-------
5
SCE [ Sp ]
Social
Consumption
Equivalent
Value
(l/e)c6p
Average
Individual
Willingness
to Pay
wL6p c5p
Human Capital
Net of
Consumption
(P/AjnJvgp.
Value of
Additional
Children
Equation (7) shows that society's willingness to pay for mortality
improvements may be greater or less than individual willingness to pay for the
same change.
Adding Health Status to the Model
The SCE model can modified to include nonfatal risks by including a term
for health status in the welfare function. We assume that each person has a
utility function U[c(x),h(x),x], where h(x) is defined as the "state of
health" at age x. Health status is also assumed to have a direct impact on
health costs, consumption, fertility, mortality, and labor productivity.
Changes in fertility, mortality, and labor productivity will induce changes in
the equilibrium stable population growth rate and the equilibrium capital-
labor ratio. Suppose that some activity (e.g., less safe roads, changed
airline regulations) alters the health state by Sh(x) over the age dimension.
Suppose also that this change has associated with it direct health costs
ScH{ Sh], and alterations in consumption Sc( «hj, labor effectiveness «X[ Sh 1,
mortality &p[Sh], and fertility &n{5h]. The latter are all directly observed
changes for a specific category of injuries.
The social welfare function now takes the following form:
u
W- J U[c(x),h(x),x] -p(x)dx. (8)
0
We can rewrite the societal budget constraint as:
CO (l) CO
J e"9*p(x)c(x)dx + J e~9*p(x)cH(x)dx * (f(k)-gk) I e"9xp(x)X(x)dx (9)
o 0 0
breaking out health costs and consumption expenses separately. The change in
welfare caused by 5h is given by:
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6
0) no
5W » 3U/3c(0) J" e~ (0
- (f(k)-gk) { J e~^xX(x)6p[5h]dx + f e"9*p(x)5X[5h]dx }
0 0
0)
- 5k[Sh](f'-g) / e~9xX(x)p(x)dx - (S6g[5h]. (11)
0
Equation (11 ) is identical to equation (N. 6 ) in footnote 1 except for the
addition of the terms related to changes in medical costs (5ch[5h]) and
changes in labor productivity related to changes in health status (5X(6hl).
Also, the change in the population growth rate now includes the combined
effect of changes in fertility and mortality.
Using equation (11 ) to substitute for the first term in equation (10)
yields:
-------
0) 0}
SW => J U[c(x) ,h(x) ,x]Sp[ Sh]dx + / 3U/3h • 5h( x )p( x )dx
0 0
(0 CO
+ 3U/3c(0) { w-[ J e-9xX(x)Sp(x)c3x - f e^SXf 5h]p(x)dx ]
0 0
CO 03
- J e'^ScuISh]p(x)dx - J e'^cufx)6p(x)dx
0 0
0)
- J" e~<3xc(x)Sp(x)dx + 0Sg[Sh] } (12)
0
This can be simplified to:
» - «Sp + «5h
Life-Cycle Utility of Utility"of
Welfare Extra Improved
Increase Life Years Health Status
+ 3U/3c(0) { wLSp
- wL5h
Value of
Extra
Labor Years
Value of
Increased
Productivity
" cH,5h
" cH,5p
Social Cost of
Health Status
Improvements
" C«P
Social Cost of
Consumption
Upkeep
Social Cost of
Health Maintenance
Over Extra Years
+
^ V5p+V5m^/Am
Value of
Additional
Children
}
(13)
Where l5 ' c5 ' and CH 5 are expected extra person-years of production,
consumption, and health costs respectively, resulting from variation in
mortality; L§h» c$h» an^ CH 5 are the expected life-cycle increases in
productivity, consumption, and health costs directly associated with improved
health status; vg and vjjj are additional children per person due to variation
in mortality and health, respectively; and is the average age of
reproduction in the stable population.
A comparison of equation (13) with equation (3) indicates that improving
health status has benefits and cost above and beyond those associated with
improved longevity. There is a quality-of-life aspect to living longer, now
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8
captured by the second term in equation (13), that was ignored in the original
model. A healthier population will also be a more productive one, but at the
additional social cost of maintaining good health. Finally, health status
changes may affect fertility rates, which in turn affect social welfare either
negatively or positively depending on the value of additional children to the
society.
Empirical Estimation
This subsection describes methods for estimating each term in equation
(13). The remainder of this section, provides illustrative applications.
Since health status is accounted for explicitly in the model, the
utility per life year (the first term in the equation) should be uniform over
time . Its value can be estimated from a study of individual willingness to
pay for a statistical life by (a) selecting a discount rate, (b) computing the
present value (in years) of the remaining expected lifespan for someone at the
average age in the study population, and (c) dividing mean willingness to pay
by mean expected life span. Miller (1986) identifies 25 studies of individual
willingness to pay for a statistical life that are of reasonable quality.
After adjusting such parameters as the value of time to make the values in the
studies more comparable and adjusting for people's misperceptions of their
fatality risks using the procedure in Blomquist (1982), the mean value of a
statistical life across the studies was $1.95 million 1986 after-tax dollars
with a standard deviation of $.5 million.
Almost all of the 25 studies involved populations with mean ages around
38. According to the Statistical Abstract (1988), the average remaining
lifespan at age 38 is roughly 39 years. At a 6 percent discount rate, the
value per life year at age 38 is about $120,000 or $350 per day. At a 2
percent discount rate, it is about $70,000 per year or $200 per day. By way
of comparison, Moore and Viscusi (1988) estimates a statistical model of wage
premiums for risk that indicates the average individual is willing to pay
$90,000 for a life year and uses a 2 percent discount rate in safety
decisionmaking.
The utility per year of improved health status—the second term in
equation (13)--presents the greatest difficulty in valuation. Computation of
differences in welfare associated with changes in health status requires
knowing the utilities of alternative health states. Recent work on the
measurement of health status (reviewed in the next section) provides the
necessary data. This work produced scales indicating how utility loss varies
with the nature and extent of functional loss.
If the utility values on a scale are normalized so that death has a
value of zero and perfect health a value of one, the value associated with
unit utility loss for one year will be the value of a life year. The utility
in the second term is the product of the functional loss averted and the
utility of this loss. To get a dollar value, this product is multiplied times
the value of a 'functional life year.
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9
The third through seventh terms in equation (13) together constitute the
change in human capital net of consumption that results from the health status
change. This is a societal externality. The value of extra labor years and
increased productivity is measured by the gain in earnings attributable to
averting the illness or injury. The social costs related to health status
changes essentially we medical costs borne by third-party payers, charity, or
government. The seventh term is the impact of the health status change on
consumption, including consumption funded by transfer payments, insurance
payouts, and earnings. Under the assumption that all bequests stay within the
family, the change in the family's after-tax earnings that results from the
illness or injury should equal the change in the family's earnings-related
consumption—so they cancel out. Thus, the externalities resulting from
reduced illness or injury equal taxes gained plus transfer payments (including
medical care reimbursement) averted. The dollar value of the externalities
generally can be computed from the extensive literature on costs of morbid
conditions and data from the Health Interview Survey.
The explicit inclusion of transfer payments in the societal benefits is
consistent with the generally accepted principle that transfer payment
reductions are not benefits (see, for example, Klarman, 1965 or Hu and
Sandifer, 1981). Rational individuals will pay less to avoid disability if
transfer payments will cover some of the associated costs. Since transfer
payments were subtracted from individual willingness to pay, their explicit
addition yields zero net transfers in the societal benefit estimate.
The final term in equation (13) is the value of additional children born
due to the health status improvement. Arthur (1981) estimates the value of
this term as -$68,125 (in 1975 dollars), based strictly on the costs society
incurs per child. This approach ignores the noneconomic benefits that parents
derive from their children. Analyses of direct costs and opportunity costs of
children (Espenshade and Calhoun, 1986) suggest these benefits are at least as
large as the opportunity costs. In this article, therefore, the net value of
this term is assumed to be negligible and is ignored in the computations.
Consistency of Empirical Estimates across Scales
The operations research and medical decision-making literature contains
many scales that examine the multi-attribute utility loss associated with dif-
ferent health states. Some articles focus on individual diagnoses--for
example, the utility loss associated with blindness or kidney failure. Others
create functional ability scales and examine the utility associated with each
state on the scale. Torrance (1982, 1986) evaluates the different
methodological approaches used in this literature.
Tables 1 through 3 compare the utility loss that different scales
suggest is associated with selected diagnoses. The studies by Green and Brown
(1978), Card (1980), His et al. (1983), Miyamoto and Eraker (1985), Pliskin
Shepard, and Weinstein (1980), Sackett and Torrance (1978), and Viscusi et al.
(1989) directly estimate the utility loss associated with specific diagnoses.
The other loss estimates in this table were computed by developing descrip-
tions of the functional impairments associated with the diagnoses, then
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10
computing the utility losses that each scale suggests are associated with
these impairments. Impairments generally were evaluated on only a subset of
the utility scales because the other scales did not include appropriate
impairment categories.
This section first describes and evaluates the studies that provide
utility loss estimates for at least two diagnostic conditions. Next, for each
diagnosis, it compares the utility loss estimates across studies and sub-
stitutes the modal utility loss estimate into equation (13) to estimate an SCE
value. This analysis is the first systematic attempt to validate the utility
scales against one another or against utilities estimated from studies of
specific illnesses and injuries. To provide a fairer test of the scales, we
generally estimated the functional impairments on all scales first, then went
back and computed the associated utility losses.
Available Scales Showing Utilities
Torrance (1982) conducted a survey of 112 parents of school-age children
in Canada. The survey yielded utility loss estimates for scales that
evaluated four dimensions of functioning: impaired physical function, role
function (ability to work, play, etc.), social-emotional function, and health
function. Pain is incorporated, somewhat cursorily, in the last category.
Further analysis of the original ratings and supplemental interviews yielded a
multiplicative equation for combining the utility losses across dimensions of
impairment (Drummond et al., 1987). The utility losses have an uncertainty
range (two standard deviations) of ± 12 percent. The four impairment scales
are easy to use and applied to the widest range of diagnoses of any scale we
tested. The equation for combining ratings is simple and conceptually
appealing; it admits the possibility of fates worse than death and recognizes
that the utility loss associated with an impairment is lower if the individual
initially lacked full utility because of other impairments
Sintonen (1981) obtained ratings from 120 randomly selected Finns of the
relative utility of each point on 11 functional scales: raving, hearing,
speaking, seeing, working, breathing, incontinence, sleeping, eating, mental
functioning, and social participation. The respondents also provided guidance
on additive methods for computing a combined utility loss from the discrete
losses. The method allows the analyst to go into considerable detail, which
is helpful in evaluating a condition where a detailed medical description of
the typical course and consequences is available. The lack of a scale related
to pain detracts from rating quality, however, especially for conscious states
worse than death. The large number of factors and additive weights also mean
that impairments which are not systemically pervasive never are rated as very
severe, which is inconsistent with the information from other utility scales.
Kind, Rosser, and Williams (1982) developed a two-dimensional scale that
is particularly easy to use. One dimension measures disability, where 1 is
fully mobile and 8 is unconscious. The second dimension measures distress,
where 1 is none and 4 is severe. Median utility values were computed from the
non-economic component of British jury awards, which follow an informal
schedule. Interviews also were conducted with a non-random sample of 70
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11
subjects including healthy volunteers, doctors, nurses, and patients in
medical and mental hospitals. The survey has methodological problems,
however, in part because the 10 mental patients provided some extreme ratings
that were not censored. It also is inconsistent with both other survey-based
estimates of utility loss and the jury award scale. Even the jury award
scale's applicability is limited because it does not deal with sensory or
mental function. In addition, both the jury and survey data indicate
virtually all health states involve utility losses less than 20 percent or
more than 60 percent, which seems unlikely and disagrees with other studies.
Kaplan (1982) and Kaplan, Bush, and Berry (1976) provide a utility loss
estimates for a scale with simultaneous dimensions of mobility, physical
activity, and social activity, as well as linear score adjustments for 36
symptom-problem complexes. The scale, which was the first developed, was
calibrated through a population survey in San Diego. It has the major
limitation of excluding the possibility that impairments can be worse than or
even almost as bad as death. In addition, the symptom-problem complexes
sometimes are inconsistent; for example, why should a cough and fever add
.007 to utility while a cough alone subtracts .007? Also, more analytic
judgment is required to select an appropriate combination of complexes using
this scale than to rate diagnoses using any of the other scales.
His et al. (1983) enlisted four physicians—specialists in orthopedics,
neurology, plastic surgery, and general surgery— then divided 476 moderate
and severe injuries into their four specialty categories. The physicians
defined six functional scales, with impairment levels ranging from 0 to 4:
mobility, daily living (self care), cognitive/psychological sensory, cos-
metic, and pain. For each injury, the appropriate specialist rated the
probable number of weeks of impairment at each level during the first year,
and the probable impairment levels during the second through fifth years and
thereafter. Separate ratings were done for four age groups. The impact on
life expectancy and the need for corrective surgery also were estimated.
Using two physicians per injury, Carsten (1986) added physician ratings of
some additional injuries and redefined others, arriving at a final set of 432
injuries. Roughly 20 injury experts then used a structured computer exercise
to develop weights for combining the ratings on five of the impairment dimen-
sions (self care was omitted) into a total impairment score. Their weighting
was adjusted using ratings from an American Medical Association guidebook
(1984), which is discussed below. A decision by Carsten, without consulting
the physicians, established that no nonfatal injury was worse than death.
Luchter (1987) added the days of productivity loss as an impairment measure
for minor injuries. Miller, Brinkman, and Luchter (1988) converted the
workdays lost for minor injuries into utility loss estimates.
Three sources provide utility estimates for a range of diagnoses rather
than for points on functional scales.
The Guides to the Evaluation of Permanent Impairment (American Medical
Association, 1984) were developed by rare than 100 physicians. They are
intended primarily for assessing impairment through physical examination and
provide guidance at a micro level. For example, (a) the impairment associated
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12
with shoulder injuries is estimated separately for the more and less dominant
arms and varies with the percentage reduction in range of shoulder rotation,
and (b) nine levels of impairment are presented for lung cancer. The guides
also provide insight into typical impairment levels for some injuries and
illnesses. The guides are perfect. They assume nothing is worse than
death. Furthermore, no central control was exerted over the influence
specialists on a body system decided that system had overall functioning.
Therefore, the average impairment scores for some body systems seem high.
Green and Brown (1978) asked about 100 British university students to
rate the relative severity of death, selected injuries, and being unhurt in an
accident. Their results are interpreted in this article as indications of the
percentage utility loss during the period of disability for acute conditions
and of lifetime loss for chronic and irreversible conditions.
Finally, Sackett and Torrance (1978) asked a small random sample of
Canadians whether they would rather live their normal lifespan with selected
chronic illnesses or live a healthy life but die prematurely. The number of
years that people would trade to avoid the different impairments determined
the utility losses associated with them. The conditions examined included
tuberculosis, depression, renal failure, mastectomy, and an unnamed contagious
disease. An important lesson of this study is that the value of an impairments
rises with its permanence. More research is needed to determine (a) whether
the value of avoiding minor illnesses and injuries is significantly overes-
timated with the approach suggested in this article and (b) how to adjust the
values based on the duration of impairment.
Estimated Investment to Reduce Selected Injuries and Illnesses
Table 1 presents estimates of the utility loss and cost associated with
selected injuries. The values in the first column of data are for blindness.
The utility loss estimates from Torrance (1982) and Green and Brown (1978) can
be used to judge the quality of our estimates using other scales because these
studies asked people about the utility loss associated with blindness; the
estimates are 37 and 34 percent respectively. The 20 percent value in Card
(1980) also is a survey estimate, but may not be representative of the general
population because it was based on a small survey of medical personnel. We
estimated a 33 percent utility loss from Carsten (1986) by doubling the
estimate for losing one eye, so the estimate may be low. Our 39 percent
estimate from the Kaplan (1982) scale is for someone who did not drive, walked
without physical problems, was limited in choice of work, and wore glasses or
had trouble seeing. These two estimates agree with the survey data. The
lowest estimate, the 15 percent loss from the Kind, Rosser and Williams (1982)
scale, is for a severely limited work choice but no distress. Because this
description omits the sensory loss, the utility loss probably is underes-
timated. Sintonen (1981) provided an adjustment factor for blindness that we
used in conjunction with the rating of the impact on functioning to obtain an
estimated utility loss of 22 to 24 percent. This estimate may be low because
blindness only affects a few aspects of functioning, which means the Sintonen
scale unduly constrains the possible utility loss. Viewed from the
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13
perspective of the other estimates, the 85 percent utility loss estimate in
the American Medical Association guide is a severe overestimate.
We conclude that the utility loss associated with blindness is probably
between 33 and 39 percent. With the $1.95 million dollar value of a life,
this range implies typical individuals would be willing to pay between
$640,000 and $760,000 to prevent a statistical person among their group from
going blind. Data on the average foregone, taxes and transfer payments per
blind individual should be added to this value to estimate the SCE.
The second column of data shows the utility loss associated with severe
brain damage or lasting unconsciousness. Kind et al. (1982), Torrance (1984),
and Green and Brown (1978) measured the utility loss associated with this
injury directly and determined it was a fate 8 to 28 percent worse than death.
The physician ratings in Carsten (1986) and American Medical Association
(1984), which did not allow fates worse than death, rated the utility loss for
unconsciousness within 5 percent of the loss for death. Sintonen (1981) found
lasting unconsciousness was 3 percent worse than death. Torrance (1984) notes
that the visually based rating method used by Sintonen implicitly may have
indicated the survey designer expected people to consider death the worst
fate, so the 103 percent utility loss may be an underestimate. Kaplan's
(1982) scale does not provide good utility loss estimates for severely
disabling conditions; for unconsciousness, we estimated a utility loss of 71
percent.
The studies that allow fates worse than death provide the best estimates
of utility loss for lasting unconsciousness, with a 116 percent loss seeming
most probable. The last three rows of data in Table 1 indicate the medical
costs, lost earnings, and other public costs associated with unconsciousness
(and other injuries). The medical and earnings data are from Miller,
Brinkman, and Luchter (1988), while the public costs are from Miller (1986).
His et al. (1983) indicates that severe head injury causes roughly a 5-year
reduction in lifespan. If we use a Federal income tax rate of 23 percent
(Minarik, 1985) and a state rate of 5 percent (Feenberg and Rosen, 1986),
these data can be used with equation (13) to estimate the SCE for a severe
head injury at $3,100,000.
As the third column of utilities in Table 1 show, complete quadriplegia
is another fate worse than death, with a utility loss of 105 to 114 percent on
the three reliable scales, implying a best estimate of 109 percent. The
Sintonen scale did not work well here, yielding an estimated utility loss of
only 49 percent because its method for combining losses does not allow a large
total loss unless the sensory, mental, and rotor systems all are severely
affected. Kaplan's scale again worked poorly, while the physician's judged
this fate almost as bad as death. Both physician judgment (Carsten, 1986) and
interviews with quadriplegics who have adapted to their injuries (Torrance,
1988) indicate the utility loss may decrease over time, leveling out at about
65 percent. Complete quadriplegic reduces expected lifespan by 21.5 years
according to His et al, (1983) . The estimated SCE for a complete quadriplegic
injury is $2,600,000.
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14
Using the scales in Kind et al. (1982), Kaplan (1982), and Torrance
(1982), we estimate the utility loss for paraplegia (data column 4) at 50 to
54 percent with incomplete paralysis and 62 to 65 percent with complete paral-
ysis. Paraplegics surveyed by Torrance (1988) and the physicians in Carsten
(1986) estimated a slightly smaller loss, around 45 percent. The students
surveyed by Green and Brown (1978) and the Sintonen (1981) scale (which did
not model paraplegia well) both gave estimates around 29 percent, which are
probably too low. As with blindness, the utility loss in the American Medical
Association (1984) guides seems much too high, 81 percent. Complete
paraplegia reduces expected lifespan by 15.3 years according to His et al.
(1983) . The best estimate of the utility loss is 50 to 65 percent, with an
SCE of $1,300,000 to $1,600,000.
For older people, severe burns (data column 5) are the worst possible
fate. They typically spend the rest of their lives bedridden with sufficient
pain that they cannot do simple arithmetic. Using the utility scales in
Torrance (1982) and Kind et al. (1982), we estimate the utility loss at 137 to
139 percent. The physician ratings, which do not allow fates to be worse than
death, yield lower and less credible values. Severe burns shorten lifespan,
perhaps by about 5 years. The SCE is about $3.6 million to prevent a person
in late middle age from being severely burned.
A broken lower leg (data column 6) typically causes no permanent
impairment according to data from the Consumer Product Safety Commission's
injury cost model (which also provided the cost data for this injury) and the
physician ratings of impairment in Carsten (1986). Four of the five scales we
applied suggest a broken leg will reduce utility by 30 to 36 percent in the
year it occurs, while Kaplan (1982) yields an excessive estimate of 54
percent. The 34 percent estimate from Green and Brown (1978) was computed as
the loss for a broken arm times the ratio of losses for amputation of a leg
and an arm. With a one-year utility loss around 33 percent, the SCE for a
broken leg is about $40,000.
As the last column in Table 1 shows, our ratings with the Kind et al.
(1982), Torrance [1982), and Kaplan (1982) scales suggest typical minor
injuries reduce utility by 36 to 38 percent for a few days. These estimates
assume the number of lost work days (counting weekends as if they were
workdays) equals one half of the impairment days for an employed person who is
injured. The 36 to 38 percent range is consistent with survey estimates of 30
percent for a bruise and 40 percent for a sprain in Green and Brown (1978).
The Sintonen scale does not work well for minor injuries, yielding a low
utility loss estimate of 15 percent, because minor injuries only affect a few
aspects of functioning. Including the externality costs, the SCE for a minor
injury is about $1,500.
Table 2 shows estimates of the utility loss associated with selected
illnesses. The first two columns of data deal with mild and severe angina.
Hartunian, Smart, and Thompson (1981) provided the description of angina's
impairment impacts that we used and the data on economic costs.
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15
For mild angina, Pliskin, Shepard, and Weinstein (1980) conducted a
small survey that indicated the utility loss was 12 percent, in the mid-range
of the 10 to 15 percent loss estimate in the American Medical Association
(1984) guides. Using the impairment scale in Kind et al. (1982), we estimated
the impairment at 0.7 to 16 percent. By assuming that mild angina reduced
physical and role function by half a level and also using half the pain score
(severe angina caused just one level of reduction on each dimension), we
estimated a 16 percent utility loss from the scale in Torrance (1982). This
scale, however, did not differentiate impairment as finely as was desirable to
analyze a largely asymptomatic condition. Using Kaplan's (1982) scale, we
estimated an 18 percent utility loss.
For severe angina, surveys by Miyamoto and Eraker (1985) and Pliskin et
al. (1980) yielded utility loss estimates of 30 to 31 percent, comparable to
the estimate of 25 to 32 percent we made from the Kind et al. (1982), Torrance
(1982), and Kaplan (1982) scales. The loss estimated by the American Medical
Association (1984) guides is slightly higher, 35 to 40 percent.
Utility losses of 12 percent for mild angina and 30 percent for severe
were used to compute SCEs of $220,000 to prevent a mild case of angina for
someone age 55 and $550,000 to prevent a severe case. These estimates seem
high, given the economic costs involved.
The third and fourth columns of data give estimates for food poisoning.
The estimates were based on the illness descriptions and cost data in Roberts
(1985). They apply to cases of salmonella and Campylobacter.
Based on Roberts' description, we estimated half the severe cases
involve four days of severe discomfort and inability to leave home. We
estimated the other half would last six days, with three days of severe
discomfort and confinement to a hospital bed and three days of severe discom-
fort and an inability to leave home or moderate discomfort and extreme
weakness. Finally, we assumed all severe cases involve four days with no
discomfort, but somewhat reduced strength and resilience. The Kind et al.
(1982), Torrance (1982), and Kaplan (1982) utility scales provide consistent
estimates of utility loss: 39 to 45 percent over 10 days. During the first
three days, both scales indicate patients with severe cases will feel as if
they would rather be dead. The SCE estimate is $2,400 to $2,600 to prevent a
severe case of food poisoning.
To estimate the utility loss associated with a mild case, we made low
and high estimates of impact.
o Low estimate. Assume 30 percent of the cases involve two days of severe
discomfort and inability to leave home and the remaining 70 percent
involve just 1.5 days of mild discomfort that is not severe enough to
prevent the sufferer from going to work. Under this assumption, the
average case involves a utility loss (on the Kind et al. (1982) or
Kaplan (1982) scales) of 24 to 25 percent for an average of 1.65 days,
with an SCE of $140 to $150. The Kaplan (1982) scale suggests an
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16
uncomfortably high 41 percent utility loss for this mild case, ascribing
an overly high 33 percent utility loss to mild discomfort that does not
prevent someone from working.
O High estimate. Assume 75 percent of the cases involve just 1.5 days of
mild discomfort, 25 percent involve two days of severe discomfort, and 5
percent are as severe as the reportable cases. Under this assumption,
the utility loss is 25 to 26 percent for an average of 2.1 days, with an
SCE of roughly $200.
The SCE per day of mild food poisoning is $85 to $95. By comparison,
Berger et al. (1985) obtained a mean willingness to pay to avoid a day of
nausea of $91 from 18 respondents, while Gerking et al. (1986) obtained a mean
of $409 from five respondents. Gerking believes that his values, and possibly
even Berger's, may be higher than people actually are willing to pay.
Consistent with his belief, his values exceed the values derived from the
impairment scales, even though food poisoning probably is slightly worse than
just feeling nauseous.
The utility loss estimates for chronic bronchitis, given in the fifth
column of data, were based on a description of the course of illness developed
for EPA by Viscusi et al. (1989) and were generated before Viscusi fielded his
willingness-to-pay survey. Estimates we made using four scales suggest a
utility loss of 35 to 45 percent. The American Medical Association (1984)
guides, again high, suggest at least a 50 percent utility loss. Viscusi et
al. (1989), based on a survey, estimated the utility loss at 32 percent, close
to the range we predicted. Data on externality costs were not readily
available to compute the SCE for chronic bronchitis.
The sixth column provides estimates of the utility loss associated with
a day in the hospital. The survey by Kaplan (1982) provides a range of
utility losses from 41 to 60 percent for hospitalization, "depending on whether
the person can move around and perform self care. Sackett and Torrance (1978)
obtained an estimate of a 40 to 44 percent utility loss for hospitalization
with a contagious disease. The utility loss estimates we made with the Kind
et al. (1982) and Torrance (1982) scales were between 55 and 65 percent,
possibly a bit high, while the 47 percent loss we estimated with the Sintonen
(1981) scale was on the mark. Adding the $550 average charge for a hospital
day in 1985 (from the Statistical Abstract, 1988) to a utility loss of 40 to
60 percent, the SCE per hospital day avoided is roughly $700 to $750.
The last column in Table 2 provides estimates of the utility loss
associated with receiving regular dialysis for end stage renal disease.
Sackett and Torrance (1978) found the loss was viewed as 60 percent by the
general public and as 48 percent by those on dialysis. Again high, the
American Medical Association (1984) guide estimated a 90 percent utility loss.
Using the Kaplan (1982) scale, we estimated the loss at 48 percent. Using the
Torrance (1982) scale, we assumed mild physical limitation; some limitation of
work, with half the patients largely unable to work; frequent anxiety, but an
average number of friends; a disfiguring dialysis shunt; and some discomfort.
These assumptions imply a 62 percent utility loss. Without anxiety, the loss
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17
would be 50 percent. The Kind et al. (1982) scale was difficult to apply to
this impairment. It suggests a utility loss of 42 to 48 percent, depending on
whether the distress level is assumed to be mild or moderate. The costs
associated with end stage renal disease derive from unpublished analyses by
The Urban Institute, which also indicate that 10 percent of dialysis patients
die each year. With a 60 percent utility loss, the SCE is $1,500,000 per case
prevented.
Table 3 presents estimates of the utility loss associated with
retardation, by severity. No direct survey data are available on this
condition. We included it because so many public health problems, among them
lead poisoning, fetal alcohol syndrome, malnutrition, foodborne listeriosis,
and workplace chemical exposures, can cause children to be retarded. In the
future, someone is likely to estimate willingness to pay to avoid retardation,
and our estimates will be available for comparison; in the meantime, they may
be useful for policy analysis.
We estimated a range of retardation levels, with a utility loss of about
20 percent associated with the need for special education, a severely limited
ability to work associated with a utility loss around 50 percent, need for
help in self care raising the utility loss to 55 to 60 percent, and very
severe retardation raising the loss above 75 percent. The American Medical
Association (1984) guides performed well in evaluating retardation, agreeing
reasonably well with our ratings from the Torrance (1982) and Kaplan (1982)
scales.
A Further Comparison
The impairment estimates in the lineage from His et al. (1983) cover all
possible injuries in motor vehicle crashes. Miller, Brinkman, and Luchter
(1988) substitute the utility losses for fates worse than death shown here for
the physician ratings, then apply the data to estimate the utility loss and
associated willingness to pay to avoid a typical injury. For each diagnosis,
they compute the present value of future impairment years at a 6 percent
discount rate. They then estimate aggregate impairment by multiplying the
impairment by diagnosis times data on 1982-1984 injury incidence derived from
a sample, compiled by the National Highway Traffic Safety Administration in
its National Accident Sampling System. The sample includes all injuries in
roughly 30,000 crashes that were reported to the police. The aggregate
impairment years next are multiplied times the $120,000 willingness to pay to
save a life year. An estimated average willingness to pay to avoid injury of
$12,800 results.
Insight into the quality of this $12,800 estimate, and of the impairment
estimates, can be obtained from a comparison with estimates of willingness to
pay to avoid nonfatal injury in the workplace. Five estimates exist that
cover all reported injuries, as opposed to just lost workday injuries. All
five derive from hedonic regressions that examine pay differentials for risky
jobs. As Table 2 shows, four of the five estimates are between $10,500 and
$13,000, satisfyingly close to the estimate from physician ratings of
impairment.
-------
18
The comparison between the willingness to pay to avoid motor vehicle and
workplace injuries implicitly assumes that the distribution of injuries is
similar in these two settings. That assumption is questionable, because back
injuries occur more frequently in the workplace. A special analysis we ran of
National Council on Compensation Insurance detailed claims data shows back
injuries account for 30 percent of all on-the-job injuries that cause lost
workdays, while Luchter (1986) indicates they account for only 5 percent of
more-than-minor injuries in rotor vehicle crashes. Thus, the agreement in
willingness-to-pay values provides only molest confirmation of the utility
loss estimates.
Conclusion
Scales on the utility of functional impairment provide a quick,
inexpensive, reasonably consistent, and theoretically supportable way to
estimate SCEs for preventing a wide range of diagnoses. Using these methods
requires estimating the functional impairment and reduction in lifespan
associated with the health status changes. The impacts on transfer payments
(including health insurance payments), administrative costs, and taxes on
earnings also must be estimated.
The available utility scales yield reasonably consistent values, but
these values occasionally seem unreasonably high compared to the economic
costs involved (witness mild angina). Pre-planned research validating the
utility losses against willingness-to-pay estimates would make it easier to
use the scales with confidence.
Scales that do not allow the possibility of fates worse than death
should not be used to evaluate severely disabling conditions. Torrance (1982)
probably is the most reliable and flexible scale presently available, but
lacks utility loss estimates for some aspects of functioning (for example,
loss of reproductive capability, sustained pain) and very mild symptoms. The
simplistic approach taken by Green and Brown (1978) of asking people to score
relative severities of different diagnoses provided surprisingly reliable
results. The American Medical Association (1982) guides to permanent impair-
ment, which are based on physician judgment, generally overestimate utility
loss.
-------
Table 1
Percentage Utility Loss and Cost Associated With Selected Injuries
Study
Kind, Rosser,
& Williams
Kaplan
Torrance
rehabed patients
Green & Brown
Card
Sintonen
Carsten
Am Med Assoc
Blind
15
39
37*
34*
20*
22-24
33*
85*
Severe
Head
108
71
116
128*
103
93-100*
95*
Quad
114
66
105
65*
109^
49
Severe
Burn
Para (age 45+)
52-65
50-64
54-62
45*
29*
29
85-86* 42-45*
99 81
137
139
91*
95*
Broken
Lower
Leg
31
54
34
30
36
Minor
Injury@
38
36
37
30-40*
15-16
Medical Cost DK 680,000
Productivity Loss DK 400,000
Legal, Admin,
Transfer DK 60,000
390,000 235,000 450,000 200 285
210,000 160,000 100,000 1,350 280
60,000 35,000 60,000 DK DK
@ Average daily utility loss until recovery, which occurs in less than 1 year.
* Direct measurement.
-------
Table 2
Percentage Utility Loss and Cost Associated With Selected Illnesses
Study
Kind et al.
Torrance
Kaplan
Sintonen
Sackett & Torrance
patients
Miyamoto & Eraker
Pliskin et al.
Viscusi et al.
Am Med Assoc
Angina
Mild Severe
.7-16
16
18
12'
25-31
32
32
30*
31*
Food Poisoning®
Severe Mild
45
39
45
24-25
25-26
41
Chronic
Bronchitis
23-37
34-45
45
30-36
10-15* 35-40*
32*
50+
Day in
HospitalB
61-62
55-65
41-60*
47
40-44*
ESRD
42-48
62
48
60*
90J
Medical Cost 2700
Productivity Loss 50
Transfer & Admin o
60
30
1000
300
DK
DK
DK
DK
500
50
DK
250,000
90,000
10,000
0 Average daily utility loss until recovery, which occurs in less than 1 year.
* Direct measurement.
-------
Table 3
Utility Loss Associated with Retardation
Condition Util Loss Source
Very severely retarded 83 Torrance
75+ Am Med Assoc
Retarded needing help with care 57 Kaplan
55 Torrance
55-75 Am Med Assoc
Moderately retarded with self-care 42-51 Kaplan
52 Torrance
25-50 Am Med Assoc
Mildly retarded 33 Kaplan
20-32 Torrance
23 Sintonen
10-20 Am Med Assoc
Table 4
Willingness to Pay to Avoid Non-fatal Workplace Injuries
(1985 After-tax Dollars)
Study
Butler (1983)
Dillingham (1983)
Olson (1981)
Smith (1983)
Viscusi (1978)
Value
$10,500
$17,000-$26,000
$12,000-$13,000
$11,000
$12,000-$21,000
Note: Values were converted to after-tax dollars using the method described in
Miller (1986).
-------
NOTES
1. The societal budget constraint represents a synthesis of Lotka stable
population growth dynamics with the standard Solow steady-state growth
model. The equilibrium population growth rate is the solution to the
integral equation of stable population theory given by:
(a)
1 = 1 e~9xp(x)m(x)c3x
0
where m(x) is the female birth rate to women aged x years. The
equilibrium capital-labor ratio is the solution to:
k= sf(k)
gk
(N.2)
where k is rate of change in k and s is savings per worker. The
comparative-static change in expected lifetime welfare (5W) resulting from
a change in mortality rates across different ages (5p(x)) is found by
taking the differential across equation (1):
ft) CO
5W = / U[c(x),x]5p(x)dx + J 3U/3c(x) '5c[Sp]p(x)dx. (N 3)
0 0
Under the assumptions of utility maximization and perfect capital markets
the life-cycle consumption pattern is given by:
w/at(x) = SU/ScfOJe-^* (N.4)
so that
(•> <0
SW - J U[c(x),x]Sp(x)dx + 3U/3c(0) J e-9*Sc[Sp]p(x)dx (N.5)
0 0
The two terms in equation (N.5) can be interpreted as the change in
expected lifetime welfare that come from extra years and the value of
changes in the consumption pattern needed to accomodate the additional
years of living. The change in consumption can be evaluated by taking
differentials across the societal budget constraint, yielding:
-------
00 0) 00
0 = J e-^ct x) £p(x )dx + J e~'?x6c[ Sp]p(x)dx - (f(k)-gk) J e~9x>,( x) 5p( x )dx
0 0 0
0)
- 5k[5p](f'-g) J e~9xX(x)p(x)dx - |3Sg[$p] (N.6)
0
where
CO CO 0)
0 = J xe~9xc(x)p(x)dx - (f(k)-gk) J xe~"9*X(x)p(x)dx - k J e-9XX(x)p(x)dx.
0 0 0
@ is the life-cycle value of a marginal increase in the population growth
rate (Arthur and McNicoll, 1978) . Following Arthur (1981) this term can
be expressed as:
0 = (1/b) [CfAc-A^-kn] (N.7)
where b is the crude birth rate in the stable population C is per capita
consumption, Pi^ and are the average ages of consumption and production,
respectively, and n is the labor/population ratio. Using equation (N.6)
to substitute for the second term in equation (N.5) results in the
expression for the change in lifetime welfare given by equation (3) in the
text.
-------
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-------
Valuing Nonmarket Goods:
A Household Production Approach*
Mark Dickie
School of Social Sciences
University of Texas at Dallas
Shelby Gerking
Department of Economics
University of Wyoming
June, 1988
This research was supported by the U.S. Environmental Protection Agency
under Cooperative Agreement #CR812054-01-2. It has not been subjected,
however, to the Agency's peer and administrative review and therefore it
does not necessarily reflect the views of the Agency, and no official
endorsement should be inferred. We thank Don Waldman for assistance and
advice concerning econometric procedures, Anne Coulson, Don Tashkin, and
John Demand for invaluable assistance in survey design and data
collection, Alan Krupnik, David Brookshire, Don Coursey, John Tschirhart
and seminar participants at Arizona State University for comments on an
earlier draft, and Alan Carlin for his patience and encouragement
throughout the project.
-------
ABSTRACT
This paper presents a unique application of the household production
approach to valuing public goods and nonmarket commodities. Technical
relationships are estimated between health attributes, private goods that
affect health, and air quality using panel data drawn from a special
survey. Statistical tests show that individuals equate marginal rates of
technical substitution in household production with relevant price ratios.
This result confirms theoretical implications in a particularly critical
context for estimating values of health attributes and air pollution.
Value estimates obtained also bear on current questions facing
environmental policymakers.
-------
I. Introduction
Individuals frequently apply a household technology to combine public
and private goods in the production of nonmarket commodities for final
consumption. Hori (1975) demonstrates that in these situations, market
prices of private goods together with production function parameters mav
encode enough information to value both public goods used as inputs and
nonmarket final consumption commodities. Although this valuation
methodology is objective and market based, it seldom has been applied for
three reasons. First, underlying technical relations either are unknown or
data needed to estimate them are unavailable. Second, even if relevant
technical information is at hand, the consumer's budget surface in
commodity space may not be differentiable when joint production and other
complicating factors are present. As a consequence, the commodity bundle
chosen is consistent with any number of marginal rates of substitution and
sought after values of public goods and nonmarket commodities remain
unknown. Third, joint production and nonconstant returns to scale also
pose serious difficulties when taking the closely related valuation
approach' of estimating the area behind demand curves for private goods
inputs and final consumption commodities Pollak and Wachter 1975;
Bockstael and McConnell 1983).
This paper presents a unique application of the household production
approach to valuing public goods and nonmarket commodities which allows for
certain types of joint production and addresses key problems identified by
previous authors. Technical relationships are estimated between health
attributes, private goods, and air quality. Data used in the analysis are
drawn from a special survey designed to implement the household production
approach. Econometric estimates allow for truncated dependent variables in
-------
2
panel data using tobit models with individual-specific variance components.
Key results are: (1) attempts to value detailed attributes of nonmarket
home produced commodities may be ill-advised; however, estimating a common
value for a broadly defined category of attributes may be possible, and (2)
statistical tests show that individuals equate marginal rates of technical
substitution in household production with relevant price ratios. This
latter result confirms behavioral implications of the theory in a
particularly critical context for estimating values of nonmarket
commodities and public goods. Also, value estimates obtained bear on
current questions concerning air pollution control policy. The Clean Air
Act of 1970 and its subsequent amendments focus exclusively on health to
justify regulation and requires air quality standards to protect even the
health of those most sensitive to pollution. The survey data are
sufficiently rich to allow separate value estimates for persons with normal
respiratory function and persons with chronic respiratory impairments.
The remainder of this paper is divided into four sections. Section II
describes a simple household production model in a health context and
reviews theoretical issues in obtaining value estimates. Section III
discusses the survey instrument and the data collected. Section IV
presents econometric estimates of production functions for health
attributes, as well as values of better air quality and improved health for
both the normal and respiratory impaired subsamples. Implications and
conclusions are drawn out in Section V.
II. PRELIMINARIES
The model specifies utility (U) as a function of market goods (Z) and
health attributes, called symptoms, (S) .
-------
3
U = U(Z, S)
(1)
For simplicity, Z is treated as a single composite good, but S denotes a
vector measuring intensity of n health symptoms such as shortness of
breath, throat irritation, sinus pain, headache, or cough. Intensity of
the symptom is reduced using a vector (V) of m additional private goods
that do not yield direct utility, a vector of ambient air pollution
concentrations (a) , and an endowment of health capital (ft) .
Elements of V represent goods an individual might purchase to reduce
intensity of particular symptoms, and ft represents genetic predisposition
to experience symptoms or presence of chronic health conditions that cause
symptoms. Notice that equation (2) allows for joint production in that
some or all elements of V may (but do not necessarily) enter some or all
1
symptom production functions. The budget constraint is
Aspects of this general approach to modeling health decisions have
been used in the health economics literature (e.g., Grossman 1972;
Rosenzweig and Schultz 1982, 1983), where medical care is an example of V
often considered. In these three papers, however, the stock of health
rather than symptoms is treated as the home produced good, and Grossman
treats decision making intertemporally in order to analyze changes in the
health stock over time. A multiperiod framework would permit a more
complete description of air pollution's cumulative physiological damage,
but the present model's focus on symptoms of short duration, suggests that
a one period model is appropriate. Moreover, long term panel data
S1 = SX(V, a; Q)
i=l, . . .,n
(2)
where P denotes the price of Z, P denotes the price of V , and I denotes
income
-------
4
containing both economic and health information necessary to assess
cumulative physiological damage are difficult to obtain.
Similar models also have been used in environmental economics to
derive theoretically correct methods for estimating values of air quality
and other environmental attributes (e.g., Courant and Porter 1981; Harford
1984; Harrington and Portney 1987) , These models, however, only consider
the case in which m = n = 1 and rule out the possibility of joint
production. In this situation, the marginal value of or willingness to pay
(WTP) for a reduction in air pollution can be derived by setting dU = 0 and
using first order conditions to obtain
wt:p« - - u^A - - p^J/s} (4)
where denotes marginal disutility of the symptom, denotes the
marginal effect of air pollution on symptom intensity, sj denotes the
marginal product of in reducing symptom intensity, and A denotes
marginal utility of income. As shown, marginal willingness to pay to
reduce symptom intensity (- U^/A) equals the marginal cost of doing so
(- p^sJ).
Extensions to situations where m and n take on arbitrary values have
been considered in the theory of multi-ware production by Frisch (1965) as
well as in a public finance context by Hori (1975). Actually, Hori treats
four types of household production technology. His case (3) involving
joint production appears to best characterize the application discussed in
Section IV because a single V may simultaneously reduce more than one
symptom. In this situation, a key result is that marginal values of
symptom intensity (- U^/X) cannot be re-expressed in terms of market prices
(pJ and production function parameters (S*) unless the number of private
J J
goods is at least as great as the number of symptoms (m >_ n)• Intuitively,
-------
5
if m < n, the individual does not have a choice among some alternative
combinations of symptom intensities because there are too few choice
variables
(v
and the budget surfaces on which each chosen value of g1 must
2
lie is not differentiable.
Another perspective on this result can be obtained from the m first
order equations for the V. shown in (5)
j
sn
•J ^ • • • o ^
. sl
®.
lyx
•
pi
•
•
-
•
•
. vx.
«
0
a
(5)
Each first order condition holds as an equality provided each private good
is purchased in positive quantities. If m < n the rank of the symptom
technology matrix S ¦ most m, the system of equations in (5) is
underdetermined, intensity of one symptom cannot be varied holding others
constant, and the marginal value of an individual symptom cannot be
determined. On the other hand, if m = n and the symptom technology matrix
is nonsingular, then the rank is n and unique solutions can be computed for
the U^/X. If m > n and the technology matrix has full rank, then the
system is overdetermined, and values for the U^/X can be computed from a
subset of the first order equations.
Solving (5) computes marginal values for the nonmarket commodities
produced by the individual. The value of the public good input, a, is the
weighted sum of the value of the commodities, where the weights are the
marginal products of o in reducing symptoms: " - E^CU^/AJS^. If the
-------
6
marginal products of a are known or estimated, solving (5) provides the
information necessary to value nonmarket commodities and public goods.
This theoretical overview yields several ideas useful in empirical
application. First, if mi n and the household technology matrix has rank
n, then values of nonmarket commodities and public goods are calculated in
a relatively straightforward manner because utility terms can be
eliminated. Second, even in cases where m_> n, the household production
approach may fail if there is linear dependence among the rows of the
technology matrix. Thus, statistical tests of the rank of the matrix
should be performed to ensure differentiability of the budget surface.
Third, if m > n, first order conditions impose constraints on values that
can be taken by the S^; validity of these constraints can be tested.
Fourth, the possibility that m < n suggests that the household production
approach may be incapable of estimating separate values for a comparatively
large number of detailed commodities and that aggregation of commodities
3
may be necessary to ensure m > n.
Fifth, if m > n, values of and need not yield positive values
for -U^/X, the marginal willingness to pay to reduce intensity of the
symptom. Of course, in the simple case where m = n = 1, the only
requirement is that >0. If m = n = 2, a case considered in the
empirical work presented in Section IV, values of -U^/x and -l^/X both will
be positive only if (sj/S^) % > (S^/S^) • If VL and V2 are not
chosen such that their marginal rates of technical substitution bracket
their price ratio, then it is possible to reduce intensity of one symptom
without increasing intensity of the other and without spending more on
symptom reduction.
-------
Sixth, complications arise in expressing symptom and air pollution
values in situations where some or all of the are sources of direct
utility, a form of joint production. This problem is important (and it is
encountered in the empirical work presented in Section IV) because of the
difficulty in identifying private goods that are purchased but do not enter
the utility function. To illustrate, assume that m = 2, n = 1 and that
but not is a source of both direct positive utility and symptom relief.
WTP^ still would equal and therefore could be calculated without
knowing values for marginal utility terms. If consumption of Vhowever,
was used as a basis for this calculation, the simple formula
would overestimate WTP by an amount equal to -(u,s;i/xs:b where U-, denotes
a 4- OL £. £
marginal utility of (Uj > 0) . When m and n take arbitrary values, the
situation is more complex, but in general nonmarket commodity and public
good values can be determined only if the number of private goods which do
not enter the utility function is at least as great as the number of final
commodities. Even if this condition is not met, however, it is possible in
some cases to determine whether the value of nonmarket commodities and
A
public goods is over- or underestimated.
III. DATA
Data used to implement the household production approach were obtained
from a sample of 22 6 residents of two Los Angeles area communities. Each
respondent previously had participated in a study of chronic obstructive
respiratory disease (Detels et al. 1979, 1981). Key aspects of this sample
are: (1) persons with physician diagnosed chronic respiratory ailments
deliberately are overrepresented (76 respondents suffered from such
diseases), (2) 50 additional respondents with self-reported chronic
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8
cough or chronic shortness of breath are included, (3) 151 respondents
lived in Glendora, a community with high oxidant air pollution, and 75
respondents lived in Burbank, a community with oxidant pollution levels
more like other urbanized areas in the U.S. but with high levels of carbon
monoxide, (4) all respondents either were nonsmokers or former smokers who
had not smoked in at least two years, and (5) all respondents were
household heads with full-time jobs (defined as at least 1,600 hours of
work annually).
Professionally trained interviewers contacted respondents several
times over a 17 month period beginning in July 1985. The first contact
involved administration of an extensive baseline questionnaire in the
respondent's home. Subsequent interviews were conducted by telephone.^
Including the baseline interview, the number of contacts with each
respondent varied from three to six with an average number of contacts per
respondent of just over five. Of the 1147 total contacts (s 226 x 5), 644
were with respiratory impaired subjects (i.e., those either with
physician-diagnosed or self-reported chronic respiratory ailments) and 503
were with respondents having normal respiratory function.
Initial baseline interviews measured four groups of variables: (1)
long term health status, (2) recently experienced health symptoms, (3) use
of private goods and activities that might reduce symptom intensity, and
(4) socioeconomic/demographic and work environment characteristics.
Telephone follow-up interviews inquired further about health symptoms and
use of particular private goods. Long term health status was measured in
two ways. First, respondents indicated whether a physician ever had
diagnosed asthma (ASTHMA), chronic bronchitis (BRONCH), or other chronic
respiratory disease such as emphysema, tuberculosis, or lung cancer
-------
9
(OTHDIS). Second, they stated whether they experience chronic shortness of
breath or wheezing (SHRTWHZ) and/or regularly cough up phlegm, sputum, or
mucous (FLEMCO) . Respondents also indicated whether they suffer from hay
fever (HAYFEV); however, this condition was not treated as indicative of a
chronic respiratory impairment.
Both background and follow-up instruments also asked which, if any, of
26 health symptoms were experienced in the two days prior to the interview.
Symptoms initially were aggregated into two categories defined as: (1)
chest and throat symptoms and (2) all other symptoms.*' Aggregation to two
categories reduces the number of household produced final goods (n)
considered; however, assigning particular symptoms to these categories
admittedly is somewhat arbitrary. Yet, the classification scheme selected
permits focus on a group of symptoms in which there is current policy
interest. Chest and throat symptoms identified have been linked to ambient
ozone exposure (see Gerking et al. 1984, for a survey of the evidence) and
federal standards for this air pollutant currently are under review.
Moreover, multivariate tobit turns out to be a natural estimation method
and aggregating symptoms into two categories permits a reduction in
computation burden. Dickie et al. (1987(a)) report that respondents with
chronic respiratory impairments experienced each of the 26 individual
symptoms more often than respondents with normal respiratory function.
This outcome is reflected in Table 1 which tabulates frequency
distributions of the total number of chest and throat and other symptoms
reported by respondents in the two subsamples.''
In the empirical work reported in Section IV, data on the number of
symptoms reported are assumed to be built up from unobserved latent
variables measuring symptom intensity. As intensity of a particular
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10
symptom such as cough rises above a threshold, the individual reports
having experienced it; otherwise he does not. Thus, the frequency
distribution tabulated in Table 1 merely reflects the number of symptoms
that crossed the intensity threshold in the two days prior to the
interview.
Private goods which indicated steps taken in the past that might
reduce symptoms over a period of years, measured whether the respondent has
and uses: (1) central air conditioning in the home (ACCEN) , (2) an air
purifying system in the home, (3) air conditioning in the automobile
8
(ACCAR), and (4) a fuel other than natural gas for cooking (NOTGASCK) .
These variables represent goods that may provide direct sources of utility
to respondents. Air conditioners, for example, not only may provide relief
from minor health symptoms; but also provide cooling services that yield
direct satisfaction. This problem is discussed further in Section V.
Socioeconomic/demographic variables measured whether the respondent
lived in Burbank or Glendora (BURB) as well as years of age (AGE) , gender,
race (white or nonwhite), marital status, and household income. Also,
respondents were asked whether they were exposed to toxic fumes or dust
while at work (EXPWORK).
Finally, each contact with a respondent was matched to measures of
ambient air pollution concentrations, humidity, and temperature for that
day. Air monitoring stations used are those nearest to residences of
respondents in each of the two communities. Measures were obtained of the
six criteria pollutants for which national ambient air quality standards
have been established: carbon monoxide (CO), nitrogen dioxide (N02), ozone
(03), sulfur dioxide (S02), lead and total suspended particulate.
Readings for lead and particulate, however, only were available for about
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11
ten percent of the days during the study period, forcing exclusion of those
pollutants from empirical work. Each of the remaining four pollutants were
measured as maximum daily one-hour ambient concentrations. Maxima are used
because epidemiological and medical evidence suggests that acute symptoms
may be more closely related to peak than to average pollution
concentrations. The air pollution variables entered then, are averages of
one hour maxima on the two days prior to the interview so as to conform
9
with the measurement of symptoms. Temperature and relative humidity data
similarly were averaged across two day periods.
IV. ESTIMATES OF HOUSEHOLD SYMPTOM TECHNOLOGY
This section reports estimates of production functions for chest and
throat and other symptoms. Empirical estimates of household production
technology in a health context also have been obtained by Rosenzweig and
Schultz (1983); however, these investigators consider determinants of birth
weight rather than health symptoms and do not focus on valuing nonmarket
10
commodities and public goods. The symptom production functions reported
below are estimated in a bivariate tobit framework with variance
11
components. Bivariate tobit estimation was performed because of the
probable correlation between disturbances across equations. Given that
symptoms often appear in clusters, individuals reporting symptoms in one
category may also report them in the other. Also, as noted in the
discussion of Table 1, the modal number of symptoms reported was zero.
Random disturbances follow an error components pattern, consisting of
the sum of a permanent and a transitory component.
£iht " wh + Uiht 1 * R' N (6)
where i denotes type of symptom (chest and throat, other), h denotes
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12
respondent, and t denotes time. The transitory error component,
captures unmeasured effects that vary over individuals, symptoms, or time.
The permanent error component in contrast, varies only over
individuals; for a given individual it is constant over time and common to
production functions for both types of symptoms. The permanent error
component serves two purposes in the model. First, it captures persistent
unmeasured but individual specific factors that influence symptoms,
including unmeasured elements of ft and/or the threshold at which symptoms
are reported. Hence, exerts an independent influence by allowing
individuals with identical measured characteristics to have different
numbers of symptoms. Second, a given individual's permanent error
component captures contemporaneous correlation between the two symptom
classes.
The are assumed to be independent drawings from identical
distributions. Mundlak (1978) and others have argued that the are
likely to be correlated with values of the explanatory variables, and the
error components. For example, if an individual knows his own then
utility maximization would imply that his choice of private goods depends
on A possible solution would be to replace the random effects with
fixed effects in which the are assumed to be constants that vary across
individuals. Mundlak notes, however, that the fixed effects model suffers
from a serious defect if is correlated with some or all covariaCes: It
is impossible to distinguish between the effects of time invariant
covariates and the fixed effects. This defect of the fixed effects model
is troublesome, because all covariates except the air pollution measures
are time invariant. Since the valuation procedure of Section 2 reguires
distinguishing marginal products of private goods from the individual's
-------
13
predisposition to illness, the fixed effects model was rejected in favor of
random effects.
Both transitory and permanent error components are assumed normally
distributed with E(p.) - 0, E(p^) - a2, and E(u,iO - 0 for h ^ h';
n hp n n
E(uiht) - 0, E(u^ht) - a2, and E(uihtui'h't') " 0 for 1 ^ i" or h f h' or
t 5* C. The permanent error component is distributed independently of the
transitory error component, so the distribution of the summed error
components is normal with E(e.. ) * 0, E(ef. ) « a* + and
ihty v iht u v
E(eiht£iht-' - au~"~^cRhteNht^'
Given and the distributional assumptions about the error
components, the likelihood for the h^*1 individual is the product of
independent tobit likelihoods: one tobit for each symptom class in each
time period. The conditional likelihood for the h^ individual is
LjjfUjj) - It fCuRElu) 1 F(uRtlu) " * r(UNt'u) (7>
SKt>0 SRt-° SNt>0
where f(-) is the normal density and F(*) is the normal distribution.
Conditioning was removed by integrating over y. In order to address the
problem of an unequal number of interviews per respondent, log-likelihood
values first were computed for each respondent, and then summed to obtain
12
totals.
Tables 2 and 3 present illustrative symptom production function
estimates for the impaired and normal subsamples. Equations presented are
representative of a somewhat broader range of alternative specifications
that are available from the authors on request. Alternative specifications
included attempts to correct for simultaneity between symptoms and private
goods. Bartik (1988) calls attention to this problem in a related context
and Rosenzweig and Schultz treat it in their previously cited birthweight
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14
study. Procedures devised for the present study are analogous to two-stage
least squares. In the first stage, reduced form probit demand equations
for each of four private goods (ACHOME, ACCAR, APHOME, NOTGASCK)^ were
estimated. In the second stage, predicted probabilities from the reduced
form probits were to be used as instruments for private goods in the tobit
symptom production function models. However, explanatory power of the
reduced form probit equations was very poor. In half of the equations for
each subsample the null hypothesis that all slope coefficients jointly are
zero could not be rejected at the 5 percent level and in all equations key
variables such as household income had insignificant and often wrongly
signed coefficients. Another problem is the absence of private good price
data specific to each respondent. The original survey materials requested
these data but after pretesting, this series of questions was dropped
because many respondents often made purchases jointly with a house or car
and were unable to provide even an approximate answer. As a consequence,
simultaneous equation estimation was not pursued further with the likely
outcome that estimates of willingness to pay for nonmarket commodities and
14
public goods may have a downward bias.
In any case, one result of interest from the bivariate tobit estimates
in Tables 2 and 3 is the outcome of testing the null hypothesis that
estimated symptom production parameters jointly are zero. In the four
equations reported, a likelihood ratio test rejects this hypothesis at
significance levels less than 1 percent. Also, estimates of the. individual
specific error components, denoted a, have large asymptotic t-statistics
which confirms persistence of unobserved personal characteristics that
affect symptoms.
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15
Table 2 shows that chronic health ailments and hay fever are
positively related to symptom occurrence among members of the impaired
group. Coefficients of ASTHMA, BRONCH, SHRTWHZ, and HAYFEV are positive in
equations for both chest and throat and other symptoms and have associated
asymptotic t-statistics that range from 2.1 to 7.6. The coefficient of
FLEMCO is positive and significantly different from zero at conventional
levels in the chest and throat equation, but its asymptotic t-statistic is
less than unity in the equation for other symptoms. The coefficient of AGE
was not significantly different from zero in either equation and the
EXPWORK variable was excluded because of convergence problems with the
15
bivariate tobit algorithm. Variables measuring gender, race, and marital
status never were included in the analysis because 92 percent of the
impaired respondents were male, 100 percent were white, and 90 percent were
married. Residents of Burbank experience chest and throat symptoms with
less frequency than do residents of Glendora. Of course, many possible
factors could explain this outcome; however, Burbank has had a less severe
long term ambient ozone pollution problem than Glendora. For example, in
1986 average one day hourly maximum ozone readings in Burbank and Glendora
were 8.7 pphm and 10.2 pphm, respectively.
With respect to private and public inputs to the symptom production
functions, the coefficient of ACCAR is negative and significantly different
from zero at the 10 percent level using a one tail test in the other
symptoms equation, while the coefficient of ACCEN is negative and
significantly different from zero at the 5 percent level using a one tail
test in both equations. Results from estimated equations not presented
reveal that NOTGASCK and use of air purification at home never are
significant determinants of symptoms in the impaired subsample. Also, 03,
-------
16
CO, and N02 exert insignificant influences on occurrence of both types of
symptoms. When four air pollution variables were entered, collinearity
between them appeared to prevent the maximum likelihood algorithm from
converging. Consequently, S02 was arbitrarily excluded from the
specification presented and the three air pollution measures included as
covariates should be interpreted as broader indices of ambient pollutant
concentrations. Variables measuring temperature and humidity were excluded
from the Table 2 specification; but in equations not reported their
coefficients never were significantly different from zero.
Table 3 presents corresponding symptom production estimates for the
subsample with normal respiratory function. HAYFEV is the only health
status variable entered because ASTHMA, BRONCH, SHRTWZ, and FLEMCO were
used to define the impaired subsample. Coefficients of HAYFEV are positive
in equations for both chest and throat and other symptoms and have
t-statistics of 1.61 and 1.87, respectively. Coefficients of BURB are
negative; but in contrast to impaired subsample results, they are not
significantly different from zero at conventional levels. AGE and EXPWORK
enter positively and their coefficients differ significantly from zero at
25 percent in the other symptoms equation. Among private goods entering
the production functions, coefficients of APHOME and ACHOME never were
significantly different from zero at conventional levels, and these
variables are excluded from the specification in Table 3. Use of air
conditioning in an automobile reduced chest and throat symptom occurrences
and cooking with a fuel other than natural gas (marginally) reduces other
symptoms. Variables measuring gender, race, and marital status again were
not considered as the normal subsample was 94 percent male, 99 percent
white, and 88 percent married. In the normal subsample, collinearity and
-------
1
algorithm convergence problems again limited the number of air pollution
variables that could be entered in the same equation. As shown in Table 3,
when 03, CO, and N02, coefficients had associated t-statistics of 1.16 or
smaller. Temperature and humidity variables are excluded from the
specification shown in Table 3. In alternative specifications not
reported, coefficients of these variables never were significantly
different from zero in alternative equations not reported.
Three pieces of information are required to use the estimates in
Tables 2 and 3 in the calculation of values for nonmarket commodities (the
two types of symptoms) and public goods (air pollutants): (1) marginal
effects of air pollutants on symptoms, (2) marginal effects of private
goods on symptoms, and (3) prices of private goods. Marginal products were
defined as the effect of a small change in a good on the expected number of
symptoms. Computational formulae were developed extending results for the
tobit model (see McDonald and Moffit 1980) to the present context which
allows for variance components error structure. However, because private
goods are measured as dummy variables and, therefore, cannot be
continuously varied, incremental, rather than marginal, products are used.
The final elements needed to compute value estimates are the prices of
private goods. Dealers of these goods in the Burbank and Glendora areas
were contacted for estimates of initial investment required to purchase the
goods, average length of life, scrap value (if any), and fuel expense.
After deducting the present scrap value from the initial investment, the
net initial investment was amortized over the expected length of years of
life. Adding annual fuel expense yields an estimate (or range of
estimates) of annual user cost of the private good. The annual costs then
16
were converted to two-day costs to match the survey data. The dependent
-------
18
variables used in the estimated equations do not distinguish between one-
and two-day occurrences of symptoms, but approximately one-half of the
occurrences were reported as two day occurrences. As a consequence, the
value estimates obtained were divided by 1.5 to convert to daily values.
Two tests were performed prior to estimating values of symptom and air
pollution reduction. First, calculations were made for both normal and
impaired subsamples to ensure that relevant ratios of incremental products
of private goods in reducing symptoms bracketed the corresponding price
ratio. Recall from the discussion in Section 2 that this condition
guarantees that value estimates for reducing both types of symptoms are
positive. A problem in making this calculation is that estimates of
incremental rates of technical substitution vary across individuals
(incremental products are functions of individual characteristics), but no
respondent specific price information is available. As just indicated,
dealers in Glendora provided the basis for a plausible range of prices to
be constructed for each good. If midpoints of relevant price ranges are
used together with incremental rates of technical substitution taken from
Tables 2 and 3, the bracketing condition is met for all 100 respondents in
the normal subsample and 117 of 126 respondents in the impaired subsample.
Of course, alternative price ratios selected from this range meet the
bracketing condition for different numbers of respondents.
Second, possible singularity of the symptom technology matrix was
analyzed using a Wald test (see Judge et al. 1985, p. 215 for details).^
In the context of estimates in Tables 2 and 3, the distribution of the test
statistic (A) is difficult to evaluate because relevant derivatives are
functions of covariate values and specific to individual respondents.
However, if derivatives are evaluated in terms of the underlying latent
-------
19
variable model, they can be expressed in terms of only parameters and A is
2
distributed as x with 1 degree of freedom. Adopting this simpler
approach, p-values for the Wald test statistic are large: p = .742 for the
impaired subsample equations and p = .610 for the normal subsample
1 8
equations. As a consequence, the null hypothesis of singularity of the
symptom technology matrix is not rejected at conventional levels. This
result suggests that in both subsamples, there does not appear to be an
independent technology for reducing the two types of symptoms, budget
constraints are nondifferentiable, and separate value estimates for
chest and throat and ocher symptoms should not be calculated.
A common value for reducing chest and throat and other symptoms still
can be obtained by aggregating the two categories and re-estimating
production functions in a univariate tobit framework. Table 4 shows
results based on using the same covariates as those reported in Tables 2
and 3 and retaining the variance components error structure. The Table 4
equations also make use of a constraint requiring that if m > n = 1, values
of marginal willingness to pay to avoid a symptom must be identical no
matter which private good is used as the basis for the calculation. In the
case where m = 2 and n = 1, as discussed in Section II, this single value
is -Uj/A - -(PjVsJ) - -(P^S*). In the impaired subsample, the restriction
can be tested under the null hypothesis, Hq : &ACCAR *
where the B. are coefficients of ACCAR and ACHOME
AULA& ACHOME ACHUML 1
in the latent model and the are midpoints from the estimated range of
two day prices for the private goods. In corresponding notation, the null
hypothesis to test in the normal subsample is, H_ : 6Ar,rAP =
(PACCAR/PNOTGASCK)SNOTGASCK- Both hyPotheses are tested against the
-------
20
alternative that coefficients of private goods are unconstrained
parameters.
P-values for the parameter restrictions are comparatively large; P =
.623 in the impaired subsample and P = .562 in the normal subsample. Thus,
the above null hypotheses are not rejected at conventional significance
levels. Respondents appear to equate marginal rates of technical
substitution in production with relevant price ratios; a result that
supports a critical implication of the previously presented household
production model. Moreover, coefficients of private good variables defined
under the null hypotheses for the two subsamples have t-statistics
exceeding two in absolute value. Performance of remaining variables is
roughly comparable to the bivariate tobit estimates. A notable exception,
however, is that in the normal subsample univariate tobit estimates,
coefficients of 03 and N02 are positive with t-statistics exceeding 1.6.
This outcome suggests that persons with normal respiratory function tend to
experience more symptoms when air pollution levels are high, whereas those
with impaired respiratory function experience symptoms with such regularity
that there is no clear relationship to fluctuations in air quality.
Intensity of particular symptoms may be greater in both subsamples when
pollution levels are high, but this aspect is not directly measured.
Table 5 presents estimates of marginal willingness to pay to avoid
symptoms to reduce two air pollutants. Unconditional values of relieving
symptoms and reducing air pollution are calculated for each respondent from
observed univariate tobit models. Table 5 reports the mean, median, and
range of respondents' marginal willingness to pay to eliminate one health
symptom for one day as well as mean marginal willingness to pay to reduce
air pollutants by one unit for one day for the normal subsample. Symptom
-------
21
reduction values range from $0.81 to $1.90 in the impaired subsample and
from $0.49 to $1.22 in the normal subsample with means of $1.12 and $0.73
19
m the two subsamples, respectively. Also, values of willingness to pay
to reduce one hour daily maximum levels of 03 and N02 by one part per
million are $0.31 and $0.91 in the normal subsample. Corresponding
calculations are not reported for the impaired subsample because, as shown
in Table 4, coefficients of air pollution variables are not significant at
conventional levels.
V. CONCLUSION
Willingness to pay values of symptom reduction and air quality
improvement just presented should be viewed as illustrative approximations
for two reasons. First, private goods used in computing the estimates are
likely to be direct sources of utility. Second, symptom experience and
private good purchase decisions are likely to be jointly determined.
Nevertheless, these estimates still are of interest because aspects of
joint production are taken into account. A key finding is that independent
technologies for home producing symptoms are difficult to identify, thus
greatly limiting the number of individual symptoms for which values can be
computed. In fact, the 26 symptoms analyzed here had to be aggregated into
a single group before willingness to pay values could be computed.
This outcome appears to have implications for estimating willingness
to pay for nonmarket commodities in other contexts. An obvious example
concerns previous estimates of willingness to pay to avoid health symptoms.
Berger et al. (1987) report one day willingness to pay values for
eliminating each of seven minor health symptoms, such as stuffed up
sinuses, cough, headache and heavy drowsiness that range from $27 per day
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22
to $142 per day. Green et al. (1978) present estimates of willingness to
pay to avoid similarly defined symptoms ranging from $26 per day to $79 per
day. In both studies, however, willingness to pay estimates were obtained
symptom by symptom in a contingent valuation framework that ignores whether
independent technologies are available to produce each. Thus, respondents
simply may have lumped total willingness to pay for broader health concerns
onto particular symptoms. Some respondents may also have inadvertently
stated their willingness to pay to avoid symptoms for periods longer than
one day.
Another example relates to emerging research aimed at splitting
willingness to pay to reduce air pollution into health, visibility, and
possibly other components. From a policy standpoint, this line of inquiry
is important because the Clean Air Act and its subsequent amendments focus
exclusively on health and give little weight to other reasons why people
may want lower air pollution levels. Analyzing location choice within
metropolitan areas, for example, may not provide enough information to
decompose total willingness to pay into desired components. Instead,
survey procedures must be designed in which respondents are either reminded
of independent technologies that can be used to home produce air pollution
related goods or else confronted with believable hypothetical situations
that allow one good to vary while others are held constant.
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23
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ENDNOTES
1. Another, possibly troublesome, aspect of joint production occurs if
some or all elements of V are arguments in the utility function. This
complication is discussed momentarily.
2. Hori identifies three sources of nondifferentiability of the budget
surface under joint production. The first occurs if the number of
private goods is less than the number of commodities. The second
arises because of nonnegativity restrictions on the private goods.
This is not treated directly in the present paper, but if each private
good is purchased in positive quantities, the chosen commodity bundle
will not lie at the second type of kink. Hori's third cause of
nondifferentiability implies linear dependence among the rows of the
technology matrix.
3. Notice that this point on aggregation may apply to other valuation
methods as well. Using contingent valuation surveys, for example,
Green et al. (1978) and Berger et al. (1987) obtained value estimates
of several specific symptoms; however, issues relating to existence of
independent symptom technologies never was faced. Future contingent
valuation surveys may do well to consider this point prior to
eliciting estimates of willingness to pay.
4. For example, suppose m = n = 2 and both private goods are direct
sources of utility. If equation (6) is used to solve for the IK/A,
then: (1) if the two marginal rates of technical substitution (MRTS)
do not bracket the price ratio, then the value of the commodity whose
-------
28
MRTS is closer in magnitude to the price ratio will be overestimated,
while the value of the other commodity will be underestimated; (2) if
the two MRTS values do bracket the price ratio, then the value of
either one or both of the commodities will be overestimated; and (3)
in no case will the value of both commodities be underestimated.
5. Both questionnaires are presented and extensively discussed in Volume
II of Dickie et al. (1987(b)).
6. Chest and throat symptoms include (1) cough, (2) throat irritation,
(3) husky voice, (4) phlegm, sputum or mucous, (5) chest tightness,
(6) could not take a deep breath, (7) pain on deep respiration, (8)
out of breath easily, (9) breathing sounds wheezing or whistling.
Other symptoms are (1) eye irritation, (2) could not see as well as
usual, (3) eyes sensitive to bright light, (4) ringing in ears (5)
pain in ears, (6) sinus pain, (7) nosebleed, (8) dry and painful nose,
(9) runny nose, (10) fast heartbeat at rest, (11) tired easily, (12)
faintness or dizziness, (13) felt spaced out or disoriented, (14)
headache, (15) chills or fever, (16) nausea, and (17) swollen glands.
7. An alternative to counting the number of different symptoms
experienced in the two days prior to the interview would be to
consider the number of symptom/days experienced. Both approaches were
used to construct empirical estimates; however, to save space, only
those based on counts of different symptoms are reported. Both
approaches yield virtually identical value estimates for symptom and
air pollution reduction.
8. The first three private goods reduce exposure to air pollution by
purifying and conditioning the air. The fourth reduces exposure
because gas stoves emit nitrogen dioxide.
-------
9. The equations also were estimated after defining the pollution
variables as the largest of the one hour maxima on the two days;
similar results were obtained.
10. Rosenzweig and Schultz also initially specify their production
functions in translog form and then test whether restrictions to CES
and Cobb-Douglas forms are justified. This type of analysis is not
pursued here as most of the covariates used are 0-1 dummy variables.
Squaring these variables does not alter their values. Interaction
variables of course, still could be computed.
11. Although there is a linear relationship between the latent dependent
variables and the private goods in the tobit model, the relationship
between the observed dependent variables and the private goods has the
usual properties of a production function. The expected number of
symptoms is decreasing and convex (nonstrictly) in the private goods.
12. The tobit coefficients and variances of the model are estimated by
maximizing the likelihood function using the method of Berndt, Hall,
Hall, and Hausman (1974). The score vectors are specified
analytically and the information matrix is approximated numerically
using the summed outer products of the score vectors. Starting values
for the coefficients and the standard deviations of the transitory
error components were obtained from two independent tobit regressions
with no permanent error component. In preliminary runs a starting
value of unity was used for the standard deviation of the permanent
error component, but the starting value was adjusted to 1.5 after the
initial estimate was consistently greater than one.
-------
30
13. Covariates in the reduced form regressions are: ASTHMA, BRONCH,
FLEMCO, SHRTWZ, HAYFEV, BURB, AGE, EXPWORK, years of education, number
of dependents, household income, and an occupation dummy variable
measuring whether respondent is a blue collar worker.
14. An alternative to the two-stage procedure was suggested by Chamberlain
(1980) for random effects probit models. Chamberlain's approach uses
information from temporal variation in choice variables to distinguish
between production function parameters and the parameters of an
assumed linear correlation between choice variables and the permanent
error component. The approach is not well-suited to the present study
because of the lack of temporal variation in the private goods.
15. In the impaired subsample, inclusion of EXPWORK frequently caused the
bivariate tobit algorithm to fail to converge. This problem arose in
the specification presented in Table 2; consequently the EXPWORK
variable was excluded.
16. The estimated two-day prices are: $2.34 for ACCEN, $1.00 for ACCAR,
$0.80 for NOTGASCK. The discount rate was assumed to be 5 percent.
For further details of the procedure used to estimate prices, see
Dickie et al. (1987(a)).
17. The Wald test was chosen because its test statistic can be computed
using only the unconstrained estimates. Since the likelihood and
constraint functions both are nonlinear, reestimating the model with
the constraint imposed would be considerably more difficult than
computing the Wald test statistic.
18. In other estimates of symptom production functions not reported here,
corresponding p-values also are large, almost always exceeding .25 and
sometimes the .80-.90 range.
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31
19. For comparison purposes, mean values also were estimated at subsample
means of all explanatory variables. Results differ little with means
computed over respondents. Evaluated at subsample means, willingness
to pay to eliminate one symptom for one day is $1.05 in the impaired
subsample and $0.70 in the normal subsample.
-------
0
1
2
3
4
5
6
8
9
10
11
12
13
14
15
16
17
e
TABLE 1
FREQUENCY DISTRIBUTIONS OF SYMPTOMS BY SUBSAMPLE
NUMBER OF CHEST AND
THROAT SYMPTOMS
EXPERIENCED IN PAST
TWO DAYS
Impaired Normal
351
408
84
41
64
18
CO
15
37
9
26
4
16
6
8
0
2
n
0
2
u
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1.348 0.453
NUMBER OF OTHER
SYMPTOMS EXPERIENCED
IN PAST TWO DAYS
Impaired Normal
257
338
123
79
85
42
73
18
45
12
28
5
14
6
9
2
4
1
2
0
1
0
1
0
2
1
0
0
0
n
0
n
U
0
u
0
0 0
1.668 0.692
-------
TABLE 2
BIVARIATE TOBIT SYMPTOM PRODUCTION FUNCTION ESTIMATES:
IMPAIRED SUBSAMPLE3
Chest and Throat
Symptoms
Other
Symptoms
CONSTANT
-3.085
-2.043
(-3.035)
(-2.125)
ASTHMA
0.8425
0.6724
(2.328)
(1.851)
SRONCH
3.774
2.936
(7.663)
(6.668)
SHRTWHZ
1 .494
1.235
(3.683)
(3.428)
FLEMCO
1.458
0.2526
(4.038)
(0.8558)
HAYFEV
1.110
0.6613
(3.509)
(2.365)
BURB
-1.431
-0.7330
(-2.728)
(-1.539)
ACE
0.2986
2.042
(0.1596)
(1.177)
EXPWORK
b
b
ACCAR
-0.3485
-0.4395
(-0.8885)
(-1.364)
ACCEN
-1.9961
-0.6291
(-2.834)
(-1.829)
03
-0.1672
0.1252
(-0.5638)
(-.4475)
CO
1.279
-0.06285
(1.259)
(-0.06356)
N02
0.5475
0.6384
(0.7744)
(0.9282)
2.617
2.454
V
(17.70)
(20.81)
a..
1.827
(21.17)
Chi-Square0
148.7
P-Value for
Wald Test
0.742
Number of ,
Iterations
21
at-statisties are in parentheses.
''Denotes omitted dummy variable. Also, long term health status covariates entering these
equations do not represent mutually exclusive categories.
°The chi-square test statistic is -21nX, where X is the likelihood ratio, for a test of the
null hypothesis that the slope coefficients in both production functions are all zero.
^The convergence criterion is 0.5 for the gradient-weighted inverse Hessian.
-------
TABLE 3
BIVARIATE TOBIT SYMPTOM PRODUCTION FUNCTION ESTIMATES:
NORMAL SUBSAMPLEa
CONSTANT
HAYFEV
BURB
ACE
EXPWORK
ACCAR
NOTCASCK
03
CO
NO 2
Chest and Throat
Other
Symptoms
Symptoms
-5.789
-5.479
(-2.157)
(-2.790)
2.316
1.461
(1.614)
(1.871)
-1.388
-0.6248
(-1.180)
(-0.8470)
4.143
7.075
(0.7873)
(2.091)
0.8707
1.329
(1.157)
(2.297)
-1.949
-0.6705
(-2.905)
(-1.057)
-0.4613
-0.856S
(-0.6312)
(-1.594)
0.2757
0.3592
(0.5867)
(0.9674)
0.1788
-0.07200
(0.07729)
(-0.05241)
1.841
1.069
(1.162)
(1.127)
3.204
2.435
(10.15)
(11.31)
a 1.828
W (10.44)
Chi-Square'' 69.81
P-Value for
Wald Test 0.610
Number of
Iterations 20
at-statisties in parentheses.
bThe chi-square test statistic is -21nA, where X is the likelihood ratio, for a test of the
null hypothesis that the slope coefficients in both production functions are all zero.
cThe convergence criterion is 0.5 for the gradient-weighted inverse Hessian.
-------
TABLE A
UNIVARIATE TOBIT SYMPTOM PRODUCTION FUNCTION ESTIMATES3,
Impai red
Normal
Subsample
Subsample
CONSTANT
-2.253
-6.085
(-1.263)
(-2.329) "
ASTHMA
1.0333
(1.953)
BRONCH
*.649
(7.708)
SHRTWHZ
1.909
(3.242)
FLEMCO
1.769
(3.607)
HAYFEV
1.574
2.216
(3.137)
(2.378)
BURB
-1.830
-1.623
(-2.927)
(-1.126)
ACE
1.200
6.351
(0.40g4)
(1.165)
EXPWORK
1.725
(2.039)
ACCAR
-0.5900
-1.260
(-2.585)
(-2.425)
03
0.1629
0.5941
(0.4846)
(1.616)
CO
1.013
0.3722
(0.8041)
(0.2163)
N02
0.8930
1.726
(1.130)
(1.784)
3.884
3.790
V
(37.29)
(22.47)
CT-f
2.582
2.516
y
(15.84)
(8.822)
Chi-Square0
77.88
36.45
P-Value for
Parameter Restrictions
0.623
0.562
Number of .
Iterations
8
5
at-statisties in parentheses.
^Denotes omitted dummy variable. Also, long term health status covariates entering these
equations do not represent mutually exclusive categories.
cThe chi-square test statistic is -21nA, where X is the likelihood ratio, for a test of the
null hypothesis that the slope coefficients in both production functions are all zero.
^The convergence criterion is 0.5 for the gradient-weighted inverse Hessian.
-------
TABLE 5
MARGINAL WILLINGNESS TO PAY TO RELIEVE SYMPTOMS AND AVOID AIR POLLUTION
IMPAIRED SUBSAMPLE
Symptoms
03
N02
CO
Mean
Median
Maximum
Minimum
$1.12
$1.09
$1.90
$0.81
Symptoms
NORMAL SUBSAMPLE
03
N02
CO
Mean
Median
Maximum
Minimum
$0.73
$0.70
$1.22
$0.49
$0.31b
$0.91b
denotes coefficient not significantly different from zero at 10 percent
level using one tail test in estimated equations presented in Table 4.
b
Estimates of willingness to pay for reduced air pollution do not vary
across sample members. In the computational ratio, respondent specific
information appears both in the numerator and denominator and therefore
cancels out.
-------
VALUATION OF MORBIDITY REDUCTION DUE TO AIR POLLUTION ABATEMENT
DIRECT AND INDIRECT MEASUREMENTS
Mordechal Shechter
Natural Resource and Environmental Research Center
University of Haifa, Haifa 31 999 Israel
Paper presented at the AERE Workshop
"Estimating and Valuing Morbidity in a Policy Context"
Research Triangle Park, NC, June 8-9, 1989
+
On leave, Dept. of Regional Science, University of Pennsylvania.
-------
ABSTRACT
The paper is a comparative study of alternative approaches to
the valuation of a public good - air quality, in terms of its
effect on morbidity levels. Three indirect approaches have been
employed in the study: (1) cost of illness, (2) household health
production, and (3) a market goods approach, involving the
derivation of willingness to pay for clean air by exploiting the
relationships among the public and market goods. The direct
valuation approach encompassed several contingent valuation
experiments: (1) open-ended, (2) probe biding, and (3) binary
choice. The estimates of welfare change valuations derived under
the various approaches are discussed and compared. The empirical
analysis is based on results from a household survey, consisting
of a stratified random sample of about 3,300 households from the
Haifa metropolitan area (in northern Israel). It was carried, out
over a period of 12 months during 1986-87.
-------
VALUATION OF MORBIDITY REDUCTION DUE TO AIR POLLUTION ABATEMENT
DIRECT AND INDIRECT MEASUREMENTS*
1. INTRODUCTION
The attributes of environmental quality, a public good,
require the adoption of different valuation approaches than those
customarily employed in studies of market goods. Basically, our
aim is to quantify the change in consumer welfare, or benefits,
measured in money units, associated with a change (an increase or
a reduction) in the quantity of the environmental good (and the
flow of services concurrent with this change). Willingness to pay
(WTP) is the term commonly used to denote this welfare change. The
monetary measures of welfare change are the compensating variation
and equivalent variation, or surplus in the case of nonmarket
goods where quantity, rather than price changes are involved. The
compensating surplus (CS) is defined as the income change which
offsets the change in utility induced by a change in the level of
the public good, y,holding utility constant at its original level.
In terms of the expenditure function, fi, it is given by:
cv = fi(y°; p£. v°) - jiCy1; p£. v°). (y^y0) (i)
where the superscripts indicate initial (0), or subsequent (1),
states, is the vector of market goods prices, V is the indirect
utility function, V(P^,M,y), M is the expenditure on the market
goods, and y is the public good. Analogously, the equivalent
Support for this research was provided by a grant from the
U.S.-Israel Binational Science Foundation. Several individuals
collaborated with me on different parts of the project, and I am
gratefully indebted to them for their contributions: L. Epstein of
Carmel Hospital, A. Cohen of the Faculty of Industrial &
Management Engineering at the Technion - Israel Institute of
Technology, M. Kim of the Department of Economics at the
University of Haifa. L. Golan, B. Miller, N. Azolai, and G.
Mehrez, all graduate students at the Department of Economics,
provided me with invaluable research assistantship. I wish also
to thanks D. Shefer, L. Lave, E. Mills, and E. Loehman for
beneficial discussions and advice. Needless to say, I remain
responsible for any remaining errors of omission or commission.
1
-------
surplus (ES) is the change in income equivalent to the utility
gain induced by a change in the level of the nonmarket good,
holding utility at its subsequent level:
ev = #x(y°;P£. v1) - iitySpJ. v1) (2)
Two totally different approaches for the valuation of air
quality have been used. The first employs indirect methods, all
of which essentially attempt to infer the implicit value of the
public good from observable (and presumably accurately measured)
prices of private goods and services. For example, air quality
affects housing prices as well as expenditures on preventive and
medical care that are associated with the effect of pollution on
health. Changes in air quality levels would be expected to shift
the observed demand schedules for these market goods. From the
extent and direction of these shifts, implicit prices (or marginal
willingness to pay valuations) of the relevant public good might
be inferred. The use of market data in the valuation of
environmental goods has been expounded by M&ler (1974), Freeman
(1979], and more recently and exhaustively by Bockstael, et al.
(1984), and Johansson (1987). One of the indirect approaches used
in this study has to the best of our knowledge seldom been used in
the valuation of public goods in general, and environmental goods
in particular, and in this sense constitutes a novel contribution.
"Traditional" indirect approaches employed in valuing
environmental resources involved techniques such as the travel
cost method (TCM), characteristically used in recreation demand
studies, or the hedonic price method (HPM) , which has been used to
monetize urban public amenities through the analysis of housing
markets (e.g., Brookshire, et al., 1982, who studied air pollution
effects on property values in California). In TCM, for example,
researchers have attempted to value the benefits of a public good,
e.g. water quality, associated with the provision of outdoor
recreation services (the latter being, at least in principle, a
market good).
2
-------
Household health production is another indirect method. It
focuses on the consequences of health damages associated with an
inadequate supply of an environmental good, such as clean air and
water (e.g., Cropper, 1981, Gerking and Stanley, 1986, Berger, et
al, 1987) . Here one posits technical relationships between the
individual consumer's health attributes, exposure to environmental
pollution, and the consumption of private goods that affect health
(such as medical services, or goods which help protect against
exposure to health risks). The maximization of utility derived
from the consumption of goods and services and from being healthy,
given these relationships, yields an implicit value assigned by
the consumer to the environmental good under study.
Closely related to the health production approach, is the
"cost-of-illness" (COI) method, long used by economists and
medical researchers to value the damages inflicted by
environmental pollution, and hence the value attributable to
Improvements in the supply of environmental goods. Here one
estimates the expenditure on medical services and the value of
lost work and productivity associated with excess morbidity or
mortality. Although easiest to apply in terms of data
availability, it can be shown Harrington and Portney, 1987) that
this method yields an underestimate of the (theoretically correct)
value of the public good.
Alternatively, an altogether different approach, less and
less hesitantly used economists, especially in the valuation of
environmental and amenity resources, is a direct approach, in the
sense that it attempts to elicit consumers' valuations through
survey interview methods. This is the contingent valuation method
(CVM) - which elicits valuations within a framework of a
hypothetical, contingent market for the good or service in
question. The "state-of-the-art" of the contingent valuation
method has been summarized by Cummings, et al ( 1986) and, more
recently, by Mitchell and Carson (1989).
3
-------
The different approaches investigated in the present study
are described in Figure 1 (the residential property hedonic model
is not dealt with here, however) . In this paper we apply them to
the valuation of benefits derived from reducing air
1
pollution-induced morbidity. To the best of our knowledge, ours
is the first comprehensive study which has employed most of the
approaches currently used by economists to derive monetary values
of pollution-induced health damages, based on a single, large
primary micro-data base.
Figure 1
The data were collected through a household survey, carried
out the author in the city of Haifa in northern Israel, over a
12 month period in 1986-87. All the approaches employed in the
study (with the exception of the residential prices hedonic model)
are based on the same set of sample observations. This made it
possible to carry out a rather comprehensive empirical analysis of
the different approaches.
*
Section 2 of the paper describes the study area, the survey
design and the data collected, as well as presenting a number of
selected epidemiological results. Section 3 deals with the CVM
experimental design and valuations. Section 4 details the specific
indirect market goods model employed in this study. In section 5
we present a brief description of the household health production
mode 1, and in Section 6 the results from the COI analyses,
focusing on the estimation of due to production gains from
reducing work losses. A comparative analysis in Section 7 sums up
1
A survey of economic studies which have dealt with the valuation
of morbidity damages associated with environmental pollution has
just recently been published. See Cropper and Freeman (1988).
Berger, et al. (1987) have compared CVM with COI using a small
sample of Chicago and Denver residents.
4
-------
the alternative valuation approaches.
2. DATA AND STUDY DESIGN
2.1 Background
Haifa, is an industrial city in northern Israel, situated on
the slopes of Mt. Carmel and the adjoining Haifa Bay area. The
combination of the region's topography and meteorological
conditions, and a concentration of heavy industry in the lower Bay
area (a power plant, oil refineries, a petrochemical complex, and
others) create conditions conducive to high ambient concentrations
of pollutants, especially SOg and particulate, in parts of the
metropolitan region (depending on topography and wind direction)
during certain periods of the year.
Maximal mean 24-hour SOg concentrations of 197 and 28 6
were recorded in 1986 and 1987, respectively, with corresponding
2
maximal half-hour readings of 1,271 and 2,552. During the period
January 1986 - April 1987, 15 violations of the absolute SOg
standard were recorded in Haifa. An Intermittent Control System
(ICS) which directs the area's major polluters to switch to
low-sulfur fuels during environmental episodes, was activated on
23 days. In one single day, April 12, 1996, the monitoring
stations registered 12 violations of the 99% standard and 2 of
the 100% standard. It had been estimated that on that day alone
the ICS had prevented the occurrence of at least 6 additional
violation of the absolute standard! (Environmental Protection
Service, 1988). It has also been noted that during the same period
measurements of sulfates concentrations at certain neighborhoods
(these are not taken on a regular basis) have registered a
2
Currently there are two ambient standards for A 99%
"statistical" standard of 780 fig/M^ (300 ppb), with a 1%
exceedance level (176 half-hours per year), and an absolute
standard of 1560 (600 ppb). An expert committee has recently
proposed converting the 99% standard into a single, 100% standard.
5
-------
three-fold increase over those measured in 1976. High values of CO
were also recorded in some areas of the city during the report
period.
Concomitantly, evidence has been accumulating indicating a
higher incidence and prevalence of respiratory illnesses in the
area. Expansion, actual or planned, of the power and
petrochemical industries has fostered the familiar Conflict
between economic development, regional employment and income, on
one hand, and the desire for a cleaner environment, on the other
hand. This, as expected, has stimulated a good deal of public
controversy and media involvement.
2.2 The Household Survey
A household survey, based on a stratified, cluster area
probability sample of about 3,600 households, in the metropolitan
area of Haifa was carried out from May 1986 through April 1987.
The sample was drawn from 137 Census Statistical Areas (CSA),
classified into four socioeconomic groups on the basis of the
latest (1983) Census. They were then further classified into three
levels of ambient pollution. 16 CSAs, each approximating a
different residential neighborhood, were selected to represent the
12 sampling strata. City blocks were randomly sampled within each
stratum. Heads (either spouse) of all the households within each
block were interviewed. The data were collected in the course of a
structured interview, lasting about 30-45 minutes. The overall
response rate was 81%; 9% refused to be interviewed, and another
10% could not be reached after a second visit.
Beside the usual socioeconomic and demographic data, and CVM
questions (discussed below), respondents were asked about
perceived air pollution levels in the neighborhood and the work
place, and attitudes towards air pollution. The questionnaire
included questions on self-assessed health status, present and
past smoking habits of household members, and respiratory
system-related symptoms and diseases of the respondent and
6
-------
household members. These included the following: Cough and phlegm;
coughing or phlegm production first thing in the morning in summer
ant/or winter, and at other times of the day; and wheezing and its
relationship to having a cold. Additional symptoms and diagnoses
were elucidated, in relation to the respondent or other household
members: Eye "infection", sinusitis, allergic irritation of nose
or eyes, eczema, headache, a running nose, dyspnoea (with or
without effort), pneumonia, bronchitis, and asthma (including
frequency of attacks over the preceding 12-month period for the
latter three). Use of medical services (primary clinic visits,
medications), bed days during a two-week recall period, and
hospitalization during the 12 months preceding the interview by
any member of the household were also recorded.
2.3 Some Epidemiological Findings
A dichotomous logit model served to characterize respiratory
system diseases and symptoms by fitting the model to a binary
(0-1) dependent variable, where 1 indicates a reported presence,
and 0 the absence of a given symptom or disease. The logit model
fits the data to an equation where the dependent variable is
specified as the natural logarithm of the odds, y = In p/(1—p), p
being the probability of observing the phenomenon (symptom or
disease) and 1-p the probability of not observing it, and y is
regressed against a set of explanatory variables. Separate
equations were estimated for respondent, his or her spouse, and
the family's children (the latter grouped as one observation).
Thus, the fitted equation is of the form:
y ¦ In p/(l-p) = a + bxPOL + (3)
where POL is the variable indicating pollution level (perceived by
the respondent, or measured) In the relevant neighborhood, and the
's are other explanatory variables. For a dichotomous
classification of neighborhood pollution (used in this analysis) ,
an odds ratio, indicating the relative "riskiness" of a polluted
neighborhood with respect to the prevalence of a given symptom or
7
-------
disease, is denoted by p, whose pint estimate is given by
y(l) - y(0) = b = in p = In [|roLll / (p/l-p) |row3]
b
••• P - e (4)
Thus it has been assumed that there is a constant ratio between
the two odds ratios for given values of the other relevant
variables, and that this ratio is independent of those variables
when individuals with similar attributes, but residing in
different neighborhoods, are compared.
Table 1 and Figure 2 give the odd ratios (in Table 1 also the
upper and lower confidence intervals) for various symptoms and
diseases. It should be stressed that there relationships are also
controlled for smoking habits (which tend to cause similar
symptoms) . Only findings in which the lower 95% confidence
interval is more than 1 are reported. There is a marked
consistency of the findings and the significant relationship
between exposure to air pollution and various measures of
morbidity is clear. The analysis of data relating to the spouse of
the respondent revealed similar findings. The findings in relation
to the children in the households also reveal a relationship
between morbidity measures and exposure to air pollution (where
the smoking habits controlled for are those of the parents).
Table 1
Figure 2
3. DIRECT VALUATIONS: CVM
3.1 Elicitation Technigue and Analysis of Responses
Economists have long since shown that the correct measure of
welfare changes due to pollution reduction, and the associated
health improvements, should be based on people's willingness to
pay (WTP) for pollution abatement (Schelling, 1968; Mishan, 1971).
Conceptually, this measure should capture the four components
8
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which constitute morbidity damages, namely, (a) opportunity cost
of time sick, (b) out-of-pocket and indirect (public) outlays for
medical services, (c) defensive expenditure, and (d) psychological
losses associated with suffering, pain, hedonic damages, and other
direct utility losses not accounted by the first three categories.
A comprehensive approach to pollution-induced health damage
valuation should incorporate all four components. The money
equivalent of these damages is represented by WTP for enhancing
ambient air quality, through the implied reduction in exposure to
morbidity risks. Of course, other benefits associated with air
pollution abatement should be excluded in this case.
In the present study, pre-testing has shown that - at least
in the case of Israeli respondents - questions which attempted to
elicit monetary valuations for reduced morbidity (e.g., reduction
in a stated number of bed days, the number of days with
respiratory symptoms, or the number of acute situations during a
given period), were ill received by the respondents, or they had
difficulties relating to the situations described in such
questions. Hence, it was imperative to state WTP in terms of
reduction in pollution levels. The Israeli public in general, and
in Haifa in particular, is well aware of the connection between
air pollution and respiratory ailments, although of course not
necessarily of the true dose-response relationships.
Interviewees were queried about the perceived air pollution
levels in their own neighborhood. In order to provide a visual
stimulus, they were shown photographs of the city of Haifa on
q
visibly polluted and on relatively clean days. They were asked to
state their maximum willingness to pay for pollution abatement:
(a) In order to prevent a 50% reduction of present air quality
level of their neighborhood; (b) To achieve a 50% Improvement in
The pollution levels shown in the pictures did not necessarily
correspond to the indicated changes in pollution levels, and
mainly served to introduce a measure of realism to the
hypothetical nature of the CVM environment.
9
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4
present neighborhood levels. The first measure corresponds to ES
(and following Randall and Stoll, 1980, will be denoted by WTE^ ) ;
c
the second corresponds to CS (denoted by WTP ) . The notation
serves to emphasize that both are willingness to pay measures, not
willingness to accept (WTA) ones. Because of the inherent
difficulties in obtaining non-inflated WTA responses it was we
decided against employing them in the questionnaire, given the
5
possibility that this could have mired the WTP responses as well.
The payment vehicle was the municipal property tax, which is
the sole local tax. Respondents were asked to state their WTP in
terms of a percentage of the annual tax assessment (over and above
their present tax assessment) , by selecting the appropriate
percentage figure from a payment card. Respondents who were not
willing to pay any sum were asked about the reasons for the zero
valuation. It was thus possible to distinguish between "true" 0's,
i.e. people who did not place any positive value on the
improvement (or, alternatively, the prevention of deterioration) ,
and those who Implicitly registered a protest vote for a variety
of reasons (objecting to the payment vehicle, believing that the
polluter should pay, and so on) , but who did not necessarily view
Specifically, they were instructed to refer back to the
perceived level which they had previously indicated as the one
prevailing in their area.
5
On the use of WTA vs. WTP m CVM, and the controversies
surrounding their derivation in empirical studies,see Bishop and
Heberlein (1979); Knetsch and Sinden (1984); Gregory (1986);
Mitchell and Carson (1989).
6
Percentage categories (from 0% to 100%) were listed on the card
in either ascending or descending order, vertically or
horizontally These options were randomly assigned to households.
The upper 100% limit did not seem to constrain the range of WTP
responses. While 90% of the WTPe or WTP values were below 100
NIS, only 0.4% of the households were in the 100 NIS or less tax
bracket.
10
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air quality improvement as valueless .
The variables found to be significant in explaining the
variation in WTP Cand WTP 6 (exclusive of protest zero bids) are
presented in Table 2. Since the analyses of the CVM experiments
focused on the subset of positive bidders, it was necessary to
correct for a possible selection bias introduced by dropping the
zero responses. A procedure accounting for this bias is described
g
in Maddala (1983) . The analysis proceeded in two steps. First, a
probit model is used to analyze the determinants of zero bids,
where the dependent variable takes a value of 1 if WTP>0, and 0
otherwise. In the second step positive responses are analyzed
separately, with the probit model providing an estimator to
correct for the selectivity effects resulting from dropping the
observations with zero bids. The adjustment factor is given by the
ratio where 0 and ~ are the normal probability density
function and cumulative density function, respectively, and
V=b'_x. The b's are maximum likelihood estimators from the probit
analysis, end x is a vector of explanatory variables belonging to
three categories: variables associated with the respondent's - or
other family members' - health status, demographic and
socioeconomic variables (age, sex, education, birth origin, work
status, family size), and attitude shaping variables, such as
perception of the authorities' involvement with pollution control,
the amount of annual taxes paid, and perceived exposure to air
Our interpretation of the data is that although some vehicle
bias exists, it has had only a limited impact upon the results.
Out of about 35% of respondents whose WTP=0, 21% (for WTE^ ) and
0
17% (for WTP ) gave reasons which could possibly imply an
objection to the payment vehicle itself ("I already pay too much
tax"; "I am not willing to pay any more taxes") . Namely,
altogether approximately not more than 7% of all respondents were
affected by the vehicle to such an extent that they refused to pay
any positive sum. Of course, the sums offered by other respondents
may have also been affected to some unknown degree.
g
It was applied by Kealy and Bishop (1986) in studying recreation
use behavior, and by Smith and Desvousges (1987) in a CVM study on
risks of exposure to hazardous wastes.
11
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pollution at home or at the work place. There has been an expected
2
marked improvement in R when the equations were estimated over the
set of nonzero bid observations.
Table 2
C ©
The estimated regressions of nonzero WTP and WTP bids, for
the subset of standard WTP responses (see the section below) are
reported in table 2 (n=2,230). Respondents who are younger,
female, and from a higher socioeconomic status tend to be willing
to pay more to improve air quality, or prevent its further
deterioration. Respondents who are more aware of pollution in
their neighborhoods or work place, who believe too little is spent
on pollution control, believe government Is not too effective in
controlling it, and are willing to devote of their time in public
activities to this end, are also willing to contribute more
towards this goal. And those who themselves, or their families,
suffer from the ill health effects of pollution, are also willing
to pay more to control it.
3.2 Contingent valuation experiments
The sampling design used in the study afforded the
possibility of experimenting with alternative CVM formats, used
for difference subsets of the sample, each of which could be
viewed as a separate random sample from the same population. The
only difference between these samples was that they were taken at
different points in time. Clearly, to the extent that time of year
affected the CVM responses, the statement above would have to be
qualified.
The first set of questionnaires (n af 2,300), the "standard"
CVM format was used, namely, an open-ended WTP question. The
respondent was asked to state his or her maximum WTP for the
proposed change.
12
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It has been suggested that a more "natural" way to conduct
CVM surveys, thereby adding realism and reducing the inherent
hypothetical element, is through the use of a "Buy - Not buy"
choice implied by the binary choice format (Cummings, et al,
1986). To this end, a second set of questionnaires (n * 450)
replaced the standard format with a binary choice format, in which
respondents were asked to state whether they would be willing to
pay a given percentage increase in the municipal tax for the same
±505i changes in pollution levels. The percentage categories were
drawn from the pay card table, and randomly assigned to
households.
To analyze these responses, behavior is usually modeled in a
stochastic fashion, often by positing a random utility model to
represent consumer behavior. While the binary choice format does
not provide the investigator with information regarding the sample
distribution of WTP valuations, it does nevertheless enable to
deduce its first moments - the mean and the median. These can be
compared with the corresponding statistics of the distributions
obtained from the other experiments. Our analysis followed the
work of Hanemann (1984) and Loehman and De (1982).
A third variant of the CVM format (n 91 490) was aimed at
attempting to elicit respondents' true maximum WTP statements, by
asking them whether they would have agreed to Increase - and then
by how much - their initial sums had they been informed that that
sum would not be sufficient to accomplish the indicated 50%
change.
In the course of the survey doubts were raised whether
respondents were indeed interpreting it to be a one-time payment,
instead of an annual contribution, in conjunction with the payment
of their annual municipal taxes. To this end, a fourth change,
involving a different subset of about 400 respondents, modified
the nature of the payment, from a one-time to an annual payment.
13
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Tables 3 and 4 display various statistics for the four
experiments, and for the overall sample: "Standard" maximum WTP,
repeat bidding, binary choice, and annual vs. one-payment, for
c e
WTP and WTP valuations, respectively, responses. We present here
the results for the analyses excluding "protest" zero-bidders
(identified through the follow-up question).
Table 3
Table 4
© c
In general, WTP >WTP , namely, on average respondents were
willing to pay more to prevent worsening of pollution than to
improve present levels. However, as noted above, unless we know
the shape of the indifference curves we cannot say a priori
whether this indeed should be the case.
Means of the binary choice format are surprisingly close to
those of the standard, and especially the repeat-bid, formats.
Though eliciting less information (WTP above or below a certain
value, but not actual WTP itself), the resulting welfare change
estimates do not very much from the standard format (particularly
6 C 0
WTP valuations), or from both WTP and WTP in the repeat bid
valuations. The results suggest that, given the simplicity of the
binary choice format, it should be considered first as the
preferred alternative, particularly where there would not be any
special interest in obtaining the sample distribution of the CVM
valuations.
Regarding the repeat bidding elicitation procedure, we found
t •r»T*C . --.6
a significant increase in mean WTP and WTP , for those
respondents who were willing to increase their payments (who make
up only a subset of all respondents, as one would expect), and who
gave a consistent answer. We tend to interpret these results as
evidence of the efficacy of this approach in deriving better WTP
estimates, supporting Mitchell and Carson's (1986) advocacy of it.
14
-------
We did not find significant differences between the responses
of the annual and one-payment groups, supporting our suspicion
that respondents processed the WTP questions in the same way they
would relate to the annual municipal tax payment.
3.3 WTP° vs. WTPC responses
A different analysis of WTP responses is presented in Table
5, where a different grouping of mean sample values of WTP and WTP
for air quality changes is presented. The table is based on
responses from the subset of standard WTP questionnaires.
Neighborhoods (=CSA's) were divided into the three pollution
g
levels. With regard to WTP , it was assumed that a 50% improvement
roughly implies that a neighborhood with moderate air quality
would be upgraded into one with good air quality, i.e., a
(relatively) clean one, and that a "bad" neighborhood would move
0
into the "moderate" category. Similarly, with respect to WTP , a
50% deterioration In pollution levels would imply a downgrading of
a relatively clean neighborhood to one with moderate levels, and
9
so on. Thus, on average, an individual living m a moderately
polluted neighborhood (according to his or her perception) would
be willing to contribute NIS 37.9 annually towards improving air
quality, and NIS 40.0 In order to prevent a worsening of present
levels.
Table 5
The relationship between these two welfare change measures
for any given sub-sample of neighborhood households is ambiguous.
6 C
While WTP > WTP for moderately polluted neighborhoods, the
£
reverse holds for those badly polluted. However, both WTP and
g
WTP increase with pollution levels, and the between-group
9 ...
The neighborhood marked "Very poor" in Table 5 is a fictitious
neighborhood, created by hypothetically downgrading the "poor"
neighborhood category.
15
-------
differences are significant (non-parametric median test) . The
C 0
two-sample mean tests indicate that although WTP and WTP differ
c ©
significantly, WTP > WTP in one case (respondents from
poor-quality neighborhoods), but the reverse holds for
moderate-quality neighborhoods.
3.4 Reliability of CVM valuations
Doubts about the truthful revelation of preferences obtained
through direct questioning procedures still dominate many
discussions involving the use of direct WTP valuations. Four
"Reference Operating Conditions" (ROC's) have been proposed by
Cummings, et al (1986), as criteria for evaluating CVM
applications in general, and for evaluating the accuracy of the
values obtained in particular. These conditions are (a)
familiarity with the commodity, (b) prior valuation and choice
experience with respect to consumption levels of the commodity,
(c) the presence of little uncertainty and, (d) the use of WTP,
rather than WTA (willingness to accept) valuations.
In examining these conditions In the context of the present
study, we note first that the city of Haifa and its environs
provide a suitable setting for obtaining WTP responses in a CVM
environment. Its topographical layout and the location of its
industry introduce inter-neighborhood variability in ambient air
quality, about which there is a fair level of public awareness. In
recent years, the local media have frequently addressed the issue
of air pollution-induced diseases. It is therefore likely that
respondents were not placed in a position of having to respond to
hypothetical CVM questions. Moreover, it has been surmised that a
willingness to pay for air pollution abatement would tend to
involve little or no strategic biases attributed to CVM surveys,
because relatively small sums of money (per household) are
typically involved. Thus, of the four conditions noted above, the
16
-------
first and the last have been satisfied in this study.
Regarding ROC #2, all that can be claimed is that subjects
were familiar with the vehicle (city property tax assessments),
although, naturally, they had had no prior experience with
valuing air quality in this particular manner. However, it is
doubtful whether ROC #3 was fulfilled in this study. First,
uncertainty is ingrained in dose-response relationships between
air pollution and health, especially when lay people are involved.
Secondly, an altogether different type of uncertainty may have
surrounded the stipulated change in the supply of the "paid-for"
commodity (the indicated level of air quality improvement) , had
the payment indeed been made. Although the phrasing of the
relevant question attempted to alleviate this source of
uncertainty, we have no way of ascertaining whether this had been
successfully achieved.
3.5 Population CVM Estimates
C A
Population estimates of WTP and WTP for the entire Haifa
metropolitan region, were derived using the following entities:
= The number of households in the i-th CSA by employment
status (s) of the head of the household (employed, self-employed,
and unemployed].
I = Average net monthly income per household of households
whose heads were employed (Central Bureau of Statistics, 1985b).
Since income of self-employed by CSA is not available, it was
determined on the basis of sample means, after proper adjustments.
Income levels were converted to 1987 NIS using the Cost-of-Living
Index and the change in real income of salaried workers (Bank of
Israel, 1988) .
All census areas were classified by socioeconomic level (e)
Indeed, the survey indicates that subjects were highly familiar
with the various pollution levels in their respective
neighborhoods. As noted in an earlier footnote, a high partial
correlation between measured and perceived pollution levels is
evident.
17
-------
and pollution level (p), corresponding to those used in
c ©
delineating the sampling strata. Using these data, WTP and WTP
totals for each CSA, were derived by grouping all CSA's (sample
and non-sample) according to their respective socioeconomic level
(e) and pollution level (p) . Each CSA was further sub-divided by
employment status. The corresponding sample CSA mean WTP value was
used for calculating population totals for each sub-group within
each CSA. Regional totals were then obtained by aggregating
employment-group totals within each CSA, and then aggregating over
all CSA's. Total regional annual benefits of pollution reduction
(ZWTPC) and of prevention (ZWTP6) amounted to NIS 3.9 and 9.9
mil., respectively (at the then prevailing exchange rate of 1.5
NIS to $ 1 US, $2.6 and 6.6 mil.)
4. INDIRECT VALUATION: DERIVING EXACT WELFARE CHANGE MEASURES
4.1 Introduction
In calculating benefits associated with a larger supply of
the environmental public good through its relationship" with some
market good(s), one might begin with estimating a demand function
for the market good from observed price-quantity data. The
benefits from the public good would be derived by computing the
change in consumers' surplus associated with a corresponding shift
in the market demand schedule. This method would be expected to
yield an approximate value of the potential welfare change (Just,
et al, 1982). Alternatively, exact (in the theoretical, not
statistical, sense) measures of welfare change may be obtained by
evaluating an expenditure function underlying the ordinary
market-good demand system, using duality theory (Hausman, 1981;
Vartia, 1983; Loehman, 1986) . This approach is discussed in this
section.
In order to eventually "untangle" the demand valuations of
the public good from those observed for the market goods, the
posited demand system ought to satisfy two conditions. The market
and nonmarket goods must be non-separable, and a price vector
which would drive the marginal utility from the nonmarket goods to
18
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zero should exist (Maler, 1974). These conditions enable the
recovery of the preference ordering for this group of goods and,
subsequently, the compensated demand (or marginal willingness to
pay) schedule for the public good, from which valuations of
changes in the quantity of that good can be derived. The demand
system specified below satisfies the first condition; the second
condition is not testable, but assumed.
Specifically, in this study a twice differentiable indirect
utility function was assumed. Duality theory (Roy's identity) is
invoked in deriving the corresponding budget share equations. This
11
partial system encompasses two market goods, housing services and
medical services, denoted by the vector X in the formulation
below," and a public good, air quality, denoted by y. The
expenditure function, derived from the posited indirect utility
function, is then used to calculate the monetary value of welfare
changes associated with shifts in the level of air quality. By
Shephard's Lemma, the partial derivative of the expenditure
function with respect to price yields a Hicksian compensated
demand function (cf. Varian, 1984) ; the derivative with respect
to the public good yields the demand "price" function for the
public good.
We know of only one recent study which adopted a similar,
indirect market good approach to the empirical estimation of the
Partial demand system are frequently encountered in empirical
studies. This is characteristically due to data limitations which
preclude the estimation of all the unknown parameters in the
complete demand system. In order to recover the preferences for
the nonmarket good from the partial system it is necessary to
assume that the group of commodities which make up the partial
system is separable in consumption from all other commodities
(Hanemann and Morey, 1987) . These authors go on to show that the
compensating and equivalent measures calculated from a partial
demand system need not be identical with those calculated from a
full system. CV would be a lower bound on the conventional
compensating measure, while EV might be greater than, less than,
or equal to the full system measure.
19
-------
benefits associated with an environmental good (Shapiro and Smith,
1981). Our paper differs in its use of individual, micro data, as
compared to their use of aggregate data, and in deriving exact
welfare measures (which was not the focus of that paper) . In
connection with measuring cost of living changes, Cobb (1987) has
used a "translating variables" specification in incorporating
nonmarket goods in budget share equation systems.
4.2 Model specification and estimation
The specification chosen for the indirect utility function is
the translog function (Christensen et.al., 1975), defined in terms
of normalized prices of the two market goods, P =P^/M, the
nonmarket good - air quality - y, and household characteristics:
• •
InV » aQ + (1 + lny) + (o^ + Tjlny) In Pj + (a2 + r2lny) In P2 +
+ | [(^n + 5n lny)tin P*]2+(012 + 512 lny)lnP* InP*
(5)
+ (*21 + 521 lny)lnP! lnP2 + (*22 + *22 ^HlnP*]2]
+ In P1 l^11h1 ~ *i2h2 - ^ghg + ^uh4 -
+ ln P2 [*21hl + *22*2 + *23*3 + *24h4 + ^sV + Z *ihi
• •
where P^ is the (normalized) price of housing services, and P2 is
the (normalized) price of medical services. The are
dichotomous variables which represent family or head of household
health characteristics: hj - smoking habits, hg - respiratory
illness symptoms (head of household) , - respiratory illness
symptoms (all other household members), - respiratory diseases
(head of household) , and hg - respiratory diseases (all other
household members).
By Applying Roy's identity to eq. (5) the following share
equations are derived:
py
a InV / aire/ _ o _ 1
~ 8lhPi / dtnM i M
20
-------
= ^(aj+rjlny) + Oil+5illny)lnP1 + |oi J+51 jlny) lnP^
* I' W1*' lnpj*1 *iA } /D 1"1-2 (6)
where
• •
D * (a^TjlnyJ + Caj+rjlny) + (0^+S^lny) InPj + (0jj+5jjlny)InPj
* 2 (3l/aijlnyHlnPI *lnPj>4(
-------
those of the first system; hence, only one equation needs to be
estimated. We may note that the present data base has made it
possible to incorporate individual health characteristics, related
to respiratory illnesses and symptoms, into the posited preference
13
function. In this sense, the present indirect valuation can also
be likened to the household health production approach used to
evaluate morbidity and mortality benefits (see below).
Annual municipal tax assessments were used as proxies for
housing prices in the estimation of the budget share (eq. 6) . Its
rates generally reflect dwelling quality and the socioeconomic
status of the neighborhood. This variable was used instead of
imputed rental value because there are no reliable, published
statistics on housing prices by neighborhood and housing quality.
Consumption of housing services has been assumed to be given by
dwelling size.
The price of medical services was calculated as a weighted
index of national, average estimates of primary clinic cost per
patient visit and hospitalization costs for all illnesses.
Consumption of medical visits was given by a predicted number of
clinic visits, derived from a logit regression analysis of the
14
survey data. Hospitalization data were taken directly from the
For the inclusion of characteristics in an indirect translog
utility function, see Woodbury (1983), in connection with a model
describing labor compensation. The characteristics there are
parameters which describe the worker or the work place. In a
similar vain, Morey (1985) incorporated personal and site
attributes in estimating a demand system for ski resorts (see also
Jorgenson and Slesnick, 1987).
14
Respondents were asked whether they visited a clinic during a
two week recall period prior to the date of the interview. The
logit regressions yielded predicted probabilities of at least one
visit during the two week period as a function of socioeconomic
and health characteristics, and a seasonal variable. These
probabilities were then converted into an expected annual number
of visits for each household.
22
-------
questionnaire, where respondents were asked to indicate whether
they had been hospitalized for respiratory system-related
15
illnesses during the 12-month period preceding the interview. The
hh^s are health attributes of the respondent (head of household)
or other household members, that are presumed to be associated
with, or induced by, air pollution (with the exception of smoking
which itself induces similar symptoms). The health variables
include coughing, wheezing, sputum emission and shortness of
breath; diseases refer to asthma, bronchitis, pneumonia, and other
lower respiratory tract diseases. As already indicated, y stands
for the perceived level of neighborhood pollution. Respondents
16
were requested to indicate this on a severity scale of 1 to 6.
To estimate the share equation (6) we employed a procedure
that combines iterative minimization methods for non-linear
regression with OLS estimation, imposing the symmetry and
adding-up restrictions. All variables were normalized through
division by their respective sample mean. Table 6 displays the
parameter estimates. Inserting the parameter estimates from the
budget share (5) into the indirect utility function (4), and
It should be noted that the majority of families belong to one
of several quasi-public health insurance schemes, and do not pay
directly for medical services. However, paying for private medical
visits and medications in order to obtain faster, and often better
quality treatment is quite common, especially with sick children.
Information on these extra costs, available from the survey, was
also used in deriving expenditure levels. It can therefore be
surmised that the number of clinic visits, in and by itself,
reflects an opportunity cost of time in obtaining medical
treatment, even though no immediate payment is necessarily
associated with it.
16
While the perceived level of pollution may directly affect the
demand for housing and hence values, its impact upon medical
expenditure is indirect; the latter, are affected by actual
pollution levels. However, there is a rather high partial
correlation between these two measures (r=0.77). On the
appropriateness of using perceived rather than actual measures of
pollution levels from a psychological perspective, see Zeidner and
Shechter (1988) . It may be noted that had it been possible to
elicit quantitative responses for perceived air quality, it
probably would have been possible to use the restricted indirect
utility function as suggested by Diewert (1978).
23
-------
evaluating its partial derivatives with respect to prices, income,
and the public good, at the point of means, it can be shown that
3V/3Pj<0 (i=l,2), 3V/3M>0, and 3V/3y>0, as expected. utility
decreases with a rise in the (normalized) prices of housing and
medical services, and rises with the level of money expenditure on
the two market goods and with the level of air quality. It can
also be shown that the function possesses the correct signs for
the second derivatives.
Table 6
4.3 Welfare change measures
The expenditure function takes on the form:
t [[a1+V(lnP1)(b1rt2)MlnP2)(b2*b3)]2
- (2^+4^+2^) ^a+anPjHaj+djHUnPgHa^+d^+ib^ lnPj)2*
1
* b2lnPllnP2 * 2*3(lnP2)2 " lnVF ' [v2Vbj (7)
J
where n=lnM, a - aQ+l+lny, ^ ¦ aj+rjlny, - a2+r2lny,
V *11+ 5lllny' b2 = P12+S12lny' b3 = *22 +522lny*
S 3
dl " WZ 'lk "k • ^ d2 - 1
k=1 k=l
Given the parameter estimates from eq. (6), CS and ES values
(eqs. 1 and 2) - associated with a ±50% shift from the baseline
air quality levels - can be calculated using eq. (7). These
calculations yielded annual payments of 2.33 end 105.10 NIS,
respectively, per household. Because the expenditure function is
nonlinear, the values which have Just been calculated are
equivalent to evaluating a function of the form f(x), which
generally would not yield the same values obtained from evaluating
f(x) instead. Thus, we have also computed the means of individual
24
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valuations by calculating the two welfare measures for each
household, using the relevant attributes for that household. These
calculations yielded the following mean valuations for the sample
of households: WTPC= 9.81 NIS (S = 38.3), and WTP6 = 73.25 (s =
106.2). As noted above, and shown by Loehman (1986), there is no a
priori theoretical Justification for expecting either EV>CV or the
reverse; both cases are consistent with theory, and the direction
of the inequality sign depends on the shape of the indifference
curves.
The expenditure function for utility kept at a level
associated with the initial (sample mean) air quality is shown in
Figure 3 (on a logarithmic scale). The corresponding Bradford-type
bid curves, showing WTP as a function of y for utility held at the
initial level (CS), and at the final level (ES), are drawn in
A
Figure 4 (marked WTP and WTP , respectively). It can be seen from
Figure 3 that the marginal bid function, or the compensated demand
for the public good (the partial derivative of the expenditure
function with respect to the public good, for given market good
prices and utility level), would be negatively sloped.
Figure 3
Figure 4
5. INDIRECT VALUATION: HEALTH PRODUCTION APPROACH
5.1 Introduction
The household health production is the basis of a valuation
approach in which the benefits from a public good, viz.,
environmental quality, are assessed indirectly through household
optimizing behavior with respect to the production (and
consumption) of good health. This health "capital" is an argument
in the utility function, along with other goods and services. The
production of health contributes to utility on two counts: (1)
Reducing expenditures on health care services, which otherwise
would have decreased the amount of income available for spending
25
-------
on utility-enhancing goods and services ; (2) Diminishing the
impact on utility through income reduction caused by work-loss
days, or increasing income through productivity gains. In this
framework, one would also have to consider decisions concerning the
money time spent on preventive or averting activities. These
contribute directly to the production of health stock (but also
reduce the budget available for goods and services). Of course,
the total effect on utility amounts to a WTP valuation of the
welfare changes attributable to changes in the quantity of the
environmental good.
Several studies have used the health production approach to
estimate the value of reducing health risk resulting from air
pollution abatement (e.g., Cropper, 1981; Gerking and Stanley,
1986; Harrington and Portney, 1987; Berger, et al., 1987; Dickie
and Gerking, 1988). The emphasis has been on the inclusion of
preventive expenditure in a utility maximizing framework, and
demonstrating the theoretical superiority of this approach
compared to the COI approach. The latter overlooks preventive
expenditure, namely, the possibility that individuals yield a
measure of control over the state of their health, any direct
utility losses associated with illness, and the value of bed-day
losses of the non-working population (cf., e.g., Cooper and Rice,
197 6). It should be noted, however, that in the various empirical
applications of the health production approach, the
budget-reducing or income-enhancing effects have generally been
not explicitly considered, and a fixed budget is assumed. What one
is left with is usually a utility maximizing framework where only
preventive activities (in addition to medical care and other
consumption expenditure) are taken into account (see the empirical
sections of the above cited studies).
In this section we outline a model which attempts to provide
17
To the extent that the utility derived from consumption of goods
and services is in turn affected by health conditions, then
reduction of bed days would also be taken into account.
26
-------
a comprehensive framework for dealing with uncertainty and the
dynamic aspects of the health production process. Since we too
assume a fixed budget, our approach yields Valuations of the
environmental good which do not take into consideration the labor
savings component. We only outline the model here (for a full
description see Shechter, 1988), and then provide some tentative
WTP estimates.
5.2 The model
Assume an individual producing different levels of health
depending upon initial health stock, the amount of medical or
preventive care consumed, the level of the environmental public
good, and socioeconomic attributes. Uncertainty is represented by
probabilities of being in an ill or a healthy state, following a
first-order Markovian process (Hey and Patel, 1983) . Several
simplifying assumptions, some quite strong, have been made: (1)
The probabilities are a function of the individual's current
health state and not affected by age or by past medical history.
(2) Two types of health stock related expenditure exist:
Preventive care and medical care, where the former is exercised
only when the individual is healthy, while the latter is consumed
only when he or she is ill.
The health production process is given by:
H^m^, y, 0 ; -a—S>0 ; >0 and §5 >0 (for h and s); <0; <0
3mh Sms 8y d
-------
where
H- the individual's health level,
"fa- amount of preventive care consumed,
m - amount of medical care consumed,
s '
y - the level of the environmental good,
WC•), and that the
individual is risk averse: V'>0, V"<0, W'>0, and W"<0.
For the Markovian process of transition between health states
28
-------
over time the following probabilities have been defined:
P - The probability that an individual who is healthy
today will also be healthy in the next period, where
P' (h) > 0;
1-p - The probability that an individual who is healthy
today will be ill in the next period;
q - The probability that an Individual who is ill today
will be healthy in the next period, Q'(h) >0;
1-Q - The probability that an individual who is ill today
will also be ill in the next period.
5.3 Optimization
The individual is assumed to maximizes lifetime expected
utility, allocating the budget among x, "k. and m , given the
" s
health production function and the budget constraint. Expected
lifetime utility from T onward is given by
I pt_T U. (X;H) (11)
t=T
where p is the rate of time preference.
One first solves for the optimal values of X, °h and nig,
subject to the constrains. As noted, these optimal values are
time-invariant, implying that all time periods are identical,
given the state of the individual' health. Upon totally
differentiating the first order condition, it is possible to
obtain an expression for the individual's willingness to pay for a
change in the level of ¦ the environmental good, , measuring the
value at the margin of the public good after all
utility-maximizing, consumption adjustments have been made. We
omit the details of the derivation (see Shechter, 1988), and give
the final expression:
29
-------
dl
dy
p.f5i
3y
"ins-
ch 5mh
5H
'V
C dm
s s
(12)
Note that expressions involving utility terms have been factored
out, facilitating in principle empirical applications (cf.
Gerkings and Stanley, 1986; Berger, et al., 1987).
We would generally expect to be negative, because a
decrease in air quality would require some compensation for
utility (at the optimal level) to remain unchanged. The change
would increase health risks and welfare losses, even after the
individual makes an attempt to offset this increase, at least
partially (depending on one's preferences), through some budget
reallocations entailing, among others, more spending on preventive
or medical care. For the following conditions, - which seem
reasonable - should simultaneously be satisfied:
(a) W'>V' -- the marginal utility of income of a non-healthy
Individual is higher than that of a healthy individual.
3H. SH
(b) P Sy < QV
That is, the change in the probability of being healthy in the
next period due to a change in air quality is higher for an ill
person than for a healthy one.
In order to apply the model to available data, an additional
simplifying assumption was made, namely that there is no
distinction between medical and preventive activities, and both
having the same unit price. Thus:
3Hh
a h
m _ m fdH _ SH _ 3H . _ __ n_ s
n s' ^ms~ ~ 3m J' h~ s~ * dy dy
From this it follow that
30
-------
dl
dy
r 5H 1
3y
(P'-Q*)
ei
-------
with no alternative but to assume that only medical care budget
reallocations matter in households' health production decisions.
19
Rewriting eg. (13) as (5m/3H) C (3H/3y), we estimated the
first term using conditional probabilities. First, specifying a
logit model, we estimated the probability of at least one doctor
visit during a two-week recall period prior to the interview, for
each of three health states: h=0, healthy; h=l, having symptoms;
h=2, having symptoms and respiratory diseases. All the other
explanatory variables (except AV14, see below) are dichotomous.
Medical services covered here include doctor visits (mostly at
primary health clinics belonging to one of the health maintenance
organizations, the so-called "sick funds") of the interviewee,
spouse, and children.Logit regressions were estimated for doctor
visits, including private consultations (separately for
respondents, spouses, and children).
Table 7
The variable representing pollution, AV14, Indicates measured
Assuming the health production function enables us to write
express it in terms of its inverse, m(H,y), namely, that the
conditions of the implicit function theorem hold.
20
In Israel almost all medical services are publicly provided,
then, unless they actually sought private medical services, people
are usually not fully informed of the out-of-pocket expanses.
However, it is reasonable to expect that they would take
cognizance of the time and psychological costs involved in a
clinic visit or a hospital stay. These may bear some relationship
to the real economic costs of providing the service. Children
visits to a physician refer to at least one visit by at least one
child from the respondent's family, since children were not
individually identified in the questions relating to health
conditions. See also footnote 15 above.
32
-------
21
(actual or extrapolated) SO_ concentrate ions (in ppb). The
22
variable AV14 is significant in every regression. Respondents
with respiratory system problems are more inclined to seek medical
help, and so are females, respondents with no children in the 0-18
age group (probably a proxy for older respondents) , and those of
Asian-North African origin (may also be related to belonging to a
lower income group) . The results for spouses and children were
similar, with AV14 figuring in all of them, but they have not
been used here.
Next, we specified a multinomial logit model to describe the
relationship between health state and pollution levels, where
Pj = prob(h£l), and = prob(h=2). The results are given in Table
8. Again, as expected from the discussion in Section 2 above, AV14
is highly significant. The coefficients of the socioeconomic
variables have also the expected sign.
Table 8
Viewing the medical care use probabilities as conditional
probabilities given one's health state, we have calculated the
change - at mean values of the other explanatory variables - of
reducing mean AV14 by 50% (going from Yg to y^. Viz.,
p(doctor visit in past 2 weeks / h^) x p(hj/y=yg)
21
Since pollution data is measured only at a few points m the
Haifa metropolitan region (and only SC>2 on a continuous basis) , it
was necessary to extrapolate ambient concentrations for the rest
of the survey neighborhoods using an ad hoc dispersion model.
Average concentrations were computed for two-week periods
preceding the date of any given interview. The two-week averages
are based on half-hour concentration readings.
22
An alternative set of regressions was run with the variable
MAX14, representing maximum daily concentration for the preceding
two-week period, but AV14 turned out to be a better predictor.
33
-------
- p (doctor visit in past 2 weeks / h^) x p(h^/y=y^), i=0,l,2
The decrease amounted to 2.26% percentage points, or about 8% from
present usage levels. Converting this result to expected number of
annual visits, and multiplying by C, the cost per visit of NIS
30,23 yields a rough approximation of WTP of NIS 32.43.
Of course, this figure is an underestimate: (a) It does not
include visits of spouse and children; (b) it is based on a
question which asked whether there was at least one visit during
the preceding two-week recall period, but did not ask for the
actual number of visits; (c) it does not include hospitalization
24 25
cost or medication costs ; (d) finally, as explained above, it
overlooks the labor cost savings.
An altogether different question is associated with the
nature of medical care services in a country like Israel, where
most of the population Is covered by one form or another of a
subsidized quasi-public health insurance scheme. In this sense
individuals do not have to make budget reallocation adjustment in
the way assumed in the model. However, as remarked above, time and
Inconvenience associated with a visit to a primary health clinic
might nevertheless be playing a major role, not much different
from that of money expenditures. This of course is another major
drawback of the empirical results, but we surmise that CVM
valuations may have well been similarly affected.
Although no statistics are available, we believe this figure to
be close, though somewhat lower than the corresponding cost of a
private consultation visit to a general practitioner.
24
Respondents were also asked about hospitalization during the 12
month period preceding the interview for illnesses connected with
the respiratory system, but the number of responses was too small
for any meaningful analysis.
25
The expected decrease in the probability of obtaining medication
resulting from pollution reduction, has been calculated to reach
17% approximately (a decrease from p=0.113 to 0.094).
34
-------
6. COST OF ILLNESS (COI) VALUATIONS
6.1 Consumption of Medical Services and Bed Day Losses
The COI approach normally covers direct (expenditures on
medical services) and indirect (income reduction due to work day
and productivity losses). As observed above, given that work loss
has been neglected in the household production model, we have made
an attempt to estimate these losses. Since individuals would not
directly suffer the consequences of work loss days because of the
almost universal coverage by employer-paid sick-day leave, this
cost is distinctly a social cost. We would not expect it to be
expressed through individual WTP valuations.
A binary response model was used to analyze bed days during
the two week recall period. The response variable, STY, was
defined as follows:
2TY_ 1 if respondent missed one or more days
0 otherwise.
Although our sample was large (n=954), the results are
nevertheless based on a relatively small number of observations,
since only 65 cases were respondents who reported that they were
absent from work for at least one day during the fortnight. A model
was fitted with both socioeconomic and health attributes, using
backwards elimination to fit the logistic regression. The
estimated equation is given in Table 9.
Table 9
When AV14 is reduced by 50%, the probability of at least one
bed day decreases from p=0.051 to 0.041, a drop of 18 percent.
Work loss days at present pollution levels constitute about 1.85%
of all work days. The total expected annual savings in number of
work loss days due to pollution abatement, AL (assuming 300
working days per year), is given by AL = E x 300 x 1.85 x Ap,
35
-------
where E is the number of employed persons (above age 15) in the
metropolitan region, and Ap = 0.18. A similar calculation was
performed for the non-working persons in the sample. The weighted
mean sample percentage of bed days (corresponding to the working
group's work loss days) is 3.57.
Assigning a money value to these savings, would of course
vary with the specific assumptions relevant in each case. The
present calculations were based on 1987 gross wages per salaried
employee, including social benefits, of NIS 1,832 per month, or
$1,221 (Central Bureau of Statistics, Statistical Monthly, April,
1988) . At this wage rate, the money value of the savings would
total NIS 10 million per year for the working group. For
illustrative purposes, if we also value a day of a non-working
person at 1/2 that of a working person, an additional savings of
almost NIS 8.5 million would be achieved, for a total of NIS 18.5
million. On a per household level, the expected savings would
amount to about NIS 185.0
7. COMPARATIVE EVALUATIONS
7.1 CVM vs. Indirect Approaches
Several writers (e.g., Randall, 1987; Mitchell and Carson,
1989) have noted that the CVM approach deals with ex ante
valuations, while the indirect approaches are usually associated
with ex post valuations. This implies that one therefore should
not expect to necessarily obtain close estimates in the two
approaches; but the opposite is not necessarily true, either.
Reliability of either approach (which one would supposedly be an
empirical question) might be questioned, however, if results
derived from the same set of observations turn out to be vastly
different. Hence, a comparison of the results from the various
approaches should be illuminating. Table 10 summarizes the values
obtained under the different approaches.
Table 10
36
-------
The closeness of the valuations is quite encouraging.
Although the indirect approaches cover all respondents, including
zero bidders, it is assumed that the this approach yields true
valuations of protest bidders as well, and hence, the comparison
should be made with the true bidders (non zero and true zero) of
the corresponding CVM experiments (Tables 3 and 4) . It should be
noted especially that the mean values of individual household
valuations in the two approaches are within the same order of
magnitude (NIS 9.8 vs. 34.5 for WTPC, and 73.3 vs. 68.6 for WTP ).
7.2 Health Production, COI and CVM valuations
Although very tenuous assumptions were made in applying the
household health production approach, one observes the closeness
of the results to the CVM valuations. Since the model measures
responses to reduction in pollution, the appropriate comparison is
c
with the WTP valuations. Indeed, if other health and preventive
Q
care components were added, the results of the WTP comparisons
could have turned out to be even closer.
Theoretically, the cost of illness estimates should have at
best provided a lower bound on WTP valuations. But this should not
have been the case in the present study, given that COI estimates
refer to social rather than individual WTP, and include components
which do not figure directly in the individual's decision making
process. Thus, households do not directly bear all the cost of air
pollution damages. They are covered by medical insurance, and do
not bear the full cost of medical services. Part of the premium is
paid by employers and, furthermore, medical services are
subsidized by the government. In addition, paid sick-leave is
almost universal for salaried workers. But, moreover, people
clearly do not possess the kind of dose-response information which
would have enabled them to fully assess the economic impact of
exposure and disease. These facts would necessarily be reflected
in WTP valuations. One should also note that cost of illness
estimates are probably more susceptible that the others to data
"manipulation". The results are sensitive to what we assume about
37
-------
the appropriate values for work loss of employed and unemployed
individuals, the ratio between privately purchased and publicly
provided prescriptions, and the cost of physician visits, etc.
In a certain sense, one might speculate that CVM responses
represent willingness to pay to reduce the direct disutility
associated with morbidity, plus maybe the aesthetic disutility of
air pollution. Namely, CVM valuations are essentially the
psychological costs associated with pollution. Indeed, results
presented elsewhere (Zeidner and Shechter, 1988) indicate that WTP
is sensitive to anger and anxiety caused by perceived exposure to
air pollution. If this were indeed the case, then the CVM
valuations, or at least part of them, should be added to cost of
illness valuations!
7.3 Some concluding comments
Within the framework of a study dealing with the valuation of
benefits from pollution abatement, several approaches were
investigated. A notable feature of the present study has been the
use of the an identical data base - households, their attributes
and responses - in all three approaches. While contingent
valuation relies exclusively on direct question techniques, so
that survey data are a sine qua non, market demand systems are
normally estimated from aggregate, secondary market data. In this
study, however, the same primary data base was used. Valid
comparable valuations pertaining to the same set of households
were thus obtained. Since all approaches are presumed to measure
the same thing(s), one should a priori expect the results to be
close.
In this vein, we view the results as rather encouraging and
believe that they provide further impetus for the use of CVM. Of
course, improved statistics on health and preventive care should
offer an improved basis for alternative, indirect appaoraches.
38
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41
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Table 1 Exposure to air pollution and morbidity in adults and
children: Odds ratios and 95% confidence intervals
Symptom or disease
Odds
Ratio
Lower Upper
Confidence limit
A. Respondents
Winter cough & cold 1.432202 0.973711 - 2.106581
Permanent cough without cold 1.718250 1.267392 - 2.329494
Winter cough without cold 1.434010 1.151725 - 1.785482
Permanent phlegm & cold 1.572290 0.979119 - 2.524816
Winter phlegm & cold 1.400047 0.977708 - 2.004823
Permanent phlegm without cold 1.347164 1.024256 - 1.771871
Winter phlegm without cold 1.282863 1.040762 - 1.581281
Cough & phlegm 1.566648 1.247142 - 1.968010
Winter phlegm & cold 1.574363 1.252040 - 1.979665
Wheezing & cold 1.358134 1.052843 - 1.751950
Wheezing while breathing 1.352105 1.065619 - 1.715611
Dyspnoea 1.802163 1.530547 - 2.121982
Rhinitis 1.305185 1.043520 - 1.632463
Eye "infection" 1.302482 1.030010 - 1.647031
Headache 1.595975 1.356035 - 1.878371
B. Ch i1dren
Cough or phlegm & cold 1.695780 1.209402 - 2.377761
Cough or phlegm without cold 1.922437 1.365540 - 2.706449
Cough or phlegm 1.969765 1.528539 - 2.538353
Wheezing with cold 1.694218 1.150931 - 2.493961
Wheezing 1.466871 1.130402 - 1.903492
Asthma or bronchitis 1.487382 1.139776 - 1.940998
Pneumonia 1.269068 1.008890 - 1.596343
Rhinitis 1.271813 1.013503 - 1.595958
Eye "infection" 1.495645 1.109688 - 2.015841
-------
Table 2. Willingness to pay equations - nonzero bids only
Regression coefficients
c ©
Explanatory variable VJTP WTP
Demographic and socioeconomic variables:
Age (years) -7.86 (0.29) -0.73 (0.073)
Sex (l=female) 55.28 (4.76)
Education (years) 12.18 (0.71)
Blue collar worker (l=blue collar) -53.33 (6.80)
Number of children ages 0-18 -24.64 (2.19) -6.93 (1.56)
Ethnic origin I (l=born in Africa/Asia) -26.93 (6.20)
Ethnic origin II (l=born in Europe) 109.38 (6.38)
Annual municipal taxes 0.22 (0.006)
Attitudinal variables:
Perceived exposure to pollution at work
(l = yes) 81.29 (5.29) 14.42 (4.31)
Perceived neighborhood air quality (1-6) -21.14 (1.51)
Believes budget share allocated to pollution
abatment too high -382.22 (57.85) 101.72 (38.87)
Believes budget share allocated to pollution
abatment too low 163.85 (5.90)
Ready to devote time to public activities
concerned with pollution abatement (l=yes) 39.62 (1.64) 5.54 (1.30)
Perception of government influence on
pollution abatement (l=yes) -26.99 (5.90)
Pollution induces defensive actions by
respondent (l=yes) 8.63 (4.48
Health status
Perceived health status (l=not healthy) -67.55 (5.46)
Family history (exc. respondent) of asthma,
pnuemonia, or bronchitis (l=yes) 24.60 (4.78) 8.81 (4.29)
Family history exc. respondent) of respi-
¦k -k
ratory system symptoms (l=yes) 55.91 (4.58)
Adjustment factor -952.98 (23.63)
Intercept 7708.53
Adj. R2 0.54 0.64
Not significant.
Cough, sputum, wheezing, dyspnoea
-------
Table 3. CVM Experiments: WTPC (in NIS, per household,
excluding protest zero bids, except in binary choice)
Elicitation N Mean Median
method
Sample 2,518 34.5
Standard max. WTP 1,855 37.7
Repeat bids: One-time payment
1st bids 343 26.4
2nd bids 195 67.8 (+22.2)
Annual payment
1st bids 343 26.4
2nd bids 195 67.8 (+22.2)
Binary choice 360 66.2 65.0
-------
Table 4. CVM Experiments: WTP6 (in NIS, per household,
excluding protest zero bids except in binary choice)
Elicitation N Mean Median
method
Sample 1,704 68.6
Standard max. WTP 1,348 70.9
Repeat bids: One-time payment
1st bids 199 64.2
2nd bids 195 89.0 (+24.8)
Annual payment
1st bids 157 54.5
2nd bids 163 77.9 (+23.4)
Binary choice 360 69.1 67.2
-------
Table 5. Direct (CVM) valuations of perceived air quality changes
(Includes zero bids)
Present Pollution level after change
pollution
level Good Moderate Poor Very poor
(a) WTP6
Mean = 2 6
Good Median= 15
N = 847
(b) WTP°
(c) WTP®
Mean =37 .9
Mean = 4 0
Moderate
Median= 28
Median= 28
N =750
N =749
(d) WTPC
(e) WTPe
Mean =47 .2
Mean =42 .7
Poor
Median= 40
Median= 32
N = 192
N =192
Values in table refer to means and medians of the indicated
sample air quality stratum, and stated in NIS per household
per year.
Significance Levels:
Nonparametric median test for 2 samples:
Hq: WTPC (cell b) « WTP° (cell d) 0.015
H^: WTP6 (cell a) = WTP® (cell c) WTP (cell e) . . 0.001
Paired t-test for means (2 tailed):
Hq: WTPC (cell b) = WTP6 (cell c)
Hq: WTP° (cell d) = WTP® (cell e)
0.001
0.049
-------
Table 6. Parameter Estimates of the Budget Share Equation
Parameter
Estimate
Parameter
Estimate
0
11
3
12
'22
11
'12
22
-0.348
(-110.38)
-0.721
(-15.74)
-1.404
(-16.42)
-0.181
(-21.06)
0.039
(2.49)
-0.159
(-4.90)
-0.417
(-12.16)
0.001
(0.06)
-0.527
(-8.77)
*
11
*
12
*
13
14
*
15
R = 0.27
N = 2,239
0.0006
(1.11)
-0.0009
(-0.73)
0.004
(3.27)
0.00002
(0.04)
0.0024
(2.12)
Asymptotic t statistics in parentheses.
-------
Table 7. Estimated Logit Regression: Consumption of Medical Care
Services (Physician Visits) - Respondents
Explanatory Variable Regression Standard
coefficient error
Intercept
-4.397
0.217
Health status
0.715
0. 097
AVI 4
0. 018
0. 005
Sex (l=female)
0.405
0.134
No children 0-18 yrs.
(l=none)
0.588
0.134
Birth origin Asia-Africa (l=yes)
0.346
0.154
n = 3,612
X = 125.5 (5 df) .
Dependent variable: 1 = visited a physician in past 2 weeks
Health status 0
1
2
= healthy
= suffers from at least one of symptom
= suffers from at least 1 disease
-------
Table 8. Estimated Logit Regression: Health Risks and Exposure to
Pollution - Respondents
Explanatory Variable Regression Standard
coefficient error
Intercept (h^)
0.880
0.134
Intercept (h^)
-0.732
0.134
AVI 4
0.011
0.002
Education (l=low level, 0-8 yrs.)
0.248
0.078
Birth origin (l=Europe or America)
0.285
0.072
Sex (l=female)
0.289
0.064
No children 0-18 yrs. (l=none)
0.254
0.088
Age of respondent (<40)
-0.845
0.120
Age of respondent (41-50)
-0.481
0.123
Age of respondent (51-60)
-0.372
0.102
n = 3,612
X = 316.5 (8 df) .
Dependent variable:
= suffers from at least 1 symptom or disease
hg = suffers from at least 1 disease
-------
Table 9. Restricted activity or bed days
Explanatory Variable Regression
coefficient
AVI4 0.028
(0.012)
Income (1= "low" income-below NIS 1,300/mo.) 0.80
(0.295)
Intercept -3.79
X =24.2 (18 df) .
Dependent variable: 1 = Stayed home at least 1 day during
the past two weeks.
-------
Table 10. Comparisons Between Direct & Indirect Valuations
(Including zero bids. Mean household values in NIS)
WTPC WTP6
zm.
Standard bids
Repeat bids
Binary choice
Indirect
Expenditure function
Health production
Cost of illness (bed days)
37.70
67.80
66.20
9.81
32.43
185.0
70. .90
89.00
69.10
73.25
Corresponding to changes in perceived pollution levels.
-------
VALUATION of an ENVIRONEMNTAL GOOD
DIRECT vs. INDIRECT APPROACHES
direct approach
contingent
valuation
(CVM)
*
wtp
r
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indirect (market)
approach
observed demand for
related market good(s)
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FIGURE 1
-------
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ATIOS FOR SYMPTOMS & DISEASES
( interviewee, children )
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-------
THE EXPENDITURE FUNCTION
I
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T
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AIR QUALITY
FIGURE 3
-------
BID CURVES FOR AIR QUALITY
6
WTP
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AIR QUALITY
FIGURE 4
-------
Risk,
Self-Protection
and
Ex Ante Economic Value*
by
Jason F. Shogren and Thomas D. Crocker
Department of Economic Department of Economics
Appalachian State University University of Wyoming
Boone, NC 28608 Laramie, WY 82071
January 1989
*This research was partly supported by the Wyoming Water Research Center.
Perri and Fred Sterbenz have made helpful comments.
-------
Abstract
We examine the impact of self-protection on the ex ante value of reduced
human exposure to an environmental hazard. Assuming a continuous distribution
of health outcomes and self-protection that influences both the probability and
the severity of an undesired outcome, we develop three propositions:
1) If risk is endogenous such that self-protection influences the
probability or the severity of an undesirable outcome, then unobservable
utility terms cannot be eliminated from the individual's ex ante valuation
expression.
2) If risk is endogenous, knowledge of the convexity or the nonconvexity
of physical dose-response relations is insufficient to sign unambiguously
the change in an individual's ex ante marginal valuation of risk, even
when consumer cognition is perfect.
3) If risk is endogenous, self-protection expenditures will not be a
consistent lower bound of the ex ante value that a risk-averse individual
attaches to a reduction in risk.
These three statements imply that several propositions originally
developed for cases of exogenous risk and which form the analytical basis for
most recent empirical work on the value of health risk changes are not
immediately transferable to settings where endogenous risks prevail.
-------
I. INTRODUCTION
Any person who might suffer harm from exposure to an undesirable state of
nature can reduce expected ex post costs by purchasing market insurance. Moral
hazard, however, compels insurers to defray only a fraction of these costs
[Arrow (1963), Shaven (1979)]. XL Consequently, individuals use self-
protection to reduce both the ex ante probability and expected costs of the
uninsured event [Ehrlich and Becker (1972)].2— We consider the implications of
this for models used to value risks to human health.
In particular, we find that:
1) Given moral hazard, when self-protection influences the
probability, the severity, or both of an undesirable state,
unobservable utility terms cannot be eliminated from the individual's
ex ante valuation expression. Consequently, empirical studies that
attribute differences across groups in ex ante value estimates solely
to unobserved differences in household health production technologies
are misplaced.
2) with moral hazard and self-protection, knowledge of the
convexity or nonconvexity of physical dose-response relations is
insufficient to sign unambiguously the change in an individual's ex
ante marginal valuation for a reduction in the level of the hazard,
even when consumer cognition is perfect. Therefore, we do not
support the traditional argument that those individuals exposed to
greater risk with greater income must place a higher value on a given
risk reduction.
3) with moral hazard, an increase in the level of the environmental
hazard does not necessarily lead to an increase in the level of self-
protection. Therefore, self-protection expenditures are not a
-------
consistent lower bound of the ex ante value a risk averse individual
attaches to a reduction in risk.
These three statements imply that several propositions originally
developed for cases of exogenous risk and which form the analytical basis for
most recent empirical work on the value of health risk changes are not
immediately transferable to settings where endogenous risks prevail. 3—
Berger, et al. (1987) appear to be among the first to consider endogenous
risks in the context of human health.4— Our treatment differs from their
seminal effort in two significant ways. First, though they state the general
continuous distribution case of risks to human health, they examine ex ante
value only in a world of two mutually exclusive and independent states of
nature: survival or death. We extend the ex ante value concept to the general
continuous case. By maintaining continuity throughout, we allow the individual
to choose between contractually defining states of nature or making an effort
to alter states of nature. Spence and Zeckhauser (1972) demonstrate that the
ability to influence states of nature enhances both the ex ante and the ex post
gains from adaptation. In particular, we assume that individuals recognize
that outcomes are stochastically related to actions, implying that predictions
of behavior and the relative values that motivate it depend not only on
preference orderings over outcomes, but also on preference orderings of
lotteries over outcomes.
Second, Berger, et al. (1987) model only probability-influencing self-
protection. They disregard the severity of the health outcome being risked,
even though they concede that prior self-protection can influence both
probability and severity. As pointed out by Ehrlich and Becker (1972) the
distinction between self-protection that influences probability and self-
2
-------
protection that influences severity is somewhat artificial. The distinction is
often said to be made for theoretical convenience [see for example Hiebert
(1983)]. In contrast, we model the effects of self-protection that influences
both the probability and the severity of the undesired state, and consider the
effects on the ex ante value of reduced risk.
2. THE MODEL
Consider an individual who is involuntarily exposed to a health risk under
a particular liability regime. Assume the risk is created by exposure to an
ambient concentration of an environmental hazard, r, taken from the real
interval, R:
R - It, r] (1)
Because of moral hazard, the individual cannot acquire enough market insurance
to avoid the risk completely. The individual must decide from a real interval,
S how much self-protection, s, to undertake:
S - [s, s] (2)
Given exposure to the. hazard, the individual is uncertain as to which, i,
of N alternative health outcomes will occur. Let
H - {hj, h2» . • • , hN} (3)
denote the outcome space where outcomes are the individual's human health
capital returns ordered from smallest to largest, given the individual's
genetic and development history.
Let f(h^; s, r) denote the probability of outcome i occurring given that
self-protection, s, is undertaken and that the exposure level to the
environmental hazard is r. Assume the following about f(*):
3
-------
Assumption 1: f(hi; s, r) > 0 for every i e [1, . . . . N] and every s e S and
r c R.
Let F(h^; s, r) denote the corresponding distribution function defined
over the support [a, b]
FCh^, s, r) - [ f; s, r)dh (4)
J a
where a and b are the minimum and maximum health outcomes. s— We assume the
following about F(«):
Assumption 2: F(h^; s, r) is twice continuously differentiable in s e S and
r e R for every i c [1, . . . . N].
Assumption 3: Fs(hi5 s, r) < o for every s e S and r c R and every i c [1,
. . . . N] in the sense of first-order stochastic dominance.
Assumption 4: Fr(h^; s, r) ^ 0 for every s c S and r c R and every i e [1,
. . . . N] in the sense of first-order stochastic dominance.
Assumption 5: No restrictions are placed on the convexity of the distribution
function in the immediate neighborhood of an optimal level of self-
protection, s*, for all s c Sand r c R and for every i c [1, . . . . N] .
The individual is risk averse with a von Neumann-Morgenstern utility index
over wealth W, U(W). The following assumptions are made about U (W) :
Assumption 6: U is defined over the real interval (W,»] where W is 0.
Assumption 7: Lim U (W) = -ED.
W-»W
Assumption 8: U is strictly increasing, concave, and thrice continuously
differentiable.
For each health outcome the individual might realize, he selects a minimum
cost combination of medical care and foregone work and consumption. Let
C - CChi; s, r) (5)
4
-------
be his ex ante expectation of realized costs which depend on the uncertain
health outcome, self-protection, and the exposure level to the hazard. Assume
the following about C(«):
Assumption 9: C is strictly decreasing, convex, and thrice continuously
differentiable in s c S for every i c [1, . . . . N] such that Cs < 0 and
css > 0 for all h c H.
Assumption 10: C is strictly increasing and thrice continuously differentiable
in r c R for every i c [1, . . . , N] such that Cr > 0. No restrictions,
however, are placed on Crr and Csr for all h c H.
Given incomplete insurance purchases, intertemporally separable utility,
and constant expected prices for medical care, the individual's choice problem
is then
rb
Max [ U(W - C(h; s, r) - s)dF(h; s, r)]. (6)
S J a
Note that the price of self-protection has been normalized to unity. The
subscript i is suppressed to maintain notational simplicity.
Given the model, we are now able to develop the propositions stated in the
introduction.
3. EX ANTE VALUE AND WILLINGNESS-TO-PAY
3.1 Endogenous Risk. A few recent refinements to the willingness-to-pay
approach to valuing environmental hazards have acknowledged the frequently
endogenous form of the problem. For example, Rosen (1981), Berger, et al.
(1987), and Viscusi, et al. (1987) note that self-protection affects survival
or injury probabilities, while Shibata and Winrich (1983) and Gerking and
Stanley (1986) allow self-protection to influence the severity of ex post
damages. In a nonstochastic world or in an uncertain world with only two
5
-------
feasible states, these studies demonstrate that marginal willingness-to-pay can
be expressed solely in terms of the marginal rate of technical substitution
between hazard concentrations and self-protection. This result cannot be
generalized to a continuous world with endogenous risk.
Proposition 1: Given the model assumptions, when self-protection
influences either the probability or the severity of health outcomes
or both, the individual's marginal willingness-to-pay for reduced
risk cannot be expressed solely in terms of the marginal rate of
technical substitution between ambient hazard concentrations and
self-protection. In particular, unobservable utility terms cannot be
eliminated from expressions for the ex ante value of reduced risk. 7—
Proof: To show that for a continuous distribution the individual's
compensating variation statement of willingness to pay for reduced risk
includes the unobservable utility terms, we examine self-protection that
influences either the distribution or the severity (costs) of the health
outcomes or both.
First, maximize the expected utility index (6) by selecting an optimal
level of self-protection s c S yielding the following first-order condition for
an interior solution
fb
EU - -E[U C ] + U C.F dh. (7)
w 1 w s J a w h s
The left-hand side of (7) represents the marginal cost of increased self-
protection in terms of the utility of foregone wealth. The right-hand side
reflects two types of marginal self-protection benefits: the first term is the
direct utility effect of enhanced wealth resulting from reduced expected ex
post costs; the second term is the indirect utility effect of a stochastically
dominating change in the distribution of health outcomes.
6
-------
The indirect effect was derived by integrating by parts the effect of
self-protection on the distribution
b b
U(*)dF (•) » UF I +
s 'a
U C, F dh
.whs.
¦i:
U C.F dh,
whs
since Fs (a;-) = Fs(b;-) = 0. Assume that improved health outcomes will
decrease the ex post costs, < 0.
Solve for the compensating variation statement of the willingness-to-pay
for reduced risk by totally differentiating the expected utility index (6), and
then applying the first-order condition (7). When self-protection influences
both the probability and severity of health outcomes such that Fs < 0 and Cs <
0, the willingness to pay expression is:
dW
dr
~JU C,F dh - JU C dF-
v h r v r
JU C.F dh - JU C dF
whs w s
> 0,
where all integrals are evaluated over the support [a, b] . Obviously, the
unobservable utility indexes cannot be removed from the individual's
willingness to pay expression (8).
Even the assumption of a simple two state world fails to remove the
utility terms from (8). For example, let tt(s, r) and (1 - t:(s, r) )
respectively represent the subjective probabilities of healthy and of sick
states. Let Uq (W - s) and Uj (W - s - C (s, r) ) be the expected utility of being
healthy or sick, where Uq > U^. The individual thus chooses s c S to maximize
EU - n(s, r)U0(W - s) + (1 - tt(s, - s - C(s, r)). (9)
Following the same steps as before, the willingness to pay expression is
dW
dr
V"o - V -
"s[°0 - V - (1 - ",U0CS
> 0.
(10)
-------
where TTr < 0, tts > 0, = 9U1/3W, and Ug - auQ/8W. Again, utility terms
cannot be removed.
Next allow, as do Gerking and Stanley (1986), self-protection to influence
the severity, Cs < 0, but not the probability, Fs - o, of health outcomes.
Further assume that Fr - 0 which, with Fs = 0, implies that neither collective
nor individual actions will influence the probability of a particular health
outcome, i.e., hazard concentrations resemble sunspots or the phases of the
moon. With these assumptions, expression (8) reduces to:
E(u c 1
dW w r
dr " E[UC ]
w s
EU EC - cov(U , C )
v r w r
EU EC - cov(U , C )
v s w s
> 0. (11)
For the unobservable utility terms to be absent from (11), the two covariance
expressions must be zero; however, our model assumptions do not allow them to
be zero. Therefore the two utility terms cannot be removed.
Finally, assume, as does Rosen (1981), that self-protection affects
probability, Fs < 0, but not severity, Cs - 0. In Rosen's (1981) terms, one
cannot be more severely dead. For similar reasons, Cr = 0. Under these
conditions, expression (8) reduces to:
/U C.F dh
dW v h r
dr JU CF dh ' UZJ
whs
and again the willingness-to-pay expression cannot be rid of the unobservable
utility terms, which concludes the proof.•—
We could examine additional cases. For example, self-protection might
influence only the probability of a health outcome, but hazard concentrations
could affect probability and severity, or vice versa. The results would not
change: utility terms would loom up in the willingness-to-pay expressions,
implying that policy efforts to aggregate across individuals and to account
-------
simultaneously for the reality of probability and severity unavoidably involve
interpersonal utility comparisons.
3.2 Nonconvex Dose-Response Relations. Proposition 1 poses hurdles to
procedures which would establish a social risk-benefit test by summing
unweighted compensating or equivalent variations across individuals. Yet
another problem for consistent aggregation is the ambiguous effect that a
change in hazard concentrations has on the sign of compensating variation. In
a contingent valuation study of the risk valuations attached to hazardous waste
exposures, Smith and Desvousges (1986, 1987) report increasing marginal
valuations with decreasing risk. This finding is but the latest in a 15-year
long series of analytical [Starett (1972), Winrich (1981)] and empirical
[Crocker (1985), Repetto (1987)] papers which use prior information on physical
dose-response relations, individual abilities to process information about
these relations, or individual perceptions of the relations to produce a
declining marginal valuation result for more of a desirable commodity.
However, when risk is endogenous, no one has yet asked whether convexity of the
marginal value of risk follows when cognition is not an issue.
An individual's compensating variation can be shown to be ambiguous in
sign even if the strongest possible case for negative effects of increased
hazard exposure is imposed. To illustrate, define strong convexity as follows.
Definition 1: Strong convexity of risk is defined as: convex ex post cost,
C rr > 0; convexity of the distribution function, Frr > 0; and declining
marginal productivity of self-protection, Csr > 0, C^r > 0, Csjj > 0 and
Fsr > 0. Strong nonconvexity describes the conditions most favorable for the
traditional argument that increased risk requires progressively increasing
compensation to maintain a constant level of expected utility. Increased
9
-------
exposure increases the probability and the expected ex post costs of
undesirable health outcomes to the hazard at an increasing rate; moreover, the
marginal productivity of self-protection is decreasing across the board.
The opposite case is strong nonconvexity. Strong nonconvexity defines the
weakest case for negative effects of increased exposure to the hazard.
Definition 2: Strong nonconvexity of risk is defined as: nonconvex ex post
cost, Crr < 0; concavity of the distribution function, Frr < 0; and increasing
marginal productivity of self-protection, Csr < 0, C^r < 0, ^sh < 0 and
Fsr < o."L
The following proposition states the result:
Proposition 2: Even in the absence of cognitive illusions or failure to
consider all scarcity dimensions of the risk-taking problem, a maintained
hypothesis of strong convexity of risk is insufficient to guarantee that
increased exposure to a hazard requires progressively increasing
compensation to maintain a constant level of expected-utility. Similarly,
strong nonconvexity is insufficient to guarantee progressively decreasing
compensation.
The proposition is supported by Dehez and Dreze (1984, p. 98) who show
that the sign of the marginal willingness-to-pay for safety given an increase
in the probability of death is generally ambiguous. Dreze (1987, p. 172)
concludes that any assertions about this sign given a change in safety "...must
be carefully justified in terms of underlying assumptions".
Proposition 2 contradicts the argument of Weinstein, et al. (1980) and
others that individuals at greater risk must have a greater demand for safety.
Consequently, contrary to Rosen (1981), individuals at greater risk with
greater wealth cannot necessarily be weighted more heavily when risk reductions
10
-------
A
are valued. Similarly, the assertions by Kahneman and Tversky (1979) and Smith
and Desvousges (1987) that increasing marginal willingness-to-pay for reduced
risk constitutes a lapse from rational economic behavior are not supported. 11 —
Proof: To demonstrate that an increase in hazard concentration has an
ambiguous effect on an individual's compensating variation, differentiate the
compensating variation in expression (8) with respect to the hazard exposure:
d(dW/dr) . _ I C2 - U C ] -2j[U C C. - U C. ]F dh
dr Q I ww r w rr ww r h w hr r
+ Ju C F dh
w h rr I
- (13)
E[U C C - U C ] + J[U C. - U CkC ]F dh
ww s r w sr whr wwhr s
+ J[U C C - U C ]F dh + /U C.F dhl,
ww s r w sr r w h sr J
where 0 - Ju CWF dh - Ju C dF > 0,
whs w s
A - /U C.F dh - /U C dF < 0,
whr w r
and all integrals are evaluated over the support [a, b].
The terms on the right-hand side of (13) can be defined in terms of direct
and indirect utility effects given an increase in exposure to a hazard. Q > 0
and A < 0 represent the combined first-order direct and indirect utility
effects of s and r. The first and fourth terms in (13) represent second-order
direct utility effects on expected costs with an increase in exposure. Given
strong convexity, the sign of the first term is negative. The sign of the
fourth term is ambiguous in the sense that alternative parameterizations are
conceivable in which either U^CjCj or UwCsr dominates in absolute magnitude.
The second, fifth, and sixth terms are second-order direct and indirect utility
effects weighted by the marginal effect on the distribution of either s or r.
Given strong convexity, the signs of all three terms are ambiguous in the above
11
-------
sense. Without prior information on the magnitude of the marginal effects on
the expected cost function, there is no reason to expect one term to dominate.
The third and seventh terms represent the second-order indirect and cross-
indirect utility effects of increased exposure. By the definition of strong
convexity, the sign on both terms is negative. Without knowing the relative
magnitude of all the direct and indirect utility effects, however, strong
convexity is insufficient to sign (13) unambiguously. Likewise, the assumption
of strong nonconvexity is also insufficient to sign (13). Whether one imposes
strong convexity or strong nonconvexity the sign of (13) is ambiguous.
Although sufficient conditions for increasing or decreasing marginal
willingness-to-pay can be determined, there is, in the absence of prior
information or simple ad hoc assumptions, no reason to expect that one or two
terms will dominate expression (13). This concludes the proof.
3.3 Self-Protection Expenditures as a Lower Bound. Consideration of self-
protection has not been limited to problems of ex ante valuation under
uncertainty. A substantial literature has emerged, e.g., Courant and Porter
(1981), and Harrington and Portney (1987), which demonstrates that under
perfect certainty the marginal benefit of a reduction in a health threat is
equal to the savings in self-protection expenditures necessary to maintain the
initial health state. This result cannot be extended to the uncertainty case
when self-protection influences both ex ante probability and ex post severity.
Proposition 3: Neither strong convexity nor strong nonconvexity of risk is
sufficient to sign the effect of a risk change upon self-protection
expenditures. Therefore these expenditures cannot be used to determine
the welfare effect of a risk change.
Proposition 3 contradicts Berger et al.'s (1987) argument that if
increased exposure increases the marginal productivity of self-protection,
12
-------
Fsr < 0} then self-protection will increase with exposure. Consequently,
Berger, et al.'s (1987 p. 975) sufficient conditions for "plausible" results do
not hold when self-protection influences both probability and severity.
Proof: To demonstrate that strong convexity is insufficient to determine
the effect increased hazard exposure has on self-protection, take the first-
order condition in equation (7) and apply the implicit function theorem. The
effect of increased exposure on self-protection is
where
71 - - ¥[U C(1+C)-UC ] + J[U C . - U C, (1 + C )]F dh
dr ww r s w rs w sh ww h s r
+ J[U CL - U C CjF dh + Ju C F dhl/D
whr wwrh s whsr |
D a E[U C (1 + C ) - U C ] + 2/[U C . - U C.C ]F dh
ww s s w ss w sh ww h s s
(14)
: 15)
-Ju CJ dh + Ju C.F dh < 0
ww h s w h ss
and all integrals are evaluated over
sufficient condition of the maximization problem (6), and is assumed to hold
whenever (7) holds.
Given D < 0, the sign of (14) depends on the sign of its right-hand-side
numerator. The first term in the numerator of (14) is the direct utility
effect of increased exposure on expected costs. Given strong convexity of risk
and (1 + Cs) > 0 from the first-order condition, the sign of the first term is
negative. The second term reflects the indirect utility effect of increased
exposure on the distribution. Given strong convexity, its sign is ambiguous in
the earlier defined parameterization sense. The third term is a direct utility
effect weighted by the marginal effect of self-protection on the distribution
(Fs < 0), and its sign is also ambiguous. The signs for the second and third
effect are ambiguous since there is no a priori reason to believe that any one
set of terms dominates the others. The fourth term in the numerator is the
13
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cross-indirect utility effect of increased exposure. Given strong convexity,
its sign is negative. Therefore, without prior information on the relative
magnitudes of the four direct and indirect utility effects, strong convexity is
insufficient to sign (14) unambiguously. Given the conditions most favorable
to the traditional argument that increased risk will increase self-protection,
we still require prior information on the impact that increased exposure has on
the marginal productivity of self-protection to support the argument.
Following the logic above, an assumption of strong nonconvexity of risk
leads to a similar conclusion of an ambiguous effect of increased exposure on
self-protection. Consequently, since self-protection may decrease as exposure
to a hazard increases, self-protection cannot be considered a consistent lower
bound on the ex ante value a risk averse individual attaches to a reduction in
risk. This concludes the proof.
4. CONCLUSIONS AND IMPLICATIONS
Individuals and policymakers use self-protection activities to influence
both their ex ante risks and their expected ex post consequences The
implications of this for models used to value risks to human health are
unequivocally negative. We show that unobservable utility terms cannot be
eliminated from marginal willingness-to-pay expressions, implying that
empirical efforts which identify marginal rates of substitution with
willingness-to-pay are misdirected. We also show that even under the most
favorable restrictions increased risk need not imply progressively increasing
levels of compensation in order to restore initial utility levels.
Consequently the traditional argument that those who are exposed to greater
risk and have greater wealth must value a given risk reduction more highly does
not follow. Finally, we demonstrate that increased risk need not imply
14
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increased self-protection expenditures; thus changes in these expenditures may
not bound the value of a risk change.
Some succor for health risk valuation efforts could be obtained by
stepping outside professional boundaries to draw upon prior information from
psychology, biomedicine, and other disciplines. Insight might therefore be
gained into the signs and the relative magnitudes of many terms in expressions
(13) and (14) . It is odd that the field of economics which explicitly
recognizes the policy relevance of incomplete markets has historically been
reluctant to use information from other disciplines in order to simulate the
valuation results of a complete market. We recognize that there is a growing
trend to incorporate restrictions drawn from other disciplines into the
behavioral postulates of economic models. 1The results of this paper suggest
that the incorporation process should be accelerated.
Incorporation will not overcome, however, the aggregation problems posed
by the presence of utility terms in individuals' willingness-to-pay
expressions. Approaches to aggregate risk-benefit analysis do exist other than
the mechanical summation of consumer surpluses calculated from the singular
value judgement that social welfare and aggregate total income are synonymous.
Given that individual consumer surpluses can be estimated, one possibility is
to draw upon the extensive equivalence scale literature, e.g., Deaton and
Muellbauer (1986), in order to weight each individual or household. Tradeoffs
can then be evaluated using an explicit social welfare function which
recognizes that personal health is in part self-produced and inalienable.
Alternatively, utilities might be calculated directly.
15
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FOOTNOTES
1. Moral hazard refers to the tendency of insurance to influence an
individual's incentive to prevent loss.
2. Self-protection includes everything from installing home water filters in
order to reduce pollutant concentrations in drinking water to medical care
and the use of tort law. [See Laffont (1980), Crocker (1984)].
3. The empirical human health valuation literature typically assumes that
health risks are: (i) independent of individual actions; and (ii) usually
for the sake of analytical and empirical tractability, individuals require
progressively increasing levels of compensation to maintain constant
expected utility when confronted by increasing risk. Jones-Lee, et al.
(1985), for example, embodies both conditions. We argue these assumptions
are unnecessarily restrictive in the sense that they stretch the ability
of economic analysis to cover the domain of risky phenomena.
4. Psychologists agree that individuals perceive that they have substantial
control over uncertain events [Perlmuter and Monty (1979)]. Stallen and
Tomas (1984) conclude that "... the individual is not so much concerned
with estimating uncertain parameters of a physical or material system as
he is with estimating the uncertainty involved in his exposure to the
threatening event and in opportunities to influence or control his
exposure" [emphasis added].
5. The [a, b] interval could also be influenced in subsequent periods by
self-protection. We disregard this issue.
6. Subscripts represent partial derivatives.
Assumptions of a risk-neutral individual with an identity map of ex post
costs would eliminate the unobservable utility expressions. These
assumptions seem excessively restrictive.
8. One might eliminate the utility terms by using the pointwise optimization
technique that Mirrlees (1974) and Holmstro'm (1979) employ. However,
pointwise optimization evaluates self-protecting choices individually at
each and every health state rather than in terms of lotteries over health
states. It thus adopts an ex post rather than an ex ante perspective.
9. See Polemarchakis, et al. (1986) for thinking on aggregation under
exogenous risk.
10. Rogerson (1985) assumes that the distribution function must generally
satisfy the convexity of the distribution function condition (CDFC).
Therefore, the assumption of a concave distribution in r and s is perhaps
restrictive. As shown by Jewitt (1988), however, the CDFC assumption is
not universally required in that it satisfies very few of the standard
distributions set forth in statistics textbooks.
11. Close inspection of the questionnaire formats upon which these assertions
are based reveals that respondent opportunities to influence risk and/or
severity were not fully controlled.
12. See Warneryd (1986), Weinstein and Quinn (1983) and Smith and Johnson
(1988), for example.
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Smith, V.K., and Desvousges, W. (1987). An Empirical Analysis of the Economic
Value of Risk Change. Journal of Political Economy 95: 89-115.
Smith V.K., and Johnson, F.R. (1988). How does Risk Perceptions Respond to
Information: The Case of Radon. Review of Economics and Statistics.
Spence, A.M., and Zeckhauser, R. (1972). The Effect of the Timing of
Consumption Decisions and the Resolution of Lotteries on the Choice of
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Starett, D. (1972). Fundamental Nonconvexities in the Theory of Externalities.
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THE ECONOMICS OF QUARANTINES: AN APPLICATION TO PESTICIDE REGULATION
Erik Lichtenberg
Department of Agricultural and Resource Economics
University of Maryland
College Park, MD
Robert C. Spear
School of Public Health
University of California
Berkeley, CA
David Zilberman
Department of Agricultural and Resource Economics
University of California
Berkeley, CA
This research was supported in part by the U.S. Environmental Protection Agency
under Cooperative Agreement CR811200-01 to the Western Consortium for Public
Health. The views expressed are those of the authors, not the agency.
Working Paper No. 88-38
December 1988
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THE ECONOMICS OF QUARANTINES: AN APPLICATION TO PESTICIDE REGULATION
One of the most common practices for dealing with hazardous situations is
simply to remove the hazard from human proximity, either spatially or temporally.
Such policies can be termed quarantines. The classic case is that of contagious
disease control, where infected individuals are kept apart from vulnerable
individuals until the threat of contagion has passed. Other examples include
imprisoning dangerous criminals; locating hazardous industries (e.g., military
testing grounds, nuclear power plants and other hazardous activities) in remote
areas; keeping dangerous chemicals, high voltage equipment, etc. in locked or
otherwise inaccessible locations; and keeping workers out of areas recently
treated with pesticides.
Any quarantine involves tradeoffs that must be evaluated whether the
decision maker is a government agency or an individual concerned with self-
protection from self-generated hazards. The benefits of quarantines obviously
consist of reductions in hazard. But quarantines typically have costs as well,
such as additional discomforts and lost wages of contagious patients or
productivity losses from suboptimal siting or scheduling. These tradeoffs must
be evaluated in determining the appropriate parameters of a quarantine, that is,
the length of time and/or location restriction. This paper develops a framework
for optimal quarantine determination and applies it to a widespread form of
quarantine, re-entry regulation of pesticide-treated fields. Section I contains
a model of optimal quarantine determination. Section II models optimal timing
of pesticide application under re-entry regulation. Interestingly, the
imposition of re-entry regulation may make it optimal for farmers to switch to
1
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prophylactic treatment of pests, a practice which has been widely criticized as
inefficient in the literature on pesticide use. Section III applies this model
to the case of pre-harvest intervals in apple production in three major producing
states. Section IV develops a model of acute poisoning from exposure to
pesticide residues under different re-entry intervals. Section V combines the
production and health models into a tradeoff model which is then used to obtain
a rough evaluation of current policy.
I. Optimal Quarantine Determination
Generally speaking, quarantine have both a spatial and a temporal
dimension: how far away the hazard is sited and how long the quarantine lasts.
Contagious disease quarantines have both: one must decide where to locate
infectious patients relative to other patients and the general populations well
as how long to continue isolation. Penal policy also does: prison location and
length of sentence will both depend on how dangerous a criminal is. In other
cases, one of these dimensions may be irrelevant. In pesticide regulation, for
example, only the temporal dimension may matter: many pesticide residues are
absorbed by touch and therefore the hazard affects only those entering a treated
field. In siting of military testing grounds, nuclear power plants or other
hazardous facilities, on the other hand, only location matters.
Let D represent the spatial dimension of the quarantine and T the temporal
dimension. Let Z represent a consumption or production activity affectedly the
quarantine. The benefits of consumption or production, B(Z,D,T), depend on Z
and on the quarantine parameters D and T, as does the level of hazard, H(Z,D,T).
Let W[B(Z,D,T), H(Z,D,T)] denote the utility function of an individual facing
a hazardous situation or a social welfare function. The relevant decision
2
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problem is to choose Z, D and T to maximize utility or social welfare. This is
typically accomplished in two stages. First, microeconomic theory is used to
derive a model of optimal consumptive or productive behavior conditional on the
quarantine parameters D and T. The resulting behavioral model is subsequently
used to derive the optimal policy parameters.
Formally, letting subscripts denote derivatives, the necessary conditions
are
(la) WbB2 + WaHz - 0
(lb) WbBd + WhHd - 0
(lc) WbBt + WhHt - 0.
The two-stage procedure described above consists of first solving equation (la)
to get the optimal level of consumption/production activity contingent on the
quarantine, Z*(D,T), and then choosing D and T to maximize W[B(Z*(D,T),D,T),
H (Z*(D,T,),D,T)] according to the necessary conditions
(2a) Vb(BzZd + B„) + Wh(H2Zd + H„) - 0
(2b) Wb(BzZt + Bt) + Wh(HzZt + Ht) - 0.
The case of pesticide regulation considered below is investigated by first
deriving profit-maximizing pesticide use patterns conditional on temporal
quarantine restrictions, Z* (T), and farm profits, B(Z*(T)). The risk of acute
organophosphate poisoning of farm workers is modeled as a function of pesticide
use, H(Z*(T)). These two components are combined into a tradeoff curve under
an assumption of equal welfare weights on farm income, B(Z*(T)) , and worker
safety, H(Z*(T)), that is WB - WH. Finally, this tradeoff curve is used to
derive the optimal length of the quarantine T* under different environmental
conditions.
One can conceptualize distance-related quarantine problems in the same way.
3
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For example, the size, operating procedures and transmission line requirements
of a nuclear power plant may depend on the distance between it and the population
and industrial centers it serves, so that one would begin with a relationship
between these factors and quarantine distance, Z*(D) : The risks posed by the
plant, H(Z*(D),D) depend on the quarantine distance D and the operating
characteristics of the plant, Z*(D). These two can be combined using the
appropriate welfare weights WB and WH to obtain a tradeoff relation that can then
be used to determine the optimal distance D*.
In sum, even in regulatory contexts it is typically necessary to solve
private optimization problems prior to considering the social decision problem,
since the private optimization problems are crucial elements of the tradeoff
relations needed. Moreover, close interdisciplinary, cooperation is often
required to specify the hazard functions H, since they depend in complex ways
on combined economic, environmental and biomedical factors.
II. Crop Production Under Re-Entry Regulation
One of the most common measures used to protect farm workers and other
rural inhabitants from the health hazards posed by applied pesticides is to
forbid entry into treated fields for a specified period of time during which
pesticide residue levels (and hence health risks) are thought to be excessive.
Similar regulations aim to protect consumers as well by forbidding harvest for
a specified interval after application of pesticides. Often, these re-entry
regulations lead to reductions in growers' incomes by preventing optimal
scheduling of harvest or intraseasonal activities like pruning or irrigation,
causing decreases in yield, quality or price received for the crop. Thus ,
whether the decision maker is a government agency charged with protecting farm
4
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workers or a farmer deciding whether to work in his/her own field, the
determination of an appropriate re-entry interval hinges on the choice of a
tradeoff between risks to human health and safety, on the one hand, and the
economic losses induced by regulation on the other.
For the sake of simplicity, we concentrate on the problem of re-entry
regulations affecting an individual farmer's harvest of a perishable crop
(fruits, vegetables), the kind of crop to which this form of regulation is
applied most often. We assume that benefits B are restricted to farm profits,
which are a function of pesticide use Z, itself a function of the re-entry
interval T. We assume also that the farmer applies the pesticide at a standard
application rate and focus on the determination of the timing of the application.
Assume that there is a time t0 representing the earliest date at which the
crop can be harvested; prior to t0, the crop will be immature and hence not
harvestable. Assume also that after to, the value of the crop declines because
of decreased quality or because of price decreases due to seasonal increases in
aggregate production, so that the farmer's revenue is maximized by harvesting
at to. Formally, this implies a revenue function R(t) such that R(t0) - max
(R(t)) - R*, and, letting subscripts denote derivatives, < 0 and R^ < 0 for
t > t0. Production costs, including pesticide materials and application costs,
will be assumed to be constant and will thus be ignored.
Now assume that a pest appears at a time ta shortly prior to the optimal
harvest time to. If left untreated, the pest will damage a proportion of the
crop which will then be unsalable. The larger the pest population is, the
greater the level of damage will be. This damage can be avoided by treating the
crop with a pesticide. To simplify matters, assume that only a single standard
treatment is available at a negligible cost. If the farmer treats the crop
5
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immediately upon arrival of the pest, i.e. , chooses a treatment time ts - ta, the
pest will be effectively eradicated and damage will be essentially reduced to
zero. If, on the other hand, the farmer treats the crop before the pest arrives
(t„ < ta), the pesticide will decay; its effectiveness will be reduced by the
time the pest arrives and the farmer will sustain some crop losses. The longer
is the interval between treatment and the arrival of the pest, the greater will
be the decay of the pesticide and the damage caused by the pest.
These characteristics can be represented formally by letting the proportion
of the crop damaged by a pest population of size k be a function g(k,ta - ts),
where ta - ts represents the time elapsed between treatment and the arrival of
the pest. The preceding discussion suggests that g* > 0, gt > 0 and g(k,0) ~ 0.
Pesticide decay curves are typically convex, so that one would expect get ^ 0 as
well.
There are two types of treatment strategies available to fartiters: a
reactive strategy of applying pesticides upon the arrival of the pest, and a
prophylactic or preventive strategy of applying pesticides in anticipation of
a pest problem. The reactive pest management strategy will maximize profits
whenever it is feasible, which implies an optimal choice of ta - ta whenever T
< t0 - ta. If the re-entry period T is sufficiently long, however (specifically
T > t0 - ta), following the reactive treatment plan may force the farmer to delay
the harvest and thereby lose revenue. In this case the farmer faces a tradeoff
between losing revenue from crop damage and losing revenue from harvesting
delays. Under some conditions, it may become optimal for the farmer to adopt
a prophylactic treatment strategy. While this practice has been much maligned
in the pest management literature, rigidities is scheduling such as those imposed
by re-entry regulation may make it desirable for farmers.
6
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Some casual empirical evidence supports the notion that re-entry intervals
actually provide a motivation for prophylactic treatment strategies. In Oregon,
plum growers expecting to need to use parathion for end-of-season codling moth
control typically apply the chemical 14 days — the length of the pre-harvest
interval — prior to the projected harvest date, regardless of whether the pest
is in evidence.
It should be clear that the farmer will never treat any earlier than needed
to be able to harvest at time t0, i.e. , that ts > t0 - T; treating any earlier
than C0 - T would imply accepting greater damage in return for no gain in revenue
and is thus less profitable than treating at t0 - T. It should also be evident
that the farmer will always harvest the crop as soon as possible, that is, at
least as soon as the re-entry period has ended. If the re-entry constraint is
non-binding, then the harvest time will be t0. if the re-entry constraint is
binding, then the harvest will occur T periods after the treatment time;
normalized (without loss of generality) to fit the revenue curve R. This can
be written ts + T - t0.
The pesticide use patterns adopted and revenues earned by the farmer thus
depend critically on whether or not the re-entry interval constitutes a binding
constraint. If it does not, then a reactive treatment strategy is always
optimal, ts - ta, the crop will be harvested at t0 and revenue will be R*. If
it does, the farmer will face a tradeoff between crop damage and decreased
revenue. The optimal pest management strategy will be determined by the choice
of a treatment time ts which maximizes realized revenue, given by:
(3) [1 - g(k, ta - t,)]R(ts + T - t0)
subject to the constraint:
7
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(4) t0 - T < ts < ta.
Because the convexity of the pesticide decay function makes the damage
function g(k,ta - ts) convex, the realized revenue function (3) will be convex
unless R is quite strongly concave. Thus , the optimal treatment plan must be
analyzed according to two cases.
Case 1: The most likely case is that realized revenue (3) will be convex,
so that the optimal treatment time will be either the maximum or minimum possible
time, that is, either ta or t0 -T. jn essence? 0r course, this constitutes a
choice between reactive (ts - ta) ancj pr0phylactic (ts - t0 - T) treatments. The
farmer will choose the one which gives the greatest profit. If ta - t„ there
will be no damage (g - 0) but the farmer will have to wait until ts + T - t0 to
harvest and will thus realize a revenue of R(ta + T - t0). If t, - t0 - T, there
will be damage g(k,ta + T - t0); the farmer will harvest at t0 and thus realize
a revenue [1 - g(k, ta + T - C0)]R*. If the difference between these two realized
revenues,
(5) V - R(ta + T - t0) - [i - g(k, ta + T - t0)]R*
is positive, the farmer will adopt the reactive strategy and treat at ta. If it
is negative, the farmer will adopt the prophylactic strategy and treat at t0 -
T. An increase in the size of the pest population k will increase V and thereby
make the farmer more likely to adopt a reactive strategy. An increase in the
re-entry interval T, though, will increase V only if the marginal increase in
the proportion of the crop damaged by treating earlier (gt) is less than the
marginal increase in the proportion of revenue lost by treating later (Rt/R*).
Thus , if gt > Rt/R*, an increase in T will make the farmer more likely to adopt
-------
a prophylactic strategy. An increase in the internal between the arrival of the
pest and the optimal harvest data, that is, in t0 - ta, will, of course, have
precisely the opposite effect of an increase in the re-entry interval T.
Case 2: If the revenue function R( ) is sufficiently concave to make
realized revenue (3) concave, the profit-maximization problem will have an
interior solution defined by:
(6) gt R + (1 - g)Rt - 0
with sufficiency assured by:
(7) Q - gtt R + (1 - g)Rtt < 0
which holds by assumption. It is readily apparent that an increase in the re-
entry interval will lead the farmer to treat earlier (dts/dT - -[Rt gt +
(l - g)Rttl/Q c 0), thereby accentuating the tendency toward prophylactic
treatment. If, as one would expect, the increase in damage from treating earlier
is greater for larger pest populations than for smaller ones (i.e. , g,^ SO), an
increase in the pest population size will induce the farmer to treat later
(dts/dk - - [ g^ R - gk Rt ] /Q > 0), thereby reducing the tendency toward
prophylactic treatment. As before, an increase in t0 - ta will have the opposite
effect of a increase in T.
III. Pesticide Use in Apple Production
Consider the case of re-entry regulation of organophosphate insecticides
used to protect apple crops from infestations of codling moth larvae from moth
flights shortly prior to harvest. The yield and quality of the apples is assumed
to increase up until the maturity date t0, which is the earliest date at which
9
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the crops may be harvested. After t0, yield and quality will remain constant
for a considerable length of time. However, the price the farmer receives for
the crop will decline as time passes because the aggregate supply of apples will
increase as producers in other regions harvest and market their crops. This
price decline will continue until the price of apples for fresh consumption
equals the price for processing uses, at which point the price will remain
constant. An analysis of the intraseasonal trends in farm-level apple prices
in three major producing states (Washington, Michigan, California) indicated that
this price decline is convex and could be represented well by an exponential
tune. Thus , the price received by a grower harvesting a full crop at time t
> t0 is R*exp(-a(t - t0)} .
The threat posed by a late-season flight of codling moths consists of an
infestation of larvae in the fruit, i.e., of wormy apples. This threat can be
alleviated by using organophosphates to kill the moths before they lay eggs.
"Standard doses of these pesticides are typically applied; without loss of
generality, normalize this standard dose to unity. Pesticide decay rates are
typically modeled as exponential curves, so that the proportion of the pest
population killed by a treatment applied at ts is exp{-b(ta - ts) and the
proportion surviving is 1 - exp{-b(ta - ts)). Assume that all infested fruit is
unsalable and that the proportion of the crop damaged is proportional to
survivorship. Letting k represent the proportion of the crop damaged by a moth
population of standard size, the damage function g(k,ta - ts) will be in this
case k[l - e{-b(ta - ts)}].
The realized revenue function (3) in this case will thus be:
(8) R - R* exp{-a(ts + T - t0)} (1 - k[l - exp(-b(ta - ts)})
10
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which is obviously convex. The difference in profit between treating at ta
and treating at t0 is thus
(7) V - R*exp(-a(ta + T- t0)} - R*(l - k[l-exp{-(ta + T - t0)}]).
which will be positive whenever
k > [1 - exp{-a(ta + T - t0)j]/[l - exp{-b(ta + T - t0))] - kc
and negative whenever k < kc. The optimal treatment strategy is thus:
(9) c -
s
t , k > k
a c
t - t, k < k
0 c
In addition to the comparative static results from the general case it is
straightforward to show that the faster the price declines over the season, the
more likely the farmer is to adopt a prophylactic strategy (dV/da < 0) and that
the faster the pesticide decays, the more likely the farmer is to adopt a
reactive strategy (dV/db > 0).
To provide a empirical mechanism for evaluating the impact of re-entry
regulation of pre-harvest use of parathion on apples in three main U.S. producing
states (Washington, California, Michigan) , the model was parameterized as
follows. A regression of weekly data on farm-level prices received in
Washington, California and Michigan over the period 1971-1980 on a time trend
and dummies to control for differences among years and states yielded an estimate
of the revenue decay parameter a - 0.0024. According to Johannes Joost,
California extension specialist on apples, the maximum price received in 1984
was about $300/ton, which, at a yield of 10 tons/acre, suggests a maximum revenue
of $150,000 for a 50-acre block. The regression analysis suggested that price
11
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levels in Michigan and Washington were about 17 percent and 32 percent above that
of California; however, because Michigan harvests about 4 weeks after California
and Washington, 2 weeks, the maximum price in these states should be 9.8 percent
and 28.2 percent higher than California, respectively, giving estimates of about
$165,000 per 50-acre block in Michigan and $192,000 per 50-acre block in
Washington. An estimate of the parathion decay parameter b = 0.8 was taken from
Spear et al. As (1975a) study, of parathion decay in California citrus orchards;
examination of parathion decay data on Washington apples (Staiff et al. (1975))
indicated that the decay patterns in the two cases were essentially identical.
Conversations with farm advisors indicated that, if left untreated, a codling
moth infestation caused by a population of normal size would damage about 10
percent of the crop; thus, k was given a value of 0.10. Calculation of the
damage threshold for prophylactic spraying over the range of reasonable re-entry
periods, kc, resulted in values ranging from .009 to .065, all well below k;
thus, it appears that reactive treatment will always be optimal. in fact, apple
prices would have to fall 2-10 times more rapidly before prophylactic treatment
would become desirable.
IV. Residue Poisoning From Parathion Exposure Among Apple Harvesters
The risk of clinical illness in workers as a result of exposure to residues
of parathion applied to apples at various locations was modelled according to
the overall scheme laid out by Popendorf and Leffingwell (1982). in essence,
the pesticide is applied, a decay process takes place in which some of the
parathion is converted to the oxygen analog, paraoxon, and exposure takes place
days or weeks later when crews enter the field to harvest the crop. If clinical
illness results, it is usually due to a dermally absorbed dose of paraoxon.
12
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There is considerable information available to quantify the various steps in this
process but very limited data on climatological effects on the decay process
itself.
The characterization of the residue decay process follows that of Spear
et al. (1975a) and Popendorf and Leffingwell (1978). In both cases, the
dislodgeable foliar residues of parathion and paraoxon are described by linear
ordinary differential equations. The parameterization of these models utilized
data obtained from citrus crops, but limited data on apples suggests a similar
decay pattern (Staiff et al. (1975)). The simplified form of the model used here
describes the residue relevant to worker hazard from day three post-application
onwards. After day three the parathion residue has decayed to the point where
the hazard to workers depends almost entirely on the paraoxon residue (Spear
(1975b)).
The form of the model is:
(10a) dx/dt - -bx
(10b) dr/dt - cx - qr
where parathion residue is denoted by x and the paraoxon residue by r. The units
are in ng/cm2. The solution to this set of equations is:
(11a) x(t) - x0 exp{-bt)
(lib) r(t) - (cx0/b + q) [exp(-qt) - exp(-bt)]
where t is the time post-application in days.
13
-------
There are, then, four parameters required to solve for r(t), the paraoxon
residue, b, c, q, and the initial condition xo • The first three parameters are
weather dependent whereas the last depends on the application rates and pre-
existing levels of foliar dust on the trees. Nigg et al. (1978) have studied
the effect of weather variables on the parathion decay process and have concluded
that rainfall and leaf wetness from other sources are the primary determinants
of the rate of residue disappearance after the period immediately post
application. Hence, climatological variability was modeled by assuming that
the decay parameters, b, c, and q, are the same for all three regions but that
the paraoxon residue is diminished as an exponential function of the cumulative
rainfall during the decay period. Under these assumptions the rainfall-modified
paraoxon residue at entry time T is given by:
(12) r'(T) - r(T) exp(-.291CR)
where CR is the cumulative rainfall during the period (0,T). A one inch rainfall
leads to a diminution of the residue by 25 percent and a two inch rainfall a 44
percent decline. These predictions are more or less consistent with the data
presented by Gunther et al. (1977).
Estimates of the parameters b, c and d are available from Popendorf and
Leffingwell (1978) . Also, the initial condition, x0 was estimated from their
data by regressing their parameter a0 against the applied amount in pounds of
active ingredient per acre (AIA). The resulting expression is:
(13) x0 - 1690(AIA) -3067 ng/cm2
The values used for the other parameters are b - 0.8, c - 0.08 and q - 0.05.
Following the procedure detailed by Popendorf and Leffingwell (1982) the
14
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dermal dose in mg/kg is related to the paraoxon residue by the expression
kdr'(t)ta where te is the exposure time in hours and kd a constant determined
empirically and set equal to 9.0 as observed in citrus crops. The exposure time
is taken to be an eight hour shift. For a single organophosphate the relation
between dermal dose and fractional inhibition of red blood cell cholinesterase
(RBCD) is given by:
(14) RBCD - 1 - exp{-w,D/LD50)
where, for paraoxon, the dermal LD50 is 1.0 and we equals to 6.0, midway in the
reported range of 4.7 to 7.3. All members of a work crew are assumed to be
exposed to the same residue environment which is further assumed to result in
the same cholinesterase depression. Individual variability is modeled only in
the relationship between cholinesterase depression and clinical illness.
The relationship between cholinesterase depression and clinical signs and
symptoms of poisoning was modeled by assuming the probability of illness depended
on the degree of cholinesterase depression according to the expression:
(15) P - 1/[ 1 + exptWi + w2RBCD}]
where and w2 were based on clinical experience and values reported in the
medical literature (Midtling et al. (1985), Milby (1988)). Two sets of
parameters were used, one relating to mild illness and the other to severe
illness. The probability of illness relates to each member of the crew at the
end of one eight-hour day and not to exposures cumulated over several days.
V. Profit-Health Tradeoffs in Re-Entry Regulation
The models presented in the two preceding sections can be used to evaluate
15
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the impact of re-entry regulations on apple growers' revenues and apple
harvesters' safety. The analysis was conducted under the assumptions that a
flight of coddling moths arrives four days before the optimal harvest date t0
(i.e., t0 - ta - 4), that parathion is applied at a rate of 2.0 pounds of active
ingredient per acre, and that, as is typical, the crop produced on a 50-acre
block will be harvested in one day by a crew of 500 (10 workers per acre).
Losses in growers' revenues were compared to the risk of severe and mild
poisoning to each individual worker. Rainfall levels of 0, 0.5, 1, 1.5, and 2
inches during the re-entry period were used to take into account the differences
in weather conditions encountered in the different regions under investigation:
California receives virtually no rainfall during the harvest period, Washington
receives an average of 0.5 inches and Michigan receives an average of 1.5 inches
under normal conditions.
Table 1 shows the expected numbers of severe and mild parathion poisoning
cases under California, Washington and Michigan conditions, plus the fraction
of revenue lost due to harvest delays. The risk of poisoning is clearly non-
negligible: With a pre-harvest interval of four days or less, there will be an
average of 2.5 severe cases and 43 mild cases under California conditions, 1.6
severe and 29 mild cases under Washington conditions and 0.8 severe and 15 mild
cases under Michigan conditions. (At any given time, there will be almost 19
times as many mild as severe cases.) Each additional day entry is prohibited
reduces the number of mild and severe cases by about 13 percent, while each
additional inch of rainfall reduces them by about 75 percent. Even so, the risk
of poisoning remains non-negligible for a relatively lengthy period of time:
If re-entry is prohibited for as much as 2 weeks, there will still be an average
of one severe poisoning incident for roughly every 2 50-acre blocks harvested
16
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in California, one severe incident for every 3 50-acre blocks harvested in
Washington and one severe incident for every 4 50-acre blocks harvested in
Michigan.
At the same time, the losses imposed by re-entry regulation can be
considerable. Each additional day's delay in harvesting reduces total revenue
by about 0.24 percent, corresponding to $360 per 50-acre block in California,
$460 per 50-acre block in Washington and $395 per 50-acre block in Michigan.
By way of contrast, total harvesting labor costs amount to about $425 per 50-
acre. block in Washington (Hinman, Tukey and Hunter). A pre-harvest internal of
2 weeks would result in a revenue loss on the order of 2.5 percent; since profit
margins in Washington apple production range from 3 to 10 percent (Hinman, Tukey
and Hunter), such a loss would represent a sizable fraction of net income.
The optimal pre-harvest interval in each state (assuming equal social
welfare weights on farmers' incomes and workers' health) is determined by
equating the marginal cost of additional harvest delays in terms of revenue lost
with the marginal benefits associated with reductions in the number of poisoning
incidents. For illustrative purposes, we calculated these optimal pre-harvest
intervals under the conservative assumptions that benefits were restricted to
average avoided costs , that is, to the average costs of hospitalization plus
average lost wages. This ignores long-term losses due to chronic neurotoxic
effects, the value of the disutility of suffering poisoning, losses caused by
additional risks to consumers from residues remaining at the time of ingestion
and so on.
A typical severe parathion poisoning case typically requires 3 days of
hospitalization, with the first day spent in intensive care, followed by two
weeks of recovery, i.e., lost work time. Assuming average costs of $1200 per
17
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day for intensive care and $500 per day for a standard hospital bed implies total
hospitalization costs of $2200. Assuming an average wage of $10 per hour for
an 8-hour day implies total lost wages of $800, for a total cost of $3000 per
severe case (Becker (1988)).
A typical mild case requires no hospitalization; medical care will
typically cost about $40 per case and there will generally be 2 days of lost work
time, for a total cost of $200 per case (Becker (1988)).
Figures 1, 2 and 3 show the respective marginal costs and marginal benefits
from severe and all poisoning cases associated with different pre-harvest
intervals in California, Washington and Michigan. The optimal pre-harvest
intervals are 15 days in California, 12 days in Washington and 9 days in
Michigan. Current EPA regulations require 14 days regardless of rainfall
conditions for applications of parathion on apples such as the one considered
here. Interestingly, the current pre-harvest interval is quite close to the
optimal levels calculated here, although our calculations suggest the
desirability of greater conservatism under California conditions and less
conservatism under Michigan conditions. They also suggest that, as long as local
rainfall can be monitored effectively, the same levels of safety implicit in the
14-day pre-harvest interval can be achieved at lower cost by making the pre-
harvest interval dependent on rainfall. For example, lowering the pre-harvest
interval from 14 to 9 days when there have been 2 inches of rain would cut the
losses suffered by Michigan apple growers by $1944 per 50-acre block, almost 50
percent, while lowering it from 14 days to 12 days when there have been 0.5
inches of rain would cut the losses suffered by Washington growers by $904 per
50-acre block, almost 20 percent.
18
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VI. Conclusions
Public authorities frequently use quarantines to ensure public safety by
removing people from hazardous situations either in time or space. Individuals
may pursue similar strategies to enhance their own safety in dealing with
hazards. This paper develops a methodology for assessing the tradeoffs between
productivity or utility losses from this type of regulation and reductions in
risk of disease, accident or illness and applies it to the case of re-entry
regulation in pesticides. We show that this form of regulation provides a
rational incentive for prophylactic applications of pesticides, a practice that
has been much maligned in the pesticide literature. In an empirical evaluation
of pre-harvest intervals for parathion used on apples, we demonstrate that the
tradeoffs involved are quite substantial, that the optimal pre-harvest intervals
implied by rather conservative benefits estimates are quite close to those
actually set by the Environmental Protection Agency, and that the same level of
worker safety as that implicitly targeted by EPA can be achieved at lower cost
by making pre-harvest intervals dependent on rainfall.
In order to focus on the main issues in deriving tradeoffs from quarantine
parameter choices, the model used here is partial and rather stylized. Obvious
improvements include incorporating considerations such as: pest population
dynamics and intraseasonal effects; general equilibrium effects of re-entry
regulation on prices and the distribution of production; choice of amounts of
pesticides and harvest crew size as well as time of application; the influence
of stochastic factors such as weather and size and time of arrival of pest
populations; and uncertainties about residue decay, dermal absorption,
cholinesterase depression and clinical response. The results we obtain, however,
strongly suggest that more elaborate modeling of re-entry regulation and other
19
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forms of quarantine is well worthwhile.
Further research along these lines is especially necessary because
environmental and occupational health problems such as the one addressed here
are a growing policy concern. While policy advice has been monopolized by
natural scientists until recently, recognition of the fact that absolute safety
is often unattainable has led to an appreciation of the importance of evaluating
tradeoffs between'enhanced safety and other social goals. A key problem is that
thorough tradeoff assessments require close interdisciplinary cooperation in
modeling a full spectrum of economic, physical and biological processes beginning
with production and terminating in risks to health.1 While the difficulties of
organizing such interdisciplinary cooperation have meant that this sort of
modeling has been performed only seldom in the past, hopefully the work reported
here will demonstrate the feasibility and importance of pursuing it.
20
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VII . Footnotes
1 While economists have studied the links between pollution and health (as in
the voluminous literature on air pollution and health initiated by Lave and
Seskin) and between production and pollution (see for example, Anderson,
Opaluch and Sullivan), to our knowledge none have modeled the entire path from
production to pollution to health.
21
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VIII. References
Glen D. Anderson, James J. Opaluch and W. Michael Sullivan, "Nonpoint
Agricultural Pollution: Pesticide Contamination of Groundwater Supplies",
American Journal of Agricultural Economics 67:1238-1243, 1985.
Charles Becker, MD, Chief of Occupational Medicine, San Francisco General
Hospital, personal Communication, September 1988.
F.A. Gunther, Y. Iwata, G.E Carman and C.A. Smith, "The Citrus Reentry Problem:
Research on Its Causes and Effects, and Approaches to Its Minimization", Residue
Revi ew 67(1977) :1.
H.R. Hinman, R.B. Tukey and R.E. Hunter, "Estimated Cost of Production for a Red
Delicious Apple Orchard in Central Washington", Extension Bulletin 1159,
Washington State University, Pullman, WA, June 1982.
L. B. Lave and E. P. Seskin, Air Pollution and Human Health. Baltimore: Johns
Hopkins, 1977.
J.E. Midtling, P. Barnett, M. Coye et al. , "Clinical Management of Field Worker
Organophosphate Poisoning," Western J. of Medicine 142(1985), 514-518.
Thomas H. Milby, MD, formerly Chief, Bureau of Occupational Health, California
Department of Health Services and Adjunct Professor, School of Public Health,
University of California at Berkeley. Personal Communication, September 1988.
H.N Nigg, J.C. Allen, R.W. King, N.P. Thompson, G.J. Edwards and R.F. Brooks,
"Dislodgeable Residues of Parathion and Carbophenothion in Florida Citrus: A
Weather Model", Bulletin of Environmental Contamination and Toxicology 1 9 (1 978) :
578-588.
W.J. Popendorf and J.T. Leffingwell, "Natural Variations in the Decay and
Oxidation of Parathion Foliar Residues", Journal of Agricultural and Food
Chemistry, 26(1978): 437-441.
W.J. Popendorf and J.T. Leffingwell, "Regulating OP Pesticide Residues for
Farmworker Protection," Residue Reviews, 82(1982), 125-200.
R.C. Spear, W.J. Popendorf, J.T. Leffingwell et al., "Fieldworkers Response to
Weathered Residues of Parathion," Journal of Occupationa1 Medicine. 19(1977),
406-410.
R.C. Spear, W.J. Popendorf, J.T. Leffingwell and D. Jenkins, "Parathion Residues
on Citrus Foliage. Decay and Composition as Related to Worker Hazard",
Agricultural and Food Chemistry 23(1975): 808-810.
D.C. Staiff, S.W. Comer and R.J. Foster, "Residues of Parathion and conversion
Products on Apple and Peach Foliage Resulting from Repeated Spray Applications",
Bulletin of Environmental Contamination and Toxicology 14(1975): 135-139.
22
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TABLE 1
HEALTH RISKS AND REVENUE LOSSES UNDER ALTERNATIVE RE-ENTRY INTERVALS
Expected number of Expected number of Fraction of
Re-entry severe poisoninps mild poisonings revenue lost
interval
(days) California Washington Michigan California Washington Michigan
0-4
2.46050
1.63800
0.81650
42.6950 .
29.2650
15.0000
0
5
1.95600
1.33250
0.69i00
34.5800
24.0600
12.7600
0.002397
6
1.57650
1.09650
0.59100
28.2250
19.9600
10.9500
0.004788
7
1.28550
0.91250
0.51050
23.2450
16.7150
9.4850
0.007174
8
1.06000
0.76750
0.44520
19.3150
14.1300
8.2900
0.009554
9
0.88350
0.65250
0.39155
16.2050
12.0600
7.3050
0.011928
10
0.74500
0.56000
0.34725
•13.7200
10.3850
6.4900
0.014296
11
' 0.63400
0.48540
0.31045
11.7300
9.0250
5.8100
0.016659
12
0.54550
0.42450
0.27965
10.1200
7.9100
5.2350
0.019016
13
0.47340
0.37450
0.25370
8.8050
6.9900
4.7555
0.021368
14
0.41470
0.33315
0.23165
7.7300
6.2250
4.3460
0.023714
15
0.36960
0.29865
0.21290
6.8400
5.5900
3.9965
0.026054
16
0.32645
0.26970
0.19680
6.1050
5.0550
3.6965
0.028389
17
0.29305
0.24530
0.18295
5.4850
4.5995
3.4380
0.030718
18
0.26500
0.22450
0.17095
4.9515
4.2130
3.2135
0.033041
19
0.24125
0.20680
0.16000
4.5245
3.8825
3.0185
0.035359
20
0.22110
0.19155
0.15135
4.1495
3.5985
2.8480
0.037672
21
0.20385 •
0.17840
0.14335
3.8280
3.3530
2.6980
0.039978
22
0.18900
0.16700
0.13635
3.5515
3.1400
2.5660
0.042280
23
0.17620
0.15705
0.13010
3.3120
2.9540
2.4495
0.044575
24
0.16510
0.14835
0.12460
3.1040
2.7915
2.3465
0.046866
25
0.15540
0.14070
0.11970
2.9230
2.6485
2.2545
0.049150
26
0.14690
0.13400
0.11535
2.7640
2.5225
2.1725
0.051430
27
0.13945
0.12805
0.11145
2.6245
2.4110
2.0995
0.053704
28
0.12835
0.12275
0.10795
2.5010
2.3120
2.0340
0.055972
qt-tab.wp/dlw/12/23/88
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Figure 1
Optimal Re-Entry Interval in California
Marginal Benefits, Costs (Dollars)
3500
3000
2500
2000
1500
1000
500
I I I I I I i i i ? ? A-.
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Re-Entry Interval (Days)
Revenue Loss In OA -B-Severe Cases (CA) —All Cases (CA)
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Figure 2
Optimal Re-Entry Interval in Washington
Marginal Benefits.-Costs (Dollars)
2500
2000
1500
1000
500
Re-Entry Interval (Days)
+—Revenue Loss In WA Severe Cases (WA) -s-All Cases (WA)
-------
Figure 3
Optimal Re-Entry Interval In Michigan
Marginal Benefits, Costs (Dollars)
1000
800
600
200
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Re-Entry Interval (Days)
^-Revenue Loss in Ml -^-Severe Cases (Ml) —^— All Cases (Ml)
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VALUING REDUCED MORBIDITY:
A HOUSEHOLD PRODUCTION APPROACH*
Mark Dickie
Department of Economics
University of Georgia
Shelby Gerking
Department of Economics
University of Wyoming
May, 1989
This research was supported by the U.S. Environmental Protection Agency
under Cooperative Agreement #CR812054-01-2. It has not been subjected,
however, to the Agency's peer and administrative review and therefore it
does not necessarily reflect the views of the Agency, and no official
endorsement should be inferred. We thank Don Waldman for assistance and
advice concerning econometric procedures, Anne Coulson, Don Tashkin, and
John Demand for invaluable assistance in survey design and data
collection, Alan Krupnik, David Brookshire, Don Coursey, Don Kenkel, John
Tschirhart and seminar participants at Arizona State University for
comments on an earlier draft, and Alan Carlin for his patience and
encouragement throughout the project.
-------
ABSTRACT
This paper presents a unique application of the household production
approach to valuing public goods and nonmarket commodities. Technical
relationships are estimated between health attributes, private goods that
affect health, and air quality using panel data drawn from a special
survey. Statistical tests suggest that individuals equate marginal rates
of technical substitution in household production with relevant price
ratios. This result confirms that input choices are rational and is
critical for estimating values of health attributes and air pollution.
Value estimates obtained also bear on current questions facing
environmental policymakers.
-------
I. Introduction
Individuals frequently apply a household technology to combine public
and private goods in the production of nonmarket commodities for final
consumption. Hori (1975) demonstrates that in these situations, market
prices of private goods together with production function parameters may
encode enough information to value both public goods used as inputs and
nonmarket final consumption commodities. Although this valuation
methodology is objective and market based, it seldom has been applied for
three reasons. First, underlying technical relations either are unknown or
data needed to estimate them are unavailable. Second, even if relevant
technical information is at hand, the consumer's budget surface in
commodity space may not be differentiable when joint production and other
complicating factors are present. As a consequence, the commodity bundle
chosen is consistent with any number of marginal rates of substitution
between commodities and values of public goods and nonmarket commodities
remain unknown. Third, joint production and nonconstant returns to scale
also pose serious difficulties when taking the closely related valuation
approach of estimating the area behind demand curves for private goods
inputs and final consumption commodities (Bockstael and McConnell 1983) .
The problems posed by joint production are, troublesome because Pollak and
Wachter (1975) have argued that jointness is pervasive in home production,
and Graham and Green (1985) found empirical evidence of substantial
jointness in their estimation of a household technology.
This paper presents a unique application of the household production
approach to valuing public goods and nonmarket commodities which allows for
certain types of joint production and addresses key problems identified by
previous authors. Technical relationships are estimated between health
-------
attributes, private goods, and air quality. Data used in the analysis are
drawn from a special survey designed to implement the household production
approach. Econometric estimates allow for censored dependent variables and
cross-equation error correlations in panel data using tobit models with
individual-specific variance components. Wilcox-Gok (1983, 1985)
previously applied variance components estimation in a health context but
did not examine censoring and cross-equation correlation. Key results of
the present paper are: (1) attempts to value detailed attributes of
nonmarket home produced commodities may be ill-advised; however, estimating
a common value for a broadly defined category of attributes may be
possible, and (2) statistical tests support the hypothesis that individuals
equate marginal rates of technical substitution in household production
with relevant price ratios. The latter result confirms that input choices
are rational in the sense of Russell and Thaler (1985): choices are
consistent with utility maximization subject to a correct understanding of
the home technology. Also, value estimates obtained bear on current
questions concerning air pollution control policy. The Clean Air Act of.
1970 and its subsequent amendments focus primarily on health to justify
regulation and require air quality standards to protect even the health of
those most sensitive to pollution. The survey data are sufficiently rich
to allow separate value estimates for persons with normal respiratory
function and persons with chronic respiratory impairments.
The remainder of this paper is divided into four sections. Section II
describes a simple household production model in a health context and
reviews theoretical issues in obtaining value estimates. Section III
discusses the survey instrument and the data collected. Section IV
presents econometric estimates of production functions for health
-------
3
attributes, as well as values of better air quality and improved health for
both the normal and respiratory impaired subsamples. Implications and
conclusions are drawn out in Section V.
II. Preliminaries
The model specifies utility (U) as a function of market goods (Z) and
health attributes, called symptoms, (S) .
U = U(Z, S) (1)
For simplicity, Z is treated as a single composite good, but S denotes a
vector measuring intensity of n health symptoms such shortness of
breath, throat irritation, sinus pain, headache, or cough. Intensity of
th
the i symptom is reduced using a vector (V) of m additional private goods
that do not yield direct utility, a vector of ambient air pollution
concentrations (a), and an. endowment of health capital (f2).
S1 => sx(vf o; fl) i - 1, ... ,n (2)
Elements of V represent goods an individual might purchase to reduce
intensity of particular symptoms, and ft represents genetic predisposition
to experience symptoms or presence of chronic health conditions that cause
symptoms. Notice that equation (2) allows for joint production in that
some or all elements of V may (but do not necessarily) enter some or all
1
symptom production functions. The budget constraint is
I = P_Z + Z.P.V. (3)
2 J J J 1 J
where P^ denotes the price of Z, P^ denotes the price of V^., and I denotes
income.
Aspects of this general approach to modeling health decisions have
been used in the health economics literature (e.g., Grossman 1972;
Rosenzweig and Schultz 1982, 1983), where medical care is an example of V
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4
often considered. In these three papers, however, the stock of health
rather than symptoms is treated as the home produced good, and Grossman
treats decisionmaking intertemporally in order to analyze changes in the
health stock over time. A multiperiod framework would permit a more
complete description of air pollution's cumulative physiological damage,
but the present model's focus on symptoms of short duration suggests that a
one period model is appropriate. Moreover, long term panel data containing
both economic and health information necessary to assess cumulative
physiological damage are difficult to obtain.
Similar models also have been used in environmental economics to
derive theoretically correct methods for estimating values of air quality
and other environmental attributes (e.g., Berger et al. 1987, Courant and
Porter 1981; Harford 1984; Harrington and Portney 1987). These models,
however, only consider the case in which m = n = 1 and rule out the
possibility of joint production. In this situation, the marginal value of
or willingness to pay (WTP) for a reduction in air pollution can be derived
by setting dU = 0 and using first order conditions to obtain
= " UlSa/A = " PlSa/Sl (4)
where denotes marginal disutility of the symptom, S* denotes the
marginal effect of air pollution on symptom intensity, sj denotes the
marginal product of in reducing symptom intensity, and X denotes
marginal utility of income. As shown, marginal willingness to pay to
reduce symptom intensity (- U^/x) equals the marginal cost of doing so
(- Vs}).
Extensions to situations where m and n take on arbitrary values have
been considered in the theory of multi-ware production by Frisch (1965) as
well as in a public finance context by Hori (1975). Actually, Hori treats
-------
four types of household production technology. His case (3) involving
joint production appears to best characterize the application discussed in
Section IV because a single V may simultaneously reduce more than one
symptom. In this situation, a key result is that marginal values of
home produced commodities cannot be re-expressed in terms of market prices
and production function parameters unless the number of private goods is at
least as great as the number of commodities (m > n). Intuitively, if
m < n, the individual does not have a choice among some alternative
combinations of symptom intensities because there are too few choice
variables (V ) and the budget surface on which each chosen value of S~ must
2
lie is not dirferentiable.
Another perspective on this result can be obtained from the first
order conditions of the individual's utility maximization problem. After
substituting, the symptom production functions into the utility function,
the first order conditions include the budget constraint and
U - XP = o
z z
EiUiSj " APj = °' j - 1. .... n. (5)
The marginal value of a reduction in air pollution is a weighted sum of the
values of the individual symptom intensities (U^/A), where the weights are
the marginal products of pollution (S*): WTTq = - E^(U^/X)S^). Estimating
values for reductions in symptoms or pollutants on the basis of observable
behavior requires solving for the (U^/x) as functions of market prices of
private goods and production function parameters. Rearranging the m first
order conditions for the V gives
-------
6
i
u. A
p
l
6
m "
m
If m < n, the rank of the symptom technology matrix S
{S.} is at most m
and the system of equations in (6) is underdetermined. Intensity of one
symptom cannot be varied holding others constant, and the marginal value of
an individual symptom cannot be determined. On the other hand, if m = n
and the symptom technology matrix is nonsingular, then the rank is n and
unique solutions can be computed for the U A. If m > n and the technology
matrix has full rank, then the system is overdetermined, and values for the
ui/x can be computed from a subset of the first order equations.
This theoretical overview yields several ideas useful in empirical
application. First, if m > n and the household technology matrix has rank
n, then values of nonmarket commodities and public goods are calculated in
a relatively straightforward manner because utility terms can be
eliminated. Second, the possibility that men suggests that the household
production approach may be incapable of estimating separate values for a
comparatively large number of detailed commodities and that aggregation of
3
commodities may be necessary to ensure m > n. Third, even if m > n, the
household production approach may fail if there is linear dependence among
the rows of the technology matrix. Thus , statistical tests of the rank of
the matrix should be performed to ensure differentiability of the budget
surface. Fourth, if m > n, first order conditions impose constraints on
rejection of these constraints would
values that can be taken by the S
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7
imply that the outcome of the choice process is inconsistent with
utility-maximization subject to a known technology.
Fifth, if m > n, values of and P. need not yield positive values
J 3
for -U^/x, the marginal willingness to pay to reduce intensity of the
symptom. Of course, in the simple case where m = n = 1, the only
requirement is that >o. I f m = n = 2, a case considered in the
empirical work presented in Section IV, values of -U./A and -U0/.\ both will
1 /L
be positive only if (sj/s*) > (Pj/Pj) > (S^/S*). If Vj and V, are not
chosen such that their marginal rates of technical substitution bracket
their price ratio, then it is possible to reduce intensity of one symptom
without increasing intensity of the other and without spending more on
symptom reduction.
Sixth, complications arise in expressing symptom and air pollution
values in situations where some or all of the V, are sources of direct
]
utility, another form of joint production. This problem is important (and
it is encountered in the empirical work presented in Section IV) because of
the difficulty in identifying private goods that are purchased but do not
enter the utility function. To illustrate, assume that m = 2, n = 1 and
that V2 -but not is a source of both direct positive utility and symptom
relief. still would equal -(P^S^/sJ) and therefore could be
calculated without knowing values for marginal utility terms. If
consumption of Vhowever, was used as a basis for this calculation, the
simple formula would overestimate WTPC, by an amount equal to
"(^S^/ASo) where denotes marginal utility of V2 (U2 > 0) . When m and n
take arbitrary values the situation is more complex, but in general
nonmarket commodity and public good values can be determined only if the
number of private goods which do not enter the utility function is at least
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8
as great as the number of final commodities. Even if this condition is not
met, however, it is possible in some cases to determine whether the value
4
of nonmarket commodities and public goods is over- or underestimated.
Each of these six issues is treated in the empirical work reported in
Section IV. Although m = n = 2 and relevant marginal rates of technical
substitution generally bracket input price ratios, statistical tests cannot
reject the hypothesis that the technology matrix has rank one. After
aggregating symptoms into one broad category, m > n (2 > 1), and first
order conditions constrain the marginal rate of technical substitution to
equal the price ratio. Failure to reject the constraint confirms that
behavior is consistent with the model's predictions; nevertheless the
likely possibility that both private good inputs are direct sources of
utility suggests that the model's value estimates should be interpreted as
lower bounds.
Ill . Data
Data used to implement the household production approach were obtained
from a sample of 226 residents of two Los Angeles area communities. Each
respondent previously had participated in a study of chronic obstructive
respiratory disease (Detels et al. 1979, 1981). Key aspects of this sample
are: (1) persons with physician diagnosed chronic respiratory ailments
deliberately are overrepresented (76 respondents suffered from- such
diseases), (2) 50 additional respondents with self-reported chronic
cough or chronic shortness of breath are included, (3) 151 respondents
lived in Glendora, a community with high oxidant air Pollution and 75
respondents lived in Burbank, a community with oxidant pollution levels
more like other urbanized areas in the U.S. but with high levels of carbon
-------
9
monoxide, (4) all respondents either were nonsmokers or former smokers who
had not smoked in at least two years, and (5) all respondents were
household heads with full-time jobs (defined as at least 1,600 hours of
work annually).
professionally trained interviewers contacted respondents several
times over a 17 month period beginning in July 1985. The first contact
involved administration of an extensive baseline questionnaire in the
respondent's home. Subsequent interviews were conducted by telephone. "
Including the baseline interview, the number of contacts with each
respondent varied from three to six with an average number of contacts per
respondent of just over five. Of the 1147 total contacts (= 226 x 5), 644
were with respiratory impaired subjects (i.e., those either with
physician-diagnosed or self-reported chronic respiratory ailments) and 503
were with respondents having normal respiratory function.
Initial baseline Interviews measured four groups of variables: (1)
long term health status, (2) recently experienced health symptoms, (3) use
of private goods and activities that might reduce symptom intensity, and
(4) socioeconomic/demographic and work environment characteristics.
Telephone follow-up interviews inquired further about health symptoms and
use of particular private goods. Long term health status was measured in
two ways. First, respondents indicated whether a physician ever had
diagnosed asthma (ASTHMA) , chronic bronchitis (BRONCH), or other chronic
respiratory disease such as emphysema, tuberculosis, or lung cancer.
Second, they stated whether they experience chronic shortness of breath or
wheezing (SHRTWHZ) and/or regularly cough up phlegm, sputum, or mucous
(FLEMCO) . Respondents also indicated whether a physician ever had
-------
10
diagnosed hay fever (HAYFEV); however, this condition was not treated as
indicative of a chronic respiratory impairment.
Both background and follow-up instruments also asked which, if any, of
26 health symptoms were experienced in the two days prior to the interview.
Symptoms initially were aggregated into two categories defined as: (1)
6
chest and throat symptoms and (2) all other symptoms. Aggregation to two
categories reduces the number of household produced final goods (n)
considered; however, assigning particular symptoms to these categories
admittedly is somewhat arbitrary. Yet, the classification scheme selected
permits focus on a group of symptoms in which there is current policy
interest. Chest and throat symptoms identified have been linked to ambient
ozone exposure (see Gerking et al. 1984, for a survey of the evidence) and
federal standards for this air pollutant currently are under review.
Moreover, multivariate tobit turns out to be a natural estimation method
and aggregating symptoms into two categories permits a reduction in
computation burden. Dickie et al. (1987(a)) report that respondents with
chronic respiratory impairments experienced each of the 2 6 individual
symptoms more often than respondents with normal respiratory function.
This outcome is reflected in Table 1 which tabulates frequency
distributions of the total number of chest and throat and other symptoms
reported by respondents in the two subsamples.
In the empirical work reported in Section IV, data on the number of
symptoms reported are assumed to be built up from unobserved latent
variables measuring symptom intensity. As intensity of a particular
symptom such as cough rises above a threshold, the individual reports
having experienced it; otherwise he does not. Thus , the frequency
distribution tabulated in Table 1 merely reflects the number of symptoms
-------
11
that crossed the intensity threshold in the two days prior to the
interview.
Private goods used to estimate symptom production functions include
durable goods which may relieve symptoms by reducing exposure to air
pollution. When asked during the baseline interview whether they changed
their activities at all when the air was smoggy, half the respondents in
the impaired group and 42 percent of the respondents in the normal group
reported that they tried to stay indoors and/or run their air conditioners
more in an attempt to avoid the pollution. The effectiveness of such a
strategy depends on the quality of the indoor air, which in turn depends
partly on whether the respondent has and uses the following private goods:
(1) central air conditioning in the home (ACCEN) , (2) an air purifying
system in the home, and (3) a fuel other than natural gas for cooking
g
(NOTGASCK) . Similarly, a respondent who has and used air conditioning in
the automobile (ACCAR) might reduce exposure to pollution, particularly
when driving or idling in traffic. Each of these private goods may provide
direct utility in addition to reducing exposure to pollution. Air
conditioners, for example, may provide not only relief from symptoms but
also cooling services that yield direct satisfaction. This problem is
discussed further in Section V.
Socioeconomic/demographic variables measured whether the respondent
lived in Burbank or Glendora (BURB) as well as years of age (AGE), gender,
race (white or nonwhite), marital status, and household income. Also,
respondents were asked whether they were exposed to toxic fumes or dust
while at work (EXPWORK).
Finally, each contact with a respondent was matched to measures of
ambient air pollution concentrations, humidity, and temperature for that
-------
12
day. Air monitoring stations used are those nearest to residences of
respondents in each of the two communities. Measures were obtained of the
six criteria pollutants for which national ambient air quality standards
have been established: carbon monoxide (CO), nitrogen dioxide (N02), ozone
(03), sulfur dioxide (S02), lead and total suspended particulate.
Readings for lead and particulate, however, only were available for about
ten percent of the days during the study period, forcing exclusion of those
pollutants from empirical work. Each of the remaining four pollutants were
measured as maximum daily one-hour ambient concentrations. Maxima are used
because epidemiological and medical evidence suggests that acute symptoms
may be more closely related to peak than to average pollution
concentrations. The air pollution variables entered then, are averages of
one hour maxima on the two days prior to the interview so as to conform
Q
with the measurement of symptoms. " Temperature and relative humidity data
similarly were averaged across two day periods.
IV. Estimates of Household Symptom Technology
This section reports estimated production functions, hypothesis tests,
and estimated values of public goods and nonmarket commodities. A
bivariate tobit model with variance components was developed to account
for: (1) probable correlation of disturbances across production functions,
(2) censoring of reported symptoms at zero, and (3) repeated observations
10
of the same individuals at different times. Both tobit and variance
components models frequently are applied; however, as discussed by Maddala
(1987), there have been few applications of tobit with variance components
to panel data.
-------
Empirical estimates of household production functions for health also
have been obtained by Rosenzweig and Schultz (1983)^ and variance
components models have been applied to health production by Wilcox-Gok
12
(1983, 1S85) ; however, neither of these investigators focus on valuing
nonmarket commodities and public goods. Rosenzweig and Schultz consider
birthweight rather than symptoms and Wilcox-Gok examines days missed from
usual activities due to illness or injury and visits to certain health care
facilities. Although the dependent variables used by Wilcox-Gok would
appear to be correlated and censored at zero, the estimation procedures
employed by Wilcox-Gok did not correct for either problem. In contrast,
the bivariate tobit model presented below allows for both censoring and
cross-equation error correlation.
The symptom production functions are specified as
'SA + *iht « v. + c.ht > 0 ^
0 otherwise
1 - 1, 2.
In equation (7) , i denotes type of symptom (chest and throat = 1, other
2), h denotes respondent, and t denotes time; S^t represents the number of
symptoms reported and is a vector including explanatory variables such
as measures of health capital, private goods, and air pollutants.
Random disturbances consist of the sum of a transitory component and a
permanent component common to both production functions
eiht " "h + ''iht i - 1. 2 (8)
The transitory error components, capture unmeasured influences that
vary over individuals, symptoms, or time. The permanent error component,
uh, varies only over individuals, capturing unmeasured individual specific
influences that persist over time. The assumption that the same permanent
-------
14
component enters both production functions results in computational savings
and is at least plausible, since the same individual produces both
categories of symptoms.
Permanent components are assumed normally and independently
n
distributed with mean zero and variance cr~. Transitory components are
assumed normally and independently distributed, conditional on the
2
permanent component, with mean zero and variance ct_. , 1 = 1, 2. Despite the
common permanent component, the correlation coefficient between the two
2 , 2 f l 9 *> 1
symptom classes in the same time period, +cp (a + , is
distinct from the correlation coefficient between the same symptom class at
2 2 2
different times, cr^/+ o^), i = 1, 2.
Let Fiht and f iht rePresent' respectively, the normal distribution and
density functions evaluated at (S^t - conditional on
The log-likelihood function is
L - Ehln / M • i *0 «iht1S(l,)du i«S
ht ht
13
where g(0 is the normal density.
An alternative to the variance components or random effects model is
the fixed effects model in which the are treated as fixed constants
rather than as random variables. Two arguments can be made in favor of the
14
random effects specification of the symptom production model.
First, treating the as constants subsumes the effects of all
individual specific, time invariant variables into the fixed effects.
Since the private goods measured in the data are fixed during the sampling
period, using the fixed effects model would make it impossible to identify
the production function parameters (S^) necessary to estimate values for
reductions in symptoms and air pollutants. Similarly, estimating the
-------
15
separate effects for the various chronic health impairment variables is of
some interest, but these effects could not be distinguished from the y^ in
the fixed effects specification.
The second argument in favor of random effects rests on the
inconsistency of the fixed effects tobit estimator. The individual effects
cannot be estimated consistently for a small number of time periods even
as the number of individuals increases without bound. Intuitively, each
individual brings to the sample a distinct y^> with the result that
increasing the number of individuals fails to increase the information
available to estimate the y^. In many nonlinear models, including tobit,
fixed effects estimators for the remaining parameters cannot be derived
independently of the y^, so that the entire set of parameters is estimated
inconsistently. By contrast, the random effects model attempts to estimate
only the mean and variance of the y^ rather than the individual effects
themselves and thus can estimate the slope coefficients of the model
consistently.
While these arguments present a compelling case for the random effects
model, biased estimation can result because the model ignores the
correlation that may exist between the explanatory variables and the
permanent error component (see, e.g., Mundlak 1978). For example, if an
individual knows his own y^> utility maximization would imply that his
choice of private goods depends on A solution to this problem proposed
for probit models by Chamberlain (1980) is to specify y^ as a linear
function of the individual's explanatory variables plus an orthogonal
residual: + nh> where includes the individual's entire time
series of observations on explanatory variables. This auxiliary regression
then could be substituted for y^ in the specification of the symptom
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16
production functions, and the likelihood derived by integrating over the
density of n rather than the density of p. But owing to the lack of
temporal variation in all explanatory variables except the measures of
pollution and weather, the substitution would produce collinearity in the
matrix of explanatory variables as each time-invariant variable in the
auxiliary regression above would be perfectly collinear with its
counterpart already included in the model specification. As a consequence,
Chamberlain's approach was not pursued.
An alternative approach to correct for correlation between covariates
and errors is analogous to the two stage least squares procedure employed
by Rosenzweig and Schultz in their previously cited birthweight study. In
the first stage, reduced form probit demand equations for each of four
private goods (ACHOME, ACCAR, APHOME, NOTGASCK) are estimated.15 In the
second stage, predicted probabilities from the reduced form probits were to
be used as instruments for private goods in the tobit symptom production
function models, but explanatory power of the reduced form probit equations
was very poor. In half of the equations for each subsample the null
hypothesis that all slope coefficients jointly are zero could not be
rejected at the 5 percent level and in all equations key variables such as
household income had insignificant and often wrongly signed coefficients.
Another problem is the absence of private good price data specific to each
respondent. The original survey materials requested these data but after
pretesting, this series of questions was dropped because many respondents
often made purchases jointly with 3 house or car and were unable to provide
even an approximate answer. As a consequence, two-stage estimation was not
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17
pursued further with the likely outcome that estimates of willingness to
pay for nonmarket commodities and public goods may have a downward bias.
Tables 2 and 3 present illustrative symptom production function
estimates for impaired and normal subsamples. Equations presented are
representative of a somewhat broader range of alternative specifications
available from the authors on request. The overall explanatory power of
the model was evaluated by testing the null hypothesis that all estimated
coefficients (excepting the constant terms) jointly are zero. A Likelihood
ratio tests rejects this hypothesis for both subsamples at significance
levels less than one percent. Also, estimates of the individual specific
error components, denoted a , have large asymptotic t-statistics which
confirms persistence of unobserved personal characteristics that affect
symptoms.
Table 2 shows that chronic health ailments and hay fever are
positively related to symptom occurrence among members of the impaired
group. Coefficients of ASTHMA, BRONCH, SHRTWHZ, and HAYFEV are positive in
equations for both chest and throat and other symptoms and have associated
asymptotic t-statistics that range from 2.1 to 7.6. The coefficient of
FLEMCO is positive and significantly different from zero at conventional
levels in the chest and throat equation, but its asymptotic t-statistic is
less than unity in the equation for other symptoms. The coefficient of AGE
was not significantly different from zero in either equation and the
EXPWORK variable was excluded because of convergence problems with the
16
bivariate tobit algorithm. Variables measuring gender, race, and marital
status never were included in the analysis because 92 percent of the
impaired respondents were male, 100 percent were white, and 90 percent were
married. Residents of Burbank experience chest and throat symptoms with
-------
18
less frequency than do residents of Glendora. Of course, many possible
factors could explain this outcome; however, Burbank has had a less severe
long term ambient ozone pollution problem than Glendora. For example, in
1986 average one day hourly maximum ozone readings in Burbank and Glendora
were 8.7 pphm and 10.2 pphm, respectively, and a similar difference in
ozone readings has persisted at least since 1983.
With respect to private and public inputs to the symptom production
functions, the coefficient of ACCAR is negative and significantly different
from zero at the 10 percent level using a one tail test in the other
symptoms equation, while the coefficient of ACCEN is negative and
significantly different from zero at the 5 percent level using a one tail
test in both equations. Results from estimated equations not presented
reveal that NOTGASCK and use of air purification at home never are
significant determinants of symptoms in the impaired subsample. Also, 03,
CO, and N02 exert insignificant influences on occurrence of both types of
symptoms. When four air pollution variables were entered, collinearity
between them appeared to prevent the maximum likelihood algorithm from
converging. Consequently, S02 was arbitrarily excluded from the
specification presented and the three air pollution measures included as
covariates should be interpreted as broader indices of ambient pollutant
concentrations. Variables measuring temperature and humidity were excluded
from the Table 2 specification; but in equations not reported their
coefficients never were significantly different from zero.
Table 3 presents corresponding symptom production estimates for the
subsample with normal respiratory function. HAYFEV is the only health
status variable entered because ASTHMA, BRONCH, SHRTWZ, and FLEMCO were
used to define the impaired subsample. Coefficients of HAYFEV are positive
-------
19
in equations for both chest and throat and other symptoms and have
t-statistics of 1.61 and 1.87, respectively. Coefficients of BURB are
negative; but in contrast to impaired subsample results, they are not
significantly different from zero at conventional levels. AGE and EXPWORK
enter positively and their coefficients differ significantly from zero at
2\ percent in the other symptoms equation. Among private goods entering
the production functions, coefficients of APHOME and ACHOME never were
significantly different from zero at conventional levels, and these
variables are excluded from the specification in Table 3. Use of air
conditioning in an automobile reduced chest and throat symptom occurrences
and cooking with a fuel other than natural gas (marginally) reduces other
symptoms. Variables measuring gender, race, and marital status again were
not considered as the normal subsample was 94 percent male, 99 percent
white, and 88 percent married. In the normal subsample, collinearity and
algorithm convergence problems again limited the number of air pollution
variables that could be entered in the same equation. As shown in Table 3,
03, CO and N02 coefficients had associated t-statistics of 1.16 or
smaller. Temperature and humidity variables are excluded from the
specification shown in Table 3. In alternative specifications not
reported, coefficients of these variables never were significantly
different from zero in alternative equations not reported.
Three pieces of information are required to use the estimates in
Tables 2 and 3 in the calculation of values for reductions in symptoms and
air pollutants: (1) marginal effects of air pollutants on symptoms, (2)
marginal effects of private goods on symptoms, and (3) prices of private
goods . Marginal products were defined as the effect of a small change in a
good on the expected number of symptoms. Computational formulae were
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20
developed extending results for the tobit model (see McDonald and Moffit
1980) to the present context which allows for variance components error
structure. However, because private goods are measured as dummy variables
and, therefore, cannot be continuously varied, incremental, rather than
marginal, products are used.
The final elements needed to compute value estimates are the prices of
private goods. Dealers of these goods in the Burbank and Glendora areas
were contacted for estimates of initial investment required to purchase the
goods , average length of life, scrap value (if any), and fuel expense.
After deducting the present scrap value from the initial investment, the
net initial investment was amortized over the expected length of years of
life. Adding annual fuel expense yields an estimate (or range of
estimates) of annual user cost of the private good. The annual costs then
17
were converted to two-day costs to match the survey data. The dependent
variables used in the estimated equations do not distinguish between one-
and two-day occurrences of symptoms, but approximately one-half of the
occurrences were reported as two day occurrences. As a consequence, the
value estimates obtained were divided by 1.5 to convert to daily values.
Two tests were performed prior to estimating values of symptom and air
pollution reduction. First, calculations were made for both normal and
impaired subsamples to ensure that relevant ratios of incremental products
of private goods in reducing symptoms bracketed the corresponding price
ratio. Recall from the discussion in Section II that this condition
guarantees that value estimates for reducing both types of symptoms are
positive. A problem in making this calculation is that estimates of
incremental rates of technical substitution vary across individuals
(incremental products are functions of individual characteristics), but no
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21
respondent specific price information is available. As just indicated,
dealers in Glendora provided the basis for a plausible range of prices to
be constructed for each good. If midpoints of relevant price ranges are
used together with incremental rates of technical substitution taken from
Tables 2 and 3, the bracketing condition is met for all 100 respondents in
the normal subsample and 117 of 126 respondents in the impaired subsample.
Of course, alternative price ratios selected from this range meet the
bracketing condition for different numbers of respondents.
Second, possible singularity of the symptom technology matrix was
18
analyzed using a Wald test (see Judge et al. 1985, p. 215 for details).
In the context of estimates in Tables 2 and 3, the distribution of the test
statistic (X) is difficult to evaluate because relevant derivatives are
functions of covariate values and specific to individual respondents.
However, if derivatives are evaluated in terms of the underlying latent
variable model, they can be expressed in terms of parameters only and A is
2
distributed as x with 1 degree of freedom. Adopting this simpler
approach, p-values for the Wald test statistic are large: p = .742 for the
impaired subsample equations and p = .610 for the normal subsample
19
equations. As a consequence, the null hypothesis of singularity of the
symptom technology matrix is not rejected at conventional levels. This
result suggests that in both subsamples, there does not appear to be an
independent technology for reducing the two types of symptoms, budget
constraints are nondifferentiable, and separate value estimates for
chest and throat and other symptoms should not be calculated.
A common value for reducing chest and throat and other symptoms still
can be obtained by aggregating the two categories and re-estimating
production functions in a univariate tobit framework. Table 4 shows
-------
results based on using the same covariates as those reported in Tables 2
and 3 and retaining the variance components error structure. The Table 4
equations also make use of a constraint requiring that if m > n = 1, the
marginal rate of technical substitution must equal the input price ratio to
insure that values of marginal willingness to pay to avoid a symptom must
be identical no matter which private good is used as the basis for the
calculation. In the case where m = 2 and n = 1, as discussed in Section
II this single value is -Uj/X = -(P^sj) = -(P^/S*). In the impaired
subsample, the restriction can be tested under the null hypothesis,
H0 : SACCAR = ^PACCAR/PACHOME^ BACHOME' where the are coefficients of
ACCAR and ACHOME in the latent model and the P^ are midpoints from the
estimated range of two day prices for the private goods. In corresponding
notation, the null hypothesis to test in the normal subsample is,
H0 : 6ACCAR = ^ACCAR^NOTGASCK^NOTGASCK' Both hyPotheses are tested
against the alternative that coefficients of private qoods are
unconstrained parameters, using a likelihood ratio test.
P-values for the parameter restrictions are comparatively large;
P = .623 in the impaired subsample and P = .562 in the normal subsample.
Thus , the above null hypotheses are not rejected at conventional
significance levels. This result supports a critical implication of the
previously presented household production model, namely that individuals
equate marginal rates of technical substitution in production with relevant
price ratios. Moreover, coefficients of private good variables defined
under the null hypotheses for the two subsamples have t-statistics
exceeding two in absolute value. Performance of remaining variables is
roughly comparable to the bivariate tobit estimates. A notable exception,
however, is that in the normal subsample univariate tobit estimates,
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23
coefficients of 03 and N02 are positive with t-statistics exceeding 1.6.
This outcome suggests that persons with normal respiratory function tend to
experience more symptoms when air pollution levels are high, whereas those
with impaired respiratory function experience symptoms with such regularity
that there is no clear relationship to fluctuations in air quality.
Intensity of particular symptoms may be greater in both subsamples when
pollution levels are high, but this aspect is not directly measured.
Table 5 presents estimates of marginal willingness to pay to avoid
symptoms and to reduce two air pollutants. Unconditional values of
relieving symptoms and reducing air pollution are calculated for each
respondent from observed univariate tobit models. Table 5 reports the
mean, median, and range of respondents' marginal willingness to pay to
eliminate one health symptom for one day as well as mean marginal
willingness to pay to reduce air pollutants by one unit for one day for the
normal subsample. Symptom reduction values range from $0.81 to $1.90 in
the impaired subsample and from $0.49 to $1.22 in the normal subsample with
means of $1.12 and $0.73 in the two subsamples, respectively. ^ Also ,
values of willingness to pay to reduce one hour daily maximum levels of 03
and N02 by one part per ten million are $0.31 and $0.91 in the normal
subsample. Corresponding calculations are not reported for the impaired
subsample because, as shown in Table 4, coefficients of air pollution
variables are not significant at conventional levels.
V. Conclusion
Willingness to pay values of symptom reduction and air quality
improvement just presented should be viewed as illustrative approximations
for two reasons. First, private goods used in computing the estimates are
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24
likely to be direct sources of utility. Second, symptom experience and
private good purchase decisions are likely to be jointly determined.
Nevertheless, these estimates still are of interest because aspects of
joint production are taken into account. A key finding is that independent
technologies for home producing symptoms are difficult to identify, thus
greatly limiting the number of individual symptoms for which values can be
computed. In fact, the 26 symptoms analyzed here had to be aggregated into
a single group before willingness to pay values could be computed.
This outcome appears to have implications for estimating willingness
to pay for nonmarket commodities in other contexts. An obvious example
concerns previous estimates of willingness to pay to avoid health symptoms.
Berger et al. (1987) report one day willingness to pay values for
eliminating each of seven minor health symptoms, such as stuffed up
sinuses, cough, headache and heavy drowsiness that range from $27 per day
to $142 per day. Green et al. (1978) present estimates of willingness to
pay to avoid similarly defined symptoms ranging from $26 per day to $79 per
day. In both studies, however, willingness to pay estimates were obtained
symptom by symptom in a contingent valuation framework that ignores whether
independent technologies are available to produce each. Thus, respondents
simply may have lumped total willingness to pay for broader health concerns
onto particular symptoms. Some respondents may also have inadvertently
stated their willingness to pay to avoid symptoms for periods longer than
one day.
Another example relates to emerging research aimed at splitting
willingness to pay to reduce air pollution into health, visibility, and
possibly other components. From a policy standpoint, this line of inquiry
is important because the Clean Air Act and its subsequent amendments focus
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25
primarily on health and give less weight to other reasons why people may
want lower air pollution levels. Analyzing location choice within
metropolitan areas, for example, may not provide enough information to
decompose total willingness to pay into desired components. Instead,
survey procedures must be designed in which respondents are either reminded
of independent technologies that can be used to home produce air pollution
related goods or else confronted with believable hypothetical situations
that allow one good to vary while others are held constant.
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26
REFERENCES
Bartik, T. J., "Evaluating the Benefits of Non-marginal Reductions in
Pollution Using Information on Defensive Expenditures," Journal of
Environmental Economics and Management (March 1988), 111-127.
Berger, M. C., G. C. Blomquist, D. Kenkel, and G. S. Tolley, "Valuing
Changes in Health Risks: A Comparison of Alternative Measures,"
Southern Economic Journal 53 (April 1987), 967-984.
Berndt, E. R., B. H. Hall, R. E. Hall, and J. A. Hausman, "Estimation
and Inference in Nonlinear Structural Models," Annals of Economic and
Social Measurement 3 (October 1974), 653-665.
Bockstael, N., and R. McConnell, "Welfare Measurement in the Household
Production Framework," American Economic Review 73 (September 1983),
806-814.
Chamberlain, G., "Analysis of Covariance with Qualitative Data," Review of
Economic Studies 47 (1980), 225-238.
Chestnut, L., and D. Violette, Estimates of Willingness to Pay for
Pollution-Induced Changes in Morbidity: A Critique for Benefit Cost
Analysis of Pollution Regulation, EPA-68-01-6543 (1984).
Courant, P. N., and R. C. Porter, "Averting Expenditure and the Cost of
Pollution," Journal of Environmental Economics and Management 8
(December 1981), 321-329.
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Detels, R., S. Rokaw, A. Coulson, D. Tashkin, J. Sayre, and F. Massey, Jr.,
"The UCLA Population Studies of Chronic Obstructive Respiratory
Disease I. Methodology," American Journal of Epidemiology 109 (1979),
33-58.
Detels, R., J. Sayre, A. Coulson, et al., "The UCLA Population Studies of
Chronic Obstructive Respiratory Disease IV. Respiratory Effects of
Long Term Exposure to Photochemical Oxidants," American Review of
Respiratory Disease 124 (1981), 673-68(30
Dickie, M., S. Gerking, G. McClelland, and W. Schulze, "Valuing
Morbidity: An Overview and State of the Art Assessment," Volume I of
Improving Accuracy and Reducing Costs of Environmental Benefit
Assessments, U.S. Environmental Protection Agency, Cooperative
Agreement #CR812054-01-2, December 1987(a).
Dickie, M., S. Gerking, W. Schulze, A. Coulson, and D. Tashkin, "Value
of Symptoms of Ozone Exposure: An Application of the Averting
Behavior Method," Volume II of Improving Accuracy and Reducing Costs
of Environmental Benefit Assessments, U.S. Environmental Protection
Agency, Cooperative Agreement #CR812054-01-2, December 1987(b).
Frisch, R., Theory of Production (Chicago: Rand McNally & Company, 1965).
Gerking, S., A. Coulson, W. Schulze, D. Tashkin, D. Anderson, M. Dickie,
and D. Brookshire, "Estimating Benefits of Reducing Community
Low-Level Ozone Exposure: A Feasibility Study," Volume III of
Experimental Methods for Assessing Environmental Benefits, U.S.
Environmental Protection Agency, Cooperative Agreement
#CR-811077-01-0, September 1984.
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28
Graham, J. W., and C. A. Green, "Estimating the Parameters of a Household
Production Function With Joint Products," Review of Economics and
Statistics 66 (May 1984), 277-282.
Green, A. E. S., S. V. Berg, E. T. Loehman, M. E. Shaw, R. W. Fahien,
R. H. Hedinger, A. A. Arroyo, and V. H. De, An Interdisciplinary
Study of the Health, Social and Environmental Economics of Sulfur
Oxide Pollution in Florida, Interdisciplinary Center for Aeronomy and
(other) Atmospheric Sciences, University of Florida, Gainesville,
Florida, 1978.
Gregory, A. W., and M. R. Veall, "Formulating Wald Tests of Nonlinear
Restrictions," Econometrica 53 (November 1985), 1465-1468.
Grossman, M., "On the Concept of Health Capital and the Demand for Health,"
Journal of Political Economy 80 (March 1972), 223-255.
Harford, J. D., "Averting Behavior and the Benefits of Reduced Soiling,"
Journal of Environmental Economics and Management 11 (September 1984),
296-302.
Harrington, W., and P. R. Portney, "Valuing the Benefits of Health and
Safety Regulation," Journal of Urban Economics 22 (July 1987),
101-112.
Hori, H., "Revealed Preference for Public Goods," American Economic Review
65 (December 1975), 947-954.
Hsiao, C., Analysis of Panel Data (Cambridge: Cambridge University Press,
1986).
Judge, G. G., W. E. Griffiths, R. C. Hill, H. Lutkepohl, and T. C. Lee,
The Theory and Practice of Econometrics, 2nd Edition (New York: John
Wiley and Sons, 1985).
-------
Maddala, G. S., "Limited Dependent Variable Models Using Panel Data,"
Journal of Human Resources 22 (Summer 1987), 307-338.
McDonald, J. F., and R. A. Moffit, "The Uses of Tobit Analysis," Review of
Economics and Statistics 62 (May 1980), 318-321.
Mundlak, Y., "On the Pooling of Time Series and Cross-Section Data,"
Econometrica 46 (January 1978), 69-85.
Pollak, R. A., and M. L. Wachter, "The Relevance of the Household
Production Function Approach and Its Implications for the Allocation
of Time," Journal of Political Economy 83 (April 1975), 255-277.
Rosenzweig, Y. R., and T. P. Schultz, "The Behavior of ^Mothers as Inputs
to Child Health: The Determinants of Birth Weight, Gestation, and
Race of Fetal Growth," in Victor R. Fuchs (ed.), Economic Aspects of
Health (Chicago: The University of Chicago Press, 1982).
Rosenzweig, M. R., and T. P. Schultz, "Estimating a Household Production
Function: Heterogeneity, the Demand for Health Inputs, and Their
Effects on Birth Weight," Journal of Political Economy 91 (October
1983), 723-746.
Samuelson, P. A., "The Pure Theory of Public Expenditures," Review of
Economics and Statistics 36 (November 1954), 387-389.
Wilcox-Gok, V. L., "The Determination of Child Health: An Application of
Sibling and Adoption Data," Review of Economics and Statistics 65 (May
1983), 266-273.
Wilcox-Gok, V. L., "Mother's Education, Health Practices and Children's
Health Needs: A Variance Components Model," Review of Economics and
Statistics 67 (November 1985), 706-710.
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30
FOOTNOTES
1
Another, possibly troublesome, aspect of joint production occurs if
some or all elements of V are arguments in the utility function. This
complication is discussed momentarily.
2
Hori identifies three sources of nondifferentiability of the budget
surface under joint production. The first occurs if the number of private
goods is less than the number of commodities. The second arises because of
nonnegativity restrictions on the private goods. This is not treated
directly in the present paper, but if each private good is purchased in
positive quantities, the chosen commodity bundle will not lie at the second
type of kink. Hori's third cause of nondifferentiability implies linear
dependence among the rows of the technology matrix, a possibility
considered below.
3
Notice that this point on aggregation may apply to other valuation
methods as well. Using contingent valuation surveys, for example, Green et
al. (1978) and Berger et al. (1987) obtained value estimates of several
specific symptoms; however, issues relating to existence of independent
symptom technologies never was faced. Future contingent valuation surveys
may do well to consider this point prior to eliciting estimates of
willingness to pay.
4
For example, suppose m = n = 2 and both private goods are direct
sources of utililty. If equation (6) is used to solve for the U./A, then:
(1) if the two marginal rates of technical substitution (MRTS) do not
bracket the price ratio, then the value of the commodity whose
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31
MRTS is closer in magnitude to the price ratio will be overestimated,
while the value of the other commodity will be underestimated; (2) if
the two MRTS values do bracket the price ratio, then the value of
either one or both of the commodities will be overestimated; and (3)
in no case will the value of both commodities be underestimated.
s
Both questionnaires are presented and extensively discussed m Volume
II of Dickie et al. (1987(b)).
6
Chest and throat symptoms include (1) cough, (2) throat irritation,
(3) husky voice, (4) phlegm, sputum or mucous, (5) chest tightness, (6)
could not take a deep breath, (7) pain on deep respiration, (8) out of
breath easily, (9) breathing sounds wheezing or whistling. Other symptoms
are (1) eye irritation, (2) could not see as weH as usual, (3) eyes
sensitive to bright light, (4) ringing in ears (5) pain in ears, (6) sinus
pain, (7) nosebleed, (8) dry and painful nose, (9) runny nose, (10) fast
heartbeat at rest, (11) tired easily, (12) faintness or dizziness, (13)
felt spaced out or disoriented, (14) headache, (15) chills or fever, (16)
nausea, and (17) swollen glands.
An alternative to counting the number of different symptoms
experienced in the two days prior to the interview would be to consider the
number of symptom/days experienced. Both approaches were used to construct
empirical estimates; however, to save space, only those based on counts of
different symptoms are reported. Both approaches yield virtually identical
value estimates for symptom and air pollution reduction.
8
Cooking with a fuel other than natural gas reduces exposure because
gas stoves emit nitrogen dioxide.
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32
9
The equations also were estimated after defining the pollution
variables as the largest of the one hour maxima on the two days; similar
results were obtained.
10
Although there is a linear relationship between the latent dependent
variables and the private goods in the tobit model, the relationship
between the observed dependent variables and the private goods has the
usual properties of a production function. The expected number of
symptoms is decreasing and convex (nonstrictly) in the private goods.
11
Rosenzweig and Schultz also initially specify their production
functions in translog form and then test whether restrictions to CES and
Cobb-Douglas forms are justified. This type of analysis is not pursued
here as most of the covariates used are 0-1 dummy variables. Squaring
these variables does not alter their values. Interaction variables of
course, still could be computed.
12
Wilcox-Gok used variance components to control for family-specific
effects in pooled sibling data rather than for individual-specific effects
in pooled cross section-time series data.
13
The tobit coefficients and variances of the model are estimated by
maximizing the likelihood function using the method of Berndt, Hall, Hall,
and Hausman (1974). The score vectors are specified analytically and the
information matrix is approximated numerically using the summed outer
products of the score vectors. Starting values for the coefficients and
the standard deviations of the transitory error components were obtained
from two independent tobit regressions with no permanent error component.
In preliminary runs a starting value of unity was used for the standard
deviation of the permanent error component, but the starting value was
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33
adjusted to 1.5 after the initial estimate was consistently greater than
one.
14
The following discussion draws heavily on Hsiao (1986) and Maddala
(1987) .
15
Covariates in the reduced form regressions are: ASTHMA, BRONCH,
FLEMCO, SHRTWZ, HAYFEV, BURB, AGE, EXPWORK, years of education, number of
dependents, household income, and an occupation dummy variable measuring
whether respondent is a blue collar worker.
16
In the impaired subsample, inclusion of EXPWORK frequently caused
the bivariate tobit algorithm to fail to converge. This problem arose in
the specification presented in Table 2; consequently the EXPWORK variable
was excluded.
^The estimated two-day prices are: $2.34 for ACCEN, $1.00 for ACCAR,
$0.80 for NOTGASCK. The discount rate was assumed to be 5 percent. For
further details of the procedure used to estimate prices, see Dickie et al.
(1987(a)).
1 8
The Wald test was chosen because its test statistic can be computed
using only the unconstrained estimates. Since the likelihood and
constraint functions both are nonlinear, re-estimating the model with
the constraint imposed would be considerably more difficult than computing
the Wald test statistic. Gregory and Veall (1985) identified a problem
with Wald tests of nonlinear restrictions: changing the restriction into a
form that is algebraically equivalent under the null hypothesis will change
the p-value of the test. To check for this problem, the constraint was
tested in two forms. The first, reported in the text, is
^0 : ^1^2 ~ ^2^1 = seconc* -'-s ~ S^/S? = 0. In all cases both
tests yielded nearly identical p-values.
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34
19
In other estimates of symptom production functions not reported
here, corresponding p-values also are large, almost always exceeding .25
and sometimes the .80-.90 range.
20
For comparison purposes, mean values also were estimated at
subsample means of all explanatory variables. Results differ little with
means computed over respondents. Evaluated at subsample means, willingness
to pay to eliminate one symptom for one day is $1.05 in the impaired
subsample and $0.70 in the normal subsample.
-------
0
1
2
3
4
5
6
8
9
10
11
12
13
14
15
16
17
e :
1 .--FREQUENCY DISTRIBUTIONS OF SYMPTOMS BY SUBSAMPLE
Number of Chest and
Throat Symptoms
Experienced in Past
Two Days
Impaired Normal
351
408
CO
0^
41
64
18
48
15
37
9
26
4
16
6
8
2
8
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1.348 0.453
Number of Other
Symptoms Experienced
In Past Two Days
Impaired Normal
257
338
123
79
85
42
73
18
45
12
28
5
14
6
9
2
4
1
2
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1.668 0.692
-------
TABLE 2. --BIVARIATE TOBIT SYMPTOM PRODUCTION FUNCTION ESTIMATES:
IMPAIRED SUBSAMPLE2
Chest and Throat
Symptoms
Other
Symptoms
CONSTANT
-3.085
-2.043
(-3.035)
(-2.125)
ASTHMA
0.8425
0.6724
(2.328)
(1.851)
BRONCH
3.774
2.936
(7.663)
(6.668)
SHRTWHZ
1.494
1.235
(3.683)
(3.428)
FLEMCO
1.458
0.2526
(4:038)
(0.8558)
HAYFEV
1.110
0.6613
(3.509)
(2.365)
BURB
-1.431
-0.7330
(-2.728)
(-1.539)
ACE
0.2986
2.042
(0.1596)
(1.177)
EXPWORK
— b
— b
ACCAR
-0.3485
-0.4395
(-0.8885)
(-1.364)
ACCEN
-1,9961
-0.6291
(-2.834)
(-1,829)
03
-0.1672
0.1252
(-0.5638)
(-.4475)
CO
1.279
-0.06285
(1.259)
(-0.06356)
N02
0.5475
0.6384
(0.7744)
(0.9282)
2.617
2.454
V
(HJO)
(20.81)
a,,
1.827
u
(21.17)
Chi-Square0
148.7
P-Value for
Wald Test
0.742
Number of
1 terati ons
21
aThe dependent variables are the numbers of symptoms reported m the "chest and throat"
category and in the "other" category. Asymptotic t-ratios are in parentheses. AGE is
measured in centuries, CO in parts per hundred thousand , and 03 and N02 in parts per ten
million. All remaining explanatory variables are dummies. Note the long term health
status dummies do not represent mutually exclusive categories.
^Omitted due to convergence problems.
°The chi-square test statistic is -21 nA, where \ is the likelihood ratio, for a test of the
null hypothesis that the slope coefficients in both production functions are all zero.
^The convergence criterion is 0.5 for the gradient-weighted inverse Hessian.
-------
TABLE 3. --BIVARIATE TOBIT SYMPTOM PRODUCTION FUNCTION ESTIMATES:
NORMAL SUBSAMPLEa
Chest and Throat Other
Symptoms Symptoms
CONSTANT
-5,
.789
-5.479
(-2.
.157)
(-2.790)
HAYFEV
0
L .
.316
1.461
(1:
614)
(1.871)
BURB
-1.
,388
-0.6248
-1.
,180)
(-0.8470
ACE
4.
143
7.075
(0,
.7873)
(2.091)
EXPWORK
0.
,8707
1.329
(1
.157)
(2.297)
ACCAR
-1.
,949
-0.6705
(-2.
,905)
-1.057)
NOTGASCK
-0.
,4613
-0.8565
(-0.
,6312)
(-1.594)
03
0,
.2757
0.3592
(0
.5867)
(0.9674)
CO
0,
.1788
-0.07200
(0,
.07729)
(-0.05241)
N02
1.
841
1.069
(1
.162)
(1.127)
0v
3.
,204
2.435
(10.
15)
(11.31)
G„
1
.828
(10.
,44)
Chi -Square'3
69.
81
P-Value for
Wald Test
0,
.610
Number of
1terati onsc
20
aThe dependent variables are the numbers of symptoms reported in the "chest and throat"
category and in the "other" category. Asymptotic t-ratios are in parentheses. AGE is
measured in centuries, CO in parts per hundred thousand , and 03 and N02 in parts per ten
million. All remaining explanatory variables are dummies.
^The chi-sguare test statistic is -21nX, where A is the likelihood ratio, for a test of the
null hypothesis that the slope coefficients in both production functions are all zero.
°The convergence criterion is 0.5 for the gradient-weighted inverse Hessian.
-------
TABLE 4. --UNIVARIATE TOBIT SYMPTOM PRODUCTION FUNCTION ESTIMATES3
Impaired
Normal
Subsample
Subsample
CONSTANT
-2.253
-6.085
(-1.263)
(-2.329)
ASTHMA
1.0333
(1.953)
BRONCH
4.649
(7.708)
SHRTWHZ
1.909
(3.242)
FLEMCO
1.769
(3.607)
HAYFEV
1.574
2.216
(3.137)
(2.378)
BURB
-1.830
-13623
(-2.927)
(-1.126)
ACE
1.200
6.351
(0.40jS4)
(1.165)
EXPWORK
1.725
(2.039)
ACCAR
-0.5900
-1.260
(-2.585)
(-2.425)
03
0.1629
0.5941
(0.4846)
(1.616)
CO
1.013
0.3722
(0.8041)
(0.2163)
U02
0.8930
1.726
(1.130)
(1.784)
3.684
3.790
(37.29)
(22.47)
CTli
2.582
2.516
(15.84)
(8.822)
Chi-Squarec
77.88
36.45
P-Value for
Parameter Restrictions
0.623
0.562
Number of
1 terati oris
8
5
aThe dependent variable is the total number of symptoms reported. Asymptotic t-ratios are in
parentheses. ACE is measured in centuries, CO in parts per hundred thousand, and 03 and N02
in parts per ten million. All remaining explanatory variables are dummies. Note the long
term health status dummies do not represent mutually exclusive categories.
^Omitted due to convergence problems.
°The chi-square test statistic is -21 nA, where X is the likelihood ratio, for a test of the
null hypothesis that the slope coefficients in both production functions are all zero.
^The convergence criterion is 0.5 for the gradient-weighted inverse Hessian.
-------
TABLE 5. --MARGINAL WILLINGNESS TO PAY TO RELIEVE SYMPTOMS AND
AVOID AIR POLLUTION
Impaired Subsample
Symptoms 03 N02 CO
Mean
Median
Maximum
Minimum
Normal Subsample
Symptoms 03 N02 CO
Mean $0.73 $0.31b $0.91b
Median $0.70
Maximum $1.22
Minimum $0.49
a_ ...
Denotes coefficient not significantly different from zero at 10 percent
level using one tail test in estimated equations presented in Table 4.
b
Estimates of willingness to pay for reduced air pollution do not vary
across sample members. In the computational ratio, respondent specific
information appears both in the numerator and denominator and therefore
cancels out.
$1.12
$1.09
$1.90
$0.81
-------