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Introduction
Cost Benefit Analysis (CBA) is an economic evaluation technique that measures all the positive (beneficial) and negative (costly) consequences of an intervention or program in monetary terms.
The valuation of all program outcomes in monetary units allows decisionmakers to directly compare the health outcomes of different types of health interventions.
CBA can also be used to compare health-related interventions to those in other economic sectors.
For example, when deciding how to allocate the limited funding approved by a state or local legislature, policy makers might have to choose between implementing a statewide, school-based screening program for tuberculosis infection or a job-training program for the unemployed.
For each of these competing programs, CBA enables policy makers to determine whether the value of its positive consequences exceeds the value of societal resources required to implement the program.
This will help policy makers choose the program that provides the best return on investing societal resources.
Cost Benefit Analysis Defined
The conceptual and theoretical framework of CBA is derived from welfare economics.
Welfare economics is the study of changes in the well-being, or welfare, of individuals and society as decisions are made regarding the production, distribution, and consumption of goods and services.
CBA incorporates theories that have been developed to address equity issues such as:
  • the distribution of potential benefits, and
  • the costs of various economic policies.
In other words, a CBA identifies who (an individual or a group) gains and/or bears the costs of a project.
For example, a CBA of publicly funded development and manufacture of vaccines against potential bioterrorism agents (e.g., smallpox or anthrax) will identify both the potential beneficiaries of vaccine development as well as who will incur the costs.
The benefits of increased protection against the bio-agents will accrue to target populations for priority vaccinations such as those administered to:
  • health-care personnel,
  • the military, and
  • the general population.
The medical research and manufacturing industry will benefit from the development and production effort.
The funding scheme details will identify whether the federal budget alone or a combination of federal and state financing will cover the costs of the project.
Historical Background
An 1844 paper by Jules Dupuit, "On the Measurement of the Utility of Public Works", is often cited as the first work on CBA.
However, as early as 1808, the "Report on Transportation" by Albert Gallatin — the fourth U.S. Secretary of the Treasury — had recommended the comparison of costs and benefits for evaluating water-related projects.
Economic analysis of social benefits and costs in federal projects was instituted in 1936 by the Flood Control Act, which required the U.S. Army Corps of Engineers to evaluate all benefits and costs of water resource projects "to whomsoever they accrue."
The first federally mandated guidelines for CBA of public projects were issued in 1952 by the Bureau of the Budget. Gradually the bureaucratic emphasis expanded to include all public goods.
When do we use CBA?
Two prominent features differentiate CBA from other forms of economic evaluation:
  • CBA adopts a broad societal perspective (thus it includes all costs and all benefits), and
  • CBA measures the outcomes in monetary terms.
CBA is the appropriate form of economic evaluation to assess the economic efficiency (whether maximum amount of output [e.g., persons screened, cases prevented, or cases treated] is produced from the given level of inputs) of public health-care interventions when health outcomes are disparate.
It is a particularly helpful tool for the following purposes:
Deciding Whether To Implement a Specific Program
Public health interventions are designed to improve the health of the population by addressing particular health problems.
The potential of a health program to achieve a specific health-related objective is a principal but not the only criterion that policy makers have to consider when making a decision to implement a program.
A further justification for the implementation of a program will be the indication that the program is also economically efficient. A CBA might demonstrate that implementing the program will yield a net gain in societal welfare. Together with other relevant criteria, this will help decide whether the program is acceptable.
For example, recent research indicates that a quadrivalent vaccine protects against two strains of human papillomavirus (HPV). (HPV is the virus that is responsible for the majority of cervical cancer cases.)
A CBA might indicate that, even if the price of the vaccine is relatively high, the savings from
  • the averted HPV infection,
  • the resulting cervical cancer treatment, and
  • the averted productivity losses outweigh the costs of vaccination and generate a net gain in societal welfare.
This provides an additional argument for public decisionmakers to support an HPV vaccination program that can prevent thousands of deaths.
Choosing Among Competing Options
The results of a CBA can help policy makers choose the best alternative among programs that are equally successful in achieving a desired health outcome.
The program with the largest net gain in societal welfare is preferable since it will provide the highest return to society in exchange for the expenditure of resources.
Ranking by net gain in societal welfare can also be used to choose the best alternative among interventions with different health outcomes.
For example, public health officials might have to choose between funding a program of free Pap smear testing for women at high risk of infection and an HPV vaccination program.
The results of a CBA might indicate that the net gain in societal welfare equals $521 million for Pap smear testing and $987 million for HPV vaccination programs.
The evident preferable alternative would be the HPV vaccination program.
In another scenario, a national health agency might be considering whether to concentrate on research and development of a therapeutic vaccine against:
  • melanoma,
  • heart disease, or
  • type 1 diabetes.
A CBA might indicate that the net gains in societal welfare for the three vaccines would be:
  • $1.7 billion,
  • $3.8 billion, and
  • $2.8 billion, respectively.
This would indicate that the development of a vaccine against heart disease is the preferable choice.
Choosing and Setting Priorities from a Group of Potential Programs
The social welfare maximization rule can also guide decisions on allocating a fixed budget among a group of potential programs.
The combination of programs that has the largest net gain in societal welfare and that can be implemented within the resource constraints of a given budget is the preferred choice.
For instance, based on its current commitments and future funding projections, the national health agency in the previous example might be able to predict that in the coming 6 years, it can commit annually up to $170 million for development of new vaccines.
At the same time, the estimates of a CBA might indicate that the development of therapeutic vaccines against melanoma, heart disease, and type 1 diabetes will require annual investments of $58 million, $93 million, and $75 million, respectively, for that 6-year period.
A simple comparison then shows that the agency budget will allow financing for two projects but not all three of them.
Focusing on development of vaccines against heart disease and type 1 diabetes will generate the largest net gain in societal welfare, equal to $6.6 billion. This will require annual financing of $168 million, which is within the budget limit of $170 million.
Therefore, the preferred choice would be to focus on development of vaccines against heart disease and type 1 diabetes.
What are costs and benefits?
Benefits are the monetary values of desirable consequences of economic policies and decisions. Together with costs they reflect the changes in individual and social welfare that result from implementing alternative programs.
Benefits are generally classified as direct, indirect, and intangible:
  • Direct benefits are the values of desirable health and nonhealth outcomes directly related to the implementation of proposed interventions that can be estimated by using market-based data.
  • Indirect benefits are the averted costs and savings resulting from the interventions but not related directly to them.
  • Intangible benefits include the values of positive outcomes (e.g., reductions in health risk, pain, and suffering), which cannot be estimated from market data.
A vaccination program against an infectious disease protects the participants from catching the infection and provides additional "herd immunity" for the population, including unvaccinated persons.
These are the program benefits:
  • The savings associated with prevented illness cases among those actually vaccinated would be classified as a direct benefit.
  • The savings resulting from lower morbidity among unvaccinated persons due to herd immunity would be an indirect benefit.
  • The reduced risks of catching the infection for those vaccinated and the peace of mind resulting from that risk reduction would be intangible benefits.
Methods of measuring and classifying costs are discussed in the Cost AnalysisOpen this in a new window tutorial.
Framing a CBA
The first stage in conducting a CBA is framing the study, which determines the research framework of the study.
We will use Influenza vaccination to illustrate this discussion of Framing.
Framing a CBA involves these six steps:
1. Defining the Problem
The study problem must be identified at the outset of any analysis. A clearly stated problem defines the objective of the study. At this initial stage of the study we must consider:
  • what questions need to be answered, and
  • which aspects of the problem need to be explained.
Influenza Vaccination Example:
CBA of a Strategy To Vaccinate Healthy Working Adults Against Influenza
Influenza is a major cause of morbidity and mortality.
Studies using different definitions of influenza illness cases that include both symptomatic and asymptomatic infections estimate annual infection rates in the range from 1% to >20% of the U.S. population.
This study was conducted in 2001 by K. Nichol to assess the economic implications of a strategy for annual vaccination of working adults in the United States aged 18–64 years.
Persons aged >64 years and other persons at high risk are more vulnerable to serious complications of influenza and are specifically targeted for annual vaccinations against influenza.
Until recently, priority groups for annual vaccination did not include the working adult population.
Previous trial studies assessing influenza vaccination benefits among healthy working adults did not demonstrate a clear association between vaccination and economic benefits.
At this first step:
  • The study problem was:
    • To compare the benefits of a program of nationwide vaccination of healthy working adults with its costs.
  • The questions that needed to be answered were:
    • What is the economic impact of influenza on the healthy adult population in USA?
    • What would be the cost of implementing the vaccination program?
    • What would be the benefits of implementing the program?
  • The aspect of the problem that needed to be explained was:
    • Benefit and cost estimates were needed to compare the efficiency of such a vaccination strategy with the results of previous economic evaluation studies of influenza vaccination programs.
We will refer to additional aspects of this "Influenza vaccination example" in the explanations of each of these Framing steps.
2. Identifying Interventions
The scope of the study and the variety of outcomes to be included are determined to a large extent by the nature of the programs under consideration.
Often the study problem itself or the decisions made by policy makers specify the interventions to be analyzed.
These questions highlight the various aspects that will help in identifying the interventions:
  1. What is the nature of each intervention (e.g., a vaccination or a screening program)?
  2. What is the technology used for the intervention (e.g., an MRI test or a blood test)?
  3. What are the target population, the delivery site, and the personnel for delivering the intervention?
  4. What are the options?
    If no alternatives are stated in the program, we must compare the proposed project with the status quo.
Influenza Vaccination Example: Interventions
Vaccination
Subdermal injection of inactivated influenza virus vaccine
Healthy working adults aged 18–64 years
Low-cost settings (e.g., work site clinics, community health department clinics, and public clinics in drug stores and grocery stores)
Proposed vaccination strategy compared with the status quo
3. Defining the Audience
Understanding what information the audience needs and how the study results will be used are the major factors that must be considered at this stage.
These questions will help to identify the audience:
  1. Who will be using the results of the analysis?
  2. What information does the audience need?
  3. How will the results be used?
Influenza Vaccination Example: Audience
Regarding the study audience for the influenza vaccination program, we can answer the following questions:
  1. Who will use the results of the analysis?
    • Public health policy decisionmakers at local, state, and federal levels
    • Health research institutions and scientists
  2. What information does the audience need?
    • What are potential benefits of a nationwide immunization strategy?
    • What are the direct and indirect costs of the program?
  3. How will the results be used?
    • To determine the economic impact of a nationwide influenza vaccination strategy for working age adults.
    • To compare the results with those of earlier studies that did not incorporate indirect costs associated with productivity losses averted.
    • To assess whether the findings from 1994–1995, 1997–1998, and 1998–1999 trial studies on the benefits of influenza vaccination can be generalized to other influenza seasons and to the general working adult population.
4. Defining the Perspective
Usually cost benefit analyses are conducted from a societal perspective. Thus all benefits and costs are considered.
The results then indicate whether the benefits to the society as a whole outweigh the total costs of a proposed project.
When using a narrower perspective, we should include only the benefits and costs relevant to that specific perspective.
For instance, a CBA from the patient perspective will estimate the benefits the patient will receive and the costs that patient will incur as a result of implementing the program.
The CBA can be conducted from any of these perspectives — depending on the audience:
  • Patient perspective
  • Provider perspective
  • Payer perspective
  • Health-care system perspective
  • Government perspective
  • Societal perspective
Influenza Vaccination Example: Perspective
The CBA was conducted from a societal perspective. The benefits and costs considered were as follows:
Benefits Costs
Direct costs averted
  • Health-care provider visit costs
  • Hospitalization costs
Direct costs
  • Vaccination costs
  • Side effect costs
Productivity losses averted
  • Work absenteeism costs averted
  • Future lifetime earnings preserved as a result of deaths prevented
  • Reduced work effectiveness averted costs
Productivity losses
  • Productivity losses attributable to vaccination
  • Productivity losses attributable to potential side effects
An analysis from the patient perspective will include only benefits and costs incurred by patients. Productivity losses are composed mostly of work absenteeism.
Patients who take paid sick leave (provided as a work benefit) will not consider these productivity losses as a cost they incur.
Similarly, vaccinations provided free of charge by public health departments and employers will not be considered as costs for patients.
5. Defining the Time Frame and Analytic Horizon
The time frame and the analytic horizon are largely determined by the treatments or interventions under consideration.
The analytic horizon is usually longer than the time frame because the majority of interventions or treatments produce multiple health and nonhealth outcomes for periods far exceeding the durations of the interventions or treatments.
Although theoretically possible, the inclusion in a study of all possible outcomes and related benefits is usually difficult and costly because of practical considerations (e.g., uncertainties associated with expected effects, time constraints, and resource constraints).
Keeping in mind the practical feasibility matters and the objective of comprehensive inclusion of relevant costs and benefits, we have to choose a time frame and an analytic horizon that are:
  • short enough that the outcomes are not unacceptably uncertain, but
  • long enough:
    • to capture fully the costs and benefits that can readily be associated with the program, and
    • to account for seasonal variations in program activity levels and targeted health problems.
Influenza Vaccination Example: Program Time and Analytic Horizon
The analytic horizon for the model was 1 year. The 1-year period was allowed to track the costs and benefits of a nationwide vaccination campaign and of side effects (e.g., Guillain-Barré syndrome).
6. Defining the Discount Rate
Discounting makes it possible to compare benefits and costs that occur at different times by adjusting their values according to the time preference corresponding to the chosen perspective.
CDC recommends that a 3% social discount rate be used in analyses.
The discount rate is one parameter that can be varied in a sensitivity analysis to test its impact on the results of analysis and to make the results of studies based on different discount rates comparable.
Influenza Vaccination Example: Discount Rate
The study was conducted from a societal perspective; the discount rates used in the model were 5% and 3%.
The worst-case scenario (in terms of vaccine efficacy as determined by the match between circulating viruses and corresponding vaccine strains) used the 5% discount rate, while the base-case and best-case scenario results were estimated at the 3% discount rate.
Test Your Understanding
Please enter your answer to each question before you click on "Our Answer" to each one.
  1. What distinguishes CBA from all the other health economic evaluation analysis?
    Our Answer
    The main difference is that all measures are in monetary (dollar) terms.
  2. Typically, CBA is conducted from which perspective?
    Our Answer
    The societal perspective.
  3. The analytic horizon for a CBA is typically shorter than the time frame.
    True   False
    Our Answer
    False. The analytic horizon is normally longer then the time frame.
  4. CDC recommends that a 3% social discount rate be used in analyses.
    True   False
    Our Answer
    True.
  5. CBA is based on the concepts and theoretical framework of the field of economics called welfare economics.
    True   False
    Our Answer
    True.
  6. Averted disease cost is an example of a cost in CBA.
    True   False
    Our Answer
    False. Averted disease cost is a cost that was prevented from occurring, so it is a benefit resulting from the program.
  7. A CBA can be conducted from the societal perspective only.
    True   False
    Our Answer
    False. It can also be conducted from other perspectives.
  8. Productivity loss is an example of a cost to the patient.
    True   False
    Our Answer
    True. This is money lost to the patient because of the disease.
  9. CBA helps to choose the best alternative among programs that are equally successful in achieving a desired health outcome.
    True   False
    Our Answer
    True.
  10. CBA is also used to compare health-related interventions to those in other economic sectors.
    True   False
    Our Answer
    True, if all costs and benefits are expressed in the same terms (dollars).
Valuation of Health Outcomes
Identifying Intervention Outcomes
Identifying the intervention outcomes and classifying them as benefits or costs is the next step in conducting a CBA.
The results of interventions are broadly classified as:
  • health outcomes,
  • nonhealth outcomes, or
  • intangible outcomes,
based on the nature of the impacts they represent.
We must include in the analysis all outcomes relevant for the study perspective while keeping in mind practical feasibility issues discussed in the previous chapter, Framing a CBAOpen this in a new window.
Each outcome is classified then as either a benefit or a cost, according to the adopted viewpoint.
Health Outcomes
The majority of health-related outcomes included in cost benefit analyses fall into one of the following categories:
  • decreased mortality,
  • decreased morbidity,
  • increased life expectancy,
  • reduced disability,
  • improved quality of life, and
  • averted medical costs.
For example, a CBA of population pre-exposure smallpox vaccination will include health outcomes such as:
  • averted medical costs, and
  • reduced disability from averted cases of smallpox disease in case of an attack.
A program considering provision of diabetes screening for persons at increased risk of disease will include outcomes such as:
  • decreased morbidity,
  • increased life expectancy, and
  • averted medical costs as a result of early detection and treatment of the disease.
Identifying the relevant health outcomes of an intervention or program often involves close consideration of available clinical and epidemiologic data.
Issues that contribute to the complexity of the task and highlight the importance of careful identification of proper outcomes include:
  • a time lag between the identification and improved health outcomes, and
  • the use of intermediate health outcomes for measuring the effectiveness of tests and screening programs.
Nonhealth Outcomes
Often nonhealth outcomes that can be attributed to the impact of a public health program include:
  • reductions in time lost from work, and
  • changes in property values attributable to:
    • provision of health services in the area,
    • improved access to health services in the area, and
    • other causes.
A CBA should account for the values of these nonhealth outcomes to arrive at a correct measure of the economic value of the proposed public health program.
If the values of nonhealth outcomes are not included in a CBA because of the relative insignificance of the effects or the absence of uncontroversial estimation methodologies, they should be discussed qualitatively.
Intangible Outcomes
Intangible health outcomes (e.g., reductions in health risks, pain, and suffering) might be major considerations in implementing an intervention or health program.
The results of a CBA will not reflect the full economic value of the effects of a program if the values of intangible outcomes are not included.
General Health Valuation Methods
Cost-of-Illness Method
The cost-of-illness (COI) method is used to estimate the direct and indirect costs of an intervention.
This method is based on the human capital approach and is discussed in detail in the Cost AnalysisOpen this in a new window tutorial.
The intangible costs are estimated using nonmarket valuation methods.
Nonmarket Valuation Methods
The choices people make in the marketplace (i.e., their behaviors) result from their valuations of the goods they buy and the prices they are willing and able to pay.
If a market exists, we can comfortably use what consumers are willing to pay as an estimate of how much they value the good. Therefore, existence of a market is relevant in this search.
However, because the majority of health outcomes (e.g., health risks) do not have markets, valuing them presents analytical challenges.
Economists have developed theoretically sound and intuitively appealing ways of estimating the value of nonmarket goods. These methods and procedures are based on generally accepted economic theories and are broadly referred to as nonmarket valuation methods.
Until recently, these methods were applied primarily to the valuation of environmental and natural resources. They are now a relevant and necessary part of contemporary health research. In general, two main valuation methods are employed: the revealed preference method and the stated preference method.
1. Revealed Preference Method (RPM)
Hedonic pricing and averting behavior are the two main types of revealed preference methods (RPMs) used in health economics.
By use of these indirect methods, a person's valuation of a health outcome is observed through actions in markets that already exist. This behavior in the market is used to make inferences about the person's valuation of the related health outcome.
Hedonic Pricing (Wage)
Most goods come in bundles. Each bundle is made up of various components (or characteristics) that are not separable but that might be presented in different ways and sold all together at one price.
Each of these components (or characteristics) might confer a different benefit on the buyer.
Therefore, a buyer might pay more to have each additional characteristic or to have more of any particular one characteristic.
The hedonic model is based on this principle. The prices that consumers pay or receive are reflections of the different components of the good in question.
For example, the wage rate that postal workers receive is a price for their labor that is determined on the labor market.
This price depends on characteristics of the postal worker that can be objectively measured, e.g.
  • number of years on the job (experience), and
  • educational level.
On the labor market (which is assumed to be competitive), employees are willing and able to pay more for each characteristic, both in quality (type) and quantity (amount).
A functional relationship therefore exists between the wage and all the measurable characteristics. This relationship can be expressed as:
W = f ( q, e, ex, a, g )
where:
W = the wage rate
q = a measure of qualification
e = education
ex = experience
a = age
g = gender
If data were available, all of these characteristics and outcomes could be subjected to a rigorous empirical analysis (e.g., a regression analysis) to obtain how much more employees pay to have a unit increase in each of the characteristics while controlling for other factors.
This amount is the implicit price received by the worker or paid by the employee for a unit of that particular characteristic.
It is used to represent the employer or worker's value of that characteristic.
Hypothetical Example: A Hedonic Wage Model of Anthrax in the Mail
In the fall of 2001, anthrax was sent through the mail on at least two occasions.
Over time, postal workers who have a greater risk of coming in close contact with mail might be at a higher risk and could demand higher wages.
A hedonic study can be used to determine the wage increase that is a result of the perceived risk of an anthrax attack.
Such a study requires data on the characteristics of postal workers (e.g., wage, experience, and education), including a variable that will identify the workers' risk of exposure to anthrax spores through close contact with mail (e.g., sorting and distributing).
An empirical analysis would then be used to obtain the average increase in wage.
In such an analysis, the variable of concern would be the variable that identifies sorters or distributors (s/d). The functional relationship can be expressed as follows:
W = f ( q, e, ex, a, g, s/d )
The results will provide an estimate of how much more sorters and distributors are paid to do their work. This is an indication of how much they agree to accept to continue performing their duties. And that is an estimate of the market value of the risk borne.
Note: An existing market (i.e., the labor market) has been used to obtain the value of risk (which has no market) to the worker.
Averting Behavior
The value of a small change in health status can be measured by the amount of money a person is willing and able to spend on some controlling or preventive device or defensive (averting) action.
This amount of money represents the person's valuation of safety against a perceived risk.
Some examples of preventive devices on which persons might spend money to mitigate perceived risk include:
  • airbags,
  • smoke detectors, and
  • larger cars.
Shortcomings of the Revealed Preference Methods
The revealed preference methods approach has at least four limitations:
  1. It does not take into account all benefits and costs.
    For example, the nuisance cost of taking and adhering to a medication regimen is not reflected in its cost, which might result in an underestimation of the cost.
  2. The market price might not be the actual value.
    For example, the price of a protective garb might not be the actual value of the reduced risk of serious injury to the person and could be an underestimate of the true value.
  3. The behavior exhibited by the person is based on the person's perception of how the device or action will be able to control or avert the damage, rather than what it can actually do.
  4. Other potential problems of estimation also are rooted in the empirical analysis (e.g., the correct specification of functional relationships).
Thus availability of information has significant influence on the results of the revealed preference methods approach.
2. Stated Preference Method
This direct method uses primary surveys that ask persons to place values on an intervention to attain a level of health outcome in question.
The technique is generally known as the contingent valuation method (CVM).
The major advantage of the CVM over the revealed preference method is that it estimates both tangible and intangible values, thereby providing a better estimate of the true value of the intervention or action.
Theoretical Basis for the CVM
When analyzing changes in consumers' overall welfare (i.e., being better off or worse off) resulting from changes in the market place, welfare economists use a concept referred to as consumer surplus (CS).
A consumer's willingness to pay (WTP) is her subjective valuation of the product in question.
If she sacrifices (pays) an amount that is less than her subjective valuation of the product, then she is made better off by the difference.
CS measures the amount by which she has been made better off, or worse off. Therefore, changes in CS are appropriately used to measure changes in a person's welfare.
The demand curve is a graphic representation of the quantities of a commodity (or product) that a person is willing to buy (pay for) at various prices, everything else being constant. Thus it depicts willingness and ability to pay for a particular product or service.
Assuming that consumers are rational and resources are limited, the higher the price of a product or service, the lower the quantity of the product or service those consumers will be willing and able to buy.
Example: Security Service
Fears of imminent bioterrorist attacks in the United States have contributed to heightened awareness of security. Security is presented on the market either as a product (e.g., detectors) or as a service (e.g., hiring of security guards) that persons are willing and able to buy/hire.
For illustration purposes, a security guard represents a unit of security that can be bought (hired) per year on the market. Also, the more security guards one can hire, the higher the security and therefore the lower the risk of bioterrorist attack.
We will express security guard prices (wages) in millions of dollars. We will use "m" to denote "million(s)", so that "$5m" denotes "5 million dollars".
Figure 1 shows a person's demand schedule for security:
Figure 1. Demand schedule: price versus the number of security guards
Figure 1. Demand schedule: price versus the number of security guards.
Each block in the graph represents a guard.
Based on the demand schedule in Figure 1, the individual will be willing to hire:
  • seven guards at $4m each,
  • one guard if the price is $10m, and
  • none if the price is $11m or more.
When the market determined current price (wage rate) for a security guard is $4m per year, he/she will hire seven of them.
The consumer was willing and able to pay different prices above the market price for each additional guard but did not have to do so because the market price was $4m per guard per year.
The sum of these amounts represents the CS.
The consumer paid:
  • $4m for the first guard instead of $10m,
  • $4m for the second instead of $9m,
  • $4m for the third instead of $8m, and so on.
The total can be computed by finding the area labeled "Consumer surplus" in Figure 2. The consumer surplus is the area above the $4m horizontal line.
Figure 2. Demand schedule showing the consumer surplus for $4m per guard per year
Figure 2. The consumer surplus is the area above the $4m horizontal line.
Figure 3 shows the dimensions of the area of CS in Figure 2:
Figure 3. Dimensions of the consumer surplus triangle
Figure 3. Dimensions of the consumer surplus triangle.
The area of a triangle is:
area = ½ ( base x height )
So the area labeled "Consumer surplus" area in Figures 2 and 3 is:
CS = ½ ( 7 x 7 ) = 24.5m
The total subjective valuation (TSV) is the value that a person puts on a product or service. It is unique and depends on individual characteristics. Figure 4 shows the TSV graphically.
Figure 4. The total subjective valuation for hiring 7 guards
Figure 4. The total subjective valuation for hiring 7 guards.
In Figure 4, the person's TSV of guards hired is the area under the curve up to the number she hired. That is given by:
TSV = ½ ( 7 x 7 ) + 4 x 7 = 52.5m
CS can also be thought of as a person's actual TSV of the security guards (reduced risk of attack) minus the market value of the security guards hired.
The total market value (TMV) is:
TMV = 4 x 7 = 28m
So:
CS = TSV TMV
CS = 52.5 28 = 24.5m
Effect of Price Changes
On the market, prices change for different reasons. These price changes affect the consumer's welfare.
Let us examine what happens to the consumer's welfare as measured by the changes in CS resulting from price changes.
Assuming the price increases to $6m, the consumer is willing and able to buy (hire) five guards instead of seven.
Figure 5 shows the change in CS (CS) from this price change:
Figure 5. The change in consumer surplus in changing from $4m to $6m for each guard
Figure 5. The change in consumer surplus in changing from $4m to $6m for each guard.
CS can be determined by computing the shaded area labeled "Change in consumer surplus (CS)" in Figure 5:
Initial CS = 24.5m
Final CS = ½ ( 5 x 5 ) = 12.5m
CS = 24.5 12.5 = 12m
Alternatively, we can find the area of the region labeled "Change in consumer surplus (CS)" in Figure 5. The rectangle and triangle in Figure 6 make up that area:
Figure 6. Areas making up the "Change in consumer surplus" area in Figure 5
Figure 6. Areas making up the 'change in consumer surplus' area in Figure 5.
The calculation is:
CS = ( 2 x 5 ) + ½ ( 2 x 2 ) = 10 + 2 = 12m
This CS calculation indicates that as a result of this price increase from $4m to $6m per guard, the consumer is worse off than before by $12m.
From the foregoing analysis, given the existence of a market, estimation is made easier because all prices and quantities are observable on the market.
When No Market Exists
The ensuing figures present a more theoretically appealing approach that provides a better approximation of changes in CS, when a market for the product or entity in question does not exist.
Po in Figure 7 represents the average price a consumer faces for all other goods.
Figure 7. Shifts in budget line as a result of income changes
Figure 7. Shifts in budget line as a result of income changes.
According to the figure:
  • The product in question is security guards.
  • PS is the price of the security that is supposed/perceived to be able to reduce the risk of bioterrorist attack.
  • I1, I2, and I3 are budget lines, which represent the various combinations of the two goods (all other goods and security) that the consumer can buy, given:
    • the consumer's income — Yo, and
    • the market prices — Po and PSo.
This can be represented mathematically as:
Yo = PoG + PSoS
The budget line is drawn from the standard equation of a straight line:
G = Yo / Po ( PSo / Po ) S
where:
Yo / Po = the intercept on the vertical axis, and
PSo / Po = the slope of the budget line.
The equation of the budget line is obtained from the income equation. The feasible region is the area under the budget line represented by the green-shaded portion. Any point outside the feasible region is not attainable.
The budget line describes the person's budget constraint. Changes in his/her income are depicted by parallel shifts (outward/inward) in the budget line. An increase in income makes a larger feasible region (the area under budget line I3 and above the horizontal axes). A decrease in her income (to I1) gives the consumer a smaller feasible region (the area under budget line I1 and above the horizontal axis).
Note: the larger the feasible region, the more the consumer can afford of both sets of products. The shift in budget line is parallel because only income changes.
As shown in Figure 8, if the price of security decreases from PSo to PS1 (with the price of all other goods remaining unchanged), the budget line:
  • shifts out from Yo / PSo to Yo / PS1 on the security axis, while
  • pivots at point Yo / Po on the all other goods axis.
Figure 8. Shifts in budget line resulting from price changes
Figure 8. Shifts in budget line resulting from price changes.
This results in an increase in the consumer's opportunity set.
Conversely, when the price of security increases to PS2, the consumer's feasible region reduces.
Indifference Curves
Economists define an indifference curve as a locus of points that is a graphic representation of various product combinations that confer the same utility (satisfaction) on the individual.
Figure 9 shows a set of indifference curves for our all other goods compared with security example.
Figure 9. Indifference curves
Figure 9. Indifference curves.
Along a single indifference curve, U1, for example, an individual consumer is indifferent to the mix of all other goods versus security.
If the consumer were to move from curve U1 to curve U2 and ultimately to curve U5, however, he/she would experience increasing levels of satisfaction.
Properties/Assumptions of Indifference Curves
  • An infinite number of curves exists between any two indifference curves.
  • For any given combination of products, indifference curves cannot cross (i.e., U1 can never be above U2).
  • They are convex to the origin (i.e., they are curved inwards toward the origin as shown in Figure 9).
  • A higher indifference curve represents greater satisfaction gained from that bundle of goods compared with a lower indifference curve, which yields less utility.
  • An increase in utility is depicted by an upward shift in the curve as shown in Figure 9.
Combining Indifference Curves and the Budget Line
The two concepts — indifference curves and the budget line — can be combined to show the quantities of both products that a person with the specified characteristics will consume.
In Figure 10, a consumer with an income level Yo, and budget line Io would prefer to be on the highest indifference curve possible (highest achievable satisfaction).
Figure 10. Budget line (income constraint) and indifference curves (individual preferences)
Figure 10.  Budget line (income constraint) and indifference curves (individual preferences).
Given the consumer's income, U1 would present a satisfaction level that is lower than that person could attain. U3, although desirable, would be unattainable because the budget constraint, Io lies below.
The consumer cannot afford points on U3 (i.e., all its points are outside the feasible region).
The rational consumer will choose to be at point O on U2 and consume S of security guards and G of all other goods.
Point O is the point of tangency, i.e., the point at which the indifference curve and the budget line touch.
Price Increase (Negative Welfare Change)
Figure 11 shows what happens to a consumer's choice when price changes occur.
Figure 11. Price changes and consumer choices
Figure 11.  Price changes and consumer choices.
Assume, for the purpose of this illustration only, that the price of all other goods stays the same.
A consumer who starts out with an initial income Yo on a budget line Io and an initial price of security at PSo will be on an initial indifference curve U2. At that price and income, the person consumes S4 of security traced down from point d.
A price increase from PSo to PS1 will cause the individual's budget line to pivot inward, giving Io'.
This puts the consumer on a lower indifference curve U1, consuming S1 traced down from point b.
Such a change is regarded as a negative welfare change because it makes the consumer worse off than before.
For a person faced with such potential market changes, one can ask two important questions:
  1. What is the income equivalent of this change? We can ask this question in these equivalent forms:
    • What is the amount of money that should be taken from the consumer (in the absence of a price increase) to be on the same indifference curve that the price increase would?
    • How much money should be taken from the consumer to yield the same satisfaction as the price increase would?
  2. If the price change did occur, how much money should be given to the consumer to be back on the initial indifference curve?
    Or we can ask the equivalent question: How much money should be given to the consumer to make him/her be as satisfied as before the price increase?
Graphically, Question 1 is answered by the income wedge labeled EV in Figure 11. (We repeat Figure 11 below.)
Figure 11 (repeated). Price changes and consumer choices
Figure 11 (repeated). Price changes and consumer choices.
Equivalent variation (EV) is the amount of money that should be taken away from a person in the absence of a price change to yield the same level of satisfaction as the change would. It is the maximum amount the consumer will be willing to pay to avert the price change.
In Figure 11, this is illustrated by a parallel inward shift of the initial budget line Io until it just touches the indifference curve U1.
The diagram indicates that if we took the same amount of money as the potential price increase from the consumer, the person would consume S3 of security, at point c.
Question 2 is answered by the income wedge labeled CV in Figure 11. (We repeat Figure 11 below.)
Figure 11 (repeated). Price changes and consumer choices
Figure 11 (repeated). Price changes and consumer choices.
Compensation variation (CV) is the amount of money that should be given to the consumer after the change to yield the same level of satisfaction as before the price change. It is the minimum amount the consumer is willing to accept as compensation for the price change.
This is illustrated by a parallel outward shift of the final budget line Io' (the budget line that reflects the price change) until it just touched the indifference curve U2. The diagram indicates that the person would consume S2 of security at point a.
Notice that when the monetary equivalent of the proposed change is taken away, or when the person is compensated after the change, the quantity consumed is different from what the person otherwise would have consumed. This is true for most people.
As a simple illustration, consider a potential employee who is offered options to receive either:
  1. company-provided insurance that meets minimum coverage requirements and is worth $5,200/year, or
  2. $5,200/year along with documentation stating that the employee has insurance that meets the minimum requirements.
Assuming the search cost is zero, an employee who finds a lower insurance rate will accept the second option and spend the rest of the money on all other goods.
These two measures (EV and CV) are rarely the same. The conditions under which they are the same are not as important as how they can be used to approximate changes in CS.
How do these concepts (EV and CV) compare with the measures of changes in CS discussed in the preceding section?
Figure 12 below graphically combines the preceding concepts to illustrate how EV, CV, and CS are related. For easier illustration, the diagrams are similar to those used to introduce the concepts.
Figure 12. Relating equivalent valuation and compensation valuation to consumer surplus
Figure 12. Relating equivalent valuation and compensation valuation to consumer surplus.
Figure 12 uses two panels to relate the scenarios in Figures 1, 2, 4, 5, and 11:
  • Both panels show the product (security guards) on the horizontal axis.
  • The upper panel shows all other goods on the vertical axis, as Figure 11 does.
  • The bottom panel shows price on the vertical axis. This panel is similar to Figure 5, with more emphasis on the area that represents the change in CS.
The product of interest is security. Therefore, we hold the price of all other goods constant.
For the discussion that follows, to see this text and Figure 12 side by side, please click: Figure 12 in a new browser windowSee this in a new window... When that window appears:
  • If the figure display is too small, click the expansion icon you see when you move the mouse over the lower right-hand corner of the figure.
  • Resize and position the new browser window to the left of this window (you might have to move this window).
In the upper panel, suppose that price is $4m. Given individual income constraints (budget constraint Io) and preferences (indifference curve U2), the consumer will hire seven guards, at the tangency labeled d.
At the $4m per security guard level, the consumer also is willing and able to hire seven guards, depicted in the bottom panel by the point labeled d.
Therefore, the two points labeled d in both panels represent the same choice point but in two different spaces. The consumer is at point d in both panels of Figure 12.
If the price per security guard increases to $6m, the consumer now hires four security guards brought about by the new income constraint (budget line Io') attributable to the price increase. This puts the consumer on a new but lower utility curve, U1. This is depicted in the upper panel at the choice point labeled b.
Also, at the new price, the consumer is willing and able to hire four guards, which can also be shown in the bottom panel at point b.
Again, point b in the two panels is the same choice point displayed in two different spaces.
All points on the upper panel can be traced down and mapped out on the bottom panel, as shown in Figure 12.
In the bottom panel, points b and d can be used to trace out the ordinary demand curve, labeled D, as we saw previously in Figure 12.
The sum of the gray and red regions (ebdcf) makes up the change in CS.
Lines bc and ad trace out demand curves that show changes in price and income that allow the consumer to stay on the same indifference curves; utility is held constant.
Consider the movement from point d to point a. From point d, a price increase is compensated for by an increase in income that puts the consumer back onto the same indifference curve, thus referred to as compensated demand curves, labeled H(U1) and H(U2):
  • H(U1) is a compensated demand curve that holds utility constant at U1, and
  • H(U2) is a compensated demand curve that holds utility constant at U2.
CV is represented in the bottom panel by the sum of all the shaded regions ebadcf (grey + red + blue).
By the same indication, EV is represented in the bottom panel by the shaded regions ebcf (shaded grey).
Notice that CV > CS > EV.
If the price change is small, there is not much difference in these measures as can be seen from the diagrams.
We can easily see why CV is greater than EV in this case.
Suppose we ask a subject two questions:
  1. "How much are you willing to pay to avert the price increase?", and
  2. "How much are you willing to accept as compensation, after the price increase?"
Our expectation is that the subject will state a higher value for the second question than the first. The reason is that the first is bounded by the subject's ability to pay, whereas the second is not.
The first question is the same as the question that resulted in EV and the second is that which resulted in CV.
Practical Application
The graphic representations presented in the preceding section closely model how a rational consumer responds to changes in the market.
However, estimating one's indifference curve (utility function) becomes the real challenge; in fact, it is practically impossible.
For goods that are traded on the market, it is somewhat easier to estimate the compensated demand curves and to compute EV and CV without having to deal with indifference curves.
Because no markets exist for the majority of health outcomes, the contingent valuation method (CVM) is relied on to arrive at estimates for EV and CV as measures of changes in CS.
The CVM
  • is used to estimate the values of intangible outcomes (e.g., reductions in health risks, pain, and suffering), and
  • relies on survey studies to elicit individuals' maximum willingness to pay or minimum willingness to accept for these intangible outcomes in hypothetical or contingent scenarios.
These measures represent respondents' valuations of the intangible outcomes.
Hypothetical Example:
Willingness to Pay for Higher Security (Reduced Risk of Bioterrorist Attack in the United States)
A CVM study could be conducted to estimate the intangible benefit of reduced anxiety of a bioterrorist attack in the United States.
A study using the CVM will involve a survey in which individuals will be asked how much they would be willing to pay for a proposed tighter security program on sea and land that will reduce the risk of an attack from one in 100 to one in 100,000.
For the purpose of illustration, let us assume that these numbers correctly reflect the actual reduction in average risk of attack attributable to increased security.
If the hypothetical scenarios from the proposal (i.e. risks and consequences of attack, including how the proposed program could achieve the set goals) are conveyed intelligibly to the respondents, then economic theory suggests that a rational consumer (the average American in this case) will:
  • consider everything else in her life together with the issue at hand,
  • decide based on her best assessment of the situation, and
  • eventually state her subjective valuation of the proposal.
This can be represented in a simplified two-good world diagram as shown in Figure 13:
Figure 13. Two-good world diagram
Figure 13. Two-good world diagram.
In Figure 13, status quo risk is one in 100. At her current valuation of risk of attack, she consumes S1. The security measures will make her better off because the risk of attack decreases.
This is equivalent to a decrease in her subjective unit value (implicit price) for security so her budget line pivots out and she enjoys a higher level of security at S2.
Note: This is an example of a positive welfare change, in contrast with the previous example, which is a negative welfare change.
Two questions can be asked:
  1. How much are you willing to pay to reduce the risk of bioterrorist attack from one in 100 to one in 100,000?
  2. If this level of security is not available, how much are you willing to accept as compensation?
The choice of the appropriate question (i.e., 1 or 2) as the right value for the benefits is one based on property rights, which is beyond the scope of this tutorial.
Steps in Conducting a Contingent Valuation Study
The CVM employs survey studies to gather data on a relevant population's:
  • maximum willingness to pay, or
  • minimum willingness to accept the intangible benefits it stands to gain or lose from a public health intervention or program.
Sophisticated regression techniques are then applied to analyze the assembled data and to estimate the population WTP.
A detailed description of the various methods of conducting survey studies and regression analyses is beyond the scope of our tutorial series.
Instead, we will present a summary of the major stages in conducting a contingent valuation study.
A systematic contingent valuation study can be conducted by following these six steps:
1. Reconnaissance Survey
A reconnaissance survey provides an overview of the characteristics of the population under study. Its characteristics are:
  • It normally involves the use of maps and socioeconomic and demographic data.
  • It is relevant for all studies because a good understanding allows one to do a good survey.
  • Visiting the area and seeing things firsthand might be necessary to best:
    • design the survey, and
    • determine the type of sampling that is suitable for the information needs of the research.
A survey to determine willingness to pay for higher security (lower risk of bioterrorist attack) in the United States would require information on multiple factors (e.g., the size of the population and its component ethnic groups and income distribution).
2. Sampling Method and Sample Size Calculation
It is important to obtain a sample that is representative of the population under investigation.
Because surveying the whole population is very costly, the statistically appropriate sample size is in order.
In a survey to determine willingness to pay for higher security (lower risk of bioterrorist attack) in the United States, sampling must be done in such a way that all ethnic groups, social classes, and regions are represented.
3. Developing the Survey Questionnaire
The major components of a CVM survey are:
  1. Introductory questions
    The introductory questions are designed to determine the knowledge, attitudes, and beliefs of respondents about the intervention and the health risks the program aims to alter.
  2. A description of the health risks and the disease that the intervention under consideration must alleviate
    The risks of an attack and the disease or health condition and their short- and long-term impacts are explained in a short scenario. The security measures that would reduce the risks are also described in this section.
  3. The main part of the questionnaire, i.e., a set of questions asking whether respondents would pay a specified amount for a specified reduction in health risks
    This part includes three types of questions:
    1. An open bid or preset bid, in which the respondent is asked whether he would pay a fixed amount. For example, "Would you pay $75 for a security measure that reduces your annual risk of attack from one in 100 to one in 100,000?"
    2. An open-ended question asks how much the respondent is willing to pay for a reduction in the risk of attack from one in 100 to one in 100,000.
    3. A closed-ended question, in which the respondent is asked to name a value within specific ranges or to pick a range within which their offer falls.
  4. A set of demographic questions concerning factors such as gender, age, occupation, and income to determine the socioeconomic status of the respondent.
    This information, together with the data collected from the introductory part, helps to explain the differences in valuation for respondents with different knowledge and experiences.
For the accuracy and statistical power of the survey to be ensured, both the bid amount and the potential reduction in risk must vary randomly.
4. Conducting a Pilot Survey
In a pilot survey, questionnaires are tested on a small sample of the subjects. Completed questionnaires are inspected for possible mistakes and for unforeseen drawbacks of the procedure or the questions in the survey.
The pilot survey is very important because it reduces cost and prevents serious mistakes in the main study. It must be performed early enough to allow for major changes.
5. Administering the Survey
Once the questionnaire is ready, we can administer the survey.
Based on a multitude of factors (e.g., questionnaire complexity, target population, and budgetary constraints), we can choose to administer the survey through face-to-face interviews, telephone interviews or mail surveys.
To determine the most suitable mode of administering the survey, each method's advantages must be weighted against its relative shortcomings:
  • Face-to-face interviews with trained interviewers are most suitable for surveys with detailed questions and answers, but are usually the most expensive.
  • Telephone interviews are the least preferred method because of the difficulty in conveying potentially complex information over the telephone.
  • Mail surveys (the least costly of the three) are frequently used but have the highest non response rate.
Each method must be checked for potential biases, such as interviewer or non response bias.
6. Collating, Analyzing, and Calculating WTP
Having collected the data from the questionnaires, we organize the data in the order and format suitable for the analysis that is to be performed.
Total WTP is achieved by deriving the population average WTP from the data and multiplying it by the population size, N. The regression techniques allow us to estimate the population average WTP, after controlling for all variables that are suspected to be relevant and for which data are available.
The regression of the survey respondents' WTP on variables that characterize the sample and the intervention, such as:
  • income (Y),
  • education (E),
  • age (A),
  • disease or health risk exposure experience (D), and
  • quantity of the intervention proposed (Q)
provides us with the functional relationship between the WTP and these variables:
WTPi = f ( Yi, Ei, Ai, Di, Qi ... )
where i indexes respondents.
To arrive at the population average WTP, we then have to insert the population average values for income, education, and other variables in the estimated regression equation.
The population WTP is then calculated as the product of the population average WTP and the size of the population, N.
Advantages and Limitations of the WTP Method
A major advantage of the CVM is that it accomplishes the task of estimating willingness to pay for services and goods with no existing markets.
The WTP estimates of intangible benefits of these non-traded goods and services complement the estimates of the benefits and costs of public health programs and thus provide a measure of the full economic value of proposed interventions.
Three concerns with the CVM method have been expressed:
  • The major concern with the CVM method is the reliability of the estimates (i.e., how accurately they reflect true willingness to pay).
    Because WTP estimates are based on stated willingness to pay rather on than actual payments made by respondents, estimates of the true value might be systematically under- or overestimated.
  • A second source of bias in WTP estimates is the potential undervaluation of health-care services costs by persons who can rely on health insurance to pay for a considerable part of their medical treatment expenses.
    By lowering the individual's financial burden of medical treatment, insurance coverage makes health services more affordable, leading to their potential overuse. Economists call this a moral hazard.
    At the same time, because work-benefit packages (e.g., paid sick leaves) shield persons from income loss associated with indirect medical costs of illness, persons might overemphasize the value of intangible outcomes of diseases.
    Together with moral hazard, this might cause a bias in respondent valuation.
  • Another problem with the method is the difficulty of explaining the CVM sufficiently well that respondents actually internalize the perceived effects.
    For example, it is difficult for people to understand the difference in probabilities/risks associated with the health intervention.
These potential problems indicate that the design of a CVM questionnaire and survey is a complex undertaking. It requires the participation of trained specialists and considerable amount of time to execute and analyze the survey results.
Test Your Understanding
Please enter your answer to each question before you click on "Our Answer".
  1. What is a consumer surplus (CS)?
    Our Answer
    CS is the difference between the amount of money that a consumer is willing to pay for something, and the actual amount she pays.
  2. Why is CS used as a measure of a consumer's welfare?
    Our Answer
    CS is used as a measure of welfare because it indicates the value of the good in excess of what the consumer paid.
    It is the consumer's total subjective valuation (TSV) minus the amount she sacrificed (market value) for it.
  3. Suppose that Figure 1, repeated here, is a perfect representation of Anne's demand for security:
    Figure 1 (repeated). Demand schedule: price versus the number of security guards
    Figure 1 (repeated). Demand schedule: price versus the number of security guards.
    Use Figure 1 above to answer the following questions, assuming that:
    • Anne would not hire any guard if the price is $11m or higher, and
    • the current market price is $3m per year.
    1. How many guards will she hire, and how much does she pay?
      Our Answer
      She will hire eight guards and pay ($3m x 8) = $24m.
    2. Compute her CS at the current market price.
      Our Answer
      CS = ½ (8 x 8) = $32m
    3. What is the total value to her (her total subjective valuation)?
      Our Answer
      Total value = ½ (8 x 8) + 3 x 8 = 32 + 24 = $56m
    4. Compute the new CS with the price changed to $5m.
      Our Answer
      New CS = ½ (6 x 6) = $18m
    5. Is Anne better off or worse off?
      Our Answer
      She is worse off. CS, as a measure of her welfare, is reduced.
    6. By how much is she better off or worse off? (This is the change in CS.)
      Our Answer
      CS = New CS – Initial CS = 18 – 32 = –$14m
      Alternatively, CS = (6 x 2) + ½ (2 x 2) = 12 + 2 = $14m.
    7. Assume a two-good world with all other goods (G) and health outcome (H).
      Suppose:
      • the unit price of health is $4,
      • the average price of all other goods is $5, and
      • Anne's income is $40.
      Please answer these questions:
      1. What is the equation for Anne's budget line?
        Our Answer
        The equation for Anne's budget line is
        40 = 5G + 4H
        where
        G = units of all other goods and>
        H = units of health outcome.
      2. Use a sheet of paper to:
        • Draw and label Anne's budget line. Label the feasible region.
        • Suppose a new health policy reduces the price of health to $2. Indicate the changes to her feasible region.
        • Draw and label Anne's new budget line on the same diagram.
        Our Answer
        Anne's initial and revised budget lines and feasible regions
        Anne's budget line, feasible region, and revised budget line.
        • The initial feasible region is the blue area
        • The feasible region increases after the price reduction to include the green area.
        • The dashed green line is Anne's new budget line.
      3. After the health policy price reduction, is Anne better off or worse off? Why? (You might explain using indifference curves.)
        Our Answer
        Anne is better off after the health policy price reduction because she moves to a higher indifference curve, i.e., a higher level of satisfaction.
        Her welfare has increased.
  4. The stated preference method, if conducted well, is a better way of valuing health outcomes.
    True   False
    Our Answer
    True. The stated preference method makes a good attempt at including all intangible benefits and costs.
  5. Willingness to pay will be the same for all respondents if the survey is conducted well.
    True   False
    Our Answer
    False. Willingness to pay can never be the same for all respondents because of differences in individual characteristics (e.g., value judgments, incomes, and age).
    The rigorous regression and statistical analysis is designed to control some of these sources of variation.
Calculating and Presenting the Summary Measures
After all the benefits and costs have been estimated, the next and final step is the presentation of results in a simple and understandable form for the audience.
The two summary measures typically used are:
  • net present value (NPV), and
  • benefit-cost ratio (BCR).
NPV is calculated by summing the dollar-valued benefits and then subtracting all of the dollar-valued costs, with discounting applied to both benefits and costs as appropriate.
Net Present Value
The formula for NPV is:
Calculating NPV.
A CBA will yield a positive NPV if the benefits exceed the costs. Implementing such a program will generate a net benefit to society.
Benefit-Cost Ratio
The benefit-cost ratio (BCR) represents the ratio of total benefits over total costs, both discounted as appropriate. The formula for calculating BCR is:
Calculating BCR.
For example, a BCR value of 1.2:1 will indicate that for every $1 invested (costs), society would gain $1.2 (benefits).
Example: CBA of School-Based Tuberculin Screening Program
This study was conducted in 1995 to compare tuberculin screening strategies:
  • screening of all kindergartners and high school entrants (screen-all strategy), versus
  • screening limited to high-risk children (targeted screening).
The tuberculosis incidence in the United States declined for three decades as a result of school-based screening programs for tuberculosis infection recommended by the U.S. Public Health Service.
As the screening programs were revised to focus on persons at high risk of infection, the majority of health departments discontinued tuberculin screening of schoolchildren. But such screening had a resurgence beginning in 1985.
This study considered the costs and benefits of two alternative school-based tuberculosis screening strategies to help in making decisions regarding initiation or continuation of screening programs. Table 1 shows the results of the study:
Table 1. Impact of two programs of tuberculin screening of kindergartners and high school entrants in Santa Clara County, California, with baseline assumptions
Strategy Group Program cost($) Benefits($) Cases prevented
(discounted cases
prevented)
Net annual cost
(net benefits)($)
Benefit-cost
ratio
Screen-all Kindergartners 183,868 58,201 11.1 (3.9) 125,628 0.31
  High school entrants 287,452 217,176 37.2 (16.1) 70,276 0.76
  Both 471,320 275,377 48.3 (20.0) 195,904 0.58
Targeted screening Kindergartners 42,218 41,099 7.9 (2.7) 1,119 0.97
  High school entrants 155,925 169,136 28.9 (11.3) (13,211) 1.08
  Both 198,143 210,235 38.6 (11.3) (12,092) 1.06
Source: Boetani M. JAMA 1995; 274(8): 613–9.
Findings: Tuberculin Screening
For the two tuberculin screening programs:
  • The program cost of the screen-all program is $471,320 per year, and the net cost is $195,904.
    The targeted screening program costs less, $198,143, and produces a net saving of $12,090.
  • For each dollar invested in the screen-all program, $0.58 is saved (BCR = 0.58).
    For each dollar invested in the targeted screening program, $1.06 is saved (BCR = 1.06).
  • On the other hand, the screen-all program results in more cases prevented than does the targeted screening.
These findings should be considered when deciding which strategy to employ in school-based tuberculosis screening programs.
Advantages and Limitations of BCR as a Summary Measure
Benefit-cost ratio is a simple summary measure that allows a straightforward communication of results of a CBA for decision making.
However, many researchers have highlighted these two shortcomings of BCR that limit its usefulness when comparing the results of various cost benefit analyses:
  1. BCR is sensitive to how costs and benefits of a project are classified. Let us consider the previous example, with an additional assumption that the analyst classified the benefits from costs averted for high school entrants as a negative cost for the program. Table 2 presents the results of calculating BCRs for both classifications:
    Table 2. Benefit-cost ratios for screen-all versus targeted screening programs
    Strategy Group Classification A
    (screen-all)
    Classification B
    (targeted screening)
    Cost($) Benefits($) Benefit-cost
    ratio
    Cost($) Benefits($) Benefit-cost
    ratio
    Screen-all Kindergartners 183,868 58,201 0.31 183,868 58,201 0.31
      High school entrants 287,452 217,176 0.76 (287,452 – 217,176) =
    70,276
    0 0
      Both 471,320 275,377 0.58 254,144 58,201 0.23
    Targeted screening Kindergartners 42,218 41,099 0.97 42,218 41,099 0.97
      High school entrants 155,925 169,136 1.08 (155,925 – 169,136) =
    –13,211
    0 0
      Both 198,143 210,235 1.06 29,007 41,099 1.42
    The reclassification of some benefits as negative costs changed the BCRs of both strategies:
    For every dollar invested in the screen-all program:
    • the return in benefits fell from $0.58 to $0.23, and
    • the BCR for the targeted screening program increased from 1.06 to 1.42.
  2. BCR is scale sensitive, i.e., it is sensitive to sizes of the numerator and denominator in the ratio.
    One reason that the targeted screening strategy with original classification has a higher BCR than the screen-all strategy (represented by Classification A in the table above) is that its costs and benefits are much lower than those of the screen-all strategy.
Therefore, a BCR is a good summary measure when we consider only one program relative to no program, in which scale (how large or small) is not a factor.
The same is true when we are interested in determining whether an intervention would have a BCR exceeding or falling short of a certain value and thus are not interested in scale considerations.
Advantages and Limitations of NPV as a Summary Measure
Unlike a BCR, an NPV is not sensitive to classification of benefits and costs because it measures the absolute difference between them.
This is one of the main reasons that most economists prefer to use NPV as the summary measure of a CBA.
Furthermore, by using NPV as summary measures of CBA we can compare alternatives among a group of projects and pick the preferred alternatives that meet our budget constraints.
This can be done both for programs equally successful in achieving a desired health outcome and for those with different health outcomes.
Choosing the alternative(s) with the largest NPV that does not exceed a given budget is the decision rule for selecting the preferred program(s).
To make the right choice when the additional consideration of budget constraint is a factor in a CBA, we have to provide information on a project's resource requirements.
Presenting the discounted costs together with the NPV of a project provides this information and allows decisionmakers to make informed choices about resource use.
Incremental Summary Measures
When we are conducting a CBA of a project or intervention, we are comparing it to a "no intervention" baseline.
NPV can also be used to consider the benefits and costs of alternatives such as:
  • expanding an existing program,
  • adopting an intervention to replace an existing intervention, or
  • the alternative with respect to a program which will definitely be adopted.
Incremental NPV is a summary measure that is used to compare programs under those circumstances. It is calculated as follows:
Incremental NPV = ( PV BenefitsB PV BenefitsA ) ( PV CostsB PV CostsA )
Incremental NPV = NPVB NPVA
Here the baseline, intervention A, is either the existing intervention or the intervention deemed to be less effective.
Example: Incremental NPV for the Screen-All Strategy
We can calculate the incremental NPV for the screen-all strategy with respect to targeted screening in a school-based tuberculosis screening program. Using the Costs and Benefits values from Table 1Jump to another place on this page. Use the Back command to return., the incremental net present value for screening all kindergartners versus targeted screening is:
Incremental NPV = ( PV BenefitsAll PV BenefitsTS ) ( PV CostsAll PV CostsTS )
  = ( $58,201 – $41,099 ) ( $183,868 – $42,218 )
  = – $124,509
The results of similar calculations for high school entrants and both groups of students are shown in Table 3.
Table 3. Incremental net present value (NPV) for the screen-all strategy
Strategy Group Program cost($) Benefits($) Incremental
annual cost
(incremental benefit)
($)
Screen-all Kindergartners 183,868 58,201 124,509
  High school entrants 287,452 217,176 57,065
  Both 471,320 275,377 183,812
Targeted
screening
Kindergartners 42,218 41,099 . . .
  High school entrants 155,925 169,136 . . .
  Both 198,143 210,235 . . .
As is evident, the incremental costs exceed incremental benefits when comparing the screen-all strategy with targeted screening.
Conducting a Sensitivity Analysis
Having estimated the summary measures, we can then study the impact of different input variables on the results of our analyses by conducting a sensitivity analysis.
Sensitivity analysis takes into account the uncertainty associated with the assumptions and parameters of CBA by studying how changes in variable values impact the results.
A conclusion of CBA is considered "robust" with respect to a variable if a relatively large change in the value of the variable does not change the conclusion.
We can conduct both one-way and multi-way sensitivity analyses, in which a single variable or multiple variables are altered, respectively.
The results of a multi-way sensitivity analysis will be more informative, however, because our estimates involve interdependent epidemiologic, clinical, and economic data.
The results of simultaneous changes in more than one variable are bound to more accurately reflect interactions between these variables and their impact on conclusions of our CBA.
Please see the Sensitivity AnalysisOpen this in a new window section of the cost analysis tutorial for more detail.
Advantages and Limitations of CBA
As a decision-making tool that helps allocate scarce resources to programs that maximize societal economic benefit, CBA compels analysts to study the full economic impact of all potential outcomes of an intervention.
Expressing the results of this comprehensive analysis in purely monetary terms makes it possible to compare:
  • different programs having different health outcomes, or
  • health programs to nonhealth programs.
Furthermore, the identification of all resource requirements (costs) and benefits of an intervention or program allows analysts to examine its distributional aspects, (e.g., who will receive these benefits and who will bear the costs).
The major limitation of CBA is the empirical difficulty associated with assigning monetary values to benefits (e.g., extended human life, improved health, and reduced health risks).
Besides the complexity of various methods designed to value these benefits, analysts usually confront controversy over the appropriateness of attaching a certain monetary value to human life.
Measuring the cost per unit of health outcome in CEA circumvents the need to make an explicit valuation of human life.
Nevertheless, when decisions are to be made as to whether to implement a life-saving intervention based on its cost-effectiveness measure, policy makers must make the implicit decision as to whether the investment is worth the lives it will save. CBA makes this consideration explicit.
Finally, as in any other study, the results of CBA are only as good as the assumptions and valuations on which they are based.
Hence, understanding the implications of analysis assumptions and methods is essential for a correct interpretation of results.
Test Your Understanding
Please enter your answer to each question before you click on "Our Answer".
  1. A negative net present value (NPV) implies that benefits exceed costs.
    True   False
    Our Answer
    False. A negative NPV implies that costs exceed benefits.
  2. NPV is a ratio of the computed present values.
    True   False
    Our Answer
    False. NPV is the difference between computed present values. Benefit-cost ratio is a ratio.
  3. The table below is a summary of a CBA study for two competing projects: A and B.
    Projects A B
    Costs (million $) 2.2 8.5
    Benefits (million $) 6.0 14.1
    Assuming that all costs and benefits:
    • are present values, and
    • were computed for the same time period,
    please answer these questions:
    1. Compute the benefit-cost ratios (BCRs) for each project.
      Our Answer
      BCRA = 6 / 2.2 = 2.7:1
      BCRB = 14.1 / 8.5 = 1.7:1
    2. How would you interpret the results to the policy maker, using layman's language?
      Our Answer
      One dollar spent on Project A returns 2.7 dollars.

      One dollar spent on Project B returns 1.7 dollars.
    3. Based solely on the results from the preceding question, which project would you recommend?
      Our Answer
      Project A has a higher return per dollar spent so we would recommend it over Project B.
    4. Compute the NPV for each project.
      Our Answer
      NPVA = 6 2.2 = $3.8
      NPVB = 14.1 8.5 = $5.6
    5. Interpret the results of the answers to the previous question.
      Our Answer
      Project A gives us a net benefit worth $3.8 million.

      Project B gives us a net benefit worth $5.6 million.
    6. Based on those results, what would be your recommendation?
      Our Answer
      Society gains more from Project B than from Project A.
      Therefore we would recommend Project B.
    7. Do these change your previous recommendations? Why or why not?
      Our Answer
      Yes. However, other relevant factors need to be taken into consideration:
      • Project B has about four times the capital outlay of Project A.
      • Society might not be able to implement Project B because of limited resources.
      • Political or societal support might also play a part.
  4. Why do we conduct sensitivity analyses?
    Our Answer
    We conduct sensitivity analyses to test the robustness of the results.
    Our conclusions are robust if they do not change when we vary parameter values over ranges that reflect the uncertainty in the underlying assumptions/data.
Glossary — Cost Benefit Analysis
Benefit-cost ratio (BCR)
A ratio that expresses benefits (in dollars) per each dollar spent. If it is:
  • greater than one, then benefits outweigh cost;
  • less than one, then costs outweigh the benefits; and
  • equal to one, then they are the same.

Budget line
A line that defines the combination of commodities that one can buy given one's income and the prevailing market prices.

Compensated demand curve
A type of demand curve that shows the relationship between price and quantity demanded when utility is held constant by income compensation (i.e. the price changes are compensated for by changes in income).

Compensation variation (CV)
The amount of money that would have to be given to or taken away from a person after a change to make her as satisfied as she was before the change.

Consumer surplus (CS)
The difference between the amount that a person is willing to pay and the amount she actually pays on the market. It is a measure of welfare.

Contingent valuation method (CVM)
A survey study that gathers data on population's willingness to pay, or accept payment for the intangible benefits/costs from a public health intervention or program.

Demand curve/schedule (ordinary demand curve)
A line that defines the quantities of a commodity that a consumer is willing and able to buy at various prices, all else constant.

Equivalent variation (EV)
The amount of money that would have to be given to or taken away from a person in the absence of the change to make her as satisfied as the change would make her.

Hedonic pricing
A statistical technique that is used to reveal how much a consumer pays (implicit price) for each of the components (or characteristic) of a commodity.

Indifference curve
A locus of points that defines the combinations of goods that gives the same utility (satisfaction).

Net present value (NPV)
The present value (discounted future value) of the net benefits of a project or program.

Point of tangency
The single point at which the budget line touches the indifference curve.

Rational consumer
A consumer, believed to be of sound mind, who makes analytically sound decisions based on all available information.

Regression analysis
A statistical procedure that is used to determine the values of parameters for a function that best fit a set of data observations.

Statistical life
A measure used to compute the value of life that is independent of the characteristics of any particular person.

Utility
Term used by economists to connote satisfaction.

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