"Cost-Benefit" is an exercise encountered in most APPs but not in all. Most APPs will have a "Cost-benefit" Criteria or a "Cost-Effectiveness" criteria. When including this criteria you will need to perform a costing exercise. There are two types of costing exercises: Cost-Benefit analysis (CBA) and Cost-Effectiveness (CEA). Most of you will probably perform a CEA.
Cost Effectiveness (CEA)
This is a technique that relates the costs of a program to its key outcomes or benefits. This ratio summarizes how "cost-effective" is a program at a particular goal.
For example, imagine a problem statement around high-school dropout rates. The analyst will compare different programs and how they mitigate high-school dropout rates.
Alternative 1: Increase # of school counselors
Alternative 2: CBT Summer Program
Alternative 3: Mentoring Program
For each alternative we can estimate a cost-effectiveness ratio by accounting the cost and the expected change in the dropout rate.
Alternative | Total Cost | Unit of Effectiveness | Cost-Effectiveness |
Increase # of school counselors | 1000 | 4 | $250 per student |
CBT Summer Program | 2000 | 5 | $400 per student |
Mentoring Program | 3500 | 6 | $583.3 per student |
I could change the unit of effectiveness to a "percentage point decrease in the dropout rate. Then the cost-effectiveness ratio would be: $250 per percentage point decrease in the HS dropout rate.
Formula
The first "key" part is to obtain the total cost of the program. This is done by accruing all cost of a giving program. In our example, we should think about taking into account:
- Wages paid to individual (salary? hourly?)
- Do we need to get equipment?
- Do we need to rent out a place?
- Material?
- Communication materials?
- Financial incentive?
The second key part is to determine the unit of effectiveness. This is straightforward when the program has a clear goal. However, even when that's the case the information may not be readily available, therefore one has to decide on a metric that is attainable across alternatives. Let’s over the following alternatives as an example.
Alternative 1: Increase # of school counselors
For this alternative, we have a paper that compares the dropout rate from schools with and without counselors, and compares schools with different counselor-per-students ratios. (Extensive and intensive margin).
Alternative 2: CBT Summer Program
For this alternative, we have a paper that studies the effect of a CBT program on crime but also on dropout rates, and they find an effect of "3 percentage point reduction in dropout rates" from the program.
Alternative 3: Mentoring Program
For this alternative, you have a brief that informs you that an in a mentoring program and 80 out of 100 kids ended up graduating.
You would have to convert all of those to one particular metric. Let's say you've decided to create a effect on decrease the dropout rate for all of them.
For the first alternative, we then use the numbers to estimate the potential decrease in the dropout rate from our alternative. This means, we would need to figure out first how much will our alternative shift the counselor-per-student ratio. Let's say this ratio will increase from 2 per 100 student to 5 per 100 student. Then we would need to estimate how much does an increase in 1 counselor per 100 student affects the dropout rate. From the study we could back out that increasing the counselor 1 per 100 students decreases the dropout rate by 0.01. This is saying that having one more counselor decreases the likelihood of dropout by 1 percentage point. Then since our program will increase it by 3 counselors, our total effectiveness will be 3 percentage points. Then our CE ratio will be something $1000/3= $333.33 per percentage point decrease in the dropout rate.
For the second alternative, we would need to understand if the scale of the programs are the same on the cost-side, but we can use the fact that the study already gives us a dropout rate effectiveness of 3 percentage points. Therefore the CEA ratio will be $2000/3= $667.7 per percentage point.
For the third alternative, we would first have to estimate the dropout rate out of the people in the program, this is around 20%, then we would need to compare it to a dropout rate for people not in the program (maybe a neighborhood or nearby school overall dropout rate) let's say that's about 18%. Then this implies that the program potential reduction on dropout rate is 2 percentage points. Notice that this is not a program that was "randomized" to that estimate has bias. This is a good place to pause and think about the potential direction of the bias. In this case, by reading about the program we learned that the program targeted people, and so we expect the effect to be biased upwards. That means that we expect the largest possible effect size is 2 percentage points. We can use this estimate, or we can use other studies from lit-review to use a mean estimate of say 0.5 percentage points. (Is not pivotal to spend much time on this decisions, just note why you making a decision and move on, you'll play with this in the sensitivity section). This estimate will imply a $7000 per percentage point.
Example in the wild: Medicaid and Mortality effects
Cost-Benefit Approach
The cost-benefit approach, aims to measure the potential benefits (direct and indirect) and cost of the given policy. This approach may be suited for different situations. Let's illustrate this with an "extreme" example. Imagine a problem about reducing poverty. The government of Peru pushes a policy of mass sterilization among poor women. The policy is relative cheap, but effective. Hence it would rank "high" under a cost-effectiveness analysis. Nevertheless it would rank "low" on a cost-benefit analysis that internalizes cost-to-society. (If you use a CEA in this case, you may want to add another criteria that captures human-rights issues…)
A cost-benefit analysis has two components: including monetary and non-monetary accounting exercise. The first step is to account all the monetary cost and benefit, and then include the non-monetary component.
Monetary: taxes, income, future income. To assess the value to society, the analyst would consider all the costs and benefits that accrue to taxpayers, neighbors, participants, competing organizations, or any number of other groups that are affected by the program under study.
Example in the wild: Effect of Education on Crime
Steps towards a Costing Exercise
Example: Costing a Program
Cost it over time
Adding Expected benefits
For Benefit Cost, converting benefits to $
Discounting and Obtaining Present Value
Money in the future is not as valuable as money today. Hence we discount the "future" to value it in the present. In the most simple example, I can pay $1 for a soda today, or pay $0.50 for a soda in a week. This implies that a soda in a week is worth less today than in the future.
How to obtain present value of dollars in the future?
Where t is how many periods into the future.
Example: In 2011, the city of Dallas considered upgrading its stadium. The cost of the upgrade would be a total of $20,000 in 2011 and $20,000 in 2012. What is the total cost in present value? The interest rate in 0.05 and these prices have already been adjusted for inflation.
Today, t=0 PV=20K
Next year, t=1
Total cost today is $39,047.62
Now imagine that this investment will pay of in 2014, $47,000. Will it be worth making the investment?
What's $47,000 today?
This means that today the stadium will cost $39,047.62 and the value of the revenue today is $35,072. This means that it doesn't make sense to invest in the stadium today. Why is this the case? this is because I could use that money today and get a better return on my investment and get the interest rate.
What would happen if the interest rate were 8%?
Total cost: $38,518.52
Total revenue: $29,617.98
Still not worth it.
For benefit and cost:
