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Chapter 8 Cost Benefit Analysis

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1 Chapter 8 Cost Benefit Analysis
Jonathan Gruber Public Finance and Public Policy Aaron S. Yelowitz - Copyright 2005 © Worth Publishers

2 Introduction The previous lesson relied on the theoretical concepts of marginal social benefit and cost of public goods. The government uses cost-benefit analysis to compare the costs and benefits of public goods projects and decide if they should be undertaken.

3 Introduction In principle, such an analysis is an accounting exercise.
In practice, cost-benefit analyses are rich economic exercises that combine theory and empirical work.

4 Introduction Consider the monorail project in Seattle, which was narrowly approved in 2002. The costs consisted of construction and equipment, buying permission from some landowners, ruined views, noise near the train, and traffic delays during construction. The benefits consisted of reduced travel time, saved parking fees, reduced car maintenance, more reliable commuting times, fewer accidents and fatalities, better views for monorail passengers, and reduced noise from busses. Analysts found that the monorail’s benefits were about $2.07 billion, while its costs were $1.68 billion. The $390 million net benefit helped swing public opinion toward the project.

Consider the example of renovating a turnpike that is in poor shape, with large potholes and crumbling shoulders that slow down traffic and pose an accident risk. Should you repair the road? Table 1 shows the factors to consider.

6 Control-Benefit Analysis of Highway Construction Project
Table 1 Control-Benefit Analysis of Highway Construction Project Quantity Price or Value Total Cost Asphalt 1 million bags Labor 1 million hours Maintenance $10 million/year First-year cost: Total cost over time: Benefits Driving time speed 500,000 hours Lives saved 5 lives First-year benefit: Total benefit over time: Benefit over time minus cost over time: The project requires several inputs – materials, labor, and maintenance over time. And it produces two main benefits – reduced commuting time and fewer fatalities.

7 Measuring Current Costs
The first goal is to measure current costs. The cash-flow accounting approach to costs simply adds up what the government pays for all the inputs. This does not represent the social marginal cost we used in the theoretical public goods analysis, however.

8 Measuring Current Costs
The social marginal cost of any resource is its opportunity cost–the value of that input in its next best use. This is not necessarily its cash costs, but by what else society could do with the input. For the asphalt, the next best use is to sell the bag to someone else. The value of the alternative use is the market price.

9 Measuring Current Costs
If the labor market is perfectly competitive, the same logic applies–the value of an hour of labor used on the project is simply the market wage. If there are imperfect markets, however, then there could be unemployment. For example, there could be a “living wage” ordinance that mandates a $20/hour wage rate. This mandate, in turn, could lead to unemployment. Imagine that those who were involuntarily unemployed had a reservation wage of $5/hour; thus, they value their leisure at $5/hour.

10 Measuring Current Costs
In this case, the “alternative activity” is not working at another job, but rather being unemployed. This alternative activity only has an opportunity cost of $5/hour, not $20/hour. This lowers the economic costs of the project (but not the accounting costs). The unemployed workers derive rents, which are simply payments to resource deliverers that exceed those necessary to employ the resource. The Table 2 illustrates this.

11 Control-Benefit Analysis of Highway Construction Project
Table 2 For asphalt, the next best use besides using it on a project is to sell it to someone else. The value is then the market price of $100. For these formerly unemployed workers, paying $20 an hour consists of a $5 opportunity cost and a $15 transfer. On the other hand, if there is involuntary unemployment. The opportunity cost for these workers is lower than the wage rate ($5). If the labor market were competitive, the market wage rate for construction workers would completely determine the price. Control-Benefit Analysis of Highway Construction Project Quantity Price or Value Total Cost Asphalt 1 million bags $100/bag $100.0 m Labor 1 million hours ½ at $20/hr ½ at $5/hr $12.5 m Maintenance $10 million/year First-year cost: Total cost over time: Benefits Driving time speed 500,000 hours Lives saved 5 lives First-year benefit: Total benefit over time: Benefit over time minus cost over time: The economic cost equals $20/hour x 0.5 million hours plus $5/hour x 0.5 million hours, for a total of $12.5 million. The accounting cost equals $20/hour x 1 million hours, or $20 million.

12 Measuring Future Costs
Technical The present discounted value of this flow of costs is computed as: How do we convert this infinite sum into something manageable? Multiply by (1+r):

13 Measuring Future Costs
The asphalt and labor costs are immediate costs, but the last one–construction–is a stream of costs over time. This cost is $10 million per year into the indefinite future. We translate this into current dollars using present discounted value.

14 Measuring Future Costs
Technical Subtracting the first equation from the second cancels out most of the terms: Or, rewriting, the present discounted value is the annual cost divided by the discount rate:

15 Measuring Future Costs
The key question then becomes choosing the right social discount rate. For a private firm, the answer would be the opportunity cost of what else the firm could do with the same funds, that is, the after tax rate of return. The government should base its discount rate on the private sector opportunity cost, but the government counts both the after-tax portion of the return and the taxes collected.

16 Measuring Future Costs
In practice a variety of discount rates are used. The Office of Management and Budget (OMB) recommended in 1992 that the government use a discount rate of 7%, the historical pre-tax rate of return on private investments, for all public investment projects. Table 3 shows the costs.

17 Control-Benefit Analysis of Highway Construction Project
Table 3 Control-Benefit Analysis of Highway Construction Project Quantity Price or Value Total Cost Asphalt 1 million bags $100/bag $100.0 m Labor 1 million hours ½ at $20/hr ½ at $5/hr $12.5 m Maintenance $10 million/year 7% disc. rate $143.0 m First-year cost: $112.5 m Total cost over time: $255.5 m Benefits Driving time speed 500,000 hours Lives saved 5 lives First-year benefit: Total benefit over time: Benefit over time minus cost over time: Which leads to a present discounted value of $143 million (=$10 million/7%). The OMB suggests a 7% discount rate. The first year cost of the project is $112.5 million. The total cost of the project is $255.5 million.

There are two main benefits from the project: Value of driving time saved Value of reduced fatalities

19 Valuing Driving Time Saved
For consumers, we need some measure of society’s valuation of time. There are several approaches to measuring this: Market based measures: Wages Survey based measures: Contingent valuation Revealed preference measures

20 Valuing Driving Time Saved
How do we compute the value of commuting time saved? For producers, the decreased costs shift the supply curve to the right (outward), leading to an increase in the total surplus. Assuming we have estimates of supply and demand in the output market, this is straightforward.

21 Valuing Driving Time Saved
If we had a perfectly functioning labor market, we could “cash out” the value of the time savings, a market-based measure. Assuming the person can freely choose the hours he wants to work, then even if the time is spent on leisure, the appropriate valuation of the time is the wage rate. The market based approach runs into problems that hours of work is “lumpy” and that there are non-monetary aspects of the job.

22 Valuing Driving Time Saved
Contingent valuation is a method of asking individuals to value an option they are not now choosing. In some circumstances, this is the only feasible method for valuing a public good. For example, there is no obvious market price to use to value saving a rare species of owl.

23 Problems with contingent valuation
Application There are serious issues with contingent valuation, however. Isolation of issues matter: respondents value a public good more when it is the only one asked about. Order of issues matter: respondents place higher values on public goods asked about first. “Embedding” matters: respondents seem to place roughly the same valuation on a public good, regardless of the quantity. These problems suggest that part of the valuation is due to survey design, not “true” valuation.

24 Valuing Driving Time Saved
The natural way for economists to value time is to use revealed preference–let the actions of individuals reveal their valuation. For example, if one compared house prices for two houses, one of which was 5 minutes closer to the workplace, this would effectively “cash out” the value of saved commuting time.

25 Valuing Driving Time Saved
In practice, this approach runs into problems because the two homes are not identical. Some of the differences (e.g., housing attributes) can be observed and accounted for with cross sectional regression. Decomposing a sale price by its attributes is the basis of hedonic market analysis. Other differences are either hard to measure or unobserved, however, which leads to bias.

26 Valuing time savings Empirical Evidence
One clever quasi-experiment to reveal the value of saved time was conducted by Deacon and Sonstelie (1985): During the oil crisis of the 1970s, the government imposed price ceilings on gasoline of large gasoline stations, but not independent ones. As a consequence, long lines formed at these cheaper, corporate gasoline stations. At Chevron stations in California, gasoline was approximately 39.5¢ lower, with an average wait time of roughly 14.6 minutes. The mean purchase was around 10.5 gallons. Thus, the tradeoff is waiting 14.6 minutes to save about $4.15, or one hour for $17. This corresponded very closely to the average hourly wage in the U.S.

27 Valuing Saved Lives The other main benefit of the turnpike improvement is valuing saved lives due to lower traffic fatalities. Valuing life runs into ethical issues, but almost all economists would agree that it is necessary for public policy decisions.

28 Valuing Saved Lives By stating that life is priceless or should not be valued, we leave ourselves helpless when facing choices of different programs that could each save lives. There are three main approaches to doing this: Using wages Contingent valuation Revealed preference

29 Valuing life Application In 1993, consumer groups demanded that General Motors recall 5 million pickup trucks. The trucks’ side-mounted gas tanks made them more likely to explode on impact, causing 150 deaths over a 15-year period. The recall would cost $1 billion, and save at most 32 more lives, or $31.25 million per life saved. GM reached a rather different settlement–provide $50 million for education about seat belts and drunk driving, and provide 200,000 child safety seats for low-income families.

30 Valuing life Application The settlement was called “the most unprecedented buyout of law enforcement officials by a culpable corporation in regulation history.” – Ralph Nader. Yet, the child safety seats alone would save 50 lives, which at a cost of $50 million, leads to a cost per life saved of just $1 million. Far more cost effective than the $31.25 million per life saved from the recall. Thus, by this measure, the settlement was much better, but only possible because the government “valued life.”

31 Valuing Saved Lives The market-based approach uses wages; the value of the life is the present discounted value of the lifetime stream of earnings. One key problem is that this approach does not value leisure. Keeler (2001) suggests that because of this, the value of a person’s life is about 5 to 10 times their future lifetime earnings.

32 Valuing Saved Lives Keeler finds that the average 20 year-old female will have future earnings of $487,000 in net present value, but will value her life at $3.1 million. Men have slightly higher values because of higher earnings. Older people have lower values because they have fewer years of life remaining.

33 Valuing Saved Lives The contingent valuation approach asks people what their lives are worth. There is obvious difficulty in a question like this, so it is often framed in terms of changes in the probability of dying. For example, how much more would you pay for an airline ticket with a 1 in 500,000 chance of a crash compared with a 2 in 500,000 chance? The estimates from contingent valuation have a very wide range, going from $825,000 to $22.3 million per life saved.

34 Valuing Saved Lives The revealed preference approach examines how much individuals are willing to pay for something that reduces their odds of dying. For example, suppose a consumer purchases an airbag for $350 that has a 1 in 10,000 chance of saving his life. The implicit valuation on life is $3.5 million.

35 Valuing Saved Lives An alternative revealed preference approach examines risky jobs: Suppose that one job has a 2% higher risk of death but pays $15,000 more in salary. The $15,000 extra salary is known as the compensating differential. The implicit valuation of life in this example is $3 million ($15,000/0.02).

36 Valuing Saved Lives There is a large literature in economics using these revealed preference approaches. Viscusi estimates that the value of life is roughly $7 million. There are drawbacks, however. Strong information assumptions about probabilities. Assumes people are well prepared to evaluate these tradeoffs. Difficult to control for other attributes of the job. Differences in valuation of life (e.g., degree of risk aversion).

37 Valuing Saved Lives Another approach focuses on how existing government spending translates into lives saved. Recent study reviewed 76 regulatory programs; the costs per saved live varied between $100,000 for childproof cigarette lighters to $100 billion from regulation of solid waste disposal facilities. Table 4 shows the results.

38 Costs Per Life Saved of Various Regulations Regulation concerning …
Table 4 Costs Per Life Saved of Various Regulations Regulation concerning … Year Agency Cost per life saved ($ millions) Childproof lighters 1993 CPSC $0.1 Food labeling FDA 0.4 Reflective devices for heavy trucks 1999 NHTSA 0.9 Children’s sleepware flammability 1973 2.2 Rear/up/should seatbelts in cars 1989 4.4 Asbestos 1972 OSHA 5.5 Value of statistical life 7.0 Benezene 1987 22 Asbestos ban EPA 78 Cattle feed 1979 170 Solid waste disposal facilities 1991 100,000 Of 76 government regulatory programs studied, 44 had a cost per life saved under the $7 million

39 Discounting Future Benefits
A particularly thorny issue for cost-benefit analysis is that the costs are mostly short-term, while the benefits are mostly long term. Global warming is a good example. This may be problematic because: The choice of discount rate will matter enormously for benefits that are far in the future. The benefits are spread out over current and future generations.

40 Cost-effectiveness Analysis
Finally, there may be cases when society is unwilling or unable to value the benefits of a public project. Cost-effectiveness analysis is the search for the most cost-effective approach to providing a public good, ignoring whether the benefits warrant such a public good.

Table 5 adds in the benefits from the turnpike renovation.

42 Control-Benefit Analysis of Highway Construction Project
Table 5 Control-Benefit Analysis of Highway Construction Project Quantity Price or Value Total Cost Asphalt 1 million bags $100/bag $100.0 m Labor 1 million hours ½ at $20/hr ½ at $5/hr $12.5 m Maintenance $10 million/year 7% disc. rate $143.0 m First-year cost: $112.5 m Total cost over time: $255.5 m Benefits Driving time speed 500,000 hours $17/hr $8.5 m Lives saved 5 lives $7 million/life $35.0 m First-year benefit: $43.5 m Total benefit over time: $621.4 m Benefit over time minus cost over time: $365.9 m The resulting time savings per year is $8.5 million. Assume we can value the driving time saved to both producers and consumers at $17 per hour. The resulting value of life savings is $35 million per year. Also, assume that the value of a life saved is $7 million. The first year benefits are therefore $43.5 million. Applying the 7% discount rate, the total benefit is $621 million ($43.5/0.07). The benefits of the turnpike project considerably exceed the costs.

Since the benefits exceed the costs, we would recommend the government pursue the project. The government needs to consider one additional factor beyond the benefits and costs of the project itself: the budgetary cost of raising the funds to finance the project. Economists typically assume some efficiency cost, or deadweight loss, from raising the tax burden to finance this spending. If the efficiency cost of raising the money is too high, some projects will not survive the cost-benefit analysis.

44 Other Issues in Cost-Benefit Analysis
There are a number of other issues in cost-benefit analysis. These concern common “counting” mistakes and distributional concerns.

45 Other Issues in Cost-Benefit Analysis
The common counting mistakes include: Counting secondary benefits (like commerce that is simply shifted from one area to another). Counting labor as a benefit rather than a cost. Double counting benefits (like the value of an irrigation project to farm income, and simultaneously the increase in the value of the land).

46 Other Issues in Cost-Benefit Analysis
There are also distributional concerns: The costs and benefits of a public project do not necessarily accrue to the same individuals. In principle, a project that improved social welfare could then involve redistribution, but in practice this rarely happens.

47 Budgetary Costs Although we would recommend that the government pursue this project because the benefits were greater than the costs, in reality governments face limited budgets. To assess which of many projects to pursue, the government must consider the budgetary cost of raising funds to finance the project. This involves some efficiency costs, or deadweight loss. This cost should be factored into the calculations.

48 Budgetary Costs For example, consider two projects that pass the cost-benefit test: One project has benefits of $150, and costs $100. The other has benefits of $110, and costs $100. If the efficiency costs of raising funds is 20¢ for each $1 of revenue raised, then only the first project (with benefits that exceed $120) should be pursued.

49 Recap of Cost-Benefit Analysis
Measuring the costs of public projects Measuring the benefits of public projects Putting it all together

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