Chapter 3: Cost and Benefit Analysis

Cost Identification Analysis

• Cost Identification Analysis – measures the total economic cost of a given medical condition or type of adverse health behavior.– Examples: Cost of asthma or Alzheimer’s

disease. Cost of cigarette smoking or excessive alcohol consumption.

Three Types of Costs

• Direct medical costs – all costs incurred by medical care providers when treating the condition.

• Direct nonmedical costs – monetary costs imposed on any nonmedical care personnel, including patients and their relatives.

• Indirect costs – opportunity cost of the time influenced by the illness or health behavior such as lost productivity because of sickness, injury, or loss of life.

Examples of Cost Identification Analysis

• Fanslow et al. (1997) Social Science and Medicine– Cost of Homicides in New Zealand

• Total cost = slightly more than $53 million in 1992• Total cost for homicide victims = $24 million

(direct medical = $800,000 and indirect costs = $23 million).

• Total cost for perpetrators = almost $30 million ($24 million direct medical costs and $6 million indirect costs).

Example - continued

• Weiss, Gergen, and Hodgson (1992), New England Journal of Medicine– Total annual cost of asthma in the U.S. > $6.2

million in 1990• Direct medical costs > $3.6 million

• Indirect costs > $2.5 million– Lost school days = $900 million

– Lost work due to illness = $800 million

– Lost work because of worker death = $800 million

Value of Cost Identification Analysis

• While valuable because it sheds light on the economic impact of illnesses and adverse health behaviors, cost identification analysis does not provide information on the wastefulness of various medical interventions or the best or efficient way of saving lives.

• Cost-Benefit Analysis and Cost-Effectiveness Analysis do offer this type of information.

Cost-Benefit Analysis

The Theory of Cost-Benefit Analysis• Suppose an “all-knowing and benevolent”

Surgeon-General (SG) is responsible for maximizing the social utility or happiness of the population in an area.

• The SG achieves the objective by maximizing the total net social benefit received from each and every good in society.

The Surgeon General of the US

Vice Admiral Richard H. Carmona was sworn in as the 17th

Surgeon General of the United States Public Health Service on August 5, 2002, and assumed the role of Acting Assistant Secretary for Health on February 9, 2003.

Theory of Cost-Benefit Analysis - continued

• For medical services, the SG faces the following objective:– Max TNSB(Q) = TSB(Q) – TSC(Q)

• Where Q identifies the decision variable- how many medical services to produce – and TSB and TSC reflect the total social benefit and total social cost associated with consuming and producing medical services, respectively. Total net social benefit (TNSB) represents the difference between the two.

TSB and TSC

• Total social benefit can be treated as the money value of the satisfaction generated from consuming different amounts of medical services. TSB increases at a decreasing rate reflecting the law of diminishing marginal utility.

• Total social cost can be looked at as the money value of all the resources used in the producing the different amount of medical services. TSB increasing at an increasing rate indicating the law of diminishing marginal productivity.

Quantity of Medical Services Q

$

TSB

TSC

Q0

A

B

Determination of the Efficient Level of Medical Services

Q0 represents the efficient level of medical services becauseTNSB, the vertical difference between TCB and TSC, is the greatest.

MSB and MSC

Marginal social benefit• (MSB) = TSB/Q or slope of TSB curveMarginal social cost• (MSC) = TSC/Q or slope of TSC curve

Geometric principle – the distance between two curves is maximized when slopes are equal.

Quantity of Medical Services Q

$

MSC

MSB

A

B

C

Q0

E

F

QL

G

H

QR

A Marginal Perspective of the Efficient Level

The amount of medical services at Q0 is efficient because MSB = MSC. QL reflects underprovisionbecause MSB > MSC and QR indicates overprovision because MSC > MSB. Triangular areas ECF and GCH reflect the deadweight losses associated with inefficient outcomes.

The Net Benefit Calculus - revisited

• The SG’s task can be restated as setting the net marginal social benefit (NMSB) of each and every good equal to zero, or

• NMSB(Q) = MSB(Q) – MSC(Q) = 0

• If NMSB(Q) > 0 produce more.

• If NMSB(Q) < 0 produce less

Practical Side of C/B Analysis

Several steps must be taken to implement C/B analysis in practice.

• Enumerate and quantify the benefits of the program or intervention, e.g.,

– Medical costs diverted because an illness is prevented

– Monetary value of any gains in productivity because death is postponed or illnesses prevented

– The monetary value associated with the utility of being in a state of good health

C/B in practice - continued

• Costs must be enumerated and quantified, e.g.,– Opportunity cost of each and every resource

involved in the program or intervention.• Should capture both the money (explicit) and time

(implicit) cost of resources.

Discounting Costs and Benefits

• Discounting considers the time value of goods and services. In general, people prefer receiving goods and services today than in the future.

• Stated in financial terms, a dollar received today is worth more than a dollar received tomorrow.

Discounting Costs and Benefits - continued

• Since a medical intervention typically yields a stream of future benefits and costs, discounting of values is necessary to state all values in present day terms for comparability. For example, the present value of $1 received at the end of the year when the discount rate is 5% is:– PV = $1/(1+.05) = $ .95

Discounting Costs and Benefits - continued

• In general, if there are N periods for which the medical intervention generates benefits and/or cost and the discount rate is represented by r, we can write:

PV = B1-C1 + B2-C2 + . . . + BN-CN

(1+r)1 (1+r)2 (1+r)N

NOr PV = Bi-Ci i (1+r)i

Discounting Costs and Benefits - continued

• Careful consideration must be given to the choice of the discount rate. The discount rate should reflect society’s time preference for goods and services.

• If the chosen rate is higher than the true rate, short-term interventions will be chosen over long-term interventions.

• The T-bill rate is often used and studies normally examine the sensitivity of the results to different discount rates.

The Value of a Human Life

• To properly estimate the benefits of a medical intervention, it is often necessary to put a value on a human life. Two approaches.– Human Capital Approach – equate the value of a person’s

life to the market value, in present value terms, of the output produced by an individual over the remaining years of that person’s life.

– For example, suppose a life-saving treatment, if implemented today, provides an estimated 2 additional years of life for an estimated 10,000 adult males, each with his human capital worth $1,500 for those 2 years. The benefit, in terms of the value of life years saved, would be $15 million.

Human Capital Approach - continued

• Although widely accepted and used, human capital values may be understated because of gender and racial discrimination in the labor market.

• Additionally, the human capital approach would assign a zero value of life for someone who is chronically unemployed.

Willingness to Pay Approach

• Willingness to pay approach assigns a value of life based upon someone’s willingness to pay for a small reduction in the probability of dying.

• This kind of information is revealed when people purchase safety equipment or are compensated for working in risky environments, for example.

Willingness to Pay Approach - continued

• To understand the logic, consider a person who is deciding to purchase a device that can reduce the probability of dying by Pr. Using the cost-benefit principle, the person with a value of life equal to V would be indifferent about buying the device of cost, C, if: – Pr • V = C (or marginal benefit equals

marginal cost.)

Willingness to Pay - continued

• Rewriting:– V = C/Pr

Thus, if society is willing to pay $100 per person per year for some device that improves environmental quality by reducing the probability of dying by 1 in 10,000, the imputed value of a life equals at least $1 million ($100 divided by 1/10,000

Willingness to Pay Approach - continued

• For figures based on various types of regulations see Table 7-2 in text.

• Viscusi (1993) JEL found willingness to pay estimates to range between $3 million and $7million in 1990 based on labor market studies where workers must be compensated for undertaking risky jobs. Note the figure for wage premiums for dangerous factory jobs in Table 7-2.

• Viscusi and others point out the willingness to pay numbers greatly exceed human capital estimates by a sizeable margin.

Willingness to Pay Approach - continued

• Advantage – measures the total value of life, both job market value and leisure time..

• Disadvantage – difficult to develop precise, reliable data about how much people value safety.

The Game of Life

Bon Chance!

Determining the Value of Your Life

• We begin with a pool of 10,000 people.

• Each person is asked to play a game, if willing.

• Each person must determine the fee that he or she will accept or be paid to participate in the game.

• The fee is based on each person’s own values and the expected level of competition.

• One thousand of the 10,000 lucky people with the lowest fees will be chosen to play the game. The assumption is that competition among the 1,000 individuals will keep fees close to actual willingness to play the game.

Determining the Value of Your Life

• One of the 1,000 players will be selected at random and executed.

• The rest will receive their fees and are allowed to withdraw from the game.

• How much will you charge to play the game?

Calculations

• Fee = probability of dying times value of life (i.e., MB = MC)

• Value of life = Fee/probability of dying

• Value of Life = 1000 X Fee

• Major Point: The value of our lives is revealed by our acceptance or avoidance of risk.

End of Game

I hope you won!

Reconciling the Human Capital and Willingness to Pay Approaches

• Keeler (2001) JHE– Points out that standard economic models of labor

supply assume that the value of leisure time at the margin is equal to the marginal wage rate (i.e., marginal cost equals marginal benefit of working).

– If we assume the value of all time is equal to the wage rate (no diminishing returns due to leisure – if so a lower bound estimate), we can calculate the value of life by multiplying the wage rate by total discounted hours of life time remaining.

Reconciliation - continued

• Makes these assumptions– Workers stay employed for 5 years after we first observe them

working.– After the initial period they revert to the 1990 participation rates:

92% of 25-54 year old mean remain employed; 70% of men 55-64; 16% of men 65 and over; 75% of 25-54 year old women; 46% of women 55-64; 9% of women 65 and older.

– Hour wage rate given by the 1990 median weekly earnings for full-time wage and salary workers in their age-sex category divided by 40.

– Workers work 2000 hours per week, if employed. – Workers live up to age 40 and then follow average US 1992

mortality rates.– Discount rate is 3%.

Initial age

of worker

Present Value of

future working hours

Present Value of future hours

Value of future working hours/ value of all future hours

Male 20 532,000 2,771,000 19.2

Male 30 491,000 2,669,000 18.1

Male 40 418,000 2,438,000 16.3

Male 50 287,000 2,000,000 14.3

Female 20 354,000 2,238,000 15.8

Female 30 311,000 2,085,000 14.9

Female 40

Female 50

248,000

156,000

1,838,000

1,496,000

13.5

10.4

Value of life based on value of work and leisure time

Keeler, 2001, JHE

Reconciliation - continued

• Keeler concludes by writing (p. 142)

– “Neither the estimates of value of life in the literature nor these estimates of value of lifetime remaining are very precise, but it is amusing that they are so close to each other. Maybe people really do make these calculations implicitly in choosing a job, or answering a survey.”

C/B Analysis – some applications

• See page 191 in text and surrounding discussion concerning Vaccination of College Students against Meningococcal Disease.

• Cutler and McClellan (2001) Health Affairs, “Is Technological Change in Medicine Worth It?”

Cutler and McClellan

• Point out that most agree that technological change has accounted for the bulk of medical care cost increases over time. But do the benefits outweigh the added costs?

• Also point out that the average newborn could expect to spend $8,000 in present value terms on medical care over his or her lifetime. An infant born in 1990 had a life expectancy that was 7 years greater than one born in 1950 and lower disability but faced costs of $45,000 on medical care during his or her lifetime. Do the benefits outweigh the costs?

Cutler and McClellan

• Cutler and McClellan focus on the costs and benefits of medical technology improvements at the disease level to get more precise estimates. Focus on:– Heart Attacks

– Low-birthweight infants

– Depression

– Cataracts

– Breast Cancer

Cutler and McClellan

• Authors point out that new technologies have a “treatment substitution effect” and a “treatment expansion effect”.

• Authors assume a 3% discount rate and the value of a year of life in the absence of disease at $100,000.

Cutler and McClellan - continued

• Authors conclude:– The benefits from lower infant mortality and better

treatment of heart attacks have been sufficiently great that they alone are about equal to the rise in medical care costs over time. Recognizing other benefits, medical spending is clearly worth the costs.

– Quality adjusted medical prices may actually have declined over time in contrast to standard figures showing rising prices for medical services.

Cost Effectiveness Analysis

• Instead of measuring if various medical intervention are wasteful or not, CEA seeks to answer the question: “What is the least cost way of achieving a given objective?”

• Objective may be number of life years saved or reduced cholesterol levels or blood pressure, for example.

CEA Analysis - continued

Cost of a life year saved = Cost of Intervention

Number of life years saved Costs would include both direct medical costs and

direct nonmedical costs. The number of life years saved may also be multiplied by a quality of life index ranging from zero (death) to one (perfect health) to measure quality-adjusted live years saved.

Lifesaving Costs

Median cost of a year of life saved by various interventions

COST

Childhood immunizations Less than zero

Prenatal care Less than zero

Flu shots $600

Water chlorination $4,000

Pneumonia vaccination $12,000

Breast cancer screening $17,000

Construction safety rules $38,000

Home radon control $141,000

Asbestos controls $1.9 million

Radiation controls $27.4 million

Source: Harvard Lifesaving Study

Health: Prevention may be costlier than a cure Wall Street Journal; New York; Jul 6, 1994; Stipp, David;

THE END!!