PARENTAL ALTRUISM AND THE VALUE OF AVOIDING ACUTE ILLNESS: 

ARE KIDS WORTH MORE THAN PARENTS? 

Mark Dickie*

Department of Economics 

University of Central Florida 

P.O. Box 161400 

Orlando, Florida 32816-1400

E-mail: Mark.Dickie@bus.ucf.edu, Voice: 407-823-4730, Fax: 407-823-3269

and

Victoria L. Ulery

Graduate Business Programs

University of Southern Mississippi 

Hattiesburg, Mississippi 

December 2002

Running Title - Valuing Acute Illness: Are Kids Worth More than Parents?

 

*

 To whom correspondence should be addressed. The U.S. Environmental Protection Agency partially funded the 

research described here under C R 825921-01-0. The research has not been subjected to Agency review and does 

not necessarily reflect the views of the agency, and no official endorsement should be inferred. We thank Glenn 

Blomquist, Laurie Chestnut, Chris Dockins, Shelby Gerking, Robin Jenkins, Bill Schulze, participants at the June 

2001 AERE Workshop, two referees and Anna Alberini for helpful comments on previous drafts. Also, we thank 

Flint Brent and Shalawn Clark for assistance with survey management, and Teresa Clark, Heather Crickenberger, 

Heather Dick, Farrah Graham, Jason Rasberry and Fitzgerald Yaw for assistance with data collection. 
1

PARENTAL ALTRUISM AND THE VALUE OF AVOIDING ACUTE ILLNESS:

ARE KIDS WORTH MORE THAN PARENTS? 

Abstract

A model describing parents’ preferences to relieve their own and their children’s acute illnesses is 

estimated using stated-preference survey data. Estimated marginal rates of substitution (MRS) between 

child and parent illness are about two, indicating that parents value children’s illness attributes twice as 

highly as their own. The MRS is larger for younger children, falls toward unity as the child approaches 

adulthood, and appears to reflect parental altruism rather than parent-child differences in initial health or 

illness costs. Intra-family allocations may compensate for chronic health impairments. Parents’

willingness to pay (WTP) to avoid own or child illness increases with income, declines with fertility, 

increases at a decreasing rate with duration and number of symptoms, and depends on perceived

discomfort and activity restrictions. Current methods of assessing morbidity benefits of environmental 

regulations may understate substantially the value of children’s health, particularly in African-American 

families. 

Key Words: altruism, benefit-cost analysis, children’s health, environmental justice, environmental policy, 

family economics, health valuation, morbidity valuation, willingness to pay. 
2

1. INTRODUCTION

Recent executive [17] and legislative [15] decisions in the U.S. have emphasized protecting 

children’s health from environmental threats, partly because children may be at greater risk than adults 

from some environmental hazards. Although a variety of policies might help protect children’s health, 

information on parents’ preferences is useful in evaluating the effectiveness and economic efficiency of 

virtually any policy that affects children. Parental preferences, along with income and fertility, influence 

family investments in children [25], and these investments may offset or reinforce effects of public policy 

[5]. Parental preferences also provide a basis for assessing benefits of improving children’s health.

This paper investigates parents’ preferences over acute health outcomes affecting themselves and 

their children. The health outcomes include common short-term effects of exposure to ambient air 

pollution. A model of family decision-making, presented in Section 2, is used to derive equivalent 

surplus functions describing parents’ willingness to pay to relieve their own and their children’s acute 

illnesses. The model is estimated using data from a stated-preference survey described in Section 3. A 

key parameter of the model is the marginal rate of substitution between health outcomes experienced by 

the child and parent. This rate of substitution serves as an index of parents’ altruism or selfishness toward 

their children. Parental preferences are “neutral” if the marginal rate of substitution equals unity when the 

child and parent experience equivalent health outcomes. In this case, a small decrement in illness 

attributes experienced by the child just offsets, in the sense of holding parental utility constant, an equal 

increment in illness attributes experienced by the parent. A larger rate of substitution indicates more 

altruism, while a smaller rate indicates less altruistic (more selfish) preferences. 

Results presented in Section 4 imply rejection of the hypothesis of neutral preferences in favor of 

substantial parental altruism toward children. The estimated marginal rate of substitution (MRS) is about 

two for a nine-year-old child, implying that parents value their children’s acute illnesses twice as highly 

as their own. The MRS is higher for younger children and falls toward unity as the child reaches adult 

age. It remains significantly greater than unity after accounting for many socioeconomic factors and for 

possible differences between parents and children in costs of illness and initial health status. Thus, the 

conclusion that parents value their children’s health outcomes more highly than their own seems more 
3

likely to reflect parental preferences than household constraints. Parents’ valuations of avoiding child and 

parent illness increase with family income, reflect a quantity-quality tradeoff by declining with fertility, 

and appear closely related to the opportunity cost of parental time. Fathers and mothers make similar 

family health decisions, and parents show no favoritism between sons and daughters. Family resource 

allocations compensate for, rather than reinforce, chronic health impairments among family members. 

Estimates of parents’ median willingness to pay (WTP) to avoid acute illness are presented in 

Section 5. Estimated WTP to relieve parental illness is broadly consistent with results of prior research 

on adults, but parents are willing to pay significantly more to relieve their children’s acute illnesses. 

Parents’ WTP depends on perceived discomfort and activity limitations, and increases at a decreasing rate 

with the number of symptoms experienced and the duration of illness. Black parents are willing to pay 

more than white parents. 

These results have at least three implications for analysis of environmental policies affecting 

health. First, the current practice of valuing children’s illnesses using WTP estimates computed for adults 

[43,45] apparently understates benefits substantially. Second, unit values used by the U.S. EPA to

estimate benefits of reduced acute morbidity are much lower than estimates presented here and in 

previous research. Third, applying an overall average WTP to all households would understate benefits 

of reducing acute illnesses for African-American families. 

Although previous studies have investigated how parental behavior, family resources and public 

programs affect child health [30,38], the research has been conducted mainly in developing countries and 

has not examined key preference parameters such as willingness-to-pay or the marginal rate of

substitution between child and parent illness. Few researchers have estimated WTP to reduce adult and 

child morbidity or mortality in a common framework. Viscusi et al. [46] found that parents were willing

to pay more to reduce injury risks to their children than to themselves, but the children’s injuries 

considered were more severe than the adult injuries. Liu et al. [31] conclude that a typical Taiwanese 

mother’s WTP to prevent her child from having a cold is about twice her WTP to avoid a cold herself. 

But these two studies did not specify an explicit model of family decision-making, did not account for 
4

key determinants of parental expenditures such as fertility and child age, and did not estimate a

theoretically consistent index of parental altruism like the marginal rate of substitution. 

2. A CONSENSUS MODEL OF HEALTH CHOICES IN THE FAMILY

A parent or adult decision-maker is assumed to maximize utility subject to a budget determined 

by the pooled income of all family members. In this “consensus” approach, developed by Becker [4] and 

commonly used for analysis of resource allocation within families [5], utility depends on consumption of 

market goods, the “quantity” or number of children (fertility), and the “quality” of children. Quality often 

is defined as the wealth, earnings, academic achievement, or health of a child. 

In the dual problem of minimizing expenditures subject to a given level of utility, let

( , ,,,,,) m p c h h znpu e% denote the expenditure function. The hi represent measures of health outcomes 

experienced by the parent (i p = ) and one child (i c = ), while health outcomes experienced by other 

family members are assumed constant and suppressed; z denotes a vector of characteristics of the parent, 

child, and household, such as age and indicators of chronic health status; n represents fertility, or the 

number of children in the family; p is a vector of prices; u is the given utility level, and e% is the 

stochastic part of the random expenditure function, reflecting heterogeneity between households. 

In the empirical analysis the health variables hi are scalar measures of acute illness, such as 

symptom-days experienced, or vectors of illness attributes, such as symptoms experienced and duration of 

illness. Parents are asked whether they would pay a dollar amount t for a treatment that would relieve 

various combinations of illness attributes. If the illness affects the child, a parent would be willing to pay 

the stated amount provided that 

1 0 1 0 0 0 ( , ,,, , , ) ( , ,,, ,,), m h h p c p c znp u e e % % − > m h h znp u t (1)

where 1

c

h and 0

c

h respectively denote the vector of child health attributes with and without the illness, 

1

e% and 0e% denote the stochastic component with and without the illness, and 0u equals the maximum 

utility attainable without the illness. Then 0( , ,,,, ), u p c = v h h znpy where v( )⋅ represents the indirect 
5

utility function and y denotes pooled family income. Assuming additive random errors, letting

1 0 eee = − % % , and substituting the indirect utility function for 0

u (see McConnell [33]), the parent would 

be willing to pay the amount t to relieve the child’s illness if

1 0 (,, ,,,,, ) , pcc s hhh znp y t e > (2)

where the equivalent surplus function s( )⋅ equals the difference in expenditure functions. Of course, a 

similar equation applies to the WTP to relieve an acute illness affecting the parent. 

The marginal WTP to reduce illness attribute k affecting family member i , such as the WTP to 

avoid a day of fever experienced by the child, is given by / / . ik ik ∂ ∂ s h = ∂ ∂ m h The ratio of any two 

marginal valuations in turn equals the marginal rate of substitution between the corresponding two 

attributes in the household utility function. 1 For example, the MRS between illness attribute

k experienced by the child and the parent is 

( / ) ( / ). MR ck pk S = ∂s ∂h ∂ ∂ s h (3)

This rate of substitution is a useful index of parental altruism because it measures the parent’s 

marginal valuation of her child’s acute illness relative to her own. An MRS of unity implies that parental 

preferences are neutral in the sense that the parent experiences an equal reduction in utility from a given 

health condition, no matter whether she or her child experiences it. In this case, adults’ WTP to avoid the 

condition would apply equally well to children. Conversely, the MRS would be greater or less than unity 

as the parent placed a higher or lower value on avoiding a given health condition when the child, rather 

than the parent, is affected. An MRS different from unity would imply that a parent’s WTP differs 

depending on whether the child or the parent is ill. 

Unless acute health outcomes affecting the parent and child are perfect substitutes in the parental 

utility function, the MRS will vary with the outcomes. The MRS thus should be estimated while holding 

the vector of illness attributes constant between parent and child. To illustrate, suppose there is one 

illness attribute per person, , hi measured as the number of days a particular combination of symptoms is 

experienced. If there were T days per period, then days free of symptoms, , , , T hi − =i p c would enter 
6

the parental utility function as goods rather than bads. Indifference curves then would have the 

conventional convex shape shown in Figure 1. The hypothesis of neutral parental preferences should be 

tested at a point like E , where the parent and child consume equal amounts of the illness attribute 

considered. If the hypothesis were tested at point A , preferences would appear altruistic because the 

MRS exceeds unity, even though the MRS =1 at point E . 

The importance of this issue increases if the family “produces” symptom-free days. In a static 

model that might be appropriate for valuing short-term health conditions (where household resource 

allocations influence the number of symptom-free days but changes in the stock of health capital are 

ignored [18]), point A would reflect the initial equilibrium, given the nonlinear budget constraint 

represented by curve 0 B . The family produces fewer symptom-free days for the child than for the parent, 

perhaps because the child has a chronic illness like asthma that raises the marginal cost of producing 

symptom-free days. The higher valuation of symptom-free days for the child reflects both preferences 

(the MRS) and constraints (the child-parent ratio of marginal costs). In this case, parents’ choices should 

be examined net of effects of child-parent differences in marginal costs of producing symptom-free days. 

Similarly, any difference in costs of illness between parent and child should be controlled.2 

Two steps are taken in an effort to estimate the MRS as an appropriate measure of parental 

preferences, under the assumption that the stock of health capital enters the utility function separately 

from, and is unaffected by changes in, short-term symptoms. First, the experimental design used in the 

survey allows illness attributes to be held constant between parents and children when estimating the 

MRS. This insures that the MRS is evaluated at points like E if short-term health conditions occur 

exogenously. If the conditions are home-produced, this design yields estimates at points like E if the 

relevant time period is short and preferences for avoiding the conditions are independent across periods 

(e.g., the value of avoiding acute bronchitis in November is independent of whether it was experienced in 

March). Second, the MRS is estimated while controlling for socioeconomic factors likely to affect the 

slope or position of the budget constraint, or reflecting costs or consequences of acute illness, such as 

parental employment and earnings, medical prices, and presence of chronic illness. 
7

3. SURVEY DESIGN AND DATA

The model is estimated using survey data collected in Hattiesburg, Mississippi, during June - July 

2000. African-Americans comprise 26 percent of the 115,000 persons living in the metropolitan

statistical area, double their share nationally, while few residents are classified as members of racial or 

ethnic groups other than black or white [42]. African-American households were sampled in proportion 

to their share of the local population to support tests for racial differences in preferences for avoiding 

illness. Some researchers have found racial differences in family health valuation, behavior or outcomes 

[20,28], and environmental health risks may disproportionately affect children who live in low-income or 

minority households [34,44]. 

Respondents were recruited by dialing local telephone numbers at random during daytime and 

evenings on weekdays and weekends. Adults contacted were informed of the study about how health, 

health care and health costs affect families. Parents or guardians of at least one child aged 3 to 17 years 

living at home were asked to schedule a convenient time to complete the survey on a local university 

campus, and would receive $20 for participating. Two-parent households could volunteer either parent to 

complete the survey; callers asked only that the responding parent be knowledgeable about family health 

and health costs. Response rates were broadly consistent with other health surveys using telephone 

recruitment and in-person interviews at a central location [3,27].3 The survey was administered in-person 

to 295 parents and required 25 minutes on average to complete; empirical analysis is based on the 284

respondents who reported their income. In developing the survey, two focus groups with six parents each 

were conducted, followed by four rounds of pre-tests with a total of 12 subjects. 

Background Data

The survey collected general information about the household and more detailed data about the 

responding parent and one child. Detailed information was not collected about other children in the 

household to limit the length of the interview and to avoid repetitive questioning. The “sample child” was 

selected at random from households with more than one eligible child, although asthmatic children were 

over-sampled to support tests for differences between children with and without asthma.4
8

The interview began with questions about household composition and continued with standard 

economic and demographic questions about the respondent, a spouse or partner, if any, and the sample 

child. Data were collected on experiences with acute illnesses during the past 12 months and on the 

chronic health status of the respondent and sample child. 5 Information was obtained about health 

insurance coverage, money and time costs of medical care, paid sick leave, and family income. 

Table I lists summary statistics on household data used as well as on variables from the valuation 

component of the survey (described below). The sample closely resembles the local population with 

respect to race, age, single-parent status, and family size [42], but nearly half of respondents were college 

graduates. Almost 80 percent were employed, and family incomes more closely match national than local 

statistics. Sample median and mean family incomes are about $47,000 and $68,000, respectively, relative 

to $51,000 and $66,000 nationally for families with children at home [41]. As in most surveys that 

inquire extensively about children, the majority of respondents (75 percent) were female. 

Health Valuation

The survey included an “attribute-based, stated-preference choice experiment” to assess parents’ 

preferences for avoiding acute illness. Respondents were given descriptions of illness episodes, and 

asked whether they would pay stated amounts for treatment to relieve the conditions described. These 

descriptions or “profiles” differed in four attributes: (1) symptoms (cough with phlegm, shortness of 

breath with wheezing, chest pain on deep inspiration, and/or fever with muscle pain and fatigue); (2) 

duration (two days or one week); (3) person affected (parent or child); and (4) price of treatment. The 

symptoms were chosen because exposure to air pollution appears to increase incidence of upper

respiratory symptoms and acute bronchitis among children, and existing valuations of these effects in the 

U.S. are based on decades-old studies of adults [43, Tables 10 and 13].6 Also, focusing on acute rather 

than chronic illness avoids complications from potential differences between parents and children in 

latency, life expectancy or discounting, and allows comparison with several previous studies of adults. 

After asking whether the respondent or child had experienced each of the four symptoms during 

the past year, interviewers indicated that the survey would next inquire, “How your family would be 
9

affected if you or your child had an illness or condition that caused some of these symptoms.” 

Interviewers explained that the respondent would be given descriptions of four separate illnesses and

would be asked some questions about each, including “whether you would buy a hypothetical medication 

to treat the condition.” Respondents were told that drug companies were working on treatments for 

illnesses causing respiratory symptoms and fever [37]. The influenza drugs released the previous autumn 

were used as examples, although respondents were advised that these were examples only because the 

survey was not about influenza or drugs currently available.7 The medication would be taken on the first 

day of symptoms and would prevent any remaining days of symptoms that otherwise would have 

occurred. It would be available in liquid, tablet or capsule form and would be FDA-approved, safe and 

effective for adults and children three years of age and older. Immediately following this introduction, 

each respondent would evaluate four profiles in sequence. 

Each profile assigned symptoms and duration to the parent or child but asked respondents to rate 

subjectively the resulting degree of discomfort and interference with usual activities. The final section of 

the profile reminded the respondent about the hypothetical medication and budget constraint, and asked 

whether she would be willing to pay a given price out-of-pocket for the medicine. Although it was not 

shown on the description viewed by respondents, a follow-up question assigned a higher or lower price 

according to whether the respondent would or would not buy the drug at the initial price.8 

Four features of the valuation procedure warrant comparison to previous research. First, 

respondents value illnesses assigned to them [8,27,39], not illnesses they have recently experienced

[2,10,11,31,35]. Symptoms were assigned so that tradeoffs between parent and child health would reflect 

identical health outcomes (to estimate the MRS at points like E in Figure 1). A disadvantage of this 

approach is that respondents may not have enough information or experience to value the assigned health 

outcomes. But the symptoms considered here are common, and data were collected to assess whether 

familiarity affects responses. Second, a key goal of the research is to estimate ratios and differences in 

valuations between parents and children. Effects of hypothetical bias, inadequate information, or other 

potential problems with stated preference data would be mitigated to the extent that these factors are 

constant between parents and children. 
10

Third, previous acute health valuation surveys often have not specified concretely how payment 

of money would prevent adverse health effects. Instead, respondents may be reminded in general terms 

of tradeoffs between money and health, for example that expenditures on medical treatment may improve 

health. This approach proved unsuccessful in pre-tests and consequently the valuation scenario involves a 

specific hypothetical medication. 9Fourth, respondents valued four illness episodes in the “double -

bound,” discrete-choice with follow-up framework. This approach aimed to balance gains from

additional questioning against respondent burden. In other research, respondents may value only one 

illness in a triple -bound framework [2] or as many as eight to 16 illnesses at a single price for each [27]. 

A limitation of the survey is the absence of “debriefing” questions to assess respondents’ 

motivations for valuation responses or acceptance of information provided. Separate debriefing questions 

for each profile would be repetitive and lengthen the survey, while a single set of questions following the 

last profile would be ambiguous if motivations or acceptance of information varied between profiles. 

Nonetheless, the absence of debriefing questions makes it difficult to assess whether respondents doubted 

the effectiveness of the hypothetical medication, were concerned about side effects, or responded

strategically if they believed drug companies were sponsoring the study. However, debriefing of pretest 

respondents suggests that these factors may not be important determinants of responses.10

The overall design, exclusive of follow-up prices, can be described as a 27 factorial, with 128 

profiles. All profiles include cough with phlegm and most include one or more of the three other

symptoms. Each symptom has two levels (present or absent), as does duration (two or seven days without 

treatment) and person affected (parent or child). There are four prices for the initial discrete choice 

question ($40, $200, $400, $600). 

Table II summarizes the 16 profiles used in the orthogonal and balanced design. Profiles one 

through eight represent a 1/16 fraction of the full factorial and by themselves would make a standard 

“main effects,” 27-4 design. Main effects plans, the most commonly used experimental designs, support 

estimation of partial effects of each attribute, but do not identify interactive effects. For example, a main 

effects plan would allow estimation of the divergence in WTP between parent and child, but would 

constrain any divergence to be equal for each symptom. To allow the child-parent WTP differential, if 
11

any, to vary over illness attributes, a second 1/16 fraction was constructed such that the two fractions 

together allow estimation of interactions between child status and all other attributes [9]. 

The four profiles assigned to a respondent were selected randomly from the set of 16, and 

assigned in random order, subject to two constraints. First, each respondent received two profiles 

describing an illness she would experience, and two describing an illness her child would experience. 

Second, to mitigate any tendency of respondents to try to appear altruistic to their children, the parent and 

child illness profiles assigned to a given respondent were never identical. For example, a respondent 

receiving the first profile, describing a seven-day cough experienced by the parent, would not be assigned 

profile nine, describing the same illness experienced by the child. 

4. EMPIRICAL ANALYSIS OF HEALTH CHOICES IN THE FAMILY

Table II summarizes responses to the initial discrete-choice valuation question, showing the 

proportion of parents who would purchase treatment for the illnesses considered. For each of the eight 

pairs of profiles, parents are more likely to purchase treatment when the illness affects the child rather 

than the parent. Seven of the eight pairwise differences in proportions are statistically significant at the 

10 percent level in two-tail tests (including five that are significant at one percent). Overall, the odds of 

purchasing treatment are twice as high (odds ratio = 2.12) for the child as for the parent. 

Table II also presents non-parametric, lower bound estimates of mean WTP for each combination 

of illness attributes administered in the survey. These Turnbull-type estimates use information only on 

the initial prices for the hypothetical medication, and the proportion of parents who would purchase the 

drug at the initial price [21]. For each illness, the lower bound estimate of mean WTP is larger for 

children than for parents. Again, seven of eight pairwise differences are significant at the 10 percent level 

in two-tail tests (including five that are significant at one percent). Taking the ratio of lower bound, mean 

WTP for the child relative to the parent for each illness, and then computing the geometric mean of these 

eight ratios, yields 1.86. This suggests that the typical parent is willing to pay almost twice as much to 

relieve an acute illness affecting her child as to relieve an equivalent illness affecting herself. 
12

Inferences drawn from information in Table II do not depend on any assumption about the 

distribution of WTP, or about the functional form of equivalent surplus functions. Continuing in a similar 

vein, the last row of the table presents Turnbull estimates of WTP per symptom-day avoided. 

Considering WTP per symptom-day gives a simple way of pooling data over profiles without specifying a 

parametric model. The Turnbull estimation procedure [21] is applied after defining the price of treatment 

as the initial price, divided by the number of symptom-days avoided. The number of avoided symptomdays is computed as the number of symptoms times the reduction in the number of days ill associated 

with use of the new medication. The lower bound estimates of mean WTP per symptom-day are about 

$86 for children and $35 for parents. The estimate is 2.47 times larger for children than for parents, and 

the child-parent difference is significant at one percent in a two-tail test. 

Tables III and IV present parametric estimates of the equivalent surplus function (inequality (2)) 

and associated MRS (equation (3)) between child and parent illness. Table III focuses on how illness 

attributes affect WTP, while estimates in Table IV account for effects of individual and household 

characteristics. Estimates are computed by maximizing the log-likelihood function of the interval

estimator for double bound, discrete-choice with follow-up data, assuming that WTP is lognormally 

distributed [2,31]. The log-likelihood function for the i

th observation is 

ln( ) ln( )

ln ln ,

U L

i i i i

i

s x s x

L

b b

s s

   − − ′ ′   

=   Φ  − Φ        

(4)

where U

i

s and L

i

s denote upper and lower bounds on the equivalent surplus, ix and b represent 

conformable vectors of explanatory variables and coefficients, s denotes the standard deviation of 

ln( ) e , and Φ denotes the standard normal cumulative distribution function. Results based on an 

alternative (Weibull) distribution for WTP are available on request. 

Illness Attributes 

The specification in column (1) of Table III defines illness according to the number of symptomdays avoided. Column (2) and all remaining columns include indicators for the degree of discomfort and 
13

activity restriction that the respondent associates with the illness. Column (3) follows Alberini et al. [2] 

and separately enters the number of symptoms and days of illness avoided, while column (4) follows 

Johnson et al. [27], using days of separate symptoms as illness attributes. The final column of Table III 

addresses effects of familiarity or recent experience with symptoms. Each specification includes a 

constant term and a dummy variable indicating whether the illness affects the child or parent, with the 

implied MRS between child and parent illness reported in the last row. 

As shown in column (1), WTP to avoid acute illness increases at a decreasing rate with symptomdays and is significantly higher for children than for parents. The estimated MRS of 2.12 differs 

significantly from unity at less than the one percent level in a two-tail test. This result implies that the 

average parent values relieving her child’s acute illness about twice as highly as relieving her own. 

Results presented in column (2) indicate that subjectively perceived discomfort and activity 

restriction are important determinants of the value of avoiding acute illness. The estimated symptomdays elasticity falls when these factors are accounted for, because illnesses with more symptoms and/or 

longer duration are associated with greater discomfort and activity restriction. Evidently, about 10 

percent of the premium that parents are willing to pay to relieve the child’s illness reflects their belief that 

the same symptoms and duration cause more discomfort and interference with activities when the child, 

rather than the parent, is ill. 

In column (3) the elasticities of WTP with respect to number of symptoms and duration are each 

significantly greater than zero and less than one, but they are statistically indistinguishable from one 

another ( p = 0.41). This indicates that the combined symptom-days measure adequately captures effects 

of both duration and symptoms. Similarly, duration elasticities reported by Alberini et al. [2] (0.31 to 

0.46) are quite close to their elasticities with respect to the number of symptoms (0.34 to 0.44). Duration 

elasticities in Johnson et al. [26] range from 0.44 to 0.51 and in Liu et al. [31] from 0.16 to 0.21. 

Researchers estimating hedonic wage equations similarly report elasticities of wages with respect 

to duration of injury, holding risk of injury constant, significantly less than unity. Estimated duration 

elasticities are 0.05 to 0.32 [14,22]. Thus, stated-preference methods applied to acute illness and
14

revealed-preference methods applied to workplace injuries both indicate diminishing marginal valuation 

of duration. Although workplace injuries and acute illnesses are different health outcomes, this result is 

consistent with the idea that the concavity of estimated WTP in symptoms and duration reflects

diminishing marginal utility of symptom-free days [18:351], rather than insensitivity to scope in

hypothetical valuation responses. 

As shown in columns (4) and (5), accounting for the separate symptoms experienced and for 

recent experience with the symptoms has little impact on coefficients of other variables, the loglikelihood value, or the MRS. Comparing column (4) to previous columns suggests that people care less 

about which specific symptoms they experience than about the number and duration of symptoms, an 

inference which echoes results obtained by Alberini et al. [2] and Johnson et al. [27]. In column (5), 

coefficients of three of four dummy variables indicating recent experience with a symptom are

statistically insignificant at 10 percent. It seems that stated preferences for avoiding common symptoms 

are not unduly sensitive to experience.11 

The coefficient of the “child” indicator gives the main effect of a child illness relative to a parent 

illness. As discussed in Section 3, the research design would allow the child-parent differential to vary 

over illness attributes, and Liu et al. [31] found significant differences in slopes of valuation functions 

between mothers and children. Table III reports outcomes of two likelihood-ratio tests for interactive 

effects. As shown, slopes and variances of equivalent surplus functions appear identical between parents 

and children, implying that the MRS is constant over the illness attributes considered here.12 

Individual and Household Characteristics

Table IV shows effects of characteristics of the parent, child and household on WTP to avoid 

acute illness. The main purpose of these regressions is to test the robustness of the MRS estimates in 

Table III and their interpretation as measures of parental altruism. As discussed in Section 2, if parents 

value relieving their children’s illnesses more highly than their own because children’s illnesses are more 

costly, or because of a difference in baseline health status between parents and children, then the parentchild tradeoffs in Table III confound preferences with constraints. Table IV regressions also account for 
15

specific features of the sample, such as the over-sampling of blacks relative to the national population, 

and would be useful in transferring benefits to populations with different characteristics. 

Family Characteristics. All regressions in Table IV show effects of variables identified in family 

economics as key dete rminants of parental investments in children – income, marital status, fertility – and 

control for race and for the sex of the responding parent. Estimated income elasticities of 0.08 to 0.22 are 

lower than those obtained in previous research [2,31,32], which lie between 0.2 and 0.6. Greater fertility 

is associated with lower WTP. This outcome partly reflects the well-established quantity-quality tradeoff 

[24], in which a larger number of children implies reduced spending on each child. Here, however, a 

larger number of children implies a lower WTP for both the child’s and the parent’s health conditions.13 

Health choices made by fathers and mothers are indistinguishable, but married parents may be 

willing to pay less than single parents. This effect, significant at ten percent in two of the four

regressions, may indicate that acute illness is a relatively greater burden in a single -parent household. 

Whites are willing to pay less than blacks, as would be expected if African-Americans have fewer or 

worse options for responding to acute illness.14 Alberini et al. [3] found that blacks are willing to pay 

more than whites for reduced adult mortality risk, and Joyce et al. [28] found that blacks mothers are 

willing to pay more than white mothers for improved infant health. Other researchers have not found 

significantly higher WTP among blacks [8,39], while many have not controlled for race

[2,10,11,27,29,31,32,46].

Health Status. Prevalence of asthma is higher among children, especially African-American 

children, than among adults. Episodes of asthma exacerbation, often involving some of the symptoms 

valued here, are associated with air pollution. As shown in column (1) of Table IV, physician-diagnosed 

asthma is associated with a significantly higher demand to avoid acute illness. Estimating the MRS 

separately by asthma status yields 2.28 when the child but not the parent has asthma, and 1.51 when the 

parent but not the child has asthma (the separate estimates are not shown in the table). 

These results suggest that acute health tradeoffs within a family depend on the chronic health 

status of family members. The shift of resources toward the person with asthma implies compensating 

rather than reinforcing allocations; incremental health spending shifts toward the person in poor health. 
16

Still, the MRS remains significantly greater than unity even when the parent, not the child, has asthma. 

The conclusion that parents value avoiding their children’s illnesses more highly than their own is not an 

artifact of over-sampling asthmatic children. More generally, the finding that parents are willing to pay 

more to protect their children than themselves from acute illness cannot be attributed to measured

differences in baseline health status between parents and children.15 

Costs and Consequences of Illness. Columns (2) and (3) of Table IV include variables associated 

with costs of illness, marginal costs of reducing acute illness, and additional indicators of the parent’s 

human capital. WTP increases with illness costs. It is higher when the parent is employed, and increases 

with wages and medical prices. The effect of medical price suggests that the hypothetical medication and 

existing treatments are viewed as substitutes. The time required for medical care, paid sick leave, and 

parental schooling appear unrelated to WTP. Measures of schooling, employment and wages are entered 

separately for mothers and fathers in column (3). The additional detail contributes little to the

explanatory power of the regression. In any event, the conclusion that the MRS significantly exceeds 

unity cannot be attributed to measured differences in costs or consequences of illness.16 

Children’s Characteristics. Apart from asthma, the only individual or household characteristic 

affecting the MRS seems to be the age of the child, as shown in column (4). Figure 2 plots the estimated 

MRS as the child ages, including extrapolation beyond the sample range of 3 to 17 years of age. The 

MRS declines as the child ages and is no longer significantly greater than unity at the five percent level 

beyond age 18. As shown in column (4), the effect of child age is estimated net of the effect of attending 

school. This regression also indicates that parents have no preference between acute health conditions 

affecting sons and daughters; in contrast, Liu et al. [31] found that Taiwanese mothers favor sons. 

Some results above suggest that the opportunity cost of parental time is closely tied to the value 

of avoiding acute illness. Models that explicitly incorporate the loss of time from market and non-market 

activities induced by acute illness (e.g., [18]) would predict that WTP increases with the opportunity cost 

of time and the amount of time lost. This perspective would account for the increase in WTP with the 

responding parent’s employment and wage, and might explain the declining MRS as the child ages, if 

more time is needed to care for a sick child who is younger.17 
17

Discussion of MRS Estimates 

The estimated MRS significantly exceeds unity after accounting for many socioeconomic factors 

and for potential differences between parents and children in initial health status and illness costs. Thus, 

the hypothesis of neutral preferences is rejected in favor of parental altruism toward children. The degree 

of altruism is difficult to reconcile with a purely genetic basis for parental preferences. Hamilton’s rule, 

in which altruism is proportional to shared genes [6], suggests that an individual parent would value her 

child’s health outcomes half as highly as her own. Of course, motivations other than altruism could cause 

the MRS to exceed unity. For example, the declining MRS with the child’s age may reflect an ethic of 

guardianship in which a parent’s sense of responsibility diminishes as the child matures. 

Whatever the explanation for MRS estimates obtained, parents’ apparent altruism has

implications for public policy. In view of parents’ legal authority over children, parental preferences are 

an important determinant of child health outcomes and of the effectiveness of policies designed to 

improve child health. Children of selfish parents would be more likely to experience poor health 

outcomes, and policies designed to benefit these children could be neutralized as parents re-allocated 

family resources in response to policy changes. But results presented above are inconsistent with the idea 

that parental selfishness or lack of concern is a major impediment to improving child health. 

This conclusion in turn bears on whether parental WTP is an adequate and politically acceptable 

benefit measure. Dockins et al. [12] conclude that parental preferences provide the best basis for benefitcost analysis of policies affecting children. Politically, however, policy-makers might be reluctant to 

accept parental WTP as a measure of child health benefits if the MRS were less than unity. 

5. WILLINGNESS TO PAY TO AVOID ACUTE ILLNESS

Parametric estimates of median parental willingness to pay to relieve acute illness episodes are 

shown in Tables V and VI. Estimates in Table V are based on regressions in Table III and show WTP to 

avoid illnesses with varying symptoms and duration, accounting for severity or for recent experience with 

symptoms. Throughout Table V, estimated WTP is about twice as high for illnesses affecting children as 
18

for equivalent illnesses affecting parents, reflecting the underlying MRS of about two. All child-parent 

differences are statistically significant at the one percent level in two-tail tests. 

The top panel in Table V shows WTP to avoid symptom-days at the sample minimum (one) and 

maximum (24) number of symptom-days avoided. Severity is defined by subjective perceptions: “mild” 

cases involve low discomfort and activity restriction, while “severe” cases involve high discomfort and 

activity restriction. Estimated WTP is about two-thirds higher for severe than for mild cases. 

The bottom panel of Table V shows WTP to avoid days of separate symptoms at the sample 

maximum number of days avoided (six). This duration shows the largest within-sample differences 

between valuations of separate symptoms, since gaps between symptom valuations widen with duration. 

Yet the coefficient of variation of WTP for the separate symptoms is only 0.13, implying that separate 

symptom values deviate from the value of the average symptom by less than 15 percent on average. This 

variation, like the effect of recent experience with symptoms, is quite modest relative to the impact of 

severity or of the family member affected. Experiencing all of the symptoms for 7 days, or 28 symptomdays altogether, is roughly equivalent to a case of acute bronchitis, an important health endpoint 

associated with children’s exposure to air pollution. WTP to avoid all but the first day of all four 

symptoms, shown in the last row of Table V, is about $320 for children and $170 for parents. 

Table VI presents median WTP estimates, based on regressions in Table IV, for avoiding one 

symptom-day applicable to specific sub-populations. Comparisons in Table VI represent partial effects of 

variables taken one at a time, holding other explanatory variables at sample means. Results underline the 

importance of family composition, race, chronic health status, and child age in determining WTP.18

Estimates of mean WTP (not presented) are almost twice as large as median WTP estimates. 

Additionally, all estimates in Tables III through VI were re-computed assuming a Weibull, rather than a 

lognormal, distribution for WTP, with no effect on any substantive conclusions.19 

Implications of WTP Estimates and Comparison to Previous Research

The WTP estimates imply that the practice of valuing children’s acute illnesses using WTP 

estimates computed for adults [43,45] substantially understates benefits. A similar conclusion would be 
19

drawn from two other studies of acute morbidity [1,31]. Also, Dickie and Gerking [12] report that parents 

are willing to pay more to reduce skin cancer risks to their children than to themselves, while Blomquist 

[7] indicates that the value of a statistical life is no lower for children than for adults.20

The relationship of WTP with income, family composition and race bears on environmentaljustice implications of evaluating policies with benefit-cost analysis. While concerns for environmental 

justice encompass income and minority status [16], economists often address the potential for a WTP 

criterion to favor the rich at the expense of the poor [36]. Concerns for equity may be countered by the 

argument that policy analysts usually apply the same WTP value to all persons affected by a policy, but 

that practice weakens the link to individual preferences [23]. Results presented here, however, indicate 

that an overall average WTP would understate benefits to disadvantaged families. 

To illustrate, the regression in Table IV, column (1), is used to estimate median WTP for three 

types of families, with each assigned US mean income for its type: white, married-couple families (mean 

income $74,913); black, married-couple families ($62,454); and black, single -parent families with no 

husband present ($26,863). Estimated median WTP is 50 percent higher for married-couple black 

families, and 57 percent higher for single -parent black families, than for white, married-couple families. 

Thus, applying an overall median (or mean) WTP to all households would substantially underestimate 

benefits to African-American families.21 

Finally, results obtained here may be compared to earlier research. Table VII presents results 

from seven previous efforts to va lue similar symptoms. Three of the studies [10,11,32,39,40] were early, 

“first-generation” efforts to value symptoms. The fourth [26] was a meta-analysis of the morbidity 

valuation literature, based partly on the three first-generation studies. The final three studies are much 

more recent but were conducted outside the U.S., in Taiwan [2,31] or Canada [27]. Only one [31] of the 

seven studies estimated WTP for children as well as adults. 

Each of the prior studies estimated WTP to avoid entirely one or more days of symptoms, while 

respondents in the present study would avoid all but the first day of symptoms. The difference in 

methodology would tend to yield lower WTP estimates here than in previous research, because of

concavity of WTP in duration. Also, WTP may include fixed and variable components, reflecting 
20

preferences for avoiding illness entirely and for reducing its duration. Previous estimates would include 

both components, while estimates in Tables V and VI would include only the variable component. 

The column of Table VII labeled “Study WTP” gives WTP estimates in U.S. dollars of the year 

2000. The final two columns adjust the earlier WTP estimates for differences in income. Mean income 

levels in previous studies were converted to USD 2000 and then adjusted to the mean income in the 

present sample. The effect of the change in income on WTP then was estimated by applying income 

elasticities of 0.15 (the median of the three statistically significant values in Table IV) and 0.4

(representative of estimated elasticities in earlier work).22 

WTP estimates for parents avoiding one symptom-day in Table V are somewhat higher than the 

median of values from previous studies, after adjusting for effects of income, of about $30 (mild) or $90 

(severe). On the other hand, estimates of WTP to avoid six days of single symptoms in Table V are 

much lower than income-adjusted multi-day, single -symptom values in previous research, of $250 to 

$385. Valuations for avoiding acute bronchitis in Table V are larger than values for avoiding multiple -

day, multiple-symptom episodes from Alberini et al. [2] and Liu et al. [31]. However, acute bronchitis 

lasts longer and involves more symptoms than the acute illnesses considered in the two Taiwan studies.23 

In summary, the values obtained here for parents’ own illnesses are broadly consistent with results of 

previous research, but values for children’s illnesses are larger than most previous estimates for adults. 

In any case, the unit values used by the U.S. EPA to estimate benefits of reduced acute morbidity 

are much lower than relevant estimates from existing valuation research. In the retrospective cost-benefit 

analysis of the Clean Air Act [43], for example, unit values inflated to USD 2000 are $7/day for shortness

of breath, $15/case for lower respiratory symptoms, and $56/case for acute bronchitis. These values are 

lower than adult valuations in existing research, but EPA identifies children as the affected population for 

air-pollution induced episodes of these endpoints. Morbidity benefits comprise 18 percent of total health 

benefits attributed to the Clean Air Act over the period 1970-1990. Aggregate benefits of avoided 

shortness of breath, acute bronchitis, and upper and lower respiratory symptoms in children, and of any 

acute symptom in adults, sum to $75 billion ($2000). Replacing EPA’s unit values with those obtained in 

this research would boost this total by a factor of six to $465 billion, increasing the share of these 
21

symptoms in total morbidity benefits from 1.5 to 8.6 percent.24 In any event, EPA estimates may

substantially understate benefits of reduced acute morbidity. 

6. CONCLUSIONS

Information on parents’ preferences for their own and their children’s acute health outcomes is 

useful for evaluating the likely effectiveness and economic efficiency of policies affecting acute illness. 

Results presented here indicate substantial parental altruism toward children. Future research should 

examine parents’ preferences for other health outcomes affecting children, test alternative models of 

family decision-making, and consider further whether parental WTP is an adequate measure of benefits of 

children’s health. Results obtained here may or may not extend to chronic, latent or fatal health effects, 

where age-related differences in cumulative exposures, latency periods or remaining lifetimes may

influence parent-child health tradeoffs. Other models of family decision-making should be explored to 

determine whether the model of consensus parental preferences is appropriate for valuing children’s 

health. Researchers should investigate whether people display “paternalistic altruism” toward children 

outside their own families, and whether these preferences should be considered in benefit-cost analysis. 
22

REFERENCES

1. M.D. Agee and T.D. Crocker, Smoking parents’ valuations of own and children’s health, Presented at 

Association of Environmental and Resource Economists conference “Assessing and Managing 

Environmental and Public Health Risks,” Bar Harbor, Maine, June 13-15, 2001. http://www.aere.org/. 

2. A. Alberini, M. Cropper, T. Fu, A. Krupnick, J. Liu, D. Shaw, and W. Harrington, Valuing health effects 

of air pollution in developing countries: The case of Taiwan, J. Environ. Econom. Management 34, 

107-126 (1997).

3. A. Alberini, A. Krupnick, M. Cropper, N. Simon and J. Cook, The willingness to pay for mortality risk 

reductions: A comparison of the United States and Canada, Resources for the Future (2001). 

4. G. S. Becker, “A Treatise on the Family,” Enl. Ed. Harvard University Press, Cambridge, MA (1993).

5. J. R. Behrman, R. A. Pollak, and P. Taubman, “From Parent to Child: Intrahousehold Allocations and 

Intergenerational Relations in the United States,” Univ. of Chicago Press, Chicago (1995). 

6. T.C. Bergstrom, Economics in a family way, J. Econom. Lit. 34, 1903-34 (1996). 

7. G.C. Blomquist, Self protection and averting behavior, values of statistical lives, and benefit cost analysis 

of environmental policy, revision of contribution in U.S. Environmental Protection Agency, National 

Center for Environmental Economics Report # EE-0064 (2002). 

8. G.C. Blomquist and R.M. O’Conor, Eliciting preferences from the general population for safety and 

efficacy of asthma treatments, Univ. of Kentucky Dept. of Economics (1998). 

9. G. E. P. Box, W. G. Hunter, and J. S. Hunter, “Statistics for Experimenters: An Introduction to Design, 

Analysis and Model-Building,” Wiley, New York (1978).

10. M. Dickie, S. Gerking, W. Schulze, A. Coulson, and D. Tashkin, Value of avoiding symptoms of ozone 

exposure: An application of the averting behavior method, Vol. II, in “Improving Accuracy and 

Reducing Costs of Environmental Benefit Assessments,” U. S. Environmental Protection Agency, 

National Center for Environmenta l Economics Report # EE-0285C (1986).

11. M. Dickie, S. Gerking, D. Brookshire, D. Coursey, W. Schulze, A. Coulson, and D. Tashkin, Reconciling 

averting behavior and contingent valuation benefit estimates of reducing symptoms of ozone exposure, 

in “Improving Accuracy and Reducing Costs of Environmental Benefit Assessments” U. S. 

Environmental Protection Agency, National Center for Environmental Economics Report # EE-0285G 

(1987).

12. M. Dickie and S. Gerking, Parents’ valuation of latent health risks to their children, in U. S. 

Environmental Protection Agency, National Center for Environmental Economics Report # EE-0064. 

13. C. Dockins, R.R. Jenkins, N. Owens, N.B. Simon and L.Bembenek Wiggins, Valuation of childhood risk 

reductions: The importance of age, risk preferences, and perspective, Risk Anal. 22, 335-46 (2002). 

14. S. Dorsey and N. Walzer, Workers’ compensation, job hazards, and wages, Ind. Labor Relat. Rev. 36, 

642-54 (1983). 

15. The Federal Insecticide, Fungicide and Rodenticide Act as Amended by the Food Quality Protection Act 

of 1996 (Public Law 104-170), 7 United States Code 136. 

16. Federal Register, Executive Order 12898 of February 11, 1994—Federal Actions to Address 

Environmental Justice in Minority Populations and Low-Income Populations, 59, FR Doc. 94-3685

(February 16, 1994).

17. Federal Register, Executive Order 13045 of April 21, 1997—Protection of Children from Environmental 

Health Risks and Safety Risks, 62, FR Doc. 97-10695 (April 23, 1997).

18. A.M. Freeman, III, “The Measurement of Environmental and Resource Values: Theory and Methods,” 

Resources for the Future, Washington, DC (1993). 

19. M.R. Gold, D.L. Patrick, G.W. Torrance, D.G. Fryback, D.C. Hadorn, M.S. Kamlet, N. Daniels and M.C. 

Weinstein, Identifying and valuing outcomes, in “Cost-Effectiveness in Health and Medicine,” (M.R. 

Gold, L.B. Russell, J.E. Siegel and M.C. Weinstein, Eds.), Oxford University Press, New York (1996). 

20. M. Grossman and T. J. Joyce, Unobservables, pregnancy resolutions, and birth weight production 

functions in New York City, J. Polit. Econom. 98, 983-1007 (1990).

21. T.C. Haab and K.E. McConnell, “Valuing Environmental and Natural Resources: The Econometrics of 

Non-Market Valuation,” Edwin Elgar, Cheltenham, UK (2002). 
23

22. D.S. Hamermesh and J.R. Wolfe, Compensating differentials and the duration of wage loss, J. Labor 

Econom. 8, S175-97 (1990). 

23. J.K. Hammitt, QALYs vs. WTP, Risk Anal. 22, 985-1001 (2002). 

24. E. A. Hanushek, The tradeoff between child quantity and quality, J. Polit. Econom. 100, 84-117 (1992).

25. R. Haveman and B. Wolfe, The determinants of children’s attainments: A review of methods and 

findings, J. Econom. Lit. 33 1829-78 (1995). 

26. F. R. Johnson, E. E. Fries, and H. S. Banzhaf, Valuing morbidity: An integration of the willingness-to-pay 

and health-status index literatures, J. Health Econom. 16, 641-65 (1997).

27. F.R. Johnson, M. Ruby Banzhaf and W.H. Desvousges, Willingness to pay for improved respiratory and 

cardiovascular health: A multiple format, stated-preference approach, Health Econom. 9, 295-317 

(2000). 

28. T. J. Joyce, M. Grossman, and F. Goldman, An assessment of the benefits of air pollution control: The 

case of infant health, J. Urban Econom. 25, 32-51 (1989).

29. A.J. Krupnick, and M.L. Cropper, The effect of information on health risk valuations, J. Risk Uncertainty

5, 29-48 (1992). 

30. L-f. Lee, M.R. Rosenzweig and M.M. Pitt, The effects of improved nutrition, sanitation, and water quality 

on child health in high mortality populations, J. Econometrics 77, 209-35 (1997). 

31. J-T. Liu, J.K. Hammitt, J-D. Wang and J-L. Liu, Mother’s willingness to pay for own and her child’s 

health: a contingent valuation study in Taiwan, Health Econom. 9, 319-26 (2000). 

32. E. T. Loehman, S. V. Berg, A. A. Arroyo, R. A. Hedinger, J. M. Schwartz, M. E. Shaw, R. W. Fahien, V. 

H. De, R. P. Fishe, D. E. Rio, W. F. Rossley, and A. E. S. Green, Distributional analysis of regional 

benefits and costs of air quality control, J. Environ. Econom. Management 6, 222-43 (1979).

33. K. E. McConnell, Models for referendum data: The structure of discrete choice models for contingent 

valuation, J. Environ. Econom. Management 18, 19-35 (1990).

34. L. Mott, The disproportionate impact of environmental health threats on children of color, Environ. 

Health Persp. 103, 33-35 (1995).

35. R.M. O’Conor and G.C. Blomquist, Measurement of consumer-patient preferences using a hybrid 

contingent valuation method, J. Health Econom. 16, 667-83 (1997). 

36. J.W. Pratt and R.J. Zeckhauser, Willingness to pay and the distribution of risk and wealth, J. Polit. 

Econom. 104: 747-63 (1996).

37. A. Regaldo, ViroPharma cold drug shows promise, Wall Street Journal Eastern Edition Thursday March 

15, 2001, B-13. 

38. M.R. Rosenzweig and T.P. Schulz, Market opportunities, genetic endowments, and intrafamily resource 

distribution, Amer. Econom. Rev., 72 (1982), 803-15.

39. G. Tolley, L. Babcock, M. Berger, A. Bilotti, G. Blomquist, M. Brien, R. Fabian, G. Fishelson, C. Kahn, 

A. Kelly, D. Kenkel, R. Krumm, T. Miller, R. Ohsfeldt, S. Rosen, W. Webb, W. Wilson, M. Zelder, 

Valuation of reductions in human health symptoms and risk, U. S. Environmental Protection Agency, 

National Center for Environmental Economics Report #EE-0092A (1986).

40. G. Tolley, D. Kenkel and R. Fabian, “Valuing Health for Policy: An Economic Approach,” Univ. of 

Chicago Press, Chicago (1994). 

41. U.S. Census Bureau, Current Population Reports, P60-213, “Money Income in the United States: 2000,”

U.S. Government Printing Office, Washington, DC. (2001). Detailed income tables accessed at 

http://www.census.gov/hhes/www/income00.html. 

42. U.S. Census Bureau, “State and Metropolitan Area Data Book 1997-98,” 5th ed. (1998).

43. U. S. Environmental Protection Agency, “The Benefits and Costs of the Clean Air Act, 1970 to 1990,” 

Washington, D.C. (1997).

44. U. S. Environmental Protection Agency, “America’s Children and the Environment: A First View of 

Available Measures” Washington, D.C. EPA 240-R-00-006 (2000).

45. U. S. Environmental Protection Agency, “Children’s Health Valuation Handbook,” Washington, D.C. 

EPA 100-R-01-002 (2001).

46. W.K. Viscusi, W.A. Magat, and J. Huber, An investigation of the rationality of consumer valuations of 

multiple health risks, RAND J. Econom. 18, 465-79 (1987). 
24

Table I. Sample Means (and Standard Deviations) or Proportions. 

Household Characteristics Individual Characteristics

Responding

Parent

Sample

Child

Family Income ($/year) 68441

(63196)

Age (years) 36.98

(8.55)

9.25

(4.36)

Married Parent Family 0.68 Physician-Diagnosed Asthma 0.10 0.18

Number of Children 1.78

(0.90) Female 0.75 0.52

Race is White 0.73

Price of Doctor Visit ($/visit) 52.54

(84.89)

44.66

(93.23)

Responding Parent is 

College Graduate 0.49 Hours Required for Doctor Visit 

2.05

(1.03)

2.09

(1.10)

Responding Parent is 

Employed 0.79 Cough with Phlegm in Past Year 0.46 0.54

Responding Parent’s 

Wage if Employed

17.37

(24.59)

Shortness of Breath with Wheezing in 

Past Year 0.13 0.21

Responding Parent Has 

Paid Sick Leave 0.45

Chest Pain when Cough or Breathe 

Deep in Past Year 0.25 0.28

Mother is Present and 

College Graduate 0.45 Fever in Past Year 0.46 0.61

Mother is Present and 

Employed 0.68 Data from Health Valuation Profiles

Mother’s Wage if 

Present and Employed

14.62

(24.93)

Symptom Days Avoided 8.66

(7.81)

8.73

(7.80)

Father is Present and 

College Graduate 0.38

Number of Symptoms 2.51

(0.87)

2.49

(0.86)

Father is Present and 

Employed 0.69

Days of Illness Avoided 3.48

(2.50)

3.51

(2.50)

Father’s Wage if Present 

and Employed

20.00

(24.23)

Cough Days 4.48

(2.50)

4.51

(2.50)

Sample Child is in 

School 0.92

Shortness of Breath with Wheezing 

Days

2.74

(2.47)

2.74

(2.48)

Chest Pain Days 2.72

(2.48)

2.74

(2.48)

Fever Days 2.73

(2.47)

2.74

(2.48)

High Discomfort (=1 if Rating>6) 0.46 0.65

High Activity Restriction (=1 if 

Rating>6) 0.40 0.62

Initial Price, New Drug 307.57

(209.95)

307.18

(209.10)

Buy New Drug at Initial Price (=1) 0.34 0.53

Number of Observations 563 a 568 a

a Eleven of 295 responding parents did not report income and are excluded. Each of the remaining 284 respondents 

received four profiles, two for a parent illness and two for a child illness. Five of the resulting 568 parent profiles 

are deleted because the follow-up question was mistakenly deleted from the interviewers’ packets. 
25

Table II. Profiles and Initial Responses 

(z-statistics in parentheses)

Proportions Buying 

Treatmentb

Non-parametric Lower 

Bound Mean WTPc

Profiles

Symptoms: 

Cough/phlegm AND...

Untreated 

Duration 

(Days)

Treatment 

Costa

($)

Child Parent DifferenceChild Parent Difference

Follow-

 up 

 Costd

 ($)

1, 9 No other symptoms 7 40 0.96 0.74 0.22 38.31 29.44 8.87 10,

(3.67) (40.12) (14.17) (3.88) 400 

2,10 Chest pain 2 200 0.49 0.24 0.25 97.22 47.06 50.16 10,

(3.08) (8.25) (4.57) (3.21) 400 

3,11 Shortness of breath/wheeze 7 200 0.58 0.35 0.23 115.07 69.57 45.5 40, 

(2.72) (9.95) (6.07) (2.79) 600 

4,12 Shortness of breath/wheeze 0.04 34.93 33.33 1.596 10, 

Chest pain

2 40 0.87 0.83

(0.67) (22.12) (18.97) (0.68) 200 

5,13 Fever 2 600 0.19 0.09 0.10 113.04 53.73 59.31 40, 

(1.66) (4.00) (2.57) (1.69) 750 

Fever 0.32 202.74 75.36 127.38 200, 

Chest pain (3.97) (8.66) (4.00) (4.24) 750 

6,14 7 400 0.51 0.19

7,15 Fever 0.17 135.21 67.53 67.68 40, 

Shortness of breath/wheeze

2 400 0.34 0.17

(2.38) (6.02) (3.96) (2.40) 600 

Fever 0.18 167.65 60.87 106.78 200, 

Shortness of breath/wheeze (2.66) (5.14) (2.79) (2.72) 750 

8,16

Chest pain

7 600 0.28 0.10

Overall 0.53 0.34 0.19

(6.35)

WTP per Symptom-Day

Avoided

86.03

(8.66)

34.85

(3.62)

51.18

(3.70)

a Initial price for new drug. 

b

 Proportion of parents who would purchase the new drug at the initial price.

c Turnbull estimate of the lowest possible mean WTP for any distribution defined over non-negative values [21:74].

WTP to reduce duration of illness to one day for each profile (first 8 rows); WTP per symptom-day avoided (last 

row.) US dollars of year 2000. 

d Price for new drug in follow-up question; the higher or lower of the pair of follow-up prices was assigned 

depending on whether the respondent would or would not buy the drug at the initial price. 
26

Table III. Logarithmic Surplus Function: Illness Attributes and Symptom Experiences.a

(Asymptotic z statistics in parentheses). 

Parameter (1) (2) (3) (4) (5)

ln(Symptom Days 

Avoided)

0.262

(5.965)

0.195

(4.436)

ln (Number of 

Symptoms)

0.273

(2.589)

ln (Days of Illness 

Avoided)

0.186

(4.104)

ln (Days of Cough with 

Phlegm)

0.147

(1.961)

0.155

(2.077)

ln (Days of Shortness of 

Breath/Wheezing)

0.0895

(1.645)

0.0868

(1.594)

ln(Days of Chest Pain) -0.0459

(-0.533)

-0.0398

(-0.462)

ln(Days of Fever) 0.146

(1.667)

0.142

(1.620)

High Discomfort 0.321

(3.121)

0.315

(3.064)

0.315

(3.034)

0.312

(3.020)

High Activity 

Restriction

0.209

(2.059)

0.203

(1.992)

0.207

(2.035)

0.205

(2.021)

Child rather than

Parent is Ill

0.753

(9.314)

0.643

(7.965)

0.645

(7.991)

0.645

(7.962)

0.665

(8.173)

Had Cough/Phlegm in 

Past Year 

-0.129

(-1.532)

Had Shrt Brth/Wheeze, 

Past Year 

0.0449

(0.353)

Had Chest Pain, Past 

Year 

-0.222

(-1.957)

Had Fever Past Year -0.0301

(-0.362)

Constant 4.321

(45.152)

4.209

(43.270)

4.157

(35.952)

4.234

(39.867)

4.349

(37.826)

s 1.187

(33.794)

1.160

(33.129)

1.159

(33.047)

1.159

(33.027)

1.152

(32.956)

Log-likelihoodb-1184.42 -1168.27 -1167.92 -1168.04 -1162.40

Test for interactions 

with Child (p-value)c

.55

.46

.74

.70

.65

.60

.75

.73

.44

.54

MRS 2.12

(12.37)

1.90

(12.39)

1.91

(12.40)

1.91

(12.35)

1.94

(12.29)

a

 Maximum likelihood estimates. The latent dependent variable is the natural logarithm of the equivalent surplus in 

dollars. 

b

 The log-likelihood value with all parameters except the constant and s set equal to zero is 1243.96. Thus, the 

null hypothesis of zero slope coefficients would be rejected at less than one percent significance for each 

specification in the table. 

c

 Likelihood ratio test of null hypothesis of equal slopes (top entry) or equal slopes and variances (bottom entry) 

between parent and child, allowing for different intercepts. 
27

Table IV. Logarithmic Surplus Function: Household Characteristics.a

(Asymptotic z-statistics in parentheses). 

Parameter (1) (2) (3) (4)

ln(Symptom Days 

Avoided)

0.187

(4.271)

0.190

(4.353)

0.193

(4.435)

0.199

(4.592)

High Discomfort 0.359

(3.455)

0.328

(3.148)

0.344

(3.314)

0.335

(3.209)

High Activity 

Restriction

0.187

(1.808)

0.214

(2.059)

0.203

(1.972)

0.178

(1.709)

Child rather than

Parent is Ill

0.618

(7.741)

0.648

(8.087)

0.638

(7.934)

1.636

(6.099)

ln (Annual Family 

Income)

0.154

(3.441)

0.0773

(1.279)

0.217

(3.547)

0.141

(3.096)

Married Parent Family -0.179

(-1.761)

-0.0524

(-0.481)

-0.0230

(-0.144)

-0.182

(-1.770)

ln (Number of Children) -0.288

(-3.150)

-0.295

(-3.229)

-0.270

(-2.939)

-0.281

(-3.092)

Responding Parent is 

Female

-0.0904

(-0.963)

-0.0249

(-0.251)

0.343

(1.289)

0.00324

(0.033)

Race is White -0.432

(-4.415)

-0.448

(-4.462)

-0.448

(-4.519)

-0.478

(-4.805)

Have PhysicianDiagnosed Asthma 0.239

(2.102)

ln(Parent Age) 0.0649

(0.372)

0.518

(2.705)

Responding Parent is 

College Graduate 

-0.0531

(-0.578)

Responding Parent is 

Employed 

0.390

(2.378)

0.207

(1.982)

ln(Responding Parent 

Wage)

0.124

(2.235)

ln(Price of Doctor's 

Visit)

0.121

(2.659)

ln(Hours Required for 

Doctor Visit)

0.0279

(0.361)

Responding Parent has 

Paid Sick Leave

-0.0163

(-0.179)

Mother is College 

Graduate

-0.0588

(-0.613)

Mother is Employed 0.0974

(0.946)

ln(Mother’s Wage) 0.0332

(0.998)

Father is College 

Graduate

0.0263

(0.248)

Father is Employed -0.0689

(-0.347)

ln(Father’s Wage) -0.0948

(-1.755)
28

Table IV. (Continued). 

Parameter (1) (2) (3) (4)

(Child Ill) x (Child 

Female)

-0.0114

(-0.105)

Child in School -0.262

(-1.750)

(Child Ill) x ln(Child 

Age)

-0.471

(-3.846)

Constant 3.183

(6.785)

3.676

(4.405)

2.196

(3.040)

1.522

(1.975)

s 1.131

(32.816)

1.125

(32.974)

1.128

(32.872)

1.119

(32.956)

Log-likelihoodb

-1146.77 -1141.68 -1143.69 -1136.82

Test for equal slopes and 

variances, Parent and 

Child (p-value)c.33 .60 .79 .94

MRS at Means 1.86

(12.53)

1.91

(12.48)

1.89

(12.44)

1.79

(11.75)

a

 Maximum likelihood estimates. The latent dependent variable is the natural logarithm of the 

equivalent surplus in dollars. 

b

 The log-likelihood value with all parameters except the constant and s set equal to zero is 1243.96.

Thus, the null hypothesis of zero slope coefficients would be rejected at less than one percent significance 

for each specification in the table. 

c

 Likelihood ratio test of null hypothesis of equal slopes and variances between parent and child, 

allowing for different intercepts. 
29

Table V. Parents’ Median Willingness-to-Pay to Relieve Acute Illness.a

(Asymptotic z -statistics in parentheses. Standard errors estimated using delta method.) 

Illness Col (1)b Col (2) b– Mild Symptoms Col (2) b– Severe Symptoms 

Symptom Days 

Avoided:

Child Parent Difference 

c

Child Parent Difference

 c

Child Parent Difference

 c

One Symptom Dayd160

(10.8)

75

(10.5)

85

(7.2)

128

(10.0)

67

(10.3)

61

(6.2)

217

(9.5)

114

(8.7)

103

(6.5)

24 Symptom Dayse367

(11.7)

173

(11.5)

194

(7.4)

238

(9.2)

125

(9.9)

113

(5.9)

404

(11.7)

212

(10.8)

191

(6.9)

Illness Col (4) b Col (5) b– Have Had Symptom Col (5)b– Have Not Had Symptom

Days of Symptoms 

Avoided:

Child Parent Difference

 c

Child Parent Difference

 c

Child Parent Difference

 c

Six Days Cough d 226

(10.2)

119

(10.3)

108

(6.3)

215

(9.7)

111

(9.6)

105

(6.4)

245

(9.1)

126

(9.3)

119

(6.1)

Six Days SB d 204

(7.3)

107

(7.0)

97

(5.5)

211

(5.9)

109

(5.6)

102

(4.9)

202

(7.2)

104

(7.0)

98

(5.6)

Six Days Chest 

Pain d

160

(5.4)

84

(5.1)

76

(4.6)

138

(4.9)

71

(4.7)

67

(4.4)

172

(5.3)

88

(5.1)

84

(4.6)

Six Days Fever d 226

(5.6)

119

(5.7)

107

(4.5)

221

(5.4)

114

(5.4)

107

(4.5)

228

(5.5)

117

(5.6)

111

(4.5)

Six Days, All 

Symptoms d

318

(10.1)

167

(10.0)

151

(6.4) ---

f

---

f

---

f

---

f

---

f

---

f

a Estimates of median WTP in U.S. dollars of the year 2000 based on equivalent surplus functions in Table III. 

b Identifies the Table III regression used to estimate WTP. Mild (severe) cases involve low (high) discomfort and interference with activities

c

 WTP for child minus WTP for parent. d One day of symptom still experienced. e Four symptom days still experienced. 

f

 Not estimated because “exp erience” could be defined arbitrarily to mean experience with one, two, three or all four symptoms. 
30

Table VI. Individual and Household Characteristics and Median Parental Willingness-to-Pay.a

(Asymptotic z -statistics in parentheses. Standard errors estimated using delta method.) 

Total Willingness to Pay to Avoid One Symptom 

Day 

Characteristic Child Parent

Married 161

(10.4)

87

(9.9)

Not Married 192

(8.7)

104

(8.3)

One Child 195

(9.7)

105

(9.3)

Two Children 159

(10.9)

86

(10.2)

Three Children 142

(9.6)

76

(9.1)

Four or More 

Children

129

(8.2)

70

(7.9)

Have Asthma 209

(7.4)

113

(7.0)

Do Not Have Asthma 165 

(10.9)

89

(10.3)

White 151

(10.7)

82

(9.9)

Black 233

(8.5)

126

(8.3)

Child Age=3 271

(6.7)

---

b

Child Age=6 196

(10.1)

---

b

Child Age=9.25 

(Sample Mean)

160

(10.2)

89

(10.4)

Child Age=12 141

(9.1)

---

b

Child Age=17 120

(7.3)

---

b

a Estimates of median WTP in U.S. dollars of the year 2000 based on equivalent surplus functions 

 in Table IV. Shows effect of changing one characteristic while holding all others at sample means. 

 Computations for child age are based on column (4) of Table IV while all others are based on

 column (1). 

b Does not vary with child age. 
31

Table VII. Acute Morbidity Values from Previous Research. a

Income-Adjusted Using 

Elasticity of:c

Symptom Days Severity Age Group Study Study WTPb0.15 0.40

One-Day Episodes of One Symptom

Cough 1 - Adults Dickie et al. 17 17 16

1 - Adults Tolley et al. 40 42 42

1 Mild Adults Johnson et al. [26] 27 28 30

1 Severe Adults Johnson et al. [26] 49 51 53

Shortness 1 - Adults Dickie et al. 10 10 10

of Breath 1 Mild Adults Loehman et al. 80 91 110

1 Severe Adults Loehman et al. 98 112 135

1 Mild Adults Johnson et al. [26] 27 28 30

1 Severe Adults Johnson et al. [26] 84 87 92

1 Mild Adults Johnson et al. [27] 0 0 0

Fever/Ache 1 Mild Adults Johnson et al. [27] 23 25 28

Multiple-Day Episodes of One Symptom

Shortness 5 Mild Adults Johnson et al. [27] 235 252 282

of Breath 7 Mild Adults Loehman et al. 239 273 329

7 Severe Adults Loehman et al. 266 304 367

Fever/Ache 5 Mild Adults Johnson et al. [27] 319 343 384

Multiple-Day, Multiple -Symptom Episodes 

Cold 5 - Adults Alberini et al. [2] 40 47 58

6 - Mothers Liu et al. 34 44 59

6 - Children Liu et al. 71 90 121

Not Cold 5 - Adults Alberini et al. [2] 61 71 87

a Sources of values are as follows. Dickie et al., Loehman et al. and Tolley et al.: taken from Johnson et al. [26], 

Table 1. Johnson et al. [26]: their Table 4, “Predicted WTP.” Alberini et al. [2]: their Table IV. Johnson et al. [27]: 

their Table 6. Liu et al.: p. 324, averaged over severity levels. Alberini et al. [2] and Liu et al. presented their 

results in USD (converted from Taiwanese currency using exchange rates). Johnson et al. [27] values converted 

from Canadian dollars using purchasing power parity for the survey year (U.S.$ 1 = CAN$ 1.19). 

b All values inflated to USD 2000 using the implicit GDP Deflator. 

c Shows effect of changing mean income level in original study to mean income of present sample using alternative 

income elasticities of WTP. Income in the Johnson et al. [26] study assumed to be average of mean incomes in 

Dickie et al., Loehman et al. and Tolley et al. 
32

Figure 1: Neutral Parental Preferences. The MRS exceeds unity at point A, where the 

indifference curve is tangent to the nonlinear budget constraint. Parental preferences are neutral, 

however, because the MRS equals unity at point E, where parent and child consume equal 

numbers of symptom-free days. 

0 2 4 6

0

2

4

6

-1

E

A

B0

U0

h

p

=hc

Parent symptom-free days (T-hp

)

Child symptom-free days (T-hc)
33

0 5 10 15 20

0

2

4

6

8

10

MRS

Child Age (Years)

Figure 2: Estimated Marginal Rate of Substitution against Child Age. The convex curve shows 

how the MRS falls as the child ages, based on column (4) of Table IV. Vertical lines mark the 

within-sample age range of 3 to 17 years. The estimated MRS significantly differs from unity (shown 

by the horizontal line) at less than 5 percent for all within-sample ages. 
34

 

1

 The MRS is defined by the implicit function theorem and rule as( / )/( / ), c p ∂u ∂h ∂ ∂ u h where u denotes 

the direct utility function and ( / ) 0. p∂u h∂ ≠ Using duality, the ratio of marginal disutility of illness 

attributes equals the ratio on the right hand side of equation (3). 

2 Benefit estimates for policy, however, should be computed at the household’s equilibrium. 

3 Of 11,018 calls to presumed working residential numbers, 19.7% yielded no contact after the maximum 

of three calls. Of 8,852 adults contacted, 55.9% declared their household ineligible, a reasonable figure 

since children are present in only about one-third of households. The remaining 3904 adult contacts are 

assumed eligible, although many refused to participate before eligibility could be verified. Interviews 

were scheduled with 487 persons, representing 12.5% of assumed eligible contacts, and 295 arrived for 

the interview. The ratio of completed interviews to adult contacts (295/8852 = 3.3%) is lower than in 

Alberini et al. [3] (930/17841 = 5.2%) or in Johnson et al. [27] (399/4517 = 8.8%), who did not have to 

exclude households without children. 

4

 Specifically, if an eligible child with physician-diagnosed asthma lived in the household, he or she was 

selected as the sample child. Otherwise, the sample child was selected based on the number of eligible 

children and the last digit of the survey number. For example, if two eligible children were present, the 

older child was chosen if the last digit of the survey number (surveys were numbered sequentially from 1 

to 295) was 1-5; otherwise the younger child was chosen. The algorithm for choosing the sample child is 

included with the survey, a copy of which may be obtained by request. A child is eligible if the adult 

respondent is the parent or legal guardian; the child lives with the respondent and is between 3 and 17 

years old. The upper age limit was chosen because adulthood legally begins at age 18, and for valuation 

purposes EPA considers children to be persons under age 18. The lower age limit was chosen in an effort 

to limit the sample to parents who had accumulated a reasonable amount of experience dealing with the 

child’s acute illness and who would be able to distinguish separate symptoms affecting the child. The 

parent of a very young child might have relatively little experience, particularly if the child were the 

oldest or only child. Also, it can be difficult for a parent to ascertain the exact symptoms being 

experienced by a very young child, and the child may be unable to communicate this information. 

5

 Acute illness experiences were measured by: work-loss days for employed respondents, school-loss days 

for children in school or day-care, restricted activity days for parents not employed or children not in 

school, and indicators of whether the four symptoms included in the valuation component of the survey 

had been experienced. Indicators of chronic health status include presence of physician-diagnosed: 

asthma, COPD, other chronic lung condition, other serious, long-term health condition, allergies; whether 
35

 

health conditions limit activities; subjectively assessed health status (excellent, very good, good, fair or 

poor). Also, measures of the child’s health in infancy were collected (birth weight, prematurity, whether 

admitted to neonatal intensive care). 

6 Acute bronchitis typically lasts about a week (a few days to two weeks) and is characterized by lower 

respiratory symptoms and a fever of less than 101° F. Symptoms include cough with phlegm, possibly 

chest pain below the breastbone when breathing deeply or coughing, and shortness of breath/wheezing.

7

 Taken soon after symptoms start Relenza or Tamiflu may reduce duration of illness. 

8

Prices used for a study in Taiwan [2] and in Canada [26] were adjusted for differences in price and 

income levels relative to Mississippi. 

9

Some pretest respondents objected to the idea of “avoiding” an illness. How would one know that an 

illness had been avoided? How would one know to make a payment to avoid a specific illness, without 

already experiencing the illness? Others wanted to know the mechanism between payment and illness 

avoidance, such as whether it was a visit to the doctor or a pill. 

10 Debriefing of pretest subjects included a relatively non-directive assessment of their reactions to the 

hypothetical medication. No one expressed concern about side effects. One pretest respondent expressed 

doubts that a real medication would be as effective as the survey description; one indicated she thought 

the hypothetical drug was similar to a real drug in development; and one asked whether drug companies 

were funding the study. None of these pretest respondents indicated that their WTP responses had been 

affected by these thoughts. Alberini et al. [3] found that about 1/3 of their sample doubted effectiveness 

of a hypothetical product reducing fatality risks, while about 1/5 were concerned about side effects. 

However, these factors had little discernible impact on WTP responses. 

11 In an unreported regression, four additional variables were added to the specification of column (5), 

constructed as interactions of symptom-experience dummies with the separate symptom-duration 

variables. None of the interaction terms was statistically significant. Previous findings on effects of 

experience or familiarity on health valuations pertain mainly to chronic illnesses. Krupnick and Cropper 

[29] found that relatives of people with chronic lung disease were willing to pay more to reduce risk of 

chronic bronchitis than persons with less familiarity. In contrast, persons with a chronic condition do not 

perceive higher losses in quality-adjusted life-years from the condition than the general public [19:100]. 

12 The first test, of whether slopes vary between children and parents after allowing for intercept shifts, is 

based on re-estimating the equations with interaction terms constructed as products of the child indicator 

variable and all other explanatory variables. The second test, of whether slopes and variances differ after 

allowing for intercept shifts (as might occur if WTP values were more variable for children than parents), 

is based on re-estimating the equations separately for parents and children. 
36

 

13 To further investigate effects of household composition, two unreported regressions allowed the 

coefficient of the child indicator to vary with birth-order or by first-born status; however, coefficients of 

these interaction terms were statistically insignificant. 

14But parents of both races appear to make identical tradeoffs between their own and their children’s 

illnesses. When the child indicator was interacted with the racial indicator, the coefficient of this 

interaction term was not statistically significant at conventional levels. 

15 In unreported regressions the asthma indicator was interacted with symptom-days, or with the measures 

of days of individual symptoms, but the interaction terms were statistically insignificant. Also, several 

unreported regressions investigated further effects of health status. Dummy variables indicating presence 

of allergies or of health conditions that limit normal activities, or indicating subjectively rated health 

status (excellent, very good, good, fair or poor) took statistically insignificant coefficients. Dummy 

variables indicating whether restricted activity days, or work- or school-loss days, had been experienced 

in the past year had statistically significant, negative coefficients, suggesting that those who recently 

experienced activity restrictions due to illness are willing to pay less to avoid an incremental episode of 

acute illness. However, MRS estimates were largely unaffected by these changes in specification. 

16 Several unreported regressions included other variables associated with parental labor supply or with 

the costs/consequences of illness. Additional variables included indicators of health insurance coverage 

and measures of hours of work, availability of paid sick leave or family leave, subjective ratings of the 

extent of problems caused by missing work, and whether work would be missed if the child were ill or 

were taken to the doctor. Few of these variables had statistically significant coefficients, and accounting 

for them left the estimated MRS largely unaffected. 

17 The parent’s rate of substitution between time spent caring for a sick child relative to another activity 

would reflect similar utility terms as the MRS for illness attributes, and would be expected to decline as 

more time is spent with the child. The rate of substitution would equal unity, however, at an interior 

optimum for a parent who could freely allocate time between activities, to insure that the marginal value 

of time would be equal across all activities. 

18 WTP estimates assume that those who would not purchase the new drug at either initial or follow-up 

prices are willing to pay a positive amount less than the lower, follow-up price. Some of these “No, No” 

responses, however, may reflect a zero WTP or rejection of the valuation scenario. Overall, 15 percent of 

responses were “No” at both initial and follow-up prices. Given a “No” at the initial price, the proportion 

of negative responses at the follow-up price is increasing with price, from five percent at $10, to 16 

percent at $40, and 56 percent at $200. Two-thirds of “No, No” responses occur at $200, the highest of 

the “No” follow-up prices. The preponderance of high prices among “No, No” responses is consistent 
37

 

with the assumption that WTP is less than the follow-up price, though not necessarily zero. These 

respondents may have been thinking of treatments already available and less expensive than the 

hypothetical medication. Also, a bivariate probit analysis indicates that the probability of a “No” 

response to either initial or follow-up questions declines as symptom days avoided increase, is lower 

when the child rather than the parent is affected, and increases with price. Thus, determinants of “No, 

No” responses appear consistent with determinants of WTP in Tables III and IV. This outcome, together 

with the fact that only one respondent answered “No, No” to each of four profiles, suggests that these 

responses do not reflect rejection of the valuation scenario. 

19 Estimates of mean WTP for the lognormal case, and all results based on the Weibull distribution, are 

available on request. Weibull-based estimates of the MRS are about five percent smaller than estimates 

in Tables III and IV, while estimated median WTP is about 20 percent higher for children, and 25 percent 

higher for adults, than estimates presented in Tables V and VI

20 A second shortcoming in current benefit assessments is not distinguishing between one-day episodes of 

one symptom and episodes with more symptoms or days, because valuations increase less than

proportionately with duration [2,26,27,31,32,39] or number of symptoms [2,39]. 

21 This outcome reflects the relatively modest estimated income elasticity, coupled with higher WTP 

among black and single-parent families. Estimates were computed by evaluating median WTP for female 

responding parents with race, marital status and income set appropriately for each family type, and all 

other explanatory variables at sample means. Mean income figures appear in Table FINC-01 [41], at 

www.census.gov/hhes/www/income00.html. 

22 The income elasticity Alberini et al. [2] use to estimate benefits is 0.41. Liu et al. [31] report four 

income elasticities that average 0.38. Loehman et al. [32] report elasticitie s ranging from about 0.25 to 

0.6, with a midpoint of about 0.43. The average of 0.41, 0.38 and 0.43 is about 0.4. 

23 For example, Alberini et al. [2] consider five days of illness with about two symptoms, while acute 

bronchitis as defined here would involve seven days of four symptoms. But cough with phlegm, fever, 

aching muscles, chest pain, shortness of breath and wheezing would count as six symptoms in Alberini et 

al.’s coding scheme, while these ailments, plus tiredness and chills, count as only four symptoms here. 

24 Unit values are listed in Table 14, p. 44 and aggregate benefits in Table I-3, p. I-17 [43]. Unit values 

were replaced with the following estimates from the present study: for children, $174 for one shortness of 

breath day, $160 for any other symptom, and $318 for acute bronchitis; for adults, $75 for any symptom. 

The first of these values is estimated from the regression in column (4) of Table III but is not reported in 

the paper while the other three estimates are taken from Table V.