Abstract
This study analyzes survey data of U.S. East Coast homeowners to characterize accuracy and determinants of homeowner flood risk (mis)perceptions. Using an array of instruments, we assess subjective risk perceptions and compare them with objective risk estimates. Reduced-form regressions suggest flood experience, worry, and flood zone classification influence relative perceptions of risk. Common probability weighting functions do not fit the divergence in risk perceptions, suggesting that the source of the probability distortions is most likely due to misperceiving the true risk rather than a widespread behavioral heuristic.
1. Introduction
Understanding the motivations behind individual decisions to manage natural hazard risks is becoming increasingly relevant, as the social and economic costs of extreme weather events have been increasing for decades (NOAA 2020a). Increased development in hazard-prone areas is partly to blame for rising costs (Kunreuther and Michel-Kerjan 2007), but the increased frequency of global catastrophic events cannot be ignored as a contributing factor (Kousky 2014; Gaiha et al. 2015; Boustan et al. 2019). By far, the costliest of these hazards are tropical cyclones and associated flooding. For homeowners in the United States, flood insurance is a primary tool for limiting fiscal impacts from flooding. Yet only about 30% of U.S. households in Federal Emergency Management Agency (FEMA)–designated special flood hazard areas (SFHAs) have a flood insurance policy (Kousky et al. 2018). Several explanations for this have been proposed, including moral hazard (Kousky, Michel-Kerjan, and Raschky 2018; Landry, Turner, and Petrolia 2021), affordability of premiums (Kousky and Kunreuther 2014; Netusil et al. 2021), and the cognitive burden and hassle of obtaining additional insurance (Landry et al. 2021).
Another explanation that has received limited empirical attention is the possibility of misperceptions of personal flood risk. If individuals perceive the likelihood of flooding or the associated damages to be low relative to the objective risk, they may forgo investing in flood mitigation strategies based on incorrect beliefs. From a policy perspective, this is particularly noteworthy; if misperceptions are driving flood mitigation behavior, the accuracy and interpretability of objective risk information available to flood-prone residents could influence personal mitigation and investment decisions (as well as support of public risk management projects).
This study assesses subjective perceptions of coastal hazards and compares them with objective measures. Using a novel survey dataset consisting of homeowners from three coastal counties in Georgia, North Carolina, and Maryland, we assess respondents’ perceived probability of their home flooding, the conditional expectation of damage, and the likelihood of a major hurricane strike; we compare these measures against objective estimates. We then analyze the role of observable characteristics on the accuracy and level of risk perceptions to establish potential determinants of risk misperceptions. To help differentiate between idiosyncratic probability misperceptions and systematic probability weighting,1 we estimate a series of structural regression models that attempt to map an individual’s unique objective flood probability to their reported subjective flood probability using six probability weighting functions that are common in the literature.
Concerning perceptions of general flood risk, we find that people do not exhibit any consistent tendencies regarding the probability of a flood; correct, optimistic, and pessimistic perceptions are all well represented in our sample. Regarding expected flood damage, almost all survey respondents overestimate the damage associated with a flood, regardless of the return period. When comparing perceived flood damages with floods of various inundation levels, we find the frequency of pessimistic and correct perceptions to be much more balanced. This suggests that individual overestimation of damage primarily stems from overestimating the water-inundation levels as opposed to misunderstanding the relationship between a fixed level of inundation and home damage. Notably, when an expected annual loss metric (flood probability × conditional expected damages) is assessed, most respondents have subjective perceptions within a small margin of error of objective risk metrics.
Our analysis of determinants of risk perceptions reveals that past flood experiences and levels of worry generally influence these perceptions. We find that objective risk metrics are correlated with perceived flood probabilities as are proxies for household income and wealth levels. Market financial factors, such as mortgage status, market value of the home, and median home value in the neighborhood, also influence flood and hurricane risk perceptions. Finally, the estimation of probability weighing parameters shows that the deviations between perceived and actual flood probabilities cannot be easily explained by probability weighting, suggesting that the observed deviations are due to idiosyncratic misperceptions of risk.
The results presented here contribute to the existing literature in several ways. First, our findings provide insight into the accuracy of risk perceptions with a novel dataset obtained from several locations along the U.S. East Coast. This is notable because there is a dearth of literature that quantifies risk perceptions and the deviations between perceived and objective coastal hazard risks. In addition, existing studies lack accord on the nature of risk misperceptions. The literature has so far found evidence of people overestimating the likelihood of flooding (Botzen, Kunreuther, and Michel-Kerjan 2015; Mol et al. 2020), underestimating the likelihood of flooding (Royal and Walls 2019; Bakkensen and Barrage 2022), underestimating flood water levels (Mol et al. 2020), underestimating expected damages (Botzen, Kunreuther, and Michel-Kerjan 2015), underestimating “flood risk exposure” (Royal and Walls 2019), and some evidence that damage expectations are generally correct (Mol et al. 2020). The variations in the findings likely reflect temporal, methodological, spatial, and institutional differences in each study, making it difficult to interpret or generalize the array of results.2 Thus, our results, representing several locations on the U.S. East Coast, help bring the literature closer to a consensus on the nature and determinants of individual perceptions of natural hazard risk.
Second, to our knowledge, we are the first to fit structural probability weighting functions to observational data in the domain of flood risk. This provides important insights for future policy discussions. As noted by Barseghyan et al. (2013b), the distinction between misperceptions and probability weighting does not matter, in the sense that both assumptions could lead to models that accurately predict behavior, but policy implications differ under each scenario. For example, if individuals misperceive probabilities of natural hazard risk, information campaigns may be an effective policy intervention that would have little to no effect if individuals instead have correct perceptions of risk but distort probabilities when using risk information for actual decisions.
2. Literature Review
Several studies have measured individual perceptions of natural hazard risk using a variety of methods (see reviews in Bubeck, Botzen, and Aerts 2012; Lechowska 2018). Other studies have assessed laypeople and expert measures of flood risk using qualitative scales and interview techniques (Siegrist and Gutscher 2006; Ruin, Gaillard, and Lutoff 2007). Empirical studies that quantify the difference in homeowners’ subjective assessments of flood risk and objective analogs of the same risk, however, are uncommon. Moreover, the few existing studies that explore this topic produce divergent findings on the general tendency to overestimate or underestimate risk. Botzen, Kunreuther, and Michel-Kerjan (2015) survey 1,000 homeowners in flood-prone regions of New York City and investigate individual awareness of living in a flood zone, perceived flood probability, and perceived flood damages. Using a series of multiple-choice questions to elicit perceived probability of a flood and expected cost to repair their home after a flood, they find that most respondents overestimate the probability of a flood but underestimate associated damages compared with objective Hazards U.S. (HAZUS) risk estimates.3 Further, they find that individual affect (e.g., fear, worry, dread) tends to increase subjective flood risk probabilities and expected repair costs.
Focusing on overoptimism in the face of natural hazards, Royal and Walls (2019) survey several hundred coastal floodplain (SFHA) residents in Maryland and investigate their perceptions of flood risk by asking them to indicate if they thought their home was more or less exposed to flood damages than the average home in the area. In addition, they compare each person’s belief about being at lower risk against objective risk assessments (again, generated by HAZUS). In both cases, they find residents to be generally overoptimistic in their perceptions of flood risk. Elicitation of the perceived probability of flooding, using an open-ended query, revealed that most homeowners believed the annualized probability of a flood to be less than 1%, despite all properties in the sample being in an SFHA (defined by at least a 1% chance of flooding a year).
Exploring flood risk perceptions in heavily diked communities in the Netherlands, Mol et al. (2020) survey roughly 2,000 homeowners to assess flood risk misperceptions and identify determinants of those misperceptions. Regarding perceived flood probability, they find that 89% of their sample have flood risk perceptions that are incorrect, even when applying a 25% margin of error. Most of their sample (55%) overestimated the probability of a flood, whereas 34% had flood risk perceptions that are lower than objective estimates. Those who underestimated the probability of a flood were primarily characterized as neglecting the risk altogether (possibly because of the flood dikes). Regarding flood consequences, they find most residents report much lower maximum water levels than objective estimates would suggest. Individuals’ expected damages, however, were roughly in line with objective estimates about half of the time (using a 25% margin of error). Those who reported expected damages that differed from objective estimates were slightly more likely to underestimate damages than overestimate them. Mol et al. (2020) find that worry tends to increase subjective flood probability and damage perceptions.
Bakkensen and Barrage (2022) survey 187 coastal residents in Rhode Island and ask them to show their level of worry regarding coastal flood hazards along with their beliefs about the probability of their home flooding at least once over the next 10 years. They compare the subjective flood probabilities with objective probability estimates generated using a variety of sea level rise projections and flood inundation mapping tools. Overall, they find that approximately 70% of residents underestimate the cumulative probability of a flood occurring in the next 10 years.
To our knowledge, Meyer et al. (2014) is the only study that directly measures subjective perceptions of hurricane risk and compares them with objective estimates. They conducted phone surveys to elicit individual risk perceptions multiple times, leading up to Hurricane Isaac and Hurricane Sandy making landfall on the Gulf Coast and New York City, respectively. Participants in the sample consistently overestimated the probability that their homes would be afflicted by hurricane-force winds.
We build on these studies in designing our survey and conducting our empirical analyses.
3. Data
Data for our analyses are composed of survey results; objective risk estimates from FEMA, the National Weather Service, and First Street Foundation; and housing data from county-level tax assessor offices.
Survey Data
The empirical analysis involves three distinct steps. The first compares objective and subjective metrics of flood and hurricane risk and categorizes respondents as being pessimistic, roughly correct, or optimistic in their risk assessments. The second step explores possible determinants of the observed heterogeneity in misperceptions by conducting reduced-form regression analyses. Data requirements for our analysis necessitate having (1) subjective risk metrics (i.e., the natural hazard risk individuals think they face), (2) objective risk metrics (i.e., reliable and accurate estimates for the natural hazard risk individuals actually face), and (3) individual characteristics that plausibly influence risk perceptions. Last, we test many probability weighting functions to assess their performance in explaining the difference among subjective and objective risk perceptions.
Subjective Risk Metrics
Most of the data used to conduct our analysis were gathered via mail surveys that occurred in five waves between October 2018 and August 2021. Each sample targeted recent residential real estate transactions in various locations along the East Coast. The first wave was administered in Glynn County, Georgia, in October 2018, followed by a second wave in Dare County, North Carolina, in June 2020. The third wave was in Worcester County, Maryland, in July 2020; the fourth wave was in Dare County in June 2021; and the fifth wave was in Worcester County in July 2021. Figure 1 shows a spatial and temporal overview of our sampling waves.
Most notable for our analysis were questions designed to elicit individuals’ beliefs regarding coastal hazard risk. Given that our analysis seeks to compare subjective assessments of risk to objective analogs, we use a battery of instruments that include open-ended, multiple-choice quantitative measures, frequencies, and Likert scales. This approach allows comparative assessment and triangulation of risk perceptions among multiple domains (i.e., hurricane and general flood risk). With proper coding and interpretation, most measures can be directly compared with publicly available objective risk measures.
Given that flood zones in the United States are characterized by explicitly defined flood probabilities,4 we use an open-ended query to elicit annualized subjective flood probabilities.5 Specifically, respondents were prompted to answer the following question:6 “In the next 12 months, what do you think the percentage chance is that your home will flood from any weather-related event (rain, storm surge, hurricane, etc.)?” Unlike flood likelihood, no publicly available measures of flood damage exist (in part because of the measure being unique for each home) to guide development of our instrument for eliciting perceptions of flood damage. To obtain an estimate of each respondent’s subjective beliefs regarding personal home damage from a weather-related flood, the following open-ended question was posed to survey participants: “If your home were to flood from any weather-related event (rain, storm surge, hurricane, etc.), approximately how much do you think it would cost to return your home to its prior condition?”
Spatial and Temporal Distribution of Survey Waves
Unlike floods, likelihoods for hurricane strike are typically measured as historical return periods—the number of hurricanes to pass within 50 nautical miles (approximately 58 statute miles) per unit of time (NOAA 2020b). To create an analogous subjective risk metric, respondents were queried on the following expected frequency response: “How many major hurricanes (category 3 or greater, with winds of 111 mph or greater, possibility of tornadoes, and storm surge of at least 10–12 ft.) do you expect to pass within 60 miles of your county over the next 50 years?” (We refer to this as an “open interval” elicitation, since respondents can forecast anywhere between zero and a relatively large number of future hurricanes [e.g., > 50].) Responses to this question were mapped to a corresponding annualized probability.7 Hurricane risk perceptions in the initial waves permitted open-ended response to this question, while the final two waves (Dare and Worcester Counties) were elicited in a slightly modified version of the frequency question that used a multiple-choice format. This allows an assessment of sensitivity of risk perception measures to modifications in the open interval, frequency-based survey instrument. Specifically, respondents were prompted to select “none,” “one,” “two,” three,” “four,” “five,” or “six or more (please specify how many),” with the last option soliciting an open-ended response. We refer to this method as hurricane risk elicitation method 2, while the former (open-ended frequency) is referred to as hurricane risk elicitation method 1.
In addition to the subjective probability of a hurricane strike, we elicit subjective perceptions of hurricane damage, framing damage as a percentage of home structure value (the same way HAZUS damage estimates are conveyed). This is carried out with the following question: “Suppose a category 3 hurricane (with winds exceeding 110 mph, possibility of tornadoes, and storm surge of at least 10–12 ft.) directly struck near your house at high tide, how much damage (expressed as a percentage of total home value) do you think your home would most likely suffer?” (We refer to this as a “closed interval” elicitation.) Respondents indicated a level of damage on an ordered categorical scale ranging from 0%–10% to 91%–100% in 10 percentage point increments.8
Objective Risk Metrics
To obtain objective estimates of the natural hazard risk faced by individuals in our sample, we used several data sources. The first is the FEMA-designated flood zone, which is obtained by cross-referencing digitized flood hazard layers against geospatial coordinates of each property. As a metric of risk, these flood zone classifications are quite crude, with only three primary classifications: “a less than 0.2% chance per annum” (typically referred to as Zone X500 or X Unshaded), “between a 0.2% and 1% chance per annum” (typically referred to as Zone X or Zone X Shaded), and “greater than or equal to 1% chance per annum” (defined by Zones A and V and often referred to as SFHAs). In addition, the accuracy of flood maps that assign homes to one of these designations has been called into question. Wing et al. (2018) estimate that 41 million U.S. households face at least a 1% chance of flooding each year, whereas FEMA flood maps indicate that only 13 million households face that same risk. Using proprietary catastrophe models designed by reinsurers, Czajkowski, Kunreuther, and Michel-Kerjan (2013) find significant differences in flood risk for identical FEMA flood zones in coastal and inland parts of Texas, similar loss distributions for properties in different FEMA flood zones, and considerable storm-surge risk not identified by FEMA flood zones.
These FEMA flood zones, however, are highly publicized and are the primary risk metric for pricing flood insurance policies; thus, they serve as an important control for analyzing determinants of risk perceptions. In addition to FEMA flood zone status, we obtain detailed flood risk data for each study property from the probabilistic flood model produced by First Street Foundation (2020), which includes the annualized probability and flood depths for flood events with 5-, 10-, 20-, 50-, 100-, 250-, and 500-year return periods.
To obtain estimates of damage in the event of a flood, we take the flood depths (for each return period, which are unique to each property footprint) and calculate flood inundation levels based on the first-floor elevation for each home in our sample. These flood inundation levels, along with other home characteristics, are used to create flood damage estimates using a variety of flood damage functions,9 which map flood inundation levels into damage as a share of total structure value. In addition, we calculate damage estimates for each home under the assumption of 1 ft., 5 ft., and 10 ft. water inundation levels. This provides a metric that allows for meaningful comparisons across homes without confounding susceptibility to water inundation with an increased probability of higher floodwaters.10
This approach provides damage estimates for the structure of the property but does not capture potential damage to home contents. To obtain estimates of contents damage, we used the same previously mentioned damage functions, which have separate mappings available for relating flood conditions to contents damage (expressed as a percentage of the value of the contents). Using contents damage functions requires knowing the value of the contents in the home. In the absence of having precise home contents valuations, we assume that each respondent has home contents equivalent to 55% of their home value. This is based on homeowners insurance companies typically recommending setting home contents coverage equal to 40%–70% of the home value (midpoint of this range).11 Once estimates for home structure and contents damage are obtained for each set of flood conditions, they are summed to produce a single estimate of flood damage.12
Objective estimates of a major hurricane landfall are obtained from the National Oceanic and Atmospheric Administration’s (NOAA) National Hurricane Center (NHC). The NHC’s online Historical Hurricane Tracks tool allows hurricanes and tropical storms to be filtered to obtain a return period for a hurricane of certain conditions (we use the conditions specified in our subjective risk assessment question) (NHC 2020). The return period is then mapped into an annualized probability.
Descriptive Statistics
The remaining data are obtained from the survey, which is discussed here alongside descriptive statistics for all data used in the analysis. Table 1, panel A, shows descriptive statistics for all variables related to subjective risk perceptions. The mean respondent believed there was an approximate 8% chance of their home flooding from any weather-related event in the next 12 months. The mean annualized hurricane strike probability derived from respondents’ expectations on the frequency of future hurricane strikes was 18%. We note heterogeneity in responses across elicitation methods. Respondents who were prompted with only an open-ended frequency had a mean subjective probability of a hurricane strike of 25%, and those who were prompted with multiple-choice options (in addition to having the option to write in their own value) had a mean subjective probability of 9%.13 Concerning perceptions of flood damage, the average respondent believed if their home were to flood, damage would be equivalent to $127,836. When normalized by building values, this equates to 91% of the average home’s structure value. Similarly, the average respondent believed a direct strike from a major hurricane would lead to home damage equivalent to 35% of their home structure value. When flood probability and damage are multiplied to obtain a subjective expected annual flood loss measure, the mean expected loss was equivalent to 9% of home structure value.
Table 1, panel B, shows descriptive statistics for the corresponding objective risk metrics. Data from the First Street Foundation suggest the average home in the sample has a 9% annual chance of flooding. Data from NOAA indicate a 4% annual chance of a major hurricane strike, although there is very little variation in this metric since it is observed at the county level. Worcester County has a 2.2% historical chance of a major hurricane strike; Glynn County has a 3% chance, and Dare County has a 6.3% chance. Flood damage estimates suggest that in the event of a five-year flood,14 the average flood damage would be equivalent to approximately 1% of the home’s structure value.15 Similarly, return intervals of 10 years, 100 years, and 500 years are associated with average damages of 2%, 9%, and 16% of home structure value. Defining a flood based on inundation levels of 1 ft., 5 ft., and 10 ft. (which are very low-probability events for most homes) suggests average damages of approximately 41%, 86%, and 118% of home structure values. Objective expected flood losses are estimated to average 1% of home structure value per year.
Descriptive Statistics
Table 1, panel C, shows descriptive statistics for the remaining variables in our analysis. Previous literature has noted the role that affect (fear, worry, dread) can influence perceptions of risk (Slovic 2010; Botzen, Kunreuether, and Michel-Kerjan 2015; Mol et al. 2020). To elicit metrics about individuals’ proclivity to worry, respondents were asked to indicate their degree of worry across multiple domains (e.g., personal health, family health, financial difficulties) using a four-point Likert scale ranging from “not at all worried” to “very worried.” We define a “relative worry” index by placing the Likert scale on worry over home loss (ranging from 1 to 4) in the numerator and the sum of Likert scale for other worries in the denominator (ranging from 7 to 28). This makes it possible to isolate the effect of worry over home loss while controlling for general levels of worry. The average worry over home loss was 2.32, and the average worry index was 0.15 (with a minimum of 0.05 and a maximum of 0.43).
The average years of education was 16.5, indicating a significant proportion of respondents with some level of postsecondary education. Thirty-two percent of respondents indicated they were female. Seventy-nine percent of the sample indicated that the survey home is their primary residence. Thirty-four percent were long-term residents, defined as those who had lived on the coast for “more than 11 years,” “my entire life,” “most of my life,” or “many years.”16 Thirty-eight percent of respondents resided in a SFHA zone. In addition to using FEMA-designated SFHA status, we construct the equivalent of SFHA using data from the First Street Foundation (i.e., an indicator for 1% chance of flooding a year using First Street’s compound flood risk measures). Overall, the First Street data suggest that 54% of households in the sample should be classified as being in a SFHA, a roughly 40% increase over officially designated FEMA SFHA properties.17
Respondents were prompted to report household income by categorical measure, ranging from less than $35,000 to more than $250,000. Most intervals were coded at their midpoint, with the exception of the lowest and highest intervals. The lowest interval was assigned a coding of $30,000, and the unbounded top interval was assigned using the methods suggested by Hout (2004), which entails extrapolating income based on a Pareto distribution. This results in top-coded income level of $284,280, resulting in a mean household income of $154,000.
Household wealth is notoriously difficult to measure, particularly in the context of a survey. To create a proxy for wealth, the survey included a categorical response question about the impact of total loss of coastal property (without insurance) on net worth (including a brief definition of net worth). The impact measures ranged from 0% (no impact) to 100% (total loss of net worth) in 20% increments. We use the property value and the midpoint of the response category to create a proxy for household wealth, for which the average is $548,000 (median = $340,000). Ten percent of respondents indicated that they had personally sustained flood damage in the past. Three percent experienced what we define as major flood damage (those who reported flood damage over $10,000), and 7% experienced minor flood damage ($10,000 or less in damages).
Given that past literature has shown that flood risk can be capitalized into housing values (Bin, Kruse, and Landry 2008; Bin and Landry 2013; Landry, Turner, and Allen 2022), we include the most recent home sale price for each property in our sample (average of $372,000) under the premise that some coastal residents may use home values to partially inform their perceptions of risk. In addition, we include the median block-level home price as reported by the 2020 census (average of $326,000) as a measure of overall market assessment of risk. Finally, 78% of respondents reported having a mortgage on their coastal property, and 33% of the sample had a mortgage and resided in a FEMA-designated SFHA zone (a condition that mandates purchase of flood insurance).
4. Empirical Methods
Objective versus Subjective Risk Metrics
Building on previous research (Botzen, Kunreuther, and Michel-Kerjan 2015; Mol et al. 2020), subjective risk perceptions were elicited using an array of instruments (open-ended for flood probability, expected cost for flood damage, and expected hurricane frequency) and were categorized as being correct as long as the difference between the subjective and objective metrics falls within a margin of error. This is considered necessary because all measures are continuous, and virtually none of the survey respondents have subjective perceptions that exactly match the objective metrics. Realizing that any chosen margin of error is arbitrary, we conduct sensitivity analysis, reporting results for 1, 2.5, 5, 10, 25, and 50 percentage point margins of error. We use these error bounds to classify each respondent as being correct, pessimistic (overestimation of risk), and optimistic (underestimation of risk), and we report the share of respondents in each category.
Subjective and Objective Probabilities
Regression Analysis
To assess whether the accuracy of risk perceptions can be explained by observable characteristics, we run a series of reduced-form regression models that focus on the variability of differences in subjective and objective measures of flood probability and expected flood damage. For each regression, we take the difference between objective and subjective risk measures. Figure 2 plots the density of the difference in flood probabilities and hurricane probabilities, and Appendix Figure C1 plots the densities for flood damage differences using each available objective reference flood we have available in our dataset.18
Considering probability differences first, we note that the differences in flood and hurricane probabilities exhibit a clear spike at zero and asymmetric tails. Thus, we use ordinary least squares (OLS) to analyze positive and (absolute value of) negative deviations separately as well as a combined model that restricts covariate effects to be equivalent above and below risk perception parity. Positive regression coefficients indicate a covariate is correlated with less accurate perceptions (magnitude of the difference increases away from zero), while negative coefficients indicate correlation with more accurate perceptions.
We apply a similar approach to modeling perceptions of flood damage, again taking the absolute value of the deviations between subjective and objective perceptions. For most reference floods considered, individuals are either primarily optimistic or pessimistic, meaning that for most reference floods there is insufficient variation to run separate regressions on optimistic and pessimistic individuals. For 1 ft. of flood water inundation, we observe a fairly even split among optimistic and pessimistic perceptions. Thus, we run separate regressions for only the 1 ft. reference flood.
In addition to regressions using the difference in subjective and objective risk measures as a dependent variable, we run a series of regressions using only subjective risk perceptions as the dependent variable. Specifically, we run regressions based on dependent variables defined by perceived flood probability, hurricane strike probability, flood damage (structure and contents), hurricane damage, and expected annual flood loss. Dependent variables for flood probability, hurricane probability, and hurricane damage are contained in the unit interval, so we estimate these specifications using a fractional response probit model, while the remaining specifications are estimated using OLS. These results provide more context and insight when interpreting our primary specifications focused on deviations in subjective and objective risk perceptions.
Misperceptions versus Probability Weighting
Our final task entails assessing the potential for probability weighting to explain the divergence between objective and subjective risk measures. The literature on probability weighting suggests that this divergence can be summarized by a systematic functional mapping. For example, suggested weighting functions transfer weight from high likelihoods (> 50%) to lower likelihoods (Barseghyan et al. 2018). Given the roughly balanced distributions in Figure 2, we do not expect standard weighting functions to fit all the data, but we explore numerous approaches to assess whether probability weighting can provide insight into the divergence of subjective and objective likelihoods.
Given that our outcome variable is a probability, we base the structural model on a beta regression, which is specifically constructed for a dependent variable of this type (Ferrari and Cribari-Neto 2004). In a standard beta regression, the parameter µ is a linear combination of observable characteristics, X, and parameter vector β that get passed through a link function g(.)−1 (equation [1]). The link function can be any function that maps the covariate domain to the unit interval (such as a logit function). To introduce probability weighting, µ is simply redefined to use a probability weighting function, Ψ(X;θ), as the link function,19 and in place of X, the objective flood probabilities, Pobj, are used (equation [2]). The parameter vector θ defines the curvature of the weighting function and contains one or two elements depending on the particular weighting function. Regardless of whether probability weighting is used, the likelihood function for the beta regression, with the subjective probability Psub as the independent variable, is defined in equation [3], where B(.) is the beta function:
1
2
3
The log-likelihood functions corresponding to structural econometric models often involve highly nonlinear functions with local optima, creating convergence and stability problems for standard estimation approaches like maximum likelihood. Accordingly, we estimate the structural beta regressions using standard Monte-Carlo Markov chain methods. Full details associated with this estimation procedure are in Appendix A.
5. Results
Accuracy of Risk Perceptions
As a first test of flood risk perceptions, we simply check what proportion of respondents reported perceptions that are consistent with their official FEMA-designated flood zone. Appendix Table B2 shows the share of respondents with flood risk perceptions that were consistent with their official flood zone designation. Overall, 38% of respondents had flood risk perceptions that were consistent with their flood zone status, with the majority being located in the SFHA, the minority located outside the flood zone, and no respondents located in the 500-year flood zone. Almost one-third of respondents (31%) had relatively pessimistic risk assessments (though located in the 500-year flood zone or outside the flood zone), and just over one-quarter (26.5%) exhibited optimistic flood risk perceptions (the majority of which were located in the 500-year flood zone).20 While somewhat insightful, FEMA flood zone classifications are too crude as an objective risk metric to be particularly useful in classifying flood risk perceptions.
Figure 3 shows the share of respondents that had subjective probabilities of flooding that were correct (top row) along with the accuracy of damage expectations for floods with various return periods (20-year to 500-year; rows 2–4) and water depths (1–10 ft., rows 5–7). The columns in Figure 3 are associated with different margins of error, ranging from 1% (first column) to 50% (sixth column). Focusing on the top left, we see that approximately 28% of respondents had subjective probabilities of flooding that were within 1 percentage point of their objectively estimated flood probability (indicated by the lightest gray region of the top left cell in Figure 3). The remaining respondents, who had perceptions that differed from the objective estimates by at least 1 percentage point, were mostly pessimistic (41%), perceiving that the likelihood of flooding was greater, with the balance being optimistic (30%). As we increase the margin of error (moving from first to last column), the “accuracy” of flood probability risk perceptions increases, with very few inaccurate assessments when allowing for a (rather large) 50% error margin. There is no overwhelming trend in the accuracy of flood risk probability perceptions. At almost every reasonable margin of error, a sizable proportion of people can be classified as having pessimistic, correct, and optimistic perceptions. Additional figures decomposing accuracy of flood probability perceptions by SFHA status are in the Appendix. Appendix Figure C4 shows accuracy among four distinct groups defined by FEMA and First Street SFHA status,21 and Appendix Figure C5 shows accuracy broken down by FEMA flood zone status.22
Perceptions of flood damage tend to be overwhelmingly pessimistic.23 Using a 1% margin of error suggests that more than 90% of the sample overestimated the extent of damage in the event of a flood, regardless of the flood’s return period. Even when applying larger margins of error, the general tendency to overestimate damages is evident; only about 20% of respondents reported expected flood costs that were within 10 percentage points of objective estimates. Applying an extremely large 50% point margin of error still only results in about half of respondents having correct flood damage perceptions.
Share of Respondents with Flood Risk Perceptions
Using objective damage estimates from 1 ft., 5 ft., and 10 ft. inundation levels suggests greater variation in accuracy of perceptions, with a significant portion of the sample having pessimistic and optimistic perceptions regardless of the permitted margin of error. Nonetheless, we note that these levels of water inundation represent exceedingly rare events. For example, First Street data suggest the average inundation level in our sample for a 500-year flood is 1.45 ft. (though the standard deviation is large, at 5.13 ft., and the maximum is 13.22 ft.). This pattern of results suggests the pessimism evident from comparison to floods of standardized return periods primarily stems from an overestimation of water-inundation levels associated with routine flood events, rather than misunderstanding the damage associated with a given level of water inundation.
Finally, using expected annual loss as a composite formulation of probability and damage (final row of Figure 3) suggests notably accurate risk perceptions compared with viewing flood probability and flood damage in isolation. Using our smallest margin of error, more than half of the respondents had correct perceptions of expected annual flood costs. This is partly attributable to a number of respondents who disregard the possibility of a flood altogether and report a subjective flood probability of zero, which is roughly “correct” given the low expected annual flood costs for most coastal homes in our sample.24 This result is similar to findings conveyed by Mol et al. (2020), who find that 28% of their sample believed that a flood would “never” occur at their current residence. In our own sample, we find that 35% of respondents reported a perceived flood probability of zero; however, this is arguably a justified response given that First Street flood probabilities for 31% of our sample are zero (out to three decimal places).25 Even if respondents who disregard flood risk altogether are removed from the sample, we still find that 32% of respondents are classified as correct using the 1 percentage point margin of error, and the majority of respondents are correct within a 2.5 percentage point margin of error.
Appendix Figure C7 shows the share of respondents who had correct beliefs (gray) about the probability of a major hurricane strike as well as those who thought the probability was higher (pessimistic, red) and lower (optimistic, blue). Since the probabilities of hurricane strike are the same for all residents in a county, we report the accuracy of perceptions for each county individually, in addition to an aggregate metric. Overall, the individuals in our sample tend to be overly pessimistic in their beliefs about the historical likelihood of a major hurricane strike, regardless of the county of residence. Using a 1 percentage point margin of error suggests that 71% of individuals overestimate the historical probability of a major hurricane strike. Applying a 5 percentage point margin of error results in slightly more than half of the respondents having correct perceptions but with a large share of individuals still overestimating the historical probability of a strike. Decomposing the accuracy of perceptions by county and elicitation method indicates similar patterns, with no major deviations being obvious when compared to the pooled results.
Determinants of Risk Perceptions
Table 2 shows regression results for the absolute value of the difference between subjective and objective flood probability as the dependent variable. Column (1) shows the results for individuals with pessimistic perceptions of flood probability, and the remaining columns show the results based on optimistic individuals and the full sample, respectively. Overall, the models exhibit modest explanatory power, with R-squared ranging from 17% to 31% (highest measure for optimistic perceptions). Relative worry over loss of home in a disaster is correlated with decreased accuracy (larger absolute difference) of perceptions for pessimistic respondents but has no statistically significant effect among optimistic individuals or overall effect in the combined sample. Years of education has a moderating effect on flood risk perception for optimistic households, reducing inaccuracies. The results suggest that household income is correlated with less accurate flood risk perceptions, while household wealth exhibits the opposite correlation (both coefficients statistically significant at the 10% level in the pessimistic model). Segmenting flood experience by magnitude of loss (above or below $10,000), we find increased accuracy for those with “major” flood damage experience for the optimistic and full samples. The magnitude of this result is limited by the array of flood experience in our sample but suggests that experience with relatively high levels of flood damage (in the context of our survey data) could help realign optimistic flood risk perceptions with objective reality. Primary homeowners exhibit less accurate risk assessments in the combined model (though not significant in the subsamples).
Determinants of Difference in Subjective and Objective Flood Probability
Binary indicators for location in zone associated with base flood (1% annual probability), from both FEMA and First Street Foundation, are correlated with less accurate perceptions of flood probability. For FEMA SFHA, this result appears to be driven by those with optimistic flood probability perceptions. Because FEMA SFHA is the most publicized flood risk designation, this finding is consistent with the idea that the “at least 1%” chance of flood language used to designate the SFHA may mask the reality of potentially much higher flood risks and anchor subjective flood probabilities near the 1% level. The larger correlations associated with First Street risk designation indicate additional inaccuracies of flood probability associated with the less publicized First Street flood risk designations. Home value, a potential indicator of financial exposure, has no significant correlation with accuracy of flood risk perception. Median home value (census-block level), however, is correlated with increased accuracy for pessimistic risk perceptions. The mortgage indicator is correlated with decreased accuracy for pessimistic households, but an interaction variable for mortgage status and wealth suggests more accurate risk perceptions for optimistic households. This suggests that flood disclosure provisions associated with mortgage processing can influence flood risk perceptions for some households with the effect being moderated by household wealth. Control variables for length of residence and sex have little explanatory power. Looking to the determinants of subjective risk perceptions in isolation provides additional insight on potential mechanisms behind the correlations between accuracy of perceptions and individual characteristics; we turn to these results.
Table 3 shows the regression results using subjective perceptions of flood risk as the dependent variable, while including objective analogs of the same risk among the independent variables. Additional specifications included in Table 3 estimate the same model using subsets of the data divided by optimism and pessimism in relation to objective estimates.26 We focus first on flood probability. Objective flood risk measures are positively correlated with subjective measures in the pessimistic and optimistic models, but not in the combined model (reflecting correlations in subsets of the data that do not appear in the combined dataset). The results suggest that relative worry significantly increases subjective flood probabilities for combined and pessimistic models; thus, affect (e.g., fear, worry, dread) can exacerbate pessimistic risk assessments.
Similar to the flood probability accuracy regression, approximate wealth level has a negative correlation in all models, whereas household income exhibits a positive correlation for pessimistic households. The wealth effect could reflect self-protection, such that wealthier households may choose safer locations to live or invest in mitigation measures that lower flood probabilities. The only flood risk experience measure that exhibits correlation is the binary indicator for minor flood damage (< $10,000), which is positively correlated with flood risk perception.
Presence in the FEMA-designated SFHA is positively correlated with risk perception but only for pessimistic households. Home value is positively correlated with flood risk perception in the combined and pessimistic models; this is consistent with the findings of Beltran, Maddison, and Elliott (2018), in which amenity effects can eclipse flood and erosion risk in high-risk coastal areas (i.e., highest risk V flood zones located on the oceanfront). Median home values negatively correlate with flood risk perception in these models, which may indicate a belief in the validity of market pricing of risk. Households with a mortgage exhibit larger subjective flood risk perceptions in the combined and pessimistic models.
Turning to flood damages in Table 3, we find negative correlations with objective damage measures for combined model, suggesting downward bias in flood damage perceptions. This result persists for the pessimistic subsample but has no effect in the optimistic subsample. Income is positively correlated with flood damage perception, which could reflect more valuable real estate and contents, while wealth is negatively correlated; the income effect persists for pessimistic households, and the wealth effect remains for optimistic households. Again, the wealth result could reflect investments in self-protection, such as flood-proofing, home elevation, or safer location. Flood experience, both minor and major damage levels, is correlated with lower perceptions of flood damage. This is consistent with the idea that flood damage perceptions are upward biased; experiencing a flood loss could permit updating of damage perceptions, resulting in lower estimates of flood damage. The only exception to this pattern is a positive correlation for major flood damage for optimistic households. Remaining covariates related to flood zone, home values, and mortgage status do not exhibit statistically significant correlations.
Determinants of Subjective Risk Perceptions by Perceptions Accuracy
Table 4 shows results based on differences in subjective and objective flood damage for several reference floods. Household income is consistently positive in most regressions, suggesting a larger absolute distance between subjective and objective flood damage perceptions. Among specifications based on 20-year and 100-year return periods, major and minor flood damages are correlated with improved accuracy of flood damage. Looking at Table 3, column (4), the experience of major and minor flood damage clearly decreases subjective perceptions of flood damage. This is consistent with the finding that damage perceptions for floods with lower return intervals (20 or 100 years) tend to be upward biases but experiencing a flood permits correction of these expectations. Looking to specifications based on 1 ft. of water inundation in Table 4 (similar to floods based on standard return periods), the combined sample also indicates that accuracy of perceptions improves in response to direct experience with both major and minor flood damage. Again, this effect varies by initial classification of perceptions. Among pessimistic people, statistical significance is present only on the effect of minor flood damage. Optimistic individuals see a varied response depending on the extent of the damage; major flood damage correlates with increased accuracy, while minor flood damage correlates (weakly) with decreased accuracy. This result, coupled with the results in Table 3, suggests that experience with flood damage generally decreases perceptions of damage, which helps bring the generally overinflated expectations of damage observed in Figure 3 in line with objective estimates. Among optimists, major flood damage appears to increase the accuracy of perceptions by elevating perceptions of damage toward objective estimates, while minor flood damage appears to reinforce their already low expectations of damage. The differences in expected annual flood loss (product of flood probability and expected damage, last column of Table 4) are not correlated with any of the covariates.
Determinants of Difference in Subjective and Objective Flood Damage
Focusing on additional measures, we turn to Appendix Table B3, which shows specifications based on subjective perceptions of hurricane risk (probability and damage) and annual expected hurricane loss (the product of hurricane probability and hurricane loss). The separate specifications for flood loss from Table 3 are reproduced in Appendix Table B3 (last two columns, shaded) for ease of comparison.27 Subjective assessment of hurricane probability is positively correlated with the objective, historical estimates but is not statistically significant. (We were not able to derive reliable objective, household-level estimates of hurricane damage.) Worry, long-term-resident status, and educational attainments are positively correlated with subjective hurricane probability; home value is negatively correlated. For expected hurricane damage, we find relative worry, household income, and location in the First Street SFHA are positively correlated, while presence in the FEMA SFHA, home sales price, and median home values are negatively correlated. The middle column in Appendix Table B3 shows that expected annual flood loss (the product of flood likelihood and consequence) is decreasing in wealth, but the regression is mostly lacking in explanatory power. This could be partly explained by the small sample size (due to various missing data).
Probability Weighting versus Misperceptions
Appendix Figure C8 plots subjective flood probabilities against objective flood probabilities along with each estimated weighting function. The root mean squared error (RMSE) for each estimated weighting function is shown in the legend (in parentheses) and can be interpreted as the expected difference between the predicted and actual subjective probability if any individual in the sample had their subjective probability predicted using only their objective probability as the input. Overall, modeling individuals as agents who engage in probability weighting does not appear to offer any notable advantage over a reduced-form model. Estimating a standard reduced-form beta regression that uses only the objective probability of a flood as a covariate results in a RMSE of 0.129. Some of the structural specifications that employ probability weighting functions produce similar RMSE values, but none are notably better than a standard beta regression.28 This suggests that the differences in observed objective and subjective flood probabilities are not easily explained using any of the literature’s canonical weighting functions. This is consistent with the narrative that individuals exhibit idiosyncratic misperceptions rather than systematic weighting of objective probabilities.
Visual inspection reveals that any increasing, monotonic function will have a difficult time fitting L-shaped empirical observations.29 A well-fitting function must simultaneously explain the large number of respondents with low objective probabilities but high subjective probabilities and the substantial number of respondents with high objective probabilities but low subjective probabilities. The monotonicity assumption of probability weighting functions is problematic in this regard. For example, a function that fits the vertical portion of the L, such as the power weighting function in Appendix Figure C8, cannot decrease to pass near the data points in the lower right corner (those who underestimate flood risk).30
6. Discussion
Using recent advances in assessment of parcel-level flood risk estimates produced by First Street Foundation, we provide a detailed assessment of objective and subjective measures of household flood and hurricane risks. Regarding flood risk, our findings suggest no broad generalization regarding flood probability perceptions: pessimistic, optimistic, and approximately correct flood probability perceptions are all well represented in our sample. This result is most closely aligned with Mol et al. (2020), who also find most individuals’ risk perceptions were incorrect, but optimistic and pessimistic outlooks were both well represented in their sample of Dutch households.
Regarding expected flood consequence, the vast majority of respondents tend to overestimate the damages associated with a flood, regardless of the return period. This result is notably different from findings in earlier literature on perceptions of flood damage. Botzen, Kunreuther, and Michel-Kerjan (2015) find that people in New York City typically underestimate potential flood damages. Focusing on heavily diked communities in the Netherlands, Mol et al. (2020) find people underestimate water levels but generally have correct damage perceptions (conditional on water level); when damage perceptions are incorrect, they are more likely to be underestimates. When we compare elicited damage perceptions against estimated damage from 1 ft., 5 ft., and 10 ft. (which are exceedingly rare events) of water inundation, most perceptions of damage are still incorrect, but pessimistic and optimistic perceptions are much more balanced. This suggests that individuals generally overestimate the inundation associated with a routine flood rather than misunderstand the relationship between damage and water level. Despite the inaccuracies observed when the probability and consequences of flood risk are analyzed separately, combining these dimensions into an expected annual loss metric suggests that individuals have a reasonably good approximation of the long-term average annual cost that flooding will cause. However, these estimates are less amenable to regression analysis (providing very little insight into variability in expected flood loss).
An important distinction among studies that attempt to assess deviations of subjective and objective risk perceptions is the instrument that is applied to measure subjective risk. Barseghyan et al. (2018) advocate for direct probability queries based on the potential of subjective risk measures to improve structural analysis of risky decisions. This approach, however, is not a panacea for analysis of risk preferences and has its own set of problems. Direct acquisition of subjective probabilities may provide the most precise elicitation format but may be challenging for less numerically literate respondents (particularly for rare events). Although several studies champion direct measurement of probabilities (Manski 2004; Hurd 2009; Delavande 2014), others have noted the proclivity to round answers when answering open-ended probability questions, particularly near the limits of the unit interval (Dominitz and Manski 1997; Manski and Molinari 2010). De Bruin et al. (2002) suggest that the tendency for 0.5 to be overrepresented in probabilistic responses evidences epistemic uncertainty rather than an expression of a precise belief. Presenting probability as an open-interval count (as we did in our elicitation of hurricane probability perceptions, number of hurricanes over next 50 years) is advantageous in this regard, as there is no natural midpoint to which respondents can default. Although elicitation of expected frequencies over a set interval eliminated the tendency to cluster at the midpoint, it also produced a slightly larger number (relative to our direct, open-ended probability queries) of subjective probabilities equal or close to 100%.
In the context of survey data, authors have used open-ended queries (Botzen, Kunreuther, and Michel-Kerjan 2015; Royal and Walls 2019), relative risk indicators (Royal and Walls 2019), and direct probability queries (often with visual depictions or predefined intervals) (Mol et al. 2020; Bakkensen and Barrage 2022) to measure the likelihood of flooding. The extent to which these different instruments can assess latent risk perceptions that drive past or future risk management decisions is unclear. Also important are aspects of mental accounting that may influence how individuals frame and bracket risk evaluation (Barseghyan et al. 2018). We use open-ended measures for assessing general flood risk, which may induce error (perhaps only among some respondents), and we use an open-interval hurricane count to infer annual hurricane probability, which may have limitations. In the hurricane count framework, we use open-ended and multiple-choice formats (during different survey waves).
We find that seemingly minor changes in question format significantly affect individual responses across the two random samples. The open-ended format for expected hurricane count results in a mean probability hurricane strike of 25%, and the multiple-choice format (which retained the option to write in any value) results in a mean probability of 9%.31 In light of objective estimates based on the average historical hurricane return probability for the entire dataset (4%), the multiple-choice format produced much more reasonable estimates of the central tendency of probability of hurricane strike (9%) than did the open-ended probability query (25%). We further note that the 9% annual probability estimate derived from multiple choice could reflect expectations of rising risk associated with climate change that are not readily evident in the historical hurricane landfall data. In this regard, both formats (open-ended and multiple choice) indicated that individuals tended to overestimate the likelihood of historical hurricane landfall.
Past research has noted that risk perceptions rarely serve as reliable predictors of flood mitigation behavior (Bubeck, Botzen, and Aerts 2012). Given the apparent influence that elicitation format can have on elicited risk perceptions, the lack of consistent correlation between risk perceptions and mitigation behavior may be a result of some instruments failing to capture true perceptions. Future research that tests and expands on the implications of using different elicitation methods in the domain of natural hazard risk could be helpful for informing appropriate methods for future studies. Lab experiments using both objective and ambiguous risky outcomes could be particularly insightful in assessing which subjective probability measures are valid and reliable in various contexts.
The results from the reduced-form regressions provide deeper insight into the sources of heterogeneity observed in the accuracy and levels of elicited risk perceptions and echo some of the findings in the previous literature; experience with floods can influence location choice, mitigation behaviors, and risk perceptions. Previous research finds that experience with previous flood events can increase subjective flood risk probabilities (Botzen, Kunreuther, and Michel-Kerjan 2015; Royal and Walls 2019; Mol et al. 2020), while the impact on perceived flood damages is apparently more complex. Flood experience can lead to rational updating for prior beliefs about flood risk (Botzen and van den Bergh 2012) but can also play a role through heuristics like availability bias—which postulates that low-probability risks are more salient for those that can bring to mind images or past experiences (Mol et al. 2020)—or through affect (fear, worry, dread).
We further postulate that flood experience could influence risk perceptions through relative impact; those who experience minor floods may exhibit less concern that maps into lower perceptions of flood probability or damage, whereas major damages may exacerbate risk perceptions. To explore this, we classify flood experience as being above or below the maximum National Flood Insurance Program deductible ($10,000). In general, we find that this approach sometimes exhibits divergent correlations with risk perceptions. For example, “major” flood damages appear to attenuate optimism in accuracy of flood risk perceptions (moving perceived flood probabilities closer to objective estimates), and “minor” damage experience increases the level of subjective flood probability for the full dataset. Similarly, for perceived flood damages, major and minor experience tend to decrease the level of subjective perceptions (consistent with our finding that subjects overestimate flood damages), but we find major damage experience increases flood damage perceptions for optimistic households (that may have harbored low damage expectations before experiencing a flood). Our results, however, are conditioned on the level of flood experience in our sample. Future research should explore the nature of flood experience, focusing on damages, displacement, and other psychological impacts.
Affect (fear, worry, dread) has been shown to influence mental accounting and perceptions of risk. Botzen, Kunreuther, and Michel-Kerjan (2015) and Mol et al. (2020) find that categorical measures of worry are correlated with an increased perception of flood probability and damage, whereas Bakkensen and Barrage (2022) evidence that worry drives risk-reducing behaviors and intentions to sell coastal housing. Similarly, we find that an index of relative worry (qualitative score on worry about home loss relative to sum of other qualitative worry scores) increases the level of flood probability perceptions (in effect, decreasing accuracy of perceptions), particularly for subjects who are pessimistic about flood risk (subjective perceptions that exceed objective probability estimates). We find similar evidence of worry increasing perceptions of subjective hurricane damage.
As is typical in survey datasets, we use categorical responses to bin household income level (using extreme value distributions to top-code the upper bracket); in addition, we use a novel survey question to approximate household wealth level. We inquire about the impact of total uninsured loss of housing structure on the respondent’s net wealth level (providing a short definition of net wealth), which allows us to place bounds around perceived household wealth level. Notably, we find distinct and sometimes divergent correlations for income and wealth in relation to subjective risk perceptions. For example, in assessing the accuracy of flood risk probabilities, we find a positive effect of income (indicating lower accuracy) but a negative effect for wealth (indicating higher accuracy) for pessimistic households (controlling for education). We also find opposing signs for income (positive) and wealth (negative) in exploring the level of subjective perceptions of flood probability and expected damage. This pattern suggests that elements of livelihood can have distinct effects on vulnerability to, and mitigation of, natural hazards, with income (resource flow) perhaps exposing households to risk (e.g., location choice influenced by risk and amenities) and wealth (resource stock) permitting greater levels of personal risk management (e.g., investing in mitigants, such as elevation, flood-proofing, insurance). These phenomena deserve further exploration.
In the United States, the most basic flood risk information is currently conveyed by FEMA flood zones, and we find individuals in the SFHA (FEMA defined 1% chance of flooding per annum) and the First Street analog of SFHA tend to have less accurate flood risk perceptions. Evidence suggests that many of these households tend to anchor on the 1% level of risk, eschewing potentially useful information that conveys likelihood of floods with lower return intervals (though we note this information could be difficult to come by given conventions in flood risk designation). In addition, no respondents in our dataset ascribed positive flood probabilities less than 1% (which would be accurate for those located in the 500-year flood zone). This could be further evidence of anchoring on the flood risk designation conveyed by SFHA but may also reflect difficulties in conceptualizing low probabilities. For perceived hurricane damage, we find lower expectations in the FEMA SFHA and greater expectations in the FS SFHA (Appendix Table B3); homes built in the FEMA SFHA (after the publication of flood insurance rate maps) must be elevated above base flood elevation (BFE), which is the level of the 100-year flood, and insurance discounts are provided for additional elevation above BFE (known as freeboard). Such requirements, which are not imposed outside of FEMA SFHA, should reduce damages. Thus, the results are consistent with mitigation practices; those households that are required to elevate their home have lower hurricane damage perceptions.
We find evidence that property ownership characteristics are correlated with subjective risk perceptions. Those respondents for which coastal property is their primary residence exhibit less accurate flood risk probabilities (controlling for income and wealth); our pattern of results is consistent with households in SFHA anchoring on baseline probability of 100-year flood (1% a year), neglecting potential for greater risk levels in the SFHA (e.g., floods with a 20-year return interval). Mortgaged property owners also exhibited greater subjective flood and hurricane risk probabilities and slightly less accurate flood risk perceptions for pessimistic households (though an interaction with wealth level indicates an opposite effect). The results indicate that the home sales value is correlated with greater subjective perceptions of flood probability, while median sales value (census-block level) has an opposite correlation (associated with lower risk perceptions). This suggests that robust market prices could signal to coastal residents that risks are lower than experts indicate, while market value of owned property may represent personal exposure to risks that has differential impacts on risk perceptions. Overall, although we find significant variation in the levels and accuracy of flood and hurricane risk perceptions, some of the variance can be explained by observable factors in intuitive ways.
We explored the role of probability weighting to explain the observed difference between subjective and objective perceptions of flood likelihood, complementing a broader literature focused on estimating risk preferences with field data (see a review in Barseghyan et al. 2018). Estimating structural risk preferences from an agent’s observed choices is fairly straightforward in laboratory environments since the probability of outcomes is explicitly stated and precisely controlled. In a field context—for example, observing an actual insurance contract purchase—it is not clear if agents internalize and act on the objective probability of each state of the word (i.e., they may misperceive the true risk).
For studies that find incorporating probability distortions to be an important component to achieving good model fit when estimating risk preferences from field data (Barseghyan et al. 2013b; Collier et al. 2021), a dilemma persists as to whether the distortions should be attributed to nonlinear weighting of probabilities or idiosyncratic misperceptions of true probability. In some specific cases, it is possible to distinguish between probability weighting and misperceptions (Barseghyan et al. 2013a), but the necessary conditions are not universally present. Our results suggest that distortions observed between objective and subjective probabilities, at least in the context of flood risk and our subjective perception measures, cannot generally be explained by probability weighting—a finding that is notable for future studies making use of field data to estimate behavioral model parameters.
There are several policy insights arising from our findings. As shown in Figure 2, we find considerable noise in the accuracy of flood and hurricane risk perceptions, despite our study sites being located in relatively high-risk coastal areas. Perceptions of the likelihood of flooding do seem to be influenced by FEMA flood zone definitions, such that respondents who are cognizant of flood probability tend to state flooding probabilities greater than or equal to 1% a year, which is the most publicized flood risk standard in the United States. No subjects reported positive subjective annual flood probabilities below 1% (though the other flood standard used by FEMA is 0.2% to less than 1% associated with the 500-year flood zone). This is further evidence that people tend to ignore what they perceive as low-probability events, and thus risk communication and framing should focus on time horizons that convey more substantive cumulative probability (e.g., 26% chance of flooding over a 30-year mortgage in the SFHA [Salman and Li 2018]). In addition, providing more detailed information on flood likelihood, as by First Street Foundation estimates (e.g., probabilities greater than 1% inside the SFHA), could facilitate better assessment of vulnerability and permit greater risk management efforts.
Unlike earlier studies, we find that most respondents exhibit upward bias in the level of flood damage they face, and our data suggest that this tendency is attributable to overestimating water-inundation levels associated with given flood frequencies. Again, this suggests a saliency threshold in risk perceptions, such that small levels of damage may be ignored. Experience with floods appears to affect risk perceptions, but differential impacts can occur based on the severity of the experience. While it is not entirely clear how to address perceptual biases, embracing new technologies, such as GIS story maps and virtual reality (Oubennaceur et al. 2021; Mol, Botzen, and Blasch 2022), offers an important avenue for new explorations. Challenges in risk communication include finding ways to package such tools for broad consumption, introducing pathways for two-way flood hazard communication (Demeritt and Nobert 2014), and monitoring investment and mitigation behavior to better understand how information flows influence protective actions.
7. Conclusion
Using a novel survey dataset representing homeowners from three distinct locations on the U.S. East Coast, this study elicits individual perceptions of natural hazard risk and compares them with equivalently defined objective risk metrics to gauge the accuracy of perceptions. People who underestimate, overestimate, and correctly estimate the probability of a flood are well represented in the survey sample. However, regarding perceptions of personal home damage in the event a flood occurs, we find that the vast majority of survey respondents overestimate the cost of flood damage. We find evidence that this is primarily a result of overestimating the level of water inundation rather than the destructiveness of a particular level of water. Notably, when measures of probability and damage are combined into an expected annual flood loss metric, respondents reported subjective information that was consistent with objective risk estimates. We also assess the accuracy of perceptions regarding a major hurricane strike and find that the vast majority of respondents overestimate the historical likelihood of a major hurricane making landfall in their county of residence (through this may reflect expectations of environmental change); moreover, subjective perceived hurricane risk exhibits framing effects arising from question format (open-ended frequency count vs. multiple choice).
In addition to classifying the accuracy of risk perceptions, we examine the determinants of risk perceptions and the divergence of these perceptions from objective measures via estimation of several reduced-form regressions. For probability of flood loss, we use a series of regressions to evaluate how differences in objective and subjective measures vary with individual and household variables and across subsets of the sample defined by their classification of either optimistic or pessimistic about perceived flood likelihood. A similar analysis is conducted to evaluate the effects on flood damage perceptions.
Finally, we evaluate deviations among objective and subjective flood probabilities with six probability weighting functions common to the behavioral economics literature. The estimated weighting parameters do not explain the probability deviations any better than a linear regression, suggesting that what we observe is related to idiosyncratic misperceptions rather than some type of widespread behavioral heuristic. It is also possible that heterogeneous framing effects manifest in diverse ways depending on underlying individual characteristics. The validity of subjective assessment measures is an important topic for future research; lab and field experiments could be particularly useful in this regard.
Acknowledgments
We thank the First Street Foundation for access to their probabilistic flood model, which made this analysis possible. The National Science Foundation funded this research, under the Coupled Natural-Human Systems-Award 1715638. The views expressed here are those of the authors and cannot be attributed to the Economic Research Service or the U.S. Department of Agriculture.
Footnotes
Supplementary materials are available online at: https://le.uwpress.org.
↵1 Previous analyses that have attempted to estimate structural decision models have struggled with distinguishing between individual probability weighting and probability misperceptions (Barseghyan et al. 2013b; Collier et al. 2021).
↵2 For example, the findings of Mol et al. (2020) are based in the Netherlands and cannot reliably be generalized to the United States, given the significant differences in institutional setting. Royal and Walls’s (2019) sample is from coastal Maryland, which had not seen a major flood event for several years before the survey; in addition, they only surveyed SFHA residents, meaning their results may not generalize to homeowners in lower-risk flood zones. Notably, Botzen, Kunreuther, and Michel-Kerjan’s (2015) survey was administered six months after Hurricane Sandy, implying that many survey respondents had vivid memories or recent direct experience with flood damage.
↵3 HAZUS is a GIS-based natural hazards analysis tool created and maintained by FEMA.
↵4 For example, FEMA SFHA zones are defined as “the area that will be inundated by the flood event having a 1% chance of being equaled or exceeded in any given year.”
↵5 In addition to being advocated for in recent publications (see Barseghyan et al. 2018, section 7.3, for a review), direct probability queries have the marked advantage of eliciting a direct input for many theoretical models of decision making under risk, which make estimation of structural models, like the one we describe in Section 5, possible.
↵6 Questions eliciting subjective assessments of general flood risk were added to the survey only after the initial survey wave in Glynn County. Thus, data from Glynn County are only used in our analysis of hurricane risk perceptions.
↵7 We divide the response by 50 and censor values greater than 1.
↵8 Although we elicit perceptions of hurricane damage and include them for informational purposes, we do not compare these to objective estimates. This is because, to our knowledge, there is no simple way to credibly estimate hurricane damage without being overly precise in the conditions. For example, hurricane damage is highly dependent on the confluence of wind speed, precipitation, storm surge, tidal conditions, and so on. In our opinion, trying to specify these conditions in a survey question would lead to an overly complicated question and risk prompting participant dropout.
↵9 We generate damage estimates using multiple damage functions and then average results to obtain a single damage estimate. The damage functions used are FEMA’s Flood Impact Analysis Damage Function and several produced by the U.S. Army Corps of Engineers (USACE), which include USACE IWR, USACE Chicago, and USACE Galveston.
↵10 In other words, this allows us to remove the stochastic element from the flood and measure the damage from essentially pouring water into each home until it reaches the same depth in all homes.
↵11 Later, as a robustness check, we assume a much higher valuation of 80% of the home value and find qualitatively similar results.
↵12 That is, flood damage due to 1 ft. of water inundation = estimated structure damage caused by 1 ft. of water inundation + estimated contents damage caused by 1 ft. of water inundation.
↵13 Clearly, there are framing effects in our measurement of hurricane risk.
↵14 A five-year flood is an event that shows a return probability of approximately 20%.
↵15 This includes estimates for home structure damage and home contents damage but is normalized by only home structure damage. Thus, reported objective estimates for damage can exceed 100% of structure value when the sum of estimates for structure damage and contents damage exceeds the structure value.
↵16 The first survey wave (Glynn County) asked respondents to report their tenure on the coast using descriptive phrases, whereas all subsequent survey waves asked respondents to select the most appropriate numerical range (e.g., 1–3 years, 4–5 years).
↵17 Appendix Table B1 shows the distribution of observations by FEMA and First Street SFHA status.
↵18 Appendix Figure C2 shows densities for respondents’ subjective flood and hurricane probabilities, and Appendix Figure C3 shows subjective perceptions of flood damage (structure and contents) normalized by home structure value.
↵19 In addition to a simple power weighting function (i.e., raising the objective probability to a power defined by an estimated parameter), the estimation uses the probability weighting functions described by Goldstein and Einhorn (1987), Prelec (1998), Tversky and Kahneman (1992), and Gonzalez and Wu (1999)
↵20 Zeros populate the diagonal of Appendix Table B2 because of the nature of FEMA flood zone classifications. Those in the SFHA classification cannot be pessimistic, since SFHA flood probabilities are unbounded above. Similarly, Zone X is bounded below at zero prohibiting an optimistic classification. Zone X500 residents could have been correct if they reported a flood probability between 0.2% and 1%, though we found no evidence of this result.
↵21 Notably, optimistic individuals are only present in the First Street SFHA, which reports annual flood probabilities as high as 50% (average 9% in our dataset). FEMA SFHA, on the other hand, does not provide additional details for flood risk greater than 1% a year. No respondent in our dataset reported subjective flood probabilities between 0% and 1%, suggesting that for those who are cognizant of flood risk, the 1% designation used to define the SFHA may act as an anchor for subjective flood probabilities.
↵22 We see slight differences across flood zones; however, we believe this can be explained by difference in the underlying objective flood probabilities, as we do not see notable differences in the distribution of subjective flood probabilities by flood zone. A series of Kolmogorov-Smirnov and nonparametric Wilcoxon tests suggest that the distribution of subjective flood probabilities for respondents in SFHA (A/V) and X/X (shaded) zones are statistically indistinguishable from each other. However, the distribution of probabilities associated with the X500/X (unshaded) zone is statistically different than the other two distributions.
↵23 As noted in Section 3, objective damage estimates are based on home contents valued at 55% of the home structure value. Appendix Figure C6 is analogous to Figure 3 but with home contents valued at 80% of the home structure value. We see qualitatively similar results when using the alternative valuation of home contents.
↵24 Our estimated expected annual loss has a mean value of $2,193, which corresponds to an average of 0.075% of home structure value.
↵25 Only three individuals reported perceived flood damages of zero and were also among the group that reported a flood probability of zero. No individuals reported a nonzero flood probability and a zero value for expected damages if a flood does occur.
↵26 For flood damage regressions, the 1 ft. inundation reference flood is used to split the sample.
↵27 Because mortgage status was lacking for the Georgia data, we exclude this covariate from the hurricane regression models; mortgage status (and interaction with wealth) did not exhibit significant correlation when included.
↵28 The Goldstein-Einhorn weighting function has a RMSE that is 0.001 lower than a fitted linear function.
↵29 Interestingly, Botzen, Kunreuther, and Michel-Kerjan (2015, fig. 1) also plot objective and subjective flood probabilities, which generates a similar-looking figure to our own.
↵30 One potentially promising way forward is to classify individuals’ probability distortions prior to estimating the probability weighting function and then estimate unique probability weighting functions for each group. If a set of observables could be identified that reliably segments individuals into the vertical and horizontal portions of the L in Appendix Figure C8, almost any weighting function could conceivably fit each segment much better than a single weighting function estimated on the full sample. Supervised machine-learning techniques could be quite useful in this case (owing to the superior regularization routines associated with them), since traditional economic theory does not provide strong guidance on the set of observables to use for this task. Unfortunately, the sample size here is too small for most machine-learning techniques; this task remains as an avenue for future research.
↵31 Kolmogorov-Smirnov and Wilcoxon nonparametric tests reject the null (p-value < 0.000) that the distributions of elicited probabilities across the two methods are equivalent.
