Seawalls and Stilts: A Quantitative Macro Study of

Climate Adaptation

Stephie Fried∗

May 18, 2018

Abstract

We develop a structural macroeconomic model of adaptation investment to reduce thedamage from extreme weather. The framework modies the Aiyagari-style model to applyin a new setting in which a continuum of heterogeneous localities experience idiosyncraticextreme weather shocks. Localities can invest in adaptation capital to reduce the damagefrom extreme weather and they can purchase insurance to smooth consumption. A federalgovernment taxes localities and provides partial disaster relief. We calibrate the model tomatch variation in FEMA aid per event across US counties with dierent risks of extremeweather. We use the calibrated model to quantify the amount and eectiveness of adaptationcapital, the moral hazard consequences of FEMA policy, and the role of adaptation in re-sponse to climate change. We nd that storm-related adaptation capital is 0.7 percent of theUS capital stock and reduces the damage from extreme weather by one third. Additionally,the moral hazard eects of FEMA policy on adaptation and the associated extreme weatherdamage are substantial. We introduce climate change into the model as a permanent, in-crease in the severity of extreme weather. We nd that adaptation reduces the welfare costof this climate change by 25 percent.

∗Arizona State University W.P. Carey School of Business. Email: sdfried@asu.edu

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1 Introduction

The severity of extreme weather events is likely to increase over time as a result of climate

change (IPCC 2000; IPCC 2014). These events often involve large costs; for example, over

half of the hurricanes that have made landfall in the US since 2000 have caused over 1 billion

dollars in damage.1 Federal aid for disaster relief through FEMA can reduce the costs to

households hit by extreme weather. Households and local governments can further mitigate

these costs by investing in capital whose primary purpose is to reduce extreme weather

damage. Examples of such adaptation capital include storm drains, levees, and wind-proof

garage doors. While adaptation investments are possible in theory and certainly occur in

practice, we have little evidence on the aggregate eects of adaptation on extreme weather

damage, or on how incentives for adaptation investment are inuenced by FEMA policy.

Understanding these questions is particularly important, given the large predicted increases

in extreme weather severity as a result of climate change.

With these questions in mind, this paper develops a quantitative macro model of adap-

tation investment. We focus explicitly on storm-related extreme weather such as tropical

cyclones, blizzards, tornadoes and heavy rain or snow storms.2 The framework modies the

Aiyagari-style heterogeneous agent model (Aiyagari, 1994) to apply in a new setting with a

continuum of heterogeneous localities that experience idiosyncratic extreme weather shocks.

A bad extreme weather shock (e.g., a storm) destroys a fraction of the locality's capital

stock. A social planner in each locality can invest in adaptation capital to reduce the dam-

age from extreme weather, and can purchase insurance to smooth consumption. A federal

government taxes localities and uses the revenue for disaster aid and subsidies for adaptation

investment, analogous to the functions of FEMA in the US.

To obtain meaningful quantitative insights, the model must capture the eectiveness of

adaptation capital at reducing the damage from an extreme weather event. We cannot es-

1Source: http://www.aoml.noaa.gov/hrd/tcfaq/E23.html and NCEI Billion dollar damage data.2Our analysis does not apply to non-storm related extreme weather such as wildres or incidents of

extreme heat.

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timate this relationship directly because we do not have comprehensive data on adaptation

capital. Such data would require cost estimates of all large scale public adaptation invest-

ments, such as sea walls and city drainage systems, and all small-scale private investments,

such as the investment required to ood-proof a home or a business. Instead, we discipline

the model parameters using a method-of-moments approach that exploits variation in the

frequency with which US counties experience extreme weather events and the FEMA aid

(one measure of damage) they receive from an event. The intuition is that, all else constant,

counties that more frequently experience extreme weather events face stronger incentives to

invest in adaptation capital, which reduces the damage per event.

The calibrated model itself yields two key ndings. First, we quantify the level of adap-

tation capital across localities with dierent risks and severities of extreme weather events.

Low risk localities with relatively mild extreme weather events do not invest in any adap-

tation capital. In contrast, in high risk localities, with more severe extreme weather events,

adaptation capital is over 1.5 percent of the total capital stock. For the aggregate US econ-

omy, adaptation capital equals 0.7 percent of the total capital stock, or approximately 400

billion in 2016 dollars.

Second, we quantify the eect of the existing levels of adaptation capital on the damage

from an extreme weather event. In the low risk localities, adaptation capital is zero and thus

has no eect on the damage per event. In contrast, the higher risk localities have substantial

adaptation capital, which reduces the damage per event by over 40 percent. Aggregating

these eects across the dierent risk regions in the US, we nd that on average the US avoids

over 74 billion (in 2016 dollars) in damage per year because of adaptation, the equivalent of

0.4 percent of 2016 GDP.

We use our calibrated model to conduct two counterfactual experiments. In the rst

experiment, we analyze the moral-hazard eects of FEMA policy. Moral hazard could occur

because FEMA disaster aid reduces localities' incentives to invest in adaptation capital. We

calculate a no-FEMA stationary equilibrium in which we set FEMA aid and adaptation

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subsidies equal to zero. We compare adaptation capital, average damage, and welfare in the

no-FEMA equilibrium with their corresponding values in our baseline equilibrium (which

includes FEMA policy). We nd that in the aggregate economy, FEMA policy reduces

adaptation capital by 10 percent, which in turn increases the average damage from extreme

weather by 5 billion (in 2016 dollars) each year. To put this result in perspective, storm-

related FEMA aid averages 6.7 billion per year.3 Thus, the increase in damage from moral

hazard is almost 75 percent of the FEMA aid for disaster relief. These large moral hazard

eects combined with substantial FEMA-induced transfers from low to high risk localities,

imply that eliminating (storm-related) FEMA has almost no eect on aggregate welfare,

measured in terms of consumption equivalent variation.

We conduct a second counterfactual experiment to evaluate the potential for adaptation

to mitigate the welfare cost of climate change. Following the scientic literature, we model

climate change as a permanent increase in extreme weather severity (Villarini and Vecchi

2013; Villarini and Vecchi 2012). Our central case corresponds to a 75 percent increase in

severity. We calculate two climate change stationary equilibria, one in which adaptation can

respond to the increase in weather severity and one in which it cannot. In our central case,

climate change increases adaptation investment by 75.4 percent. This adaptation response

reduces the increase in damage as a result of climate change by 40 percent, and decreases

the associated welfare cost of climate change by 25 percent.

While these results suggest large potential for adaptation, we caution that adaptation

investment is characterized by substantial diminishing returns. We calculate the average

elasticity of damage with respect to adaptation capital for increases in storm severity ranging

from 50 -100 percent.4 This elasticity is negative, indicating that adaptation reduces damage.

However, the magnitude of the elasticity falls from -25 percent to -20 percent as the severity

of climate change increases from 50 to 100 percent, implying that the marginal eects of

3The average is taken over the period for which FEMA data are available, 2004-2016.4The elasticity of damage with respect to adaptation capital is the percent change in damage divided by

the percent change in adaptation capital.

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adaptation on damage are smaller at higher levels of adaptation capital.

This paper builds on an earlier environmental literature that allows agents to reduce the

damage from climate change through adaptation. Many of these earlier models focus on the

role of adaptation as a component of optimal or second-best climate policy.5 As a result,

adaptation capital is typically decided at the country level and applies to many types of

damage from climate change, ranging from extreme weather to disease. Such an aggregate

perspective makes it dicult to obtain a realistic calibration to quantify the existing levels

and eectiveness of adaptation capital. A primary contribution of the present paper is to

model adaptation in a way that is consistent with the historical data on extreme weather

events and FEMA aid for disaster relief. This approach allows for an empirically grounded

calibration of the key model parameters and thus produces plausible estimates of the existing

levels and eectiveness of extreme weather adaptation capital across US regions.

The intuition for the calibration strategy derives from an earlier empirical literature

that looks for evidence of adaptation from the frequency with which an area experiences an

event, such as a hurricane or a very hot day, and a measure of the associated damage per

event, such as mortality or crop loss.6 While these papers often nd evidence of adaptation,

the methodology does not permit the authors to quantify the amount of adaptation or its

eectiveness at reducing the damage. Understanding current levels of adaptation and its

eectiveness are key to quantifying adaptation's role in mitigating the damage from climate

change.

Finally, this paper also contributes to the growing literature on environmental macroe-

conomics. For example, Golosov et al. (2014) use a dynamic stochastic general equilibrium

model to calculate the optimal carbon tax. Barrage (2017) modies a Ramsey-style optimal

5See for example Agrawala et al. (2011), Barrage (2015), Bosello et al. (2010), Brechet et al. (2013),DeBruin et al. (2009), Felgenhauer and Bruin (2009), Felgenhauer and Webster (2014), Kane and Shogren(2000), and Tol (2007). Bosello et al. (2011) provides a nice overview.

6A negative relationship between frequency and damage per event suggests that it is possible to adapt.Barreca et al. (2016), Gourio and Fries (2018), Heutal et al. (2017), Hsiang and Narita (2012), Keefer etal. (2011), and Sadowski and Sutter (2008) nd evidence of a negative relationship, and thus suggest thereis potential for adaptation. Dell et al. (2012) and Schlenker and Roberts (2009) do not evidence of thisnegative relationship. Hsiang (2016) provides a nice overview of this literature.

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tax model to analyze the interactions between a carbon tax and scal policy. Acemoglu

et al. (2012), Casey (2017), and Fried (2018) adapt models of directed technical change to

evaluate the eects of climate policy on innovation.7 Like this earlier work, the present paper

modies a quantitative macroeconomic model to study environmental policy. However, to

my knowledge, this is the rst paper to apply an Aiygari-style heterogenous agent model to

a setting with extreme weather shocks and adaptation.8

The paper proceeds as follows: Section 2 describes the model and Section 3 discusses the

calibration. Section 4 reports the quantitative results. Finally, Section 5 concludes.

2 Model

Time is discrete and innite. The economy is composed of N regions which are dieren-

tiated by their risk of an extreme weather event and the corresponding severity of the event.

We use the term extreme weather event to refer any severe storm-related weather including

tropical cyclones, blizzards, tornadoes, or very heavy rain or snow. Each region i contains a

continuum of measure one of ex-ante identical localities. Each locality, j, is populated by a

unit mass of innitely lived, identical agents. An agent can take two actions to decrease the

welfare cost of extreme weather events: (1) she can invest in adaptation capital to reduce

the damage from extreme weather and (2) she can purchase weather insurance to smooth

consumption. A federal government presides over all the localities and provides aid for those

localities that experience extreme weather, analogous to actions of FEMA in the US.

Each locality is run by a social planner who makes investment, consumption, and insur-

ance decisions to maximize the expected lifetime welfare of households in her locality, taking

the actions of other localities as given. In practice, adaptation capital can be either public

or private. For example, an individual household can raise its house on stilts to reduce ood

7Hassler et al. (2016) and Heutal and Fischer (2013) both provide a nice overview of this literature.8In a similar style to the present paper, ongoing work by Krusell and Smith develops a global Aiyagari-

style model to analyze the progression of climate change and the eects of climate policy across dierentregions (Krusell and Smith, 2017).

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damage while a local government can construct a seawall to protect coastal properties from

storm surges. Private investment in adaptation capital or the private purchase of insurance

does not generate any obvious local externalities. For example, the ood damage for one

household does not depend on whether the neighboring household raises its house on stilts

or purchases ood insurance.

Since there are no obvious local externalities, the model solution to this local planning

problem is equivalent to that of a Ramsey planning problem; that is a planner who makes

public adaptation investment decisions only, taking into account households' private adap-

tation investments and insurance purchases. Given this equivalence, we present the model

as a local social planning problem, its simplest possible form. We do not distinguish be-

tween public and private investments in adaptation capital, as this is not important for our

quantitative conclusions.

2.1 Extreme Weather

In each period, t, locality j in region i experiences a weather shock εijt ε 0, 1. We

interpret ε = 1 as extreme weather occurs and ε = 0 as extreme weather does not occur.

The weather shocks are i.i.d across localities.9 The realization of extreme weather damages

the productive capital stock, kp. Let dijt denote the capital stock destroyed by extreme

weather in county j in region i in period t,

dijt = εijtΩih(kaijt)kpijt. (1)

Parameter Ωi determines the severity of the extreme weather event in region i; all else

constant, increases in Ωi imply that extreme weather destroys a larger fraction of the capital

stock.

9In practice, extreme weather shocks are spatially correlated. However, event severity held constant, thedamage a locality experiences from an extreme weather event is independent of whether or not the neighboringlocality also experiences an extreme weather event. Given this independence, the spatial correlation ofextreme weather shocks is not important for the paper's quantitative results.

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Variable, ka denotes the capital stock used for adaptation. The planner in each locality

can invest in adaptation capital, ka, to reduce the damage from extreme weather in her local-

ity. Function h(ka) governs the process through which adaptation capital reduces damage.

Function h(ka) is decreasing and convex in ka, h′(ka) < 0, h′′(ka) > 0 implying that there are

diminishing returns to adaptation capital. For example, a planner might rst install storm

drains and then build a levee. Compared to the levee, the storm drains are relatively cheap

and more eective per dollar spent.

Variable pi is the region-specic probability of an extreme weather event (e.g., the proba-

bility that εijt = 1). By the law of large numbers, pi corresponds to the fraction of localities

in region i with ε = 1 in any period t.10

2.2 Production

Firms in each region, i, in each locality, j, produce a homogeneous nal good, yij, from

labor, lij and the non-damaged productive capital, kpij ≡ kpijt−dij, according to the production

function yij = F (kpij, lij). The nal good is the numeraire.

2.3 Federal Government

The rst purpose of the federal government in our model is to capture the benets and

incentives created by FEMA in the US. FEMA has two major functions: (1) it provides

nancial assistance to localities that experience extreme weather and (2) it subsidizes invest-

ment in hazard mitigation. Analogous to FEMA, our model federal government provides

aid for localities that experience extreme weather and provides a region-specic subsidy, si,

for investment in adaptation capital. Aid for extreme weather equals ψdijt, where ψ ε [0, 1] is

10Recent empirical studies suggest that agents do not internalize the true probability of extreme weatherinto their decision making process (Bin and Landry (2013) and Kousky (2010) and Gallagher (2014)). Inparticular, Gallagher (2014) shows that a Bayesian model in which agents update their ood risk beliefsbased on recent ood experiences and then forget ood experiences farther in the past can match theseempirical patterns. Modeling the planner's beliefs using Gallagher (2014)'s partial information model ofBayesian updating does not substantially change the aggregate implications of the model.

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the fraction of damage covered by the aid. The federal government nances the aid payments

and subsidies with uniform lump sum taxes, T ft , on the household.

The second purpose of the federal government is to run an insurance market for extreme

weather. The insurance market is designed to incorporate the benets and incentives created

by homeowners insurance and the National Flood Insurance Program (NFIP). The assump-

tion that the federal government runs the insurance market is reasonable in the case of the

National Flood Insurance Program (which is administered by the Federal government) but

less reasonable for homeowners insurance. Either way, it is not important for the quantitative

conclusions.

The local planner in each locality chooses her level of insurance coverage, xijt ε [0, 1].

Insurance claims equal xijtdijt. The insurance premium, qijt(xijt) in locality j in region i in

year t is

qijt(xijt) = λpixijth(kaijt)Ωikpijt.

Expression h(kaijt)Ωikpijt is the value of damage from an extreme weather event. Thus expres-

sion xijth(kaijt)Ωikpijt is the value of the associated insurance claims from the event. Multiply-

ing this expression by the probability of an extreme weather event, pi, yields the expected

value of insurance claims from extreme weather. This value is the actuarially fair insurance

premium.

Parameter λ is a wedge between the actuarially fair premium and the actual premium.

Perfectly functioning insurance markets would allow agents to completely smooth consump-

tion, eliminating all idiosyncratic risk. However, in practice insurance markets are not perfect

and thus agents cannot fully smooth consumption. For example, agents are not compen-

sated for the many transactions costs associated with the destruction of the capital stock.

Furthermore, the political history of the National Flood Insurance Program implies that

ood insurance premiums for many households do not equal the actuarially fair price (CBO

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2017; NRC 2015). The model is not suciently detailed to incorporate the many nuances of

the insurance market. Instead, we take a reduced form approach and model the insurance

premium as a wedge, λ, multiplied by the actuarially fair price.

Summing across localities in any period t, total premiums do not necessarily equal total

claims. This discrepancy creates a small surplus or shortage of funds in the insurance market.

We assume that the government nances a shortage with equal lump sum taxes on the

household, T h > 0, and returns a surplus with equal lump-sum transfers to the household,

T h < 0. Total lump sum taxes, T , are given by T ≡ T f + T h.

The role of insurance is simply to smooth a locality's damage from extreme weather

events across time. If the planner invests in adaptation capital, this investment reduces the

expected insurance claim, lowering the insurance premium.

2.4 Optimization

The planner in each locality divides output among consumption, investment in productive

and adaptation capital, and insurance premiums. Productive and adaptive capital accumu-

late according to the standard law of motion,

kpij,t+1 = (1− δ)kpijt + ipijt and kaij,t+1 = (1− δ)kaijt + iaijt + si,

where δ is the depreciation rate of capital and si is the region specic adaptation subsidy.

Variables ip and ia denote investment in productive and adaptive capital, respectively.

Following the realization of the extreme weather shock, the planner chooses consumption,

both types of investment, and next period's level of insurance coverage to maximize the

expected lifetime welfare of the representative household. The planner's value function is

given by,

V (kaijt, kpijt, xijt; εijt) = max

kaijt+1,kpijt+1,xijt+1

u(cijt) + ρEV (kaijt+1, k

pijt+1, xijt+1; εijt+1)

(2)

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subject to the damage from extreme weather (equation (1)), and the locality's resource

constraint,

cijt = yijt + (ψ + xijt)dijt − iai,j,t − ipi,j,t − Tt − qijt(xijt). (3)

Function u(c) denotes household utility and c denotes consumption. The planner forms her

expectation over εijt+1 based on the regional probability of extreme weather, pi.

An underlying assumption embedded in the resource constraint (equation (3)) is that the

representative agent's wealth is entirely contained within her locality. In practice, of course,

this is not true. Households can own stock which exists outside the locality and thus would

not be destroyed by an extreme weather event. However, for most households, the share

of stock holdings relative to total assets is relatively small, making the assumption that all

wealth is local more reasonable. For example, Wol (2017) calculates that stocks account for

less than 10 percent of middle class assets.11 Furthermore, many of these stock holdings are

tied up in retirement accounts; less than 5 percent of middle class assets are direct holdings

of corporate stock, nancial securities, mutual funds, and personal trusts. Thus, for the

typical US citizen, the vast majority of wealth is locally owned.12

2.5 Stationary equilibrium

We dene a stationary equilibrium in which aggregate macroeconomic variables are con-

stant. We suppress the t subscripts throughout the stationary equilibrium denition; we

signify a planner's chosen levels of capital and insurance coverage in the next period as k′

11The term middle class household refers to a household with wealth in the middle three wealth quintiles.12Relaxing the assumption that all wealth is local considerably complicates the model and introduces

assumptions that make the underlying mechanisms governing adaptation investment less transparent. Forexample, one could incorporate a portfolio choice where households allocate their wealth between local andnon-local capital. This introduces an additional state variable. Furthermore, under this setup, householdswould choose to fully diversify, investing all of their wealth in non-local capital. Matching the empiricalfact that most household wealth is local would require an additional behavioral assumption or underlyingpreference for local capital. Given, that almost all wealth for the typical US household is local, we choose toabstract from modeling the portfolio choice between local and non-local capital and thus avoid the associatedcomplications.

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and x′. The local state variables are adaptation capital, kaij, productive capital, kpij, the level

of insurance, xij, and the current realization of extreme weather εij. Let z denote the vector

of these state variables. The summations are taken over the distribution of localities over

the state space, z.

Given the level of FEMA aid, ψ, the adaptation subsidy, si, the probability of an

extreme weather event, pi, a stationary equilibrium consists of planners' decision rules

cij, ka′ij , k

p′

ij , x′ij, lump sum taxes, T , and the joint distribution of localities Φ(z), such that

the following holds:

1. The social planner in each region solves the optimization problem in Section 2.4.

2. The government budget balances:

∑TΦ(z) =

∑[ψdij + si + xijdij − qij(xij)]Φ(z)

3. The aggregate resource constraint holds:

Y + (1− δ)(Ka + Kp) = C +Ka′ +Kp′

where

Kp =∑

kpijΦ(z), Ka =∑

kaijΦ(z), Y =∑

yijΦ(z), and C =∑

cijΦ(z)

4. The distribution, Φ(z) is stationary.

3 Calibration and functional forms

The model calibration presents three key challenges: (1) we do not have an aggregate

comprehensive measure of adaptation capital, (2) we must determine when a locality expe-

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riences extreme weather, and (3) reliable, disaggregated data on extreme weather damage

are not readily available. We discuss our approach to each challenge in turn.

First, the absence of comprehensive data on adaptation capital means that we cannot use

adaptation capital as an input to the calibration. Instead, the aggregate value of adaptation

capital in the US is a key output from our quantitative model.

Second, to determine when a locality experiences extreme weather, we follow Gallagher

(2014) and use Presidential Disaster Declarations (PDDs) as a source for extreme weather

events. We map the localities in the model to counties in the US. We say that a county

experiences an extreme weather event in year t if it experiences at least one storm-related

weather incident in year t that received a PDD.13 An extreme weather event receives a

presidential disaster declaration when the damage is suciently large such that it is beyond

state and local capabilities to address.14

We divide the US counties into two risk regions, low and high, based on the annual

probability of an extreme-weather event. For each county, we calculate the probability of

an extreme-weather event as the number of extreme-weather events during the 29 years for

which consistent data on PDD events are available (1989-2017) divided by the total number

of years.15 We dene a county as low risk if its probability of an extreme weather event is

less than one third and high risk if its probability of extreme weather is greater than one

third. The average probability of an event in the low and high risk regions is 0.2, and 0.4,

respectively.

Figure 1 shows a map of the dierent counties shaded according to their risk region.

13Our analysis primarily includes tropical cyclones, blizzards, tornadoes, and other heavy rain or snowstorms.

14To request a PDD for extreme weather, local government ocials partner and FEMA regional ocialsto conduct a preliminary damage assessment which includes estimates of the total damage from the event,the unmet needs of individuals, families, businesses, and the impact to public property. If the total damageis so large that it is beyond state and local capabilities to address, the state governor can request a PDDfrom the FEMA regional director who can, in turn, request a PDD from the US president (FEMA, 2003).Specically, the total damage must exceed 1.30 per capita in 2011 dollars to warrant a PDD (McCarthy,2011).

15We begin in 1989 because the Staord Act, passed in 1988, considerably changed the FEMA system(FEMA, 2003).

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The high risk counties are predominately located in coastal areas that are susceptible to

hurricanes and tropical storms and in the Midwest where severe storms are also common.

Per-capita income in 2016 is similar across the high and low risk regions, equal to 40,535

in the low risk region and 41,274 in the high risk region (in 2016 dollars). Approximately

42 percent of the 2016 US population lives in high risk counties, while 45 percent of 2016

aggregate income derives from these counties.16

Figure 1: Map of US Counties By Risk Level

One potential concern with using PDD events to indicate extreme weather is that politics

could aect the declaration of a presidential disaster. For example, presidents may be more

likely to issue a disaster declaration in states with large swing voter populations or in states

with political ties to the White House or to congressional committees that oversee FEMA

(Reeves 2011; Davlasheridze et al. 2014).

However, for politics to aect our calibration, there would need to be systematic dier-

ences in the political power across the low and high risk counties over the 1989-2016 time

period. For example, we might worry that the high risk counties are high risk because they

are more politically connected and thus able to declare more disasters. However, the location

16County-level data on personal income are from the Bureau of Economic Analysis, downloaded on1/18/2018.

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of the high and low risk counties in Figure 1 suggests that this is not the case. The high

risk counties are primarily in areas with a high meteorological risk of extreme weather (e.g.

the gulf coast) and in states that span the political spectrum from Texas on the right to

New York on the left. Additionally, there was a lot of political turmoil during the 1989-2016

time period with presidents and house and senate majority leaders from both parties, major

within party divisions, and lots of turnover on the congressional FEMA oversight commit-

tees (Davlasheridze et al., 2014). Such turmoil makes it dicult for any particular county

to consistently receive political favors in the form of PDDs over this period.

To address the third calibration challenge, that reliable county-level data on all storm-

related extreme weather events is not readily available, we use data on FEMA aid instead of

data on damage.17 A PDD authorizes the federal government to provide disaster aid through

FEMA.18 To calculate FEMA aid for a year-t extreme-weather event, we take the sum of

all FEMA aid from all events that occurred in year t in the specic county. For example,

in 2005, Acadia Louisiana experienced two dierent PDD events (from hurricanes Katrina

and Rita) and received approximately 31 million (in 2005 dollars) in FEMA aid for both

events combined. We code this observation as Acadia experienced an extreme-weather event

in 2005 with aid payments equal to 31 million. Complete data on FEMA aid is available

from 2004-2016.19

A key assumption for our calibration strategy with FEMA aid to be meaningful is that

the fraction of damage the county receives in FEMA aid, ψ, is uncorrelated with total

17The Spatial Hazards and Losses Database for the United States (SHELDUS) reports county-level dam-age information for extreme weather events in the US. However, this data is severely incomplete. Theprimary source of the data are self-reports by individual weather stations and as a result, many observationsare missing. In particular, Gallagher (2014) reports that only 8.6 percent of ood-related PDD events from1960-2007 are included in SHELDUS and many of those events have no reported damage. As Gallagher(2014) notes, this is implausible, since damage estimates are prerequisite to a PDD declaration.

18FEMA aid includes both direct assistance to households through the Individuals and Households pro-gram (IHP) and assistance to local governments through the Public Assistance program (PA). Examplesof IHP aid include grants to help pay for emergency home repairs, temporary housing, personal propertyloss, and medical, dental and funeral expenses caused by the disaster. Examples of PA aid include funds foremergency relief and to repair or replace damaged public infrastructure. Data is available from fema.gov.

19Specically, data on IHP aid is available from fema.gov from 2004-2016 and data on PA aid is availablefrom fema.gov from 1998-2016.

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damage from the event. For example, if this assumption did not hold, then one might worry

that more severe events would receive a smaller fraction of damage in FEMA aid because of

government budget constraints. If counties in the high risk region systematically experience

more severe extreme weather, then these budget constraints imply that the high risk counties

would also systematically receive a smaller fraction of damage in FEMA aid.

To rule out this possibility, we construct an event level measure of FEMA aid relative

to damage. While county-level damage estimates are hard to nd, event-level damage and

fatality estimates for almost all tropical cyclones are available from NOAA's tropical cyclone

reports. Additionally, estimates of the direct damage and deaths for large disasters (those

with more than one billion dollars in estimated damage) are available from the Billion-Dollar

Weather and Climate Disasters database assembled by NOAA's National Center of Envi-

ronmental Information.20 Combined, NOAA's tropical cyclone reports and NCEI database

cover over half of the PDD events in our sample. Using the NOAA data, we dene the

damage from an event as the direct damage and plus any reported deaths multiplied by the

value of a statistical life.21

The left panel of Figure 2 plots FEMA aid as a fraction of damage for each event in the

NOAA sample. Hurricanes Katrina and Sandy are two clear outliers with damage estimates

of 63 and 150 billion in 2009 dollars, respectively. Similarly, midwest storms in 2008 and 2010

are also outliers with FEMA aid as a fraction of damage equal to 0.5 and 0.46, respectively.

The right panel of Figure 2 plots the data without these outliers. Visually, there is not

an obvious correlation between damage and the fraction of FEMA aid. Empirically, the

correlation coecient between these two variables is not statistically dierent from zero with

a p-values of 0.41 in the full sample and 0.52 in the sample without outliers. Furthermore, the

20To account for uninsured or under-insured losses, NOAA scales up insured loss data by a factor equal tothe reciprocal of the insurance participation rate in that region. For example, if a region had approximately50 percent policy protection under the National Flood Insurance Program (NFIP), NOAA would apply afactor of two to the region's NFIP claims in their calculation of total losses. We interpret the NOAA damageestimate as the actual damage from any extreme-weather event that is included in the NOAA data.

21We use the EPA's value of 7.6 million (in $2006) for the value of a statistical life (seewww.epa.gov/environmental-economics/mortality-risk-valuation).

16

coecient estimate in a simple regression of the fraction of FEMA aid on the total damage

equals 5.73e-13 with a standard error of 6.86e-13.22 Based on this evidence, we conclude that

a systematic correlation between damage and FEMA aid as a fraction of damage is highly

unlikely.

Figure 2: FEMA Aid as a Fraction of Damage For Extreme Weather Events

0 20 40 60 80 100 120 140 160

NOAA damage estimate (billions of 2009 $)

0

0.1

0.2

0.3

0.4

0.5

FE

MA

aid

as a

fra

ction o

f dam

age

NOAA sample

0 5 10 15 20 25 30 35

NOAA damage estimate (billions of 2009 $)

0

0.05

0.1

0.15

0.2

0.25

0.3

FE

MA

aid

as a

fra

ction o

f dam

age

NOAA sample without outliers

3.1 Parameter values and functional forms

The calibration has two steps. In the rst step, we choose parameter values for which

there are direct estimates in the data. In the second step, we calibrate the remaining pa-

rameters so that certain targets in the model match the values observed in the US economy.

Table 1 reports the parameter values.

22Similarly, in the sample without outliers, the coecient estimate in a simple regression of the fractionof FEMA aid on the total damage equals -1.01e-12 with a standard error of 1.56e-12.

17

Table 1: Calibration Parameters

Parameter Value Source

Production

Depreciation: δ 0.094 Method of moments

Capital's share: α 0.33 Data

Productivity: A 1 Normalization

Preferences

Discount factor: ρ 0.98 Method of moments

CRRA coecient: σ 2 Assumption

Federal policy

Adaptation subsidy: si = sIai 0.13 Method of moments

FEMA aid: ψ 0.11 DataInsurance wedge: λ 1.02 Method of moments

Extreme weather and adaptation

Low risk probability: pl 0.20 Data

High risk probability: ph 0.40 Data

Low risk event severity: Ωl 0.0075 Method of moments

High risk event severity: Ωh 0.0205 Method of moments

Adaptation: θ 10.00 Method of moments

3.2 Production

We use the standard Cobb-Douglas production function,

F (kpi,j, li,j) = A(kpij)αl1−αij , (4)

where parameter α = 0.33 is capital's income share and A is total factor productivity. We

determine the depreciation rate, δ to match the US investment-output ratio of 0.255 (Conesa

et al., 2009). We normalize A to unity.

18

3.3 Preferences

We determine the discount rate, ρ, to match the US capital-output ratio of 2.7 (Conesa

et al., 2009). We set the coecient of relative risk aversion equal to the standard value of 2.

3.4 Extreme weather

Parameters Ωl and Ωh determine the severity of extreme weather events in the low and

high risk region, respectively. We pin down Ωl to target the the ratio of FEMA aid per

event relative to county income in low-risk counties. The average value of this ratio from

2004-2016 is 0.0022.

To determine Ωh, we calculate the relative severity of an event in the high risk region

compared to the low risk region. We split events into four categories: (1) cyclones in the

high risk region, (2) non-cyclones in the high risk region, (3) cyclones in the low risk region,

and (4) non-cyclones in the low risk region.23 We normalize the damage from a non-cyclone

in the low risk region to unity and compute the relative damage for the remaining three

categories.

To calculate the damage from a cyclone event in the low risk region, we compute the

ratio of FEMA aid for cyclone events relative to non-cyclone events within each county, and

average across all low-risk counties.24 The implicit assumption is that adaptation does not

aect the relative damage from a cyclone compared to a non-cyclone event within a county.

We use the maximum sustained wind speed to calculate the damage from a cyclone in

the high risk region.25 Estimates from the economic literature suggest that cyclone damage

23Our analysis is at the annual level. We dene a county to have a cyclone event in year t if it experiencedone or more cyclones in year t, and zero non-cyclones. Similarly, we dene a county to have a non-cycloneeven in year t if it experienced one or more non-cyclones in year t and zero cyclones. In 2.5 percent of thecounty-year observations, counties experience both cyclone and non-cyclone events in a given year. Sincethis fraction is very small, we drop these observations from the calculation of relative severity.

24We can only calculate FEMA aid for cyclone events relative to non-cyclone events in counties thatexperienced both cyclone events and non-cyclone events. We drop all other counties from the calculation.

25For each county-cyclone pair, we calculate the maximum sustained wind-speed as the maximum sus-tained wind speed of the cyclone during the six hour time interval that the cyclone was closest to the countycentroid. Data on maximum sustained wind speed are from NOAA's best track data for Atlantic and Pacichurricanes, HURDAT2 (https://www.nhc.noaa.gov/data/).

19

increases with at the eighth power of maximum sustained wind speed (Nordhaus, 2010). We

calculate the ratio of the average of maximum sustained wind speed raised to the eighth

power for cyclones in the high risk region relative to cyclones in the low risk region.26 We

use this ratio, together with our value of damage for low-risk cyclones, to calculate damage

for high-risk cyclones. Lastly, to compute average damage for a non-cyclone event in the

high risk region, we again calculate the ratio of FEMA aid for cyclone events relative to

non-cyclone events within each county, and average across all high-risk counties.

We use our relative damage values for cyclones and non-cyclones in the high and low risk

regions to compute the severity of the average event in each region. Specically, we average

the damage values for the cyclone and non-cyclone events in each region and weight by the

region-specic fractions of cyclone and non-cyclone events. We nd that the average event

in the high risk region is 2.7 times as severe as in the low risk region, yielding the target

Ωh/Ωl = 2.7.

3.5 Adaptation

We use a simple functional form for h(ka) that is decreasing and convex in ka,

h(ka) =1

1 + θka. (5)

Parameter θ determines the eectiveness of adaptation capital. To calibrate θ, we compare

average FEMA aid per event in the high and low risk regions. The intuition is the following.

Under the assumptions of the model, FEMA aid is a constant fraction of total damage.

Therefore, any dierence in FEMA aid per event across the high and low risk regions must

result from dierences in damage per event. Damage per event (and hence FEMA aid) varies

across the two regions because of dierences in event severity and dierences in adaptation.

If adaptation is the same in the high and low risk counties, then average FEMA aid per

26For county-years that experience two or more cyclones, we sum the eighth power of maximum sustainedwind speed for each cyclone to calculate the maximum sustained wind speed in that county-year.

20

event in high risk counties would be 2.7 times larger than in low risk counties, because the

average event is 2.7 times as severe (Ωh/Ωl = 2.7). However, high risk counties face stronger

incentives to adapt because extreme weather events are more frequent and more severe.

Larger levels of adaptation imply that average FEMA aid per event in the high risk region

is less than 2.7 times as large as its value in the low risk region. The dierence between

the relative FEMA aid per event and the relative severity is indicative of the eectiveness

of adaptation. We choose θ to target FEMA aid per event relative to county income in the

high risk region. The average value of this ratio from 2004-2016 is 0.0035, implying that

average FEMA aid per event (relative to county income) in the high risk region is only 1.55

times larger than in the low risk region.

A potential concern with the above calibration is that the average fraction of damage

covered by FEMA aid, ψ, is not the same in the high and low risk regions. Fraction ψ could

vary across regions if ψ is correlated with damage (since high risk events are more severe

on average) or if there are persistent political dierences between the two regions. However,

as argued in Section 3, systematic dierences in political power across the two regions are

unlikely and there is no statistical correlation between FEMA aid as a fraction of damage

and the total damage. We conclude that the regional dierences in FEMA aid per event are

the result of dierences in event severity and dierences in event damage and are therefore

informative about the eectiveness of adaptation capital, θ.27

3.6 Federal policy

Parameter ψ is the fraction of total damage covered by FEMA aid. We calibrate ψ from

the subset of cyclones and storms that are included in the NOAA data plotted in Figure 2.

27One other possibility is that FEMA is subject to a county-specic donor fatigue, and thus providesless aid in counties that more frequently declare disasters, severity held constant. However, we are not awareof any empirical evidence to support this hypothesis. Furthermore, as a government organization, FEMAis less likely than individual households to exhibit behavioral responses to charitable giving, such as donorfatigue. FEMA's mission is to support our citizens and rst responders to ensure that as a nation we worktogether to build, sustain, and improve our capability to prepare for, protect against, respond to, recoverfrom and mitigate all hazards. (www.dhs.gov/disasters-overview). This mission statement is independentof how many disasters a locality has previously experienced.

21

We set ψ equal to the average ratio of the FEMA aid to total NOAA damage from 2004-2016.

This process yields ψ = 0.11, implying that federal aid covers 11 percent of the damage from

an extreme weather event.

Parameter λ is the wedge between the actuarially fair insurance premium and the pre-

mium agents pay. If λ = 1, then the insurance premium equals the actuarially fair value and

each local planner would choose to fully insure her capital stock, x = 1. Empirically, trans-

actions costs, deviations from actuarially fair premiums, and other nuances of the insurance

market imply that agents do not fully insure their capital stocks. We choose λ so that the

ratio of insured losses relative to total damage in the model matches that in the data.

To calculate the ratio of insured losses relative to total damage, we use data on insured

losses and the NOAA damage estimates. Event-level data on federally insured losses through

the National Flood Insurance Program (NFIP) is available from fema.gov for all ooding

events with $1,500 or more in paid losses. Data on privately insured losses (e.g. through

homeowners' insurance policies) is available for most tropical cyclones. These data are from

estimates reported in NOAA's tropical cyclone reports for each individual storm and from

the Insurance Information Institute.28 We calculate the average ratio of total insured losses

to total NOAA damage for all cyclones and for the subset of non-cyclone events that are

included in the NOAA and NFIP data. The average value of this ratio from 2004-2016 is

0.42.

Finally, to calibrate the adaptation subsidy, we use information on federal funding for

adaptation investment. One major source of funding is Hazard Mitigation Assistance (HMA)

administered by FEMA. There are ve separate HMA programs that provide support for

adaptation: (1) Repetitive Flood Claims (RFC), (2) Severe Repetitive Loss (SRL), (3) Flood

Mitigation Assistance (FMA), (4) Pre-Disaster Mitigation (PDM) and (5) Hazard Mitiga-

tion Grant Program (HMGP). Programs (1)-(3) only provide funding for ood-related events.

28See https://www.iii.org/fact-statistic/hurricanes#Estimated Insured Losses For The Top 10 HistoricalHurricanes Based On Current Exposures (1). Data on insured losses is not available for the following tropicalcyclones: Dolly, Earl, Matthew, and Hermine.

22

Thus, we include the total expenditures by these programs. Program (4), PDM, includes

expenditures to reduce storm risk as well as expenditures for adaptation to res and earth-

quakes. To lter out these non-storm expenditures, we exclude all expenditures in which

the project type or the project title contains the word re or seismic. Finally, program

(5), HMGP, subsidizes adaptation investment following the declaration of a presidential dis-

aster. We include all HMGP expenditures for the storm-related PDD events. A second

major source of federal adaptation funding is the US Army Corps of Engineers (USACE).

We include all components of the budget that primarily relate to ooding.29

We measure the federal subsidy for adaptation in each year as the sum of the relevant

HMA and USACE expenditures discussed above. Most of this data is not available at the

county level, implying that we cannot separately estimate the adaptation subsidy for each

region. Instead, we assume that the adaptation subsidy in region i is proportional to average

adaptation investment in region i, Iai ,

si = sIai .

We choose the size of the subsidy scale-factor, s, to target total adaptation expenditures

relative to GDP in the US. Complete data on HMA programs RFC and SRL is only available

from 2008-2017. Therefore we target the average value of adaptation expenditures relative

to GDP from 2008-2017.

Table 2 reports the value of the moments we target in the model and their corresponding

values in the data. Overall, the model ts these targets quite closely.

29Complete USACE budget reports are available fromwww.usace.army.mil/Missions/Civil-Works/Budget/. We the include the following budget line items fromthe budget overview (page 3): "Flood, Control, Mississippi River and Tributaries", and "Flood Control andCoastal Emergencies." Occasionally, the descriptions of some of the other line items on pages one and tworeport specic ood-related expenditures. We include these if they are present.

23

Table 2: Model Fit

Moment Model Target

I/Y 0.255 0.255

K/Y 2.7 2.7

(HMA+USACE)/Y 2.5e-4 2.5e-4

Ωh/Ωl 2.74 2.74[FEMA/Y ]l 0.0022 0.0022[FEMA/Y ]h 0.0035 0.0035x 0.42 0.42

4 Model results

We use our calibrated model to quantify the proportion of adaptation capital and its eect

on average damage. Then, we run two counter-factual experiments. In the rst experiment,

we quantify the eects of FEMA on adaptation investment and expected damage. In the

second experiment, we quantify the eects of adaptation on the welfare costs of climate

change. We report the results for the low and high risk regions and for the aggregate US

economy. To calculate the aggregate values, we weight the values in the low and high risk

regions by their relative shares of US GDP, 0.54 and 0.45 respectively.

4.1 Quantifying adaptation

Figure 3 plots adaptation capital as a percent of the total capital stock in the low and

high risk regions and for the aggregate economy. Localities in the low risk region do not

invest in adaptation capital. The expected benet of adaptation investment is primarily

determined by the probability of an extreme weather event pi, and its severity, Ωi. In low

risk localities, extreme weather events are rare, pl = 0.2, and destroy only 0.75 percent of the

capital stock when they occur (Ωl = 0.0075). Combined, the low probability and severity of

extreme weather imply that the expected marginal benet of adaptation investment never

exceeds the marginal cost, and thus low risk localities do not invest in adaptation capital.

24

In contrast, adaptation capital is 1.56 percent of the total capital stock in the high risk

localities. The probability and severity of extreme weather events is much larger in the

high risk localities, ph = 0.4 and Ωh = 0.02, leading to substantial benets from adaptation

investment. In the aggregate US economy, adaptation capital represents 0.71 percent of the

total capital stock. The total value of the US capital stock in 2016 was approximately 56.7

trillion in 2016 dollars, implying that US adaptation capital is approximately 400 billion in

2016 dollars.30

Figure 3: Percent of Adaptation Capital

0.00

1.56

0.71

Low High Aggregate

Region

0

0.5

1

1.5

2

Pe

rce

nt

of

the

ca

pita

l sto

ck

Figure 4 shows the eects of adaptation on the average damage in the low and high risk

regions and for the aggregate economy. The green bars plot the average damage when the

social planner in each locality optimally chooses adaptation investment. The blue bars plot

the average damage with adaptation capital equal to zero (kaijt = 0) and all other variables

equal their values in our baseline model. The dierence between the green and the blue bars

represents the amount that adaptation reduces current damage from extreme weather.

Average damage is larger in the high risk region than in the low risk region because both

the probability and severity of an extreme weather event are larger. However, adaptation

30Data on the capital stock are from: www.fred.stlouisfed.org.

25

substantially reduces this gradient. Average damage in the high risk region is only 3.4 times

higher in than in the low risk region, even though the high risk region is twice as likely to

experience an event and the event is almost three times as severe.

Adaptation investment reduces damage by 40 percent in the high risk region, and by 33

percent for the aggregate economy. Scaling these estimates by 2016 US GDP implies that on

average the US avoids 74 billion (in 2016 dollars) in damage each year because of adaptation,

the equivalent of 0.4 percent of US GDP.

Figure 4: Eects of Adaptation on Damage

0.38

1.30

0.80

0.38

2.18

1.20

Low High Aggregate

Region

0

0.5

1

1.5

2

2.5

Pe

rce

nt

of

ou

tpu

t

Adaptation

No adaptation

To measure the distributional impacts of FEMA aid and subsidies across regions, Figure

5 plots average FEMA receipts relative to taxes. If this ratio equals unity, then expected

receipts equal tax payments, implying no transfers across regions. A value less than unity

indicates that the average locality makes transfers to localities in the other region. Similarly,

a value greater than unity indicates that the average locality receives transfers. On average,

FEMA receipts are 38 percent of total tax payments in the low risk region and are over 174

percent of total tax payments in the high risk region, implying substantial transfers from

the low to high risk regions.

26

Figure 5: Average FEMA Receipts Relative to Tax Payments

0.38

1.74

1.00

Low High Aggregate

Region

0

0.5

1

1.5

2

4.2 Eects of FEMA on adaptation

The provision of FEMA aid for disaster relief decreases the damage a locality experiences

from extreme weather, reducing its incentives to invest in adaptation capital. FEMA subsi-

dies for adaptation mitigate this moral hazard eect by increasing investment in adaptation

capital. To quantify the total eect of FEMA policy on adaptation capital and the associated

implications for damage, we solve for a counterfactual stationary equilibrium in which we

set both the aid and the adaptation subsidy equal to zero (ψ = 0 and s = 0). We refer to

this stationary equilibrium as the no-FEMA equilibrium. In the results that follow, Figures

6 - 8, the green bars plot the value of the variable in the baseline stationary equilibrium

(our benchmark model with FEMA policy) and the blue bars plot its corresponding value

no-FEMA equilibrium.

Figure 6 shows the eects of FEMA on adaptation capital. The low risk region does

not invest in adaptation capital in the baseline or in the no-FEMA equilibrium. However,

in the high risk region, adaptation capital is higher in the no-FEMA equilibrium than in

the baseline, implying that FEMA reduces adaptation investment. Aggregating the low and

27

high risk results, we nd that FEMA reduces adaptation capital by 10 percent in the US

economy, from 0.8 percent of the capital stock in the no-FEMA equilibrium to 0.71 percent

of the capital stock in the baseline.

Figure 6: Adaptation Capital

0.00

1.56

0.71

0.00

1.74

0.80

Low High Aggregate

Region

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Pe

rce

nt

of

tota

l ca

pita

l

Baseline

No FEMA

Figure 7 shows the implications of FEMA for the average damage in each region. In the

low risk region, average damage in the no-FEMA equilibrium is the same as in the baseline

because the low risk localities do not invest in adaptation capital in either case. In contrast,

in the high risk region, average damage is larger in the baseline than in the no-FEMA

equilibrium because FEMA policy reduces adaptation capital. For the aggregate economy,

we nd that FEMA policy increases average damage 3.5 percent. Scaling the aggregate

results by 2016 US GDP implies that damage from extreme weather is 5 billion higher in

2016 dollars as a result of FEMA policy. To put this result in perspective, storm-related

FEMA aid averaged 6.7 billion per year. Thus, the increase in damage from moral hazard

is 75 percent of the total FEMA aid each year, suggesting large moral hazard consequences

from FEMA policy.

28

Figure 7: Average Damage

0.38

1.30

0.80

0.38

1.24

0.77

Low High Aggregate

Region

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Pe

rce

nt

of

ou

tpu

t

Baseline

No FEMA

Localities can also by purchase insurance to reduce the welfare cost of extreme weather.

Figure 8 shows the eects of FEMA on insurance purchases. Similar to the results for

adaptation capital, FEMA policy reduces the amount of insurance agents purchase. In both

the high and low risk regions, insurance coverage is approximately 15 percent lower in the

baseline compared to the no-FEMA equilibrium.

Figure 8: Insurance Coverage

0.47

0.38

0.43

0.56

0.43

0.50

Low High Aggregate

Region

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Baseline

No FEMA

29

To measure welfare eects of FEMA policy, we use the consumption equivalent variation

(CEV). The CEV is the percent increase in consumption an agent would need in every period

in the baseline so that she is indierent between the baseline and the no-FEMA equilibrium.

A negative value indicates that FEMA makes agents better o (expected welfare is higher in

the baseline) while a positive value indicates that FEMA makes agents worse o (expected

welfare is higher in the no-FEMA equilibrium). Table 3 reports the CEV for each region

and for the aggregate economy.

Table 3: Welfare Eects of FEMA (CEV)

Low risk High risk Aggregate

0.18 -0.094 0.0059

The CEV in the low risk region is 0.18, indicating that low risk localities are better o in

the no-FEMA equilibrium. FEMA aid compensates localities for a fraction of the damage

they experience from extreme weather. In the no-FEMA equilibrium, localities mitigate the

eects of forgone aid through additional adaption investment (Figure 6) and insurance pur-

chases (Figure 8). However, the provision of FEMA aid also generates substantial transfers

from the low to high risk localities (Figure 5), which are not present in no-FEMA equilib-

rium. For low risk localities, the benet of eliminating these transfers dominates the cost of

the forgone aid, and thus low risk localities are better o in the no-FEMA equilibrium. In

contrast, high risk localities are worse o in the no-FEMA equilibrium because they suer

from both the forgone aid and the elimination of transfers. In the aggregate, the net gains

in the low risk region dominate the costs in the high risk region, leading to a near-zero ag-

gregate CEV. Thus, eliminating (storm-related) FEMA policy would have almost no welfare

impact on the aggregate economy.

30

4.3 Eects of climate change

We analyze the interactions between adaptation investment and the progression of climate

change. Climate models predict that climate change will substantially increase the intensity

and damage potential of hurricanes and other severe storms. In particular, Villarini and

Vecchi (2013) use CIMP5 models to simulate the increase in the power dissipation index

(PDI) for dierent climate change scenarios. The PDI is an index that incorporates storm

duration, frequency, and intensity. Their projections imply that the PDI of Atlantic basin

cyclones is likely to increase by 50-100 percent, depending on time path of atmospheric

CO2.31 Additionally, Villarini and Vecchi (2012) argue that tropical cyclone frequency is

not projected to change signicantly over the 21st century, regardless of the climate change

scenario. Thus, the projected increase in PDI indicates an increase in storm intensity and

severity.

Based on this evidence, we dene a climate change stationary equilibrium as our baseline

model with a larger severity parameter, Ωcci = µ × Ωbaseline

i . Scale-factor µ > 1 represents

the climate-change induced increase in storm severity. We consider three climate change

scenarios, represented by µ = 1.5, µ = 1.75, and µ = 2. For each climate change scenario,

we calculate two climate change equilibria. In the rst climate change equilibrium, agents

optimally choose adaptation capital, just like they do in the baseline. In the second climate

change equilibrium, we x adaptation capital at its value in the baseline, thus agents can-

not adjust to climate change through adaptation. We refer to these two equilibria as the

adaptation and no-adaptation climate change equilibria, respectively.

Figure 9 plots percent increase in aggregate adaptation capital from the baseline for each

climate change scenario. Even with the most optimistic climate change projections (µ = 1.5)

adaptation capital still increases by over 50 percent from its value in the baseline.

31Specically, Villarini and Vecchi (2013)'s results imply that a doubling of atmospheric CO2 by 2100 willlikely increase the PDI of Atlantic basin cyclones by 50 percent and that a quadrupling of atmospheric CO2

by 2100 will likely increase the PDI by 100 percent.

31

Figure 9: Percent Increase in Adaptation Capital From the Baseline

54.67

75.43

96.23

50 75 100

Percent Increase in Storm Severity

0

20

40

60

80

100

Pe

rce

nt

Incre

ase

in

Ad

ap

tatio

n C

ap

ita

l

This adaptation investment reduces the increase in damage the localities experience as

a result of climate change. Figure 10 plots the eects of climate change and adaptation

on average damage. Specically, for each climate change scenario, the green and blue bars

plot the percent increase in average damage from the baseline in the no adaptation and

adaptation climate change equilibria, respectively. In the no-adaptation equilibria, average

damage is approximately µ times the value of damage in the baseline; since agents cannot

adapt, they have no way to mitigate the increase in extreme weather severity. As a result,

average damage increases by the same scale-factor as the storm severity.32

When agents can adapt, average damage increases by considerably less than the increase

in severity. For example, the ability to adapt implies that a 50 percent increase in severity

leads to an increase in average damage of approximately 28 percent, instead of 48 percent.

Looking across all three scenarios, adaptation reduces the increase in average damage as a

result of climate change by 40-42 percent.

32Small changes in the level of productive capital imply that average damage is not exactly equal to µtimes baseline damage.

32

Figure 10: Percent Increase in Average Damage From the Baseline

48.00

70.54

93.51

27.78

42.15

55.31

50 75 100

Percent Increase in Storm Severity

0

20

40

60

80

100

Pe

rce

nt

Incre

ase

in

Da

ma

ge

No Adaptation

Adaptation

While the reductions in damage from adaptation are considerable, there are nonetheless,

diminishing returns to adaptation. To quantify these diminishing returns, Table 4 reports

the average elasticity of damage with respect to adaptation capital for each climate change

scenario. We dene this elasticity as the percent dierence in damage between the adaptation

and no-adaptation climate change equilibria, divided by the percent dierence in adaptation

capital. Across all three climate change scenarios, the elasticity is negative, implying that

damage decreases with adaptation investment. However, the magnitude of the elasticity

is considerably larger when climate change is less severe (smaller µ) and hence adaptation

capital is smaller.

Table 4: Elasticity of Damage With Respect to Adaptation Capital

µ = 1.5 µ = 1.75 µ = 2

-25.00 -22.07 -20.52

A second channel through which localities can respond to climate change is through

insurance. Figure 11 plots the eects of climate change and adaptation on the aggregate

33

level of insurance coverage. Specically, for each climate change scenario, the green and blue

bars plot the percent increase in insurance coverage from the baseline in the no adaptation

and adaptation climate change equilibria, respectively. For all scenarios, insurance coverage

increases in response to climate change. The curvature in the utility function implies that

climate change raises the utility cost of an extreme weather event by more than the insurance

premium, leading localities to purchase more insurance. Insurance coverage is largest when

agents cannot adapt to climate change because the increase in the damage is larger in this

case.

Figure 11: Percent Increase in Insurance Coverage From the Baseline

54.05

61.45

70.69

22.7726.05

32.12

50 75 100

Percent Increase in Storm Severity

0

20

40

60

80

100

Pe

rce

nt

Incre

ase

in

In

su

ran

ce

Co

ve

rag

e No Adaptation

Adaptation

To measure the welfare eects of climate change, we again use the consumption equivalent

variation (CEV). The CEV measures the percent increase in consumption an agent would

need in every period in the baseline such that she is indierent between the baseline and the

climate change equilibrium. Table 5 reports the CEV in the adaptation and no adaptation

equilibria for each climate change scenario. All values of the CEV are negative, indicating

that climate change makes agents worse o. However, even when agents can adapt, the

magnitude of the CEV increases considerably with the climate change scenario, from -0.62

percent when µ = 1.5 to −1.08 percent when µ = 2.

34

Finally comparing the CEVs across the adaptation and no-adaptation climate change

equilibria, we see that adaptation reduces the welfare cost of climate change. For example,

when µ = 1.5, the CEV is -0.81 when agents cannot adapt, but only -0.62 when agents can

adapt. Looking across all three scenarios, we nd that adaptation reduces the welfare cost

by approximately 25 percent.

Table 5: Welfare Eects of Climate Change (CEV)

µ = 1.5 µ = 1.75 µ = 2

Adaptation -0.62 -0.85 -1.08

No Adaptation -0.81 -1.13 -1.44

5 Conclusion

We develop a structural macroeconomic model to quantify the links between adaptation,

extreme weather damage, FEMA policy, and climate change. The framework is a dynamic

general equilibrium model in which heterogeneous localities experience idiosyncratic extreme

weather shocks that damage their capital stocks. A social planner in each locality can invest

in adaptation capital to reduce the damage from an extreme weather event and can purchase

insurance to smooth consumption.

We calibrate the model and use it to quantify the amount and eectiveness of adaptation

capital. We nd that in localities with a high risk of extreme weather, adaptation capital

is approximately 1.56 percent of the capital stock and reduces the damage from extreme

weather by 40 percent.

Additionally, we use our model to run two counterfactual experiments. First, we quantify

the eects of FEMA policy on adaptation investment and welfare. We nd evidence of

considerable moral hazard eects of FEMA. Specically, FEMA reduces adaptation capital

by 10 percent. This reduction in adaptation capital increases the average damage from

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extreme weather by 5 billion per year, the equivalent of 75 percent of average storm-related

FEMA aid per year.

Second, we quantify the interaction between adaptation and climate change. Climate

change (modeled as a permanent increase in extreme weather severity) leads to substantial

investment in adaptation capital. The additional adaptation capital reduces the increase in

damage from climate change by over 40 percent. Furthermore, the adaptation investment

reduces the aggregate welfare cost of climate change by 25 percent.

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