2.1. Survey design

We investigate the relative value of fatality risks from heat, cancer, and traffic accidents using the results from a questionnaire with randomized elements, which we administered to the Prolific web-based panel of respondents.Footnote ² Two-thirds of our sample was drawn to be nationally representative based on age, gender, and race, and the remaining third was drawn exclusively from senior citizens. The first series of questions engaged respondents to contemplate the types of risks that would be addressed by asking respondents about their personal experiences with, and their perceived own fatality risks from, extreme heat, cancer, and traffic injuries. The next six questions asked subjects to choose between two policies which decreased fatalities, including an initial attention check question involving a dominated choice. Six additional policy questions followed the initial six questions, with the latter set randomly varying whether the policies that subjects considered decreased fatality risks among the general population or senior citizens. Finally, the survey asked subjects a set of demographic and behavioral questions.

The survey instrument randomized subjects along two primary dimensions. First, the survey sorted subjects into either the cancer or traffic groups. Subjects in the cancer group answered policy questions concerning heat and cancer fatality risks, while subjects in the traffic group answered policy questions concerning heat and traffic fatality risks. Subjects in the cancer group never chose between heat and traffic policies, and the traffic group similarly never compared heat and cancer policies. Assigning subjects to a particular risk should reduce the cognitive burden of the questionnaire relative to evaluating three risks at once. Next, for each of the final six policy questions, the survey randomly assigned one of the two policies to affect seniors and the other policy to affect members of the general population, as discussed in more detail below.

The questionnaire began with two questions assessing respondents’ personal experience with the risks which they would compare. These questions acclimate subjects to the survey context, establish definitions for the types of risks that they would be asked to evaluate, and determine their experience with each cause of risk and their self-perceived risk beliefs for these risks. All subjects answered questions about extreme heat and their assigned secondary risk, in a randomized order. None of the questions indicated that global warming was the cause of the heat risks to avoid having the survey questions become a referendum on support for climate change policies. The two introductory questions defined the relevant risks and described the nature of the fatality event. The details regarding the health implications serve to standardize respondents’ conception of the heat-related impacts that they value. For example, regarding heat, the survey asked subjects:

• ○ Yes

• ○ No

  Compared to the average person, how would you rate your risk of dying due to extreme heat?

• ○ I have an above-average risk of dying due to extreme heat.

• ○ I have an average risk of dying due to extreme heat.

• ○ I have a below-average risk of dying due to extreme heat.

Once subjects completed the risk assessment questions, the survey presented a series of twelve questions to choose between two different policies that affected heat fatality risks and the other risk to which they were randomly assigned. Each policy would provide hospitals with a grant, improving those hospitals’ treatment of individuals suffering from the identified risks. The questionnaire specified that the grant would be provided to an unspecified set of hospitals, rather than any particular hospital or a hospital near where the respondent lived, to prevent subjects from rejecting the questions if they live in areas where the specific type of death is too rare for the question to be plausible. Contextualizing the policies as providing grants to hospitals enforces symmetry in terms of the context in which lives are saved for the different health risks and provides subjects with a common understanding of the mechanism by which the policies reduce fatalities. However, subjects’ responses may not reflect their preferences for valuations of mortality or morbidity effects outside of the hospital context, such as when fatalities are prevented via ex ante risk reduction rather than improved treatments. For such a conclusion to be warranted, the relative valuations of the health impacts outside of the hospital setting must be consistent with the risk-risk tradeoffs for patients treated in hospitals. The risks that our subjects considered are public risks, corresponding to the desire to identify whether a valuation premium exists for the purposes of regulatory benefit-cost analyses. The questions accordingly elicited social ex ante regulatory preferences, with some questions including groups to which subjects belonged. (Dolan et al., Reference Dolan, Olsen, Menzel and Richardson2003).

All twelve policy questions had the same basic format, spaced into three blocks of questions. Each block of questions began by presenting subjects with a vignette explaining that they would be asked to express a choice between one of two policies. The three blocks included an initial introductory question and an attention check question, a block of five basic policy questions, and a block of six questions randomly varying the population policies targeted. The description of each of the policies varied to reflect the context. Example text from the vignette that preceded the second block is below:

After the vignette, which appeared on a new screen, the survey provided subjects with different policies and asked them to vote. Subjects could choose to vote for either Policy 1, Policy 2, or state that both policies were equally good. Each voting question included an easily reviewable table identifying the effects of each policy. An example that immediately followed the preceding vignette is below:

• ○ 20 fewer heat deaths

• ○ 20 fewer traffic deaths

• ○ Both equally good

The first question in the policy comparison set introduced respondents to the survey format and served as an attention check. Subjects were randomly assigned to consider either two policies that would reduce extreme heat risks or two policies that would reduce cancer or traffic risks, consistent with subjects’ group assignment. The risk presented in the introductory question was randomized to avoid any bias arising from subjects inferring that the study’s primary interest was heat risks. Under the first policy, fatalities would decrease by 20 while the second policy would decrease fatalities by 50. Policy 2 strictly dominated Policy 1, which should lead all rational subjects that understand the question to choose Policy 2. If subjects voted for Policy 1 or stated that both policies were equally good, they were asked to reconsider, for example, as follows: “You chose Policy 1. Under Policy 1, 20 deaths from extreme heat are prevented. Under Policy 2, 50 deaths from extreme heat are prevented.” The survey then presented another table analogous to the one above, and asked, for example, “Are you sure that you prefer Policy 1?” Respondents that answered correctly initially or upon reconsideration are retained in the analyses, while respondents that confirmed their initially dominated answer are excluded.Footnote ³

The next five policy questions directly asked subjects to choose between policies that would decrease heat fatalities and either cancer or traffic fatalities by 20, 30, or 50 deaths, as in the example question above. Respondents considered a series of five different tradeoff combinations: (20, 20), (20, 30), (30, 20), (50, 20), and (20, 50). The fatality values permit the questionnaire to identify relative mortality risk valuations ranging from 0.4 to 2.5, covering a wide range of premia that include the tradeoff rates in Alberini and Šcasný (Reference Alberini and Šcasný2024) and Chilton et al. (Reference Chilton, Duxbury, Mussio, Nielsen and Sharma2024). Further, the relative ratios of the risks are similar to those used in prior risk-risk studies and are analogous to the risk magnitudes used in dichotomous choice studies to measure subjects’ willingness to pay for heat-related mortality risks (Alberini, Reference Alberini2005; Chilton et al., Reference Chilton, Duxbury, Mussio, Nielsen and Sharma2024). By comparing two different types of fatal risks, the survey captures respondent preferences associated with both the mortality and morbidity components of the different causes of death.

The five isolated heat tradeoff questions provide the data for our core findings regarding the relative value of heat fatalities and also provide a transitivity check for respondents. For example, if a rational subject voted to reduce heat fatalities when the tradeoff was 20 heat fatalities and 20 cancer fatalities, the same subject should prefer to reduce heat fatalities when the tradeoff is 30 or 50 heat fatalities and 20 cancer fatalities. We exclude respondents who violate transitivity from the following main analysis.Footnote ⁴

The next six questions asked subjects to choose between policies that would decrease fatalities, with the added dimension that each question randomly assigned the heat or secondary risk to reduce senior citizen fatalities, while the comparison risk reduced fatalities among the general population. The survey’s stated justification for the policy to exclusively benefit senior citizens was that one of the two grants must be used to treat patients on Medicare. The first of the six questions in this set asked respondents to compare two policies that both reduced fatalities from heat, but one policy targeted senior citizens, while the other targeted members of the general population. The remaining five questions resembled the prior policy questions, in that one policy targeted heat risks, while the other targeted cancer or traffic risks. The introductory text to the second block of policy questions is as follows:

The text of the question that followed the preceding vignette is as follows:

• ○ 20 fewer heat deaths

• ○ 20 fewer traffic deaths

• ○ Both equally good

Finally, the survey concluded by asking subjects a series of demographic and behavioral questions. The demographic questions included questions about respondents’ age, gender, race, education, income, marital status, whether they have minor children, and the zip code in which they live. Subjects’ zip codes provided the basis for determining the historical average high temperatures and the high temperatures during the week we fielded out survey in the area where subjects live. Data on daily high temperatures are from the Daily Global Historical Climatology Network. We match subjects to the nearest weather station in the Network to determine the high temperatures subjects faced. The behavioral questions elicited information that could be relevant to how respondents think about heat risks, including who they voted for in 2020, whether they have air conditioning in their home, whether they received a COVID-19 vaccine, whether they are smokers, whether they always or almost always wear a seatbelt, and whether they regularly engage in outdoor work or recreation. The survey concluded by asking subjects whether they found the questions in the survey clear or confusing.Footnote ⁵

2.2. Sample

After a series of pretests, the Prolific platform administered the survey to its panel of respondents. Prolific actively maintains a pool of more than 85,000 active U.S.-based survey respondents (as of July 2024), where membership in the panel excludes participants with low-quality responses. Prior research has found that Prolific respondents perform better than respondents from other platforms and panels, such as Amazon’s Mechanical Turk or Dynata (Peer et al., Reference Peer, Rothschild, Gordon, Evernden and Damer2022). The full sample consisted of 1,170 respondents. The sample that we used decreased to 1,048 respondents after excluding the 122 respondents who failed the attention and transitivity checks discussed in Section 2.2, or who chose the same answer in response to all policy choice questions (e.g., choosing “both equally good” for all 11 questions after the attention check).Footnote ⁶

We fielded the survey to two different samples: a general sample representative of the United States population along gender, race and ethnicity, and age dimensions, and a smaller sample of respondents of senior citizens whose age was 65 or greater. As discussed previously, heat presents a more serious risk for older adults, as measured in U.S. government heat death statistics. Heat may therefore be a more salient risk for senior respondents. Oversampling senior citizens permits us to explore how salience and personal exposure to the risk influences subjects’ preferences. To be sure, other risks, including mortality risks from extreme cold, are likely also more salient to seniors than other populations.Footnote ⁷ However, it seems unlikely that one category of salient risks for seniors should crowd out other salient risks, particularly given that senior citizens are a population who experience larger fatality risks from many causes. As a result, we expect that if heat is a salient risk to any particular group, it may be to seniors.

The sample includes a diverse set of respondents that parallel the U.S. population, conditional on the intentional oversampling of senior citizens. Female respondents, respondents who have a bachelor’s degree or higher, and respondents that voted for Joe Biden or voted at all in 2020 are somewhat overrepresented relative to the U.S. population. As described in the next subsection, most individual characteristics do not enter the model explicitly because of the panel structure of the data and the structure of the conditional logit model. The full set of summary statistics is provided in Table A1 in the Online Appendix.

Respondents took the questionnaire during the week of June 18, 2024. During that week, abnormally high temperatures affected much of the United States. Buffalo, New York, for example, had daytime high temperatures that were higher than Austin, Texas on June 19, 2024. The sharp increase in temperatures that week serves as an exogenous shock that enables identification of how subjects’ preferences over extreme heat risks vary with unexpected increases in the outdoor temperature. It also had the benefit of increasing the salience of the risks the survey explored, increasing the likelihood that respondents provided authentic preferences. To be sure, fielding the survey during a heat wave could have inflated subjects’ preferences to reduce heat risks rather than other mortality risks. If subjects’ valuations of heat risks are at their highest point during a heat wave, this situation should provide a favorable context for whether U.S. respondents place a valuation premium on mortality risk reductions from heat, as compared to mortality risks from transportation or cancer.

2.3. Random utility model

The stated preference survey design provides data to estimate a random utility model. Other papers in the literature analyzing risk-risk tradeoffs frequently rely on similar models (e.g., Viscusi, Reference Viscusi2009; Dalafave & Viscusi, Reference Dalafave and Viscusi2021). The survey presents respondents with a series of discrete policy choices involving the number of heat deaths prevented and either the number of cancer or traffic deaths prevented. The stated preferences from these choices can be used in a random utility framework to analyze subjects’ utility tradeoffs between the relevant fatality risks.

Consider a representative individual with preferences over mortality risks from different causes.Footnote ⁸ For any policy $ i $ , individual preferences correspond to a utility function that varies with mortality risk reductions and individual characteristics, and includes a random component. Let $ {h}_i $ represent the reduction in heat deaths, $ {c}_i $ represent the reduction in cancer deaths, and $ {t}_i $ represent the reduction in traffic deaths from policy $ i $ . Let the vector $ {x}_n $ represent an individual’s demographic characteristics and let $ {\epsilon}_{ni} $ be the random component of utility for individual $ n $ from policy $ i $ . Then an individual’s utility function for a given policy can be expressed as follows:

(1) $$ {u}_{ni}=\alpha {h}_i+\beta {c}_i+\gamma {t}_i+\delta {x}_n+{\epsilon}_{ni}. $$

The absolute value of utility $ {u}_{ni} $ is not of primary interest, as utility levels are unique only up to a positive linear transformation, but the marginal rate of substitution between the different risk categories is. Totally differentiating $ {u}_{ni} $ along the policy dimensions yields:

(2) $$ 0=\alpha \mathrm{dh}+\beta \mathrm{dc}+\gamma \mathrm{dt}. $$

The marginal rate of substitution between heat fatalities and cancer fatalities is accordingly $ -\alpha /\beta $ , while the marginal rate of substitution between heat and traffic fatalities is $ -\alpha /\gamma $ . If, for example, $ -\alpha /\beta =2 $ , respondents would be indifferent between a policy that reduced their heat fatality risk by 2/1,000 and cancer fatalities by 1/1,000. It follows that if respondents would be willing to pay $10,000 to decrease their cancer fatality risk by 1/1,000, they would be willing to pay $20,000 to decrease their heat fatality risk by 1/1,000, assuming that relevant income effects are sufficiently small. The marginal rate of substitution consequently provides the value of heat fatalities relative to cancer or traffic fatalities.

To recover the marginal rates of substitution of interest, we exploit the fact that individuals vote for the policy that yields greater utility when asked to choose between multiple policies. Symbolically, from equation 1, an individual chooses policy $ j $ over policy $ i $ if:

(3) $$ {u}_{nj}>{u}_{ni}\iff \alpha \left({h}_j-{h}_i\right)+\beta \left({c}_j-{c}_i\right)+\gamma \left({t}_j-{t}_i\right)+{\epsilon}_{nj}-{\epsilon}_{ni}>0. $$

Because individual characteristics $ {x}_n $ are common to all policy options, they are not included in the basic model.Footnote ⁹ In the survey, policies affect reductions from only a single fatality type, and subjects compare heat and only one of the two alternatives. For ease of exposition, assume that policy $ i $ affects heat, policy $ j $ affects cancer, and policy $ k $ affects traffic. Then Equation 2 simplifies to the following two possible comparisons:

(3a) $$ {u}_{nj}>{u}_{ni}\iff -\alpha {h}_i+\beta {c}_j+{\epsilon}_{nj}-{\epsilon}_{ni}>0, $$

and

(3b) $$ {u}_{nk}>{u}_{ni}\iff -\alpha {h}_i+\gamma {t}_k+{\epsilon}_{nk}-{\epsilon}_{ni}>0. $$

The probability $ {p}_{nji} $ or $ {p}_{nki} $ that an individual prefers policy $ i $ to policy $ j $ or $ k $ for any policy comparison is correspondingly:

(4a) $$ {p}_{nji}=\mathrm{P}\mathrm{r}\mathrm{o}\mathrm{b}(-\alpha {h}_i+\beta {c}_j+{\epsilon}_{nj}-{\epsilon}_{ni}>0), $$

and

(4b) $$ {p}_{nk i}=\mathrm{Prob}\left(-\alpha {h}_i+\gamma {t}_k+{\epsilon}_{nk}-{\epsilon}_{ni}>0\right). $$

The regression analysis presents estimates of equations 4a and 4b using a conditional logit model. The model simultaneously estimates equations 4a, 4b, and an equation corresponding to indifference between the two policy options.Footnote ¹⁰ Simultaneously estimating the two equations of interest and the equation corresponding to indifference between the two options maximizes the precision of our estimates. The results for the “both equally good” choice regressions are reported in the Online Appendix, but are not a focus in the main results reported in the analysis. The observations in the regression are each policy choice that subjects considered (the policy reducing heat deaths, the policy reducing other deaths, and expressing that both policies were equally good). The panel model accounts for using multiple observations per individual by clustering the estimated standard errors by individual respondent.

The output of the conditional logit model enables identification of how the subjects value heat mortality risks relative to cancer and traffic risks. The coefficients in the model provide the marginal utility of choosing one policy alternative relative to the marginal utility of choosing another. The marginal utilities are of directional interest as they demonstrate whether respondents are responding rationally to the survey instrument, but their magnitudes are not meaningful in isolation. The ratio of the coefficients within an equation, however, provide marginal rates of substitution between different sources of utility (McFadden & Train, Reference McFadden and Train2000), such as the mortality risks in the model. The ratios of the coefficients for the magnitude of fatalities averted accordingly provide the relative valuations of heat fatalities to cancer and traffic fatalities.

Beyond the basic model in equations 1–4, we make several additional refinements to the analysis. At various points, we relax the implicit assumption that the parameters $ \alpha $ , $ \beta $ , and $ \gamma $ are comparable across groups of respondents and separately estimate equations 4a and 4b for members of the samples who are older or younger than 65, who live in higher temperature areas, or who experienced higher heat shocks during the heat wave. We also investigate whether individual characteristics such as respondents’ beliefs about their own risk of suffering from heat affect their relative valuation of heat fatalities by including interactive effects in the regression model. Such refinements add additional terms to the equations above but do not alter the fundamental structure of the model. And in the Online Appendix, we report results that relax the assumption that utility is linear in risk levels.Footnote ¹¹

In sum, the experimental questionnaire is calibrated to produce results that are likely to demonstrate subjects’ authentic preferences regarding heat-related mortality risks.Footnote ¹² The instrument includes several rationality checks, which respondents overwhelmingly passed. The tabulations of subjects’ responses demonstrate that they pass scope tests, which the analyses in Part III further illustrate.Footnote ¹³ And most importantly, the structure and timing of the survey experimentally randomize our subjects into groups to test our major hypotheses: whether subjects have a heat valuation premium, whether exogenous heat shocks affect heat mortality valuation, and whether subjects differentially value risks to senior citizens.