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 the damage from extreme weather. The framework modi es the Aiyagari-style model to apply in a new setting in which a continuum of heterogeneous localities experience idiosyncratic extreme weather shocks. Localities can invest in adaptation capital to reduce the damage from extreme weather and they can purchase insurance to smooth consumption. A federal government taxes localities and provides partial disaster relief. We calibrate the model to match variation in FEMA aid per event across US counties with dierent risks of extreme weather. We use the calibrated model to quantify the amount and eectiveness of adaptation capital, the moral hazard consequences of FEMA policy, and the role of adaptation in response to climate change. We nd that storm-related adaptation capital is 0.7 percent of the US 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 weather damage are substantial. We introduce climate change into the model as a permanent, increase in the severity of extreme weather. We nd that adaptation reduces the welfare cost of this climate change by 25 percent.
∗
Arizona State University W.P. Carey School of Business. Email:
[email protected]
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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.
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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 in uenced 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 adaptation investment.
We focus explicitly on storm-related extreme weather such as tropical
cyclones, blizzards, tornadoes and heavy rain or snow storms.
2
The framework modi es 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 damage 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-
1 Source: http://www.aoml.noaa.gov/hrd/tcfaq/E23.html and NCEI Billion dollar damage data. 2 Our analysis does not apply to non-storm related extreme weather such as wild res 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 investments, 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 adaptation 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 adaptation 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 economy, 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, stormrelated FEMA aid averages 6.7 billion per year.
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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 scienti c 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
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from 50 -100 percent.
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
3 The average is taken over the period for which FEMA data are available, 2004-2016. 4 The 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.
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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 di cult 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
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event, such as mortality or crop loss.
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 macroeconomics. For example, Golosov et al. (2014) use a dynamic stochastic general equilibrium model to calculate the optimal carbon tax. Barrage (2017) modi es a Ramsey-style optimal
5 See 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.
6 A 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 et al. (2011), and Sadowski and Sutter (2008) nd evidence of a negative relationship, and thus suggest there is potential for adaptation.
Dell et al. (2012) and Schlenker and Roberts (2009) do not evidence of this
negative 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.
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Like this earlier work, the present paper
modi es 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.
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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 in nite. 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 continuum of measure one of ex-ante identical localities. Each locality,
j,
i
contains a
is populated by a
unit mass of in nitely 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 insurance 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
7 Hassler et al. (2016) and Heutal and Fischer (2013) both provide a nice overview of this literature. 8 In a similar style to the present paper, ongoing work by Krusell and Smith develops a global Aiyagaristyle model to analyze the progression of climate change and the eects of climate policy across dierent regions (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 adaptation 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, interpret
ε=1
t,
locality
j
in region
i
experiences a weather shock
as extreme weather occurs and
The weather shocks are i.i.d across localities. the productive capital stock, weather in county
j
in region
kp. i
Let
dijt
in period
9
ε=0
εijt {0, 1}.
as extreme weather does not occur.
The realization of extreme weather damages
denote the capital stock destroyed by extreme
t,
p a dijt = εijt Ωi h(kijt )kijt .
Parameter
Ωi
determines the severity of the extreme weather event in region
constant, increases in
Ωi
We
(1)
i;
all else
imply that extreme weather destroys a larger fraction of the capital
stock.
9 In practice, extreme weather shocks are spatially correlated. However, event severity held constant, the damage a locality experiences from an extreme weather event is independent of whether or not the neighboring locality also experiences an extreme weather event.
Given this independence, the spatial correlation of
extreme 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, ity. Function Function
h(k a )
k a , to reduce the damage from extreme weather in her local-
governs the process through which adaptation capital reduces damage.
h(k a ) is decreasing and convex in k a , h0 (k a ) < 0, h00 (k a ) > 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 bility that in region
i
pi
is the region-speci c probability of an extreme weather event (e.g., the proba-
εijt = 1). with
By the law of large numbers,
ε=1
in any period
pi
corresponds to the fraction of localities
t.10
2.2 Production Firms in each region,
i,
in each locality,
j,
produce a homogeneous nal good,
labor, lij and the non-damaged productive capital, function
yij = F (k˜ijp , lij ).
yij ,
from
p k˜ijp ≡ kijt −dij , according to the production
The nal good is the numeraire.
2.3 Federal Government The rst purpose of the federal government in our model is to capture the bene ts 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 investment in hazard mitigation. Analogous to FEMA, our model federal government provides aid for localities that experience extreme weather and provides a region-speci c subsidy, for investment in adaptation capital. Aid for extreme weather equals
si ,
ψdijt , where ψ [0, 1] is
10 Recent empirical studies suggest that agents do not internalize the true probability of extreme weather into their decision making process (Bin and Landry (2013) and Kousky (2010) and Gallagher (2014)). In particular, Gallagher (2014) shows that a Bayesian model in which agents update their ood risk beliefs based on recent ood experiences and then forget ood experiences farther in the past can match these empirical patterns.
Modeling the planner's beliefs using Gallagher (2014)'s partial information model of
Bayesian 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,
Ttf ,
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 bene ts and incentives created by homeowners insurance and the National Flood Insurance Program (NFIP). The assumption 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, Insurance claims equal year
t
xijt dijt .
The insurance premium,
qijt (xijt )
in locality
j
xijt [0, 1].
in region
i
in
is
p a qijt (xijt ) = λpi xijt h(kijt )Ωi kijt .
Expression sion
p a h(kijt )Ωi kijt
p a )Ωi kijt xijt h(kijt
is the value of damage from an extreme weather event. Thus expres-
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 consumption, 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
9
2017; NRC 2015). The model is not su ciently 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.
T h > 0,
and returns a surplus with equal lump-sum transfers to the household,
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 accumulate according to the standard law of motion,
p p kij,t+1 = (1 − δ)k˜ijt + ipijt
where
δ
and
is the depreciation rate of capital and
Variables
ip
and
ia
a a kij,t+1 = (1 − δ)kijt + iaijt + si ,
si
is the region speci c adaptation subsidy.
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,
p a V (kijt , kijt , xijt ; εijt ) =
max p
a kijt+1 ,kijt+1 ,xijt+1
p a , xijt+1 ; εijt+1 ) u(cijt ) + ρEV (kijt+1 , kijt+1
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(2)
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 ).
Function
u(c)
denotes household utility and
expectation over
εijt+1
c
(3)
denotes consumption. The planner forms her
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.
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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. typical US citizen, the vast majority of wealth is locally owned.
Thus, for the
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2.5 Stationary equilibrium We de ne a stationary equilibrium in which aggregate macroeconomic variables are constant.
We suppress the
t
subscripts throughout the stationary equilibrium de nition; we
signify a planner's chosen levels of capital and insurance coverage in the next period as
k0
11 The term middle class household refers to a household with wealth in the middle three wealth quintiles. 12 Relaxing the assumption that all wealth is local considerably complicates the model and introduces assumptions that make the underlying mechanisms governing adaptation investment less transparent. For example, one could incorporate a portfolio choice where households allocate their wealth between local and non-local capital. This introduces an additional state variable. Furthermore, under this setup, households would choose to fully diversify, investing all of their wealth in non-local capital.
Matching the empirical
fact that most household wealth is local would require an additional behavioral assumption or underlying preference for local capital. Given, that almost all wealth for the typical US household is local, we choose to abstract from modeling the portfolio choice between local and non-local capital and thus avoid the associated complications.
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and
x0 .
The local state variables are adaptation capital,
of insurance,
xij ,
kija , productive capital, kijp , the level
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, extreme weather event, 0
0
{cij , kija , kijp , x0ij },
pi ,
ψ,
the adaptation subsidy,
si ,
the probability of an
a stationary equilibrium consists of planners' decision rules
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:
X
T Φ(z) =
X
[ψdij + si + xij dij − qij (xij )]Φ(z)
3. The aggregate resource constraint holds:
˜ p ) = C + K a0 + K p0 Y + (1 − δ)(K a + K
where
˜p = K
X
k˜ijp Φ(z),
4. The distribution,
3
Φ(z)
Ka =
X
kija Φ(z),
Y =
X
yij Φ(z),
and
C=
X
cij Φ(z)
is stationary.
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 weather incident in year
t
t
if it experiences at least one storm-related
13
that received a PDD.
An extreme weather event receives a
presidential disaster declaration when the damage is su ciently 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
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of years.
We de ne 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.
13 Our analysis primarily includes tropical cyclones, blizzards, tornadoes, and other heavy rain or snow storms.
14 To request a PDD for extreme weather, local government o cials partner and FEMA regional o cials
to 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 damage is so large that it is beyond state and local capabilities to address, the state governor can request a PDD from the FEMA regional director who can, in turn, request a PDD from the US president (FEMA, 2003). Speci cally, the total damage must exceed 1.30 per capita in 2011 dollars to warrant a PDD (McCarthy, 2011).
15 We begin in 1989 because the Staord Act, passed in 1988, considerably changed the FEMA system
(FEMA, 2003).
13
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
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aggregate income derives from these counties.
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 dierences 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
16 County-level data on personal income are from the Bureau of Economic Analysis, downloaded on 1/18/2018.
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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 committees (Davlasheridze et al., 2014). Such turmoil makes it di cult 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 stormrelated extreme weather events is not readily available, we use data on FEMA aid instead of data on damage. FEMA.
18
17
A PDD authorizes the federal government to provide disaster aid through
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 speci c 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
17 The Spatial Hazards and Losses Database for the United States (SHELDUS) reports county-level damage information for extreme weather events in the US. However, this data is severely incomplete.
The
primary source of the data are self-reports by individual weather stations and as a result, many observations are missing. In particular, Gallagher (2014) reports that only 8.6 percent of ood-related PDD events from 1960-2007 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.
18 FEMA 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). Examples of IHP aid include grants to help pay for emergency home repairs, temporary housing, personal property loss, and medical, dental and funeral expenses caused by the disaster. Examples of PA aid include funds for emergency relief and to repair or replace damaged public infrastructure. Data is available from fema.gov.
19 Speci cally, data on IHP aid is available from fema.gov from 2004-2016 and data on PA aid is available
from 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-
20
ronmental Information.
Combined, NOAA's tropical cyclone reports and NCEI database
cover over half of the PDD events in our sample.
Using the NOAA data, we de ne 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 coe cient 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
20 To account for uninsured or under-insured losses, NOAA scales up insured loss data by a factor equal to the reciprocal of the insurance participation rate in that region. For example, if a region had approximately 50 percent policy protection under the National Flood Insurance Program (NFIP), NOAA would apply a factor of two to the region's NFIP claims in their calculation of total losses. We interpret the NOAA damage estimate as the actual damage from any extreme-weather event that is included in the NOAA data.
21 We use the EPA's value of 7.6 million (in $2006) for the value of a statistical life (see
www.epa.gov/environmental-economics/mortality-risk-valuation).
16
coe cient estimate in a simple regression of the fraction of FEMA aid on the total damage
22
equals 5.73e-13 with a standard error of 6.86e-13.
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
NOAA sample
NOAA sample without outliers
0.3
FEMA aid as a fraction of damage
FEMA aid as a fraction of damage
0.5
0.4
0.3
0.2
0.1
0
0.25
0.2
0.15
0.1
0.05
0 0
20
40
60
80
100
120
140
160
0
NOAA damage estimate (billions of 2009 $)
5
10
15
20
25
30
35
NOAA damage estimate (billions of 2009 $)
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 parameters so that certain targets in the model match the values observed in the US economy. Table 1 reports the parameter values.
22 Similarly, in the sample without outliers, the coe cient estimate in a simple regression of the fraction of 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
0.094
Method of moments
0.33
Data
1
Normalization
0.98
Method of moments
2
Assumption
0.13
Method of moments
0.11
Data
1.02
Method of moments
Low risk probability:
0.20
Data
High risk
0.40
Data
Low risk event severity:
0.0075
Method of moments
High risk event
0.0205
Method of moments
10.00
Method of moments
Production
δ
Depreciation:
α
Capital's share:
A
Productivity: Preferences
Discount factor:
ρ
CRRA coe cient:
σ
Federal policy
Adaptation subsidy: FEMA aid:
si = sI¯ia
ψ
Insurance wedge:
λ
Extreme weather and adaptation
pl probability: ph
Adaptation:
Ωl severity: Ωh
θ
3.2 Production We use the standard Cobb-Douglas production function,
p 1−α F (k˜i,j , li,j ) = A(k˜ijp )α lij ,
where parameter
α = 0.33
is capital's income share and
determine the depreciation rate, et al., 2009). We normalize
A
δ
A
(4)
is total factor productivity. We
to match the US investment-output ratio of 0.255 (Conesa
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 coe cient 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
25
the high risk region.
Estimates from the economic literature suggest that cyclone damage
23 Our analysis is at the annual level. We de ne a county to have a cyclone event in year one or more cyclones in year even in year
t
t,
t if it experienced
and zero non-cyclones. Similarly, we de ne a county to have a non-cyclone
if it experienced one or more non-cyclones in year
t
and zero cyclones. In 2.5 percent of the
county-year observations, counties experience both cyclone and non-cyclone events in a given year. Since this fraction is very small, we drop these observations from the calculation of relative severity.
24 We can only calculate FEMA aid for cyclone events relative to non-cyclone events in counties that
experienced both cyclone events and non-cyclone events. We drop all other counties from the calculation.
25 For 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 county centroid. Data on maximum sustained wind speed are from NOAA's best track data for Atlantic and Paci c hurricanes, 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. Speci cally, we average the damage values for the cyclone and non-cyclone events in each region and weight by the region-speci c 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(k a )
h(k a ) =
Parameter
θ
that is decreasing and convex in
ka,
1 . 1 + θk a
determines the eectiveness of adaptation capital. To calibrate
(5)
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
26 For county-years that experience two or more cyclones, we sum the eighth power of maximum sustained wind 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 high risk region.
θ
to target FEMA aid per event relative to county income in the
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, vary across regions if
ψ,
ψ
is not the same in the high and low risk regions. Fraction
ψ
could
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.
27 One other possibility is that FEMA is subject to a county-speci c donor fatigue, and thus provides less aid in counties that more frequently declare disasters, severity held constant. However, we are not aware of any empirical evidence to support this hypothesis. Furthermore, as a government organization, FEMA is less likely than individual households to exhibit behavioral responses to charitable giving, such as donor fatigue. FEMA's mission is to support our citizens and rst responders to ensure that as a nation we work together to build, sustain, and improve our capability to prepare for, protect against, respond to, recover from and mitigate all hazards. (www.dhs.gov/disasters-overview). This mission statement is independent of 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 Mitigation Grant Program (HMGP). Programs (1)-(3) only provide funding for ood-related events.
28 See https://www.iii.org/fact-statistic/hurricanes#Estimated Insured Losses For The Top 10 Historical Hurricanes Based On Current Exposures (1). Data on insured losses is not available for the following tropical cyclones: 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 earthquakes.
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 disaster.
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).
29
We include all components of the budget that primarily relate to ooding.
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 adaptation investment in region
i is proportional to average
i, I¯ia , si = sI¯ia .
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.
29 Complete USACE budget reports are available from www.usace.army.mil/Missions/Civil-Works/Budget/. We the include the following budget line items from the budget overview (page 3): "Flood, Control, Mississippi River and Tributaries", and "Flood Control and Coastal Emergencies." Occasionally, the descriptions of some of the other line items on pages one and two report speci c ood-related expenditures. We include these if they are present.
23
Table 2: Model Fit
4
Moment
Model
Target
I/Y K/Y
0.255
0.255
2.7
2.7
(HMA+USACE)/Y
2.5e-4
2.5e-4
Ωh /Ωl [F EM A/Y ]l [F EM A/Y ]h x
2.74
2.74
0.0022
0.0022
0.0035
0.0035
0.42
0.42
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. invest in adaptation capital.
Localities in the low risk region do not
The expected bene t of adaptation investment is primarily
determined by the probability of an extreme weather event risk localities, extreme weather events are rare, capital stock when they occur (Ωl
= 0.0075).
pi ,
and its severity,
Ωi .
In low
pl = 0.2, and destroy only 0.75 percent of the
Combined, the low probability and severity of
extreme weather imply that the expected marginal bene t 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 bene ts 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
Percent of the capital stock
2
1.56
1.5
1 0.71
0.5
0
0.00
Low
High
Aggregate
Region
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
a the average damage with adaptation capital equal to zero (kijt
= 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
30 Data 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
2.5 Adaptation No adaptation
2.18
Percent of output
2
1.5 1.30 1.20
1 0.80
0.5
0.38
0.38
0 Low
High
Aggregate
Region
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
2 1.74
1.5
1.00
1
0.5
0.38
0 Low
High
Aggregate
Region
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 subsidies 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 1.74
Percent of total capital
1.6
Baseline No FEMA
1.56
1.4 1.2 1 0.80
0.8
0.71
0.6 0.4 0.2 0
0.00
0.00
Low
High
Aggregate
Region
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
1.4 Baseline No FEMA
Percent of output
1.2
1.30 1.24
1 0.80
0.8
0.77
0.6 0.4
0.38
0.38
0.2 0 Low
High
Aggregate
Region
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
0.8 0.7
Baseline No FEMA
0.6
0.56
0.5
0.50 0.47 0.43
0.4
0.43
0.38
0.3 0.2 0.1 0 Low
High
Region
29
Aggregate
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 purchases (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 equilibrium. For low risk localities, the bene t 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 aggregate 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 signi cantly 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 de ne a climate change stationary equilibrium as our baseline model with a larger severity parameter,
baseline . Ωcc i = µ × Ωi
the climate-change induced increase in storm severity. scenarios, represented by
µ = 1.5, µ = 1.75,
and
µ = 2.
Scale-factor
µ>1
represents
We consider three climate change 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 cannot 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.
31 Speci cally, Villarini and Vecchi (2013)'s results imply that a doubling of atmospheric CO by 2100 will 2 likely 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
Percent Increase in Adaptation Capital
100
96.23
80
75.43
60
54.67
40
20
0 50
75
100
Percent Increase in Storm Severity
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. Speci cally, 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.
32 Small changes in the level of productive capital imply that average damage is not exactly equal to times baseline damage.
32
µ
Figure 10: Percent Increase in Average Damage From the Baseline
100
93.51
Percent Increase in Damage
No Adaptation Adaptation
80 70.54
60
55.31 48.00 42.15
40 27.78
20
0 50
75
100
Percent Increase in Storm Severity
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 de ne 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 -25.00
-22.07
µ=2 -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. Speci cally, 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
Percent Increase in Insurance Coverage
100 No Adaptation Adaptation
80 70.69
60
61.45 54.05
40 32.12 26.05
22.77
20
0 50
75
100
Percent Increase in Storm Severity
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
5
Adaptation
-0.62
-0.85
-1.08
No Adaptation
-0.81
-1.13
-1.44
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. Speci cally, FEMA reduces adaptation capital by 10 percent.
This reduction in adaptation capital increases the average damage from
35
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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