In each of these studies, the authors found that increases in blood lead levels were associated with increased risk of CVD mortality. All the studies informing the quantitative relationship between lead and cardiovascular mortality are based on NHANES, which provides a single blood lead measurement for each participant, at a time period prior to death.
Menke et al. (2006)
In their study Blood Lead Below 0.48 umol/L (10 ug/dL) and Mortality Among US Adults, Menke et al. (2006) used NHANES III data to examine the association between blood lead levels and all-cause and cause-specific mortality among U.S. adults who have blood lead levels below 10 ug/dL. The following text describes analyses and results pertaining to CVD mortality only. Menke et al. (2006) included 13,946 participants 20 years of age and older. Follow-up for each participant was calculated as the time between their NHANES III examination and the date of death, the date on which they turned 90 years of age, or December 31, 2000. The authors used ICD-9 (World Health Organization, 1975) codes 390 to 434 and 436 to 459 and ICD-10 (World Health Organization, 1992) codes I00-I99 to identify CVD mortality. Maximum duration of mortality follow-up, which varies depending on date of the participant's NHANES examination, was approximately 12 years. The mean blood lead level for the participants in the Menke et al. (2006) study was 2.58 ug/dL.
Menke et al. (2006) performed several statistical analyses. In one statistical analysis, Menke et al. categorized the participants into blood lead tertiles based on the weighted population distribution. The tertiles were <1.93 ug/dL, 1.94 ug/dL  -  3.62 ug/dL, >=3.63 ug/dL. Baseline confounders were calculated for each tertile after standardizing to the U.S. population by age, sex and race-ethnicity. The hazard ratios (HRs) and 95% CIs were calculated using multivariable Cox regression models by comparing each tertile with the first (low lead) tertile. The authors constructed three models to adjust for various potential confounders. In the first model, adjustment was made only for age, sex, and race-ethnicity. Additional potential confounders of the association between lead and CVD mortality were added in Model 2 (see Exhibit J.5 for list). In the final model, Menke et al. (2006) additionally adjusted for hypertension and kidney function, which are potential intermediates in the causal pathway for the association.
 Exhibit J.5 displays results of the analysis for CVD mortality. When comparing the second (middle) tertile to the first tertile, a slight increase in CVD mortality was observed. When comparing the third tertile to the first tertile, a larger and statistically significant increase in risk was found. CVD mortality remained statistically significantly associated with blood lead levels in all three models.

Exhibit J.5: Hazard Ratios and 95% Confidence Intervals of CVD Mortality Associated with Tertile of Lead (Menke et al., 2006)

                                   Tertile 1
                             (<0.09 umol/L or
                               <1.93 ug/dL)
                                   Tertile 2
                              (0.09-0.17 umol/L
                                      or
                               1.94-3.62 ug/dL)
                                   Tertile 3
                               (>=0.18 umol/L
                                      or
                                >=3.63 ug/dL)
                                    Ptrend
Cardiovascular disease mortality, n
                                      104
                                      219
                                      443

  Age, race-ethnicity, and sex adjusted
                                     1.00
                              1.01 (0.68 - 1.51)
                              1.51 (1.07 - 2.14)
                                     0.004
  Multivariable 1 adjusted*
                                     1.00
                              1.06 (0.70 - 1.60)
                              1.64 (1.14 - 2.35)
                                     0.001
  Multivariable 2 adjusted†
                                     1.00
                              1.03 (0.69 - 1.55)
                              1.55 (1.08 - 2.24)
                                     0.003
Note: Sample sizes (n) refer to the number of events.
* Adjustment included age, race-ethnicity, sex, diabetes mellitus, body mass index (BMI), current or former smoking, alcohol consumption, physical activity, low income, c-reactive protein (CRP), total cholesterol, high school education, urban residence, and post-menopausal status.
† Adjustment includes variables in model 1, hypertension, and level of kidney function.
Source: Menke et al. (2006, Table 2)

Tests for linear trend across tertiles of blood lead were computed by including tertile of lead as a continuous variable in the Cox regression models. The trend analysis found statistically significant increases in CVD mortality risk. The results of this analysis are also presented in Exhibit J.4 and support the finding of a concentration-response relationship between blood lead and CVD mortality.
In an additional analysis, due to the skewedness of the distribution of blood lead, lead was log-transformed and treated as a continuous variable. The study authors calculated HRs for a 3.4-fold increase in blood lead levels or the difference between the logged 80[th] (4.92 ug/dL) and 20[th] (1.46 ug/dL) percentiles of blood lead distribution. After the multivariate adjustment, the HR for a 3.4-fold increase in blood lead level was 1.53 (1.21-1.94) for CVD mortality. That is, for each 3.4-fold increase in blood lead level, there is a subsequent 53% increase in risk of CVD mortality for the adult population. Menke et al. (2006) also determined the association between blood lead as a continuous variable and CVD mortality for subgroups defined by age, race-ethnicity, sex, menopausal status, urban or rural residence, cigarette smoking, overweight, diabetes mellitus, hypertension, and level of estimated glomerular filtration rate (GFR). However, no subgroup interaction terms were statistically significant at the 5% level.
Aoki et al. (2016)
The purpose of Aoki et al. (2016) was to "examine the blood Pb-CVD mortality association with hematocrit/hemoglobin-corrected blood lead using NHANES 1999 to 2010" (p. 1). The authors opted to use the hematocrit or hemoglobin corrected values of blood lead in order to examine whether these measures are better biomarkers of exposure than whole blood lead. This is because the majority of blood lead is in red blood cells; if lead causes total red blood cell count to decrease (i.e., lead-induced anemia), there will be an underestimation of the relationship between blood lead and CVD mortality. To explore this idea, Aoki et al. (2016) used data on 18,602 individuals, 40 years of age and older, from the 1999-2010 NHANES. The mean whole, hematocrit- and hemoglobin- corrected blood lead levels in this subset of the NHANES population were 1.73 ug/dL, 1.73 ug/dL, and 1.74 ug/dL, respectively. Follow-up occurred from the date of NHANES examination through December 31, 2011. Deaths were identified by reviewing death records for ICD-10 codes I00-I99, which correspond to CVD mortality. In this population there were 985 CVD deaths with a median follow up time of 6.2 years.
To model the relationship between blood lead and CVD mortality, Aoki et al. (2016) used a Cox proportional hazard regression analysis, with age during follow-up (as opposed to elapsed time since enrollment in the cohort) as the time scale. The authors used three blood lead measurements as the main exposure variable in three separate models: (1) hematocrit-corrected blood lead; (2) hemoglobin-corrected blood lead; and (3) (uncorrected) whole blood lead. To correct for hematocrit/hemoglobin, the authors divided whole blood lead by the hematocrit and hemoglobin concentration measured in NHANES. Aoki et al. then multiplied the corrected blood lead variable by the weighted geometric mean of hematocrit and hemoglobin, respectively, in the analytic sample so that results for the corrected variables would be comparable to those for whole blood.
Aoki et al. (2016) examined several variables as confounders in the blood lead-CVD mortality relationship. The authors considered the standard confounders that are often included in analyses related to lead exposure and adverse health outcomes, such as demographic data, smoking status, education, and alcohol intake. The authors also evaluated five non-lead biomarkers as confounders: blood cadmium, serum iron, serum C-reactive protein, serum calcium, and bone mineral density. When entering the confounders and blood lead measurements into the model, all of the right-skewed variables (i.e., the three blood lead measurements, blood cadmium and C-reactive protein) were log-transformed.
To demonstrate the nature and magnitude of the confounding due to non-lead biomarkers, the authors conducted multiple models for each blood lead measurement, where each non-lead biomarker (i.e., blood cadmium, serum iron, C-reactive protein, and serum calcium) was removed from the fully model adjusted model. In addition, the authors also conducted models in which they adjusted for hemoglobin or hematocrit instead of correcting for it. In the "adjusted for" models, both whole blood lead and the red blood cell concentration (i.e., hemoglobin or hematocrit) are included in the regression model. This is in contrast to the "corrected for" model in which the ratio of whole blood lead to hemoglobin/hematocrit is a single variable in the regression equation. Lastly, the authors also conducted each of the fully adjusted models on a subset of the NHANES population (n=10,264) with bone mineral density (BMD) measures and included BMD as an additional adjustment in the model. Results showed that hematocrit/hemoglobin-corrected blood lead variables are similarly associated with CVD mortality. Additionally, comparing results from the fully adjusted model across lead exposure variables indicated that not correcting for red blood cell concentration may underestimate the risk of CVD mortality. This is exemplified by the fact that the hazard ratio associated with a 10-fold increase in hematocrit- or hemoglobin-corrected blood lead levels is 1.44 or 1.46, respectively, both with confidence intervals that do not include 1. However, the hazard ratio for whole blood lead and CVD mortality is 1.27 with a confidence interval that does encompass the null value of 1. This pattern, with whole blood lead underestimating the relationship with CVD mortality, persists through the models.
An additional notable pattern is that when blood cadmium and serum iron are excluded from the model, the relative risk increases. The authors interpret this finding as evidence that not adjusting for these variables would result in residual confounding, which could result in an overestimate of the relationship between blood lead and CVD mortality. Removing both serum iron and C-reactive protein did not dramatically increase the relative risk, compared to when only serum iron was removed. Therefore, C reactive-protein was not operating as a strong confounder in this study. Serum calcium also does not appear to be acting as a strong confounder, because removing it from the model does not dramatically shift the relative risk estimate. Additionally, including BMD in the model also did not greatly impact the hazard ratio. Lastly, the adjustment (rather than correction) for hematocrit/hemoglobin resulted in a lower hazard ratio. The authors argue that "if red blood cell concentration acted as an intermediate variable in the causal pathway between exposure to lead and mortality then the lead exposure's effects would have been absorbed into the coefficient representing the association between low red blood concentration and mortality. In fact, we found that the adjusted hazard ratios were attenuated compared to the corresponding hazard ratios for hematocrit/hemoglobin-corrected blood lead." According to Aoki et al. (2016), this is likely due to uncontrolled confounding due to pre-existing anemia (p. 6).
Ruiz-Hernandez et al. (2017)
In their paper "Declining exposures to lead and cadmium contribute to explaining the reduction of cardiovascular mortality in the US population," Ruiz-Hernandez et al. (2017) aimed to evaluate whether changes in blood lead and cadmium exposures in the US population would account for changes in rates of CVD mortality between 1988-1994 and 1999-2004, after controlling for established cardiovascular risk factors. Participants in NHANES were included in the study (n = 21,418) if they were aged 40 years old or older and had complete data on lead, cadmium, and other CVD risk factors. Mortality outcomes were determined using National Death Index records and ICD codes for CVD mortality (ICD-10 codes 100-178) and coronary heart disease (ICD-10 codes 120-125). To ensure that the same length of follow-up was used for both cohorts, participants in NHANES 1988-1994 and in NHANES 1996-2004 were followed through December 31, 1996 and December 31, 2006, respectively. The authors used weighting techniques to adjust NHANES data to be representative of the US population.
To calculate mortality rate ratios associated with a two-fold increase in blood lead, Ruiz-Hernandez et al. (2017) estimated Poisson regression models for individual mortality data on log-transformed metal concentrations, which were adjusted for age at follow-up, sex, race, survey period and traditional CVD risk factors. These risk factors were: baseline smoking status, physical inactivity, obesity, hypertension, diabetes, high total cholesterol, low HDL cholesterol and lipid-lowering medication. Ruiz-Hernandez et al. (2017) additionally conducted analyses including interaction terms for age, smoking status, and survey period. The authors additionally used three approaches to examine mediation of CVD mortality by exposures to lead and cadmium: the causal inference mediation approach, the difference in coefficients approach and the product of coefficients method. For all approaches, three models with varying levels of adjustment were used. In the first model, only age, race, and sex were adjusted for; CVD risk factors and cadmium levels were added in turn to all previous confounders in the second and third models, respectively. Results of the mediation analyses were absolute decreases in deaths attributable to decreases in lead and cadmium exposures, and the percentage of total deaths attributable to these decreases in exposures.
After adjusting for differences in age, sex, race and risk factors between the two NHANES cohorts, Ruiz-Hernandez et al. (2017) found that decreases in lead exposures were associated with 51.9 avoided deaths per 100,000 person-years. Similar patterns were observed for coronary heart disease mortality. Results were consistent across methods, and in sensitivity analyses when using different methods to adjust for CVD mortality. Exhibit J.6 displays the rate ratios for cardiovascular and coronary heart disease mortality associated with a doubling of blood lead.
Exhibit J.6: Rate Ratios for Cardiovascular and Coronary Heart Disease Mortality Associated with a Two-Fold Increase in Baseline Blood Lead

                            Cardiovascular Disease
                            Coronary Heart Disease

                             Mortality rate ratio
                                   (95% CI)
                               P for interaction
                             Mortality rate ratio
                                   (95% CI)
                               P for interaction
Overall
                               1.19 (1.07, 1.31)
                                       -
                               1.24 (1.10, 1.41)
                                       -
Sex
Men
                               1.09 (0.95, 1.25)
                                     0.07
                               1.14 (0.98, 1.33)
                                     0.11
Women
                               1.31 (1.13, 1.52)

                               1.44 (1.14, 1.82)

Smoking
Never
                               1.35 (1.14, 1.59)
                                     0.07
                               1.63 (1.32, 2.01)
                                     0.003
Ever
                               1.10 (0.96, 1.25)

                               1.10 (0.95, 1.28)

Survey
1988-94
                               1.17 (1.04, 1.31)
                                     0.47
                               1.25 (1.10, 1.42)
                                     0.77
1999-2004
                               1.26 (1.05, 1.50)

                               1.20 (0.88, 1.62)

Source: Ruiz-Hernandez et al. (2017), Table 1

Lanphear et al. (2018)
In their paper Low-level lead exposure and mortality in US adults: a population-based cohort study, Lanphear et al. (2018) aimed to estimate the relative contribution of lead exposure to all-cause and CVD mortality using a nationally representative sample from NHANES III. Additionally, the authors aimed to expand upon findings on the association between lead and CVD mortality from Menke et al. (2006) by using a longer duration of follow-up. Participants in the study were enrolled in NHANES from 1988 to 1994 and were aged 20 years or older at baseline. NHANES conducted household interviews to obtain demographic information from participants. Participants also underwent medical examinations, during which health information (e.g., BMI, alcohol consumption) and blood and urine samples were collected. Samples were analyzed for concentrations of lead, cadmium, and creatinine. For the blood lead analyses, the limit of detection (LOD) was 1.0 ug/dL. Study participants with blood lead levels below the LOD were assumed to have blood lead of 0.7 ug/dL (i.e., the LOD divided by the square root of 2). Follow-up of all participants occurred through December 31, 2011; personal identifiers (e.g., birth date, social security number) were used to link participants to National Death Index data up to this date. Based on ICD codes, deaths from all causes, CVD (ICD-9 codes 390-459; ICD-10 codes I00-I99), and ischemic heart disease (ICD-9 codes 410-414; ICD-10 codes I20-I25) were identified.
In the statistical analyses, the authors weighted results to account for the oversampling methods used in NHANES III. Cox proportional hazards models were used to calculate hazard ratios (HRs) for the associations between continuous blood lead and the three types of mortality. Additionally, the shape of the dose-response relationships between lead and the three types of mortality were investigated using five-knot restricted cubic splines. Analyses were adjusted for variables known to be potential confounders for CVD mortality: age, sex, income, ethnicity, BMI, smoking status, alcohol consumption, physical activity, urinary cadmium levels, blood pressure, glycated hemoglobin, and cholesterol. The authors used population attributable fractions to estimate the proportional reduction in mortality that would occur if blood lead levels decreased to 1.0 ug/dL in all U.S. adults aged 20 years and above. They additionally investigated the effects of low-level lead exposures by restricting analyses to participants with blood lead levels below 5.0 ug/dL.
The study analyzed information on 14,280 individuals from NHANES III. The geometric mean blood lead level was 2.71 ug/dL, and 9% (1150) of participants had blood lead below the LOD of 1 ug/dL. During the follow-up period (median of 19.3 years), 4422 participants died. Of these deaths, 38% were attributable to CVD and 22% to ischemic heart disease. Increases in blood lead from 1.0 ug/dL to 6.7 ug/dL (i.e., from the 10[th] to 90[th] percentile) were associated with significant increases in all-cause mortality, CVD mortality, and ischemic heart disease mortality.
 Exhibit J.7 shows the adjusted HRs for these increases and all types of mortality, as well as population attributable fractions and avoidable deaths assuming a decrease in lead to 1.0 ug/dL.
Exhibit J.7: Adjusted Hazard Ratios, Population Attributable Fractions, and Avoidable Deaths Associated with Lead Exposures (Lanphear et al. 2018)
                               Type of Mortality
                            Unadjusted HR (95% CI)
                             Adjusted HR (95% CI)
                   Population Attributable Fraction (95% CI)
                           Avoidable Deaths (95% CI)
All-cause mortality
                                     3.79
                                  (3.18-4.50)
                                     1.37
                                  (1.17-1.60)
                                    18.0%
                                  (10.9-26.1)
                                    412,000
                               (250,000-598,000)
CVD mortality
                                     4.44
                                  (3.47-5.68)
                                     1.70
                                  (1.30-2.22)
                                     28.7%
                                  (15.5-39.5)
                                    256,00
                               (138,00-352,000)
Ischemic heart disease mortality
                                     5.31
                                  (4.06-6.93)
                                     2.08
                                  (1.52-2.85)
                                     37.5%
                                  (23.4-48.6)
                                    185,000
                               (116,00-241,000)
Source: Lanphear et al. (2018, Table 2)

The cubic spline analyses indicated that the adjusted HRs for all types of mortality were steeper at lower concentrations of lead than higher concentrations. When the analysis was restricted to participants with blood lead levels below 5 ug/dL, the HR for CVD mortality was 1.95 (95% CI = 1.46-2.60).
Cardiovascular Mortality Uncertainty Discussion
EPA begins this section by providing background on bone and blood lead biomarkers, as well as on the timing of effects and potential modes of action for the association between lead and CVD mortality. Next, EPA describes uncertainties and provides a discussion of their implications for approaches that EPA would develop for modeling benefits of reduced lead exposure in adults. EPA also provides an overview of evidence on applicability of concentration-response functions between lead and CVD mortality in the general population.
Bone and Blood Lead Biomarkers
Once lead enters the body (through either inhalation or ingestion), it enters the blood stream and has a clearance half-life of approximately 30 days. Although lead can circulate throughout the body and can be found in all organs and tissues, blood is the most readily available biomarker for lead exposure. It is reflective of both recent exposures (<30 days) from exogenous sources and past exposures (years to decades) that had been stored in tissues (e.g., bone) and released endogenously (National Toxicology Program, 2012; U.S. EPA, 2013). Clearance of lead from blood occurs through "the distribution into soft tissues and bone as well as excretion, primarily through kidney filtration and elimination in urine" (Hu et al. 2007, p. 456). The loss of bone lead occurs slowly through bone resorption, the dominant transfer process for bone lead, and by diffusion (U.S. EPA, 2013). Half-life of lead in bone is dependent on age, intensity of exposure, and bone type. EPA states that for cortical bone, the half-life of lead at birth is 0.23 years, 1.2 years at 5 years of age, 3.7 years at 15 years of age, and 23 years in adults; for trabecular bone, the half-life of lead at birth is 0.23 years, 1.0 years at 5 years of age, 2.0 years at 15 years of age, and 3.9 years in adults (U.S. EPA, 2013). As stated previously, the half-life of blood lead is approximately 30 days, but Hu et al. (2007) point out that this half-life is:
      "a reflection of the 120-day lifespan of erythrocytes and only applies in practice if the total exposure is short (e.g., <30 days). If lead exposure is long-term (i.e., with a duration of years), upon cessation the kinetics of clearance of lead from blood is considerably more complicated, with an initial rapid decline in levels reflecting partial clearance from blood and other soft tissues followed by a much slower clearance, reflecting the replenishment of soft tissue polls of lead with lead from long-lived deposits in bone" (p. 457).
Therefore, bone lead and blood lead are correlated. This is particularly true in older populations, because of the mobilization from bone later in life (Morrow et al. 2007).
Mode of Action and Timing of Effects
Lead has been associated with adverse impacts to the cardiovascular system in numerous studies. In the Integrated Science Assessment for Lead, EPA deemed the association between lead exposure and coronary heart disease (including cardiovascular disease (CVD) mortality) to be causal. Specifically, EPA stated, "despite the differences in design and methods across studies, with few exceptions associations between higher levels of Pb biomarkers and higher risk of [coronary heart disease]-related mortality were consistently observed" (p. 4-412). Both short term and longer term exposure may be important for the role of lead and adverse cardiovascular outcomes, and evidence of lead influencing cardiovascular effects via both acute pathways and cumulative injury has been found (Glenn, 2006).
There are likely to be plausible mechanisms by which lead could contribute to both the long-term processes of cardiovascular disease progression (such as atherosclerosis and chronic increases in blood pressure) and the short-term exacerbating events such as the acute precipitation of "heart attacks" and "strokes." The adverse effects of lead include indirect impacts (e.g., increasing oxidative stress, disturbing hormone homeostasis, disrupting calcium signaling) for which the cascading impacts can adversely impact cardiovascular health. There is evidence that lead can directly impact cardiovascular health through mechanisms such as damaging the endothelial lining, causing dose-dependent increases in vasoconstriction and impacting heart performance directly.
Because cardiovascular health status is a function of a variety of genetic and lifestyle/behavioral factors as well as exposure to lead, modeling the impact of very small changes in lead exposure is challenging. Additional work is also needed on modeling the cessation lag. For example, how likely is it that changing average blood lead levels in the range of 0.25, 1, or 2 ug/dL for individuals over age 60 is likely to prevent death from CVD at age 70? EPA would have to consider how to take this uncertainty into account in its consideration of methods for modeling lead-related cardiovascular mortality.
Implications for Benefits Modeling
When EPA published the lead ISA in 2013, questions remained about the time frame over which lead biomarkers most accurately represent risk. As stated in the EPA ISA, "uncertainties remain regarding the timing, frequency, duration and level of Pb exposures contributing to the effects observed in epidemiologic studies" (U.S. EPA, 2013, p. Ixxxv). There is uncertainty over whether the observed associations between lead and CVD are applicable to current cohorts of individuals. This is, in part, because the available studies use a one-time blood lead measure from NHANES rather than examining adult lead exposure over their lifetime. Since environmental levels of lead have been decreasing over time as a result of interventions such as the lead in gasoline ban, individuals examined in these studies may have had a higher exposure profile in childhood and early adulthood than those born in recent years. However, these higher exposures will likely be reflected in higher blood lead levels in their NHANES blood lead samples, as blood and bone lead levels will be correlated. It is not known what their blood lead levels were many years ago, but it is known that on average, older adults have higher blood lead levels than younger adults based on NHANES data.
As described, studies examining different NHANES cohorts, including several published since the 2012 lead ISA, have found significant quantitative associations between blood lead and CVD mortality.  Four key studies on the association were selected by EPA to highlight: Aoki et al. (2016), Lanphear et al. (2018), Menke et al. (2006), and Ruiz-Hernandez et al. (2017). These selected studies represent all studies available from the literature that met the criteria described at the beginning of Section J.3.1
All of these studies are large, population-based studies that analyze NHANES data and use the National Death Index database to identify cases of CVD mortality among NHANES participants. NHANES is based on a nationally representative sample of individuals throughout the United States and uses a rigorous methodology that includes trained interviewers, standardized procedures, and quality control measures. Another advantage of the use of NHANES is the availability of detailed information on potential confounders, though the possibility of residual confounding remains in each study, and each study looked a slightly different set of potential confounders. The National Death Index is a comprehensive source for death records in the United States. Since all of the studies use this source, the potential for misclassification of CVD mortality cases is similar in each study.
The EPA ISA indicates that "available human data at ambient concentrations for ... lead [Pb] ... [does] not exhibit thresholds for ... noncancer health effects," (U.S. EPA, 2013, p. Ixiii) thus the association between blood lead and CVD mortality is anticipated, by the Agency, to hold in cohorts with declining blood lead levels.  However, "uncertainties remain regarding the timing, frequency, duration and level of Pb exposures contributing to the effects observed in epidemiological studies" (U.S. EPA 2013). Although EPA finds evidence that reductions in adult lead exposure are likely to result in decreases in CVD mortality, the Agency did not quantify the relationship for the LCRR analysis given these uncertainties.
Applicability of Observed Concentration-Response Functions to the General Population
Ruiz-Hernandez et al. (2017) investigated interactions in the association between blood lead and CVD mortality by sex, smoking status and survey period. Interactions for sex and smoking status failed to reach significance (p = 0.07), and no interaction was found for survey period (p = 0.47). Menke et al. (2006) also evaluated associations in different portions of the population, such as those above and below 60 years old, and pre- and post-menopausal women, race, smoking status, hypertension and diabetes status and did not find any significant interactions for any groups.
Based on the above findings from Ruiz-Hernandez et al. (2017) and Menke et al. (2006) and the fact that the studies are based on sampling of the U.S. adult population from NHANES, EPA concluded that each function is applicable to the general population of U.S. adults. Additionally, Lanphear (2018) confirmed that association holds in those with blood lead levels below 5 ug/dL.
Similar associations between lead and CVD mortality have been observed across different NHANES cohorts and in different segments of the population. In addition, available studies have examined individuals with low blood lead levels (<5 ug/dL) that are within the range of those observed in the current NHANES cohort. The identified concentration-response functions from Aoki et al. (2016), Lanphear et al. (2018), Menke et al. (2006), and Ruiz-Hernandez et al. (2017) are expected to be applicable to the general U.S. population. In an effort to address the uncertainties in the estimation of changes to CVD mortality risk associated with the changing frequency and level of lead exposures which may occur as a result of regulatory actions, EPA will be soliciting peer-reviewer feedback on the appropriate methods for the quantification of lead related CVD mortality benefits in the regulatory context.
Low Birth Weight
Zhu et al. (2010)
Zhu et al.'s study, Maternal Low-Level Lead Exposure and Fetal Growth (2010), examined the association between low-level (<10 ug/dL) lead exposure and decreased fetal growth, specifically measures of birth weight, pre-term birth, and small for gestational age. In their retrospective cohort study, Zhu et al. matched the blood lead records from New York State's Heavy Metals Registry (HMR) to birth certificate data for singleton births in the state of New York for 43,288 mother - infant pairs from upstate New York (New York State excluding New York City). The mothers were 15 - 49 years of age in 2003 - 2005. The study restricted the cohort to mothers with blood lead levels < 10 ug/dL. The mean and median blood lead levels for the cohort were 2.1 ug/dL and 2 ug/dL, respectively. The mean birth weight was 3,331 grams.
To assess the relationship between maternal blood lead and the continuous outcomes (e.g., birth weight in grams), Zhu et al. (2010) used a multiple linear regression with fractional polynomials (Royston et al. 1999). They explored one or two terms of fractional polynomials in terms of x[p] where the power of p was -2, -1, -0.5, 0.5, 1, 2, and 3, and also used a natural logarithmic transformation of lead.
The authors state that the model that assumed a linear relationship between birth weight and the square root of blood lead fit the data better than models with all other combinations of fractional polynomials. The final model developed by Zhu et al. (2010) was adjusted for timing of the lead test, gestational age, maternal age, race, Hispanic ethnicity, education, smoking, alcohol drinking, drug abuse, in wedlock, participation in special financial assistance program, parity, and infant sex. The dose-response relationship from Zhu et al. is:
BW=b0+(-27.4gug/dLxPbB0.5)
Where:
BW		= 	Birth weight in grams
b0 		= 	Birth weight when blood lead is equal to 0 ug/dL
    PbB 	= 	Blood lead in ug/dL

The results from the study are presented in Exhibit J.8, which shows that changes in birth weight associated with a 1 ug/dL change in blood lead vary based on the starting blood lead concentration. For example, the reduction in birth weight from blood lead 0 to 2 ug/dL is approximately 40 grams and from 8 to 10 ug/dL is approximately 10 grams. As Zhu points out, "the model predicts the strongest estimated effects at the lowest levels of exposure, without a lower threshold of PbB [blood lead] below which there would be no predicted effect on birth weight" (p. 1473).

Exhibit J.8: Association between a Change in Blood Lead Concentration and Birth Weight, Upstate New York, 2003 - 2005 from Zhu et al. (2010)
Change in Blood Pb Concentration (μg/dL)
Estimate (grams)
95% CI (grams)
                                       0
                                   Reference
                                       -
                                       1
                                     -27.4
                                -17.1 to -37.8
                                       2
                                     -38.8
                                -24.1 to -53.4
                                       3
                                     -47.5
                                -29.6 to -65.4
                                       4
                                     -54.8
                                -34.2 to -75.5
                                       5
                                     -61.3
                                -38.2 to -84.4
                                       6
                                     -67.2
                                -41.8 to -92.5
                                       7
                                     -72.5
                                -45.2 to -99.9
                                       8
                                     -77.6
                                -48.3 to -106.8
                                       9
                                     -82.3
                                -51.2 to -113.3
                                      10
                                     -86.7
                                -54.0 to -119.4
The model was a linear regression with fractional polynomials after adjustment for timing of Pb test, gestational age, maternal age, race, Hispanic ethnicity, education, smoking, alcohol and drinking, drug abuse, in wedlock, participation in special financial assistance programs, parity, and infant sex. Blood Pb concentration was transformed using a square root. The coefficient was -27.4 with a standard error (SE) of 5.3.
Source: Table 3 from Zhu et al. (2010).

Zhu et al. (2010) conducted sensitivity analyses by rerunning their models and excluding blood lead values that were equal to 0 ug/dL in one analysis and also <= 1ug/dL in the second, as the level of detection for the blood lead measurements was 1 ug /dL. They found that the analysis with all blood lead values included provided "robust estimated effects of Pb on birth weight" (p. 1473).
References
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: Estimated Value of an IQ Point
The benefits of the final rule are the monetary value of the avoided IQ decrements in children attributable to final revisions to the LCRR primarily in the areas of CCT and LSLR. EPA's approach to estimating the benefits of regulations that reduce exposure to chemicals and pollutants affecting children's cognitive function relies on two separate literatures: studies that link chemical or pollutant exposures to intelligence quotient (IQ), and studies that link IQ to lifetime earnings.
This appendix describes EPA's method for estimating an average value per IQ point. Section K.5 provides a summary of the economics literature estimating the relationship between IQ and earnings. Section K.6 describes EPA's reanalysis approach that follows Salkever (1995). Section K.7 provides a critical review of the Salkever approach. Section K.8 describes how EPA estimated lifetime earnings, and Section K.9 describes EPA's method for estimating educational costs and summarizes the IQ value results. Section K.10 discusses limitations to the methods described in this appendix.
Exhibit K.1 summarizes this appendix's estimates of the IQ point dollar values produced in 2016 dollars. The values can be used to estimate the benefits of avoiding IQ decrements.
Exhibit K.1: Summary of IQ Point Dollar Values (2016$)
Estimate Parameter
Discount Rate

3%, Male
3%, Female
7%, Male
7%, Female
Present value of lifetime earnings
$1,046,830
$680,742
$239,634
$160,998
IQ value
$19,591
$23,206
$4,484
$5,488
Additional education costs and lost earnings
$1,324
$1,343
$612
$611
Net value of an IQ point (IQ value less additional education costs and lost earnings) discounted to the third year of life
$18,267
$21,862
$3,873
$4,877
Net value of an IQ point, weighted average
$19,993
$4,355
Net value of an IQ point, discounted to birth
$18,296
$3,555
IQ and Earnings
The economics literature provides a robust basis for estimating the relationship between IQ change and lifetime earnings. Because the literature relies on large datasets that are representative of the US population, it is appropriate to use the results to infer subpopulation-level impacts (though not individual-level impacts) from changes in environmental policy, even when average impacts are very small in magnitude. The estimated effects of IQ on lifetime earnings are not predicated on a particular type or pathway of pollutant exposure. Rather, they are broadly applicable to evaluating any type of policy intended to improve children's cognitive development (Lin et al. 2018).
First, this review discusses Salkever (1995), the study used to derive this estimate most frequently in EPA regulatory analyses. Next, more recent studies are discussed. Then the role that educational attainment plays in mediating the link between IQ and wages or earnings is discussed. A discussion of the uncertainties and limitations of the literature follows, noting a few areas for future research. Last, the implications for use of the literature in regulatory analysis is summarized.
In the context of lead exposure, which has well-known adverse effects on cognitive development (e.g. U.S. Environmental Protection Agency 2013), Salkever (1995) and Schwartz (1994) proposed conceptual frameworks to describe the relationships between IQ, education, labor participation, and earnings. IQ can directly affect both participation in the labor force and wages conditional on labor participation, and it can also indirectly affect these outcomes via educational attainment. Some chemicals and pollutants, including lead, can also cause other adverse neurological effects. Some of these effects, such as reduced executive function, also affect wages and labor participation, either directly or indirectly through educational attainment (Heckman et al. 2006; Gensowski 2018). Some studies have found that non-cognitive personality traits are at least as predictive of life outcomes as IQ (Cawley et al. 2001; Heckman et al. 2006; Heckman & Kautz 2012; Borghans et al. 2016). Thus, IQ is one of many proxy variables for the more comprehensive concept of human capital that are predictive of important life outcomes.
Most studies linking cognitive function to earnings have used data from the National Longitudinal Survey of Youth 1979 cohort (NLSY79) (U.S. Bureau of Labor Statistics 1979). NLSY79 is a nationally representative survey of over twelve thousand Americans born from 1957 to 1964 that has tracked participant information about schooling, employment, and earnings for almost four decades. It also includes detailed information about participants' family backgrounds, such as parents' education and income, which allows researchers to isolate the effect of IQ on earnings by controlling for these other potential determinants of earnings. Studies typically use performance on the Armed Forces Qualifying Test (AFQT), administered to NLSY79 participants in 1980, as a proxy for IQ. The AFQT includes tests of verbal and mathematics skills and has been widely used as a measure of cognitive ability. While AFQT scores are an imperfect measure of cognitive ability and suffer from test-retest variability, the large sample size in the AFQT allows for relatively precise estimates of the effect of IQ on earnings across the sample.
Salkever (1995) estimated the relationships between IQ, educational attainment, labor participation, and log wages for males and females using data from the NLSY79 on 1990 earnings, when participants were roughly 30 years old. Salkever's analysis included race/ethnicity, region, family income in 1979, and parents' education to control for socioeconomic factors that may be correlated with both IQ and earnings. Salkever found that each 1-point increase in IQ score was associated with an average total gain in earnings of 1.93 percent for males and 3.23 percent for females. While the effect of IQ on schooling and the direct effect of IQ on earnings (after conditioning on schooling) were similar across males and females, the effects of schooling on wages and labor participation were larger for females, resulting in a larger total effect. While Salkever was motivated by the desire to estimate the benefits of reductions in lead exposure, Salkever's empirical analysis was focused only on the IQ to earnings link  -  it does not include data on lead exposure and is based on variation in IQ across the cohort regardless of lead levels.
Since Salkever's 1995 study, other studies in the labor economics literature have used the NLSY79 dataset to examine different aspects of the relationship between IQ and earnings. Neal and Johnson (1996) and Johnson and Neal (1998) examined the wage gap between blacks and whites. Heckman et al. (2006) compared the roles of cognitive and non-cognitive factors in determining earnings, finding that both had statistically significant effects. Ganzach (2011) used more recent data from the NLSY79 to examine the effects of socioeconomic background and IQ on wages over the lifecycle to age 40 for respondents with exactly 12 years of schooling. Zax and Rees (2002) used a different dataset -- the Wisconsin Longitudinal Survey -- to examine the relationship between IQ, academic performance, and earnings for white male high school graduates, contrasting effects at age 35 (in 1974) and 53 (in 1992). Both Zax and Rees and Ganzach found that the importance of IQ grows with age, but the effects of socioeconomic background variables on wages are stable over time.
The results of these studies are qualitatively consistent with Salkever in finding a statistically significant positive relationship between IQ and wages. However, estimates from these studies are not directly comparable to Salkever's because they excluded data from participants with zero earnings, so their findings did not incorporate the effect of IQ on labor participation (Salkever, David S 2014). In addition, Zax and Rees limited their analysis to a subpopulation (white males) in which estimated earnings effects of IQ have been found to be smaller compared to effects for other demographic groups (Salkever, David S 2014). The studies also varied in the extent to which they controlled for educational attainment. Controlling for planned or actual educational attainment without accounting for the endogenous effect of IQ on education will bias the effect of IQ on earnings downward, because higher IQ individuals are likely to attend more years of school and to generate higher earnings (Heckman et al. 2006). This bias is a concern in Zax and Rees, who limited their sample to high school graduates and included educational aspiration variables in some specifications, as well as Ganzach, who limited their sample to participants with exactly 12 years of schooling. The Salkever (1995) approach addressed this potential source of bias by estimating the impact of IQ on schooling in addition to the direct impacts of IQ on labor participation and wages when schooling is held constant and summing the relevant effects together when estimating the total effect of IQ on earnings.
Lin et al. (2018) is a recent addition to the labor economics literature using the NLSY79 to examine how the effect of IQ on earnings varies over the lifecycle to age 50. Lin et al. generated estimates that are comparable to Salkever's because they included participants with zero earnings in the analysis to capture effects related to labor participation. Rather than Salkever's approach of explicitly modeling the links between IQ, education, and earnings, Lin et al. modeled a reduced form relationship by including IQ in the earnings equation without controlling for education due its endogeneity. Therefore, the coefficient on IQ captures both the direct effect on earnings and the indirect effect resulting from increased educational attainment. Lin et al. included a similar but not identical set of socioeconomic background variables as Salkever. In addition, Lin et al. included three non-cognitive personality traits -- sociability, self-esteem, and perceived level of control over one's life. Lin et al. also compared the results to estimates using a more recent survey -- the NLSY 1997 cohort (NLSY97), a survey of roughly 9,000 Americans born in 1980-1984 (U.S. Bureau of Labor Statistics 2015). They found that the effect of IQ on earnings at age 30 was not significantly different across the two cohorts. Lin et al. noted that, after adjusting for years worked, reference age, and IQ scale, their central estimate of the effect of IQ on lifetime earnings is within two percent of EPA (2008b) range of estimates. However, because the Lin et al. estimates of the IQ-earnings effect increase with age, Lin et al.'s estimate of the IQ-earnings effect at age 30 is smaller than Salkever's estimate. Lin et al. note that their estimates are "applicable to a broad variety of policy interventions aimed at improving cognitive performance, such as those designed to reduce exposure to lead or other neurotoxicants, improve children's nutrition, increase breastfeeding, or to promote early childhood development and education."
Salkever and Lin et al. both incorporated features that make them useful for regulatory analysis. Salkever explicitly modeled the role of education in the IQ-earnings relationship, which sheds light on the mechanism by which cognitive skills affect earnings and also allows EPA to account for educational costs when calculating the change in net lifetime earnings from a change in IQ. However, extrapolating the Salkever (1995) IQ-earnings effect at age 30 will generate an estimate of lifetime earnings that is biased downward if the effect of IQ on earnings grows over the lifecycle, a result found in Zax and Rees, Ganzach, and Lin et al. Salkever et al. (1995) relied on older data from the NLSY79 cohort, but EPA's reanalysis of Salkever uses more recent data from the NLSY97 cohort. Lin et al. also used both the NLSY79 and NLSY97 data and examined data that extend throughout the lifecycle, including earnings at age 50 and beyond. However, their analysis lacked some control variables included in Salkever, and the use of estimates from a model that includes non-cognitive traits in the regression is problematic if EPA is unable to estimate the effect of a chemical or pollutant's exposure on these characteristics. Since these variables are correlated with IQ, their inclusion may attenuate the effect of IQ on earnings, leading to a downward bias on EPA's estimate of the total earnings effects of reduced chemical or pollutant exposure.
Education and Earnings
The labor economics literature discussed above confirms that there is a measurable link between cognitive skills and earnings (as well as a link between non-cognitive skills and earnings). However, the role education plays as a potential pathway from cognitive skills to earnings is challenging to estimate quantitatively. Cognitive skills and level of schooling are highly correlated, and cognitive ability is endogenous with years of education at the time of the test, making it difficult to separately identify these effects on lifetime earnings. Some researchers have made assumptions about the functional form of the earnings function in an attempt to separate out the two effects. However, these assumptions are problematic because not every ability-education combination is observed in the data (Cawley et al. 2001). For a portion of the sample, there is no observable counterfactual: there are not many observations for individuals with high cognitive ability and low levels of education or individuals with low cognitive ability and high levels of education. That said, studies that have examined the effect of IQ on wages or earnings have found statistically significant effects even after fully or partially controlling for educational attainment (Salkever 1995; Zax & Rees 2002; Heckman et al. 2006; Ganzach 2011), suggesting that education is not the only pathway by which cognitive skills affect earnings.
Researchers have observed a growing wage premium (adjusted for the average share of total hours worked by gender-education-experience) associated with completing a four-year college degree. In 2008, the earnings of an average college graduate exceeded those of an average high school graduate by 97 percent. The wage premium between skilled (college) and unskilled (high school) workers has been mainly driven by rising wages for individuals with post-college degrees and large decreases in wages for the less educated (high school or less) (Acemoglu & Autor 2011). Consistent with Acemoglu and Autor (2011), Cunha et al. (2011) found that shifts in supply and demand for high school and college workers were the main drivers of the change in the wage premium. The increase in the wage premium for college graduation has been mainly due to an increase in the return to cognitive skills.
Some have argued that a degree marking the completion of a stage of schooling -- high school or college -- matters more than years of schooling. Studies that have allowed for nonlinearities have found some support with respect to college graduation (Hungerford & Solon 1987; Belman & Heywood 1991). Others have observed that the relationship between earnings and years of schooling is largely linear (Park 1994), except at the highest levels of education (MDs and PhDs) (Card 1999). Recent work by Heckman et al. (2018) found that high school and college graduation have important effects on earnings even after controlling for years of schooling, but that attending some college had a positive causal effect on earnings relative to high school graduation only. Returns to education also vary by cognitive ability; they found that low-ability individuals gained the most in lifetime earnings from high school completion but saw fewer additional returns from more schooling. They also found that cognitive and non-cognitive skills were important predictors of educational attainment and therefore lifetime earnings.
Uncertainties and Areas for Future Research
The literature summarized above contributes to EPA's understanding of the relationship between cognitive skills, education, and earnings, but several uncertainties remain. One limitation of the studies is measurement error in the test scores used to proxy for IQ. Test scores are not perfect proxies for intelligence and can be affected by contextual factors such as hearing bad news before the test or receiving incentives such as candy or money (Aronson & Steele 2005; Borghans et al. 2011). There is also potential for racial or gender bias in cognitive testing (Aronson & Steele 2005; Nguyen & Ryan 2008; Walton & Spencer 2009).
Classical measurement error in an independent variable leads to attenuation, biasing the coefficient estimate toward the null (Hausman 2001). When other independent variables in the regression are correlated with the variable of primary interest, their coefficient estimates are also biased, though the sign of the bias depends on the direction of correlation among the variables (Schofield 2014). While error in the earnings data is also likely, measurement error in the dependent variable typically does not bias the coefficient estimates (Hausman 2001). Measurement error in an independent variable also biases t-test statistics toward the null, so researchers are less likely to reject the null hypothesis of no effect (Pischke 2007). Thus, measurement error in AFQT scores implies that the literature may underestimate the association between cognitive ability and earnings.
Use of standardized test scores to measure intelligence is further complicated by the fact that test performance is affected by other personality traits. Respondents with anxiety perform worse on IQ tests, and incentives disproportionately affect IQ scores of respondents who score low on the traits of conscientiousness and emotional stability (Borghans et al. 2011). However, some chemical or pollutant exposures affect both cognitive and non-cognitive traits. For example, lead exposure affects attention-related behaviors and other problem behaviors (National Toxicology Program (NTP) 2012; U.S. Environmental Protection Agency 2013). Earnings are affected by non-cognitive traits (Heckman et al. 2006; Gensowski 2018). Indeed, school achievement test scores and grades -- which are more strongly affected by non-cognitive traits than are IQ scores -- are more predictive of earnings and other life outcomes than IQ scores (Borghans et al. 2016).
Therefore, estimates of the IQ-earnings relationship that do not control for non-cognitive skills may overstate the effect of cognitive skills alone but are not biased upward relative to the full impact of chemical or pollutant exposures on earnings, including non-cognitive factors for chemicals or pollutants that affect both cognitive and non-cognitive skills. Valuing changes in non-cognitive skills has not frequently been done in benefit-cost analysis (Jones et al. 2015), but valuation of the impacts of reduced chemical or pollutant exposures on earnings would ideally account for both sets of factors. A goal for future research is to explicitly estimate the links between chemical and pollutant exposures, non-cognitive traits or skills, and earnings, to yield a more complete picture of the effect of lead exposure on earnings and incorporate these effects into EPA's analyses. Another alternative is to examine the effect of chemical and pollutant exposures on achievement test scores and then the impact of test scores on earnings, since achievement test scores reflect both cognitive and non-cognitive skills. An emerging literature has assessed the effect of lead on achievement test scores (e.g., Miranda et al. 2007; Miranda et al. 2009; Elliot et al. 2015; Aizer et al. 2018), while other research has linked test scores or class rank to earnings or wages (Zax & Rees 2002; Chetty et al. 2011). In this case, the specific impacts of cognitive and non-cognitive factors would not need to be distinguished because EPA would estimate the aggregate or net effect.
Another limitation of the literature is the potential for bias due to other omitted variables likely to be correlated with both test performance and earnings, such as a supportive household or extra educational resources. Most studies discussed here include socioeconomic characteristics such as parents' income, education, or occupation to control for important determinants of earnings and help isolate the impact of IQ. However, the IQ coefficient will be biased if there are additional unobserved individual or household characteristics correlated with both IQ and earnings. Heckman et al. (2006) discussed the potential bias in analyses that do not control for schooling received prior to taking the AFQT, since schooling affects both scores and future earnings. Heckman, et al. also noted that biases due to omitted variables and measurement error tend to have opposite effects, so the net direction of bias when regressing earnings on test scores is ambiguous. Using simulation approaches to reduce both sources of bias decreased their estimated effect of IQ on wages by 9-24 percent. Lin et al. used an approach proposed by Oster (2017) to derive a lower bound on the effect of IQ on earnings, assuming that all omitted variables are positively correlated with both IQ and earnings. This approach reduced the estimated effect of IQ on lifetime earnings by 31 percent. Because this procedure yields a lower bound based on one potential source of bias without generating an upper bound estimate adjusting for potential biases in the opposite direction, use of this approach is not appropriate in regulatory analysis. However, instrumental variables or other quasi-experimental approaches that address both measurement error and omitted variable bias are a potential avenue for future research. For instance, Reyes (2015) used exogenous variation in the rates of phase-out of lead in gasoline across states to identify the effects of lead on criminal behavior and teen pregnancy.
Another understudied area is the potential for non-linearities or thresholds in the relationship between IQ, education, and earnings. Most of the literature assumed a continuous (typically linear or log-linear) relationship between IQ and earnings. An important exception is Lin et al. (2018), who investigated the stability of the IQ-earnings relationship across the distribution of AFQT scores by estimating a model with polynomial terms. They found that higher order AFQT terms were not significantly associated with earnings, confirming that linearity is a reasonable assumption. As previously described, there is some research on potential thresholds in the relationship between education and earnings (also referred to as "sheepskin effects"), but the evidence is somewhat mixed. Future research could delve further into this issue by examining different functional forms for the relationship between IQ and educational outcomes, as well as using quantile regression to assess whether IQ and education have constant effects across the distribution of earnings (e.g., Arias et al. 2002).
Still another uncertainty is to what extent estimated relationships from the published literature, which are based on historic data, will apply to future populations. Regulatory analysis for new policy is prospective, while econometric studies are inherently retrospective. It is possible that economic changes will lead to either a larger or smaller IQ premium in the future. Assuming that historic relationships will apply in the future may be reasonable both because historic estimates are the best available and because Lin et al. (2018) found no evidence that the relationship between IQ and earnings at age 30 differed in the NSLY79 cohort compared to the NSLY97 cohort twenty years later. Similarly, uncertainties may be introduced from applying average estimates based on a representative sample of the US population to smaller subgroups that may be disproportionately affected by regulation. Some of the studies discussed examined the effect of IQ on earnings by gender and race/ethnicity and found significant heterogeneity, with larger effects for women and non-whites.
Implications for Regulatory Analysis
The studies reviewed here derive statistical relationships that represent average effects at a population level. Even when studies have estimated heterogeneous effects across broad demographic subgroups, it is not appropriate to use the estimates to predict a change in earnings at the individual level. Rather, the findings can only be interpreted as representing incremental changes in earnings associated with IQ changes on average across a population. EPA's Science Advisory Board (SAB) has previously recommended that predicting changes in IQ, including mean changes of less than a single IQ point, is appropriate for a population in economic and risk analysis but is not defensible at the individual level (U.S. EPA, 1998). The SAB noted that, "small effects distributed across a large population exert large total health effects," and "the characterization of IQ point loss by the summation of fractional IQ points over the entire population of children is considered defensible and appropriate."
Because the literature finds support for a continuous relationship between IQ and earnings, it is possible to quantify the impacts of even very small IQ changes. The uncertainty in this relationship can be characterized using confidence intervals derived from the standard errors of the relevant coefficient estimates and/or bootstrapping approaches. Due to the large datasets used in this literature, relatively precise estimates are possible, regardless of the magnitude of the change in IQ. In addition, it is standard practice in the EPA regulatory analysis to quantify benefits that represent incremental improvements toward a threshold (U.S. EPA, 2010).
A review of the labor economics literature points to a few areas for future research that could improve EPA's understanding of the relationship between IQ and lifetime earnings. EPA recognizes that the labor market impacts of changes in educational attainment and behavioral function, among many determinants of income, are active areas of research in the economics literature. Going forward, EPA will continue to review the economics literature and to evaluate new data and methods that could result in improved estimates and a better understanding of the uncertainties surrounding the estimated effect of changes in IQ on lifetime earnings.
In the meantime, the published literature provides a strong basis for quantifying the effect of IQ on lifetime earnings as a measure of the benefits of reduced chemical and pollutant exposures. David S Salkever (1995) still represents the most comprehensive attempt to estimate the effect of IQ on earnings accounting for both labor participation and intermediate effects on educational attainment. Lin et al. (2018)'s use of lifecycle earnings data for a nationally representative sample of the population represents another significant contribution that can inform regulatory analysis (see Appendix F for a sensitivity analysis that considers the implications of deriving the value of an IQ point using Lin et al. (2018) instead of EPA's reanalysis of David S Salkever (1995).

Reanalysis of the IQ Effect on Lifetime Earnings
The value of an IQ point as a percentage of lifetime earnings is a reanalysis of Salkever (1995), which estimated the effect of IQ on earnings, accounting for both labor participation and intermediate effects on educational attainment. The method begins with an identity relationship between income (I), probability of employment (P), and earnings from employment (E):
I=P xE.
A change in income depends on changes in employment and earnings:
∆I= ∆P xE+ P x∆E+ ∆Px∆E.
Assuming the last term in negligible and rearranging terms, the equation becomes
                          ∆I= I x( ∆PP+ ∆EE ).
Thus, a change in income equals baseline income multiplied by the sum of a percent change in probability of employment and a percent change in earnings.
The reanalysis followed the same approach as the original analysis, but used more recent 1997 NLSY data instead of the original 1979 NLSY data. This analysis indicates that a one point change in IQ results in a 1.865 percent and 3.397 percent change in lifetime earnings for males and females, respectively. The estimates incorporate the direct and indirect effects that changes in IQ have on earnings. Direct effects include the effect of IQ test scores on participation in employment and earnings with the years of schooling held constant. Indirect effects include the effect of IQ test scores on years of schooling attained, and the subsequent effect on participation and earnings.
Salkever (1995) also produced adjusted estimates that incorporate non-IQ related effects caused by lead exposure on schooling from Schwartz (1994), yielding a 2.094 percent and 3.631 percent change in lifetime earnings for males and females, respectively. Non-IQ effects on schooling caused by lead exposure include effects on hearing, balance, hyperactivity, and perceptual and attention disorders (Schwartz 1994). Schwartz (1994) estimates lead exposure on schooling to be 0.131 years per IQ point, whereas Salkever (1995) estimates the effect to be 0.1007 years per IQ point−the former estimate unsurprisingly larger given that it captures IQ and non-IQ effects of lead exposure.
In his meta-analysis, however, Salkever (2014) only defended his unadjusted results, implying a belief that his unadjusted results are the most defensible. For this reason, Salkever's (1995) adjusted estimates incorporating Schwartz's (1994) effect on schooling were not updated and are not used to measure the effect of lead exposure on earnings in this analysis, despite the fact that omitting non-IQ effects on schooling may underestimate the actual IQ point dollar value associated with reducing lead exposure.
Because EPA's reanalysis omits the non-IQ effects on schooling, the valuation results may be applied more generally to value IQ decrements resulting from exposure to any toxin.
Reanalysis of Salkever (1995) Using NLSY 1997 Data
The variables available in the 1997 NLSY are generally very similar to those available in the 1979 NLSY used by Salkever. Therefore, EPA was able to use the more recent data in their reanalysis without making many changes to the variable definitions or approach that Salkever (1995) used for his estimates. However, some changes were necessary, and the discussion below details the variable definitions used, the assumptions made, and compares the EPA reanalysis results with Salkever's (1995) analysis.
Salkever appears to have dropped a set of the individuals not in the labor force from his 1995 analysis (as evidenced by the "participation" rates (rates of individuals with positive earnings) he reports). Although detailed specifics for which individuals were excluded were not included in his paper, based on the high "participation" rate reported it appears that anyone not in the labor force was excluded, except for respondents that reported their employment status as "keeping house." However, "keeping house" is not a labor force variable available in the 1997 data. Thus, there was no way to use the 1997 data while excluding those not in the labor force, except for those "keeping house" or in school. Therefore, the reanalysis includes individuals not in the labor force, excluding only those enrolled in school and 17 observations with missing or unknown employment status. The final analysis included 8,984 respondents. EPA excluded the following respondents because of missing data: 1,843 respondents did not participate in the 2012 survey (the reanalysis uses the income and schooling level reported in the 2012 survey, so the reanalysis can only include respondents that participated in the 2012 survey)
1,371 respondents did not have the Armed Services Vocational Aptitude Battery (ASVAB) Math and Verbal combined score percentile
67 respondents did not report highest grade completed
36 respondents did not report race/ethnicity
128 respondents who were active duty military (excluded from the participation and income regressions, which include (2012 employment status variable by week)
17 respondents had incomplete employment status for at least one week (excluded from the participation and income regressions)
759 respondents enrolled in college during 2012 (excluded from the participation and income regressions.
Whether or not excluding respondents with missing data results in any bias is not known because it is not clear how the various types of missing data result in systematic differences in the effect of IQ, schooling, and family history on earnings. Final respondent counts are as follows:
The schooling data includes 2,869 females and 2,798 males
The participation data includes 2,378 females and 2,385 males
The income data include 1,663 females and 1,886 males.
Exhibit K.2 includes detailed descriptions of the variables used in the EPA reanalysis and summarizes the differences between the reanalysis variables and the variables used in Salkever's (1995) analysis.
Exhibit K.2: Map Between Variables in Salkever (1995) Analysis and EPA's Reanalysis Estimates Using the 1997 NLSY Data
Salkever 1995 Variable
Updated Reanalysis Variable
Notes
Highest Grade
Highest Grade
The variable EPA used appears equivalent to what was used in Salkever's 1995 analysis. EPA used respondent's highest grade completed as of the date of the survey in 2013. The variable name is T8128900.
Participation
Participation (2012)

Log 1990 Earnings
Log 2012 earnings
The variables EPA used appear equivalent to what was used in Salkever's 1995 analysis. EPA used total income from wages and salary in the past year from the 2013 survey. The variable name is T8976700. If the value is positive, then the participation variable is 1; otherwise it is zero.
Family Income Unknown
Family Income Unknown

Family Income (in 1979) x 10[-3]
Family Income (in 1997) x 10[-3]
The variable EPA used appears equivalent to what was used in Salkever's 1995 analysis. EPA used variable R1302500,

Race/Ethnicity Variables:
   African American
   Hispanic
Race Variables:
   White (omitted from regressions)
   African American
   American Indian, Eskimo or Aleut
   Asian or Pacific Islander
   Other
Ethnicity Variable:
   Hispanic
   Non-Hispanic (omitted from
   regressions)
EPA used the more detailed race (R0538700) and ethnicity (R0538600) variables that were available in the 1997 data. They are not available in the 1979 data.
Binary Geographic:
   Urban
   Rural nonfarm
   Nonsouth

Binary Geographic:
   Urban
   Rural
   Nonsouth
EPA used variable R1217500 to define binary variables for urban and rural. Unknown is the omitted dummy variable in the regression. EPA used R1200300 to define the binary variable for nonsouth. These indicate the respondent's location in 1997.
Age (in 1987)
Age (on December 31, 2002)
The variable EPA used appears equivalent to what was used in Salkever's 1995 analysis. Variable R0538700 (age in 1981) plus 6.
IQ (AFQT)
IQ (ASVAB)
Estimated with variable R0538700, which indicates the ASVAB Math and Verbal combined score percentile. This was converted to IQ by assuming IQ is normally distributed with mean 100 and standard deviation 15. Salkever 1995 estimates IQ the same way, using the score percentile for the Armed Forces Qualification Test (AFQT).
Mother's Highest Grade
Father's Highest Grade
Mother's Highest Grade
Father's Highest Grade
The variable EPA used appears equivalent to what was used in Salkever's 1995 analysis. R1302500 is the variable for mothers and R1302400 is the variable for fathers.

Exhibit K.3 presents the estimated parameters from Salkever's 1995 model and the updated model using Salkever's approach and 1997 NLSY data (2012 earnings are used here). As noted above, there are differences in labor force participation rates. This difference explains why the participation effect parameters are larger for the EPA reanalysis estimates compared to Salkever's 1995 analysis. However, as the overall participation rate is lower for the EPA reanalysis estimates, the total effect on earnings ends up being similar in both analyses. The direct IQ effect on earnings is very similar for females comparing the original and updated analyses, but decreased for males. At the same time, for males, the schooling effect on earnings increased in the updated analysis compared to the original. This variation might be due to multicollinearity between schooling level and IQ. However, if schooling is picking up some of the effects of IQ on earnings or vice versa, the two effects appear to cancel each other out given that the total effects on earnings are very similar when comparing the original and updated analyses for both males and females.
Exhibit K.3: Parameters from Salkever 1995 and EPA's Reanalysis Estimate Using Salkever's Approach and 1997 NLSY Data
Parameter Name
Male
Female

Parameter Value
Standard Error
Parameter Value
Standard Error
Salkever (1995)
IQ Effect on Schooling
                                    0.1007
                                    0.0022
                                    0.1007
                                    0.0025
IQ Effect on Participation
                                    0.0016
                                 Not Presented
                                    0.0037
                                 Not Presented
Schooling Effect on Participation
                                    0.0035
                                 Not Presented
                                    0.0282
                                 Not Presented
Schooling Effect on Earnings
                                    0.0476
                                    0.0071
                                    0.0960
                                    0.0100
IQ Effect on Earnings
                                    0.0124
                                    0.0013
                                    0.0140
                                    0.0021
Total Effect on Earnings[1]
                                    1.931%
                                not applicable
                                    3.225%
                                not applicable
EPA Reanalysis Estimate using Salkever Approach and 1997 NLSY Data
IQ Effect on Schooling
                                    0.0811
                                    0.0031
                                    0.0916
                                    0.0034
IQ Effect on Participation
                                    0.0036
                                    0.0007
                                    0.0053
                                    0.0009
Schooling Effect on Participation
                                    0.0186
                                    0.0039
                                    0.0297
                                    0.0042
Schooling Effect on Earnings
                                    0.0818
                                    0.0088
                                    0.1089
                                    0.0092
IQ Effect on Earnings
                                    0.0052
                                    0.0016
                                    0.0120
                                    0.0018
Total Effect on Earnings[1]
                                    1.865%
                                not applicable
                                    3.397%
                                not applicable
1. Following Salkever (1995), the total effect on earnings is calculated as ((IQ Effect on Schooling)*(exp(Schooling Effect on Earnings)-1)+exp(IQ Effect on Earnings)-1)+(((IQ Effect on Schooling)*(Schooling Effect on Participation)+(IQ Effect on Participation))/(Labor Force Participation Rate)). The labor force participation rate was 79% for males and 70% for females for the EPA reanalysis. Labor force participation rates from Salkever (1995) were higher, 96% and 81% for males and females, respectively.
EPA used a bootstrap approach to estimate the model parameters and their underlying uncertainty. To implement this approach, EPA drew 10,000 random samples of observations from the schooling data sets (samples of 2,869 and 2,798 for females and males, respectively), using random sampling with replacement, and estimated the model parameters for each of the 10,000 replicates. Exhibit K.4 presents the mean, median, 5[th] and 95[th] percentiles for the resulting estimates. The range between the 5[th] and 95[th] percentiles represents the 95 percent confidence interval for the parameter.
Note that the value of an IQ point used in the benefits analysis relies on the bootstrap model mean parameter results shown in Exhibit K.4.
Exhibit K.4: EPA Reanalysis Mean, Median, 5th and 95th Percentile Parameter Estimates from Bootstrap Model
Parameter Name
Mean
Median
5[th] Percentile
95[th] Percentile
Males
IQ Effect on Schooling
                                    0.08125
                                    0.08119
                                    0.07512
                                    0.08761
IQ Effect on Participation
                                    0.00362
                                    0.00363
                                    0.00239
                                    0.00485
Schooling Effect on Participation
                                    0.01859
                                    0.01864
                                    0.01222
                                    0.02492
Schooling Effect on Earnings
                                    0.08168
                                    0.08181
                                    0.06752
                                    0.09577
IQ Effect on Earnings
                                    0.00529
                                    0.00528
                                    0.00266
                                    0.00801
Total Effect on Earnings
                                    1.871%
                                    1.867%
                                    1.571%
                                    2.184%
Females
IQ Effect on Schooling
                                    0.09170
                                    0.09164
                                    0.08398
                                    0.09965
IQ Effect on Participation
                                    0.00529
                                    0.00528
                                    0.00380
                                    0.00680
Schooling Effect on Participation
                                    0.02983
                                    0.02981
                                    0.02296
                                    0.03688
Schooling Effect on Earnings
                                    0.10899
                                    0.10896
                                    0.09484
                                    0.12326
IQ Effect on Earnings
                                    0.01198
                                    0.01193
                                    0.00900
                                    0.01516
Total Effect on Earnings
                                    3.409%
                                    3.402%
                                    3.010%
                                    3.820%
1. Following Salkever (1995), the total effect on earnings is calculated as ((IQ Effect on Schooling)*(exp(Schooling Effect on Earnings)-1)+exp(IQ Effect on Earnings)-1)+(((IQ Effect on Schooling)*(Schooling Effect on Participation)+(IQ Effect on Participation))/(Labor Force Participation Rate)). The labor force participation rate was 79% for males and 70% for females for the EPA reanalysis. Labor force participation rates from Salkever (1995) were higher, 96% and 81% for males and females respectively.
Critical Review of Salkever's Estimates
Salkever's estimates of the impacts of IQ decrements on future earnings are greater than those of other authors, which has led to claims that they overstate the true impacts. Most notably, Grosse (2007) and Robinson (2013) present critical reviews of Salkever's estimates. Their concerns fall into two categories:
 Measurement and statistical issues, and
 Comparability of earnings impact results with recent findings in the labor economics literature.
Salkever (2014) addresses the concerns of Grosse (2007) and Robinson (2013) by providing a meta-analysis of related studies. Salkever (2014) provides convincing evidence in support of his original estimates. For example, the author found that many of the studies only included males and/or considered hourly wages instead of annual earnings with a participation effect. Because impacts are lower for males (Salkever 2014), Salkever indicates that results from studies that only consider the impact of IQ decrements on male wages will be biased downward. In reference to the latter observation, Salkever (2014) concludes that studies examining impacts on hourly wages omit the impact that IQ decrements have on workforce participation, again biasing the results downward. In fact, Salkever (1995) is the only analysis that separately estimates the IQ effect derived from average annual earnings and the participation effect for both males and females. For a full discussion of Salkever's response to critical review articles see Salkever (2014).
Method for Estimating Lifetime Earnings Stream
This section describes the methods used to estimate the average present value of the earnings stream of the affected birth cohort from age 16 to age 80. The universe of individuals from which annual earnings and enrollment are estimated includes the civilian population only, excluding individuals living in institutional and non-institutional group quarters and unpaid workers. Estimates are presented in 2016 dollars and are discounted using both a rate of 3 percent and of 7 percent.
Section K.8.1 describes the method used to estimate the distribution of educational attainment associated with each age in the age profile. Section K.8.2 describes the method used to estimate the annual earnings associated with each level of educational attainment for each age in the age profile. Section K.8.3 describes the life tables used in the lifetime earnings estimation and the derivation of male-female population ratios from the life tables. Section K.8.4 summarizes the lifetime earnings estimates. Section K.9 describes the effect changes in IQ have on lifetime earnings. Section K.10 presents a discussion of the limitations of this method.
Educational Attainment
Increases in educational attainment also increase education costs and diminish short-term earnings by reducing hours worked while in school. To accurately portray the benefits of a population with a higher average IQ, the average value of an IQ point must include an offset to reflect the cost of additional education and the opportunity cost of foregone income while in school. EPA used two methods to estimate the distribution of educational attainment over the age profile of the target birth cohort. One method is to estimate primary and secondary school attainment, with the exception of grade 12; and a second method is to estimate postsecondary school attainment. The first subsection below describes primary and secondary school attainment, and the second subsection describes postsecondary school attainment.
Primary and Secondary School Attainment
Primary and secondary school attainment is estimated for ages 1 to 19 by estimating the average proportion of the population that has completed grades 1 to 11 for each age. Primary and secondary school attainment is estimated for ages 20 and older by estimating the average proportion of 20 to 25 year olds that have completed grades 1 to 11. ACS single-year PUMS from 2008 to 2017 are used to produce ten-year average primary and secondary school attainment estimates (U.S. Census Bureau 2017c).
Postsecondary School Attainment
Postsecondary educational attainment is estimated first by determining the age-sex distribution of degrees conferred and then by applying this distribution to the total number of degrees conferred. The age-sex distribution of enrollment in college and graduate school is used as a proxy for the age-sex distribution of degrees conferred. Lag times are used to stagger enrollment because of the length of time it takes to earn a degree. A lag time of one year is assigned to Associate's and Master's degrees, two years to Bachelor's degrees, and three years to doctoral degrees. For example, if 20 percent of males enrolled as undergraduates in college are 20 years old then it is assumed that 20 percent of Bachelor's degrees are awarded to 22 year old males.
The proportion of an age group receiving a degree is then calculated by dividing the number of degrees awarded at a particular age by the total number of people of the same age. To account for individuals receiving successive degrees from postsecondary institutions the proportion of individuals with a bachelor's degree that previously received an associate's degree (21 percent) is subtracted from the proportion of individuals with an associate's degree (U.S. Department of Education 2009); the proportion of individuals receiving a master's degree or receiving a doctoral degree without previously receiving a master's degree (25 percent; U.S. Department of Education, 2003) is subtracted from the proportion of individuals receiving a Bachelor's degree; and the proportion of individuals receiving a doctoral degree that previously received a Master's degree is subtracted from the proportion of individuals with a Master's degree (75 percent; U.S. Department of Education, 2003).,  The cumulative proportion of degrees conferred at a particular age represents the proportion of the population for whom the corresponding degree is the highest level of education attained.
Enrollment statistics are estimated from 2008 to 2017 using ACS single-year PUMS data. Data describing Associate's, Bachelor's, Master's, and doctoral degrees conferred are taken from the 2016 Digest of Education Statistics, published by the National Center for Education Statistics (NCES) (Snyder and Dillow, 2018). Data describing degrees conferred in the years 2016 and 2017 are projected by the NCES.
Average Annual Earnings
Annual earnings for males and females are estimated from ACS single-year PUMS for each of the levels of educational attainment previously described for ages ranging from 16 to 80, for each year from 2008 to 2017. Average annual earnings for males and females are equal to the sum of annual earnings associated with each level of educational attainment weighted by the distribution of educational attainment for each year in the age profile of the target birth cohort. Earnings consist of pre-tax wages and salary.
Topcodes
For confidentiality reasons, the Census Bureau topcodes reported income components if it falls below or above a predetermined threshold before making the data publicly available. Amounts above or below the threshold are replaced with the state mean value above or below the threshold (U.S. Census Bureau, 2013).
Real Earnings Growth Rate
Real earnings fluctuate from one year to the next in response to trends in the economy-wide productivity growth rate (Thornton et al., 1997). An annual growth rate of 1 percent is incorporated into the annual earnings estimates. Grosse et al. (2002) and Schwartz (1994) calculate lifetime earnings using a 1 percent growth rate in similar analyses. This rate is also consistent with long term historical averages; for example, the average percent change in real annual earnings from the year 1967 to 2016 as derived from Historical Income Tables published by the U.S. Census Bureau (U.S. Census Bureau, 2017).
Life Tables
Life tables present the survival rate or the probability that an individual will survive from age N to age N+1 (e.g. a 60 year old living to 61). Because some individuals die before retirement, the survival rate represents the probability of receiving earnings each year. As an individual ages, the probability declines. Future birth cohorts are expected to live longer, increasing the probability of living to age N+1, thereby increasing the average lifetime earnings for the cohort.
This analysis relies on the Life tables underlying the SSA Trustees' 2015 annual report, which are published on the website of Value Economics LLC (SSA, 2015). The SSA develops projected life tables for future birth cohorts. In this analysis, the life tables associated with the 2015 birth cohort are incorporated to represent a recent cohort.
Present Value of Lifetime Earnings
Age-earnings profiles are estimated for the years 2008 through 2017. Average earnings are calculated for each year, Step 1, and then the ten averages are averaged to produce the grand mean earnings estimates presented in this report, Step 2:
Step 1
      NPVyr=∑N=380[ YNPNRN1+XN-A+0.51+rN-A+1 ]
where:
NPV = the net present value of earnings between ages A and 80;
yr= survey year from 2008 to 2017
A = current age, which is 3 in this analysis;
N = ages in the future (3, ..., 80);
Y = average annual earnings among earners for a particular age (N);
P = survival rate for a particular age (N);
R = percent of population with earnings;
X = productivity rate assumed at the midpoint of age N; and
r = discount rate for the beginning of age N.
Step 2
      NPVaverage=110∑yr=20082017 NPVyr
where:
NPV = the net present value of earnings between ages A and 80; and
yr = survey year;
Lifetime earnings are discounted at both 3 percent and 7 percent, and the model assumes that real earnings will increase by 1 percent per year. Earnings are assumed to be zero for individuals under the age of 16 and over the age of 80. Exhibit K.5 presents average lifetime earnings for males and females from 2006 to 2017.

Exhibit K.5: Lifetime Earnings (2016$)
Earnings Group
3% Discount Rate
7% Discount Rate
Male
$1,046,830
$239,634
Female
$680,742
$160,844

Effects on Earnings from Changes in IQ
The value of an IQ point is estimated by considering the direct and indirect effects of changes in IQ on earnings, as well as the costs associated with additional years of education. The cost of additional education is comprised of the direct cost of education and forgone earnings while in school.
Section K.9.1 describes the parameter used to estimate the total value of an IQ point, Section K.9.2 describes the methods used to estimate the components of costs associated with additional education, and Section K.9.3 presents the estimate for the net value of an IQ point.
Total Value of an IQ Point
EPA's updated analysis based on Salkever (1995) yields a value of an IQ point equal to 1.865 percent and 3.397 percent of earnings for males and females, respectively. The average value of an IQ point is $23,269 and $5,398 discounted at a rate of 3 percent and 7 percent, respectively.
Additional Education: Costs and Lost Earnings
The effect of lead exposure on schooling is estimated to be 0.0811 years per IQ point for males and 0.0916 years per IQ point for females in EPA's reanalysis of Salkever (1995). Increases in educational attainment signify analogous increases in education costs and diminished earnings resulting from working fewer hours while in school. To accurately portray the benefits of a population with a higher average IQ, the average value of an IQ point is adjusted to reflect the cost of additional education and the opportunity cost of being in school.
ACS PUMS data on enrollment were used to estimate both: (1) the ages at which the marginal increases in educational attainment due to higher IQ would be realized, and (2) the levels of additional educational attainment that would be achieved.
The distribution of ages at which the last year of education was obtained was estimated based on changes in the percentages of the population enrolled in school by age. For example, if 95 percent of 16 year olds are enrolled in school and 90 percent of 17 year olds are enrolled in school, it was estimated that 5 percent (95 percent minus 90 percent) of the population attained their last year of education at age 16. Thus, the analysis assumes that for 5 percent of the population, the marginal increase in educational attainment would be realized at age 17  -  one year after they achieved their highest level of education in the baseline.
The level of additional education attained is estimated based on the enrollment for the ages at which the additional education is realized. For example, if 30 percent of enrolled 18 year olds are enrolled in 12th grade and 70 percent of enrolled 18 year olds are enrolled in university, the analysis estimates that additional education attained at age 18 is 30 percent 12th grade and 70 percent university.
Education Costs
Education costs associated with pursuing additional education are determined by the level of education being pursued. Three categories of education are considered in estimating costs:
Public elementary and secondary schools (expenditures per pupil enrolled);
Average undergraduate tuition (including fees, room, and board); and
Average graduate tuition (including required fees).
Data describing the cost of education are taken from the 2016 version of the Digest of Education Statistics (Snyder and Dillow 2018-).
For each age in the age profile an individual has a likelihood of pursuing additional education in one of the three categories listed above, and therefore of incurring corresponding education costs. Enrollment is used to determine each category's relative likelihood thereby allowing costs to be apportioned appropriately with respect to each age in the age profile. For example, at age 17, most individuals will be enrolled in secondary schools causing the cost of education to primarily reflect the costs associated with the first category of education.
The total cost of education for the target cohort is estimated by calculating the sum of education costs corresponding to each level of attainment, weighted by enrollment and the probability of pursuing additional education at age N. For example, suppose that 100 percent of the target cohort's females attain additional education at age 18 or age 19. Twenty-five percent of the target cohort females attain additional education at age 18 and 75 percent of the target cohort females attain additional education at age 19. At age 18, 30 percent of the target cohort currently enrolled in school is enrolled in 12th grade and 70 percent is enrolled in an undergraduate university. At age 19, 10 percent of the target cohort females currently enrolled in school are enrolled in 12th grade and 90 percent are enrolled in an undergraduate university. The annual cost of a secondary school and an undergraduate university is $12,000 and $20,000, respectively. As shown in Exhibit K.6, the weighted cost of education per IQ point (assuming 0.0916 additional years of education) for the target cohort females is $1,722, $403 and $1,319 for 18 and 19 year olds, respectively.
Exhibit K.6: Example of Education Cost Calculation

Enrollment
Annual Cost of Ed.

Age
12th Grade
a
University
b
12th Grade
c
University
d
Additional Ed. Weight
e
Weighted Costs
f=((a∙c)+(b∙d))∙e
Cost per IQ Point
f ∙.0916
18
30%
70%
$12,000
$20,000
25%
$4,400
$403
19
10%
90%
$12,000
$20,000
75%
$14,400
$1,319
 Total

$18,800
$1,722

Lost Earnings
Lost earnings are calculated by separately estimating annual earnings for individuals enrolled in school and not enrolled in school and taking the difference of the two estimates. The difference in earnings is assumed to be zero for a given age and sex combination if enrolled and/or not enrolled earnings estimates rely on fewer than 150 observations. As with education costs, the differences in annual earnings are weighted by the probability that an individual will pursue additional education at their current age, N, as described at the beginning of this section. Lost earnings associated with an additional IQ point are generated by applying EPA's IQ effect on schooling to the difference in annual earnings between the enrolled and not enrolled populations.
Summary of Additional Education Costs
The average estimated costs for additional education (tuition plus lost earnings) are $1,592 and $691, discounted at a rate of 3 percent and 7 percent, respectively.
Net Value of an IQ Point
The net value of an IQ point is equal to the total value minus the costs of attaining additional education. The estimates presented in Exhibit K.7 are averages produced from ten years of ACS single-year PUMS covering the years 2008 through 2017. The overall estimate for males and females combined is estimated assuming a population that is 52 percent male based on the male:female ratio of births (CDC, 2017).
Exhibit K.7: Effects of a One Point Change in IQ on Earnings (2016$)
Estimate Parameter
3% Discount Rate
7% Discount Rate

Male
Female
Overall
Male
Female
Overall
1. IQ Value
$19,591
$23,206
$21,326
$4,484
$5,488
$4,966
2. Additional education costs
$992
$1,123
$1,055
$463
$513
$487
3. Forgone earnings
$332
$250
$278
$149
$98
$124
4. Additional education costs and forgone earnings [2 + 3]
$1,324
$1,343
$1,333
$612
$611
$611
5. IQ value without education costs and lost earnings [1  -  4]
$18,267
$21,862
$19,993
$3,873
$4,877
$4,355

Limitations
Nonmarket Work
The use of earnings is an incomplete measure of an individual's value to society. This is particularly true for individuals who choose to not participate in the labor force for all of their working years. If the opportunity cost of non-wage compensated work is assumed to be the average wage earned by persons of the same sex, age, and education, the average lifetime earnings estimates for these people would be significantly higher.
Multiple Degrees
Individuals receiving a second degree within the same attainment group later in life are not taken into account. For example, a second Master's degree is treated as two individuals with a Master's degree. This would increase the proportion of individuals with degrees from postsecondary schooling institutions. Given that a minority of individuals would fall into this attainment category, the lifetime earnings estimate is not expected to be substantially impacted.
Earnings Growth Rate
The earnings growth rate for females is substantially higher than the rate for males. A portion of the difference is likely due to females approaching equal pay to males over time. However, a portion of the difference is likely an artifact of rising female labor force participation, hours worked per year, and educational attainment. These trends have tapered off overtime and in all likelihood will continue to do so. Therefore, the average growth rate of real wages for the 2017 birth cohort may be closer to the earnings growth rate for males compared to older cohorts.
Income vs. Earnings
Although earnings is a significant component of income for the middle quintiles of the distribution of income, Barth et al. (1984) indicates that income may be substantially different from earnings for the tails of the income distribution. Therefore, earnings are assumed to be a good proxy for income in accordance with Salkever (1995).
Benefits
Because benefits have become a greater portion of income, their exclusion could result in lifetime earnings to be underestimated.
Impact of Ability on Earnings
Barth et al. (1984) found that many studies concluded that the impact of ability on earnings increases with age. Therefore, estimates of the impact of IQ on earnings derived from younger individuals may be smaller than if estimates were derived from individuals over the age of 30 (Barth et al. 1984). The EPA reanalysis of Salkever (1995) relies on data where respondents range in age from 27 to 32. Thus, the estimate of the impact of IQ on earnings may underestimate the true impact of ability on earnings.
References
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