CostBenefit 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 middleschool students living in disadvantaged neighborhoods. The program offers several service components, including communityenhanced policing, case management, juvenile justice intervention, family services, afterschool 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 
(1/1beta) 
$33,640 


1.219 
$2,136 

Girls 
(1/1beta) 
$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 oneyear 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 longterm 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 longterm 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 longterm benefits.
References
French, M., H. Salomé, J. Sindelar, and A. McLellan (2002). BenefitCost Analysis of Addiction Treatment: Methodological Guidelines and Empirical Application Using the DATCAP and ASI. Health Services Research. 37(2): 433455.
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
Harrison, Nia, Nikola Juris, Dori Stern, and Steven Stern (2008). “Methodology for Youth Development CostBenefit Analyses.” http://www.people.virginia.edu/~sns5r/ccfstf/youthdevmethodology.pdf.
[1] Details of Methodology are available at Harrison,
Juris, Stern, and Stern (2008).
[3] See Harrison,
Juris, Stern, and Stern (2008) for details.
[4] Commission on Children and Families