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$)

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.
The present discounted value of the stream of annual WTPs for someone who gets asthma at age a is
where
       denotes the annual WTP,
	 denotes the age at onset of asthma (e.g.,  = 6, 7, ..., or 17),
	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 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

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.
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

Equation Error! Reference source not found. can then be used to calculate the resulting value for.  The weighted PDV (in 2010$) of willingness to pay values using this method is $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

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 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

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).

The willingness to pay for any given housing and age cohort is

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

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][(1.02][7][)*(-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+
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][(1.02][7][)∙(-1)]].  If we had a 10 ppb reduction, we would see 9,200∙[1 - e [ln][(1.02][7][)∙(-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.

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 period. 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][(1.02][7][)∙(-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.

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][(1.02][7][)∙(-][0.833][)]] = 202 fewer cases, represented by the light and dark red areas. However, only 17 of those cases would occur in the 17[th] 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.

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 , the willingness to pay for an individual who is age k at the time of policy implementation would be
Upper bound:

Lower bound:

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 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.
Table 10: Illustrative formaldehyde exposure scenarios using three housing profiles
                                   Scenario
                                Housing Profile
                       Preschool / School Child Avg. ADC
                        Non-Industrial 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

3.3.3 Example calculationThe 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 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

 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

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.
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.

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) 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 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, 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).

And the willingness to pay for any given housing and age cohort is

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.

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:

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 1/20[th] 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 40[th] birthday.) This means that for any time period , the willingness to pay for an individual who is age k at the time of policy implementation would be

Upper bound:

Lower bound:

Table 14: Illustrative formaldehyde exposure (is ppb) using three housing profiles
                                   Scenario
                                Housing Profile
                        Non-Industrial 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

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 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 obtaining treatment is from CDC 2005
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 20[th] 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 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