1

US-EPA

Approach to Assessing Non-cancer Health Effects from Formaldehyde 

and Benefits from Reducing Non-cancer Health Effects as a Result of 

Implementing Formaldehyde Emission Limits for Composite Wood 

Products
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Table of Contents

Title Page

Section 1: Background and Scope 4

1.0 Background 4

1.1 Scope of the Document 5

Section 2: Non-cancer Health Effects—

Derivation of Concentration-Response Functions 6

2.0 Background on the Identification of Non-Cancer Health Effects 6

2.1 Sensory Irritation 7

2.1.1 Sensory Irritation: Background 7

2.1.2 Sensory Irritation: Relevant Studies 7

2.1.3 Sensory Irritation:

Derivation of Concentration-Response Relationship for Eye Irritation 8

2.1.4 Sensory Irritation: Discussion of Uncertainties 14

2. 2 Asthma 16

2.2.1 Asthma: Background 16

2.2.2 Asthma: Relevant Studies 16

2.2.3 Asthma: Derivation of Concentration-Response Relationship 17

2.2.4 Asthma: Discussion of Uncertainties 19

2.3 Female Reproductive Toxicity 21

2.3.1 Female Reproductive Toxicity: Background 21

2.3.2 Female Reproductive Toxicity: Relevant Studies 21

2.3.3 Female Reproductive Toxicity:

Derivation of Concentration-Response Relationship 22

2.3.4 Female Reproductive Toxicity: Discussion of Uncertainties 25
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2.4 References 30

Section 3: Benefits Assessment Approach 33

3.1 Introduction/Background 33

3.1.1 General Model 33

3.1.2 Simplified Model 34

3.2 Sensory Irritation 37

3.2.1 Monetization 37

3.2.2 Annual approach 39

3.2.3 Example calculation 40

3.2.4 Discussion of uncertainties 46

3.3 Asthma incidence 47

3.3.1 Monetization 47

3.3.2 Annual approach 52

3.3.3 Example calculation 58

3.3.4 Discussion of uncertainties 62

3.4 Reduced Fertility 62

3.4.1 Monetization 62

3.4.2 Annual Approach 66

3.4.3 Example Calculation 68

3.4.4 Discussion of uncertainties 71

3.5 References 74
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Section 1: Background and Scope

1.0 Background

In March 2008, the Sierra Club and other organizations and individuals petitioned EPA under 

Section 21 of the Toxic Substances Control Act (TSCA). The petitioners requested that EPA use 

TSCA Section 6 to adopt a newly-promulgated California Air Resources Board (CARB) 

Airborne Toxic Control Measure (ATCM)1as a national standard for formaldehyde emissions 

from hardwood plywood, particleboard, and medium-density fiberboard products. The 

petitioners expressed particular concern over the levels of formaldehyde found in emergency 

housing provided for Hurricane Katrina survivors, but noted that there are no federal regulations 

on formaldehyde emissions from composite wood products other than those applicable to 

manufactured housing regulated by the U.S. Department of Housing and Urban Development. In 

response to the petition, EPA announced in the Federal Register on June 27, 2008 (73 FR 

36504)2that EPA would initiate a proceeding to investigate whether and what type of regulatory

or other action might be appropriate to protect against risks that may be posed by formaldehyde 

emitted from composite wood products. In December 2008, EPA published an Advance Notice 

of Proposed Rulemaking (ANPR) to publicly initiate the investigation and obtain stakeholder 

input (73 FR 73620).3 

On July 7, 2010, the Formaldehyde Standards for Composite Wood Products Act (FSCWPA) 

was signed into law. This statute, which adds a Title VI to TSCA, establishes formaldehyde 

emission standards for hardwood plywood, particleboard, and medium-density fiberboard that 

are identical to the CARB ATCM Phase II standards. 4 TSCA Title VI directs EPA to 

promulgate implementing regulations by January 1, 2013 that address: sell-through dates for 

products; stockpiling; third-party testing and certification; auditing and reporting of third-party 

certifiers; recordkeeping; chain of custody; labeling; enforcement; products made with no-added 

formaldehyde (NAF) and ultra-low emitting formaldehyde (ULEF) resins; laminated products; 

finished goods; hardboard; and products containing de minimis amounts of composite wood 

products. 

In support of the implementing regulations, as with other rulemakings that are determined to be 

“significant regulatory action[s]” under Executive Order 12866—Regulatory Planning and 

Review, EPA is required to conduct an economic analysis of the costs and benefits associated 

with the rulemaking. On June 2, 2010, EPA released a draft document titled Toxicological 

Review of Formaldehyde-Inhalation Assessment: In Support of Summary Information on the 

Integrated Risk Information System (IRIS).5This draft IRIS assessment, which recently 

underwent independent scientific peer review by the National Academy of Sciences (NAS)6, 

addresses both non-cancer and cancer human health effects that may result from chronic 

inhalation exposure to formaldehyde. However, this draft IRIS assessment does not include 

 

1 Available at http://www.arb.ca.gov/toxics/compwood/compwood.htm

2 Available at http://www.gpo.gov/fdsys/pkg/FR-2008-06-27/pdf/E8-14618.pdf

3 Available at http://www.gpo.gov/fdsys/pkg/FR-2008-12-03/pdf/E8-28585.pdf

4 Available at http://www.arb.ca.gov/toxics/compwood/compwood.htm

5 Available at http://cfpub.epa.gov/ncea/iris_drafts/recordisplay.cfm?deid=223614

6 Available at http://www.nap.edu/catalog.php?record_id=13142
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concentration-response functions for non-cancer health effects, which are needed for the benefits 

assessment. Therefore, this draft report titled Approach to Assessing Non-cancer Health Effects 

from Formaldehyde and Benefits from Reducing Non-cancer Health Effects as a Result of 

Implementing Formaldehyde Emission Limits for Composite Wood Products (referred to 

hereafter as draft Approach Document) was developed, which provides discussion of several 

non-cancer endpoints as well as a discussion of the derivation of concentration-response 

functions, uncertainties, and EPA’s proposed approach for using the concentration-response 

functions in the benefits assessment. 

1.1 Scope of the Document

The economic analysis to support EPA’s implementing regulations under the TSCA Title VI will 

weigh the costs of complying with the regulations against the benefits to society. Benefits from 

both reduced cancer cases and non-cancer health effects will be assessed; however, this draft 

Approach Document does not include a discussion of EPA’s approach to assessing benefits from 

reduced cancer cases. 

As part of the economic analysis, EPA is also assessing inhalation exposure to formaldehyde. 

EPA has developed an indoor air model, which has already been peer reviewed, to assess 

exposure to formaldehyde in different types of homes. EPA has also assessed occupational 

exposure to formaldehyde during resin manufacture, composite wood product manufacture, and 

manufacture of products made with composite wood (e.g., furniture), as well as exposure from 

wholesale and retail of composite wood products and products made with composite wood, and 

exposure to formaldehyde in office buildings. Using the indoor air model and the occupational 

exposure assessment, EPA is estimating formaldehyde inhalation exposure to the general 

population at baseline (prior to implementing the rule) and the change in exposure as a result of 

the rule. The occupational and general population exposure assessments are discussed in detail 

in other documents, which will be publicly available at www.regulations.gov when the proposed 

rule is published. This draft Approach Document uses preliminary estimates from the exposure 

assessment as examples, but it does not describe how they were derived, as the derivation is 

covered in a separate document.

The purpose of this draft Approach Document is to describe how EPA derived concentrationresponse functions for formaldehyde effects on sensory irritation, asthma, and female 

reproductive toxicity as well as the approach EPA will take to use these concentration-response 

functions to estimate benefits from the contribution of reduced non-cancer effects as a result of 

the rule. This document describes in detail how the concentration-response functions were 

derived as well as uncertainties. This document also briefly describes the epidemiological 

studies that were used to derive the concentration-response functions; however, a detailed 

analysis of these studies (as well as others) is included in the draft IRIS assessment for 

formaldehyde, which was already peer reviewed by the NAS, and therefore is not provided here. 

This draft Approach Document also describes how EPA plans to use the concentration-response 

functions to estimate benefits. It provides sample calculations but not the actual benefits 

assessment. The full benefits assessment will be provided in the economic analysis that will be 

publicly available (at www.regulations.gov) when the proposed rule is published.
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Section 2: Non-cancer Health Effects—

Derivation of Concentration-Response Functions 

2.0 Background on the Identification of Non-Cancer Health Effects 

In 2010, EPA released a draft IRIS assessment of adverse cancer and non-cancer health effects 

from inhalation of formaldehyde (U.S. EPA, 2010). This draft identified non-cancer health 

effects for which quantitative concentration-response relationships were sought for the purpose

of deriving a reference concentration (RfC), which represents an exposure level expected to be 

without an appreciable risk of deleterious effects in human, including susceptible populations, 

with little uncertainty (within an order of magnitude). The draft IRIS assessment has since been 

externally peer-reviewed by the National Academy of Sciences (NAS, 2011).

This section is largely a recapitulation of portions of the text from EPA’s draft IRIS assessment 

specific to the identified non-cancer health effects, taking the external peer-review comments 

into consideration. The aim of the current effort is to describe the quantitative inhalation 

concentration-response relationship (i.e., the concentration-response function) for each of the 

identified non-cancer health effects, where possible, to inform the economic benefits assessment 

of potential economic welfare gains which could reasonably be expected to be attributable to 

decrements in formaldehyde exposures resulting from the proposed implementing regulations 

under FSCWPA.

The following subsections describe the studies of non-cancer health outcomes which were 

judged in the draft IRIS assessment to be the most informative for candidate RfC derivation 

within health effect categories. These studies were judged to have been adequately conducted,

and all were published in the peer-reviewed literature. The relative merits and limitations of 

these studies were evaluated with respect to the characteristics of the study population, the 

quality and frequency of exposure measurements, and the exposure levels at which effects were

observed. The studies identified in the draft IRIS assessment as the best available for candidate 

RfC derivation also represent the best available studies from which to quantitatively estimate the 

concentration-response relationship between inhalation exposures and non-cancer health effects

for the purposes of the economic benefits assessment. Additional details on specific studies 

discussed here may be found in the draft IRIS assessment (Chapters 4 and 5 of U.S. EPA, 2010).

Only the studies reviewed in the draft IRIS assessment were further evaluated for use in the 

concentration-response modeling in support of the economic benefits assessment. It should be 

noted that one of the comments in the NAS report was that it was not always clear how EPA 

selected and advanced studies for further consideration in RfC development. In two specific 

instances, the NAS peer-review report recommended not using particular studies for the 

derivation of candidate RfCs and, consequently, those studies were not used here to estimate 

quantitative concentration-response relationships. 

 The draft IRIS assessment identified seven categories of health outcomes for potential RfC 

derivation including: 1) Sensory Irritation; 2) Upper Respiratory Tract Pathology; 3) Pulmonary

Function Effects; 4) Asthma and Allergic Sensitization (Atopy); 5) Immune Function Effects; 6) 
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Neurological and Behavioral Toxicity; 7) Developmental and Reproductive Toxicity. From 

those categories, the draft IRIS assessment proposed RfCs based on four effects: sensory 

irritation, pulmonary function effects, asthma and allergic sensitization (atopy), and reproductive 

toxicity. The NAS supported the derivation of candidate RfCs for each of these four endpoints 

based on human epidemiologic data. For some non-cancer endpoints, it was possible to derive a

candidate RfC for a particular health outcome based on a no-observed-adverse-effect level 

(NOAEL) or a lowest-observed-adverse- effect level (LOAEL), but those same data may not 

have supported a more fully characterized concentration-response function. At this time, only 

three of the health effect categories were judged to have sufficient data for quantitative 

concentration-response modeling in support of the economic benefits assessment: sensory 

irritation, asthma, and female reproductive toxicity. The available data on pulmonary function 

effects showing an association between increased formaldehyde concentrations and decreased 

peak expiratory flow rates could not be advanced in this Approach document because it was not 

possible to link specific decrements in pulmonary function with specific economic costs.

2.1 Sensory Irritation

2.1.1 Sensory Irritation: Background 

Formaldehyde, a chemical irritant, binds to protein receptors of the trigeminal nerve, triggering a 

burning and painful sensation in humans. This process is distinct from taste and smell (Nielsen 

1991; Cometto-Muniz and Cain, 1992). Stimulation of the trigeminal nerve may also result in 

reflex responses including lacrimation, coughing, and sneezing. Both the reflex responses and

sensations such as burning, pain, and itching of the eyes, nose, and throat are considered adverse.

Formaldehyde-induced eye, nose, and throat irritation has been well documented in a wide range 

of epidemiologic and other human studies. Common effects of chemically induced sensory 

irritation include lacrimation, burning of the eyes and nose, rhinitis, burning of the throat, and 

cough (Feron et al., 2001). Studies examining these endpoints were either controlled chamber 

studies with a defined population (e.g., healthy volunteers or sensitive individuals), 

worker/student studies, or general population studies (e.g., residential). Chamber studies, by

design, are acute studies, although some researchers have investigated the outcomes after 

repeated exposures. Occupational, student, and residential exposures are generally of longer 

duration, although there is variability in exposure level and duration among subjects. The 

endpoints for assessing irritation include self-reporting of symptoms (e.g., pain, burning, itching) 

and objective measures of irritation (e.g., eye-blink counts, lacrimation).

2.1.2 Sensory Irritation: Relevant Studies

Eye irritation is the most sensitive of reported effects in human studies. Two different short-term 

chamber studies provide similar benchmark concentrations for 10% extra risk of eye irritation of 

560 ppb and 240 ppb for 3 and 5 hour exposures, respectively (Kulle, 1993; Andersen and 

Molhave, 1983, modeled by Arts et al., 2006b). Various occupational studies have noted 

increased eye irritation for average exposures ranging from 180 ppb to 690 ppb (e.g., Horvath et 
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al., 1988, Alexandersson and Hedenstiera, 1988; Holmstrom and Wilhelmsson, 1988). The 

results of residential studies of the general population, where in-home formaldehyde levels are 

used as the exposure metric, indicate eye irritation may increase with increasing exposure from 

less than 100 ppb to more than 500 ppb for these chronic exposure scenarios (Ritchie and 

Lehnen, 1987, Hanrahan et al., 1984; Liu et al., 1991.)

Details of the human studies reporting associations between formaldehyde inhalation exposures 

and sensory irritation and a review of their findings are presented in Chapter 4 of the draft IRIS

assessment of formaldehyde (U.S. EPA, 2010) along with experimental animal evidence 

supporting the plausibility of these epidemiologic findings. A synthesis of the most relevant 

findings and conclusions is also presented in Chapter 4 (U.S. EPA, 2010). Although exposure 

concentrations are well-defined in the chamber studies, the chamber studies are not appropriate 

for estimating the effects of chronic exposures because they are acute studies. The participants 

in the chamber studies also typically represent healthier individuals (although some studies do 

include asthmatics) and do not include either young or old people. The occupational studies also 

typically represent healthier individuals and do not include either young or old people, and both 

chamber and occupational studies involve higher exposure levels than occur in most residential 

settings, which are the focus of the formaldehyde rule. Additionally, occupational exposures 

often include short-term “peak” exposures of higher concentrations. Thus, the human 

epidemiology studies of lower, chronic residential exposures are more relevant and convey less 

uncertainty than the acute chamber studies or the occupational studies and are preferred for the 

purposes of application in the economic analysis.

Of the various independent sensory irritation effects for which one may wish to estimate 

economic benefits ensuing from the formaldehyde rule, only eye irritation had adequate 

quantitative data from residential studies for the derivation of a concentration-response function.

2.1.3 Sensory Irritation: Derivation of Concentration-Response Relationship for Eye Irritation

There are three studies that report sensory irritation in humans from chronic exposures in a 

residential environment and provide sufficient exposure data to support quantitative assessment 

(Ritchie and Lehnen, 1987; Hanrahan et al., 1984; Liu et al., 1991). Each study reports sitespecific exposure measurements and presents some metric of individual exposure. These studies 

employ in-home measurements for each study participant, either as average exposure level in the 

home (Ritchie and Lehnen, 1987; Hanrahan et al., 1984) or as calculated cumulative exposure 

based on the time in the home (Liu et al., 1991). Eye irritation is the most sensitive endpoint 

representing sensory irritation and is reported at similar levels of residential formaldehyde 

exposure in the three studies (U.S. EPA, 2010, Figures 5-8 and 5-9). Each study provides an 

estimated concentration-response relationship for prevalence of eye irritation in relation to inhome formaldehyde exposure based on individual-level data, including levels of exposure below 

100 ppb. Liu et al. (1991) additionally evaluated responses by season (summer and winter). 

These studies generally assume a constant concentration-response over time which may have 

been attenuated due to acclimatization to relatively constant formaldehyde exposure levels in 

residential environments. It has been shown that short-term responses to formaldehyde 

exposures including reductions in pulmonary function, and irritation of the eyes, nose and throat 

can diminish over time with repeated episodic exposure (Kriebel et al., 1993; 2001). The 
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detailed exposure information and chronic nature of the exposures support the selection of these 

residential epidemiology studies for concentration-response modeling.

While the concentration-response relation reported in Ritchie and Lehnen (1987) was consistent 

with those reported in the two other studies, it is possible that the Ritchie and Lehnen results 

were impacted by potential selection bias − owing to the need for a doctor’s note to be able to 

participate; thus, these results may not accurately describe the concentration-response in the 

general public and are not considered further here.

The two remaining studies report eye irritation in humans from chronic exposures in a residential 

environment and provide sufficient exposure data to support quantitative assessment (Liu et al., 

1991; Hanrahan et al., 1984). The Liu et al. (1991) residential study is a random-sample study of 

over 1,000 mobile home residents across the State of California (1,394 in the summer; 1,096 in 

the winter) that included both young children (< 4 years) and the elderly (> 65 years). 

Cumulative weekly exposures were based on in-home formaldehyde sampling and a participant 

survey of time spent at home. Air sampling was conducted for a 7-day period using 2 passive 

samplers in each home (for both summer and winter). One passive sampler was placed in the 

kitchen and one in the master bedroom; however, there was no significant difference in exposure 

levels between the two locations, so the two values were averaged to reflect the household 

concentration. The resulting estimates of cumulative exposure assumed no formaldehyde 

exposure outside of the home. The authors based their measure of exposure on the product of the 

measured concentration of formaldehyde in the home and the number of hours per week the 

individual spent in the home. Liu et al. (1991) reported that this measure of cumulative 

formaldehyde exposure was a significant predictor of numerous irritant symptoms in a 

multivariate linear logistic regression, including “burning eyes” (p < 0.05). The highest 

prevalence rates were reported for those aged 20−64 years and the prevalence of eye irritation 

increased with increasing cumulative exposure in a categorical analysis of participants in this age 

group for both summer and winter exposure estimates, as shown in Figure 1 below (U.S. EPA, 

2010, Figure 5-9). 

Liu et al. (1991) presented results for three categorical levels of cumulative exposure. The 

lowest exposure group extended from 0 to 7.0 ppm×hours/week and did not constitute a ‘nonexposed’ reference group but rather a comparative lower exposure level. The mid-level exposure 

group encompassed exposure from 7.0 to 12.0 ppm×hours/week and the high exposure group 

covered exposure greater than 12.0 ppm×hours/week. Liu et al. reported that the average 

concentration of formaldehyde in the homes was 88 ppb in the summer and 89 ppb in the winter. 

The range of cumulative exposures extended from 0 to 53.4 ppm×hours in the summer and 0 to 

40.9 ppm×hours in the winter, with respective average cumulative exposures of 9.8 ppm×hours 

and 9.9 ppm×hours. Dividing the average 7-day cumulative exposures reported by Liu et al. 

(1991) by the average concentrations, the average time spent in the homes can be estimated as 

approximately 111 hours (about 16 hours per day). The prevalence of eye irritation was above 

10% in the lowest exposure group (0–7.0 ppm×hours/week) and increased to 17.1% in the midexposure group (7.0−12.0 ppm×hours/week) and to 21.4 % in the high-exposure group (12.0 

ppm×hours/week) in the summer survey time; winter rates were slightly lower but showed a 

similar increase with increasing cumulative exposure.
10

13.3%

17.1%

21.4%

10.8%

14.7%

20.6%

0%

5%

10%

15%

20%

25%

< 7 7 - 12 > 12

Formaldehyde Exposure (ppm-hr per week)

Prevalence of burning/tearing eyes (%)

Summer

Winter

Figure 1. See Figure 5-9 U.S. EPA (2010). Positive concentration-response relationships 

reported for in-home formaldehyde exposures and sensory irritation (burning eyes). Cumulative 

formaldehyde exposure was estimated for each participant from measured in-home formaldehyde 

levels (7-day passive air samples) and reported hours spent in the home. Prevalence rates are 

given for the 20-64 year-old age group for both summer (n = 739) and winter (n = 587) survey 

periods. Adapted from Liu et al. (1991).

While these data are not well suited to developing continuous concentration-response 

relationships because there are only three categories of exposure and the distributions of 

exposures and times spent indoors within each category are unknown, this study does provide the 

most specific information on the relative timing of exposure to formaldehyde and the occurrence

of sensory irritation symptoms, which is important for the economic benefits assessment. The 

described methodology states that the symptoms were reported for a two-week period that 

included the week preceding and the week of exposure monitoring. Knowledge of the timing of 

exposure is an important aspect for the application of a concentration-response function to 

inform the economic benefits assessment, and the data from the paper by Liu et al. (1991) 

provide supportive information on the shape of the concentration-response function as well as an 

estimate of the general prevalence of sensory irritation in a highly relevant population.

Hanrahan et al. (1984) reported a concentration-response relationship for burning eyes in a study

of 61 teenage and adult residents of mobile homes in Wisconsin. Note that ocular discomfort 

was recorded in two related ways as ‘eye irritation’ and as ‘burning eyes’; however, only the 

concentration-response relationship for ‘burning eyes’ was reported and this endpoint was used 

by EPA to represent eye irritation more broadly. In-home formaldehyde measurements were 

obtained for all participants, and measured formaldehyde levels (average of two approximately 

1-hour air samples – one from the kitchen or living room and one from a bedroom) were used to 

characterize average in-home exposures. Measured residential formaldehyde concentrations 
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ranged from less than 100 ppb to 800 ppb. The median (geometric mean) was reported as 160 

ppb. No information was provided on the arithmetic mean or standard deviation of the indoor 

measurements. However, the standard deviation of the outdoor measurements was reported as 

30 ppb and effectively serves as a lower bound on the standard deviation of the indoor 

concentrations because indoor levels are generally considerably higher and more variable than 

outdoor levels. Given the information provided by Hanrahan et al. (1984) on the indoor 

geometric mean and a lower bound estimate on the indoor arithmetic standard deviation, the 

percentages of indoor formaldehyde measurements below 100 ppb and below 50 ppb can be 

estimated. Using an estimated expected value (arithmetic mean) of 163 ppb based on an 

arithmetic standard deviation of 30 ppb [for log-normally distributed concentrations, the 

arithmetic mean is a function of the geometric mean and the standard deviation], and an 

assumption that the measured concentrations were log-normally distributed, 44% of actual 

residential measurements are estimated to have been below 100 ppb with 36% below 50 ppb. If 

the actual, but unreported, standard deviation of the indoor measurements was greater than 30 

ppb, then these percentages would be expected to increase. This information is important, as it 

shows that the underlying residential exposure data which inform the concentration-response 

relationship are relevant to concentrations modeled in the exposure assessment for use in the 

economic analysis. Different distributional assumptions would produce different estimates of the 

proportion of measured samples which were below 50 ppb, but, under the assumption of a lognormal distribution, which is common for exposure estimates, at least one third of the 

measurements informing the concentration-response function were in the range that is most 

applicable to the economic analysis.

Hanrahan et al. (1984) reported that eye irritation was associated with in-home formaldehyde 

exposures (p < 0.05) (both as “burning eyes” and “eye irritation”), and the authors provided a 

graphical representation of the best-fitting logistic regression model results of predicted 

prevalence of “burning eyes” for exposures from 100 to 800 ppb. From inspection of this graph 

(shown here as Figure 2), EPA determined the prevalence of eye irritation predicted at 100 ppb is 

approximately 4%. Although, as discussed above, a large percentage (44%) of the indoor 

formaldehyde measurements were estimated to have been below 100 ppb, the predicted model 

results were simply not shown below 100 ppb. At the time of publication, the World Health 

Organization standard was 300 ppb and the central conclusion of Hanrahan et al. (1984) was that 

indoor formaldehyde levels below 100 ppb would lower the risk of sensory irritation for most 

residents. Nonetheless, it is possible to approximate the functional form of the concentrationresponse relationship below 100 ppb from the graphical results provided in the plot from 

Hanrahan et al. (1984) presented below in Figure 2 because a single functional form was used to 

plot the results shown and reconstruction of that form can show the results of the Hanrahan et al. 

(1984) model where they were omitted below 100 ppb.
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Figure 2. See Figure 5-8 U.S. EPA (2010). Regression of prevalence of ”burning eyes” versus 

indoor formaldehyde concentration (ppm) in mobile homes (approximately 1-hour air samples). 

Dashed lines show upper and lower 95th percentile confidence intervals on model results. 

Model based on reported eye irritation from individuals in 42 mobile homes. Adapted from 

Hanrahan et al. (1984).

In this figure, the dependent variable is displayed as predicted % prevalence of eye irritation. 

However, the method used by Hanrahan et al. (1984) to model prevalence was logistic 

regression, which predicts the log odds of prevalence, which the authors then transformed to 

prevalence for graphing. In order to describe the underlying functional form of the results 

displayed, EPA converted the prevalence data back to prevalence odds. Table 1 shows the 

prevalence values which EPA visually estimated from the plot as well as the associated 

prevalence odds, which EPA calculated as estimated prevalence divided by the complement of 

estimated prevalence, that is p/(1-p). Figure 3a plots the estimated prevalence of eye irritation 

against the residential concentration of formaldehyde. Figure 3b plots the estimated prevalence

odds against the residential concentration of formaldehyde.

Table 1. Concentration-response information extracted from Hanrahan et al. (1984).

Residential Formaldehyde

Concentration (ppb)

Prevalence

(p)

Prevalence Odds

(p/[1-p])

100 0.0375 0.039

200 0.175 0.212

300 0.35 0.538

400 0.52 1.08

500 0.66 1.86

600 0.725 2.64

700 0.8 4

800 0.85 5.67
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Figure 3a & b. Plot of residential concentration-response information from Table 1.

Using MS Excel®, the EPA fit a simple trend line to the discrete prevalence odds data in Figure 

3b and not the continuous raw data and found that a power function could be fit which yielded an 

R

2

value of 0.9997. This indicates nearly a perfect fit. A similar fit would not have been 

achieved from analysis of the raw data (unavailable), but the objective here was to recreate the 

functional form of the modeled data presented by Hanrahan et al. (1984). Note that this power 

function will asymptotically approach zero for a zero formaldehyde exposure concentration. 

The following describes the functional form for the prevalence odds:





= 7 ∗ 10∗ ()

. (2-1)

Solving for prevalence (p) itself:

 =

∗∗()

.

[∗∗()

.]

(2-2)

Figure 4a shows the predicted prevalence odds from the functional form above overlaid on the 

prevalence odds estimates extracted from Hanrahan et al. (1984). This concentration-response 

function is clearly consistent with the reported model results and provides an estimate of the 

concentration-response relationship below 100 ppb residential exposure, in the region of 

exposures of interest for the economic benefits analysis. Figure 4b shows the same plot with 

greater focus on the lower range of the concentration-response relationship. 
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Figure 4a. Relationship between residential formaldehyde exposures and the predicted 

prevalence of sensory irritation (burning eyes) as report by Hanrahan et al. (1984) [red squares] 

and the continuous concentration-response relationship as estimated by EPA.

Figure 4b. Relationship between residential formaldehyde exposures and the predicted 

prevalence of sensory irritation (burning eyes) as report by Hanrahan et al. (1984) [red square] 

and the continuous concentration-response relationship as estimated by EPA for formaldehyde 

concentration below 150 ppb.

2.1.4 Sensory Irritation: Discussion of Uncertainties

Both studies (Liu et al., 1991; Hanrahan et al., 1984) have the strength of having individual inhome exposure measurements, and each demonstrates a positive concentration-response 

relationship for eye irritation within a range of residential formaldehyde exposures (for both 

conventional and mobile homes). The assessment of formaldehyde concentrations in these 

studies were by two different methods. Liu et al. (1991) measured formaldehyde concentration 

using passive monitors over seven days. Hanrahan et al. (1984) based their exposure assessment 

on short-term samples taken over approximately one hour. Short-term sampling is a less precise 

methodology and the resulting measures can be reasonably expected to include a greater degree 

of exposure measurement error than those from week-long passive monitoring. The short-term 
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nature of the exposure sampling in Hanrahan et al. (1984) is a limitation; however, the results in 

Liu et a. (1991) based on the stronger exposure assessment methodology (although still prone to 

some measurement error) are well aligned and strengthen the validity of the Hanrahan et al. 

(1984) results. 

One weakness of these studies was that the assessment of sensory irritation was conducted by

surveys and not objectively assessed by trained observers of physiological measurements. While 

it was considered a common strength that these studies did have in-home measurement of 

formaldehyde exposures in temporal proximity to the assessment of irritation, those 

measurements were of relatively short sampling duration and they do not reflect daily 

fluctuations which may include relative peak exposures. Both studies were based on randomly 

selected people representative of the general population, although the study size in Hanrahan et 

al. (1984) was small with just 61 participants.

Both studies did control for major potential confounders but did not measure and control for all 

the factors that could potentially be confounders. Liu et al. (1991) controlled for the potentially

confounding effects of age, gender and smoking as well as controlling for chronic respiratory 

and allergy problems. The analysis by Hanrahan et al. (1984) controlled for age, gender and 

smoking, and the authors reported that the presence of either smokers or gas appliances was not 

associated with indoor concentrations of formaldehyde, making those factors unlikely 

confounders. Nonetheless, there is always the potential for other possible confounders, such as 

molds or other volatile organic compounds, to have played a role in the observed concentrationresponse relations described by Liu et al. (1991) and Hanrahan et al. (1984). No data on these 

potential confounders were noted in these papers, but the reported concentration-response 

relationships are strong evidence of a formaldehyde effect and, for these reported relationships to 

have been the spurious product of confounding, those unmeasured confounding factors would 

need to have been strongly associated with both eye irritation and the concentrations of 

formaldehyde.

Both studies support a finding of increased eye irritation with increasing exposures to 

formaldehyde at concentrations starting below 100 ppb. Liu et al. (1991) reported an average 

concentration of 88 ppb, with measured concentrations from 10 ppb (the limit of detection) to 

460 ppb. Hanrahan et al. (1984) reported exposures ranging from less than 100 ppb to 800 ppb, 

with a median of 160 ppb. While it is not clear from the published report what the distribution of 

exposures below 100 ppb was, if it can reasonably be assumed that the formaldehyde 

concentrations were log-normally distributed with median of 160 ppb and a standard deviation of 

30 ppb (based on the reported standard deviation from the outdoor measurements), then it would 

be expected that about 44% of the measured indoor samples were below 100 ppb, with 36% 

below 50 ppb. Given that the measured indoor levels were likely to have been more variable 

than the reported outdoor levels, the true indoor standard deviation would likely have been

higher than 30 ppb and, consequently, the percentages below 100 ppb and below 50 ppb would 

have been greater.

The results as graphed in Hanrahan et al. (1984) did not show the shape of the concentrationresponse curve below 100 ppb even though the study had exposure data at these exposure levels. 

EPA was able to derive a concentration-response function that closely approximated the results 

from Hanrahan et al. (1984) and, from this functional form, to infer the shape of the published 
16

concentration-response function below 100 ppb – a range EPA considers to encompass at least 

44% of the indoor measurements. Thus, while there is clearly uncertainty in estimating effects 

below 100 ppb residential exposure, these effects can be estimated from the published 

concentration-response curve. Re-modeling of the reported results from Hanrahan et al. (1984) 

provided the best available estimate of the adverse response below 100 ppb, and this 

concentration-response function can be used in the economic benefits assessment.

These studies provided a reasonable basis for quantitative concentration-response modeling, with 

Liu et al. (1991) supporting the modeling based on Hanrahan et al. (1984). Additionally, the 

study populations have been drawn from the general population, including children and the 

elderly, and have not been limited to those healthy enough for full-time employment (as is often 

the case in occupational cohorts). The results in these studies are further supported by the 

consistent findings of an extended concentration-response relationship reported in some nonresidential studies at higher levels of exposure. For example, Kriebel et al. (2001) reported that 

increasing formaldehyde exposures were positively associated with symptoms of eye irritation 

(p<0.001) among anatomy students with measured exposure concentrations having a geometric 

mean of 700 ppb but with 25% of exposures below 300 ppb. 

2. 2 Asthma

2.2.1 Asthma: Background

Asthma is a chronic respiratory disease characterized by inflammation of the airways. 

Sensitization to inhalational chemical exposure may manifest as an allergic or asthmatic response 

that is characterized by bronchial constriction or bronchial hyper-responsiveness. This may be a 

result of immune involvement, as in the case of hypersensitivity, or a neurogenic sensitization, 

where a chemical may directly stimulate inflammation. In the United States, the prevalence of 

asthma is common. The Centers for Disease Control and Prevention estimated that in 2005 

approximately 9% of children had asthma (6.5 million children) and that the prevalence rate of 

asthma in children had more than doubled from 1980 to the mid-1990s and has remained at 

historically high levels (Akinbami, 2006). In 2009, it was estimated that nearly 10% of children 

had asthma (CDC, 2009).

2.2.2 Asthma: Relevant Studies

Multiple epidemiologic studies have reported associations between formaldehyde inhalation 

exposures and childhood asthma. Details of these epidemiologic studies and a review of their 

findings are presented in Chapter 4 of the draft IRIS assessment of formaldehyde (U.S. EPA, 

2010) along with experimental animal evidence supporting the plausibility of these 

epidemiologic findings. A synthesis of the most relevant findings and conclusions is presented 

also in Chapter 4 (U.S. EPA, 2010).

The study that is most relevant for developing a concentration-response function for use in the 

economic benefits assessment is the meta-analysis of formaldehyde-associated asthma conducted 

by McGwin et al. (2010) based on seven peer-reviewed studies providing quantitative 
17

concentration-response results for children. All of the studies were observational in nature and 

were predominantly cross-sectional or case-control in design. The mean ages of the children in 

the seven studies ranged from 1.9 years up to 14.3 years. Details of the individual studies were 

provided by the authors in their Table 1 reproduced below (see Table 2 of this document). For 

the meta-analysis, odds ratios (ORs) and confidence intervals (CIs) were abstracted from the 

studies, and effect estimates were standardized to OR per 10 μg/m3increase in formaldehyde 

concentration. Funnel plots were used to assess publication bias and did not show such a bias 

(McGwin et al., 2010). Fixed- and random-effects models were used to calculate pooled ORs 

and 95% CIs following a test of heterogeneity. A fixed-effect model assumes that all the 

individual studies provided estimates of the same effect or slope, while the random-effects model 

allows for different effects or slopes in the source studies that may reflect differences in baseline 

risk factors within the study populations. McGwin et al. (2010) preferred the fixed-effect model 

when heterogeneity was low and the random-effects model when the data were more 

heterogeneous. Both models were presented, as the degree of heterogeneity, measured by the Qtest and the I

2

statistic, indicated the presence of low to moderate heterogeneity, depending on 

the analysis. The referenced Q-test is also known as Cochran’s Q and is a classical measure of 

heterogeneity calculated as the sum of the weighted squared differences between the individual 

study effects and the pooled effect across studies, where the weights are those used in the 

pooling method. The I

2

statistic described the percentage of variation across studies that is due 

to heterogeneity rather than chance and is computed as 100%*(Q – degrees of freedom)/Q.

Table 2. Reproduction of McGwin et al. (2010) Table 1: Summary of studies selected for 

inclusion in meta-analysis.

 

2.2.3 Asthma: Derivation of Concentration-Response Relationship

Of the seven studies that were included in the McGwin et al. meta-analysis, six reported 

increased risks of asthma associated with exposure to formaldehyde. The results of the randomeffects model showed an overall effect estimate of OR = 1.17 per 10 μg/m3

formaldehyde (95% 

CI: 1.01-1.36) (see U.S. EPA, 2010: Figure 4-2). The three studies with the highest statistical 

weights based on the inverse of the variance of the study ORs were the studies by Rumchev et al. 

(2002), Garrett et al. (1999) and Krzyzanowski et al. (1990). Higher weights reflect the narrower 

confidence intervals in these studies, which implied that the studies were able to yield more 

precise effects estimates, warranting greater weight in the meta-analysis. Note that the two 
18

results from the Zhao et al. (2008) study, including the school results, which showed a health 

protective effect of formaldehyde, had such large confidence intervals that their weights in the 

meta-analysis were virtually zero.

Source: McGwin et al. (2010), Fig. 2.

McGwin et al. (2010) noted that the study by Rumchev et al. (2002) may have had ‘undue 

influence on the study data’ and recomputed the fixed- and random-effects model results without 

that study. They also suggested that one aspect of Rumchev et al. (2002) which was unique 

among the seven studies was the focus on very young children. According to the National Heart 

Lung and Blood Institute, a diagnosis of asthma is most reliable when it is based on a physical 

exam, a medical history and a test of pulmonary function. However, conducting lung function 

tests on young children is difficult and doctors may rely on signs and symptoms rather than 

spirometry in making diagnostic decisions (U.S. HHS, 2007). In the peer-review report of the 

draft IRIS formaldehyde assessment (U.S. EPA, 2010), the NAS (2011) noted that many of the 

studies of childhood asthma in the epidemiologic literature were decades old and that the 

understanding of asthma was not characterized as well then as it is now. The NAS report (2011) 

noted that while Rumchev and coauthors (2002) interpreted the health outcome in their study as 

a diagnosis of asthma, study participants of such young ages are now thought to have been more 

likely to have actually had lower respiratory illnesses with wheezing of an infectious etiology, a 

diagnosis which could often have been mislabeled as asthma. For these reasons, the results from 

the Rumchev et al. (2002) study are not included in the approach proposed here to estimate the 

concentration-response relationship for asthma-related formaldehyde exposures.

Excluding Rumchev et al. (2002) from the meta-analysis, McGwin et al. (2010) reported the 

summary measure of the concentration-response relationship based on the random-effects model 

as OR = 1.24 per 10 μg/m3formaldehyde (95% CI: 1.07-1.45) with a p-value of 0.0026, while 

for the fixed-effect model they reported an OR = 1.24 (95% CI: 1.09-1.42) with a p-value of 
19

0.0013. Without including Rumchev et al. (2002), the heterogeneity statistics, Q and I

2

, were 

6.76 and 11.3, respectively, which indicate low heterogeneity. Consistent with the low 

heterogeneity, both models estimated a similar magnitude of effect (the same OR estimate in this 

instance) but with the fixed-effect estimate having a narrower confidence interval. 

This concentration-response relationship (OR = 1.24 per 10 μg/m3) is recommended for 

application in the economic benefits assessment for the formaldehyde rule. The units of this 

concentration-response relationship can be converted to show the effects per part per billion 

(ppb) of formaldehyde. Converting from μg/m3to ppb depends on the molecular weight of 

formaldehyde, which is 30.03 g/mol. The formula to convert concentrations in air (at 25°C) 

from μg/m3to ppb is: ppb = (μg/m3) × (24.45 L) / (gram molecular weight of the compound). 

The number 24.45 in the equations above is the volume (liters) of a mole (gram molecular 

weight) of a gas or vapor when the pressure is at 1 atmosphere (760 torr or 760 mm Hg) and at 

25°C. For formaldehyde, 1 μg/m3 = 0.814 ppb. Therefore, the effect estimate from McGwin et 

al. (2010) of OR = 1.24 per 10 μg/m3is equivalent to OR = 1.24 per 8.14 ppb. This odds ratio 

represents the exponentiated linear slope (beta) derived from the fixed-effect regression model. 

In order to rescale this effect to one ppb, the slope (beta) should be rescaled to represent the 

change in response per unit increase in exposure. The natural log of 1.24 is 0.215 and this 

represents the slope for each 8.14 ppb increase in exposure. Dividing by 8.14 yields a slope 

(beta) per one ppb increase in exposure of 0.0264. Exponentiating back to the odds ratio scale, 

the rescaled OR = 1.027 per one ppb increase in formaldehyde exposure. The variance of the 

rescaled OR based on the random-effects model and the associated 95% CI can also be scaled by 

the same methods. This OR = 1.027 per one ppb increase in formaldehyde exposure has a 95% 

CI: 1.008-1.047. The p-value for the rescaled OR remains unchanged (p=0.0026). Note that this 

function is in terms of residential or (in-school) exposure levels.

2.2.4 Asthma: Discussion of Uncertainties

As noted by the NAS (2011), the health endpoints described as asthma constitute a broad range 

of respiratory effects that differ in cause, and the definition of asthma has changed over time, as 

the asthma phenotype has become better characterized. The meta-analysis included studies from 

a wide geographic range, and there are some inconsistencies in the studies included in the metaanalysis, including different effect sizes across different exposure ranges. The studies that 

contributed to the McGwin et al. (2010) meta-analysis span a time period from 1990 to 2008 and 

include both self-reported and physician-diagnosed asthma. Due to this heterogeneity of 

location, effect size, exposure range, calendar time and diagnostic criteria, there is some 

uncertainty in summarizing all these findings in a single summary concentration-response 

measure as representative of the effect on asthma. However, once the study by Rumchev et al. 

(2002) was excluded from the meta-analysis, McGwin et al. (2010) did not observe that the 

various findings were heterogeneous in the magnitude of the effect estimates. This observation 

might mitigate some potential uncertainty regarding the different ways in which the related 

health endpoints may have been defined. This appears to have been further substantiated by

additional random-effects models which were fit by McGwin et al. (2010) based on diagnostic 

criteria — studies in which the ORs were for self-reported asthma yielded a summary OR = 1.26 

(95% CI: 0.97−1.64), which was very similar to the overall summary OR = 1.24. 
20

In addition to differences in the calendar year of each source study in the meta-analysis, there 

were also differences in the exposure settings and in the range of exposure values. Some studies 

were based on measured residential exposures, while others were based on exposures measured 

in schools. Both exposure settings appear to be relevant for the economic benefits assessment 

approach proposed here. It also appears that the range of exposures in the studies on which the 

concentration-response function for formaldehyde-associated asthma was based is appropriate 

for use in the economic analysis described in this document. Exposure concentrations in the 

source studies for the meta-analysis ranged from 1 μg/m3up to more than 87.5 μg/m3(1 ppb to 

70+ ppb). 

Another difference among the studies was the differing levels of adjustment for potential 

confounders. McGwin et al. (2010) noted that some of the source studies provided adjusted 

estimates but others did not. Thus, they stated that their pooled results may be subject to residual 

confounding. This is a weakness that reflects the limitations of the data available for the metaanalysis. However, a strength of the McGwin analysis is that it incorporated different studies 

from different investigators in different countries over different time frames. Such diversity can 

be considered a strength since if there were any operative biases in the study design, such as 

confounding, they would be less likely to be replicated throughout all the studies in the same

fashion. 

Finally, these data describe the effects in children but do not provide information on potential 

effects among adults. As the onset and diagnosis of asthma is more common before a person 

reaches the age of 18 years, many fewer persons would be expected to develop asthma and be 

diagnosed in adulthood. While the identified concentration-response relationship discussed here 

is limited to children, any potential adult-onset asthma incidence that is associated with 

formaldehyde exposure is considered to be relatively small. Excluding the study by Rumchev et 

al. (2002), the range of the mean ages of the participants in the included studies was from 8.1 to 

14.3 years and is considered to be appropriate for application to all but the youngest children in 

the economic analysis.

In summary, the meta-analysis results in McGwin et al. (2010) estimated an increased risk of 

asthma among exposed children for incremental increases in formaldehyde inhalation 

concentration. While the effect estimates from the fixed-effect modeling and the random-effects 

modeling were equivalent and the lack of appreciable heterogeneity led McGwin et al. to select 

the fixed-effect result, the observation of some heterogeneity and the remaining uncertainties in 

the individual studies support the selection of the random-effects result, with its wider 

confidence interval. The magnitude of this effect was reported by McGwin et al. (2010) as an 

odds ratio of 1.24 per 10 μg/m3increase in formaldehyde concentration (95% CI 1.09 – 1.42)

with a p-value of 0.0026 for the random-effects analysis. Scaling this finding to parts per billion, 

the odds ratio is 1.027 per ppb increase in formaldehyde concentration (95% CI: 1.008-1.047) 

with p-value of 0.0026.

2.3 Female Reproductive Toxicity

2.3.1 Female Reproductive Toxicity: Background
21

Although the available database for assessment of the effects of formaldehyde exposure on the 

female reproductive system was limited, epidemiologic studies suggest an association between 

occupational exposure to formaldehyde and adverse reproductive outcomes in women. Several 

of these studies examined the risks of spontaneous abortion following maternal occupational 

formaldehyde exposure with increased relative risk estimates for those exposed versus those 

unexposed in the range of 1.7 to more than 3.0 (Taskinen et al., 1999, 1994; John et al., 1994; 

Seitz and Baron, 1990; Hemminki et al., 1985, 1982; Axelsson et al., 1984). However, other 

studies (Hemminki et al., 1985, 1982) did not identify an association between occupational 

formaldehyde exposure and spontaneous abortion. A general weakness of these studies is the 

lack of rigorous exposure assessment, which could diminish the power to detect a true 

association and also limit the ability of the studies to appropriately control for any potential 

confounders. Nonetheless, these studies of formaldehyde exposure are generally consistent in 

their reporting of adverse reproductive effects, an association similar to other air pollutants such 

as particulate matter (Glinianaia et al., 2004a; Glinianaia et al., 2004b) and reactive gaseous air 

pollutants such as nitrogen oxides, sulfur dioxide, carbon monoxide (Lacasana et al., 2005; 

Maisonet et al. 2004; Sram et al., 2005).

Details of the epidemiologic studies reporting associations between formaldehyde inhalation 

exposures and reproductive and developmental outcomes and a review of their findings are 

presented in Chapter 4 of the draft IRIS assessment of formaldehyde (U.S. EPA, 2010) along 

with supportive experimental animal evidence of these epidemiologic findings. A synthesis of 

the most relevant findings and conclusions is also presented in Chapter 4 (U.S. EPA, 2010).

2.3.2 Female Reproductive Toxicity: Relevant Studies

On review of the developmental and reproductive toxicity studies in humans and laboratory

animals in the draft IRIS assessment (U.S. EPA, 2010), the Taskinen et al. (1999) Finnish 

retrospective cohort study was considered to represent the best available study evidence of 

female reproductive toxicity for the purpose of deriving a concentration-response relationship for 

use in the economic benefits assessment. The subjects, recruited from a woodworkers’ union 

and other businesses involving wood processing, were linked to a national register of births. 

Women were included if they were born between 1946 and 1975, had a live birth at age 20−40 

years during 1985−1995, had worked in the wood processing industry for at least 1 month, and 

had first employment in the wood processing industry beginning at least 6 months before the 

index pregnancy. The first pregnancy that fulfilled the above criteria was the index pregnancy. 

There were 1,094 women with these criteria. Information about personal characteristics, 

pregnancies, and exposures were collected from mailed questionnaires for which the response 

rate was 64%. After other exclusions (primarily infertility history, unknown time to pregnancy, 

and contraceptive failure), the final sample included 602 women.

Estimates of mean daily exposure to formaldehyde were based on measurements taken at the 

women’s factories of employment during the early 1990s. Where measurements were 

unavailable, measurements from equivalent industries were used. An exposure index 

representing a time-weighted average exposure (TWA) was established for every person in the 

study based on the concentration of their workplace formaldehyde multiplied by the proportion 

of the workday exposed to formaldehyde. The investigators categorized the time-weighted 
22

average formaldehyde exposure into categories of low (mean of 18 ppb), medium (mean of 76 

ppb), and high (mean of 219 ppb) exposure. Personal protection equipment included gloves and 

respirators. Taskinen et al. (1999) reported that 40% of the women noted that they always wore 

gloves, with 19% wearing them occasionally, and that respirators were rarely used (4-6%).

Time-to-pregnancy data were analyzed by a discrete proportional hazards regression procedure 

with a fecundability density ratio (FDR) as the outcome. In this method, a time scale (typically 

age or calendar time) is divided into discrete units to allow for the comparison of exposures and 

events within narrow time periods thereby effectively controlling for time. Taskinen et al. 

(1999) do not state explicitly that age was used as the timescale in the proportional hazards 

regression analyses but this is standard practice and would effectively control for age by design. 

The FDR compares the average incidence density of pregnancies for exposed women with that of 

the employed, unexposed women. As explained by Taskinen et al. (1999), an FDR significantly 

below unity suggests that conception was delayed – and indicates reduced fertility. The

employment-, smoking-, alcohol consumption-, number of children-, and menstrual irregularityadjusted FDR was 0.64 (95% CI: 0.43−0.92) for women exposed to high formaldehyde levels 

compared with the unexposed controls, indicating that there was a substantial, and statistically

significant, delay in time to conception in this group of women. At the medium exposure, there 

was a smaller adverse effect on fecundity that appeared to be concentration-dependent.

The investigators further conducted an analysis of the risk of spontaneous abortion, which also 

showed a trend towards increased risk associated with increased air concentrations of 

formaldehyde. The risk of spontaneous abortion was reported to be elevated with formaldehyde 

exposure in the low exposure group (OR = 2.4 [95% CI: 1.2−4.8]), in the medium exposure 

group (OR = 1.8 [95% CI: 0.8−4.0]), and in the high exposure group (OR = 3.2 [95% CI: 

1.2−8.3]). Endometriosis was also associated with the highest formaldehyde level (OR = 4.5 

[95% CI: 1.0−20.0]).

2.3.3 Female Reproductive Toxicity: Derivation of Concentration-Response Relationship

The available evidence that formaldehyde exposure could be associated with spontaneous 

abortion and reduced fertility (subfertility) is a serious concern. Given this association of 

formaldehyde with a reduction in fertility, based on the statistically significant reduced fecundity 

density ratio, one method to estimate the monetary cost of infertility potentially attributable to 

exposure to formaldehyde is to define the concentration-response relationship for the inability to 

conceive within 12 months. An inability to conceive within 12 months is the generally accepted 

definition of infertility; however, since the Taskinen et al. study is only of women who did at 

some point conceive and give birth to a live child, this study is measuring subfertility but not all 

forms of infertility. Table 5 in Taskinen et al. (1999) provides data on the number of women 

whose time to pregnancy exceeded 12 months at four occupational levels of exposure to 

formaldehyde: ‘non-exposed’ (0 ppb), ‘low exposure’ (mean of ~18 ppb), ‘medium exposure’ 

(mean of ~76 ppb), and ‘high’ exposure (mean of ~219 ppb). Typically, exposures from 

occupational studies are adjusted to account for the daily breathing volume appropriate to an 

environmental (versus occupational) setting and for continuous exposure across the total 

exposure period (U.S. EPA, 1993). However, with formaldehyde, there is potential for exposure 

outside of work from in-home and environmental sources of formaldehyde. A contemporaneous 
23

study of formaldehyde exposures in Finland reports an average exposure level of 21.4 ppb 

(measured over 48 hours with a personal monitor) (Jurvelin et al., 2001). It should be noted that 

both the mean exposure (18 ppb 8hr TWA) and lowest reported exposure (10 ppb 8hr TWA) of 

the ‘low exposed’ category in the Taskinen et al. (1999) study are below the reported average 

exposure level for Finland (21.4 ppb). The investigators in Taskinen et al. (1999) appear to have 

assumed that while the women were away from their “exposed” work areas their exposure to 

formaldehyde was zero. Thus, the reported occupational exposure levels did not account for 

levels of formaldehyde outside the workplace or away from “exposed” work stations within the 

workplace. This would explain why both the mean exposure and the lower end of work shift

exposures for women in the low exposure group were reported at and below expected average 

exposure levels. The draft IRIS assessment (Table 5-5 of U.S. EPA, 2010) provides details of 

the exposure adjustments needed to convert the reported exposure levels from Taskinen et al. 

(1999) to 8-hour TWA exposure levels taking estimated background (i.e., “non-exposed” work 

area) exposure levels in the workplace into account. Jurvelin et al. (2001) reported average 

formaldehyde exposures of 21.4 ppb among 15 randomly selected residents of Helsinki, Finland 

in 1997 based on 48-hour measurements with personal monitors. While major metropolitan 

formaldehyde concentrations likely exceed those of other locations in the country where the 

study subjects lived and worked and the 1997 sampling date occurred after the study period 

(1985-1995), 21.4 ppb serves as a reasonable estimate of the non-work-station exposure 

experienced by the study subjects. Factoring in the average non-work-station exposure 

concentration of 21.4 ppb (Jurvelin et al., 2001) for all times when the study subjects were not 

working in “exposed” workplace areas, the 8-hr TWA exposure levels are ‘non-exposed’ (21 

ppb), ‘low exposure’ (mean of 34 ppb), ‘medium exposure’ (mean of 86 ppb), and ‘high’ 

exposure (mean of ~226 ppb). The same approach can be used to derive 24-hour TWAs, with

the average exposure level of 21.4 ppb from Jurvelin et al. (2001) serving as an estimate of 

background exposure levels outside of work. The adjusted 24-hour TWA exposure levels are 

‘non-exposed’ (21 ppb), ‘low exposure’ (mean of 26 ppb), ‘medium exposure’ (mean of 43 ppb), 

and ‘high’ exposure (mean of 89 ppb). These data are summarized in Table 2 below. 

Table 2. Concentration-response data on time to pregnancy from Taskinen et al. (1999) 

Table 5 with reported and adjusted exposure concentrations.

< 1 

year

≥ 1 

year Total

Risk of 

Not 

Conceiving 

within 12 

months RR

Formaldehyde 

conc w/o 

background 

(ppb)

8-hour 

TWA 

exposure 

conc 

adjusted 

for 

background 

(ppb)

24-hour 

TWA 

exposure 

conc 

adjusted 

for 

background 

(ppb)

Unexposed 261 27 288 0.094 1.00 0 21 21
24

Low 107 12 119 0.101 1.08 18 34 26

Medium 68 9 77 0.117 1.25 76 86 43

High 31 8 39 0.205 2.19 219 226 89

Regression equations for linear and exponential fits to the adjusted 24-hour TWA data in Table 2 

are provided below. The estimated concentration-response functions are shown in Figure 6.

Figure 6. Linear and exponential concentration-response relationships between 

formaldehyde exposure and subfertility (24-hour TWA exposure with adjustment for 

background exposure concentration) based on data from Table 5 of Taskinen et al. (1999). 

The linear function of subfertility risk based on estimated 24-hour TWA exposure concentrations 

adjusted for background exposures yielded a measure of fit of R

2

=0.987 indicating a good fit to 

these data. The linear function can be expressed as:

 = 0.056 + 0.0016() (2-3)

Here the estimated background risk of subfertility is 5.6% (in the hypothetical absence of any 

ambient formaldehyde), which is somewhat lower than reported rates for the general United 

States population. Stephen and Chandra (1998) cite data from the National Survey of Family

Growth showing the infertility rates in the United States range from 4-6% among females age 

15-24 years, from 10-11% among those aged 25-34 years and from 11-13% among those aged 

35-44 years.

0

0.05

0.1

0.15

0.2

0.25

0 20 40 60 80 100

Risk of N

ot C

onceiving Within 12 M

onths

24-hour TWA Formaldehyde Concentration (ppb)

obs risk

linear model

exponential model
25

The exponential function of risk (which is equivalent to the linear function of ln(risk)) yielded a 

measure of fit of R2=0.997, also indicating a good fit to these data. The exponential function can 

be expressed as:

 = 0.074 ∗ 

.()

(2-4)

Here the background risk of subfertility is 7.4%, which is closer to the reported rates cited above.

The results based on the estimated 24-hour TWA exposures adjusted for background are 

considered the most applicable for use in the economic benefits assessment. Both the linear and 

exponential models appear to slightly underestimate background rates for subfertility for a 

hypothetical zero exposure concentration for formaldehyde; however, exposure scenarios for the 

benefits analysis are more in the range of the data (i.e., 24-hour ADCs near or > 20 ppb), and 

both models fit well in that range. Thus, the linear function is preferred (see Equation 2-3)

because of its ease of applicability in the benefits analysis. Note that this function is based on 

formaldehyde concentration in terms of a 24-hour average exposure; this is in contrast to the 

functions provided for sensory irritation and asthma above, where the formaldehyde 

concentrations are in terms of residential (and some in-school for asthma) concentration levels.

2.3.4 Female Reproductive Toxicity: Discussion of Uncertainties

Systemic effects of formaldehyde beyond the portal of entry are unlikely to arise from the 

systemic delivery of formaldehyde; however, it was noted by the NAS (2011) that it is important 

to differentiate between systemic delivery and systemic effects and that the delivery of 

formaldehyde to distal sites was not a prerequisite for systemic effects. As mentioned 

previously, adverse reproductive effects of other air pollutants, including other reactive gases, 

have been reported in the literature.

The study by Taskinen et al. (1999) was a well-designed population-based study that appears to 

have been well executed and analyzed using appropriate methods. The study population of 

Finnish women appears well defined and adequately selected so as to allow for meaningful 

comparisons of health effects between individuals with different levels of exposure to 

formaldehyde, with qualifications discussed below. The participation rate was 64%, which is 

low enough to raise a concern about the potential for selection bias. However, the authors noted 

that selection bias has not influenced the results of other reproductive epidemiology studies 

reporting results on smoking, irregular menstruation, and earlier miscarriages, which are known 

to lengthen the time to pregnancy (Bolumar et al., 1996; Sallmén et al., 1995; Baird and Wilcox, 

1985). Furthermore, there is no evidence to support the conjecture that an individual’s decision 

to participate in this study would be differential with respect to their workplace formaldehyde 

exposures while being nondifferential with respect to the other exposures examined in the study, 

including organic solvents, wood dust, and phenols. Similarly, since the women who chose to 

participate in this study were not likely to be aware of the specific hypotheses under 

investigation, they could not have known their formaldehyde exposures, which were 

independently estimated by an industrial hygienist. Thus, selection bias is not a likely

explanation for the findings of adversity. The findings by Taskinen et al. (1999) of reduced 

fertility and increased risk of spontaneous abortion are internally consistent and coherent with 
26

other reports of increased risk of pregnancy loss associated with exposure to formaldehyde (John 

et al., 1994; Taskinen et al., 1994; Seitz and Baron, 1990; Axelsson et al., 1984). 

Other strengths include the linking of workers with the national database of birth outcomes and 

the exposure assessment by workplace measurement and an industrial hygienist. It is possible, 

however, that the women in the study may have inaccurately recalled their workplace histories. 

Weaknesses include the collection by questionnaire of data on pregnancy history, including 

spontaneous abortions and time to pregnancy. However, spontaneous abortion is the most 

common adverse outcome of pregnancy (Kline et al., 1989), and retrospective self-report of 

spontaneous abortion has been found to match well with prospectively collected reproductive 

histories (Wilcox and Horney, 1984). Many spontaneous abortions, however, are missed with 

self-reporting, with the magnitude likely exceeding 25%, but only rarely do women self-report 

false positive events (Wilcox and Horney, 1984). The effect of such an undercount is to cause a 

bias towards the null when the likelihood of undercounting is unrelated to exposure. The 

implication is that the observed association of increased risk of spontaneous abortion associated 

with occupational exposure to formaldehyde may be an underestimation of the true risk. 

Taskinen et al. (1999) state that only a few women could not report the length of time to 

pregnancy, so it is unlikely that there could have been differential accuracy in this outcome 

variable by difference in formaldehyde exposures, and, therefore, any systematic bias is also 

unlikely. Non-differential errors in reporting of outcomes is generally understood to obscure any 

true associations making them more difficult to detect statistically.

There is a possibility of exposure measurement error in the computation of mean daily exposure 

concentrations. The exposure assessment was based on a detailed questionnaire on workplace, 

occupation, and work tasks, which were matched to industrial hygiene measurements from the 

same factory, when available, or from other work places of the same industrial activity. 

Differential recall of workplaces, occupations and work tasks as an explanation for the reported 

findings is a realistic concern in general. However, it is unclear why recall would have been 

differential for formaldehyde in such a way as to create bias for that exposure but not for 

exposures to phenols or dusts which were also evaluated as potential exposures of concern. Had 

there been differential recall, such a phenomenon would likely have been across all exposures. 

As the industrial hygiene exposure estimates of all exposures were done without knowledge of 

the pregnancy history, any measurement error would likely have been non-differential. It is well 

known that non-differential (random) measurement error tends to create a bias towards the null. 

In this case, the implication would be that the true effect of the formaldehyde exposures may

have been an even lower FDR, which was attenuated towards the null value of 1 (unity). It is 

difficult to estimate the magnitude of such exposure measurement bias. Recent methodological

work which imposed substantial measurement error on simulated exposure values showed that 

attenuation was as high as 50% (Bateson and Wright, 2010), with more modest error resulting in 

a 20% attenuation. For the concentration-response function derived here, the true slope may be 

somewhat steeper than estimated due to potential exposure measurement error. There is also 

uncertainty in the adjustment for non-work-station exposures, which was based on the average 

exposure concentration from 48-hour sampling of 15 individuals (who were not part of the 

Taskinen et al. study).

In addition, there is uncertainty regarding the extent to which the effect of formaldehyde on FDR 

involves inhalation and/or dermal exposure. While there did appear to be a trend towards greater 
27

reductions in fertility associated with greater air concentrations of formaldehyde, only the most 

highly exposed group showed a statistically significant effect, with a FDR of 0.64 [95% CI: 0.43-

0.92]. Taskinen et al. (1999) noted that of the 39 women with the highest exposures, 22 wore 

gloves. The FDR for the 17 women who did not wear gloves was 0.51 [95% CI: 0.28−0.92]. 

The FDR for women who did wear gloves was 0.79 [95% CI: 0.47−1.23]. Results stratified by

respirator use were not presented. 

The FDR estimates stratified by glove use can be interpreted in at least three ways. First, these 

results may indicate that there was some protective effect of glove use since when the highly 

exposed group was separated based on glove use, the FDR for women who did wear gloves 

appeared higher and was not significantly different from one (FDR=0.79 [95% CI: 0.47−1.23]). 

If the route of exposure were dermal rather than by inhalation, then the use of protective gloves 

may have a beneficial effect on the time to pregnancy.

Second, while only the results for all highly exposed women (FDR = 0.64; 95% CI: 0.43-0.92) 

and those who did not wear gloves are statistically significantly different from 1, which may

suggest a role for dermal contact in the observed subfertility associated with formaldehyde 

exposure, all 3 results are below 1 and the confidence intervals have substantial overlap with 

each other. The substantial overlap of the confidence intervals suggests that there is not a 

statistically significant difference between the results with and without gloves. Thus, the 

difference in adverse effect estimates based on glove usage may simply be the result of random 

variability in subdividing the 39 highly exposed women into smaller groups of 17 and 22. 

Third, it is well understood that workplace safety protocols will result in the correlation of use of 

protective equipment. Therefore, it is plausible that women who were more likely to wear 

gloves were also more likely to wear respirators and that the difference in FDR estimates 

between those who used gloves and those who did not may be partially explained by the joint 

usage of gloves and respirators.

EPA used a general form of a Wald statistic to test the homogeneity hypothesis that the FDR of 

0.64 reported for all highly exposed women was uniform across both strata of glove use. The 

Wald statistic is the sum of the squared differences between the stratum-specific effect estimates 

and the hypothesized common value of the effect estimate divided by the variance of the 

stratum-specific effect estimate (Rothman and Greenland, 1998). For ratio measures such as the 

FDR, the natural logarithm should be taken. The variances of the stratum-specific ln(FDR) were 

calculated by extracting the standard errors from the confidence intervals. The Wald statistic 

was computed as follows:



 =

[(.)(.)]



.

+

[(.)(.)]



.

= 1.30 (2-5)

The Wald statistic has one less degree of freedom than the number of strata. Here the p-value is 

0.25, so the hypothesis of homogeneity of effect across strata of reported glove use is not 

rejected.

This assessment relied on the facts that the a priori null hypothesis that air concentrations of 

formaldehyde were not associated with reduced fertility was statistically rejected based on the 
28

FDR for all highly exposed women and that, in a sub-group analysis of glove use, a statistical 

test of the homogeneity of effect across levels of glove use did not show that the effect was 

modified by glove use. Therefore, this assessment developed a concentration-response function 

assuming that the reduced fertility effects as measured by the increased time to pregnancy are 

attributable to inhalation exposure, recognizing that there are potentially important uncertainties 

which remain. 

Lastly, although Taskinen et al. (1999) controlled for several possible confounding variables 

(employment, smoking, alcohol consumption, number of children, and menstrual irregularity), it 

is not explicitly clear that they controlled for the age of the women in the study (which ranged 

from 20-40 years) in the proportional hazards regression model. However, the authors did 

explicitly state that age was controlled for in the other analyses which were presented. It is well 

known that age is negatively correlated with female fertility. Consequently, if, for any reason, 

older women tended to have higher exposures and they did not control for age, then this may

lead to a misattribution of the fertility effect to formaldehyde rather than age. Exposure to 

solvents, wood dust and other dusts, and phenols was not associated with decreased fecundability 

and these agents would not be expected to have been confounders. Xylene was reported to be 

associated with an increased risk of spontaneous abortion in an earlier study in laboratory

workers (Taskinen et al., 1994) but was not mentioned as an exposure for the wood workers.

As noted at the outset of this section, the database on the effects of formaldehyde exposure on 

the female reproductive system was limited. The available evidence from epidemiologic studies 

is suggestive of an association with an increased risk of spontaneous abortion, which is coherent 

with and contributory to diminished fertility and increased infertility since the loss of a 

pregnancy delays the time until delivery of a live born child. Evidence from animal toxicology

studies is also supportive of the observed association in humans. While the evidence base is 

small and somewhat varied, the potential impact of the suggested association, however uncertain, 

remains important. In their peer-review of the draft IRIS assessment, the NAS (2011) affirmed 

that the derivation of quantitative concentration-response estimates from such available evidence 

is in keeping with EPA’s non-cancer practices even if there is uncertainty about the effect (U.S. 

EPA, 2002).

In summary, Taskinen et al. (1999) reported a finding of an association between formaldehyde 

exposure and reduced fertility that appeared to be concentration dependent. While this may only

be suggestive of an association, it does appear to be consistent with the relatively small data base 

of other studies of female reproductive toxicity. Evidence that formaldehyde could be associated 

with reduced fertility (subfertility) is a serious concern and more research would be helpful in 

reducing uncertainty in the hazard identification and quantifying any concentration-response 

relationship. The available data from Taskinen et al. (1999) do allow for the derivation of a 

concentration-response function which can provide a basis for use in the economic analyses. 
29

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NY Acad Sci 641:137–151.

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Crit Rev Toxicol 31:313–347.

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to formaldehyde exposure in homes. Allergy 34:330–337.

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Systematic Review of the Epidemiologic Evidence. Epidemiology 15, 36-45. 

Glinianaia, S.V.; Rankin, J.; Bell, R.; et al. (2004b) Does Particulate Air Pollution Contribute to 

Infant Death? A Systematic Review. Environ. Health Perspect. 112, 1365-1371. 

Hanrahan, LP; Dally, KA; Anderson, HA; et al. (1984) Formaldehyde vapor in mobile homes: a 

cross sectional survey of concentrations and irritant effects. Am J Public Health 74(9):1026–27.
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Hemminki, K; Kyyrönen, P; Lindbohm, ML. (1985) Spontaneous abortions and malformations 

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hazards in hospitals, based on registered information of outcome. J Epidemiol Community

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Hemminki, K; Mutanen, P; Salonienmi, I; et al. (1982) Spontaneous abortions in hospital staff 

engaged in sterilizing instruments with chemical agents. Br Med J 285:1461–1463.

Holmström, M; Wilhelmsson, B. (1988) Respiratory symptoms and pathophysiological effects of 

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membranes and lungs: A study of an industrial population. JAMA 259:701–707.

John, EM; Savitz, DA; Shy, CM. (1994) Spontaneous abortions among cosmetologists. 

Epidemiology 5:147–155.

Jurvelin, J; Vartiainen, M; Jantunen, M; et al. (2001) Personal exposure levels and 

microenvironmental concentrations of formaldehyde and acetaldehyde in the Helsinki 

metropolitan area. J Air Waste Manag Assoc 51:17–24.

Kline J, Stein Z, Susser M. Conception to birth: epidemiology of prenatal development. New 

York: Oxford University Press, 1989.

Kriebel, D; Sama, SR; Cocanour, B. (1993) Reversible pulmonary responses to formaldehyde. A 

study of clinical anatomy students. Am Rev Respir Dis 148:1509–1515.

Kriebel, D; Myers, D; Cheng, M; et al. (2001) Short-term effects of formaldehyde on peak 

expiratory flow and irritant symptoms. Arch Environ Health 56(1):11–18.

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Prenatal and Early Childhood Health Effects. Eur. J. Epidemiol. 20, 183-199. 

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mobile homes. Environ Health Perspect 94:91–94.

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Effects of Ambient Air Pollution on Fetal Growth. Environ. Res. 95, 106-115. 

McGwin, G; Lienert, J; Kennedy, JI. (2010) Formaldehyde Exposure and Asthma in Children: A 

Systematic Review. Environ Health Perspect 118:313–317.
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National Academy of Science. (2011) Review of the Environmental Protection Agency’s Draft 

IRIS Assessment of Formaldehyde. National Research Council.

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chemicals. Crit Rev Toxicol 21:183–208.

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mobile and conventional homes. Am J Public Health 77:323–328.

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exposed to organic solvents. Am J Ind Med 27(5):699–713.

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Vernon, Kentucky. National Institute for Occupational Safety and Health, U.S. Department of 

Health and Human Services, Cincinnati, OH; HETA 87-349-2022.

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Outcomes: a Review of the Literature. Environ. Health Perspect. 113, 375-382. 

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United States: 1995–2025. Fertility and Sterility 10:30-34.

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Occup Med 36:311-319.

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workers exposed to formaldehyde. Am J Ind Med 36:206–212.

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116:90–97.
32

Section 3: Benefits Assessment Approach

3.1 Introduction/Background

The economic benefit of a risk reduction to an individual can be approximated by his or her 

willingness to pay to avoid a small change in the risk times the reduction in risk. This willingness 

to pay is denominated in dollars and represents the amount of money the individual would pay to 

obtain the risk reduction and be just as well off as before the change. For example, if an 

individual would pay $0.10 to avoid an additional 1% risk of having a bad headache on the job 

and some policy reduced the chance of experiencing that headache by 25%, then the value of that 

policy change to the individual would be $2.50. In some cases, the cost of the illness can be used 

as a proxy for the willingness to pay but, as should be obvious in the case of a headache, this cost 

of illness may be less than the true willingness to pay to avoid the outcome. This is all relatively

straightforward if the risk reduction occurs in the current time period. Evaluating the economic 

value of a series of changes in risk that occur to a number of individuals in the future, however, 

can be tricky because one must keep track of the benefit to each individual over time and then 

discount back to the present. 

3.1.1 General Model

Following the life-cycle consumption literature (Cropper and Portney 1990; Cropper and 

Sussman 1990), an individual’s willingness to pay for a future risk reduction is the discounted 

willingness to pay in the period in which the risk reduction occurs, discounted at the 

consumption rate of interest, which could vary over time. This must be done for all risk 

reductions throughout an individual’s life. From an intergenerational standpoint, a future 

individual’s discounted willingness to pay must be discounted back to the present using a social 

rate of discount, which could also vary over time.

Mathematically, the total willingness to pay by an individual, n, at time 0 for a risk 

reduction at age a is

Total WTP ,0 WTP , ,   ,0 , ,

, 

a

n n a n a n n a     r e  e

,

(1)

where WTPn,a is the marginal willingness to pay of individual n for a risk reduction at age a. λ is 

a standard exponential discount factor equal to 1/(1+δ), where δ is a constant consumption rate of 

discount. Δrn,a(en,0,...,en,a) is the change in risk at age a, which could depend upon the exposure, 

en,t, from the beginning of the individual’s life, k=0, until age a. 

If we look at the total willingness to pay from an intergenerational perspective, then we further 

discount the individual’s value back to the present using the social rate of discount. For 

simplicity, we assume that the social rate of discount equals the consumption rate of discount, 

and that both are constant over time.7If we denominate each generational cohort, g, by the year 

 

7 Technically, the social rate of discount, αi

, does not have to equal the consumption rate of discount, δk, and both 

can vary over time. In this case, the correct discount factor for an individual of age a would be 

0 0

1 1

1 1

g a

i k     i k

   

            . 
33

in which the cohort was born, with g=0 for individuals born this year, then the total willingness 

to pay at time 0 for a risk reduction for individual ng (that is, individual n of generation g) at age 

a would be

   

( ) Total WTP ,0 WTP ,

, , ,0 ,

,

g g g g g

a g

n n a n a n n a  r e e



    .(2)

The willingness to pay for all risk reductions that this individual will receive over his or her 

lifetime, from age 0 to death at age An, would be 

   

( )

,0 , , ,0 ,

0

Total WTP WTP , ,

n

g g g g g

A

a g

n n a n a n n a

a

 r e e





    

.

(3)

To get a comprehensive measure of the total willingness to pay for any set of future risk 

reductions, this exercise must be carried out for all individuals in a generation, ng = 1,...,Ng, for 

every year of each individual’s life, a=0,...,An, and across all generations, g = 0,...,G. The total 

willingness to pay for all future risk reductions would then be

   

( )

, , ,0 ,

0 1 0

Total WTP WTP , ,

g n

g g g g

g

G N A

a g

n a n a n n a

g n a

 r e e



  

     

. (4)

3.1.2 Simplified Model

Equation (4) represents the general model, in which the willingness to pay for each individual is 

calculated as the sum of discounted willingness to pay for the risk reduction experienced in each 

period. The difficulty with equation (4) is that is requires us to know both the risk reduction and 

the willingness to pay for each individual in each period. Given that this is generally impractical, 

we modify the problem to make it tractable. For example, if every individual in a given 

generation were to experience the same risk reduction, and if we assume that the real (as opposed 

to nominal) willingness to pay value is constant across time and individuals, then equation (4) 

simplifies to

   

( )

, ,0 ,

0 0

Total WTP WTP , ,

G An

a g

g g a g g a

g a

 Pop r e e



 

     

,

(5)

where Popg is the population of individuals of generation g. An example might be the value of a 

reduction in exposure to a uniformly mixed pollutant in an airshed. Each individual experiences 

the same exposure reduction and, by assumption, the same risk reduction. If we use an average 

marginal willingness to pay to obtain this risk reduction, then we can estimate the economic 

 

However, following Cropper and Sussman (1990) , if the individual can invest his or her income in any period at a 

riskless rate of interest, d, and the individual is not wealth constrained (that is, he or she is never a net borrower), 

then the consumption rate of interest is equal to the riskless rate of interest for all periods. That is, δk = d for all k. If 

the intergenerational social discount rate is equal to the consumption rate of discount (that is, if we discount future 

generations at the same rate that we discount our own generation), then d = αi = δk in every period. In this case, a 

fixed discount factor of λ(a+g) can be used.
34

benefit of the action using equation (5). This is important because we no longer have to 

aggregate across individuals. Instead, we can simply calculate the average benefits in any given 

year, WTP , r e g a, ,  g g 0 , ,e a , multiply times the population in that year, Ng, and discount 

back to the present using the discount factor λ(a+g).

In the case of formaldehyde exposure, however, we cannot assume that each individual 

experiences the same risk reduction. However, we can still avoid aggregating across individuals 

through two simplifying assumptions. First, if the risk reduction is only a function of the 

exposure at age a rather than the lifetime exposure, then the change in risk for individual ng, is

  r e n a g g , ,  n n 0 , , ,  e r

g g a n   , , a n eg

a . Second, if we assume a linear concentration-response 

function (or approximate linearity around the change in exposure), then the change in risk is 

some proportion of the change in exposure. That is, 

, ,   , g g gn a n a n a   r e e . With these two 

changes, equation (4) simplifies to

   

( )

,

0 0

Total WTP WTP

n

g

G A

a g

g n a

g a

  Pop e



 

     

.

(6)

This is the correct formula if every individual experiences the same change in exposure at the 

same age, but can be expanded if different groups experience different exposure changes. For 

formaldehyde, individuals in different housing types (e.g., detached single family homes, 

attached single family homes, apartments, mobile homes, and campers/RVs) experience different 

levels of formaldehyde based on the amount of composite wood products in these housing units 

and the air volume. In addition, different age groups (infants, children, adult workers, and 

retirees) experience different exposure levels based on the amount of time they are in the home 

and where they go when they are not in the home. 

Dividing the population up into exposure groups based on age cohorts, c=0,...,C, and housing 

type, h = 1,...,H, and letting t=a+g, the simplified equation for total willingness to pay can be 

written as

  , ,  , , 

0 1 1

Total WTP WTP

T H C

t

hct hct

t h c

  Pop e

  

       

,

(7)

where Poph,c,t is the population in each exposure group at time t and Δeh,c,t is the change in 

exposure experienced by that group. The advantage to this approach is that the willingness to pay 

can be calculated for each year individually and the total willingness to pay will be calculated as 

the sum of discounted values. 

Equation (7) can now be applied to each endpoint to obtain the total willingness to pay for a 

policy change. The change in exposure in any given year will vary by individual depending on 

the type of housing structure, the age of that housing, and the climate (specifically, the 

temperature and humidity). The complete benefits analysis will use approximately 220 exposure 

scenarios associated with four housing types (mobile homes, apartments, single family attached 
35

homes, and single family detached homes), eleven age-of-unit profiles (new structure, 1-year-old 

structure, ..., 10 year-old structure), and five geographic climate zones. (illustrated in Figure 8).

Figure 8. The U.S. Energy Information Administration’s five climate zones based on the average 

number of heating degree-days (HDD) and cooling degree-days (CDD) over a 30-year period. 

Climate zones do not necessarily follow State boundaries, because climate is affected by

elevation, proximity to coast lines, latitude, and other physical features. 

To simplify this exposition, however, we illustrate the benefits analysis using just three housing 

profiles: a new mobile home in climate zone 1, a 1-year-old mobile home in climate zone 1, and 

a new single family detached home in climate zone 1. The population in each housing type will 

be the population for that climate zone, estimated from the Residential Energy Consumption 

Survey (EIA 2008) and scaled by aged to match the age distribution for the general population

(U.S. Bureau of Census 2009). An example of this application is given below for each of the 

three endpoints (sensory irritation, asthma incidence, and reduced fertility). The discussion for 

each endpoint is organized into four parts: monetization; the application of the annual approach, 

a worked example, and a discussion of the uncertainties. These three endpoints represent the 

non-cancer effects for which a quantitative concentration exposure-response relationship can be 

derived. It is possible, even likely, that there are other non-cancer health impacts associated with 

formaldehyde exposure for which concentration exposure-response relationships cannot derived 
36

due to lack of data or sufficient research. If this is true, then the total economic benefits may be 

underestimated in the analysis here.

3.2 Sensory Irritation

The valuation of sensory irritation is the most straightforward of the three non-cancer endpoints 

because the monetization has been used in numerous EPA rules and the concentration-response 

relationship is for a time period less than the one year time step of the exposure model.

3.2.1 Monetization

Loehman and others conducted a survey of 396 respondents to estimate the willingness to pay to 

avoid one symptom-day of shortness of breath, coughing and sneezing, and head congestion 

(including eye, ear, and throat irritation). A survey of this sort, in which respondents are asked 

to state their willingness to pay based on the policy described is called stated preference survey. 

Loehman used a specific type of stated preference survey called a contingent valuation survey. 

They report a median willingness to pay of $2 - $79 per avoided symptom-day. The value for 

severe head congestion (which includes eye irritation) was $8.17 for one symptom-day. (Green 

et al. 1978; Loehman et al.1979)

Tolley et al. (1986) conducted a contingent valuation study from the personal interviews of 176 

respondents in 1984-1985 regarding the willingness to pay to avoid seven “light” (i.e., less 

severe) symptoms. The symptoms were coughing, stuffed sinuses, throat congestion, itching 

eyes, drowsiness, headache, and nausea. The willingness to pay to relieve one symptom-day of a 

light symptom ranged from $25 to $50, with a mean value of $27.73 and a median value of 

$12.50. (Kenkel, Berger, and Blomquist 1994) Berger et al. (1987) reanalyzed these data to 

compare the mean willingness to pay and the private cost of illness for these symptoms and 

found similar values. Dickie and Gerking (1991 and 1998) used a household production function 

approach to estimate the willingness to pay to avoid 26 respiratory symptoms related to air 

pollution in 1985 and 1986. The symptoms included were cough; throat irritation; husky voice; 

phlegm, sputum or mucous; chest tightness; could not take a deep breath; pain on deep 

respiration; out of breath easily; breathing sounds, wheezing or whistling; eye irritation; could 

not see as well as usual; eyes sensitive to bright light; ringing in ears; pain in ears; sinus pain; 

nosebleed; dry and painful nose; runny nose; fast heartbeat at rest; tired easily; faintness or 

dizziness; felt spaced out or disoriented; headache; chills or fever; nausea; and swollen glands. 

They found a range of estimates between $0.49 and $190 to relieve one symptom for one day. 

Industrial Economics Incorporated, IEc (1993a and 1993b), conducted a survey of the literature 

and provided a range of willingness to pay estimates for a variety of morbidity effects, including 

throat congestion, head and sinus congestion, coughing, asthma attack, chronic allergy attack, 

eye irritation, headache, shortness of breath, chest tightness, nausea, drowsiness, chronic 

bronchitis, and angina pectoris. While IEc recommend averaging a number of studies for many 

of the health effects, they relied only on Tolley et al. (1986) for the value for eye irritation. 

Based on these estimates, eye irritation had the highest (mid-range) estimate of the willingness to 

pay for to avoid a single symptom for one day. 
37

IEc 1993a, 1993b also estimated the willingness to pay to avoid a minor respiratory restricted 

activity day using the willingness to pay estimates from Tolley et al. (1986) assuming a 

combination of three symptoms: coughing, throat congestion, and sinusitis. The assumption 

behind a minor restricted activity day is that it is a combination of symptoms, but the term is not 

exactly defined. Krupnick and Kopp (1988) previously suggested that a reasonable lower bound 

for the willingness to pay for a minor respiratory restricted activity day would be the willingness 

to pay to avoid a single mild symptom, since any combination of symptoms and various levels of 

restriction might be considered part of a restricted day. Since a restricted activity day is 

something less than a lost work day, an upper bound would be the value of a work loss day. 

Based on IEc’s (1993) average values, eye irritation has the highest (mid-range) willingness to 

pay value. Therefore, the value to avoid eye irritation serves as the best single mild symptom to 

use to represent a lower bound on a combination of symptoms.

These results have been used by EPA in a number of contexts. In 1997, EPA conducted a 

retrospective analysis of the benefits and costs of the Clean Air Act (EPA 1997), including the 

benefits of reduced upper respiratory symptoms associated with air pollution. The upper 

respiratory symptoms are defined by Pope et al. (1995) as consisting of one or more of the 

following symptoms: runny or stuffy nose; wet cough; and burning, aching, or red eyes. A 

central estimate of $19 (in 1990 dollars), with a range from $7 to $33, was developed for one 

symptom-day, based on the mid-range estimate produced by IEc (1993). The value for a minor 

restricted activity day is $38, with a range between $16 and $61 (and an assumption of a 

triangular distribution). The lower bound of $16 is based on the IEc estimate of eye irritation.

In 1999, EPA conducted a prospective analysis of the Clean Air Act (EPA 1999) and used the 

same values as it used in the 1997 retrospective analysis. In 2011, EPA conducted a second 

prospective analysis of the Clean Air Act from 1990 to 2020 (EPA 2011a). In this second 

prospective analysis, the values were updated to 2006 dollars and were adjusted to reflect the 

expected rise in income level between 1990 and 2020. The value for upper respiratory symptoms 

was $28.80 at 1990 income levels (in 2006$) and $30.70 at 2020 income levels, with a range of 

$10.80 to $50.50. The value for a Minor Restricted Activity Days is $59 at 1990 income levels 

and $64 at 2010 income levels, a range of $24 to $94. As before, the lower bound of the minor 

restricted activity days of $24 is based on the highest estimate for a single symptom, which is for 

eye irritation. 

These values are also used for regulatory analysis by EPA’s Office of Air and Radiation. While 

the Economic Analysis for each regulation includes a comprehensive discussion of the 

willingness to pay values used, the Office of Air and Regulation (EPA 2011b) describes the most 

common values in its Environmental Benefits Mapping and Analysis Program (BenMAP) 

program. BenMAP is a publicly available GIS-based program distributed by the EPA to estimate 

the health impacts and economic benefits from air quality improvements. Table 3 reports the 

median values as given in the BenMAP documentation (EPA 2011a)

The value for eye irritation is listed as $20.03 in 1999 dollars, based on the median value of 

Tolley et al. (1986).

Table 3: Median Willingness to Pay Estimates for Morbidity Symptoms
38

Source: Table J-10 in EPA BenMAP documentation ((EPA 2011a).

In summary, the willingness to pay to avoid eye irritation has been used in a number of EPA 

studies. The use of different base years for different analyses obscures the fact that the value 

used is almost always based on the IEc (1993) estimate derived from Tolley et al. (1986). 

Therefore, a value of $24 in 2006 dollars, as was used in the last EPA study to use this number 

(EPA 2011a), is the value that will be used here as the willingness to pay to reduce eye irritation 

from formaldehyde exposure. 

3.2.2 Annual approach

The concentration-response function for the prevalence of eye irritation (as a proxy for sensory 

irritation, as described in Section 2.1 of this document) takes the form exposure

1 exposure

b

b

a

p

a





 

. 

Because this relationship is modeled for a time of less than one year, the total willingness to pay

to reduce eye irritation for one year, t, is a straight-forward application of equation (7) above. 

 

1

0

, , , ,

, ,

1 1 , , , ,

exposure exposure

Total WTP WTP

1 exposure 1 exposure

t H C b b

t hcbaseline h c policy

t h c t b b

t t h c hcbaseline h c policy

a a

Pop

a a



  

       

       

             

,

(8)

where 
39

 

, , , ,

, ,

, , , ,

exposure exposure

WTP

1 exposure 1 exposure

b b

hcbaseline h c policy

hct b b

hcbaseline h c policy

a a

Pop

a a

       

     

            (9)

is the willingness to pay for any given housing and age cohort. Poph,c,t is the population in that 

particular cohort, and WTP is the estimate of the WTP for eye irritation (described above). This 

willingness to pay can then be calculated for each year of analysis. If we were to assess the total 

benefits of a policy action, we would need to discount each year’s benefits back to the base year 

using the discount factor λ.

 

, , , ,

, ,

0 1 1 , , , ,

exposure exposure

Total WTP WTP

1 exposure 1 exposure

b b T H C

t hcbaseline h c policy

hct b b

t h c hcbaseline h c policy

a a

Pop

a a



  

       

       

             

.

(10)

3.2.3 Example calculation

The concentration-response function for the prevalence of eye irritation given in Section 2.1 of 

this document is 

 

 

7 2.3743

7 2.3743

7 10 exposure

1 7 10 exposure

p





 



  

based on Hanrahan et al. (1984). While 

Hanrahan does not provide the relevant time period for this relationship, Liu et al. (1991) 

produced qualitatively similar results for a two-week time period. Therefore, the following 

development assumes that the concentration-response relationship for eye irritation is for a twoweek period. This means that for one year, 26 two-week periods, the concentration-response 

function would be 

   

 

7 2.3743

7 2.3743

26 7 10 exposure

1 7 10 exposure

p





  



  

.

Table 4, below, lists the exposure for three housing profiles for both the baseline and a “CARB2” 

policy scenario (i.e., emission limits set at the California phase 2 levels, which are also the 

emission limits mandated by FSCWPA). This exposure assessment comes from a spreadsheet 

model based on an application of the Matthews model (Hawthorne and Matthews 1987). A 

model housing structure is simulated for each housing profile using assumptions about the 

emissions from the wood found in each housing type for the baseline scenario. The policy 

scenario is then simulated by assuming that any composite wood in the baseline scenario that is 

not compliant with California’s CARB phase 2 standard is made to be compliant. Any wood 

[product] that already meets and has lower emissions than specified by CARB2 is assumed to 

remain the same. In spreadsheet form the formaldehyde exposure results are reported in mg/m3; 

for display in Table 1, the results have been converted to ppb by assuming that 814 ppb 

formaldehyde = 1 mg/m3. This assumption corresponds to a temperature of 25°C, a pressure of 1 

atm, and a molecular weight for formaldehyde of 30.03 g/mol., which is line with the approach 

for performing unit conversions as described by the National Research Council’s standing 

operating procedures for developing acute exposure guideline levels for hazardous chemicals 

(NRC 2001).

Table 4: Illustrative formaldehyde exposure scenarios using three housing profiles
40

Scenario Housing Profile Infants Avg. 

ADC

Preschool / 

School Child 

Avg. ADC

Non-Industrial 

Worker Avg. 

ADC

Retirees Avg.

ADC

Weighted average ADC (mg/m3) during current exposure year

Baseline

New Mobile Home 0.0394 0.0344 0.0349 0.0419

1-year-old Mobile Home 0.0280 0.0248 0.0256 0.0296

New Detached Home 0.0356 0.0312 0.0319 0.0381

CARB2

New Mobile Home 0.0375 0.0328 0.0333 0.0398

1-year-old Mobile Home 0.0268 0.0238 0.0247 0.0283

New Detached Home 0.0354 0.0311 0.0318 0.0379

Weighted average ADC (ppb) during current exposure year

Baseline

New Mobile Home 32.07 28.00 28.41 34.11

1-year-old Mobile Home 22.79 20.19 20.84 24.09

New Detached Home 28.98 25.40 25.97 31.01

CARB2

New Mobile Home 30.53 26.70 27.11 32.40

1-year-old Mobile Home 21.82 19.37 20.11 23.04

New Detached Home 28.82 25.32 25.89 30.85

Weighted average ADC (ppb) during current exposure year

Change

New Mobile Home -1.55 -1.30 -1.30 -1.71

1-year-old Mobile Home -0.98 -0.81 -0.73 -1.06

New Detached Home -0.16 -0.08 -0.08 -0.16

* Note: These are preliminary estimates and will likely change in the final exposure and benefits assessments.

ADC = Average Daily Concentration.

The average daily concentration (ADC) for four categories of classes of individuals (infants, age 

0-2; preschool and school-aged children, age 2-16; non-industrial workers, age 16-65; and 

retirees, age 65-100) are reported in Table 1. Each individual is assumed to enter the next age 

group at the birthday on the lower bound of the age category. So, for example, an individual is 

classified as an infant until his or her second birthday, whereupon that individual is classified as 

a preschool/school-aged child. Individuals in different age categories but living in the same 

housing type have different ADCs because they have different levels of exposure to 

formaldehyde outside of the home. The exposure model accounts for formaldehyde 

concentrations in schools and daycare, in automobiles, workplace exposure, outside. The final 

benefits analysis will include exposure for a larger group of individuals (e.g., workers exposed to 

higher levels of formaldehyde in the workplace), but the four classifications given here are 

sufficient to illustrate the benefits methodology.

Individuals in a new mobile home have the highest baseline exposure of these three profiles, 

based on ppb, ranging from 34.11 ppb for retirees (in the last column of Table 1) to 28.00 ppb for 

school-aged children (in the fourth column of Table 1). The exposure is different for each 

individual because of the amount of time each individual spends in the home compared to other 

activities. For example, children spend more time outside where formaldehyde exposure is 

comparatively lower than in the home. The policy scenario results in a reduction of 1.71 ppb to 

1.30 ppb for new mobile homes.
41

Individuals in new single-family detached home have the next highest exposure in this example, 

ranging from 31.01 ppb to 25.40 ppb. New single family homes have lower emissions than new 

mobile homes because of the larger ratio of air volume to surface area of wood in the home. A 1-

year-old mobile home has a baseline range of exposure from 24.09 ppb to 20.19 ppb. The 1-yearold mobile home has lower emissions than a new mobile home because the stepwise 

approximation of off-gassing of formaldehyde, with the largest emissions coming from the first 

year and declining exponentially thereafter. Notice, however, that even though a new detached 

home has higher overall emissions than a 1-year-old mobile home, the emissions reductions from 

the policy scenario are larger in the 1-year-old mobile home. This is because the volume of wood 

which is assumed to be affected by the rule and the effect that it has in the unit differs by housing 

type, as predicted by the Matthews model.

Table 5, below, illustrates how this exposure assessment and the concentration-response function

for eye irritation would be used in a benefits analysis for these three housing profiles in climate 

zone 1. Each profile has an 8-column block in the table. The first column block represents the 

population of 21,670 individuals living in new mobile homes (EIA 2008). This population is 

distributed across ages (represented by rows) in proportion to the age distribution for the nation 

as a whole (U.S. Bureau of Census 2009). The baseline exposure, policy scenario exposure, and 

associated change in ppb are listed for each age. The number of cases for the baseline, policy, 

and the change in cases (in absolute value) for each age is then calculated using the difference in 

the concentration-response function at baseline and CARB2 exposure levels. Using a willingness 

to pay of $24 per case, the willingness to pay at any age is given by equation (9). For example, 

for an individual age 0 (that is, an infant before his or her first birthday) living in a new mobile 

home, this would be 

   

     

   

     

   

2.3743 2.3743 7 7

0 2.3743 2.3743 7 7

26 7 10 32.07 26 7 10 30.53

Total WTP $24 302 $55

1 7 10 32.07 1 7 10 30.53

 

 

           

          

             

In total, 129.3 cases (the sum of all rows from age 0 on) of eye irritation would be avoided from 

formaldehyde exposure reduction in new mobile homes in climate zone 1 for one year. The total 

willingness to pay for this housing profile across all ages would be $3,103.
42

Table 5: Illustrative benefits calculations for sensory irritation using three housing profiles

Age Population

Baseline 

Exposure 

(ppb)

CARB2 

Exposure 

(ppb)

Exposure 

Reduction 

(ppb)

Baseline 

Cases

Policy 

Cases

Change 

in Cases WTP Population

Baseline 

Exposure 

(ppb)

CARB2 

Exposure 

(ppb)

Exposure 

Reduction 

(ppb)

Baseline 

Cases

Policy

Cases

Change in 

Cases WTP Population

Baseline 

Exposure 

(ppb)

CARB2 

Exposure 

(ppb)

Exposure 

Reduction 

(ppb)

Baseline 

Cases

Policy 

Cases

Change 

in Cases WTP

21,670 129.3 $3,103 21,670 48.9 $1,174 302,507 115.4 $2,770

0 302 32.07 30.53 -1.55 20.75 18.44 2.30 $55 302 22.79 21.82 -0.98 9.21 8.30 0.91 $22 4,213 28.98 28.82 -0.16 227.49 224.46 3.03 $73

1 299 32.07 30.53 -1.55 20.58 18.30 2.28 $55 299 22.79 21.82 -0.98 9.13 8.23 0.90 $22 4,180 28.98 28.82 -0.16 225.71 222.70 3.01 $72

2 302 28.00 26.70 -1.30 15.02 13.42 1.61 $39 302 20.19 19.37 -0.81 6.90 6.26 0.64 $15 4,214 25.40 25.32 -0.08 166.27 165.01 1.26 $30

3 304 28.00 26.70 -1.30 15.15 13.53 1.62 $39 304 20.19 19.37 -0.81 6.96 6.31 0.65 $16 4,249 25.40 25.32 -0.08 167.65 166.37 1.27 $31

4 296 28.00 26.70 -1.30 14.76 13.18 1.58 $38 296 20.19 19.37 -0.81 6.78 6.15 0.63 $15 4,139 25.40 25.32 -0.08 163.30 162.06 1.24 $30

5 293 28.00 26.70 -1.30 14.61 13.04 1.56 $38 293 20.19 19.37 -0.81 6.71 6.08 0.63 $15 4,097 25.40 25.32 -0.08 161.64 160.41 1.23 $30

6 294 28.00 26.70 -1.30 14.62 13.06 1.57 $38 294 20.19 19.37 -0.81 6.72 6.09 0.63 $15 4,101 25.40 25.32 -0.08 161.81 160.58 1.23 $30

7 290 28.00 26.70 -1.30 14.46 12.91 1.55 $37 290 20.19 19.37 -0.81 6.64 6.02 0.62 $15 4,055 25.40 25.32 -0.08 159.98 158.76 1.22 $29

8 288 28.00 26.70 -1.30 14.35 12.81 1.54 $37 288 20.19 19.37 -0.81 6.59 5.98 0.61 $15 4,025 25.40 25.32 -0.08 158.79 157.58 1.21 $29

9 292 28.00 26.70 -1.30 14.55 13.00 1.56 $37 292 20.19 19.37 -0.81 6.69 6.06 0.62 $15 4,082 25.40 25.32 -0.08 161.07 159.84 1.22 $29

10 281 28.00 26.70 -1.30 14.00 12.50 1.50 $36 281 20.19 19.37 -0.81 6.43 5.83 0.60 $14 3,928 25.40 25.32 -0.08 154.99 153.81 1.18 $28

11 277 28.00 26.70 -1.30 13.78 12.31 1.48 $35 277 20.19 19.37 -0.81 6.33 5.74 0.59 $14 3,866 25.40 25.32 -0.08 152.54 151.38 1.16 $28

12 277 28.00 26.70 -1.30 13.76 12.29 1.47 $35 277 20.19 19.37 -0.81 6.32 5.73 0.59 $14 3,861 25.40 25.32 -0.08 152.33 151.17 1.16 $28

13 278 28.00 26.70 -1.30 13.82 12.34 1.48 $36 278 20.19 19.37 -0.81 6.35 5.76 0.59 $14 3,876 25.40 25.32 -0.08 152.93 151.76 1.16 $28

14 283 28.00 26.70 -1.30 14.09 12.58 1.51 $36 283 20.19 19.37 -0.81 6.47 5.87 0.60 $14 3,952 25.40 25.32 -0.08 155.92 154.73 1.19 $28

15 288 28.00 26.70 -1.30 14.32 12.78 1.53 $37 288 20.19 19.37 -0.81 6.58 5.96 0.61 $15 4,015 25.40 25.32 -0.08 158.42 157.21 1.20 $29

16 290 28.41 27.11 -1.30 14.96 13.38 1.58 $38 290 20.84 20.11 -0.73 7.16 6.58 0.58 $14 4,055 25.97 25.89 -0.08 168.65 167.40 1.25 $30

17 297 28.41 27.11 -1.30 15.30 13.69 1.62 $39 297 20.84 20.11 -0.73 7.32 6.73 0.60 $14 4,147 25.97 25.89 -0.08 172.49 171.21 1.28 $31

18 303 28.41 27.11 -1.30 15.61 13.96 1.65 $40 303 20.84 20.11 -0.73 7.47 6.86 0.61 $15 4,231 25.97 25.89 -0.08 175.97 174.66 1.31 $31

19 309 28.41 27.11 -1.30 15.91 14.23 1.68 $40 309 20.84 20.11 -0.73 7.62 7.00 0.62 $15 4,313 25.97 25.89 -0.08 179.40 178.07 1.33 $32

20 316 28.41 27.11 -1.30 16.26 14.55 1.72 $41 316 20.84 20.11 -0.73 7.78 7.15 0.63 $15 4,408 25.97 25.89 -0.08 183.32 181.96 1.36 $33

21 306 28.41 27.11 -1.30 15.74 14.08 1.66 $40 306 20.84 20.11 -0.73 7.54 6.92 0.61 $15 4,267 25.97 25.89 -0.08 177.48 176.16 1.32 $32

22 302 28.41 27.11 -1.30 15.57 13.92 1.64 $39 302 20.84 20.11 -0.73 7.45 6.84 0.61 $15 4,220 25.97 25.89 -0.08 175.50 174.20 1.31 $31

23 301 28.41 27.11 -1.30 15.48 13.84 1.63 $39 301 20.84 20.11 -0.73 7.41 6.80 0.60 $14 4,195 25.97 25.89 -0.08 174.48 173.19 1.30 $31

24 303 28.41 27.11 -1.30 15.63 13.97 1.65 $40 303 20.84 20.11 -0.73 7.48 6.87 0.61 $15 4,235 25.97 25.89 -0.08 176.14 174.83 1.31 $31

25 305 28.41 27.11 -1.30 15.73 14.07 1.66 $40 305 20.84 20.11 -0.73 7.53 6.91 0.61 $15 4,263 25.97 25.89 -0.08 177.31 175.99 1.32 $32

26 300 28.41 27.11 -1.30 15.47 13.83 1.63 $39 300 20.84 20.11 -0.73 7.40 6.80 0.60 $14 4,191 25.97 25.89 -0.08 174.33 173.03 1.30 $31

27 305 28.41 27.11 -1.30 15.70 14.04 1.66 $40 305 20.84 20.11 -0.73 7.51 6.90 0.61 $15 4,254 25.97 25.89 -0.08 176.95 175.63 1.32 $32

28 306 28.41 27.11 -1.30 15.76 14.10 1.67 $40 306 20.84 20.11 -0.73 7.55 6.93 0.62 $15 4,272 25.97 25.89 -0.08 177.70 176.37 1.32 $32

29 308 28.41 27.11 -1.30 15.86 14.19 1.68 $40 308 20.84 20.11 -0.73 7.59 6.97 0.62 $15 4,300 25.97 25.89 -0.08 178.84 177.51 1.33 $32

30 306 28.41 27.11 -1.30 15.76 14.10 1.66 $40 306 20.84 20.11 -0.73 7.54 6.93 0.62 $15 4,272 25.97 25.89 -0.08 177.67 176.34 1.32 $32

31 291 28.41 27.11 -1.30 14.97 13.39 1.58 $38 291 20.84 20.11 -0.73 7.16 6.58 0.58 $14 4,057 25.97 25.89 -0.08 168.74 167.49 1.26 $30

32 282 28.41 27.11 -1.30 14.52 12.99 1.53 $37 282 20.84 20.11 -0.73 6.95 6.38 0.57 $14 3,935 25.97 25.89 -0.08 163.67 162.45 1.22 $29

33 277 28.41 27.11 -1.30 14.28 12.78 1.51 $36 277 20.84 20.11 -0.73 6.84 6.28 0.56 $13 3,871 25.97 25.89 -0.08 161.02 159.82 1.20 $29

34 270 28.41 27.11 -1.30 13.89 12.43 1.47 $35 270 20.84 20.11 -0.73 6.65 6.11 0.54 $13 3,766 25.97 25.89 -0.08 156.63 155.46 1.17 $28

35 277 28.41 27.11 -1.30 14.25 12.75 1.51 $36 277 20.84 20.11 -0.73 6.82 6.27 0.56 $13 3,863 25.97 25.89 -0.08 160.66 159.46 1.20 $29

36 268 28.41 27.11 -1.30 13.81 12.35 1.46 $35 268 20.84 20.11 -0.73 6.61 6.07 0.54 $13 3,743 25.97 25.89 -0.08 155.69 154.53 1.16 $28

37 274 28.41 27.11 -1.30 14.11 12.62 1.49 $36 274 20.84 20.11 -0.73 6.76 6.20 0.55 $13 3,825 25.97 25.89 -0.08 159.10 157.92 1.18 $28

38 287 28.41 27.11 -1.30 14.77 13.21 1.56 $37 287 20.84 20.11 -0.73 7.07 6.49 0.58 $14 4,004 25.97 25.89 -0.08 166.53 165.29 1.24 $30

39 302 28.41 27.11 -1.30 15.57 13.93 1.64 $39 302 20.84 20.11 -0.73 7.45 6.85 0.61 $15 4,220 25.97 25.89 -0.08 175.53 174.23 1.31 $31

40 308 28.41 27.11 -1.30 15.85 14.18 1.67 $40 308 20.84 20.11 -0.73 7.59 6.97 0.62 $15 4,297 25.97 25.89 -0.08 178.71 177.38 1.33 $32

41 291 28.41 27.11 -1.30 14.98 13.40 1.58 $38 291 20.84 20.11 -0.73 7.17 6.59 0.58 $14 4,060 25.97 25.89 -0.08 168.88 167.62 1.26 $30

42 285 28.41 27.11 -1.30 14.69 13.14 1.55 $37 285 20.84 20.11 -0.73 7.03 6.46 0.57 $14 3,982 25.97 25.89 -0.08 165.62 164.39 1.23 $30

43 286 28.41 27.11 -1.30 14.71 13.16 1.55 $37 286 20.84 20.11 -0.73 7.04 6.47 0.57 $14 3,988 25.97 25.89 -0.08 165.87 164.64 1.23 $30

44 293 28.41 27.11 -1.30 15.11 13.52 1.60 $38 293 20.84 20.11 -0.73 7.23 6.64 0.59 $14 4,096 25.97 25.89 -0.08 170.36 169.09 1.27 $30

45 313 28.41 27.11 -1.30 16.12 14.42 1.70 $41 313 20.84 20.11 -0.73 7.72 7.09 0.63 $15 4,370 25.97 25.89 -0.08 181.75 180.40 1.35 $32

46 317 28.41 27.11 -1.30 16.35 14.62 1.73 $41 317 20.84 20.11 -0.73 7.83 7.19 0.64 $15 4,431 25.97 25.89 -0.08 184.30 182.93 1.37 $33

47 316 28.41 27.11 -1.30 16.28 14.56 1.72 $41 316 20.84 20.11 -0.73 7.79 7.16 0.64 $15 4,412 25.97 25.89 -0.08 183.49 182.12 1.36 $33

48 317 28.41 27.11 -1.30 16.31 14.59 1.72 $41 317 20.84 20.11 -0.73 7.81 7.17 0.64 $15 4,420 25.97 25.89 -0.08 183.85 182.48 1.37 $33

49 319 28.41 27.11 -1.30 16.45 14.71 1.74 $42 319 20.84 20.11 -0.73 7.87 7.23 0.64 $15 4,459 25.97 25.89 -0.08 185.46 184.08 1.38 $33

50 325 28.41 27.11 -1.30 16.72 14.96 1.77 $42 325 20.84 20.11 -0.73 8.00 7.35 0.65 $16 4,533 25.97 25.89 -0.08 188.52 187.12 1.40 $34

New Mobile Home, Climate Zone 1 1 Year Old Mobile Home, Climate Zone 1 New Single Family Detached Home, Climate Zone 1
43

Table 5: Illustrative benefits calculations for sensory irritation using three housing profiles (cont.)

Age Population

Baseline 

Exposure 

(ppb)

CARB2 

Exposure 

(ppb)

Exposure 

Reduction 

(ppb)

Baseline 

Cases

Policy 

Cases

Change 

in Cases WTP Population

Baseline 

Exposure 

(ppb)

CARB2 

Exposure 

(ppb)

Exposure 

Reduction 

(ppb)

Baseline 

Cases

Policy

Cases

Change in 

Cases WTP Population

Baseline 

Exposure 

(ppb)

CARB2 

Exposure 

(ppb)

Exposure 

Reduction 

(ppb)

Baseline 

Cases

Policy 

Cases

Change 

in Cases WTP

51 311 28.41 27.11 -1.30 16.02 14.33 1.69 $41 311 20.84 20.11 -0.73 7.67 7.04 0.63 $15 4,343 25.97 25.89 -0.08 180.62 179.28 1.34 $32

52 311 28.41 27.11 -1.30 16.00 14.31 1.69 $41 311 20.84 20.11 -0.73 7.66 7.03 0.62 $15 4,336 25.97 25.89 -0.08 180.35 179.01 1.34 $32

53 306 28.41 27.11 -1.30 15.78 14.11 1.67 $40 306 20.84 20.11 -0.73 7.55 6.94 0.62 $15 4,277 25.97 25.89 -0.08 177.89 176.57 1.32 $32

54 294 28.41 27.11 -1.30 15.14 13.54 1.60 $38 294 20.84 20.11 -0.73 7.25 6.65 0.59 $14 4,103 25.97 25.89 -0.08 170.64 169.38 1.27 $30

55 295 28.41 27.11 -1.30 15.17 13.57 1.60 $38 295 20.84 20.11 -0.73 7.26 6.67 0.59 $14 4,112 25.97 25.89 -0.08 171.04 169.76 1.27 $31

56 281 28.41 27.11 -1.30 14.48 12.95 1.53 $37 281 20.84 20.11 -0.73 6.93 6.37 0.57 $14 3,924 25.97 25.89 -0.08 163.23 162.01 1.21 $29

57 271 28.41 27.11 -1.30 13.96 12.49 1.47 $35 271 20.84 20.11 -0.73 6.68 6.14 0.54 $13 3,784 25.97 25.89 -0.08 157.38 156.21 1.17 $28

58 261 28.41 27.11 -1.30 13.45 12.03 1.42 $34 261 20.84 20.11 -0.73 6.44 5.91 0.53 $13 3,646 25.97 25.89 -0.08 151.67 150.54 1.13 $27

59 254 28.41 27.11 -1.30 13.06 11.68 1.38 $33 254 20.84 20.11 -0.73 6.25 5.74 0.51 $12 3,539 25.97 25.89 -0.08 147.19 146.09 1.09 $26

60 252 28.41 27.11 -1.30 12.97 11.60 1.37 $33 252 20.84 20.11 -0.73 6.21 5.70 0.51 $12 3,516 25.97 25.89 -0.08 146.26 145.17 1.09 $26

61 241 28.41 27.11 -1.30 12.44 11.12 1.31 $32 241 20.84 20.11 -0.73 5.95 5.47 0.49 $12 3,371 25.97 25.89 -0.08 140.19 139.15 1.04 $25

62 238 28.41 27.11 -1.30 12.26 10.97 1.30 $31 238 20.84 20.11 -0.73 5.87 5.39 0.48 $11 3,323 25.97 25.89 -0.08 138.20 137.18 1.03 $25

63 248 28.41 27.11 -1.30 12.78 11.43 1.35 $32 248 20.84 20.11 -0.73 6.12 5.62 0.50 $12 3,464 25.97 25.89 -0.08 144.07 143.00 1.07 $26

64 184 28.41 27.11 -1.30 9.50 8.49 1.00 $24 184 20.84 20.11 -0.73 4.55 4.18 0.37 $9 2,574 25.97 25.89 -0.08 107.06 106.26 0.80 $19

65 183 34.11 32.40 -1.71 14.53 12.86 1.67 $40 183 24.09 23.04 -1.06 6.36 5.71 0.64 $15 2,549 31.01 30.85 -0.16 161.78 159.76 2.01 $48

66 179 34.11 32.40 -1.71 14.21 12.57 1.64 $39 179 24.09 23.04 -1.06 6.21 5.59 0.63 $15 2,492 31.01 30.85 -0.16 158.15 156.18 1.97 $47

67 183 34.11 32.40 -1.71 14.56 12.89 1.68 $40 183 24.09 23.04 -1.06 6.37 5.73 0.65 $15 2,555 31.01 30.85 -0.16 162.12 160.10 2.02 $48

68 160 34.11 32.40 -1.71 12.75 11.28 1.47 $35 160 24.09 23.04 -1.06 5.58 5.01 0.56 $14 2,237 31.01 30.85 -0.16 141.96 140.19 1.77 $42

69 147 34.11 32.40 -1.71 11.73 10.38 1.35 $32 147 24.09 23.04 -1.06 5.13 4.61 0.52 $12 2,057 31.01 30.85 -0.16 130.55 128.92 1.63 $39

70 142 34.11 32.40 -1.71 11.29 9.99 1.30 $31 142 24.09 23.04 -1.06 4.94 4.44 0.50 $12 1,980 31.01 30.85 -0.16 125.67 124.11 1.56 $38

71 134 34.11 32.40 -1.71 10.63 9.40 1.22 $29 134 24.09 23.04 -1.06 4.65 4.18 0.47 $11 1,864 31.01 30.85 -0.16 118.31 116.83 1.47 $35

72 129 34.11 32.40 -1.71 10.30 9.11 1.19 $28 129 24.09 23.04 -1.06 4.51 4.05 0.46 $11 1,807 31.01 30.85 -0.16 114.68 113.25 1.43 $34

73 120 34.11 32.40 -1.71 9.59 8.48 1.10 $27 120 24.09 23.04 -1.06 4.19 3.77 0.42 $10 1,682 31.01 30.85 -0.16 106.72 105.39 1.33 $32

74 117 34.11 32.40 -1.71 9.27 8.20 1.07 $26 117 24.09 23.04 -1.06 4.06 3.65 0.41 $10 1,626 31.01 30.85 -0.16 103.21 101.93 1.28 $31

75 115 34.11 32.40 -1.71 9.13 8.08 1.05 $25 115 24.09 23.04 -1.06 3.99 3.59 0.40 $10 1,601 31.01 30.85 -0.16 101.61 100.35 1.26 $30

76 103 34.11 32.40 -1.71 8.23 7.28 0.95 $23 103 24.09 23.04 -1.06 3.60 3.24 0.36 $9 1,444 31.01 30.85 -0.16 91.64 90.50 1.14 $27

77 102 34.11 32.40 -1.71 8.09 7.15 0.93 $22 102 24.09 23.04 -1.06 3.54 3.18 0.36 $9 1,418 31.01 30.85 -0.16 90.01 88.89 1.12 $27

78 98 34.11 32.40 -1.71 7.82 6.92 0.90 $22 98 24.09 23.04 -1.06 3.42 3.07 0.35 $8 1,372 31.01 30.85 -0.16 87.07 85.98 1.08 $26

79 95 34.11 32.40 -1.71 7.57 6.70 0.87 $21 95 24.09 23.04 -1.06 3.31 2.98 0.34 $8 1,328 31.01 30.85 -0.16 84.27 83.22 1.05 $25

80 94 34.11 32.40 -1.71 7.46 6.60 0.86 $21 94 24.09 23.04 -1.06 3.26 2.93 0.33 $8 1,308 31.01 30.85 -0.16 83.01 81.98 1.03 $25

81 86 34.11 32.40 -1.71 6.83 6.04 0.79 $19 86 24.09 23.04 -1.06 2.99 2.68 0.30 $7 1,198 31.01 30.85 -0.16 76.01 75.07 0.95 $23

82 82 34.11 32.40 -1.71 6.55 5.79 0.75 $18 82 24.09 23.04 -1.06 2.86 2.57 0.29 $7 1,148 31.01 30.85 -0.16 72.87 71.97 0.91 $22

83 77 34.11 32.40 -1.71 6.11 5.40 0.70 $17 77 24.09 23.04 -1.06 2.67 2.40 0.27 $6 1,071 31.01 30.85 -0.16 67.98 67.14 0.85 $20

84 70 34.11 32.40 -1.71 5.60 4.95 0.64 $15 70 24.09 23.04 -1.06 2.45 2.20 0.25 $6 982 31.01 30.85 -0.16 62.29 61.51 0.78 $19

85 66 34.11 32.40 -1.71 5.24 4.64 0.60 $15 66 24.09 23.04 -1.06 2.29 2.06 0.23 $6 920 31.01 30.85 -0.16 58.37 57.64 0.73 $17

86 59 34.11 32.40 -1.71 4.68 4.14 0.54 $13 59 24.09 23.04 -1.06 2.05 1.84 0.21 $5 821 31.01 30.85 -0.16 52.13 51.48 0.65 $16

87 52 34.11 32.40 -1.71 4.11 3.63 0.47 $11 52 24.09 23.04 -1.06 1.80 1.61 0.18 $4 720 31.01 30.85 -0.16 45.71 45.14 0.57 $14

88 46 34.11 32.40 -1.71 3.64 3.22 0.42 $10 46 24.09 23.04 -1.06 1.59 1.43 0.16 $4 639 31.01 30.85 -0.16 40.56 40.05 0.50 $12

89 40 34.11 32.40 -1.71 3.15 2.79 0.36 $9 40 24.09 23.04 -1.06 1.38 1.24 0.14 $3 553 31.01 30.85 -0.16 35.07 34.63 0.44 $10

90 33 34.11 32.40 -1.71 2.62 2.32 0.30 $7 33 24.09 23.04 -1.06 1.15 1.03 0.12 $3 460 31.01 30.85 -0.16 29.18 28.82 0.36 $9

91 26 34.11 32.40 -1.71 2.06 1.82 0.24 $6 26 24.09 23.04 -1.06 0.90 0.81 0.09 $2 362 31.01 30.85 -0.16 22.95 22.67 0.29 $7

92 22 34.11 32.40 -1.71 1.72 1.52 0.20 $5 22 24.09 23.04 -1.06 0.75 0.68 0.08 $2 301 31.01 30.85 -0.16 19.12 18.88 0.24 $6

93 16 34.11 32.40 -1.71 1.31 1.16 0.15 $4 16 24.09 23.04 -1.06 0.57 0.51 0.06 $1 229 31.01 30.85 -0.16 14.54 14.36 0.18 $4

94 13 34.11 32.40 -1.71 1.04 0.92 0.12 $3 13 24.09 23.04 -1.06 0.45 0.41 0.05 $1 182 31.01 30.85 -0.16 11.58 11.43 0.14 $3

95 10 34.11 32.40 -1.71 0.81 0.71 0.09 $2 10 24.09 23.04 -1.06 0.35 0.32 0.04 $1 142 31.01 30.85 -0.16 8.98 8.87 0.11 $3

96 7 34.11 32.40 -1.71 0.60 0.53 0.07 $2 7 24.09 23.04 -1.06 0.26 0.23 0.03 $1 105 31.01 30.85 -0.16 6.63 6.55 0.08 $2

97 5 34.11 32.40 -1.71 0.43 0.38 0.05 $1 5 24.09 23.04 -1.06 0.19 0.17 0.02 $0 76 31.01 30.85 -0.16 4.84 4.78 0.06 $1

98 4 34.11 32.40 -1.71 0.30 0.27 0.03 $1 4 24.09 23.04 -1.06 0.13 0.12 0.01 $0 53 31.01 30.85 -0.16 3.34 3.30 0.04 $1

99 3 34.11 32.40 -1.71 0.21 0.19 0.02 $1 3 24.09 23.04 -1.06 0.09 0.08 0.01 $0 37 31.01 30.85 -0.16 2.34 2.31 0.03 $1

100 5 34.11 32.40 -1.71 0.38 0.33 0.04 $1 5 24.09 23.04 -1.06 0.16 0.15 0.02 $0 66 31.01 30.85 -0.16 4.20 4.14 0.05 $1

New Mobile Home, Climate Zone 1 1 Year Old Mobile Home, Climate Zone 1 New Single Family Detached Home, Climate Zone 1
44

The second column block of Table 5 represents the benefits to individuals living in a 1-year-old 

mobile home. Here assume again that there are 21,670 individuals living in this type of structure 

(an assumption of convenience due to lack of data), so the population distribution across ages is 

exactly the same as for new mobile homes. In fact, the only change between column block 1 and 

column block 2 is the smaller exposure due to the fact that the wood in a one-year-old structure 

has had time to off-gas. In total, a projected 48.9 cases of eye irritation annually would be 

reduced in this housing profile, with a total benefit of $1,174 for any 

year of analysis.

The third column block of Table 5 represents the benefits to individuals 

living in a new single-family detached home. An estimated 302,507 

individuals live in this type of home. Even though the magnitude of the 

exposure reduction experienced in new detached homes is smaller than 

that experienced in either mobile home profile presented, the number of 

cases reduced is larger because the exposure reduction is applied to a 

larger population. An estimated 115.4 cases of eye irritation are 

projected to be reduced each year by this policy change, with a benefit 

of $2,770.

The benefits of all housing profiles are then summed to produce the 

total benefits in one year. If we assume that the populations and 

distributions across housing types are stable, then the benefits value for 

each housing cohort will the same for every year except the first one. In

other words, individuals may move from one house to another and we 

are not capable of predicting those movements, but, if we assume that 

there will be 21,670 individuals living in a new mobile home in climate 

zone 1 during every year of our analysis, then we will continue to see 

$3,149 worth of benefits from this housing profile every year.

An additional conclusion from this analysis is that even after the policy 

is implemented, there will be a lag in its effect based on the age of the 

housing structure. This is why, in the example here, the first year is 

different from the others. A policy requiring “CARB2” compliant wood 

will affect new houses immediately. It will, however, not affect the 

existing housing stock, unless those existing houses are remodeled with 

new wood products. (The proposed rule will include this remodeling 

impact, but it has not been included here to simplify the exposition.) 

The effect of the policy will not be seen in one-year-old homes until 

one year after its implementation. 

Table 6, to the right, illustrates how the total estimated benefits of the 

rule will be calculated for 30 years using a discount rate of 3% 

(implying a discount factor of 0.9709).8In the year immediately 

 

8 EPA generally expresses costs and benefits that occur over time as present values by exponentially discounting 

them to a common base year. Most EPA rules use a 3% discount rate, which is approximately the return to 

Government-backed securities. This rate reflects how individuals discount future consumption and how government 

should value policy-related consumption changes. Most EPA analyses also include present values suing a 7% 

Table 6: Discounted

Willingness to Pay

Year

Annual

WTP

Discounted 

WTP

$144,009

0 $5,873 $5,873

1 $7,048 $6,842

2 $7,048 $6,643

3 $7,048 $6,450

4 $7,048 $6,262

5 $7,048 $6,079

6 $7,048 $5,902

7 $7,048 $5,730

8 $7,048 $5,563

9 $7,048 $5,401

10 $7,048 $5,244

11 $7,048 $5,091

12 $7,048 $4,943

13 $7,048 $4,799

14 $7,048 $4,659

15 $7,048 $4,524

16 $7,048 $4,392

17 $7,048 $4,264

18 $7,048 $4,140

19 $7,048 $4,019

20 $7,048 $3,902

21 $7,048 $3,788

22 $7,048 $3,678

23 $7,048 $3,571

24 $7,048 $3,467

25 $7,048 $3,366

26 $7,048 $3,268

27 $7,048 $3,173

28 $7,048 $3,080

29 $7,048 $2,991

30 $7,048 $2,904
45

following the policy implementation, year 0 in Table 3, the annual benefits are the sum of the 

benefits for new mobile homes and new detached houses, which is ($3,103 + $2,770 =) $5,873. 

The benefits in the second year, and each year thereafter are the benefits from all three housing 

types, ($3,103 + $1,174 + $2,770 =) $7,048. Discounting these benefits to present value terms by

multiplying them times 0.9709t, where t is the year, produces total benefits of $144,009 for this 

policy change.

3.2.4 Discussion of uncertainties

The example above assumes that the population is constant from year to year (births = deaths + 

net migrations) and that the future distribution across housing types is exactly the same as the 

present distribution, neither of which is likely to be true. However, the method described above 

can be modified to accommodate a growing population and a different housing and age 

distribution by changing the population values for each year. 

The concentration-response function used here is non-linear. This means that annual approach 

may not produce an exact measure of the benefits. However, given that the change in exposure is 

relatively small, the results from using the non-linear concentration-response function are 

probably very similar to the results if we were to use a linear function. Furthermore, because the 

non-linear concentration-response function applies to a period of time less than one year, there 

should be no problems in applying the annual approach.

The contingent valuation estimates of willingness to pay to avoid eye irritation are rather dated. 

The values obtained by Tolley et al., which are the underlying values used in the analysis, are 25 

years old. While EPA still uses these estimates, there have been a number of advances over the 

years in the application of stated preference methods aimed at reducing hypothetical bias which 

causes stated preference estimates of willingness to pay to be too high. On the other hand, the 

same willingness to pay value is attributed to both adults and children. There is some evidence 

that parents are willing to pay more to avoid adverse health effects in their children than they are 

to avoid the same adverse health effects in themselves (Dickie and Gerking, 2003; Dickie and 

Ulery, 2002; Liu et al., 2000). EPA (2000a) reviewed the results of several contingent valuation 

studies (Loehman et al. 1979, 1979; Rowe and Chestnut 1986; and Tolley et al. 1986) for various 

symptoms. Both Loehman et al. (1979) and Tolley et al. (1986) found that the willingness to pay 

to avoid multiple days of a condition is greater than the willingness to pay to avoid one 

symptom-day. However, the willingness to pay per symptom-day declined as the number of 

symptom-days avoided increased. In other words, the value to reduce two symptom-days of 

some effect is generally less than two times the value for one symptom-day. This point was also 

made in Kenkel, Berger, and Blomquist (1994) and declining marginal willingness to pay for 

avoided illnesses was also found more recently in Bosworth, Cameron, DeShazo (2009). 

Therefore, multiplying the marginal willingness to pay for one symptom-day times the number 

of symptom-days, as has been done here, may overstate the total value and, hence, the benefit of 

the policy change. However, a reasonable upper bound of the annual value of the total effect for 

one symptom-day would be the sum of the willingness to pay for one symptom-day of each 

 

discount rate, reflecting opportunity costs in terms of foregone investments and therefore future consumption. 

Alternate approaches to exponential discounting are discussed in EPA 2011a.
46

effect individually. This would be what have reported in Table 5 if we assume that a different set 

of people experience these symptoms in each of the two week periods.

This analysis only valued one symptom, eye irritation, largely because this is the only symptom 

for which an effective concentration-response function could be derived. However, there is 

evidence that there are other forms of irritation (e.g. nose, throat irritation) associated with 

formaldehyde exposure. If this is true and the reduction of formaldehyde exposure reduces these 

symptoms concurrently, then the values of those other minor effects should, in theory, be 

included in the analysis. This limitation will be acknowledged qualitatively in the economic 

analysis for the proposed rule.

The report by Tolley et al. (1986) suggested that the impact of multiple symptoms is close to, but 

slightly lower than the aggregate sum of the willingness to pay for individual effects. That is, the 

willingness to pay for a group of three to five symptoms jointly was slightly less than the sum of 

the willingness to pay for each symptom individually. Therefore, if we were to produce a 

concentration-response function for all of these symptoms of sensory irritation associated with 

formaldehyde exposure, then a reasonable upper bound of the total effect for one symptom-day

would be the sum of the willingness to pay for one symptom-day of each effect individually. 

EPA (2000a) suggested that a reasonable lower bound would be the high-end value for one 

symptom. Since eye irritation is the lower end of the median values as reported by IEc (1993a 

and 1993b), the values used here likely probably represent a lower bound on the true effect of 

multiple symptoms.

3.3 Asthma incidence

Valuing asthma incidence is more difficult than sensory irritation. First, monetization is more 

difficult because the valuation is based on the incidence of asthma. Most economic analysis of 

asthma value the exacerbation of asthma symptoms rather than development of new cases. 

Second, the concentration-response relationship is based on an odds ratio for asthma prevalence, 

whereas we are need an annual incidence rate. Third, as illustrated in the sensory irritation 

section, the exposure model produces results for one-year of exposure to formaldehyde for each 

age, housing type, climate cohort. If the concentration-response relationship produces an 

incidence rate for a time period longer than this one year window, then an adjustment to the 

simple model given by equation (7) needs to be made.

3.3.1 Monetization

EPA has included asthma as a health effect in many of its economic analyses. However, this 

valuation usually takes the form of valuing an increase, or exacerbation, of asthma symptoms 

rather than an increase in the incidence of asthma. The Office of Air uses two values to monetize 

the effect of asthma exacerbation in adults and three values for asthma exacerbation in children. 

Rowe and Chestnut (1986) estimate a mean willingness to pay of $43 in 2000$ for avoiding a 

“bad asthma day” as $43 in 2000$, with a range of $16 to $71. This unit value is applicable to 

both adults and children. A second value for adults is $74, derived from Dickie and Ulery (2002) 

and Dickie and Messman (2004), assuming that asthma exacerbation consists of 1 symptom-day. 
47

Two unit values for children are available from Dickie and Ulery (2002) and Dickie and

Messman (2004). One of these is $86 , twice the adult unit value for adults based on evidence 

that parents are willing to pay about twice as much to avoid symptoms and illness in their 

children as in themselves. The other value for children is $156, based on a statistical model 

including a dummy variable for children. These values were used in all three analyses of the 

benefits and costs of the Clean Air Act (EPA 1997, 1999, and 2011a) and are summarized in the 

EPA’s Office of Air’s BenMAP program (EPA 2011b). The problem with applying these values 

to formaldehyde exposure is that, as of yet, a statistical relationship between formaldehyde 

exposure and asthma exacerbation has not been sufficiently well established to develop a 

concentration-response function. 

As described in the section on concentration-response functions, however, there is a statistical 

relationship between formaldehyde exposure and asthma occurrence or incidence. While valuing 

asthma incidence is less common in EPA analyses than valuing asthma exacerbation, it has been 

done. This approach was used in the first prospective study of the benefits and costs of the Clean 

Air Act (EPA 1999). The number of new cases of chronic asthma as a function of ozone 

exposure was estimated based on a study by McDonnell et al. (1999). Using an approach similar 

to the one that EPA uses to value reductions in chronic bronchitis, the willingness to pay to avoid 

chronic asthma was based as the net present value of a willingness to pay to avoid the disease 

over a lifetime. The central estimate (in 1990 dollars) was $25,000, with a triangular distribution 

and a range between $19,000 and $30,000. 

This range and distribution was based on two studies that estimated the willingness to pay to 

avoid chronic asthma in adults. Blumenschein and Johannesson (1998) used two different 

contingent valuation methods to estimate mean willingness to pay for a cure for asthma. Using 

their mean estimate of $2,268 per year, a three percent discount rate, and 1997 life expectancies 

for males in the United States, they estimated a present discounted value of the stream of annual 

willingness to pay values of $47,637 (in 2000$). O’Conor and Blomquist (1997) estimated the 

willingness to pay to avoid chronic asthma by offering respondents a choice between 

hypothetical medications which differed in safety and efficacy. They then combined this risk-risk 

tradeoff with a statistical value of life to derive an annual willingness to pay to avoid asthma. 

EPA (2011b) reports that, using a value of a statistical life of $5,894,400 (in 1997$), the implied 

annual value of avoiding chronic asthma, based on O’Conor and Blomquist, would be $1,474. 

Assuming a three percent discount rate and 1997 life expectancies for males in the United States, 

the present discounted value of the stream of annual WTPs would be $30,257 (in 2000$). The 

implied annual value of asthma control of $1,474 (in 1995$) is also close to the best estimates 

from more recent work by Blomquist, Dickie, and O’Conor (2011). For the average age adult (45 

years old) the annual value of asthma control is $1,960 in 2007 dollars, or $1,441 in 1995 

dollars.

These willingness to pay values are higher, in real terms, than the direct medical costs for an 

average asthma patient reported by EPA (2000d) and repeated below in Table 7.

Table 7: Lifetime Direct Medical Costs for Asthma (in 1999$)
48

Source: Table IV.2-17 in EPA 2000d

The cost-of-illness estimates in this table are based on the cost of medical services, 

reimbursement by Medicare, and national recommendations and private sector costs regarding 

drug therapy. The values were obtained by multiplying the probabilities of patients utilizing 

various services times the cost per service, and then discounting over time to form a present 

value at various discount rates. One important assumption embedded in the estimate for the 

average patient is that 30 percent will become asymptomatic as they move into adulthood, so 

they do not incur costs beyond their seventeenth year, and 70 percent will have the disease 

throughout their life. All of the high-use patients are assumed to have asthma throughout their 

life. 

It is not necessarily surprising that the direct medical costs are below the willingness to pay

estimates. In general, cost-of-illness estimates understate the willingness to pay to avoid a given 

health effect because they often omit averting expenditures and the value of lost utility associated 

with pain and suffering. Although the cost-of-illness approach could be used to value asthma 

incidence, the use of willingness to pay values is considered to be a more appropriate measure 

(EPA 2010).

Curiously, beside the prospective analysis of the Clean Air Act, monetization of asthma 

incidence has not been used in economic analyses of regulatory action. This is probably due to a 

lack of an appropriate concentration-response relationship. Nevertheless, the EPA’s Office of Air 

includes recommended values for the monetization of chronic asthma in its BenMAP 

documentation (EPA 2011b) based on Blumenschein and Johannesson (1998) and O’Conor and 

Blomquist (1997). The value of avoiding one statistical case of chronic asthma is the average of 

the two estimates, based on a three percent discount rate, or $38,947 (in 2000$). This is the value 

that will be used as the willingness to pay for reduced asthma incidence from formaldehyde 

exposure.

There are two reasons why this is not the appropriate value to use for an asthma case developed 

in the 6-17 age range. First, the value reported in BenMAP represents the average value for 

adult-onset asthma. The method used to calculate the willingness to pay is based on the present 

discounted value of a stream of annual values derived from Blumenschein and Johannesson 

(1998) and O’Conor and Blomquist (1997). Using this method, the willingness to pay to avoid 

child-onset asthma should be larger because of more years associated with having asthma. 
49

The present discounted value of the stream of annual WTPs for someone who gets asthma at age 

a is 1

1

(1 )

LEa

annual

a j

j

WTP

pdv

dr 



 

     

 (10)

where

WTPannual denotes the annual WTP,

a denotes the age at onset of asthma (e.g., a = 6, 7, ..., or 17),

LEa denotes the life expectancy for an individual age a, and

dr denotes the discount rate,

Note that this implicitly assumes that an individual who develops asthma will suffer with the 

disease for the rest of his or her life (i.e., he or she will never become asymptomatic). A

weighted average pdv can be calculated using the percentages of the population in the age 

categories as the weights. If pj denotes the percent of children in the age range [6-17] who are 

age j, j = 6, ..., 17 and assuming that any child in the age range is equally likely to have asthma,

then 

17

[6 17]

6

j j

j

pdv p pdv 



  (10)

Inflating the willingness to pay values for adult-onset asthma derived from the annual values of 

Blumenschein and Johannesson (1998) and O’Conor and Blomquist (1997) using the CPI-U 

implies values of $60,322 and $38,314 (2010$) respectively. In contrast, the willingness to pay

to avoid child onset-asthma between the ages of 6 and 17 using equation (12) would be $93,341 

and $59,287 (2010$) respectively.

The second reason why the values reported in BenMAP may not be appropriate is that there is 

substantial evidence that non-trivial percentages of asthmatics become asymptomatic at some 

point in their lives. The 2009 population and prevalence rate results for the total U.S. population 

in the current asthma and lifetime asthma tables are available online from the Centers for 

Disease Control, National Health Interview Survey (NHIS) and are shown in Table 8 below.
50

Table 8: Results of the 2009 National Health Interview Survey Questions on Asthma and Implied 

Percentage of Asymptomatic Individuals

Characteristic Total 

Population

Children (<18) Adults (18+)

Lifetime asthma population (in 1000s) (CDC Table 1-1 ) 39,930 10,196 29,734

Current asthma population (in 1000s) (CDC Table 3-1 ) 24,567 7,111 17,456

Percent of asthmatics who still have asthma:

61.5% 69.7% 58.7%

Percent of asthmatics who are now asymptomatic:

38.5% 30.3% 41.3%

Source: Centers for Disease Control and Prevention 2009

The percent of asthmatics who still have asthma can be calculated by dividing the “current 

asthma population” by the “lifetime asthma population.” The percent of asthmatics that are 

asymptomatic is found by subtracting this value from 100%. For example, the adult age group

(age 18+), 29,734,000 individuals said they had been diagnosed with asthma; of these, 

17,456,000 – or 58.7% -- said they still have asthma. That implies that 100% - 58.7% = 41.3% 

of asthmatics in this age group are asymptomatic.

For simplicity, we assume that an asthmatic child who becomes asymptomatic is equally likely 

to do so at any age after childhood. However, rather than calculate this probability for each age, 

we discretely represent this equal probability 10 year intervals, starting with age 17 – ages 17, 

27, 37, 47, 57, and 67. Since the total proportion of child asthmatics who will become 

asymptomatic at some point after childhood is assumed to be 41%, and each age is assumed to 

have an equal probability of being the age at which the individual becomes asymptomatic, we 

assume that (41%/6 =) 6.8% of child asthmatics become asymptomatic at each of the 6 

representative ages (17, 27, 37, 47, 57, and 67).

For each of the representative ages (17, 27, 37, 47, 57, and 67), the analysis calculated , given 

that age-when-asthma-stops, using equations (27) and (28) above and replacing in equation (27) 

with the representative age, for all values of a. If we assume that asthma starts at the beginning 

of an age and stops in the middle of an age, then if a child gets asthma at age x and becomes 

asymptomatic at age y, the number of years the child has asthma is y – x + 0.5. For example, 

the present discounted value of willingness to pay values for an asthmatic child of age a that 

become asymptomatic at age 27 is 

 

27 0.5

1

1

for each in 6 17 .

(1 )

a

annual

a j

j

WTP pdv a

dr

 





 

      

 (10)

Equation Error! Reference source not found. can then be used to calculate the resulting value 

for pdv[617]. The weighted PDV (in 2010$) of willingness to pay values using this method is 
51

$79,214 and $50,314 using the derived annual values of Blumenschein and Johannesson (1998) 

and O’Conor and Blomquist (1997) respectively. The average of two studies is $64,764 (in 

2010$). This is the value that will be used in this analysis.

3.3.2 Annual approach

The concentration-response relationship for asthma incidence is given as an odds ratio for 

children exposed to formaldehyde. An odds ratio is a way of comparing the probability of an 

event, in this case asthma diagnosis, occurring between two groups and is commonly used in 

epidemiology and risk assessment. Mathematically, “odds” is the ratio of the probability that an 

event will occur, P, to the probability that the event will not occur, (1-P). That is, odds = P/(1-P). 

The “odds ratio” is simply the ratio of the odds of the event occurring to an exposed group to the 

odds of the event occurring in the control group. That is

exposed

exposed

control

control

1

odds ratio

1

P

P

P

P

   

  



      

(11)

An odds ratio is used to estimate how strongly exposure is associated with the probability that an 

event, such as asthma diagnosis, occurs. For example, if the odds ratio is 1.027 for a 1 ppb 

change in formaldehyde exposure and we see 100,000 cases of asthma in our control population, 

then we would expect to see 102,700 cases of asthma in a population exposed to one additional 

ppb of formaldehyde.

The odds ratio can be related to the logistic model. The logistic function

( )

( ) ( )

1

y x

y x

e

F x

e





varies 

between 0 and 1 and is used to represent the cumulative density function of some event 

occurring. y(x) is often expressed as a linear function of the form y = β0 + β1∙x. So, in our case, 

F(x) is the probability of being diagnosed with asthma, P, and x is exposure to formaldehyde. 

The logit of P is then defined as the natural logarithm of the odds. That is, 

logit(P) = ln(P/(1-P)) = β0 + β1∙x.

Therefore, the odds of asthma incidence for the entire population is e(β0 + β1∙x), and the log-odds is 

β0 + β1∙x. This means that the result of a logistic regression is nothing more than the log of the 

odds, or the log-odds. 

The odds ratio of an exposed group, x = x1, to some control group, x = x0, is then 
52

     

1 1 0

1 1 1 0 0 0 1 1 0

1 0 0

exposed

exposed

control

control

1

odds ratio

1

x

x x x x

x

P

P e

e e

P e

P

  

         

  

   

  

          

(12)

So β1 gives the impact of a one unit change in exposure (that is, where x1 –x0 = 1). Furthermore, 

β1 can be recovered by taking the log of the odds ratio given in the epidemiology literature. So, if 

the odds ratio of a 1 ppb increase in formaldehyde is 1.027, then the β1 in the implied logistic 

model would be ln(1.027) = 0.0266.

This can be used to determine the willingness to pay for any change in emissions. Given a fixed 

willingness to pay for one case of asthma, the willingness to pay for a change in exposure over 

some period of time, t0-t1, is given by a modified version of equation (7).

 

1

0 1

0

0 1 0 1

, ,

1 1

Probability Effective

Total WTP WTP 1

of Asthma Odds Ratio

t H C

t

hct t

t t h c t t t t

 Pop 

    

     

                 

 

(13)

The willingness to pay for any given housing and age cohort is

 

0 1

0 1 0 1

, ,

Probability Effective

WTP 1

of Asthma Odds Ratio hct t

t t t t

Pop 

 

     

                (14)

The “effective odds ratio” is defined here as the odds ratio for a given change in exposure based 

on the odds ratio from the literature

 

0 1

0 1

Effective ln exposure

Odds Ratio

t t

Odds

Ratio

t t

e



    

 



   

        

(15)

So, continuing with the example above, if the odds ratio is 1.02 for a 1 ppb change in 

formaldehyde exposure and we would like to determine the effect of a -1.28 ppb change, the 

effective odds ratio would be e ln(1.027)*(-1.28) = 0.966. 

A problem arises when the time period, t, is longer than the time step of the exposure model. 

This can be illustrated using childhood asthma incidence and formaldehyde exposure. The odds 

ratio for asthma prevelance is based on the random effects model of McGwin et al. (2010), 

excluding Rumchev et al. (2002). The mean age for the six remaining studies in McGwin et a.. 

ranges from 8 to 14 years old. The minimum age across the six studies was 6 and the maximum 

was 17. This is the age range for which we estimate benefits in this analysis. 

We assume that probability of being diagnosed with asthma can be taken from the prevalence 

rate reported in the 2008 National Health Interview Survey and reported in Table 9. 

Table 9: Lifetime Asthma Prevalence, 2008

All ages 0 - 4 5 - 14 15 - 19 20 - 24 25 - 34 35 - 64 65+
53

Asthmatics 38,450 1,499 6,576 3,653 3,609 5,119 13,887 4,107

Prevalence Rate 12.9 7.2 16.4 17.4 17.4 12.7 11.7 11

Population 298,062 20,819 40,098 20,994 20,741 40,307 118,692 37,336

Percentage 100.00% 3.90% 17.10% 9.50% 9.39% 13.31% 36.12% 10.68%

Source: CDC 2008 (Tables 1-1 and 2-1)

The data indicate that the asthma prevalence among 0-4 years olds is 7.2 percent and asthma 

prevalence among 5-14 year olds is 16.2 percent. We assumes that once a child gets asthma, he 

or she does not outgrow it within that age range. For example, for ages 0-4, the prevalence rate 

is 7.2%. This means that 7.2% of individuals ages 0-4 have asthma. Since this age range starts 

at birth, all of these asthma cases must have started within the age range – i.e., in this case, 

prevalence equals cumulative incidence. For any age range that starts at an age greater than 0, 

however, prevalence does not equal incidence, since some of the prevalent cases may have

started at an age less than the lower bound of the age range. For example, the 16.4% of 

individuals with asthma between the ages of 5 and 14 include those individuals whose asthma 

started during ages 0-4. The incidence rate for the age range 5-14 was estimated by subtracting 

7.2 percent from 16.4 percent to estimate that 9.2 percent of individuals in the age range of 5-14 

are newly diagnosed with asthma. For this analysis, we assume that this 9.2 percent applies to the 

12 years that we are analyzing and that new cases are uniformly distributed over these 11 years. 

Thus, the annual incidence rate for our analysis is 0.092/12 = 0.0076, or 0.76% for children aged 

6 to 17. 

Using this assumption, the expected number of asthma cases that we would expect to see in the 

baseline per 100,000 children age 6 to 17 is illustrated by the red and blue areas in Figure 9. We 

would expect 760 cases per year each year for twelve years, for a sum total of 9,200 cases of 

If the odds ratio for a 1 ppb reduction is 1.027, then we would expect a 2.7% reduction in the 

area under this curve for a 1 ppb reduction in exposure. That is, we would see 242 fewer asthma 

cases, found by multiplying 9,200 times the effective odds ratio for a 1 ppb reduction, [1 - e

ln(1.027)∙(-1)]. If we had a 10 ppb reduction, we would see 9,200∙[1 - eln(1.027)∙(-10)] = 2,152 fewer 

cases, an 23% reduction. If we were to allocate these 2,152 fewer cases uniformly then we would 

see approximately 179 fewer cases in each. This is illustrated by the dark red areas in Figure 9.
54

Figure 8. Number of asthma cases per 100,000 from ages 6 to 17, 

assuming an odds ratio of 1.02 and a 10 ppb change in 

formaldehyde exposure

Allocating cases uniformly across the age brackets given by the CDC data provides us with a 

way to calculate the annual benefits of any exposure reduction that occurs for the entire time 

period9. We now ask the more difficult question of how to model the annual reduction if the 

representative individual does not experience the exposure reduction over the entire time period. 

For example, how do we calculate the benefits to an individual who is 15 years old at the 

beginning of the policy and experiences only one year of the 10 ppb exposure reduction. We 

consider two possible approaches.

The first approach is to assume that the odds ratio can be applied to the one year reduction in the 

same fashion as it was applied for the 12 year time period. This is illustrated in Figure 9. In the 

baseline, we expect 760 cases of asthma among 17 year-olds. Applying the odds ratio to the one 

year interval implies that a 10 ppb reduction would produce 760∙[1 - e

ln(1.027)∙(-10)] = 178 fewer 

cases, represented by the red area in Figure 9. This is same area as the red area for the 15 to 16 

age bracket in Figure 8. 

 

9 A more sophisticated approach than this uniform distribution could be developed by making assumptions about the 

nature of the concentration-response relationship for each year. For example, if the concentration-response 

relationship is linear for a 12 year period, the health can occur more than once, and the probability is dependent 

only on the exposure in one year, then the probability of the event not occurring over a 12 year period would be the 

product of the probability not occurring in each year. If we assume that the concentration-response relationship is 

linear for one year, than this can be solved for the probability of the event in each year. A similar calculation could 

be done if the probability of an event is a function of the cumulative exposure. This analysis may be extended in this 

fashion for the final rule.
55

Figure 8. Upper bound estimate of the reduced number of asthma 

cases per 100,000, assuming an odds ratio of 1.02 and a 10 ppb 

change in formaldehyde exposure for one year

The problem with this first approach is that it effectively treats the exposure as an one year

effect. The odds ratio that indicated an 23% reduction in asthma cases from a 10 ppb reduction in 

formaldehyde exposure over 16 years is treated as implying an 23% reduction in asthma case for 

a 10 ppb reduction in formaldehyde in one single year. However, it serves as an upper bound to 

the number of asthma cases that might be avoided by an exposure reduction of one year.

At the other extreme, we might assume that the exposure reduction of 10 ppb for one year 

produces the same effect as if that 10 ppb was spread out over the entire 12 year time period. In

other words, a 10 ppb reduction in one year is modeled like a 10/12 = 0.833 ppb reduction for 12

years. This is illustrated in Figure 8. The baseline is represented by the red and blue areas. A 

0.625 ppb exposure reduction experienced over 16 years would result in 9,200∙[1 - e

ln(1.027)∙(-

0.833)

] = 202 fewer cases, represented by the light and dark red areas. However, only 17 of those 

cases would occur in the 17th year. This would be the number of fewer asthma cases we would 

see in a population of 760 fifteen-year-old children who experience only one year of a 10 ppb 

exposure reduction. This second approach provides a lower bound to the number of asthma cases 

that might be avoided from an exposure reduction over one year.
56

Figure 8. Lower bound estimate of the reduced number of asthma 

cases per 100,000, assuming an odds ratio of 1.02 and a 10 ppb 

change in formaldehyde exposure for one year

This same logic for both the upper and lower bound can be used to determine the benefits of an 

exposure reduction for any individual who does not experience the exposure reduction for the 

full period. Mathematically, this means that for any time period 0 1 t t [ ,t ], the willingness to pay

for an individual who is age k at the time of policy implementation would be 

Upper bound:

 

 , , 

0 1

0 1

ln exposure exposure

, ,

Probability

WTP 1

of Asthma

policy t baseline t

odds

Ratio

t h c t t

t t

WTP Pop e

    

 





     

                  (16)

Lower bound:

 

 

1

, ,

1 0

0 1

0 1

exposure exposure

ln

, ,

Probability

WTP 1

of Asthma

t

policy t baseline t

k

odds

Ratio t t

t h c t t

t t

WTP Pop e

        

  

 





    

     

           

    (17)

The reason that this adjustment is necessary is because there are individuals between the ages of 

6 and 17 who are alive when the policy is implemented and we must calculate the benefits of the 

exposure reduction to them. In other words, we need this to model the transition path as we move 

from the year after policy implementation, where the benefits are presumably lower, to a time 

when everyone is enjoying the full benefit of the policy. After 12 years, every individual will 

experience the full 12 years of exposure reduction (in one housing type or another), so won’t 

need to worry about bounding the willingness to pay. Note that the upper bound estimate reflects 
57

full benefit for the 17

th year, so it is the same as if the individual had experienced the full 

exposure reduction for the 11 years prior.

While we allocated the cases proportionally across age brackets in this case, calculating the 

transition path of the willingness to pay as the rule is fully phased may be important if the 

probability of the outcome is small in the final years. For example, consider the case of lifetime 

cancer risk. The risk of being diagnosed with cancer is greatest in the middle years and smaller in 

the last year of one’s life. If we were to stop dosing an individual with a carcinogen in the final 

year of his or her life, the upper bound estimate suggests that he or she would receive the same 

benefit in this last year of life as an individual who had experienced the exposure reduction for 

his or her entire life. The lower bound estimate would treat this final year exposure reduction as 

if it had been spread out over the entire lifetime and then allocates the last year’s benefit.

3.3.3 Example calculation

The odds ratio for asthma incidence 

given earlier in the document is 

1.027 per one ppb increase in 

formaldehyde exposure over a 16 

year period. Using the CDC data 

from Table 9, above, we assume that 

the probability of being diagnosed 

with asthma between ages 6 and 17

is 9.2% and that this probability is

uniformly distributed across the age 

bracket. This can now be used for 

the benefits analysis using equations 

(19) and (20) above.For this 

example, we will use the same three 

housing profiles in climate zone 1 

that we used for sensory irritation: a 

new mobile home; a 1-year-old 

mobile home; and a new single 

family detached. We also use the 

same exposure changes for these 

three housing profiles, listed in 

Table 10 for the demographics of 

interest: school-aged children, age 

2-16, and non-industrial workers.

Table 11 lists the benefits for the 

assumed exposure reductions in 

these three housing profiles. The first block represents the 3,436 children living in new mobile 

homes in climate zone 1 (EIA 2008, U.S. Bureau of Census 2009). Notice that the population 

assumptions are the same as those that we assumed for the sensory irritation analysis, but we are 

only concentrating on the children age 6-17. Under the baseline, we expect 26.34 asthma cases 

Table 10: Illustrative formaldehyde exposure scenarios using three 

housing profiles

Scenario Housing Profile Preschool 

/ School 

Child 

Avg. 

ADC

NonIndustrial 

Worker 

Avg. 

ADC

Weighted average ADC (mg/m3) during current exposure year

Baseline New Mobile Home 0.0344 0.0349

1-year-old Mobile Home 0.0248 0.0256

New Detached Home 0.0312 0.0319

CARB2 New Mobile Home 0.0328 0.0333

1-year-old Mobile Home 0.0238 0.0247

New Detached Home 0.0311 0.0318

Weighted average ADC (ppb) during current exposure year

Baseline New Mobile Home 28.00 28.41

1-year-old Mobile Home 20.19 20.84

New Detached Home 25.40 25.97

CARB2 New Mobile Home 26.70 27.11

1-year-old Mobile Home 19.37 20.11

New Detached Home 25.32 25.89

Weighted average ADC (ppb) during current exposure year

Change New Mobile Home -1.30 -1.30

1-year-old Mobile Home -0.81 -0.73

New Detached Home -0.08 -0.08
58

for this housing profile. Given the assumed exposure reductions, we would expect 0.898 fewer 

asthma cases.

Table 11: Illustrative benefits calculations for asthma incidence using three housing profiles.

New Mobile Home, Climate Zone 1

Age Population

Baseline 

Exposure 

(ppb)

CARB2 

Exposure 

(ppb)

Exposure 

Reduction 

(ppb)

Expected 

Baseline 

Cases

Effective 

Odds Ratio

Cases 

Avoided WTP

3,436 26.34 0.898 $58,181

6 294 28.00 26.70 -1.30 2.2524 0.9659 0.077 $4,975

7 290 28.00 26.70 -1.30 2.2270 0.9659 0.076 $4,919

8 288 28.00 26.70 -1.30 2.2104 0.9659 0.075 $4,882

9 292 28.00 26.70 -1.30 2.2421 0.9659 0.076 $4,952

10 281 28.00 26.70 -1.30 2.1574 0.9659 0.074 $4,765

11 277 28.00 26.70 -1.30 2.1234 0.9659 0.072 $4,690

12 277 28.00 26.70 -1.30 2.1204 0.9659 0.072 $4,683

13 278 28.00 26.70 -1.30 2.1288 0.9659 0.073 $4,702

14 283 28.00 26.70 -1.30 2.1704 0.9659 0.074 $4,794

15 288 28.00 26.70 -1.30 2.2052 0.9659 0.075 $4,871

16 290 28.41 27.11 -1.30 2.2270 0.9659 0.076 $4,919

17 297 28.41 27.11 -1.30 2.2777 0.9659 0.078 $5,031

1 Year Old Mobile Home, Climate Zone 1

Age Population

Baseline 

Exposure 

(ppb)

CARB2 

Exposure 

(ppb)

Exposure 

Reduction 

(ppb)

Expected 

Baseline 

Cases

Effective 

Odds Ratio

Cases 

Avoided WTP

3,436 26.34 0.556 $35,980

6 294 20.19 19.37 -0.81 2.2524 0.9785 0.048 $3,129

7 290 20.19 19.37 -0.81 2.2270 0.9785 0.048 $3,094

8 288 20.19 19.37 -0.81 2.2104 0.9785 0.047 $3,071

9 292 20.19 19.37 -0.81 2.2421 0.9785 0.048 $3,115

10 281 20.19 19.37 -0.81 2.1574 0.9785 0.046 $2,998

11 277 20.19 19.37 -0.81 2.1234 0.9785 0.046 $2,950

12 277 20.19 19.37 -0.81 2.1204 0.9785 0.045 $2,946

13 278 20.19 19.37 -0.81 2.1288 0.9785 0.046 $2,958

14 283 20.19 19.37 -0.81 2.1704 0.9785 0.047 $3,015

15 288 20.19 19.37 -0.81 2.2052 0.9785 0.047 $3,064

16 290 20.84 20.11 -0.73 2.2270 0.9807 0.043 $2,788

17 297 20.84 20.11 -0.73 2.2777 0.9807 0.044 $2,851

New Single Family Detached Home, Climate Zone 1

Age Population

Baseline 

Exposure 

(ppb)

CARB2 

Exposure 

(ppb)

Exposure 

Reduction 

(ppb)

Expected 

Baseline 

Cases

Effective 

Odds Ratio

Cases 

Avoided WTP

47,964 367.72 0.797 $51,591

6 4,101 25.40 25.32 -0.08 31.4420 0.9978 0.068 $4,411

7 4,055 25.40 25.32 -0.08 31.0871 0.9978 0.067 $4,361

8 4,025 25.40 25.32 -0.08 30.8555 0.9978 0.067 $4,329

9 4,082 25.40 25.32 -0.08 31.2980 0.9978 0.068 $4,391

10 3,928 25.40 25.32 -0.08 30.1165 0.9978 0.065 $4,225

11 3,866 25.40 25.32 -0.08 29.6410 0.9978 0.064 $4,159

12 3,861 25.40 25.32 -0.08 29.5995 0.9978 0.064 $4,153

13 3,876 25.40 25.32 -0.08 29.7162 0.9978 0.064 $4,169

14 3,952 25.40 25.32 -0.08 30.2970 0.9978 0.066 $4,251

15 4,015 25.40 25.32 -0.08 30.7836 0.9978 0.067 $4,319

16 4,055 25.97 25.89 -0.08 31.0880 0.9978 0.067 $4,362

17 4,147 25.97 25.89 -0.08 31.7959 0.9978 0.069 $4,461
59

The effective odds ratio and willingness to pay are calculated using the upper bound, equation 

(16) above, assuming a willingness to pay to avoid one asthma case of $64,764. For example, the 

willingness to pay for a six-year old child in this housing profile would be

   

   

 

ln 1.027 26.70 28.00

0

9.2% $64,764 294 1 $4,975

12

WTP e

   

             

The total willingness to pay for this housing profile would be $58,181.

The second block of Table 11 represents the benefits to individuals living in a 1-year-old mobile 

home. As with sensory irritation, we assume that the population distribution across ages is 

exactly the same as for new mobile homes but the exposure profile is different. In total, 26.34

asthma cases would be expected in the baseline (the same as for new mobile homes because the 

age distribution is the same). 0.556 cases would be avoided from the policy intervention, and the 

total willingness to pay for this intervention would be $35,980.

The third block of Table 11 represents the benefits to individuals living in a new single-family 

detached home. An estimated 47,964 children live in this type of home and the exposure 

reduction expected from the policy is smaller than for mobile homes. An estimated 367.72

asthma cases would be expected in the baseline, 0.797 cases would be avoided from the policy

intervention, and the total benefits of this action would be $51,591.

As was true in the case for sensory irritation, the sum of these willingness to pay values for new 

mobile homes and new detached houses ($58,181 + $51,591= $109,772) is the willingness to pay 

for the reduction in asthma incidence in the first year. The sum of the willingness to pay for all 

three housing types ($58,181 + $35,980 + $51,591= $145,751) is the willingness to pay for any 

given year of analysis after the first year, assuming that the population remains constant and the 

distribution across housing types is the same in the future as it is now. 

These aggregate results are appropriate for the case where every individual is afforded the 

exposure reduction over their entire 12 year exposure, but it may not be valid for the early years 

of policy implementation. To calculate the transition path from initial to full policy implantation, 

we use the upper and lower bound equations, equations (19) and (20) respectively. The results of 

these calculations are given in Table 12. 

The left hand block of Table 12 gives the upper bound estimate of the policy for thirty years of 

implementation. In this case, the undiscounted willingness to pay is the same value, $145,751, 

for each year after the first year. This is because the upper bound estimate assumes that the odds 

ratio is appropriate for an exposure reduction experience for one year. So, for example, a child

who is seventeen years old in the first year of policy implementation will only enjoy one year of 

exposure reduction associated with this concentration-response function. In the upper bound 

estimate, that child receives the same benefit in that year as all seventeen-year-old children do in 

every year thereafter. Assuming a discount rate of 3%, the present discounted value of 30 years 

of the policy is about $2.9 million dollars for these three housing profiles. 
60

Table 12: Upper and lower bound benefits calculations for asthma incidence using three housing 

profiles

Upper Bound Estimate Lower Bound Estimate

Year

New 

Mobile 

Home

1-Year Old 

Mobile 

Home

New SF 

Detached 

Home

Total WTP

Total 

Discounted 

WTP

New 

Mobile 

Home

1-Year Old 

Mobile 

Home

New SF 

Detached 

Home

Total WTP

Total 

Discounted 

WTP

$1,803,609 $1,079,385 $1,599,309 $4,482,303 $2,966,556 $1,681,291 $1,023,670 $1,496,535 $4,201,497 $2,706,869

0 $58,181 $51,591 $109,772 $109,772 $31,019 $27,971 $58,990 $58,990

1 $58,181 $35,980 $51,591 $145,751 $141,506 $35,452 $22,080 $31,902 $89,434 $86,829

2 $58,181 $35,980 $51,591 $145,751 $137,384 $39,455 $24,607 $35,470 $99,532 $93,818

3 $58,181 $35,980 $51,591 $145,751 $133,383 $43,082 $26,878 $38,676 $108,636 $99,417

4 $58,181 $35,980 $51,591 $145,751 $129,498 $46,279 $28,887 $41,517 $116,683 $103,671

5 $58,181 $35,980 $51,591 $145,751 $125,726 $49,067 $30,646 $44,005 $123,718 $106,720

6 $58,181 $35,980 $51,591 $145,751 $122,064 $51,461 $32,158 $46,147 $129,766 $108,677

7 $58,181 $35,980 $51,591 $145,751 $118,509 $53,454 $33,425 $47,942 $134,822 $109,622

8 $58,181 $35,980 $51,591 $145,751 $115,057 $55,059 $34,447 $49,390 $138,896 $109,646

9 $58,181 $35,980 $51,591 $145,751 $111,706 $56,271 $35,218 $50,485 $141,974 $108,811

10 $58,181 $35,980 $51,591 $145,751 $108,452 $57,073 $35,735 $51,219 $144,027 $107,170

11 $58,181 $35,980 $51,591 $145,751 $105,294 $58,181 $35,980 $51,591 $145,751 $105,294

12 $58,181 $35,980 $51,591 $145,751 $102,227 $58,181 $35,980 $51,591 $145,751 $102,227

13 $58,181 $35,980 $51,591 $145,751 $99,249 $58,181 $35,980 $51,591 $145,751 $99,249

14 $58,181 $35,980 $51,591 $145,751 $96,359 $58,181 $35,980 $51,591 $145,751 $96,359

15 $58,181 $35,980 $51,591 $145,751 $93,552 $58,181 $35,980 $51,591 $145,751 $93,552

16 $58,181 $35,980 $51,591 $145,751 $90,827 $58,181 $35,980 $51,591 $145,751 $90,827

17 $58,181 $35,980 $51,591 $145,751 $88,182 $58,181 $35,980 $51,591 $145,751 $88,182

18 $58,181 $35,980 $51,591 $145,751 $85,613 $58,181 $35,980 $51,591 $145,751 $85,613

19 $58,181 $35,980 $51,591 $145,751 $83,120 $58,181 $35,980 $51,591 $145,751 $83,120

20 $58,181 $35,980 $51,591 $145,751 $80,699 $58,181 $35,980 $51,591 $145,751 $80,699

21 $58,181 $35,980 $51,591 $145,751 $78,348 $58,181 $35,980 $51,591 $145,751 $78,348

22 $58,181 $35,980 $51,591 $145,751 $76,066 $58,181 $35,980 $51,591 $145,751 $76,066

23 $58,181 $35,980 $51,591 $145,751 $73,851 $58,181 $35,980 $51,591 $145,751 $73,851

24 $58,181 $35,980 $51,591 $145,751 $71,700 $58,181 $35,980 $51,591 $145,751 $71,700

25 $58,181 $35,980 $51,591 $145,751 $69,612 $58,181 $35,980 $51,591 $145,751 $69,612

26 $58,181 $35,980 $51,591 $145,751 $67,584 $58,181 $35,980 $51,591 $145,751 $67,584

27 $58,181 $35,980 $51,591 $145,751 $65,616 $58,181 $35,980 $51,591 $145,751 $65,616

28 $58,181 $35,980 $51,591 $145,751 $63,704 $58,181 $35,980 $51,591 $145,751 $63,704

29 $58,181 $35,980 $51,591 $145,751 $61,849 $58,181 $35,980 $51,591 $145,751 $61,849

30 $58,181 $35,980 $51,591 $145,751 $60,048 $58,181 $35,980 $51,591 $145,751 $60,048

The right hand block of Table 12 gives the lower bound of the policy. The undiscounted total 

willingness to pay in the first year, $58,990, reflects the fact that most of the individuals 

receiving benefits have already been exposed to the baseline level of formaldehyde for part of 

their life and will not experience the full benefit of the program. Each year, a new cohort of 

children is added who will experience the full exposure reduction, so the undiscounted 

willingness to pay grows for the next 12 years, until it stabilizes at $145,751. The present 

discounted value of 30 years of the policy in this case would be about $2.7 million.
61

3.3.4 Discussion of uncertainties

As with sensory irritation, this example assumes that the population is constant and that the 

future distribution across housing types is exactly the same as the present distribution. 

Accommodating a growing population and a different housing and age distribution would be 

implemented in the same way as described above, by simply by changing the population values 

for each year.

As with sensory irritation, the concentration-response function is non-linear. One way to deal 

with this would be to linearize this concentration-response function over the relevant range of 

exposure, for example with a first order Taylor approximation. However, given that the upper 

and lower bound calculations require us to form an annual change in risk and the change in 

exposure is relatively small, the results from using the non-linear concentration-response 

function are probably very similar to the results if we were to use a linear function.

The prevalence rates from the CDC are higher than those used for the most recent prospective 

analysis of the benefits and costs of the Clean Air Act (EPA 2011a) as reported by IEc (2011). 

IEc assumed a prevalence rate of 5.27% for children less than 18 years of age, based on data 

from the American Lung Association (2002). The rates are also higher than the prevalence rates 

recommended by the EPA’s Office of Air for their BenMAP program (EPA 2011b). The Office 

of Air suggests a prevalence rate of 6.14% for children less than 5 years old and 10.7% for 

children 5-17 based on current prevalence rates in 2008 American Lung Association (2010).

3.4 Reduced Fertility

Valuing reductions in fertility is the most difficult of the three non-cancer effects. Similar to 

valuing asthma incidence, the concentration-response relationship is based on a period of time 

longer than the modeled one year exposure window, so adjustments will have to be made similar 

to those for asthma incidence. Monetization, based on either the cost of illness or a willingness to 

pay framework, has been discussed in the literature but has not been included in EPA rules.

3.4.1 Monetization

The effect of pollution on pregnant women is a legitimate economic endpoint and has been 

included qualitatively in a number of contexts. The Safe Drinking Water Act (SDWA 1974) 

explicitly mentions special consideration of pregnant women when setting priorities for 

maximum contaminant level goals for public drinking water systems. However, this is generally 

interpreted as evaluating the health impact on the mother rather than the ability to become 

pregnant. For example, EPA’s Ground Water Rule (EPA 2006) and Proposed Revised Total 

Coliform Rule (EPA 2010) both evaluate the effect of pollutants on the health of pregnant 

women but do not discuss potential impacts on fertility or other reproductive issues.

When reproductive issues are monetized, they almost always take the form of valuing the health 

impact on the fetus rather than the ability to become pregnant. For example, both the Lead-Based 

Paint Hazard Standards (EPA 2000c) and the EPA Clean Air Mercury Rule (EPA 2005a) 
62

monetize the impact of IQ losses from in utero exposure to the pollutant, but not fertility effects. 

In the case of lead, there was an explicit recognition that exposure can cause reproductive 

difficulty in both men and women (EPA, CPSC, and HUD 2003), but the endpoint was not 

included in the quantitative analysis. 

In a few cases, fertility impacts have been included in the economic analysis, but without full 

monetization. For example, the Arsenic in Drinking Water rule explicitly mentioned 

“reproductive and developmental effects” (including spontaneous abortions, perinatal death, and 

stillbirth) as “potential non-quantifiable health benefit” (EPA 2000b). This was based on a 

National Research Council review of the EPA’s 1988 risk assessment for arsenic in drinking 

water (NRC 1999). However, the EPA chose not to monetize the endpoint because of a lack of 

human data or strong evidence on the risks of this health effect. 

The furthest that the EPA has gone in the past in valuing fertility impacts is the quantification, 

but not monetization, of fetal losses in the Stage 2 Disinfectants and Disinfection Byproducts 

Rule (EPA 2005b). In this analysis, EPA calculated the odds-ratio or relative risk ratio for fetal 

loss from four population-based epidemiological studies. Because the exposure in these four 

studies was significantly greater than the exposure for the general population, survey data were

used to derive a Population Attributable Risk (PAR) values for the general population. Using the 

annual incidence of fetal loss, EPA estimated a range of 0 to 18,700 annual fetal losses 

attributable to exposure to chlorinated drinking water. 

EPA chose neither to monetize these impacts nor to include them in the primary benefits analysis 

because it believed that the scientific knowledge on reproductive and developmental health 

effects was not strong enough to quantify risk in the primary benefits analysis. In particular, the 

lower 95 percent confidence intervals for the PAR for all four studies were less than zero, 

meaning that the possibility of no effect could not be ruled out with 95 percent confidence. 

However, the calculations did indicate that the potential monetized value of this effect could be 

significant. In the same rule, EPA also mentioned other potential adverse reproductive impacts. 

For example, disinfectants are associated with miscarriages, which have associated medical costs 

as well as associated pain, suffering, and loss. These costs were estimated to range from $5,000 

to $11,000 depending on the conditions of the miscarriage. 

For the case of formaldehyde, exposure has been associated with delayed conception (Taskinen 

et al. 1999) rather than fetal loss. Fertility problems are not uncommon during an individual’s

reproductive cycle. Garceau et al. (2002) claims that one in six couples experience fertility

difficulty at some point in time in their reproductive lives. The CDC (2005) reports that 7% of 

married couples of reproductive age reported not using contraception for 12 months and not 

becoming pregnant and 12% of women of childbearing age in the United States have used an 

infertility service at some point in their reproductive cycle. While obtaining some fertility service 

is common, only 3.8 percent obtain ovulation drugs, 1.1 percent undergo artificial insemination 

and 0.3 percent engages in assisted reproductive technology, primarily in-vitro fertilization 

(IVF). The remainder seeks advice, undergoes tests, or obtains medical help to prevent 

miscarriages or surgery for blocked tubes.

Ovulation drugs, artificial insemination, and IVF are considered cycle-based treatments (Katz 

2011). Artificial insemination is a process in which the sperm is placed in either the cervix 

(intracervical insemination, or ICI) or the uterus (intrauterine insemination, or IUI) by artificial 
63

means. IVF is a process by which human egg cells are fertilized by sperm outside the body and 

then transferred back to the patient's uterus. Success rates have been rising over time, with about 

40% of couples undergoing IVF ultimately becoming pregnant (de La Rochebrochard 2009). In

an 18 month cohort study, Katz (2011) finds a 23.5% success rate for medication only; a 38.5-

55.6% success rate for IUI, depending on the accompanying fertility drug used; and a 47.3-

52.4% rate for IVF, depending on whether or not donor eggs were used. 

Katz (2011) reports median treatment costs, successful or not, of $1,182 for medication only; 

$3,595-$8,594 for IUI; and $24,373-$38,015 for IVF. The median treatment costs per successful 

outcome were $925 for medication; $4,124-$8,542 for IUI; and $24,010-$38,545 for IVF. This 

is roughly consistent with the cost estimates reported from other studies. The average cost per 

IVF cycle and per live-birth were estimated by Omurtag (2009) to be $9,226 and $56,419, 

respectively, and were estimated by Chambers (2009) to be $12,513 and $41,132, respectively. 

While there appear to be good data on the cost of treatment, there are few studies on the 

willingness to pay to reduce delayed conception. Most economic valuation studies regarding 

fertility focus on an individual or a couples’ willingness to pay for infertility treatment, 

particularly in-vitro fertilization (IVF). 

Granberg et al. (1995) conducted a study of 40 couples in Sweden using open-ended questions 

about the maximum number of treatments that they would be willing to undergo at various price 

level and their willingness to pay to have a child. The combined direct and indirect cost at the 

time of the study was ₤3,880 per treatment and ₤11,490 per delivery. The willingness to pay for 

a child ranged from ₤0 to ₤25,000, with more than half of the couple’s willing to pay more than 

₤10,000.

Ryan (1996) conducted a contingent valuation survey of 339 women seeking fertility services in 

Australia and found a mean willingness to pay of about $2,500 per IVF attempt. Because this 

study included a subset of women who had completed their treatment, it allowed Ryan to 

estimate the willingness to pay with certainty and to distinguish between undergoing treatment 

and having a child versus completing the treatment but ending childless. Having a child 

increased the willingness to pay by about 30%. 

A second study (Ryan, 1997) surveyed 458 women using a fertility service in Scotland. Using a 

randomized bid and a dichotomous choice model, Ryan estimates a mean willingness to pay of 

just over ₤5,000 per IVF attempt. There was a lower willingness to pay among individuals who 

had completed their treatment, likely reflecting the lower value associated with undergoing the 

treatment with the certainty of ending the process with no child. 

Note that both Ryan studies reflect a sample of individuals who are already seeking infertility 

services. This suggests a potential sample selection bias for individuals with a preference for 

increasing their chances of having a child.

Neumann and Johannesson (1994) conducted a study of 231 nurses, doctors, parents, students, 

and administrative staff in the Boston area. The contingent valuation survey used a payment card 

and a randomized bid to obtain the willingness to pay for IVF treatment with varying 

probabilities of success. The survey compared the respondents' willingness to pay for treatment 

in the event that they are infertile (an ex-post analysis) with the willingness to pay for insurance, 
64

assuming that they do not know their infertility status (an ex-ante analysis). The ex-post 

willingness to pay for a 10% chance of success was $17,730, suggesting about $175,000 per 

statistical pregnancy. The mean ex-ante willingness to pay was $865 per IVF treatment with a 

10% chance of success. The authors take this latter value to imply a willingness to pay of $1.7 

million per statistical pregnancy, but this is based on the authors’ subjective assumption about 

couples’ ex-ante belief that they will need IVF treatment. Curiously, the willingness to pay per 

statistical successful outcome drops as the level of certainly of success rises. The authors 

estimate a willingness to pay of $40,000 per statistical pregnancy in the ex-post case and 

$216,000 in the ex-ante case given 100% certainty of ending with a child. Again, the ex-ante 

value is based on the author’s assessment of a couple’s ex-ante belief that they will need IVF 

treatment.

All of these studies reflect willingness to pay for fertility treatment. The one study that comes 

close to valuing a reduction in delayed conception is Van Houtven and Smith (1999). They 

conducted a pilot study of 188 individuals in four cities using a mall intercept survey. 

Respondents were asked to consider taking a completely safe medication on a weekly basis 

which would delay the increase in infertility risk for up to five years based on randomly assigned 

monthly payment amounts. They found a willingness to pay of willingness to pay of $16,500 to 

$49,400 per statistical pregnancy using a 3% discount rate (and $15,200 to $45,700 using a 5% 

rate).

Valuing difficulty in conceiving due to formaldehyde exposure could be done using either the 

cost of treatment or some measure of the willingness to pay. Conceptually, the willingness to pay

approach is preferable and could be deduced from the studies described above. For example, the 

van Houtven and Smith (1999) value of approximately $15,000 - $50,000 for a statistical 

pregnancy and a probability of success of 25% from ovulation drugs suggests a willingness to 

pay of between $3,750 and $12,500 for fertility treatment. Alternatively, the Ryan (1996) 

willingness to pay of $2,500 per IVF attempt plus 30% for certainty, an average of 3.5 IVF 

cycles per patient, and a 50% success rate for IVF suggests a willingness to pay of just under 

$6,000. 

However, given that there is there has been less research on these willingness to pay values than 

other values and the fact that the values have not been used in previous economic analysis, it 

may be more straight-forward to use a cost of illness approach. Futhermore, many of these 

willingness to pay studies apply to the more serious infertility rather than to the delayed fertility

being modeled here. In this respect, the willingness to pay studies are not suitable for benefits 

transfer. For this analysis, we will use rounded values of the midpoint from the median cost of 

treatment values for fertility services taken from Katz (2011): $1,000 for medication; $6,000 for 

IUI; and $30,000 for IFV.

3.4.2 Annual Approach

The linear concentration-response function accounting for background exposures based on 

Taskinen et al. (1999) provides the most direct application of equation (7).
65

     

1

0

, , , , , ,

1 1

Total WTP WTP exposure exposure

t H C

t

t h c t hcbaseline h c policy

t t h c

  Pop   

  

             

(18)

And the willingness to pay for any given housing and age cohort is

Total WTPt h WTP e  Pop , , c t   xposurehcb , , aseline    exposureh c, , policy             

(19)

The number of women in the U.S. wishing to become pregnant can be estimated using the 

number of women of child-bearing age and information on pregnancy and contraception use 

(CDC 2010). The Taskinen (1999) study examined the fecundity of women age 20-40, so this is 

the age group which we will consider. The percentage of women seeking pregnancy over the 

course of a year can be estimated as the sum of the percentage of women who reported not using 

contraception because they were seeking pregnancy and the percentage who are intentionally 

pregnant or postpartum after an intentional pregnancy. The percentages of women who reported 

not using contraception because they were seeking pregnancy were 4.3%, 6.3%, 5.9%, and 5.1% 

for age ranges 20-24, 25-29, 30-34, and 35-39, respectively. The percentages of women who 

were pregnant or postpartum were 10.0%, 7.7%, 8.1%, and 1.9% for age ranges 20-24, 25-29, 

30-34, and 35-39, respectively. Since half of pregnancies are intended, according to CDC 

(2010), the percentage of women seeking pregnancy over the course of a year was estimated as 

the percentage of women currently seeking pregnancy plus half of the percentage of women who 

are pregnant or postpartum. These estimates are 9.3%, 10.2%, 10.0%, and 6.1% for age ranges 

20-24, 25-29, 30-34, and 35-39, respectively.

The percent of women seeking fertility treatment varies by age group. Table 13 presents the 

probabilities of seeking pregnancy and of obtaining cycle-based treatment based on tables 

provided by the CDC (2005 and 2010). Note that the last three columns, which present the 

percentages of women using a particular fertility treatment conditional on seeking some fertility 

treatment, do not sum to one hundred percent. This is because the costs associated with fertility 

treatments other than the three presented in the table were not estimated. Thus, these costs are 

implicitly assumed to be zero for the purpose of this analysis.
66

Table 13: Probability of Obtaining Cycle-Based Treatment by Age Group

Percent Obtaining Treatment

Percent Obtaining Treatment 

Conditional on Some Fertility 

Treatment Being Sought

Age 

Group

Percent 

Seeking 

Pregnancy

Any 

Fertility 

Service

Ovulation 

drugs IUI IVF Ovulation drugs IUI IVF

20-24 9.3% 4.9% 1.0% 0.2% 0.0% 20.41% 4.08% 0.00% 25-29 10.2%

30-34 10.0% 17.7% 5.3% 1.8% 0.4% 29.94% 10.17% 2.26%

35-39 6.1% 17.3% 4.6% 1.4% 0.3% 23.96% 7.29% 3.65%

Source: Percent seeking pregnancy is from CDC 2010 and percent obtaining treatment is from CDC 2005

The willingness to pay for an exposure change for some time period, t0 to t1, would then be:

  0 1

0 1 0 1

0 1 0 1 0

, ,

,

, ,

Total B Prob of seeking aseline Policy

WTP e pregnancy xposure exposure

Cost of Cost of

Pr(Meds) Pr(IUI) Pr(IVF)

Meds IUI

t t

t t t t

h c

c

h c h c

t t t t t t

Pop  

 

  

       

                   

   

      

    1

Cost of

Meds

   

        

(20)

where Pr(∙) is the probability of needing the cycle-based treatment conditional upon requiring 

fertility assistance.

As with asthma prevalence, the time period associated with the exposure-response relationship is 

longer than the 20 year time step examined by Taskinen (1999). Therefore, the linear model 

estimated above would be the probability of having difficulty conceiving based on an exposure 

for that time period. As before, this causes a problem if we have an individual who does not 

experience the exposure reduction for the full time period. We can form an upper and lower 

bound of this willingness to pay as we did for asthma prevalence. The upper bound is based on 

the assumption that the linear concentration-response function holds for an exposure reduction of 

one year. The lower bound assumes that an exposure reduction for one year represents 1/20th of 

an exposure reduction for the entire 20 year time period. (For convenience, the 20-40 time period 

is considered to be inclusive, so we are only modeling up to the individual’s 40th birthday.) This 

means that for any time period 0 1 t t [ ,t ], the willingness to pay for an individual who is age k at 

the time of policy implementation would be 

Upper bound:

  0 1

0 1 0 1

0 1 0 1 0

, ,

,

, ,

Total Prob of seeking Baseline Policy

WTP pregnancy exposure exposure

Cost of Cost of

Pr(Meds) Pr(IUI) Pr(IVF)

Meds IUI

t t

t t t t

h c

c

h c h c

t t t t t t

Pop  

 

  

       

                   

   

      

    1

Cost of

Meds

   

        

(21)
67

Lower bound:

 

1

0 1

0 1 0 1

0 1 0 1

, ,

, 1 0

Baseline Policy

Total Prob of seeking exposure exposure

WTP pregnancy

Cost of Cost of

Pr(Meds) Pr(IUI)

Meds IU

t t

t t t t

t

k

t t

h c

c

t t t t

Pop

t t

 

 

 

                         

   

  

 

 

       



0 1

Cost of

Pr(IVF)

I Meds t t 

     

             

(22)

3.4.3 Example Calculation

The linear concentration-response function for 

the risk of having difficulty conceiving is 

Risk = 0.056 + 0.0016∙(exposure)

We will use the same three housing profiles as 

we did in the previous examples. The assumed 

ADC for formaldehyde exposure for a woman 

age 20-40 is given in Table 14. This can be 

combined with the probability of reduced 

fecundity to produce a probability of 

undergoing fertility treatment.

The willingness to pay for fertility treatment 

will be treated in an expected value context. The average cost and probability of obtaining 

various cycle-based fertility treatments at various ages is given in Table 14. The first column 

gives the age ranges and the second column provides the proabililty that a woman is seeking 

pregnancy. Women between 20 and 34 years old have around a 10% probability of seeking 

pregnancy. From 35 to 40, the probability of a woman seeking pregnancy drops to 6.1%. The 

final three columns give the probability of obtaining treatment, conditional upon seeking some 

fertility treatment. Women seeking fertility treatment have no chance of being recommended for 

the more invasive and expensive IVF in their 20s, but have an increasing chance of obtaining this 

procedure in their 30s. In contrast, obtaining medication and IUI peaks between ages 30-34. It is 

true that women older than age 39 also obtain fertility treatment, but the costs and probabilities 

have been truncated at age 39 to remain consistent with Taskinen et al. (1999). The average cost 

of the three types of cycle-based fertility treatment, based on Katz (2010), is given in the final 

row.

Table 14: Illustrative formaldehyde exposure (is 

ppb) using three housing profiles

Scenario Housing Profile NonIndustrial 

Worker 

Avg. ADC

Weighted average ADC (ppb) during current 

exposure year

Baseline New Mobile Home 28.41

1-year-old Mobile Home 20.84

New Detached Home 25.97

CARB2 New Mobile Home 27.11

1-year-old Mobile Home 20.11

New Detached Home 25.89
68

Table 16 shows the illustrative 

benefits calculation for fertility 

effects in women living in the 

three housing types in climate 

zone 1. The population size is 

assumed to be half of the total 

population living in this housing 

structure because we are only 

dealing with women.

The first seven columns of Table 

16 represents the 2,943 women 

living in new mobile. Given 

reduced emissions of 1.30 ppb 

for every year, we would expect 

0.548 fewer cases of women having difficulty conceiving for this housing profile. The total 

willingness to pay to obtain this reduction is $543. The next six columns represent women living 

in one year old mobile homes. Since the emission reduction is smaller, we expect to see 0.308

fewer cases, with a willingness to pay of $300. The last six columns reflect the impact on women 

of child-bearing age in new homes. Here we expect 0.478 fewer cases and estimate a total 

willingness to pay of $465.

Table 17 gives the upper and lower bound estimate of the policy for the three housing types for 

thirty years of implementation. As before, the first year of implementation (year 0) does not 

affect individuals in 1-year-old homes. The upper bound estimate (left hand block of Table 17) 

produces the same willingness to pay for each year after the first year. The lower bound estimate 

(right hand block of Table 17) produces steadily increasing undiscounted willingness to pay 

estimates until the 20th year, reflecting the fact that earlier years were accounting for women who 

only experience part of the benefit of the exposure reduction. Discounting these values at 3%, the 

total discounted willingness to pay from this illustration is between $26,461 and $21,779.

Table 15: Average cost and probability of obtaining cycle-based 

fertility treatment

Age 

Group

Percent 

Seeking 

Pregnancy

Percent Obtaining Treatment 

Conditional on Some Fertility 

Treatment Being Sought

Ovulation 

drugs

IUI IVF

20-24 9.30%

20.41% 4.08% 0.00% 25-29 10.20%

30-34 10.00% 29.94% 10.17% 2.26%

35-39 6.10% 23.96% 7.29% 3.65%

Average Cost $1,000 $6,000 $30,000

Source: Percent seeking pregnancy is from CDC 2010 and percent 
69

Table 16: Illustrative benefit calculations for reduced fertility effects to women living in new mobile homes

New Mobile Home, Climate Zone 1 1 Year Old Mobile Home, Climate Zone 1 New Single Family Detached Home, Climate Zone 1

Age Population Baseline 

Exposure 

(ppb)

CARB2 

Exposure 

(ppb)

Exposure 

Reduction 

(ppb)

Cases 

Avoided

WTP Population Baseline 

Exposure 

(ppb)

CARB2 

Exposure 

(ppb)

Exposure 

Reduction 

(ppb)

Cases 

Avoided

WTP Population Baseline 

Exposure 

(ppb)

CARB2 

Exposure 

(ppb)

Exposure 

Reduction 

(ppb)

Cases 

Avoided

WTP

2,943 0.548 $533 2,943 0.308 $300 41,081 0.478 $465

20 158 28.41 27.11 -1.30 0.0306 $14 158 20.84 20.11 -0.73 0.0172 $8 2204 25.97 25.89 -0.08 0.0267 $12

21 153 28.41 27.11 -1.30 0.0296 $13 153 20.84 20.11 -0.73 0.0167 $7 2134 25.97 25.89 -0.08 0.0258 $12

22 151 28.41 27.11 -1.30 0.0293 $13 151 20.84 20.11 -0.73 0.0165 $7 2110 25.97 25.89 -0.08 0.0256 $11

23 150 28.41 27.11 -1.30 0.0291 $13 150 20.84 20.11 -0.73 0.0164 $7 2098 25.97 25.89 -0.08 0.0254 $11

24 152 28.41 27.11 -1.30 0.0294 $13 152 20.84 20.11 -0.73 0.0165 $7 2117 25.97 25.89 -0.08 0.0256 $12

25 153 28.41 27.11 -1.30 0.0325 $15 153 20.84 20.11 -0.73 0.0183 $8 2132 25.97 25.89 -0.08 0.0283 $13

26 150 28.41 27.11 -1.30 0.0319 $14 150 20.84 20.11 -0.73 0.0179 $8 2096 25.97 25.89 -0.08 0.0278 $12

27 152 28.41 27.11 -1.30 0.0324 $15 152 20.84 20.11 -0.73 0.0182 $8 2127 25.97 25.89 -0.08 0.0283 $13

28 153 28.41 27.11 -1.30 0.0325 $15 153 20.84 20.11 -0.73 0.0183 $8 2136 25.97 25.89 -0.08 0.0284 $13

29 154 28.41 27.11 -1.30 0.0327 $15 154 20.84 20.11 -0.73 0.0184 $8 2150 25.97 25.89 -0.08 0.0286 $13

30 153 28.41 27.11 -1.30 0.0319 $51 153 20.84 20.11 -0.73 0.0179 $28 2136 25.97 25.89 -0.08 0.0278 $44

31 145 28.41 27.11 -1.30 0.0303 $48 145 20.84 20.11 -0.73 0.0170 $27 2029 25.97 25.89 -0.08 0.0264 $42

32 141 28.41 27.11 -1.30 0.0294 $47 141 20.84 20.11 -0.73 0.0165 $26 1968 25.97 25.89 -0.08 0.0256 $41

33 139 28.41 27.11 -1.30 0.0289 $46 139 20.84 20.11 -0.73 0.0163 $26 1936 25.97 25.89 -0.08 0.0252 $40

34 135 28.41 27.11 -1.30 0.0281 $45 135 20.84 20.11 -0.73 0.0158 $25 1883 25.97 25.89 -0.08 0.0245 $39

35 138 28.41 27.11 -1.30 0.0176 $31 138 20.84 20.11 -0.73 0.0099 $18 1931 25.97 25.89 -0.08 0.0153 $27

36 134 28.41 27.11 -1.30 0.0170 $30 134 20.84 20.11 -0.73 0.0096 $17 1872 25.97 25.89 -0.08 0.0149 $26

37 137 28.41 27.11 -1.30 0.0174 $31 137 20.84 20.11 -0.73 0.0098 $17 1913 25.97 25.89 -0.08 0.0152 $27

38 143 28.41 27.11 -1.30 0.0182 $32 143 20.84 20.11 -0.73 0.0103 $18 2002 25.97 25.89 -0.08 0.0159 $28

39 151 28.41 27.11 -1.30 0.0192 $34 151 20.84 20.11 -0.73 0.0108 $19 2110 25.97 25.89 -0.08 0.0168 $30
70

Table 17: Upper and Lower bound benefits for reduced fertility effects using three housing 

profiles

Upper 

Bound 

Estimate

Lower Bound 

Estimate

Year New Mobile 

Home

1-Year Old 

Mobile 

Home

New SF 

Detached 

Home

Total WTP Total 

Discounted 

WTP

New 

Mobile 

Home

1-Year Old 

Mobile 

Home

New SF 

Detached 

Home

Total WTP Total 

Discounted 

WTP

$16,538 $9,003 $14,429 $39,970 $26,461 $14,272 $7,901 $12,450 $34,623 $21,779

0 $533 $465 $999 $999 $226 $197 $422 $422

1 $533 $300 $465 $1,299 $1,261 $252 $141 $219 $612 $595

2 $533 $300 $465 $1,299 $1,224 $277 $156 $242 $674 $635

3 $533 $300 $465 $1,299 $1,189 $302 $170 $263 $734 $672

4 $533 $300 $465 $1,299 $1,154 $317 $178 $284 $779 $692

5 $533 $300 $465 $1,299 $1,121 $349 $196 $304 $850 $733

6 $533 $300 $465 $1,299 $1,088 $372 $209 $324 $905 $758

7 $533 $300 $465 $1,299 $1,056 $393 $221 $343 $958 $779

8 $533 $300 $465 $1,299 $1,025 $415 $233 $362 $1,010 $797

9 $533 $300 $465 $1,299 $996 $446 $251 $380 $1,077 $826

10 $533 $300 $465 $1,299 $967 $455 $256 $397 $1,107 $824

11 $533 $300 $465 $1,299 $938 $472 $265 $412 $1,149 $830

12 $533 $300 $465 $1,299 $911 $487 $274 $425 $1,185 $831

13 $533 $300 $465 $1,299 $885 $499 $281 $436 $1,215 $828

14 $533 $300 $465 $1,299 $859 $509 $286 $444 $1,240 $820

15 $533 $300 $465 $1,299 $834 $517 $291 $451 $1,259 $808

16 $533 $300 $465 $1,299 $810 $524 $295 $457 $1,275 $795

17 $533 $300 $465 $1,299 $786 $528 $297 $461 $1,287 $779

18 $533 $300 $465 $1,299 $763 $532 $299 $464 $1,295 $761

19 $533 $300 $465 $1,299 $741 $533 $300 $465 $1,299 $741

20 $533 $300 $465 $1,299 $719 $533 $300 $465 $1,299 $719

21 $533 $300 $465 $1,299 $698 $533 $300 $465 $1,299 $698

22 $533 $300 $465 $1,299 $678 $533 $300 $465 $1,299 $678

23 $533 $300 $465 $1,299 $658 $533 $300 $465 $1,299 $658

24 $533 $300 $465 $1,299 $639 $533 $300 $465 $1,299 $639

25 $533 $300 $465 $1,299 $620 $533 $300 $465 $1,299 $620

26 $533 $300 $465 $1,299 $602 $533 $300 $465 $1,299 $602

27 $533 $300 $465 $1,299 $585 $533 $300 $465 $1,299 $585

28 $533 $300 $465 $1,299 $568 $533 $300 $465 $1,299 $568

29 $533 $300 $465 $1,299 $551 $533 $300 $465 $1,299 $551

30 $533 $300 $465 $1,299 $535 $533 $300 $465 $1,299 $535

3.4.4 Discussion of uncertainties

As with the previous endpoints, this example assumes that the population is constant and that the 

future distribution across housing types is exactly the same as the present distribution. Correcting 

for trends in population and housing could be done in the same fashion as for the other 

endpoints.
71

The willingness to pay estimates above reflects the positive value that women who have trouble 

conceiving would obtain by not suffering this difficulty. However, it should be pointed out that 

there is probably a much smaller opposite effect associated with an increase in pregnancy by 

women who do not want to become pregnant. A complete analysis would incorporate this 

opposite effect, but is much more difficult and controversial to estimate and value.

The equation for probability of having trouble conceiving is used to produce an estimate of the 

number of women who whose time to pregnancy will exceed 12 months. The valuation treated 

this estimate as equal to the number of women who seek fertility treatment. This might be

justified as an upper bound estimate, but there are certainly women to have trouble becoming 

pregnant and do not seek fertility treatment. This is not reflected in this analysis.

The willingness to pay values are based on the average cost of obtaining fertility services. While 

this is not the theoretically correct value to use for monetization, it is a reasonable estimate if 

most fertility treatment costs are paid for out-of-pocket by the patients rather than by insurance. 

In actually paying the cost, the patient reveals that the treatments is worth at least as much as she 

paid. The maximum willingness to pay, however, would be expected to be greater than these 

costs because many consumers receive more utility from service than they pay for it. Note that 

this does not take into account any utility or disutility of treatments. This suggests using cost-ofillness will produce an underestimate.

On the other hand, these values are being applied to all women who are exposed to 

formaldehyde, but not all of the women whose fertility is affected will pay the market prices for 

the treatments. In other words, we have an estimate of the willingness to pay for the women who 

choose to undergo these treatments. However, we do not have an estimate of the willingness to

pay for the women whose fertility is affected but choose not to undertake the treatment. Their 

values are likely to be positive, but they are less than the costs. For example, it may be that 

women with lower household incomes are less likely to pay for treatments at the going prices. In 

this sense, the estimate of fertility benefits using the average cost of obtaining fertility service 

may be biased upward.

Also, all of the women in the Taskanen study whose pregnancies were delayed ultimately had 

successful pregnancies. The “health endpoint” being modeled is therefore delayed fertility, not 

infertility. If women would be willing to pay more to increase the chance of getting pregnant 

than they would to decrease the time to pregnancy then the cost-of-illness estimates based on a 

successful pregnancy used here would overstate the true willingness to pay.

The willingness to pay for reduced time to conceive could, theoretically, be estimated with a 

stated preference survey, but this would require women to place an ex-ante value on their 

willingness to pay to undergo various types of fertility treatment, each with an uncertain 

outcome. Since the women producing this ex-ante value will likely have had little or no 

experience with the various fertility treatments, such a study would require extensive pre-testing 

to assure that the women understand the commodity. 

There are also reasons to believe that the cost of treatment may not even reflect the correct 

endpoint. For example, women are willing to pay to reduced time to conceive but, at the same 

time, are reluctant to undergo fertility treatment. Furthermore, the cycle-based treatments 
72

described here may not even be the appropriate treatment to reduce delayed fertility associated 

with formaldehyde exposure.

Finally, the values reflect that ages reported in the Taskinen (1999) study, ages 20-40. However, 

women older than age 40 obtain fertility treatment. The CDC (2005) study that was used to 

produce probabilities for the 20-40 age group reports 19.2% of the women studied who were age 

40 to 44 had obtained some type of infertility treatment, with 8.4% obtaining ovulation drugs, 

2.6% undergoing artificial insemination, and 0.7% utilitizing assisted reproductive technology 

(assumed to be IVF). The value of reduced infertility effects from reduced formaldehyde 

exposure is not reflected in this analysis in order to remain consistent with Taskinen (1999), but 

could be included by simply extending the ages considered.
73

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