Chapter 8 Cost Benefit Analysis

Cost benefit analysis is the formal process of computing all the costs of a project or policy and all the benefits of the project or policy to help inform decisions about going forward with the idea. In this process, each cost and benefit is made explicit. When we do this, we are best able to understand and evaluate the trade-offs any policy brings.

8.1 Costs

8.1.1 Economic versus Accounting Costs

Cost benefit analysis is different from traditional accounting, known as cash flow accounting, in what it considers a cost. In cash flow accounting, the money spent on something is the cost of the something. For instance, if one hour of labor costs $20, then the cost of the labor is $20 per hour.

Cost benefit analysis uses a more ``economic’’ understanding of cost. Instead of cost being the money spent to purchase the good or service, the cost is defined as the opportunity cost. This is the cost of the product is it’s next best use. In a free, fair, and competitive market, the cash flow accounting price and the opportunity cost are the same. However, often these values are different.

Instead, we say the cash flow accounting price is the opportunity cost plus the rents. Rents are payments made for a resource, such as material or labor, that is above and beyond the amount required to freely purchase the resource. Rents are common, and not always bad. For instance, your dentist has a greater income than we would observe if dental practice were not regulated and anyone could open up a shop as a dentist. Because of the added regulation and the deviation from the free market assumptions, the dentist’s income increases and those increases are called rents. Since rents are payments above the opportunity cost, they are not considered part of the economic costs of the project.

Suppose, for instance, a construction worker normally works for $15 per hour. If I want a concrete patio poured at my house, for example, I would pay $15 per worker per hour in labor. However, some state’s have laws requiring higher pay for people working on state contracts or grant preference for union workers that have higher wages. Say they are now paid $25 per hour. Since if they were not working for the state’s road project, they would be being paid $15 per hour, we use that as their economic cost per hour. The cash flow accounting cost, as in the money paid, is $25 per hour. The $10 difference is the rents transferred from the purchaser to the seller.

8.1.2 Discounting Future Costs

Often policy choices or programs incur future costs. If I build a structure, I have to pay to maintain that structure. Likewise, unless the program is a one-off, I have to continue to fund and provide those services.

We use a concept called the present discounted value (PDV) to measure the costs of future services in ``today’’ dollars. Because money I have today could be put to productive use (say invested) and earn a return, future money is worth less. To make this more concrete, if I have $100 today, which I invest and earn a 10% per year return, one year from today I will have $110.52 next year. Since this is worth more than $100, we’d prefer to take and invest $100 today then wait 1 year for the same payout. Since future money is worth less than present money, we need to discount future money to account for this fact.

Another way to think about the PDV is that the PDV is an estimate of how much money you would need to invest today to meet your future obligations. For instance, if you need $100 a year from today, you could invest $90.49 and, with a 10% return, have $100 in 1 year.

We use the social discount rate to discount the spending. The social discount rate, \(r\), is the measure of the expected return on investment or the opportunity cost of the future spending in today’s dollars. The US government’s Office of Management and Budget uses a discount rate of 7% per year, which has been used by many others as an estimate of \(r\).

Suppose the policy will have on-going costs of $100,000 per year after the first year. We want to discount that figure for the second year:

\[ \text{Discounted Costs in Year 2} = \frac{100,000}{1 + r} \]

For the third year, it gets a little more tricky. We need to first discount the prices since they are 1 year in the future and then discount them a second time for the next year.

\[ \begin{eqnarray*} \text{Discounted Costs in Year 3} &=& \frac{\frac{100,000}{1 + r}}{1 + r} \\ &=& \frac{100,000}{1 + r} \frac{1}{1 + r} \\ &=& \frac{100,000}{(1 + r)^2} \end{eqnarray*} \]

This can be generalized as

\[ \text{Discounted Costs in Year } k = \frac{100,000}{(1 + r)^k} \]

We would then need to sum up over all the years that the policy would be in place to get the total present discounted value:

\[ \begin{eqnarray*} \text{Total PDV} &=& \frac{100,000}{1 + r} + \frac{100,000}{(1 + r)^2} + \ldots + \frac{100,000}{(1 + r)^k} \\ &=& \Sigma_{i = 1}^k \frac{100,000}{(1 + r)^i} \end{eqnarray*} \]

If the policy is intended to be in place for a large number of years (say greater than 50), then the present discounted value is often reasonably well approximated by \(\frac{\text{cost per year}}{r}\), or \(\frac{100,000}{0.07}\) for our example. Our example policy would have a lifetime carrying cost with a PDV of $1,428,571.

8.2 Benefits

Often, we measure benefits from policy interventions that save time or save life, in addition to direct economic benefits (e.g., greater employment). However, assigning a value to time and life is challenging. Economists have developed a few methods for determining the value that we assign to time and the value that we assign to life.27

8.2.1 Value of Time

When assigning a value to time, one simple approach is to assume that the value is equal to the person’s wage. This makes sense because if the person was not engaging in leisure, the next best use of their time would be to work. In the US, the median wage is approximately $27 per hour and we’d use that value for an estimate of the value of time. However, there are some issues with using wage to estimate the value of time. Chiefly, many of us cannot freely trade hours between leisure and work. For instance, if you are a salaried employee, working extra hours does not increase your pay. Additionally, some of the benefits of working may not appear in the wage benefit (e.g., work has A/C while your home does not).

Another common way to estimate the value of time is to ask people a series of questions about trading off money and time. This approach is called contingent valuation. For instance, you may ask how much would you spend to shorten your daily driving commute by 5 minutes?'' The answers to these questions helps reveal the value of those 5 minutes. However, there are issues with this approach, largely expressed in behavioral economics terms. The order of questions matter: asking the value of saving one seal and the value of saving one whale gives different answers than the value of saving one whale and the value of saving one seal. Asking a question by itself versus with other questions gives different values: people are willing to pay more to protect views at the Grand Canyon when asked that question alone versus when asked as part of a series of other questions. Finally, people often have a hard time assigning value to things that are moreconcepts’’ than actual events. For instance, people assign the same value to saving 2,000, 20,000, and 200,000 birds. In that case, it seems more likely they were reporting a value for saving “birds” and not the value for saving that number of birds.

Due to the issues with using wages or contingent valuation, economists commonly use a revealed preferences to assign values. Instead of asking people how much they value time or using wages, economists use people’s behavior to determine the value they assign to time. For instance, in some cities like Iowa City, there is a very large employer that many of the residents work for (University of Iowa and the UI Hospitals and Clinics). Houses that are nearer UIHC tend to be sold for more money because they have shorter commutes. You could compare the value of a house, say 2 miles from UIHC, to another house, say 5 miles from UIHC. You would make sure (or adjust for) the aspects of a house that determine value (number of bedrooms, bathrooms, house square footage, lot size).

In Iowa City and Coralville, houses and land further from UIHC tend to be worth less. Specifically, for each mile further from UIHC, a house and associated lot are worth about $1.13 per square foot less. Assuming both of our houses are on 10,000 square foot lots, the house that is further way is worth \(10,000 * \$1.13 * 3 = \$33,900\) less than the house located 2 miles away.

In exchange for that savings, the purchaser of the further house has a longer commute. Let’s suppose the commute, being 3 miles longer, takes an extra 10 minutes each way. Over the course of the year (allowing for holidays), that is \(50 * 5 * 10 * 2 = 5000\) more minutes or 83 additional hours spent commuting.

The lower cost of the house comes out to a slightly lower mortgage payment, about $175 less a month, and a slightly lower tax bill in exchange for a slightly longer commute. Specifically, a person is willing to spend an extra 83 hours per year driving to save \(\$175 * 12 = \$2,100\). That comes out to a revealed preference value of time of $25 per hour.

During the 1970s OPEC oil embargo, some gas stations had price caps while others were able to charge the fair market price. Based on line lengths and gas prices at the different stations, it was estimated that people valued their time at (in 2019 dollars) $22 per hour. While other researchers are considered the amount of time saved using express toll lanes versus free lanes on interstates and have found a willingness to pay of about $10 per hour.

8.2.2 Value of a Statistical Life

Similar methods are used to estimate the value of a statistical life. However, they run into similar problems. With contingent valuation, estimates range from $1 million to $29 million. These questions are often phrased as ``how much would you spend to reduce your risk of dying in a plane crash from 2 per 500,000 flights to 1 per 500,000 flights.’’ People are very bad at assigning value with statements like that - we are not great intuitive statisticians.

Wages present other issues - what is the value of retired people who have little wage earning potential left? Additionally, wages omit the value that people get from other people being happy they are alive. This presents many issues with constructing a great value for a life.

As with time, economists have largely used revealed preferences to determine how much we value life. The compensating differentials are the greater wage income observed in fields with higher risk of death and we can use the different wage rates and different risks of death to determine how much people value their lives. Additionally, we can also look at consumer behavior. For instance, when people drive, do they wear their seatbelt? Do cars that have better safety features, like air bags and better crash test ratings, have higher prices? Using the safety provided by these better crash test rated cars and their price difference, we can determine how much people are willing to pay to increase their safety.

Based on a variety of both compensating differential and revealed preference purchasing decisions, economists commonly use a consensus value of $9.6 million per life.

8.3 Common Pitfalls When Using Cost Benefit Analysis

There are several ways in which cost benefit analysis may be misused or misapplied. The three most common are discussed here.

If a new road enabled commercial development of a new area, the new development is a potential benefit. However, if the new development is relocated businesses from elsewhere or consumer spending is simply shifted from one location to another, then this is not a new benefit. The total amount of economic activity and consumer spending is the same as before the road is constructed and therefore there are no new benefits. We are only interested in the net benefits.

Likewise, the simply relocation of a business or activity across a governmental boundary is likely not a true benefit. Coralville provided significant incentives for Von Maur, a department store, to locate in Coralville instead of in Iowa City when they were building a new store. This store did not create new business, the Iowa City location closed, so the net benefit was zero. It did provide a benefit to the City of Coralville’s government (this is the theory behind the incentives; however, the case that the incentives were inframarginal is relatively strong) but did so at a cost to the City of Iowa City’s government. From a larger prospective, since no new business was the result of the move, there was no benefit accrued to the area.

Frequently, when discussing a project, politicians will discuss the number of jobs created by the project as a benefit. However, labor costs are costs, not benefits of a project.

For instance, if I build a railroad between Iowa City and Cedar Rapids to run a higher speed train, the labor that goes into the project is a cost and not a benefit. My reason for building the railroad is not to create jobs and therefore they are not a benefit.

If you have a second order benefit that derives from one that is already counted, you should not count the second order benefit. For instance, suppose I build a road shortening commute times for workers. The workers would get the benefit of the shorter driving time. It is also likely that the value of their homes would increase as they are now closer to the employment center of the city thanks to the new road. However, since both the travel time cuts and the increase in house value are the results of the same thing (shorter commutes), counting both is double counting. Instead, only one (either the shorter commute saving time or the shorter commute increasing property values) should be counted.

8.4 Using Cost Benefit Analysis for Influenza Vaccination

With cost benefit analysis, it is useful to first articulate all of the costs and all of the benefits associated with a project. For instance, suppose we are considering a policy of universal free flu vaccinations.

We would have some costs:

  • Cost of the shot
  • Cost to deliver the shot
  • Cost of adverse events

and some benefits:

  • Fewer days missed work/school the flu
  • Fewer deaths from the flu
  • Less spent on flu treatments

Let’s suppose a flu shot costs $12 to make and $3 to deliver.

The cost of the adverse reactions are a little harder to assign. One of the biggest risks, although not firmly linked to the vaccine, is Guillain-Barre syndrome (GBS), which is a serious neurological cause of paralysis. GBS occurs in about 1 or 2 in every 1,000,000 people vaccinated. Let’s suppose other serious complications, such as unexpected allergic reactions, occur at the rate of about 1 in a 1,000,000 as well. We’ll assume then that 2.5 per 1,000,000 people vaccinated will have a serious adverse reaction. We’ll assume that 95% of these people will ultimately be fine but, perhaps, with an impaired quality of life. We’ll say that costs $500,000. The 4% are more seriously and permanently harmed and we’ll suppose that cost to be $2,500,000. The final 1% suffer life ending complications costing $9,600,000 each.

We have then an expected adverse reaction cost per vaccination of:

\[\begin{eqnarray*} \text{Cost of Adverse Reaction } &=& \frac{2.5}{1,000,000} * (0.95 * 500,000 + 0.04 * 2,500,000 + 0.01 * 9,600,000) \\ &=& \frac{2.5}{1,000,000} * 671000 \\ &=& 1.68 \end{eqnarray*}\]

So the vaccine cost is $12 to make, $3 to deliver, and $1.68 in adverse events or $16.68 total.

The benefits are given by the probability of getting the flu in any given year and the effectiveness of the vaccination. Let’s suppose that your annual risk of getting the flu is about 7.81% and the flu vaccine, on average, reduces that risk by 70% to 2.34%.

If you get the flu, let’s suppose that the flu lasts 5 days. Each one of those days ``incurs’’ a cost of $100 in lost productivity, so $500 per case of the flu. Let’s suppose 25% of people with the flu see their doctor ($100) and the average amount spent on treatments (OTC and RX) is $20. Each year, about 1.6% of people with the flu die. We’ll use the $9,600,000 as our value of a life. We’ll suppose the flu vaccine only reduces the risk of death through preventing people from getting the flu in the first place.

Based on these assumptions, the average costs incurred by the flu are:

for a total cost, per case of flu, of $15,900. Since the risk of getting the flu is reduced by 5.47%, the benefits of the flu shot are \(\$15,900 * 0.0547 = \$869.73\).

Since the benefits ($869.73) exceed the costs ($16.68), offering everyone a free flu shot makes sense as a policy measure. It would cost approximately 5.3 billion dollars annually, but the reduced incidence of the flu would save 278.3 billion dollars annually.

This is still true even if the flu vaccine does not reduce or alter the risk of death. Omitting the cost of death from the calculations, the flu vaccine still produces a value of $29.54 per vaccination.

  1. This isn’t saying life is not priceless but rather we do accept some level of risk in our lives willingly. We drive cars, we fly in plans, we walk across the street with traffic. We are simply attempting to balance the costs of some intervention with our risk tolerance.↩︎