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					  Cost-Benefit Analysis: Introduction
 Cost-Benefit Analysis is a practical technique for
  determining the relative merits of alternative
  government projects over time.
 The government uses cost-benefit analysis to
  compare the costs and benefits of public goods
  projects and decide if they should be undertaken.
 Essentially 3 steps:
  1.   Enumerate all costs and benefits of proposed project
  2.   Evaluate all costs and benefits in dollar terms
  3.   Discount future net benefits
                   Introduction

 In principle, such an analysis is an accounting
  exercise. (tracking cost expenditures and benefits)
 In practice, cost-benefit analyses are rich economic
  exercises that combine theory and empirical work.
                       Example #1
 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.
  MEASURING THE COSTS OF PUBLIC
           PROJECTS:
          Transportation Example
 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.
 Table 1

  Control-Benefit Analysis of Highway Construction Project
                                 Quantity        Price or     Total
                                                  Value
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:
Valuing Public Benefits and Costs

 For private company:
    Benefits = revenues received
    Costs = firm’s payments for inputs

 For public sector, market prices may not reflect
  social benefits and costs.
      Externalities, for example
 Several ways of measuring benefits and costs
    Market prices
    Adjusted market prices
    Consumer surplus
    Inferences from economic behavior
    Valuing intangibles
          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.
            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.
             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.
            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.
 Table 2
  Control-Benefit Analysis of Highway Construction Project
                                 Quantity            Price or      Total
                                                      Value
Cost       Asphalt            1 million bags      $100/bag         $100.0 m
           Labor              1 million hours     ½ at $20/hr       $12.5 m
                                                  ½ at $5/hr
           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:
           Measuring Future Costs

 The asphalt and labor costs are immediate costs, but
  the last one–maintenance–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.
Present Value:
Future Dollars into the Present

 Suppose someone promises to pay you
  $100 one year from now.
 What is the maximum amount you should be
  willing to pay today for such a promise?
 You are forgoing the interest that you could
  earn on the money that is being loaned.
Present Value:
Future Dollars into the Present

 The present value of a future amount of
  money is the maximum amount you would
  be willing to pay today for the right to receive
  the money in the future.
Present Value:
Present Dollars into the Future

 Define
    R = amount to be received in future
    r = rate of return on investment
    T = years of investment

 The present value (PV) of the investment is:


                  R
    PV 
              1  r    T
Present Value:
Future Dollars into the Present

 In previous equation, r is often referred to as the
  discount rate, and (1+r)-T is the discount factor.
 Finally, consider a promise to pay a stream of money,
  $R0 today, $R1 one year from now, and so on, for T
  years.


               R1       R2              RT
   PV  R0                   ...
             1  r 1  r 2
                                     1  r T
Present Value:
Future Dollars into the Present

 Present value is an enormously important
  concept
 A $1,000,000 payment 20 years from now is
  only worth today:
     $376,889 if r=.05
     $148,644 if r=.10
           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.
           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.
 Table 3
  Control-Benefit Analysis of Highway Construction Project
                                 Quantity         Price or     Total
                                                   Value
Cost       Asphalt            1 million bags    $100/bag       $100.0 m
           Labor              1 million hours   ½ at $20/hr     $12.5 m
                                                ½ at $5/hr
           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:
  MEASURING THE BENEFITS OF
       PUBLIC PROJECTS
 There are three main benefits from the project:
      Value of driving time saved
      Value of reduced fatalities
      Value of reduced accidents
           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
         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.
         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.
           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.
    Problems with contingent valuation

 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.
         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.
         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.
              Valuing time savings

 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.
               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.
                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
Valuing Public Benefits and Costs


 Economists use two methods to assign finite values
  to human life:
      Lost earnings: Net present value of individual’s
       after-tax earnings over lifetime.
         Taken literally, no loss for aged, infirm, or severely

           handicapped
      Probability of death: Most projects affect probability
       of death (e.g., cancer research). People are willing to
       accept increases in the probability of death for a finite
       amount of money.
                   Valuing life
 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.
                   Valuing life
 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.”
www.law.georgetown.edu/gelpi/papers/pricefnl.pdf
CBA Criticisms
 Applications to health and environmental
  safety is flawed because of difficulty
  measuring non market items
 Substituting risk of death with death is wrong
 CBA ignores who suffers from an
  environmental or health risk problem
               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.
              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.
                Valuing Saved Lives

 The contingent valuation approach asks about
  the valuation of a life
 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.
                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.
                 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).
               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).
              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.
 Table 4

      Costs Per Life Saved of Various Regulations
                                                      Cost per life
                                                         saved
    Regulation concerning …           Year   Agency
                                                      ($ millions)
Childproof lighters                   1993   CPSC         $0.1
Food labeling                         1993   FDA          0.4
Reflective devices for heavy trucks   1999   NHTSA        0.9
Children’s sleepware flammability     1973   CPSC         2.2
Rear/up/should seatbelts in cars      1989   NHTSA         4.4
Asbestos                              1972   OSHA         5.5
Value of statistical life                                 7.0
Benezene                              1987   OSHA          22
Asbestos ban                          1989   EPA           78
Cattle feed                           1979   FDA          170
Solid waste disposal facilities       1991   EPA        100,000
           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.
          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.
     PUTTING IT ALL TOGETHER

 Table 5 adds in the benefits from the turnpike
  renovation.
 Table 5
  Control-Benefit Analysis of Highway Construction Project
                                 Quantity         Price or        Total
                                                   Value
Cost       Asphalt            1 million bags    $100/bag          $100.0 m
           Labor              1 million hours   ½ at $20/hr        $12.5 m
                                                ½ at $5/hr
           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
     PUTTING IT ALL TOGETHER

 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.
Private Sector Project Evaluation


 The present value criteria for project
  evaluation are that:
     A project is admissible only if its present
      value is positive.
     When two projects are mutually exclusive,
      the preferred project is the one with the
      highest present value.
Private Sector Project Evaluation


 Table 11.2 shows two different projects
  (R&D or Advertising).
 The discount rate plays a key role in
  deciding what project to choose, because
  the cash inflows occur at different times.
 The lower the discount rate, the more
  valuable the back-loaded project.
Table 11.2
Private Sector Project Evaluation


 Several other criteria are often used for
  project evaluation, but can give misleading
  answers
      Internal rate of return
      Benefit-cost ratio
Private Sector Project Evaluation

 The internal rate of return, ρ, is defined as the ρ that
  solves the equation:

   0   B0  C0  
                      B1  C1  ...  BT  CT 
                       1             1   T



 The IRR is the discount rate that would make the
  present value of the project equal to zero.
      Admissible if ρ>r.
      The flawed analysis would choose an admissible project
       with the higher internal rate of return, ignoring scale.
Private Sector Project Evaluation


 The benefit-cost ratio divides the discounted
  stream of benefits by the discounted stream of
  costs. In this case:
  B=stream of benefits and C=stream of costs:

             B1             BT
  B  B0          ...
           1  r       1  r T



             C1              CT
  C  C0           ...
           1  r        1  r
                                  T
Private Sector Project Evaluation


 Admissibility using the benefit-cost ratio requires:

   B
     1
   C
 This ratio is virtually useless for comparing across
  admissible projects, however.
 Ratio can be manipulated by counting benefits as
  “negative costs” and vice-versa.
Discount Rate for Government
Projects

 Government decision making involves
  present value calculations.
 Costs, benefits, and discount rates are
  somewhat different from private sector.
Valuing Public Benefits and Costs:
other considerations

 Consumer surplus
     Public sector projects can be large and
      change market prices.
     Figure 11.1 measures the change in
      consumer surplus from a government
      irrigation project that lowers the cost of
      agricultural production.
Figure 11.1
   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.
   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).
   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.
                   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.
                   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.
      Recap of Cost-Benefit Analysis

 Measuring the costs of public projects
 Measuring the benefits of public projects
 Putting it all together
Cost Benefit example
 Analyzing a project $20 mil costs and benefits
 Benefits:
     $14 m year 0, $5 in yr 1 $1 yr 3
 Costs:
     All $20 million in yr 2


 Social discount rate: 10%

				
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