Cost-Benefit Evaluation for the Children at Risk Program

Nia Harrison, Nikola Juris, Dori Stern, and Steven Stern

 

The Children at Risk program is a youth development program targeting middle-school students living in disadvantaged neighborhoods. The program offers several service components, including community-enhanced policing, case management, juvenile justice intervention, family services, after-school and summer program activities, tutoring and homework educational services, and mentoring (Guide, 2003). Using an evaluation of this program by Harrell, Cavanagh, and Sridharan (1999), we calculated the net benefits of the program based on our evaluations of its costs and benefits. These evaluations are shown below in Table 1. Furthermore, some of the assumptions that we made in the initial calculations were then altered to determine the sensitivity of our analysis and are shown in Table 2.[1]

 

 

           

Table 1

 

 

 

Boys

Girls

Effect on the short term probability of not using gateway drugs

0.14

0.14

Effect on the long run probability of not using drugs

0.07

0.07

Effect on the long run probability of not selling drugs

0.09

0.09

Effect on the probability of not committing a crime

0.065

0.065

Effect on the probability of graduating high school

0.041

0.041

The probability of being convicted/committing a crime

0.088

0.088

Average high school wage rate per hour

$15.00

$13.50

Annual earnings

$30,000

$27,000

Cost of the program

$4,700

$4,700

Annual benefit of not doing drugs

$5,103

$5,103

Annual benefit of not selling drugs

$0

$0

Annual benefit of not being in jail

$41,080

$40,228

Annual benefit of not committing a crime

$37,841

$37,841

Other potential benefits

$561

$505

Discount factor

0.9

0.9

Long term benefit of not using drugs

$3,572

$3,572

Long term benefit of not selling drugs

$0

$0

Long term benefit of not going to jail

$26,702

$26,148.20

Long term benefit of other potential benefits

$5,606

$5,046

Net benefit of the program

$33,640

$32,526

           

Harell, Cavanagh, and Sridharan (1999) found that the Children at Risk program reduced the short term probability of using gateway drugs by 14%, the long run probability of using drugs by 7%, and the long run probability of selling drugs by 9%. Furthermore, it reduced the probability of committing a crime by 6.5%.[2]  The probability of getting convicted conditional on committing a crime is 8.8%.[3]  Harrell, Cavanagh, and Sridharan (1999) also estimated that the cost of the program per child is $4700.  We calculated the program’s effect on the probability of graduating high school by making the probability of committing a crime and the probability of graduating high school proportional between this program and those of the Service Learning program. In addition, we needed to make other assumptions in order to progress further. We assumed that an average male (female) high school graduate earns $15.00 ($13.50) per hour. Assuming one works 2000 hours per year, we have base annual earnings of $30,000 ($27,000) for males (females).

 

Table 2

 

 

Net Benefit of the Program

Average high school wage per hour

Boys

$15

$33,640

 

 

$30

$44,785

 

Girls

$13.50

$32,526

 

 

$27

$42,556

Annual benefit of not committing a crime

Boys

$37,841

$33,640

 

 

$18,920

$32,410

 

Girls

$37,841

$32,526

 

 

$18,920

$31,296

Discount factor

Boys

0.9

$33,640

 

 

0.8

$15,700

 

Girls

0.9

$32,526

 

 

0.8

$15,143

Annual benefit of not selling drugs

Boys

$0

$33,640

 

 

$10,000

$42,640

 

Girls

$0

$32,526

 

 

$10,000

$41,526

Depreciating benefits

Boys

(1/1-beta)

$33,640

 

 

1.219

$2,136

 

Girls

(1/1-beta)

$32,526

 

 

1.219

$2,001

Cost

Boys

$4,700

$33,640

 

 

$24,520

$13,820

 

Girls

$4,700

$32,526

 

 

$24,520

$12,706

 

 

 

 

 

In the base scenario, we assume costs are incurred for only one year. Adjusting estimates from French et al. (2002) to fit a one-year time period, we calculated that the annual benefit of not doing drugs is $5,103 and conservatively assumed that there is no annual benefit to not selling drugs. The annual benefit of no jail time was calculated by adding the cost of jail,[4] $32,560, to the amount that one’s annual earnings would be reduced as a result of being imprisoned. We calculated the benefit of no crime as the cost to the victim of the crime (assumed to be $3330) multiplied by the program’s effect on the probability of committing a crime (6.5%) divided by the program’s effect on not getting arrested (8.8%). Other potential benefits involve the increase in annual earnings one would attain from graduating high school. This was calculated as the annual earnings of a high school graduate multiplied by the percentage of these earnings that are a result of graduating from high school, 4.6%,  multiplied by the program’s effect on the probability of graduating high school, 4.1%. This results in a benefit of $561 ($505) for men (women). In order to translate these calculations into long-term benefits, we used an annual discount factor was 0.9.  We calculated the long term benefit of not using drugs as the decrease in probability of using drugs multiplied by the annual benefit of not using drugs, and then added up the discounted benefits over the remainder of the individual’s life. We used similar calculations for the long term benefit of not committing a crime. Other potential benefits were discounted for the remainder of one’s life, resulting in a long term benefit of $5,606. We assumed there are no long term benefits of not selling drugs. Adding up all of the long term benefits and  then subtracting the cost of the program, we are left with a net benefit of the program for boys (girls) of $33,640 ($32,526).

 

In Table 2, we changed various assumptions we had made for the base case, one at a time while holding the others constant, in order to measure the sensitivity of the base case analysis. First, changing the hourly wage received by a high school graduate to double the base assumption yields a new net benefit of $44,785 ($42,556) for boys (girls). If we reduce the annual benefit of not committing a crime by half, we get a new net benefit of $32,410 ($31,296) for boys (girls). Next, changing the discount factor from .9 to .8 resulted in a new net benefit of $15,700 ($15,143) for boys (girls). Assuming that there is a $10,000 benefit of not selling drugs rather than no benefit yields a net benefit of $42,640 ($41,526) for boys (girls).  

 

There was significant concern that the benefits of the program would dissipate over time.  To measure the impact of this concern, we considered the possibility that benefits would depreciate by 80% per year during teen years.  Harrell, Cavanagh, and Sridharan (1999) estimates the average age of participation in the Children at Risk program for students to be 12, implying 6 years of depreciation. This leads to a different multiplier for the discounting of future benefits, listed in Table 2 under “Depreciating Benefits.”  Without depreciation, as in the base case, the multiplier is 10; with depreciation, it falls to 1.219.  The reduction in the multiplier causes long-term benefits to decrease to $4,377 ($4,241) for boys (girls). Subtracting the cost yields a new net benefit of the program to be $2,136 ($2,000) for boys (girls).

 

One way to deal with this concern is to consider the possibility that the participant would continue with the program every year until he/she is 18 years old, thus not allowing for dissipation of benefits. This implies an extra cost of program participation, resulting in a new cost of $24,520 and a new net benefit of the program of $13,820 ($12,706) for boys (girls).

 

By examining the net benefit of the program and all of the sensitivity analyses, we see that the data indicate that the Children at Risk program is expensive but worthwhile, yielding high long-term benefits.

 

References

 

French, M., H. Salomé, J. Sindelar, and A. McLellan (2002). Benefit-Cost Analysis of Addiction Treatment: Methodological Guidelines and Empirical Application Using the DATCAP and ASI. Health Services Research. 37(2): 433-455.

 

Guide to Effective Programs for Children and Youth: Children at Risk (2003). http://www.childtrends.org/Lifecourse/programs/ChildrenAtRisk.htm.

Harrell, A., S. Cavanagh, and S. Sridharan (1999). “Evaluation of the Children at Risk Program: Results 1 Year After the End of the Program.” National Institute of Justice. http://www.ncjrs.gov/pdffiles1/nij/178914.pdf.

 

Harrison, Nia, Nikola Juris, Dori Stern, and Steven Stern (2008). “Methodology for Youth Development Cost-Benefit Analyses.”  http://www.people.virginia.edu/~sns5r/ccfstf/youthdevmethodology.pdf.

 

 



[1] Details of Methodology are available at Harrison, Juris, Stern, and Stern (2008).

[2] We assumed that these behavioral changes do not vary with gender as there was lack of any information to the contrary.

[4] Commission on Children and Families