio in months (100/85)

Length of stay in days (1.18 X 30.4 )

100

  85

     1.18

  36


Estimation Bias

As any measure of length of stay is likely to involve bias, corrections planners may want to use several estimators to understand how the length of time served is changing. By understanding the conditions that characterize the corrections system—such as increasing admissions and slowing rates of release—the user of length-of-stay information can assess the likely direction of the bias in the measures of length of stay. Once the potential direction of the bias in each measure is assessed, the measures can be compared and conclusions can be drawn about whether persons are spending more, less, or about the same amount of time in custody.

Length of Stay in This Bulletin

This Bulletin presents an analysis of the change in the juvenile commitment population between 1993 and 1997, and it projects the commitment population for the year 2002. Both these analyses require measuring average length of stay. After considering and computing several measures of length of stay, including “exit cohort” and “days since admission” measures, the authors decided to use stock/flow measures to provide the estimates of length of stay used in these analyses. The bias inherent in a stock/flow ratio is usually less than it would be for other length-of-stay measures (i.e., exit cohorts and days since admission), and using the stock/flow ratio provided a consistent and uniform method of measuring length of stay that was conducive to measuring the change in length of stay over the period.

A stock/flow measure for length of stay was calculated for 1993 and 1997 using data on the number of out-of-home placements taken from NCJJ’s National Juvenile Court Data Archive (NJCDA) and data on the number of youth in corrections taken from OJJDP’s Children in Custody (CIC) census and its Census of Juveniles in Residential Placement (CJRP). The use of admissions rather than releases is required because national-level data on releases are not available. This choice assumes that releases are estimated by admissions. Under this assumption, if admissions are greater than releases (likely during the study period), then a stock/flow ratio may underestimate length of stay. Conversely, if admissions are less than releases (unlikely during the study period), then a stock/flow ratio would overestimate length of stay. The table below displays the stock/flow ratios used in the analyses presented in this Bulletin.

Offense 1993 CIC
Stock/NJCDA
Flow Ratio (days)
1997 CJRP
Stock/NJCDA
Flow Ratio (days)

Total

Person

Property

Drugs

Public order

    96

  162

    89

  148

    22

    109

    180

    104

    113

      49


* Using “days since admission” to estimate a facility’s total length of stay would be similar to estimating the life expectancy of Americans by calculating the average age of all people alive now.

Number of days in the average month, 365/12.



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Anticipating Space Needs in Juvenile Detention and Correctional Facilities Juvenile Justice Bulletin March 2001