Socioeconomic distributional impacts of evaluating flood mitigation activities using equity-weighted benefit-cost analysis

As the global impact of climate change intensifies, there is an urgent need for equitable and efficient climate adaptation policies. Traditional approaches for allocating public resources for climate adaptation that are based on economic benefit-cost analysis often overlook the resulting distributional inequalities. In this study, we apply equity weightings to mitigate the distributional inequalities in two key building and household level adaptation strategies under changing coastal flood hazards: property buyouts and building retrofit in New York City (NYC). Under a mid-range emissions scenario, we find that unweighted benefit cost ratios applied to residential buildings are higher for richer and non-disadvantaged census tracts in NYC. The integration of income-based equity weights alters this correlation effect, which has the potential to shift investment in mitigation towards poorer and disadvantaged census tracts. This alteration is sensitive to the value of elasticity of marginal utility, the key parameter used to calculate the equity weight. Higher values of elasticity of marginal utility increase benefits for disadvantaged communities but reduce the overall economic benefits from investments, highlighting the trade-offs in incorporating equity into adaptation planning.


Introduction
Climate-induced sea-level rise (SLR) is accelerating flood hazards in many coastal areas around the world, potentially compounded by changing storm climatology in many regions (Fox-Kemper et al 2021).This global challenge necessitates effective and equitable climate adaptation policies and investments, particularly since flood risk is not equally distributed across socioeconomic and demographic groups (Qiang 2019).In general, those who are most vulnerable and least resilient to natural hazards, which tend to be racial and ethnic minorities and low-income households, are disproportionately exposed to flood hazards (Collins et al 2019, Wing et al 2022).Public investments in climate adaptation have the potential to mitigate or exacerbate these existing social inequities.Relatedly, highincome communities and households may have the resources to adapt independently, while low-income communities will require greater public assistance to cope with these challenges.Consideration of these factors is essential to ensure that climate adaptation policies promote fairness and maximize overall societal well-being.
Addressing these challenges will require the implementation of a multitude of adaptation measures, including building retrofit, property buyouts, and construction of levees, seawalls, and surge barriers to protect coastal areas (Aerts et al 2014, 2018, Peng and Song 2018, Haasnoot et al 2020, Bongarts Lebbe et al 2021, Griggs and Reguero 2021, Han and Mozumder 2021).These adaptive measures can significantly reduce flood risk, but are often costly and their efficacy may vary spatially.In guiding adaptation decisions and federal disaster mitigation funding, economic benefit-cost analysis (BCA) plays a crucial role in ensuring the efficiency of investments, often in the form of comparing the benefits and costs of various measures and project alternatives through mean benefit-cost ratio (BCR).In the U.S., federal project approval often requires that the expected benefits exceed costs of a project, such that every dollar invested yields more than one dollar in return, as stipulated by the office of management and budget (OMB) in OMB Circular A-94 (White House 2023).
BCA is crucial for efficient federal spending but can exacerbate distributional inequities (Fothergill et al 1999, Hallegatte et al 2020).Federal regulatory impact assessments rarely evaluate distributional impacts (Robinson et al 2016).The USACE typically measures flood mitigation benefits by avoided property damage, favoring higher value properties and ignoring the diminishing marginal utility of income.This method risks biasing investments towards affluent households without enhancing overall societal welfare or equity (Kind et al 2020).Ideally, accounting for the diminishing marginal utility of income suggests maximizing social welfare through protection of high-value properties with compensatory transfers to low-income households .However, such transfers are rarely politically viable.A 'second-best' approach prioritizes maximizing social welfare directly through resource allocation, despite potential efficiency losses as per the Kaldor-Hicks criterion.In economic terms, 'efficiency losses' here refer to situations where the economic benefits are reduced for a given level of investment-specifically, the value of benefits foregone by not following the allocation that maximizes unweighted economic returns.
Equity-weighted utility functions are designed to address distributional inequalities by assigning more value to the benefits for lower-income groups and less for higher-income ones.Central to this approach is the elasticity of marginal utility (ϵ), which measures how utility changes with increased consumption.This concept suggests that an additional $100 enhances the welfare of a low-income individual more significantly than it does for a wealthy one.The U.S. OMB recommends using 1.4 as the income elasticity of marginal utility in regulatory analysis.
Equity weights have been applied in a range of academic contexts, including assessments of flood impacts (Frontuto et al 2020, Gourevitch et al 2020) and estimates of the social cost of carbon (Anthoff et al 2009).They are also used by the U.K. government to assess alternative policy options (HM Treasury 2022), but have traditionally not been used in U.S. regulatory analysis.However, in the recent additions to Circular A-4 and A-94, released in November 2023, the U.S. Office of Management of Budget states that 'Agencies may choose to conduct a BCA that applies weights to the benefits and costs accruing to different groups in order to account for the diminishing marginal utility of goods when aggregating those benefits and costs' (White House 2023).
The application of equity weights in federal benefit-cost analyses is controversial among economists (Office of Management & Budget 2023) as evidenced by the pushback OMB received in its public comments on the proposed updates to Circular A-4.First, there are practical analytical concerns about the feasibility of adequately disaggregating benefits and costs among sub-groups.Second, there are empirical concerns regarding interpersonal comparisons of utility and parametric uncertainty in the elasticity of marginal utility of income.Third, there are political concerns about evaluating improvements to social welfare rather than Kaldor-Hicks efficiency.We attend to each of these concerns by: (1) demonstrating the feasibility of distributional analysis, (2) examining the sensitivity of our results to a range of equity weights, and (3) evaluating trade-offs between welfare and efficiency.
In this research we evaluate the impact of applying income-based equity functions in adaptation decision-making in the face of changing coastal flood hazards, focusing on building-level retrofit and buyout policies.Given BCA's potential impact on socioeconomic disparities, this research will analyze how applying equity weightings to flood mitigation BCA can mitigate inequalities and benefit disadvantaged communities.Additionally, the study will explore the sensitivity of decision making to changes in marginal utility values and the trade-offs between equity considerations and economic efficiency in flood mitigation.The goal is to enhance the understanding of the effectiveness of weighted BCA and its implications for equitable flood adaptation decision making.

Flood damages and exposure data
We model storm tide flood hazards using storm tide distributions for current  and future (2081-2100) climates under the SSP2-4.5 scenario of moderate emissions reductions and balanced demographic and economic growth (Xi et al 2023).These hazards are modeled using a coupled climatologicalhydrodynamic model (Lin et al 2012, Gori et al 2022), previously applied in coastal adaptation studies for New York City (NYC) (e.g.Aerts et al 2014).We integrate these projections with SLR distributions from the IPCC 6th Assessment Report (Fox-Kemper et al 2021, Garner et al 2022), focusing on median SLR estimates and the 33% and 66% percentiles.These SLR projections incorporate oceanographic changes, land ice loss, and vertical land movement, excluding subsidence from human activities.The storm tide and SLR data for NYC are interpolated over the 21st century for our analysis.
We access building data for NYC from the MapPLUTO database of the NYC Department of City Planning (New York City Department of City Planning 2023).This database contains various information about each structure: the number of stories; the building type; the year of construction; the year of renovation; the building's assessed value and the square footage.We focus for this study only on residential property to incorporate equity considerations.
Following Aerts et al (2014), we assess flood depths for each building using a static inundation method (known as a 'bathtub' approach) where regions are flooded if the coastal water level exceeds the level of ground elevation.The 'bathtub' static approach was shown to generate results similar to those from dynamic modeling for the NYC region (Orton et al 2015).The elevation of each building is derived from LiDAR data with a resolution of 1 square meter (City of New York 2023).
We focus here on two common adaptation measures at the building level: building buyouts (an example of retreat) and retrofit (an example of accommodation).We apply these measures only to properties that are exposed to the 100 year flood event, as a proxy for repetitive loss properties, resulting in 407 429 residential buildings considered in the study.A 'buyout' typically refers to the process where government agencies purchase homes from private homeowners in flood-prone areas, effectively relocating residents to areas that may have lower exposure to flood hazard.The buyout cost is assumed to be the cost of the structure and land value.
Retrofit is the combination of building elevation of 1 foot above FEMA's Base Flood Elevation (BFE; representing the 100 year flood level) and wetproofing.Following the framework of Aerts et al (2014), if the building is a mutli-dwelling with more than 5 units (RES3C-RES3F) we apply wetproofing, otherwise we apply elevation measures.Additionally, if the building is above 4 floors, we apply wetproofing regardless of building type.Wetproofing is assumed to reduce damage by a factor of 50% (Aerts et al 2014).We apply these measures only to properties that are exposed to 100 year flood event, as a proxy for repetitive loss properties.The unit cost of building elevation for each building is obtained from FEMA (Federal Insurance and Mitigation Administration 2009).To calculate the cost of building retrofit for each residential structure, the building footprint for each building is multiplied by the estimated cost per square feet to elevate or wetproof the structure.
Damage assessment for each event is determined through the utilization of stage depth-damage curves, which delineate the proportion of damage sustained by a building and its contents based on the water level above the building's first flood elevation or wetproof level.The damage computation adheres to the HAZUS-MH methodology (Federal Emergency Management Agency 2009), which serves as the prevailing standard for flood risk assessments in the United States (Federal Emergency Management Agency 2009).HAZUS is equipped to evaluate damage across a spectrum of 33 distinct building types, encompassing 11 categories of residential structures.
For each building with a given adaptation measure, we evaluated the present value of expected avoided damages over a 50 year time horizon from 2005 (chosen to align with the flood hazard simulations) to 2055.In any given year, the annual exceedance probability, p, of a damage level is 1 j , where j equals the expected recurrence interval.The expected annual damages for each building for a given year (t), EAD t , can be calculated as an integration of the damages for flood levels, D, with respect to p: Following Olsen et al (2015), we solved the integral for a given scenario using the trapezoidal rule, a simple and commonly applied numerical integration technique.In this equation, j represents the flood recurrence interval from the 2 year interval to the 3000 year interval (assuming jth year flood would cause jth year flood damage): ,10,25,75,100,2000,3000} The benefits of each measure for each building is referred to as the avoided EAD (EAD avoided ): where, for build retrofit, EAD adaptation is the damage for a building when a measure is enacted and EAD baseline is the damage assuming no adaptive measure has been taken.The assumed benefit, EAD avoided , for retreat represents the damages that would occur if no measures were taken, and EAD adaptation is assumed to be zero.
We then estimated the present value of benefit for each building (PV t ) from 2005 to 2055.We used a discount rate of 2%, which is consistent with the value suggested in OMB guidelines: where t is the year, and ρ is the discount rate.

Equity weighted BCA
We apply equity weights to our estimated avoided damages to account for the diminishing marginal utility of income.These weights operationalize the assumption that a dollar of avoided damages to a low-income household yields great improvement to social welfare than a dollar of avoided damages to a high-income household.We estimate these weights at the Census tract level, based on the guidance in the recently revised OMB Circular A-4 (White House 2023).We calculate the weight for Census tract i (w i ) using census level median income data (ȳ i ) and the medium income for all census tracts in NYC (y med ).The 12 month mean census level income data used here is from 2022 (United States Census Bureau 2022).The weight is where ϵ is the elasticity of marginal utility.OMB has concluded that 1.4 serves as a justifiable estimate for the income elasticity of marginal utility to be employed in regulatory assessments, based on the study of Acland and Greenberg (2023) where the present values of benefits and costs for each measure are summed over all buildings (k) in each census tract (i).

Socio-economic metrics
A 'disadvantaged community' can be broadly defined as a community that experiences a higher degree of socio-economic, health, and environmental burdens compared to other communities (White House Council on Environmental Quality and U.S. Digital Service 2022).This definition encompasses not only economic hardship, as indicated by metrics such as income levels and employment rates but also includes factors such as exposure to pollution, limited access to clean water and healthy food, inadequate housing, and insufficient healthcare and educational facilities.We identify disadvantaged communities using socioeconomic metrics from two sources to explore the impact of the equity-weightings on distributional inequalities: the first is the Climate and Economic Justice Screening Tool (CEJST) (White House Council on Environmental Quality and U.S. Digital Service 2022) and the second is the New York State Climate Justice Working Group Disadvantaged Communities data set (New York State Climate Justice Working Group 2023).
The CEJST aims to highlight disadvantaged census tracts across all 50 states, the District of Columbia, and the U.S. territories.From this data set we use the 'Identified as disadvantaged' metric to categorize whether each census tract in NYC is classified as 'disadvantaged' .Specifically, a census tract is identified as disadvantaged if it is above a defined threshold for one or more 'burdens' related to the environmental, energy, housing and pollution conditions, amongst others.The disadvantaged threshold for each burden is typically greater than the 90th to 95th percentile compared to all other census tracts.For this analysis in NYC, 760 of the 1796 census tracts are identified as 'disadvantaged' .
The indicates the share of people earning less than twice the federal poverty level, identifying those with low incomes but not in extreme poverty.This measure helps evaluate economic hardship and eligibility for social programs.

Results
Our analysis uncovers complex patterns in the values of the BCR among census tracts that have diverse socio-economic characteristics.Negative correlations are found between the unweighted BCR and socio-economic indices across different census tracts (figures 1 and 2).Specifically, the BCR for building retrofit policies exhibited a negative correlation with the vulnerability score (−0.32; 95% confidence interval (CI) −0.36 to −0.27), the proportion of disadvantaged neighborhoods (−0.09; 95% CI −0.14 to −0.04), and the percentage of population living below 200% of the federal poverty line (−0.13;95% CI −0.18 to −0.08; figure 1).Similarly, the BCR for building buyout policies also show negative correlations with these socio-economic metrics: vulnerability score (−0.11; 95% CI −0.16 to −0.06), share of disadvantaged neighborhoods (−0.09; 95% CI −0.14 to −0.05), and percentage below the poverty line (−0.14;95% CI −0.18 to −0.09), as depicted in figure 2. These results initially suggest that unweighted benefits of avoided damages tend to aggregate in advantaged communities.
Applying equity weighting based on median household income results in shifts in these correlations.With equity weighting ϵ values of 1.4 and 3, we  observed a reversal in the trends, turning the correlations positive (figures 1 and 2).For building retrofit, the BCR correlation with vulnerability score, share of disadvantaged neighborhoods, and percentage below the poverty line increases to 0.33 (95% CI 0.29-0.38),0.21 (95% CI 0.16-0.26),and 0.49 (95% CI 0.45-0.52)respectively with an ϵ value of 3, as shown in figure 1.This shift indicates that the incorporation of income-based equity weightings redistributes benefits, favoring vulnerable and less economically stable communities.Furthermore, the strength of these correlations intensifies with increasing marginal utility values, suggesting a robust relationship between equity weightings and the redistribution of benefits.
In a further analysis, we categorize the census tracts based on the CEJST's 'Identified as disadvantaged' metric.The resulting bar charts in figure 3 demonstrate a stark contrast in unweighted BCR values between disadvantaged and non-disadvantaged tracts.Notably, disadvantaged tracts have considerably lower BCR values compared to census tracts not identified as disadvantaged.However, the inclusion of equity weightings significantly elevates the mean BCR in these disadvantaged tracts while simultaneously lowering it in the non-disadvantaged ones.
We also explore the spatial distribution of BCR, particularly under the influence of equity weightings.In the unweighted BCA, Manhattan, Brooklyn and Jamaica Bay show the highest BCR values for building retrofit, while also showing high values for buyout policies (figure 4).With the inclusion of equity weights, there are notable decreases in BCR values for some regions, particularly in western Manhattan and Brooklyn, as well as a substantial increase in BCR across most of Jamaica Bay, the Bronx, and the Lower East Side of Manhattan (figures 4(c)-(f)).This spatial redistribution highlights how equity weightings can significantly influence the geographical distribution of benefits.
Finally, we seek to assess the economic efficiency of adaptation measures as a function of the ϵ value for different levels of hypothetical investment (ranging from $150 million to $750 million; figure 5), distributed based on the BCR for each census tract.The analysis reveals significant reductions in the absolute benefits of adaptation measures as the ϵ value  increases, particularly noting that the magnitude of benefit reduction escalates with higher investment levels.Specifically, for retrofit measures, an investment of $500 million witnesses a decrease in benefits from $1.6 × 10 10 to 0.4 × 10 10 with with ϵ value changing from 0 to 5 (figure 5(a)).Concomitantly, as the ϵ value rises, there's a marked increase in the percentage of investment directed towards disadvantaged communities, escalating from 50% to over 90% for building retrofit (figure 5(c)).This shift illustrates the trade-off between maximizing total economic benefits and achieving a more equitable distribution of those benefits among affected populations using this approach.We observe a plateau in the total benefits curves beyond an elasticity of 3, as illustrated in figure 5.This trend suggests that at higher levels of elasticity, interventions continue to target the same properties within disadvantaged communities.Consequently, increases in elasticity beyond this point do not substantially alter the total benefits accrued.This indicates a saturation point where further increases in elasticity yield diminishing effects on the equity condition.
Comparatively, retrofitting measures typically exhibit lower BCR values than buyouts (figure 4), likely reflecting retrofitting's relatively constrained effectiveness in mitigating repetitive flooding compared to the more definitive flood risk elimination offered by buyouts.Thus, retrofit initiatives are predominantly implemented in more affluent and less disadvantaged areas (figure 5), and applying equity weights under retrofitting measures shifts a more significant proportion of investments towards disadvantaged communities, compared to buyouts.

Discussion
In this study, we examined the implementation of adaptive measures in NYC with the goal of understanding the distributional impacts of applying equity weights to BCA.In general, the benefits of building level adaptation and retreat outweight the costs, providing an economically viable opportunity to reduce flood damages.When benefits are unweighted, BCRs are generally highest in census tracts with low vulnerability and less disadvantaged communities.These results indicate a potential implicit bias in resource allocation towards areas with lower proportions of vulnerable or economically challenged populations.Our results demonstrate that the incorporation of equity weightings can substantially alter this bias.
The process of setting equity weights bears notable similarities to the challenges encountered in establishing appropriate discount rates, as discussed by Weitzman (2013).In both instances, decisions regarding the appropriate parameter value require normative judgements.The White House OMB offers guidance to federal agencies on these parameter values, yet there remains a lack of consensus among economists.Determining the appropriate equity weight should be grounded in rigorous analysis of the elasticity of marginal utility (e.g.Viscusi and Aldy 2003, Acland and Greenberg 2023), but also requires careful evaluation of community preferences for what constitutes an equitable distribution of benefits and costs.This task is inherently subjective, as it involves balancing diverse and often conflicting interests and values within a community.This subjectivity introduces a degree of uncertainty and complexity in the application of equity weights, as the chosen weights may reflect the preferences of only a subset of the community or be influenced by the decision-makers' biases.
The findings of our study shed light on the potential impact of equity weightings on hazard mitigation funding within the United States, particularly under the frameworks of the USACE investments in flood mitigation infrastructure and FEMA's BRIC program.The introduction of equity weights into the BCR calculations significantly alters the decisionmaking landscape at the census tract level, underscoring the tangible on-ground consequences of such an approach.This analysis also underscores the tradeoffs involved in integrating equity considerations into adaptation planning and investment.While higher ϵ values significantly enhance the share of benefits for disadvantaged communities, they also lead to substantial reductions in the absolute economic benefits derived from such investments.This highlights the critical need for balancing efficiency and equity in climate adaptation strategies to ensure both effective and fair outcomes.
While our findings are immediately applicable to the NYC context, the methodology developed can be adapted for other regions.The goal of this study is not only to enhance understanding of the effectiveness of weighted BCA in NYC but also to provide a framework that other regions could modify to reflect their unique circumstances, thus supporting broader applicability in equitable flood adaptation decisionmaking.
By incorporating equity weights, our BCA indirectly considers factors like income, housing, education, and resident impacts.Our study, while focused on quantifiable aspects of hazard mitigation, acknowledges the omission of non-monetized and nonquantified benefits and costs (Sinden 2019) that are challenging to measure but critical for a comprehensive evaluation (Federal Emergency Management Agency 2023) such as long-term environmental impacts and ecosystem services vital for community wellbeing.Although not fully quantified, the significance of these elements necessitates a detailed qualitative evaluation.Environmental effects are particularly important as they directly affect natural environments and their associated benefits.

Figure 1 .
Figure 1.The census-aggregated benefit-cost ratio (BCR) for building level retrofit is compared with three metrics from the New York State Climate Justice Working Group: (a) the vulnerability index, (b) the proportion of neighborhoods classified as disadvantaged, and (c) the percentage of the population living below 200% of the federal poverty level.In the visualization, non-weighted BCR values are shown in blue, while equity-weighted values, using marginal utility values of 1.4 and 3, are depicted in green and red, respectively.

Figure 2 .
Figure 2. The census-aggregated benefit-cost ratio (BCR) for building buyout is compared with three metrics: (a) the vulnerability index from the New York State Climate Justice Working Group, (b) the proportion of neighborhoods classified as disadvantaged, and (c) the percentage of the population living below 200% of the federal poverty level.In the visualization, non-weighted BCR values are shown in blue, while equity-weighted values, using marginal utility values of 1.4 and 3, are depicted in green and red, respectively.

Figure 3 .
Figure 3. BCR for all census tracts based on whether the census tract has been identified as disadvantaged according to the CEJST dataset.The bars show the unweighted and equity weighted BCR values based on median SLR estimates.The error bars show the range of the results from 33% and 66% uncertainty in SLR estimates.

Figure 4 .
Figure 4. Maps of unweighted BCR for (a) retrofit and (b) buyout adaptation measures.(c)-(f) Spatial changes in the BCR with the incorporation of equity weights.

Figure 5 .
Figure 5. Panels (a) and (b) compare the total benefits of retrofit and buyout measures for ϵ values for different levels of investment.Panels (c) and (d) focus on the distribution of benefits by percentage of neighborhoods that are identified as disadvantaged with investment level (shape of point).The colors of the points on (c) and (d) represent the value of elasticity.
who collected 1711 estimates from 158 separate studies from the U.S. and U.K.However, in these studies the ϵ value ranges from 0.5 (Viscusi and Aldy 2003, Viscusi and Masterman 2017) up to 4 (Pindyck 1988).We primarily concentrate on two specific values of 1.4 and 3, but also investigate the sensitivity of decision making to range of values.The weighted BCR for each census tract (BCR i ) is calculated as: