# Exposing Disparities in Flood Adaptation for Equitable Future Interventions

Lidia Cano Pecharroman<EMAIL_ADDRESS>Department of Urban Studies and
Planning, Massachusetts Institute of Technology, 77 Massachusetts Ave,
Cambridge, MA 02139, USA  ChangHoon Hahn  Department of Astrophysical
Sciences, Princeton University, Peyton Hall, Princeton NJ 08544, USA

###### Abstract

As governments race to implement new climate adaptation policies that prepare
for more frequent flooding, they must seek policies that are effective for all
communities and uphold climate justice. This requires evaluating policies not
only on their overall effectiveness but also on whether their benefits are
felt across all communities. We illustrate the importance of considering such
disparities for flood adaptation using the FEMA National Flood Insurance
Program Community Rating System and its dataset of $\sim$2.5 million flood
insurance claims. We use CausalFlow, a causal inference method based on deep
generative models, to estimate the treatment effect of flood adaptation
interventions based on a community’s income, diversity, population, flood
risk, educational attainment, and precipitation. We find that the program
saves communities $5,000–15,000 per household. However, these savings are not
evenly spread across communities. For example, for low-income communities
savings sharply decline as flood-risk increases in contrast to their high-
income counterparts with all else equal. Even among low-income communities,
there is a gap in savings between predominantly white and non-white
communities: savings of predominantly white communities can be higher by more
than $6000 per household. As communities worldwide ramp up efforts to reduce
losses inflicted by floods, simply prescribing a series flood adaptation
measures is not enough. Programs must provide communities with the necessary
technical and economic support to compensate for historical patterns of
disenfranchisement, racism, and inequality. Future flood adaptation efforts
should go beyond reducing losses overall and aim to close existing gaps to
equitably support communities in the race for climate adaptation.

##  1 Introduction

Flooding constitutes nearly a third of all losses from natural disasters
worldwide (Reuters, 2022). In the US alone, flooding causes more damage than
any other severe weather-related event, with annual losses averaging over $5
billion (NOAA, 2014). These losses are only expected to multiply as climate
change raises the sea level and increases the frequency of extreme weather
events (Rodell & Li, 2023). By the end of the century, rising sea levels and
coastal flooding are estimated to cost the global economy $14.2 trillion (a
fifth of the global GDP) in damaged assets (Kirezci et al., 2020). In
response, communities are rapidly enacting flood adaptation measures (Jongman
et al., 2014; Wahl et al., 2015; Alfieri et al., 2016). As these measures have
emerged so has evidence of their success (Deegan, 2007; Highfield & Brody,
2017; Asche, 2013; Brody et al., 2009; Davlasheridze et al., 2013; Kousky &
Michel-Kerjan, 2017). However, there is still a gap in understanding whether
and how the effectiveness varies across different communities.

A better understanding of the effectiveness of flood adaptation policies and
their connections to the communities implementing them can ensure that they
have the intended effect. It can also ensure that flood adaptation investments
deliver on the desired goals and effectively allocate limited resources for
climate adaptation. Furthermore, it can prevent climate interventions from
unknowingly replicating historical patterns of discrimination (Mitchell et
al., 2015; Simpson et al., 2022; Ranganathan & Bratman, 2021). This is
especially critical in light of recent evidence highlighting patterns of
inequality in flood preparedness and recovery processes in the US (Cutter &
Finch, 2008; Emrich et al., 2020; Tate et al., 2021; Wing et al., 2022; Flores
et al., 2023).

We reexamine the effectiveness of flood adaptation interventions by evaluating
not only whether they are effective but also for whom. We measure the
effectiveness of flood adaption interventions across different types of
communities using a US wide data set on flood insurance payments from the
National Flood Insurance Program (NFIP) Community Rating System (CRS). FEMA
initiated the CRS in 1990 in order to improve community flood adaptation and
resilience. The program is based on a set of prescriptive activities
recognized as best practices for flood risk reduction. These constitute flood
adaptation recommendations that are prevalent in flood planning across the
world. To join the CRS, communities must implement a series of flood
adaptation activities: _e.g._ floodplain mapping, open space preservation,
stormwater management activities, or public information and participation
programs. In exchange, residents of the community receive a discount on their
flood insurance premium rates. More than 1,500 out of roughly 20,000
communities in the NFIP are currently part of the CRS program (FEMA, 2021).

In 2019, FEMA released the NFIP Redacted Claims data set that contains roughly
2.5 million flood insurance claims. It contains claims from communities
participating in the CRS as well as claims from communities who did not
participate in the CRS, but were eligible for insurance coverage because they
complied with minimum floodplain regulation requirements. Thus, the Redacted
Claims data set provides an ideal quasi-experimental setup. Insurance claims
losses, which we use as a proxy for flood loss, can be compared between CRS
participants and non-participants to quantitatively assess the effectiveness
of the CRS flood adaptation activities.

Capitalizing on this quasi-experimental setup, past literature examined
whether the CRS led to a reduction in flood claims (Michel-Kerjan & Kousky,
2010; Davlasheridze et al., 2013; Highfield & Brody, 2017; Kousky & Michel-
Kerjan, 2017; Gourevitch & Pinter, 2023). Despite some studies finding the
contrary (Asche, 2013), the overall consensus is that flood losses are reduced
by the CRS. There has been, however, little investigation on whether the
program’s effectiveness varies across different types of communities. There
has also not been any systematic analysis on the disparities in flood
adaptation initiatives across communities in the broader international
literature.

Past literature has shown that low-income communities respond to risks
differently to safeguard their livelihoods (Haque, 2021) and deploy flood-
coping mechanisms in the absence of flood protection (Brouwer et al., 2007).
It also highlighted the need to promote pro-poor climate adaptation
initiatives and acknowledge the need need to strengthen low-income household’s
asset base to improve their adaptation (Mearns & Norton, 2010). Furthermore,
some studies have predicted flood losses and vulnerabilities for different
types of communities (Knighton et al., 2020; Wing et al., 2020; Yang et al.,
2022). Nevertheless, no work so far quantifies how the benefits/savings of
flood adaptation activities are distributed across different communities. That
is the main goal of this paper.

Accurately estimating the causal effect of flood adaptation policies and its
dependence on community characteristics requires modeling their relationship.
This is especially challenging since the relationship can be highly non-
linear, complex, and correlated, which violates the assumptions of many
standard causal inference methods. In this work, we tackle these challenges
using CausalFlow, a novel method that leverages deep generative models to
measure the causal effect in a data-driven approach. With our method, we
examine for the first time the effectiveness of the CRS as a function of key
community characteristics such as population, income, diversity, and
educational attainment at high-resolution on a zip code level over the entire
continental US. We conclusively assess the effectiveness of the CRS flood
adaptation activities and shed light on who benefits the most from it and
under which circumstances. Our results provide key insight for communities
tailoring flood adaptation interventions. It also provides a path forward to
re-envisioning flood adaptation in ways that can benefit a broader spectrum of
communities in the face of climate change.

Figure 1:  Top panel: We compile our dataset (blue) from the FEMA FIMA NFIP
Redacted Claims dataset (black) with additional information on community geo-
demographic characteristics (precipitation, flood risk, income, population,
renter fraction, educational attainment, and diversity fraction) from
additional datasets (Section 2). Bottom panel: Communities that participated
in the CRS are part of the treated group (orange), while the communities that
did not are part of control group (blue)

##  2 Data

For this work, we compile a dataset based on the FEMA Flood Insurance
Mitigation Administration NFIP Redacted
Claims111https://www.fema.gov/openfema-data-page/fima-nfip-redacted-claims-v1
data with additional information on community characteristics. From the NFIP
dataset, we use data on CRS participation, the date of flood loss, and the
total claims paid on building damages and content from the loss. We combine
all the entries for a zip code and calculate the total claims paid per policy.

For each zip code, which we refer to as a community, we quantify its flood
risk using scores compiled in the First Street Foundation
dataset222https://firststreet.org/data-access/getting-started-with-first-
street-data/. The risk scores are computed based on factors including risk of
flooding from high-intensity rainfall, overflowing rivers and streams, high
tides, and coastal storm surges. We further supplement the dataset with census
data from the US Census Bureau American Community
Survey333https://www.census.gov/programs-surveys/acs/news/data-releases.html,
which is compiled in four year intervals: $2008-2012$, $2012-2016$, and
$2016-2020$. We assign median income and number of residents (population) of
the communities based on their zip code and date of loss. We also calculate
the fraction of residents that rent, have a Bachelor’s degree or more advanced
degrees, and do not identify as only white. We refer to each of the
characteristics as the renter fraction, educational attainment, and diversity
fraction, respectively. Lastly, we include average precipitation in
millimeters during the month of the flood event for each community. This data
was extracted by splitting the PRISM climate group
data444https://prism.oregonstate.edu/ compiled by the Northwest Alliance for
Computational Science and Engineering using US zip code boundaries from 2020.

In total, our dataset includes 14,729 unique communities. In the top panel of
Figure 1, we mark the communities that are included in our dataset (blue) from
the full NFIP dataset (black) on a map of the US. Our final dataset is
publicly available at XXXXX.

##  3 Methods: CausalFlow

One of the main goals of causal inference is to measure the treatment effect
of a policy, like the CRS. For heterogeneous treatments, the effect is
quantified using the conditional average treatment effect (CATE), the ATE as a
function of covariates. By revealing the dependence of the treatment effect on
covariates, CATE provides a more detailed understanding of the causal path.
Given outcome $Y$, covariates $X$, and variable $T$ that indicates the control
($T=0$) or treated ($T=1$) groups, CATE is estimated as:

${\rm CATE}=E[~{}Y\,|\,X,T=1~{}]-E[~{}Y\,|\,X,T=0~{}].$ (1)

$E[~{}Y\,|\,X,T=0,1~{}]$ represents the expected value of $Y$ given $X$ for
the control and treated groups, respectively.

Typically, CATE is estimated using either matching or linear regression. In
matching, samples in the treated group are matched to ones in the control
based on their $X$ values. CATE is then estimated by comparing the outcomes of
the matched samples. Even prevalent methods, such as synthetic control (Abadie
& Gardeazabal, 2003; Abadie et al., 2010) or propensity score matching
(Rosenbaum & Rubin, 1983), match samples based on some finite volume in
covariate space, which can lead to incorrect estimates of the CATE.

The other approach is regression, most commonly with linear models (Angrist,
1990; Miguel & Kremer, 2004). A model of $Y$ as a linear function of $X$ is
fit to the data and then used to estimate CATE. In many scenarios, assuming a
linear model is incorrect. For instance, there is no reason to expect flood
losses to depend linearly on its population, or median household income.
Furthermore, there is often no a priori knowledge of the functional form that
should be adopted for a model of $Y$.

We can instead estimate the CATE without any of these assumptions. We rewrite
Eq. 1 as

${\rm CATE}=\int Yp(Y|X,T=1)\,{\rm d}Y-\int Yp(Y|X,T=0)\,{\rm d}Y,$ (2)

where $p(Y|X,T=1)$ and $p(Y|X,T=0)$ are the conditional probability
distribution of $Y$ given $X$ for the treated and control groups. If we can
estimate $p(Y|X,T=1)\approx q_{T}(Y|X)$ and $p(Y|X,T=0)\approx q_{C}(Y|X)$ and
sample from them, $Y_{T,i}^{\prime}\sim q_{T}(Y|X)~{}{\rm
and}~{}Y_{C,j}^{\prime}\sim q_{C}(Y|X)$, we can estimate CATE using Monte
Carlo integration:

${\rm
CATE}=\frac{1}{N_{T}}\sum\limits_{i=1}^{N_{T}}Y_{T,i}^{\prime}-\frac{1}{N_{C}}\sum\limits_{j=1}^{N_{C}}Y_{C,j}^{\prime}.$
(3)

Deep generative models from machine learning (_e.g._ ChatGPT, Dall-E) enable
us to accurately estimate and sample from $p(Y|X,T=0,1)$. In this work, we use
normalizing flow models (Tabak & Vanden-Eijnden, 2010; Tabak & Turner, 2013),
which use a bijective transformation, $f:z\mapsto x$, that maps a complex
target distribution, $p(x)$, to a simple base distribution, $\pi(z)$, in our
case a Gaussian. $f$ is defined to be invertible and to have a tractable
Jacobian so that target distribution can be evaluated from the base
distribution: $p(x)=\pi(z)|\det\frac{\partial f}{\partial x}^{-1}|$. A neural
network is used for $f$ to provide an extremely flexible mapping that can
estimate complex distributions. This neural density estimation approach has
been used extensively in a variety of fields spanning neuroscience (_e.g._
Gonçalves et al., 2020) to astrophysics (_e.g._ Alsing et al., 2019; Hahn &
Melchior, 2022).

Using normalizing flows555We use Masked Autoregressive Flow (MAF; Papamakarios
et al., 2018) models implemented by Greenberg et al. (2019); Tejero-Cantero et
al. (2020), we estimate $p(Y|X,T=1)\approx q_{\rm T}(Y\,|\,X)$ and
$p(Y|X,T=0)\approx q_{\rm C}(Y|X)$ for the treated and control groups
separately. We describe the training of our normalizing flows $q_{\rm T}$ and
$q_{\rm C}$ in Appendix A. Our outcome, $Y$, is the total insurance claims per
policy in dollars. We use seven covariates, $X$: precipitation, flood risk,
income, population, renter fraction, educational attainment, and diversity
fraction (Section 2). The treated group consists of communities participating
in the CRS, while the control group consists of non-participants. In the
bottom panel of Figure 1, we mark the communities in the treated (orange) and
control (blue) groups of our dataset.

Once trained, we can evaluate CATE at any given value of the covariates using
$q_{\rm T}$, $q_{\rm C}$, and Eq. 3, as long as it is within the support of
the covariates in our data. We detail how we ensure this in Appendix B.
CausalFlow relaxes the strong assumptions made in standard causal inference
methods. It learns the detailed relationship between $X$ and $Y$ from the data
to provide an accurate and robust estimate of the treatment effect.

Lastly, we introduce a correction, $\Delta Y$, to the CATE to account for the
outreach component of the CRS program:

${\rm CATE}^{\prime}={\rm CATE}+\Delta Y.$ (4)

Communities in the treated group are informed of how to successfully file
their claims. We estimate in Appendix C that the outreach component alone
increases the total insurance claims per policy by $\Delta Y\sim$ $9,780.
Since this increase is not a reflection of any change in flood losses, the
CATE in Eq. 3 underestimates the impact of the CRS. Thus, we include $\Delta
Y$ and correct for the effect of outreach to more accurately quantify the
treatment effect on flood loss. Throughout this work, we refer to ${\rm
CATE}^{\prime}$ as the CRS savings.

Figure 2:  Flood loss savings from the CRS program (CATE’) for 27 community
typologies with different population, income, and diversity. In each panel, we
vary a single community characteristic, (a) average monthly precipitation, (b)
educational attainment, and (c) flood risk score, to highlight its impact on
CRS savings. All other characteristics are fixed to fiducial values (Appendix
D). The CRS saves policyholders an average of $5,000–15,000 per policy.
However, the efficacy of flood adaption depends significantly on income,
population, diversity, precipitation, educational attainment, and flood risk.

##  4 Results

###  4.1 The Effectiveness of Flood Adaptation Measures

With CausalFlow, we can estimate the impact of the CRS flood adaptation
activities on the total insurance claims per policy for any set of community
(zip code) characteristics. In other words, we can measure the “treatment
effect” of implementing CRS activities and quantify how much a policyholder
saves on average thanks to the program. In order to systematize our results,
we define 27 distinct community typologies categorized by population, income,
and diversity (see Appendix D for details). Then, we compute their CATE’ for
different values of average precipitation, flood risk, renter fraction, and
educational attainment.

In Figure 2, we present the CATE’ of all 27 community typologies as a function
of (a) average precipitation, (b) educational attainment, and (c) FSF flood
risk score. In each panel, we vary a single characteristic while keeping all
others fixed. We do this for each typology, represented by a single line. This
enables us to isolate and examine the effect of a specific characteristic on
the CATE’. Overall, we find that the CRS saves policyholders an average of
$5,000 - 15,000 per policy. For certain communities, the savings can exceed
$20,000. Our findings are consistent with previous evidence, which found that
the CRS led to a 40 percent reduction in losses at the county level (Highfield
& Brody, 2017) and a $2.8 – 5.5 million reduction in damages for a particular
flood event (Michel-Kerjan & Kousky, 2010).

Beyond estimating the overall savings on flood losses, we can also assess the
CRS by examining the effect of average precipitation on savings. Flood losses
are typically worsened by compounded water runoff from higher precipitation
(_e.g._ Bevacqua et al., 2019; Jang & Chang, 2022; Xu et al., 2023). Yet in
Figure 2a, we find that for nearly all of the community typologies, the CRS
savings increase with higher average precipitation. Our results firmly
illustrate the CRS program’s overall effectiveness in mitigating flood losses.

The program’s overall success does not paint the full story. Our results show
that while the CRS is effective, the benefits are not felt evenly across
different communities. This serves as critical evidence for rethinking and
reimagining future flood adaaptation policies that aim to equitably reduce
flood losses for all communities. In the following, we present two lines of
action in designing and evaluating future strategies.

###  4.2 Tailored Requirements and Resources

Community characteristics play a major role in the effectiveness of current
flood adaptation measures. To increase flood savings for all communities will
require tailoring such measures. For example, while the CRS is effective at
reducing flood losses at higher precipitation, certain communities go against
this trend. In particular, communities with high population, high diversity,
and mid to high income (black dotted in Figure 2a), see their savings steeply
decrease with higher precipitation — _i.e._ flood adaptation measures are less
effective. A geospatial analysis of these communities indicates that nearly
all of them are in urban areas (Figure 7, Appendix E). Urbanized areas have
higher percentages of impervious surfaces that increase water runoff and can
cause or worsen flooding (Pasquier et al., 2022). For these urban communities,
flood adaptation programs should require activities geared towards  _e.g._
decreasing surface imperviousness.

Figure 3:  The population dependence on the CRS savings. We present the CRS
savings for the 27 community typologies, same as in Figure 2, highlighting the
high population (orange) and low population (blue) communities. Flood
adaptation measures are more effective for high population communities, who
save $\sim$$4000 per policy more than low population communities.

We also find a significant population dependence. In Figure 3, we present the
CRS savings for the 27 community typologies as a function of precipitation,
flood risk score, and educational attainment, same as in Figure 2. We
highlight the communities with a high population in orange and a low
population in blue. Overall, flood adaptation measures are more effective for
high population communities. They save $\sim$$4000 per policy more than less
populated communities. Combined with previous work, which found that highly
populated communities are also more likely to adopt CRS activities (Asche,
2013), our results suggest that flood adaptation programs favor populous
communities.

Less populated communities may not have the personpower required to implement
the prescribed activities,  _e.g._ lacking access to public servants and
workers with a wide range of technical expertise. The smaller tax base may
also limit the resources available to implement flood adaptation. In field
interviews, we found that the acquisition or relocation of flood-prone
buildings was limited by the lack of resources available at the local level.
The implementation of some CRS activities may also require the types of public
services or resources that are not economically feasible for small
communities. For instance, the implementation of a flood mapping exercise may
prove resource intensive. Hence, future programs should provide the necessary
technical support and incentivize collaboration among adjacent communities.

Finally, we find that the effectiveness of the CRS depends on the communities’
educational attainment. In Figure 2b, we present the CRS savings for the 27
community typologies as a function of educational attainment, which we define
as the fraction of inhabitants with a Bachelor’s or higher degree. Past
evidence already suggests that there is an initial barrier to joining the CRS
related to education, where communities with higher educational attainment are
more likely to participate (Posey, 2008; Li, 2012; Fan & Davlasheridze, 2014).
Our results show that even after communities join, the effectiveness hinges on
their education. The dependence on education translates into a gap of up to
$\sim$$2,000 per policy in savings.

Out of the 19 creditable activities that communities can implement, many
require significant capacity building and technical expertise: _e.g._ the
establishment of flood warning systems and the building and inspection of
levees. Communities with lower educational attainment may not have the
expertise readily available and community buy-in may be more difficult. In
response, future programs should include interventions that reduce the
educational/technical barriers and provide the necessary technical assistance
along with tailored community outreach resources.

The trends presented in this section make it clear that future flood
adaptation programs should tailor their required adaptation measures. This is
especially the case if program implementation is linked to incentives such as
flood insurance price reduction. If programs reward a community’s adaptation,
then not all “low hanging fruit” interventions should qualify for the reward.
Instead, communities should be required to implement the types of flood
adaptation interventions that are most effective for their needs. At the same
time, future programs must furnish communities with the necessary resources to
overcome any financial/technical/educational barriers in complying with such
requirements. Only then we can expect a just and equitable distribution of the
benefits of climate adaptation. Next, we illustrate the importance of
considering the inequities and disparities of flood adaptation programs.

###  4.3 Climate Justice

An effective and far-reaching flood adaptation strategy requires embedding
climate justice at its core. Our results show that the effectiveness of a
program is tied to economic and racial disparities. For example, although
flood adaptation is effective overall for low-income communities, it is less
effective when they are located in high flood risk zones. The trend is
reversed for affluent communities. We highlight this in Figure 2c, where we
show CRS savings as a function of flood risk for low (light blue) and high-
income (dark blue) communities. Our results suggests that the most economical
CRS activities may only be effective at lower risk. Meanwhile interventions
that fare well at higher risk can only be afforded by high-income communities.
Evidently, flood adaptation cannot be left to a community’s resources alone,
especially since average annual flood losses are disproportionately borne by
poorer communities (Wing et al., 2022).

Figure 4:  CRS savings for low-income communities with high (solid) and low
diversity (dotted; predominantly white) as a function of precipitation (left),
educational attainment (center), and flood risk (right). We include the other
community typologies for reference (gray). Although both communities have the
same income level, highly diverse communities have significantly lower flood
loss savings. The gap between high and low diversity exists for communities
with low (blue; top), mid (green; middle), and high (orange; bottom)
populations. This diversity gap exceeds $6,000 per policy in certain cases.

Furthermore, we find that even within low-income communities, there is a
systematic gap in the CRS savings between diverse and predominantly white (low
diversity) communities. In Figure 4, we present the CRS savings for low-income
communities with high (solid; predominantly white) and low diversity (dotted;
predominantly non-white). Since the highlighted communities have the same low
income, the comparison between the solid and dotted lines illustrates the sole
effect of diversity. Overall, the program is significantly less effective for
communities with higher diversity. In some cases, the gap exceeds $6,000 per
policy. This points to the program’s inability to breach existing patterns of
discrimination and racial inequality (Mitchell et al., 2015; Ranganathan &
Bratman, 2021; Simpson et al., 2022).

This gap is consistent with patterns of inequality found in flood preparedness
and recovery more broadly (Cutter & Finch, 2008; Emrich et al., 2020; Tate et
al., 2021; Wing et al., 2022). Flores et al. (2023) exposed inequalities in
the delineation of flood zones in FEMA maps, where “Black and Asian
neighborhoods experience disproportionate risk in federally overlooked pluvial
and fluvial flood zones” (p.1). Other works have shown that the type of flood
adaptation measures employed correlate with diversity (Siders & Keenan, 2020).
Measures like “retreat” correlate with high racial diversity while measures
like “shoreline armoring” correlate with a less diverse population. Such
differences reflect the real choices that historically disenfranchised
communities make based on the accessibility of certain types of solutions.

We show that flood adaptation programs can perpetuate institutional racism,
through tangible effects on savings, or lack thereof. Future programs should
re-examine the processes, structures, and existing assumptions of flood
adaptation prescriptions and incentives under the lens of equity, diversity,
and inclusion. This will be particularly salient as the evidence
overwhelmingly shows that the currently most disadvantaged communities are
projected to suffer the most from the consequences of climate change.
Embedding these priorities at the core of future programs will be crucial to
close existing gaps and support all communities in mitigating flood losses.

##  5 Discussion & Conclusion

In this work, we find clear trends between flood loss savings and community
characteristics. This provides strong evidence that the success of future
flood adaptation interventions should not only be measured based on whether
they reduce losses, but also on whether the benefits are equitably
distributed. Below, we discuss some of the caveats and limitations of our work
and outline future research.

First, we note that our results are measured using data from households with
access to flood insurance. Hence, our results do not reflect the communities
without flood insurance. Even though the threshold to access it is relatively
low, it is not negligible. While some of the communities without insurance are
ones that face no significant flood risks, they disproportionately include
communities without access. Kousky et al. (2020) found that income of
policyholders was higher than non-policyholders, which suggests that
affordability is a significant concern. In fact, while a quarter of
policyholders are classified as lower income, the fraction is over a half for
non-policyholders (FEMA, 2018). Although we cannot quantify flood losses for
uninsured communities using our dataset, we expect that including their losses
would only widen the gaps in savings between privileged and disenfranchised
communities.

We also note that the savings estimates in this work are conservative. In
calculating the CRS savings, we correct for the outreach component, where
communities receive information on how to successfully file their claims
($\Delta Y$ in Eq. 4). This correction is estimated by comparing non-CRS
communities to CRS communities that participated in activities for public
information and scored below 10% on all other activities. The ideal comparison
would be to compare non-participants to CRS communities that only participated
in public information activities. However, this includes very few communities,
so we relax this selection. This likely leads to an underestimate of $\Delta
Y$ and, thus, the CRS savings. Furthermore, our control group consists of
communities that did not participate in the CRS but have access to the NFIP,
which requires them to regulate floodplain development. Although the
requirements are minimal, they may already have a slight effect in reducing
losses, which would also make our savings estimate conservative. In subsequent
work, we will explore the impact of the outreach component in further detail
by examining the proportion of successful payments before and after the
implementation of the CRS. Along these lines, we also find signs that the
outreach component could be driving elite capture. Savings on flood losses
decline for communities with the highest levels of educational attainment
(>50%; Figure 2c). Field interviews support the possibility that some
households are learning to “game the system” in order to refurbish their homes
after a flooding event. Further research, however, is necessary for a more
systematic understanding.

Our estimate of flood loss savings is also conservative because preventing
damage to homes mitigates further ripple effects in the livelihoods and well-
being of communities. Exposure to flood-damaged homes is linked to an increase
in mental and health disorders (Graham et al., 2019), death and injury risk,
disease outbreaks (_e.g._ gastroenteritis; Alderman et al., 2012), trauma,
anxiety (Walker-Springett et al., 2017), and work disruption (Peek-Asa et al.,
2012). For every dollar saved in flood losses in our results, we can expect a
far larger reduction in the true loss.

This study underscores the importance of accounting for complex dependencies
when evaluating the effectiveness of adaptation efforts and designing future
ones. The CRS, as a program that prescribes a wide range of flood adaptation
interventions, serves as an ideal example to showcase the importance of
evaluating these efforts from a climate justice lens. The complex dynamics of
climate change require a granular understanding of its effect as well as the
impact of interventions aimed to combat it. In this regard, the rapid
development of deep generative models presents a unique opportunity to move
beyond current causal inference approaches. Together with increased investment
in data generation, CausalFlow and similar approaches will be capable of
addressing previously intractable causal inference queries that are crucial in
designing future policy interventions.

In summary, this study shows that even though current flood adaptation
practices reduce flood losses, the savings vary greatly across communities.
Future adaptation pathways need to consider key community characteristics in
providing the necessary solutions and resources. They must also embed equity
priorities at their core to break existing patterns of inequality and
discrimination so that all communities can benefit from climate adaptation
investment into the future.

## Acknowledgements

We would like to thank Peter Melchior, Sebastian Sandoval Olascoaga, Mariana
Arcaya, and Lawrence Susskind for their valuable discussions. LC was supported
by the La Caixa Foundation. CH was supported by the AI Accelerator program of
the Schmidt Futures Foundation.

##  Appendix A Normalizing Flow Training

We estimate the CATE of the CRS on total insurance claims per policy using two
normalizing flows, $q_{\rm T}$ and $q_{\rm C}$, that estimate the distribution
of insurance claims given the covariates for the treated and control samples,
respectively (Eq. 3). Below, we describe how we train $q_{\rm T}$ and $q_{\rm
C}$ using our data sets from Section 2. We use the same training procedure for
both $q_{\rm T}$ and $q_{\rm C}$.

We begin by splitting each of the treated and control data sets into training,
validation, and test sets with a 80/10/10 split. We then use the ADAM
optimizer (Kingma & Ba, 2017) to maximize the total log likelihood
$\sum_{i}\log q(Y_{i}\,|\,X_{i})$ over the training set. This is equivalent to
minimizing the Kullback-Leibler divergence between $q$ and the target
distribution. We prevent over-fitting by evaluating the total log likelihood
on the validation data at every epoch and stopping the training when the
validation likelihood fails to increase after 20 epochs.

We train $\sim$2000 flows with architectures determined by the Akiba et al.
(2019) hyperparameter optimization. We select the five flows with the lowest
validation losses and construct our final flow as an equally weighted ensemble
of the flows: $q_{\phi}(Y\,|\,X)=\sum_{j=1}^{5}q_{\phi,j}(Y\,|\,X)/5$.
Ensembling flows with different initializations and architectures has been
shown to improve the overall robustness of normalizing flows (_e.g._
Lakshminarayanan et al., 2016). After training, we use the test set to verify
that $q_{\rm T}$ and $q_{\rm C}$ accurately estimate $p(Y|X,T=1)$ and
$p(Y|X,T=0)$. Specifically, we use simulation-based calibration (Talts et al.,
2020) and the Lemos et al. (2023) coverage test to confirm that both $q_{\rm
T}$ and $q_{\rm C}$ are near optimal estimates $p(Y\,|\,X,T=1)$ and
$p(Y\,|\,X,T=0)$.

Figure 5: Distribution of $\log\mathcal{Q}_{\rm C}(X^{\prime})$ evaluated for
covariate values in the control (blue) and treated (orange) sample. For a
given set of covariate values, $X^{\prime}$ we evaluate $\log\mathcal{Q}_{\rm
C}(X^{\prime})$ and $\log\mathcal{Q}_{\rm T}(X^{\prime})$. If both are above a
conservative threshold (black dashed), we consider it within the support of
our treated and control sample. Otherwise, we consider it outside of the
support and refrain from evaluating CausalFlow on $X^{\prime}$.

##  Appendix B Covariate Support

CausalFlow can evaluate the CATE at any given value of the covariates within
the support of the treated and control data, _i.e._ the given covariate is
within the covariate distribution of the treated and control groups.
CausalFlow is based on normalizing flows $q_{T}$ and $q_{C}$, trained on the
treated and control data, respectively. So evaluating the CATE for any
covariate outside their support would mean evaluating $q_{T}$ and $q_{C}$
beyond the covariate distribution they were trained on, _i.e._ extrapolation.
The accuracy of CausalFlow is not be guaranteed in this regime. In this work,
we avoid this scenario by only evaluating CausalFlow on covariate values
classified as being within our treated and control distributions.

For the classification, we train two additional normalizing flows,
$\mathcal{Q}^{T}(X)$ and $\mathcal{Q}^{C}(X)$, that estimate the distribution
of X (community properties) of the treated and control samples. We follow
roughly the same training procedure outline in Appendix A; however, unlike
$q_{T}$ and $q_{C}$, $\mathcal{Q}_{\rm T}$ and $\mathcal{Q}_{\rm C}$ are not
conditional distributions. For a given coviarate $X^{\prime}$, we evaluate the
log probabilities $\log\mathcal{Q}_{\rm T}(X^{\prime})$ and
$\log\mathcal{Q}_{\rm C}(X^{\prime})$. If both are above the threshold -10, we
classify $X^{\prime}$ as within the treated and control support and proceed
with evaluating CausalFlow. Otherwise, we classify $X^{\prime}$ as outside of
the support. The threshold log probability value is empirically determined and
conservatively set to correspond to the $\sim$1 percentile of the log
probability distribution. We illustrate this in Figure 5, where we present the
distribution of $\log\mathcal{Q}_{\rm C}(X^{\prime})$ values evaluated on the
control (blue) and treated (orange) sample. We mark our threshold in black
dashed. Our approach for classifying out-of-distribution covariate values is
similar to methods for outlier detection (_e.g._ Liang et al., 2023; Böhm et
al., 2023).

Figure 6:  The distribution of total insurance claim per policy for non CRS
communities (black) and CRS communities that mainly participate in the 300
Series activities (orange). The distribution qualitatively show that the
outreach component of the CRS increases claims overall. The outreach
activities provide guidance for the community on successfully filing claims.
Based on a comparison of these two sets of communities in Appendix C, we find
that the outreach component alone increases claims by $\sim$$9,780 USD per
policy. We correct for this effect in the CATE in Eq. 4 to derive CATE’, the
CRS savings.

##  Appendix C Impact of Outreach on CRS Savings

The CRS includes an outreach component where communities are informed how to
successfully file their flood loss claims. The outreach itself would not
impact actual flood looses. Yet, we expect this outreach to increase the total
insurance claims per policy for communities in the CRS. If uncorrected, this
would lead to an overall underestimation of the savings from the CRS program.
Since our primary goal is to accurately measure the impact of the CRS on flood
losses, we correct for this effect. Below, we describe how we estimate the
effect of outreach alone.

FEMA compiles a CRS Communities Credit File data set, which provides detailed
information on the points each CRS community receives for how effectively they
implement the various CRS activities. Following a request to FEMA, we received
access to these scores over the years 2010 to 2020 and cross-matched the
scores to entries in our NFIP Flood Losses dataset (Section 2). The activities
are categorized into 4 sets of activities: 300, 400, 500, and 600 series. They
refer to activities for public information, mapping and regulations, flood
damage reduction, and warning and response, respectively. This means that we
can isolate the effect of outreach by comparing the insurance claims of CRS
communities that primarily participate in the 300 activities to our control
group, the non-CRS communities.

We first select communities in the CRS that participate in the 300 activities
and score below 10% on the 400, 500, and 600 activities. These are communities
that participate in outreach activities but do not effectively implement other
flood management activities. This “CRS 300 Series” sample contains 36 zipcodes
with 1955 entries. In Figure 6, we compare the distribution of total insurance
claims per policy of this sample (orange) to the distribution of our control
group (black). The comparison reveals that communities participating in
outreach have significantly higher insurance claims per policy than the
control sample.

To quality the effect of outreach more accurately, we take a similar approach
as CausalFlow. For each entry in the “CRS 300 Series” sample with covariate
values, $X^{\prime}$, we compute the expected insurance claim per policy if
the entry was in the control group: $E[\,Y\,|\,X^{\prime},T=0]$ (Eq. 1). We
use the normalizing flow, $q_{\rm C}$, from CausalFlow, with the same
procedure as Eq. 3. We then calculate the difference between the actual
insurance claim of the entry and the expected control value:
$Y^{\prime}-E[\,Y\,|\,X^{\prime},T=0]$. The median value of the effect in the
CRS 300 Series sample is $9,780 USD.

Our estimate confirms that the outreach component of the CRS indeed
significantly increases the total insurance claims per policy. In principle,
if there were more communities in the CRS that only participated in the 300
activities, we could estimate the effect of outreach as a function of the
covariates using the same approach as CausalFlow. However, given our limited
sample size, we examine the effect as a function of each covariate. We find no
significant trends. Therefore, we use the median value as a fixed correction
for the effect of outreach on the CRS savings.

##  Appendix D Community Typologies

With CausalFlow, we can examine the effectiveness of flood management
activities (CATE) as a function of our 7 covariates: income, population,
diversity, preciptation, flood risk, renter fraction, and educational
attainment. A 7 dimensional covariate space, however, is challenging to
interpret. Instead, we systematize our results by examining the CATE for a
fixed set of 27 communities typologies defined by a permutation of income,
population, and diversity.

The flood planning literature has shown that income, population, and diversity
can explain uneven flood damage and loss exposure, as well as differing
capabilities in preparing for and recovering from floods. For instance, Tate
et al. (2021) illustrated that social vulnerability is a crucial indicator of
flood exposure. Where population, race/ethnicity, and socioeconomic status
have been found as the main components of such social vulnerability in
relation to natural hazards (Cutter & Finch, 2008). Previous work has also
found that community income and race/ethnicity are associated with
disproportionate flood impacts and unequal recovery (Tate et al., 2021; Wing
et al., 2022). The contribution of population, income, and race/ethnicity to
the communities’ vulnerability vary significantly across counties (Cutter et
al., 2003), so we define our community typologies using all of three
characteristics.

| Low | Mid | High
---|---|---|---
Median Income (USD) | 40,000 | 60,000 | 90,000
Population | 2,500 | 12,000 | 30,000
Diversity Fraction | 0.05 | 0.15 | 0.4
Table 1:  Income, population, and diversity fraction values used to define the
27 community typologies for which we examine the CRS savings. For the
typologies, we use all possible permutations of the low, mid, and high values.

For the actual income, population, and diversity values of the community
typologies, we use values that roughly correspond to the 16, 50, and 84th
percentiles of the full data set. In Table 1, we list the low, mid, and high
income, population, and diversity fraction values used in this work. We take
all possible permutations of the values to define $3\times 3\times 3=27$
community typologies.

In addition to income, population and diversity, we also determine the
fiducial values of the other covariates for the 27 typologies. For each
typology, we first select communities in our full data set with similar
income, population and diversity. Afterwards set the fiducial covariate value
of the typology as the median precipitation, flood risk, renter fraction, and
educational attainment values of the selected communities. By taking the
median values, we select the covariate valuesto form each typology.

##  Appendix E High Population, High Diversity, Mid to High Income

In Figure 7, we examine the geospatial distribution of high population, high
diversity, and mid to high income communities (orange) compared to the rest of
the communities in our data set (gray). The communities are highly localized
and adjacent to the major cities that we labeled for reference. This
localization suggests that these communities are in major urban areas.

Figure 7:  We highlight the communities in our data set (gray) that have high
population, high diveristy, and mid to high income (orange). For reference, we
mark the location of major cities near these communities. Compared to other
communities in the data set, these communities are clearly located in major
urban areas.

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