Upload
others
View
3
Download
0
Embed Size (px)
Citation preview
Flood Insurance Take-up in the US after
Large Regional Floods∗
Justin Gallagher†
Department of EconomicsUniversity of California at Berkeley
October 4, 2010
Note: Preliminary Draft. Please do not cite or distribute.Comments are welcomed and encouraged.
∗I would like to thank David Card, Mariana Carrera, Stefano DellaVigna, Michael Greenstone, Teck Ho,Brad Howells, Matt Kahn, Pat Kline, Vikram Maheshri, Enrico Moretti, Owen Ozier, Philippe Wingender, aswell as UC Berkeley Labor Lunch and University of California Energy Institute Lunch seminar participants,for their many helpful comments on this project. I am grateful for the financial support provided by EPA’sScience to Achieve Results (STAR) graduate fellowship. All errors are my own.†Please direct correspondence to [email protected].
1 Introduction
Standard economic models assume that economic agents efficiently incorporate all past
information when making important decisions. Recent evidence from a range of settings
suggests that economic agents use a Bayesian statistical learning process to update beliefs.
Examples include: Publicized leukemia diagnoses and location specific cancer risk (Davis
2004), Employer learning of employee productivity (Farber and Gibbons 1996, Altonji and
Pierret 2001, Lange 2007, Ichino and Moretti 2009), and Physician own skill learning (John-
son 2010). In each of these settings, agents use new information to learn about a fixed, but
unknown, parameter of interest.
Alternative models of learning include two features not part of the classical Bayesian
statistical learning model. The first feature is that individuals may “forget” over time.
[CITATIONS] If the parameter being estimated is fixed, then individuals who “forget”
make the mistake of considering new information as more relevant, when all past information
should be weighted equally. The second feature is the possibility that first-hand experience
can effect how past information is processed and in turn how current beliefs are formed.
Two otherwise identical individuals, when provided with the exact same information, might
form different beliefs based on their previous experience. For example, a recent empirical
study on investment decisions and past stock market returns finds evidence that personal
experience effects expectations of future stock market returns (Ulrike and Nagel 2010).
In this paper I examine learning in an important new setting and ask the question:
How do past floods effect beliefs over future flooding? This setting is important for at least
two reasons. The combination of readily available statistical information, but infrequent
personal experience, makes flooding a good context in which to study learning. In the US,
historical flooding information and detailed engineering flood maps are accessible to all
citizens. However, for the residents of most communities, flooding is a relatively rare event.
This is precisely the setting where one might expect deviations from Bayesian learning
(CITATIONS.
A second reason to study flooding is its economic significance. The risk of flooding in
1
the US is largely a financial risk.1 For a typical homeowner in the US the home represents
X% of his total wealth. Moreover, most homeowner insurance policies explicitly exempt
coverage for damage due to flooding. Homeowners in the US must decide each year whether
to purchase flood insurance for the following year. In the US, flood damages averaged $6
billion per year from 1955-1999 (Sarimiento and Miller 2006).
The first goal of this paper is to document whether homeowners update their beliefs
over the likelihood of future floods after observing a large regional flood.2 To answer this
question I construct a unique nationwide community-level panel dataset on flood insurance
policies and the timing of large regional floods. The dataset includes information on all
flood insurance policies in the US for each calender year and whether a community is hit
by a Presidential Disaster Declaration (PDD) flood that year. The logic of looking at flood
insurance policies is that the decision to purchase flood insurance for a home or business
can reveal changing beliefs over the expectation of future floods.
Figure 1 previews a primary finding of this paper. In this figure I graph the event
time dummy variable coefficients from an event study regression of (log) per capita flood
insurance policies in a community on whether the community is in a county hit by a flood.
The event study includes 9, 479 communities and covers the years 1980-2007. Event time
is plotted on the x-axis. Year zero corresponds to a year of a flood, while years −1, ...,−15
and 1, ..., 15 are the years before and after a flood respectively. I bin the tail ends of the
event study, so the leftmost (rightmost) point on the graph is a pooled coefficient for the
years −16 to −27 (16 to 27). The results are normalized to the year before a flood. The
plotted event time coefficients can be interpreted as the percent change in the take-up of
flood insurance policies in the community relative to the year before a flood. The bands
around each coefficient represent the 95% confidence interval and show whether the point
estimate is statistically different from zero.
The increase in the take-up of flood insurance in the year of a flood is strong evidence
that homeowners update their belief of future floods when their community is hit by a
1There are relatively few lives lost from flooding in the US. STATISTIC and CITATION2All property owners (e.g. business owners) can purchase insurance, but for the ease of exposition in this
paper I refer to flood insurance policy holders as homeowners. Homeowners are estimated to make up XX%of all flood insurance policy holders.
2
flood. In the year of a flood there is an 9% increase in the number of insurance policies
per capita in a community that is part of a flooded county. The effect on flood insurance
take-up persists for 9 years before it is no longer statistically different from zero. The event
study regression includes community and year fixed effects, and controls for all past and
future regional floods from 1980-2007. The identifying assumption is that, conditional on a
community’s geography and yearly time trends, whether or not the community is flooded
in a particular year is random.
The event study results are similar under a number of different panel specifications and
robustness checks. For the period 1990-2007 I am able to determine whether a community
in a flooded county was hit by the flood. The take-up of flood insurance estimated from an
event study using this more precise geographic flood variable, gives a coefficient estimate of
10% in the year of the flood with a persistence of 9 years. I also run the event study with
state by year fixed effects to control for state specific yearly trends. The point estimates
in the year of a flood in these specifications are 8% (1990-2007 panel) and 6% (1980-2007
panel). Robustness checks confirm that the effect on take-up is greater for those floods that
caused greater economic damage or were more “unexpected”. Additionally, there is greater
take-up after a flood in communities with a higher percent of the community falling within
the 100 year flood plain.
I also look at if homeowners near to a flood, but not directly hit by the flood, reevaluate
their beliefs over future flooding in their community. I consider different measures for
whether a homeowner is near to a flood. First, I use the 1990-2007 community specific hit
panel to estimate the effect on take-up in communities in a Presidential Disaster Declaration
county that are not hit by the flood. The take-up in these communities is approximately
one-forth as large take-up in hit communities in the preferred specification.
I then use the 1980-2007 panel to estimate the effect on homeowner take-up in commu-
nities not included in the Presidential Disaster Declaration, but “near” to a PDD county.
The effect of a nearby PDD flood on insurance take-up for those communities that are ge-
ographic neighbors is approximately 1.0% and not statistically significant in the preferred
specification.
Next, I run the event study analysis using a second definition of indirect exposure to a
3
PDD flood. I identify those communities in counties not included as part of the Presidential
Disaster Declaration, but which are in the same media market as other PDD communities.
Insurance take-up in the year of a flood in those communities that are in the same media
market, but not in a PDD county, is statistically significant at the 1% level. The coefficient
estimate is about one third as large as that for communities in a PDD county. Insurance
take-up in these communities persists for 5 years before the take-up is no longer significantly
different from zero. Controlling for the geographic distance from a PDD county does not
change the statistical or economic significance of sharing the same media market.
The media neighbor take-up results suggest two things. First, the geographic distance
from PDD flooded counties does not effect insurance take-up. This is evidence against the
hypothesis that less severe flooding near to, but outside a PDD county, leads homeowners
to purchase flood insurance. Second, media news coverage of a large regional flood leads
homeowners in nearby communities to purchase flood insurance at a rate approximately
one-third as high as homeowners in communities that were hit by the flood.
To interpret these findings I consider a simple insurance model and two alternative
learning processes. I assume that homeowners choose the level of insurance that maximizes
their utility. The parameter of interest in the insurance model is the expected yearly
community flood probability. The yearly community flood probability is assumed to be
fixed for each community. Homeowners update their expectation of a flood each year
and then decide whether to purchase flood insurance for the following year. The federal
government sets the rates for flood insurance. Flood insurance is available for purchase by
homeowners before and after each flood at nearly identical rates.
The homeowner flood insurance model implies that each homeowner’s utility maximiz-
ing level of flood insurance will increase when the expected probability of future flooding
increases. I observe community level insurance counts. This paper uses the change in the
number of community level insurance policies as a measure of changing homeowner beliefs
and tests two homeowner learning models using 50 years of data from large regional floods.
The second goal of the paper is to compare two different models of homeowner learning
and provide evidence as to which model better explains the observed homeowner flood
insurance purchasing behavior. I first consider the Beta-Bernoulli Bayesian learning model.
4
Homeowners use information on yearly floods to update their expectation of a future flood
in their community. Current and past yearly flood information is weighted equally when
updating beliefs over floods.
The second learning model I consider is a modified Beta-Bernoulli Bayesian model mo-
tivated by the view that first-hand experience can effect how past information is processed,
and that homeowners might “forget” over time. I introduce one additional parameter to
the conditional expectation updating formula of the Beta-Bernoulli Bayesian model. I refer
to this model as the “EWA Beta Bernoulli” model. This model is a simplified version of the
‘Experience Weighted Attraction’ model first proposed by Camerer and Ho (1999). There
are two interpretations of the additional parameter in the EWA Beta-Bernoulli model, given
that the flood insurance data are aggregated at the community level:
(i) All homeowners discount older flood information
(ii) Homeowners who have experienced or “lived though” past floods may interpret the
same statistical flood information differently than newer residents.
I use the two learning models to simulate expected flood probabilities for each county
using the complete 50 year history of Presidential Disaster Declaration floods. To simulate
the probabilities, I assume that in 1958 (beginning of time series) that each homeowner
knows the national distribution of county-level flood probabilities, but not where his county
falls in this distribution. Each homeowner assumes that he is in the mean county. I allow
the expected flood probabilities to adjust for more than 30 years before the start of the
1990-2007 event study panel. This lengthy “burn in” period helps to minimize the influence
the assumption over the homeowner’s initial beliefs has on the estimation results.
To compare the two learning models, I run flood event study regressions identical to
the estimating equation for Figure 1, except with the simulated Beta-Bernoulli and EWA
Beta-Bernoulli probabilities as dependent variables. An event study regression using the
EWA Beta-Bernoulli probabilities reproduces an important finding implied by Figure 1 and
the insurance model. The change in expected probability in the event study regression is
statistically indistinguishable from zero at the end of the event study. The same event
study analysis using the Beta-Bernoulli probabilities estimates that the change in expected
probability after a flood (relative to the year before a flood) is statistically positive and
5
economically significant for the duration of the event study. Said differently, the simulated
Beta-Bernoulli probabilities imply that the change in flood insurance take-up should be
positive for the entire event study post flood period. This contradicts the finding that the
effect of a flood on the take-up of flood insurance is zero after approximately 10 years.
2 Flooding and Flood Insurance in the US
The first objective of this paper is to document whether being hit by a large regional
flood leads homeowners to reevaluate their belief about the likelihood of future floods.
Homeowner flood beliefs are unobservable. This paper uses the timing of the purchase of
flood insurance as evidence of changing homeowner beliefs over future floods. The goals of
this section are to summarize the relevant institutional details regarding the purchase of
flood insurance, and to introduce and describe the flooding and flood insurance data used
in the paper.
2.1 The National Flood Insurance Program
Flood insurance was not available to home or business owners in the US for most of the 20th
Century. An American Insurance Association study from 1958 claims that in their view “in-
surance against the peril of flood cannot be successfully written.”3 There are several stated
reasons for the apparent breakdown in the private flood insurance market. These include
the lack of accurate flood risk information that could prevent averse selection and repeated
losses on the same policy-holders, as well as, the recognition that many homeowners are
apparently unwilling to pay actuarially fair prices.4
The federal government created the National Flood Insurance Program (NFIP) in 1968.
The establishment of the NFIP was motivated by an economic rationale and by the fiscal
realization that the de facto flood insurance regime was becoming too costly for the federal
government. A series of large floods in the 1960’s led to record amounts of government
assistance for rebuilding. The economic rationale is that unless individuals are able to self-
3Studies of Floods and Flood Damage, 1952-1955 (New York: American Insurance Association, May,1956). Quoted in Anderson (1974).
4Studies of Floods and Flood Damage, 1952-1955 (New York: American Insurance Association, May,1956).
6
insure against floods then there is likely to be an inefficient level of development in flood
prone areas.5
The NFIP sets flood insurance premiums at “actuarial” rates based on historical flood
data and detailed community flood maps created by the Army Corps of Engineers. En-
gineering data and historical observations are used to determine expected damage. The
expected damage based rates are then increased by 30− 40% to cover the expenses of run-
ning the program. The exception to this rate setting process are structures built before
1975 (or the introduction of NFIP in each community). These structures have subsidized
rates that are estimated to be 35−40% of the rate that would be set if they were “actuarial”
rates (GAO 2008). The decision to offer subsidized rates to existing structures was done as
a political concession to minimize opposition to the introduction of the NFIP.
To simplify the rate setting process the NFIP specifies a limited number of nation-
ally designated flood zones. The Corps of Engineers flood maps divide each part of each
community as falling into one of approximately 10 flood zones. The effect is a pooling
of “actuarial” rates within each zone. The zones with the highest flood risk correspond
to the 100 year flood plain. Different premium base rates are offered for each zone and
adjusted within each zone according to a number of factors including: the elevation of the
lowest floor (in feet) above the base flood elevation, whether the building has a basement,
if contents are stored on the first floor, and the level of insurance purchased. 6
Homeowners decide whether to purchase flood insurance each calender year.7 Flood in-
surance polices are sold by private insurance companies at the rates specified by the NFIP.8
Flood insurance and risk information is transmitted to home and business owners in a num-
5The 1966 Task Force report that preceded the introduction of the NFIP states “premiums proportional torisk and equal to both the private and social cost of the flood plain occupance will serve as a rationing device,eliminating economically unwarranted uses of flood plain lands on the one hand, while not prohibiting usesfor which a flood plain location has merit on the other hand.” (John V. Krutilla, “An Economic Approachto Coping with Flood Damage”, Water Resources Research, 1966. Quoted in Chivers and Flores (2002))The NFIP so far has only considered the private cost of insurance when setting premiums.
6See Insurance Manual 2008 (published by FEMA) for more details regarding the rate setting process.7Flood Insurance can only be purchased in those communities that officially participate in the NFIP.
Community participation in the NFIP is not mandatory and requires that a community commit to followingcertain flood plain management principals (e.g. building materials and structural designs). However if acommunity does not participate in the NFIP then residents of the community are not able to avail themselvesof some other federal programs (e.g. Department of Veteran Affairs loan guarantees, and grants to rebuildafter a Presidential Disaster Declaration).
8Before 1983 flood insurance was sold directly by the federal government.
7
ber of ways. First, private insurance companies market flood insurance to homeowners. The
companies are compensated by the NFIP for each flood insurance policy transaction. Sec-
ond, each community offering NFIP insurance posts detailed publicly accessible copies of
the Corps of Engineers flood maps. These maps allow each homeowner to precisely identify
the location of his home and its corresponding flood zone. Third, flood zone documents
are required at the time of purchase or construction of a new home or business if the home
or business is within the 100 year flood plain. There are often building restrictions on new
structures within the 100 year flood plain. In addition, all new structures that have a bank
loan underwritten by the federal government are ostensibly required by law to have current
flood insurance for the duration of the loan. However, this law does not appear to be widely
enforced.9
One important implication of the NFIP rate setting process is that premium rates are
essentially unaffected by whether your home or community is hit by a flood. The base
premium rates (and adjustments) for the 10 nationally designated flood zones are set for
the entire country. The NFIP expects that some communities will be flooded each year. The
base flood rates for the various zones remain virtually unchanged in real dollars. This aspect
of the year to year rate setting process for flood insurance is markedly different from many
other insurance markets. For example, most car insurance companies will substantially
raise premium rates for a driver the year after an accident.
2.2 Flood Insurance Data
All flood insurance policies in the US are sold through the National Flood Insurance Pro-
gram (NFIP). Through a Freedom of Information Act Request, I received NFIP data on all
flood insurance policies from 1980-2007.10 The NFIP data are aggregated at the community
level for each calender year and include: the number of insurance policies, total premiums
9Amendments to the NFIP in 1973 mandated flood insurance for home and business owners that havefederally regulated mortgages and are located in the flood plain. In 1994 the US government estimated thatonly 20% of properties in the flood plain had flood insurance (Mandatory Insurance 2007). An amendmentto the NFIP was passed in 1994 that established penalties for lenders if they issue loans to properties in theflood plain that don’t have flood insurance. A 2006 RAND study estimates that 50% of properties in theflood plain don’t have flood insurance.
10I would like to thank Tim Scoville, NFIP Systems Development Manager, and Andy Neal, NFIP Actuary,for their assistance in providing and interpreting the data.
8
paid by policyholders, the number of damage claims, and the total dollars distributed to
claimants. Non-aggregated individual-level flood insurance data are not available for this
time period for two reasons. First, the NFIP no longer retains disaggregated electronic
records for each policy before the year 2000. Second, privacy considerations prohibit the
NFIP from releasing disaggregated policy data under the Freedom of Information Act Re-
quest for the years 2000-2007.
Panel A of Table 1 shows aggregate flood insurance statistics for the years 1980, 1990,
and 2007. These years were selected because they correspond to the first and last years of
the two event study panels (1980-2007 and 1990-2007) estimated in Section III. All statistics
in Table 1 are calculated at the community level using the same sample of 9,479 communities
that are included in the 1980-2007 event study panel. The exact number of communities
used to generate each statistic in the table varies depending on data availability. The notes
to Table 1 provide sample sizes for each sample statistic. Statistics in parentheses are
medians, while those without parentheses are means. The Premium and Paid Out amounts
are calculated in 2008$.
The first row of Panel A shows the number of community flood insurance polices per
1,000 residents. The mean number of insurance policies is vary similar in 1980 and 1990,
but increases about 50% over the 18 years between 1990 and 2007. The yearly premium
per holder in the median community increases from $191 in 1980 to $562 in 2007. Yearly
Pay Out data vary greatly from year to year. Officials at the NFIP attribute this to yearly
correlation in flooding among areas of the US. In 1980, the ratio of insurance dollars paid
out in the median community to the insurance dollars collected in the median community
is .97. This same ratio for the years 1990 and 2007 is 1.00 and .43. It is important to note
that the decreasing ratio when comparing the years 1980 and 1990 to 2007 is not indicative
of an overall time trend. However, there is a trend in the amount of insurance dollars paid
out per claim (conditional on a claim) in the median county during this time period. The
1980 (approximately $5,000) and 2007 (approximately $10,000) are representative of an
increasing time trend in the size of a flood claim.
There are several limitations of using the aggregated flood insurance policy data sum-
marized in Panel A of Table 1. The first is that I am not able to distinguish between new
9
and continuing flood insurance policies. If the total number of flood insurance policies in-
creases in a community then it is clear that this must include some new policies. However,
I am not able to determine the exact composition of new and continuing policies. The
converse is true for communities where the number of policies decreases. Surprisingly, the
NFIP is also unable to distinguish between new and continuing policies. The reason for this
is that all of the policy transactions occur by private insurance companies. Until recently,
the NFIP has not acquired and retained these data from the private insurers. A second
limitation is that the NFIP does not track which policies are for properties that have been
grandfathered into the program at non-actuarial rates or which policies are for properties
located in the flood plain. The NFIP is currently revamping its data storage system to
keep track of this information in the future. For similar reasons, aggregated homeowner
demographic data are not available.
I supplement the NFIP insurance data with information I generate directly from each
community’s Corps of Engineers flood zone map. In 2003 the NFIP began a process to
digitize each community’s flood map. Through a Freedom of Information Act Request I
received copies of all digitized community flood maps. As of May 2009, there were digital
maps available for approximately one quarter of the communities. I used GIS software
to generate three descriptive variables for each community with a digital flood map: the
percent of the community in the (100 year) flood plain, the percent of the community
in the 100-500 year flood plain, and the percent of the community outside both of these
designations.
Panels B and C of Table 1 display summary information for the subset of communities
in my primary sample with non-missing digital flood maps. Panel C lists the percent of a
community that falls within each of the three flood map designations. The mean (median)
percent of a community’s land area that falls with the flood plain is 14 (8) percent. The
vast majority of each community is within the Corps of Engineers estimated 500 year flood
plain. The median amount of each community falling outside the 500 year flood plain is just
4%. Panel B divides flood insurance take-up in 1980, 1990, 2007 by whether the community
contains more than or less than the median amount of the community land within the (100
year) flood plain. Not surprisingly, the number of flood insurance policies per person is
10
higher in those communities with more land falling within the flood plain. For example, in
2007 the mean number of policies in communities with more than the median amount of
land zoned in the flood plain is 35, while those communities with less than 8 percent have
a mean of 8 policies.
2.3 Presidential Disaster Declaration Process and Flood Data
One challenge in answering the primary research questions of this study is to find nation-
ally representative flood information to link to the community level flood insurance panel
data. Presidential Disaster Declaration floods provide this opportunity. In this subsection
I describe the Presidential Disaster Declaration process and the flood data used in this
paper.
The Disaster Relief Act of 1950 established the Presidential Disaster Declaration (PDD)
system. The legislation formalized a process through which state governments can request
federal assistance in responding to natural disasters that occur in their state. The rationale
is for the federal government to provide assistance when natural disasters are of a scale that
local and state governments are unable to effectively manage the disaster on their own. The
first Presidential Disaster Declaration occurred in Georgia in 1953 in response to tornados.
Since 1953, natural disasters that have led to Presidential Disaster Declarations include:
droughts, earthquakes, fires, floods, hurricanes, and severe storms.
The declaration process has several steps. The governor of a state must write an official
letter to the President requesting that a Presidential Disaster Declaration be declared for
specific counties in the state. The formal request for a Presidential Disaster Declaration
is sent after local and state officials have had time to assess the damage. In the letter
the governor outlines the scope of the disaster including weather and damage information
collected by local agencies. The letter must specify the list of counties in the state that
would be part of a Presidential Disaster Declaration. Historically three-quarters of flooding
Presidential Disaster Declaration requests have been granted. Those requests that are
not granted are referred to as “turndowns”. In 1986 the Federal Emergency Management
Agency established a set of criteria to use when evaluating whether to grant a declaration
request. These criteria included estimated damage costs. Nevertheless, there is institutional
11
discretion when deciding whether to grant requests (Downton and Pielke 2001; Sylves
(2002)???).
A Presidential Disaster Declaration opens the door to two major types of disaster assis-
tance. The largest component of disaster assistance in Public Assistance. Public Assistance
is available to local and state governments, as well as, non-profit organizations located in a
PDD county. These groups can access grant money to remove debris, repair infrastructure,
and to aid in reconstruction of public buildings. The damage must have been caused by
the natural disaster. The Stafford Act of 1988 specifies that the federal government will
cover at least 75% of the replacement value of infrastructure or building repairs. States are
required to pay the remaining 25% as a condition of receiving the federal Public Assistance
money.11
The second type of disaster assistance is Individual Assistance. Individual Assistance
is available to home and business owners in Disaster Declaration counties. Home and
Business owners can access low interest disaster loans to rebuild and a limited amount of
grant money capped at approximately $30, 00012. Existing flood insurance policies are first
applied to the estimated damages when determining levels of eligibility for disaster loans
and grants. As of 1994, home and business owners who don’t have current flood insurance
and are located in the flood plain, can be forced to purchase flood insurance as a condition
of receiving disaster loans or grants.
This paper uses Presidential Disaster Declaration events as a data source of large re-
gional floods. I downloaded information on all Presidential Disaster Declarations involving
flooding from the Public Risk Institute (PERI) website.13 The data collected include the
date of the Presidential Disaster Declaration, the type of disaster, location information
(state and county), and an estimate of disaster cost. I only consider Disaster Declarations
that list coastal storms, severe storms, hurricane, or floods as the primary type of disas-
ter. Unfortunately, I have (so far) been unable to use “turned down” Presidential Disaster
11QUESTION: what was the level of assistance before 1988?12The 2007 threshold for the largest component of the Individual Assistance Program–the Individual and
Housing Program–was capped at $28,200. Most of the grant money is for temporary or emergency expensessuch as covering the cost of interim housing while the home is uninhabitable.
13I would like to thank Richard Sylves for helpful conversations about these data.
12
Declarations as PERI does not list the counties included for these requests.14
Figure 2 displays the number of flooding Presidential Disaster Declarations by county
from 1990-2007. Figure 2 is created using the same dataset used to run the event study
analysis in Section 3. All communities participating in the National Flood Insurance Pro-
gram that have non-missing population data for the 1990-2007 panel are included in the
event study analysis. There are 2704 such counties (or county equivalents). This includes
approximately 90% of all US counties. The vertical axis of Figure 3 measures the percent
of counties with each number of Presidential Disaster Declarations. Nearly every county in
the sample, 92%, is hit by at least one Presidential Disaster Declaration flood during the 18
years from 1990-2007. The median number of PDD floods for a county is three. There are
twelve counties with ten or more PDD floods. Eleven of these twelve counties are located
in North Dakota near to the Red River.
Figure 3a graphs the number of flooding related Presidential Disaster Declarations from
1953-2007. Each bar in the graph corresponds to a single calender year. The vertical axis
measures the number of disaster declarations in each year. There is large year to year
variability in the number of flooding PDDs, with a low of 3 in 1988 and a high of 62 in
2007. Overall there is an upwards trend in the number of yearly Presidential Disaster
Declarations.
This upward trend in Presidential Disaster Declaration floods parallels an increasing
trend in all types of PDDs. Sylves (2002) documents an increasing trend when looking at
all types of Presidential Disaster Declaration requests. From 1953 to 2001, two-thirds of all
Presidential Disaster Declaration requests from state governors were accepted. However,
from 1988-2001 the acceptance rate was three-quarters (implying that from 1953-1987 the
acceptance rate was lower than two-thirds).15 Sylves attributes this increase in overall
acceptance rates of PDD requests to the Stafford Act of 1988. The Stafford act increased
14County for “turned down” Presidential Disaster Declarations are currently not publicly available throughFEMA. I have an outstanding Freedom of Information Act Request, submitted in September 2009, to accessthese data.
15The shift in PDD acceptance rates is similar when the analysis is limitted to flooding events only. Overall,from 1953-2007 three-quarters of the PDD flooding requests are accepted and one-quarter is “turned down”.Splitting the sample at 1988, I find that 70% of flooding PDDs are accepted from 1953-1987, while 82%are accepted from 1988-2007. Said differently, there are 40% fewer “turndowned” flooding PDD governorrequests since 1988.
13
the flexibility for the President to accept PDD requests, and increased the incentive for
states to request a PDD. Sylves writes that “the broader authority to judge what is or is
not a disaster under the Stafford Act has provided presidents since 1988 with more latitude
to approve unusual or “marginal” events as disasters or emergencies.”16 Beginning in 1988,
states can expect a larger federal contribution for PDD flood repairs. The Stafford Act
also clearly specified that the federal government is obligated to pay at least 75% of the
replacement value of all public infrastructure and buildings in PDD counties. Prior to 1988,
the federal government was not required to pay 75%.
If it is true that the increasing number of PDD floods is due to institutional factors
surrounding the PDD process then overall county flood costs should be stable over time.17
Figure 3b plots mean per person flood costs from 1969 to 2007 using National Climatic Data
Center (NCDC) county level flood costs. The National Climatic Data Center collects data
from the National Weather Service. The NCDC data I use in this paper were compiled by
the Hazards and Vulnerability Research Institute and maintained as part of the SHELDUS
online database.18 The NCDC Sheldus data track county level yearly flood costs and
ostensibly include data from all floods in each county for each calender year. The Sheldus
data include smaller floods and occasionally multiple PDD floods that occur in the same
county in the same calender year.
The vertical axis of Figure 3b plots the mean per person yearly flood cost for all PDD
counties with non-missing flood cost data in the year of a Disaster Declaration. There is
large amount of year to year variability. The per capita flood cost in the median PDD
county ranges from a low of $1.0 in 1970 to $11.6 in 1979 (2008 $). There doesn’t appear
to be a discernable trend in the per person flood cost in the median PDD county from
16Sylves 200217The increasing number of PDD floods and stable county flood costs should also imply that the cost per
PDD flood is decreasing. Unfortunately, the data that would allow me to measure costs per Presidential Dis-aster Declaration are confounded by institutional changes in the reimbursement of flood costs. The StaffordAct led the federal government to cover a larger portion of damaged public buildings and infrastructureafter 1988. The PERI Presidential Disaster Declaration cost variable measures the federal government shareof flood costs associated with PDDs. It is difficult to use this variable to compare the cost of floods beforeand after 1988.
18The Hazards and Vulnerability Research Institute is housed at the The University of South Carolina.SHELDUS stands for “Spatial Hazard Events and Losses Database for the United States”. The SHELDUSwebsite is: http://webra.cas.sc.edu/hvri/products/sheldus2.aspx I would like to thank Chris Emrich forassistance in interpreting the SHELDUS cost data.
14
1969-2007. Overall, the mean per person flood cost in Presidential Disaster Declaration
flooded counties that report data has been roughly constant since 1969.19
Presidential Disaster Declaration floods are determined at the county level. However,
not all communities within a county may be effected by the flood. I construct a variable
to identify which communities in PDD counties are “hit” by each Presidential Disaster
Declaration using information on claims via the Public Assistance program. As described
above, state and local governments–as well as non-profits–are entitled to grant money to
repair infrastructure and rebuild structures damaged by flooding in counties included in
a Presidential Disaster Declaration. Through a Freedom of Information Act Request, I
received a datafile that lists the location of every Public Assistance damage claim paid
out from 1990-2007.20 There are more than 800,000 unique observations. All observations
are linked to the Presidential Disaster Declaration under which it was filed. From these
data I create an indicator variable for whether a community within a PDD county is “hit”
by a particular flood. I consider a community to be “hit” if there is at least one Public
Assistance claim with a damage location within the community.
One challenge in using the Public Assistance claims data has been identifying the com-
munity name from each claim’s location information and correctly matching it with the
NFIP flood insurance information. Each claim lists an address for the location of the
damage. The electronic address is entered directly from the paper claims form by NFIP
personnel and saved as a single string variable in the database. Unfortunately, the addresses
are not always complete due either to the initial omission of data from the claims form or
from error in data entry. A second complication is that the Public Assistance addresses
will sometimes list a political sub-jurisdiction as the the community name, while the NFIP
uses the entire community (or vice versa).21 I am able to match over 90% of the Public
Assistance claims to a NFIP community. I almost certainly fail to code some communities
19The NCDC data are voluntarily reported by individual weather stations. There are numerous cases ofmissing data. For more than 40% of the years in the panel, the median flood cost of a county with a PDDflood is reported as $0. I spoke to analysts who compiled the Sheldus NCDC database. Their view is thatthe missing county data are random. I have not yet done any independent analysis of this assumption.
20I would like to thank Deni Taveras and Paul Weschler for preparing the data and shepherding the datarequest through the FOIA process.
21For example, the Town of Hampton, NH includes the village district of Hampton Beach. The PublicAssistance damage location might list Hampton Beach, while all of the NFIP flood insurance informationis for the Town of Hampton.
15
as being “hit” by a Presidential Disaster flood due to the non-matched claims data.22 The
effect on the event study regression estimates will be to bias insurance take-up coefficient
estimates after a “hit” towards zero.23
Panel D of Table 1 provides summary statistics for the percent of communities in PDD
counties “hit” by Presidential Disaster Declarations from 1990-2007. Overall, 32% of com-
munities in counties with a Presidential Disaster Declaration are “hit” by a PDD county
level flood in the year of a flood. The percent of communities “hit” by a PDD flood is sim-
ilar for those communities with less than the median amount of community land mapped
in the flood plain, as it is for communities with more than the median amount of land
considered within the flood plain. 29% of less than median communities are “hit” by a
PDD flood whereas 35% of more than median communities are “hit”. [NEED sentence or
2 here explaining the interpretation/significance of this]
3 Econometric Model and Estimation Results
The first goal of this paper is to document whether home and business owners update their
beliefs over future flooding after experiencing a large flood. I use changes in the number of
homeowners with flood insurance policies as a measure of changing beliefs. The economic
model underlying the relationship between floods, flood beliefs, and flood insurance will be
discussed in detail in the next section. The key prediction of the model is that if homeowner
beliefs over future floods increase then more homeowners will purchase flood insurance. This
paper uses the timing of large regional flood events as exogenous events that potentially
lead homeowners to revise upwards their beliefs of future floods. This section discusses the
statical model and the main estimation results.
22I have an outstanding FOIA request, submitted in August 2008, for claims data from the IndividualAssistance Program. I intend to use the Individual Assistance program claims data as a means to cross-checkthe “hit” designation determined from the Public Assistance claims data.
23In the event study regressions I identify the effect on insurance take-up of being “hit” off of thosecommunities that are not “hit” by the flood. Accidently assigning “hit” communities to the not hit groupwill bias upwards the insurance take-up of the non-hit group (assuming that there is a positive correlationbetween being “hit” by a flood and take-up), and bias downwards the coefficient estimate of the take-up of“hit” communities relative to the non-hit group.
16
3.1 Event Study Empirical Specification
This subsection outlines the empirical specification I use to test whether homeowners update
their beliefs over future flooding after their community is hit by a flood. I use a flexible
event study framework that nonparametrically estimates the causal effect that large regional
floods have on the take-up of flood insurance. Equation 1. shows the main estimating
equation.
log(takeupct) =T∑
τ=−TβτWcτ + αc + γt + εct (1)
The unit of observation is a community calender year. The dependent variable in
Equation (1), log(takeupct), is Log Flood Policies Per Person for community c in year t.
The independent variables of interest are the event time indicator variables, Wcτ . These
variables track the year of a Presidential Disaster Declaration hit and the years immediately
preceding and following a hit. The indicator variable Wc0 equals 1 if community c is hit
by a flood in that calender year. The indicator variable Wcτ equal 1 if a community is hit
by a Disaster Declaration in −τ years. For example, Wc−5 equals 1 if community c was
hit by a flood 5 years ago, and Wc5 equals 1 if community c is hit 5 years in the future.
Many communities are hit by more than one PDD flood during the event study. For these
communities each flood is coded with its own set of indicator variables. For example,
Hazlehurst, GA is hit by a Presidential Disaster Declaration in 1991 and 2004. Thus for
Hazlehurst, GA in Year 2000, Wc9 == 1 since it has been 9 years since the 1991 PDD and
Wc−4 == 1 since it is 4 years before the 2004 PDD.
In most of the specifications of equation (1) I bin the Wcτ by creating a single indicator
variable for the end periods. The bin indicator variables serve a practical purpose. These
variables pool the effect on take-up over multiple event years to increase statistical power.
I am most interested in the years shortly before and after a flood. The indicator variables,
Wcτ , near the tails of the event study are identified off of many fewer observations and
therefore have large standard errors. For example, in the 1990-2007 panel event study
Wc,17 = 1 only if there is a Presidential Disaster Declaration in 1990. In the 1990-2007
panel event study I create Wc,early = 1 if τ ∈ [−17,−11] and Wc,late = 1 if τ ∈ [17, 11].
Equation (1) is then estimated with these 2 bin indicator variables rather than including
17
the individual variables Wc,11, ...,Wc,17 and Wc,−11, ...,Wc,−17.
Two flood data coding decisions deserve comment. First, occasionally a community is
hit by more than one PDD flood in the same calender year.24 I don’t distinguish between
communities hit by one or more than one PDD flood in a particular year when estimating
equation (1). The reason for this is that the flood insurance policy count data are aggregated
by year. I am concerned with whether a community is hit by any flood in a calender year.
Second, I only consider leads and lags for a Presidential Disaster Declaration if the PDD
occurred within the time frame of the event study. Therefore the Wcτ indicator variables
all equal 0 for a community with respect to any event that occurs outside the event study
window. I run a number of robustness checks to test the sensitivity of this coding decision.
Equation (1) also includes community fixed effects, αc, and calendar year fixed effects γt.
These fixed effects control for unobserved (and unchanging) community characteristics and
yearly factors. Community geography is important in predicting the likelihood of a flood.
For example, the underlying community geography includes surface characteristics, such as
the percent of a community located in the flood plain, and location specific factors such as
average rainfall. Year fixed effects account for year to year changes in NFIP institutional
factors and other yearly trends that may effect take-up.
The preferred specification of equation (1) replaces the year fixed effects, γt, with a
full set of state by year fixed effects. The state by year fixed effects non-perimetrically
control for state specific time trends.25 εct is a stochastic error term. Finally, the causal
interpretation of Equation (1) comes from the assumption that whether a community is hit
by a flood in a particular year is random conditional on community and year (or state by
year) fixed effects.
The event time indicator variable Wc−1 is normalized to zero when I estimate Equation
(1). In practice this is done by excluding Wc−1 from the regression. Normalizing Wc−1 to
zero provides for a useful interpretation of the remaining event time indicators in Equation
1. The estimated coefficients for all other event time variables are interpreted as the percent
24Conditional on a community being in a county with a Presidential Disaster Declaration in a particularyear, 11% of the time there are more than one PDD’s in the same year (for communities in the 1990-2007panel).
25When running the preferred specification I often first demean the data...
18
change in the take-up of flood insurance in community c relative to the year before a flood.
In other words, the event study answers the question: “How much greater is the take-up of
flood insurance in each year after a flood compared to the year before a flood?”
I estimate Equation 1 on a panel of communities over two different time periods:
(i) 1980-2007, (ii) 1990-2007. These time periods are selected based on data availabil-
ity. Community-level flood insurance policy data are available beginning in 1978, but the
community-level population data is not as available until 1980. Thus, the 28 year period
from 1980-2007 is the longest panel for which I can estimate flood insurance take-up for a
large sample of communities. In all of these regressions the definition of a flood is whether
a homeowner resides in a community that is in a Presidential Disaster Declaration county.
For the period 1990-2007 I can use a more detailed definition of a flood hit. Beginning in
1990 I confirm whether a PDD flood declared at the county-level damaged infrastructure or
public buildings in each community in the county. I estimate Equation (1) over this period
using the community-level definition of a flood.
3.2 Estimation Results for Communities Hit by a Flood
Figures 4a and 4b graph the event study estimation results of equation (1) on the 1990-2007
panel. Each figure plots the event time dummy variable coefficients, βτ , from a regression
of (log) per capita flood insurance policies in a community on whether the community is in
a Presidential Disaster Declaration county and hit by a flood. Both event studies include
10, 665 communities. Event time is plotted on the x-axis. Year zero corresponds to a year
a community is hit by a PDD flood, while years −1, ...,−10 and 1, ..., 10 are the years
before and after a flood respectively. I bin the tail ends of the event study, so the leftmost
(rightmost) point on the graph is a pooled coefficient for the years −11 to −17 (11 to 17).
The results are normalized to the year before a flood hit. The plotted event time coefficients
can be interpreted as the percent change in the take-up of flood insurance policies in the
community relative to the year before a flood. The bands around each coefficient represent
the 95% confidence interval and show whether the point estimate is statistically different
from zero. Standard errors are clustered at the state level.
Figure 4a is the preferred specification of equation (1) and includes state by year fixed
19
effects. There is no event year time trend in the years before a flood. The effect of a future
flood is not statistically different from zero for all time periods before the flood. The point
estimates for the pre-flood event years range from −1.4% to 1.5%. In the year of a flood
there is an 8% increase in the take-up of flood insurance relative to the year before a flood.
Take-up peaks at 9% the year after a flood. Flood insurance take-up after the flood remains
positive and statistically significant for 10 years. After 10 years, flood insurance take-up is
not statistically different relative to the year before a flood.
Figure 4b plots the event time coefficients from the estimation of equation (1) that
includes year fixed effects. The estimation results are very similar to Figure 4a. There is
no time trend before a community is hit by a PDD flood. In the year of a flood there is a
10% increase in the take-up of flood insurance. The effect of a flood on the take-up of flood
insurance persists for 9 years. Overall the point estimates and standard errors in Figure
4b are larger than those in Figure 4a. Controlling for state specific time trends increases
the precision of the estimation. The point estimates are somewhat smaller in magnitude,
particularly in the years immediately following a flood.
Table 2 shows the estimation results of equation (1) from six separate regressions. Given
the large number of independent variables, I save space by only including the point esti-
mates. Statistically significant coefficients are displayed in bold. The level of statistical
significance is indicated by the number of stars: 1% (***), 5% (**), and 10% (*). The
coefficient for the year before a flood is not included in the table because this coefficient is
normalized to zero. The first three columns of Table 2 are estimated with year fixed effects,
while the second three columns include state by year fixed effects. Figure 4b corresponds
to Column (1) and Figure 4a corresponds to Column (4).
Columns (2) and (5) of Table 2 estimate specifications of equation (1) that include event
time dummy variables for whether a community is in a PDD county, but not hit by the
flood. Table 2 only includes the event time coefficient for non-hit communities in the year
of a flood. In column (2) the coefficient estimate for take-up in the year of a Presidential
Disaster Declaration for communities in a PDD county and not hit by the flood, is 4.0%.
The coefficient for communities in a PDD county and not hit by the flood is 1.8% and
statistically significant at the 10% level in the preferred specification (column 5). Take-up
20
in non-hit communities remains statistically significant at the 5% or 10% level for the first
5 years after the county Presidential Disaster Declaration. The point estimates for these
years range from 2.2% to 3.4%.
The level of insurance take-up is approximately one third the magnitude of take-up for
hit communities in the year of a flood. However, take-up in communities not directly hit
by the flood is not statistically different from zero when equation (1) includes state specific
yearly trends. This result implies that only those homeowners in communities directly
impacted by the flood revise their beliefs over the likelihood of future flooding.
One threat to the interpretation of the event time point estimates is if a community
was hit by a previous flood before 1990. The effect on take-up due to a previous flood
might be absorbed into the point estimates for a hit during the 1990-2007 panel. The most
likely result would be to decrease the estimated coefficients in the 1990-2007 panel over
what they otherwise would have been. Each post flood coefficient now reflects the effect
on take-up of more than one flood. Since the year before a flood is normalized to zero
and the take-up impulse response function decreases over time then unaccounted for floods
occurring shortly before the event study will bias down the estimated post flood event time
coefficients.
Columns (3) and (6) are estimation results for the 1990-2007 panel of communities,
except that all communities in a county with a Presidential Disaster Declaration from
1980-1989 are excluded from the panel. I am not able to determine whether a community
in a PDD county is hit by the flood before 1990. However, I do know which counties
were included as part of Presidential Disaster Declarations from 1958-2007. Restricting the
sample to communities without a PDD flood in the 1980’s leads to a flood take-up impulse
response function that is very similar to that from the complete 1990-2007 panel. Overall
the estimation results from columns (3) and (6) suggest that floods occurring before 1990–
and not explicitly controlled for in the event study–do not greatly impact the results.26
26Excluding communities in counties hit by a Presidential Disaster Declaration during the 1980’s couldchange the composition of the panel in an important way. Those counties with higher underlying floodprobabilities would be more likely to have had a PDD flood in the 1980’s. If this were true, homeowners inthe remaining communities may be more “surprised” to be hit by a flood. Thus, excluding communities incounties with a Presidential Disaster Declaration from the 1980’s may lead to higher post flood estimatesof take-up. This doesn’t appear to be the case for the sample estimated in Columns (3) and (6). In SectionV I provide further evidence on how take-up varies in communities with different PDD flood histories.
21
Figure 5 limits the 1990-2007 event study panel to those communities that have elec-
tronic Corps of Engineer (CORPS) Flood Maps. The electronic flood maps are available
for about 25% of the communities and reduces the sample of communities from 10,665
to 2,626. I estimate equation (1) on two different sub-samples of communities based on
whether or not the community has more than the median amount of land (8%) within the
100 year flood plain. Both event studies include the preferred state by year fixed effects.
The event time coefficients from the sample of communities with more than 8% of land in
the flood plain are graphed in red. Event time coefficients from a sample of communities
with less than 8% of the land in the flood plain are graphed in black. Coefficient estimates
that are statistically significant are graphed with the solid dots. Coefficient estimates not
statistically significant at the 5% level are displayed with open circles.
The post flood insurance take-up event time point estimates for communities with more
than the median amount of land in the 100 year flood plain are consistently larger than
those for communities with less than the median amount of land in the flood plain. Similar
to the baseline 1990-2007 panel regressions, all event time coefficient estimates before a
flood are not statistically different from zero. Homeowner take-up in a community in the
year a community is hit by a PDD flood is twice as large (7.7% compared to 3.6%) for those
communities with more land in the flood plain. I can reject at the 5% level an F-test for the
null hypothesis that take-up in the year of a PDD flood hit is the same for the two groups
of communities27 Take-up after a PDD flood in those communities with more than 8% of
the land in the flood plain persists for 8 years. The take-up impulse response function in
those communities with less than 8% of the land in the flood plain is statistically different
from zero only for the first three years. These results suggest that a higher percentage of
homeowners increase their expectation of future flooding in communities with more than the
median amount of land in the flood plain. It should be noted, however, that the standard
errors are large given the smaller sample size.
I use the PERI Presidential Disaster Declaration flood cost variable to distinguish be-
27I test for the difference in the coefficient in a regression that includes both above and below mediancommunities in the same estimating equation. The results from estimating a single equation that includesall of the communities with non-missing map data are similar to those from the two separate regressionsplotted in Figure 5a.
22
tween large and small floods. I interact each post flood event time variable with an indicator
variable for whether or not the PDD flood is above or below the median PERI flood cost.
Figure 6 graphs estimates of equation (1) using the 1990-2007 panel.28 The red dots repre-
sent the post flood impulse response function for those floods that are above median cost.
The black dots, beginning with the year of a hit, are for take-up in those communities that
are below the median. I do not interact the event time coefficients before a flood with the
flood cost indicator variable. The estimated coefficients for the years before a flood are
common to all PDD floods. The estimation equation includes state by year fixed effects.
Not surprisingly, flood insurance take-up in communities hit by above median cost PDD
floods is greater than in those communities hit by below median cost floods. The slope of the
take-up impulse response function is similar following the two types of floods. The entire
above median cost flood insurance take-up impulse response function is shifted upwards
relative to that for below median cost floods. Take-up after an above median cost flood is
significantly different from zero for the ten years following a flood. Take-up after a below
median cost flood is significant only in the year after a flood and four years after a flood.
An F-test which tests the null hypothesis of no difference between the post flood event time
coefficients can be rejected at the 5% level for the first three flood years and the 8th year
after a flood.
There are two possible interpretations of Figure 6. First, the flood is larger in size so
that more homeowners are directly flooded. This leads a greater number of homeowners
in the community to revise upwards their belief over future floods and to purchase flood
insurance. Second, is the possibility that above and below median cost floods have the
same effect on homeowner expectation of future floods, but that the above median cost
floods also lead homeowners to revise their expectation of flood damages conditional on a
flood. The assumption of this paper is that homeowners observe floods and update their
expectation of a flood, but not the amount of damage conditional on having a flood. The
amount of (real) dollar damage to a home conditional on a flood is assumed to be constant
28Institutional changes are likely to mechanically increase the PERI flood cost variable after the passageof the Stafford Act in 1988 relative to before 1988. I estimate a 1990-2007 event study panel. Institutionalfactors that increased access to federal Public Assistance reimbursement money do not change over theperiod of the event study.
23
over time.
The fixed damage assumption could be violated in three ways. First, perhaps the same
sized flood now causes more damage than in the past. As an example, a flood four feet deep
might cause more damage to a home because a home is larger, or the materials used in home
construction are more expensive. Second, more recent floods may be larger in magnitude.
For example, suppose that the average depth of a flood is now 8 feet whereas in the past it
was 4 feet. A flood 8 feet deep would likely damage the second floor of a house, while the
4 foot flood might only damage the first floor. Third, homeowners may have expectations
over how much assistance the government would provide if there is a flood. If initially
homeowners anticipate a large amount of government assistance, but over time learn that
the government assistance is limited, then the expected (own) cost of flooding will increase.
Estimation of equation (1) on the 1980-2007 panel has the advantage of a longer panel
with more PDD floods. However, I am not able to determine whether a community is “hit”
by a PDD flood before 1990. As such, the geographic definition of a flood for the event
study regressions using the 1980-2007 panel is whether a homeowner lives in a community
that is part of a county included in a Presidential Disaster Declaration. Using the county
as the geographic designation of a flood averages the effect of a flood on flood insurance
take-up over those communities that were hit by a flood and those not hit by a flood.
Figures 7a and 7b plot the event time coefficients from the estimation of equation (1)
on the 1980-2007 panel. The interpretation of both figures is the same as in the 1990-
2007 panel (Figures 4a and 4b) except that now each flood is measured at the county
level. Each figure plots the event time coefficients from a separate event study regression
of (log) per capita flood insurance policies in a community on whether the community is in
a Presidential Disaster Declaration county. I estimate equation (1) with a pooled indicator
variable so the leftmost (rightmost) point in each graph is a pooled coefficient for the years
−16 to −27 (16 to 27). The 1980-2007 panel includes 9,479 communities.
Figure 6a is the preferred specification that flexibly controls for state specific year trends.
All of the event time coefficient estimates before the year of a PDD flood are statistically
not different from zero and economically small. The point estimates range from -0.5% to
1.0%. In the year of a flood there is 5.7% increase in the take-up of flood insurance relative
24
to the year before a flood. Flood insurance take-up peaks the year after a flood at 7.4%.
The effect of a flood on the take-up of insurance persists for 7 years, after which take-up is
not statistically different from what it would have been relative to the year before a flood.
Figure 6b plots the coefficients from the 1980-2007 panel estimated with year fixed
effects. The event study specification is the same as Figure 1 in the Introduction. The
overall pattern is the same as in Figure 6a. However, similar to the 1990-2007 panel
estimates, the point estimates and standard errors are slightly larger for the specification
that includes flexible yearly trends (Figure 6b), rather than state specific yearly trends
(Figure 6a).
3.3 Estimation Results for Neighboring Communities
This subsection returns to the question of whether homeowners update expected flood
probabilities if they are not directly hit by a flood. The last subsection provided evidence
that homeowners in Presidential Disaster Declaration counties who live in communities not
directly hit by the flood update their belief of that their community will be hit by a future
flood. The take-up of flood insurance is about one-third as large in the non-hit communities
relative to the hit communities.
Next, I use the 1980-2007 panel to estimate the effect on homeowner take-up in com-
munities in counties not included in the Presidential Disaster Declaration, but “near” to a
PDD county. Table 3 shows selected coefficients from ten separate regressions of equation
(1) using the 1980-2007 panel. Note that for these regressions I first demean the data for
each community using a fixed effect transformation. I then estimate equation (1), excluding
the community fixed effects, on the demeaned data.29 The first five columns are from event
study regressions that include year fixed effects, while the second five columns include state
by year fixed effects. All of the regressions include the complete set of event time variables
for PDD counties. However, only disaster county, the event time variable for the year of a
PDD flood, is shown in the table. Each regression also includes event time coefficients for
the relevant neighbor designation. Only the neighbor coefficient for the flood is included in
29I manually correct the standard errors to account for having one fewer independent year for eachcommunity. I need to first do the within community transformation due to computing power restrictionsgiven the size of the data set.
25
the table.
The purpose of Table 3 is to estimate flood insurance take-up for communities in counties
“near” to a PDD county. Columns (1) and (2) estimate homeowner take-up for commu-
nities in counties that are geographic neighbors to a PDD county, but not included in the
Presidential Disaster Declaration. Column (1) considers geographic neighbors to be all
adjacent counties.30 Column (2) defines a geographic neighbor as the 5 closest counties by
the distance between county centroids.31 Both definitions of a geographic neighbor give
similar results. In the year of a PDD flood, homeowners in communities that are geograph-
ically close to the PDD flood increase the take-up of flood insurance by a 1.6% and 2.0%
respectively. The point estimates are approximately one fifth the magnitude of the take-up
by homeowners in PDD counties and statistically significant at the 10% level.
Next I consider the effect on take-up of being a “media neighbor”. Nielson Media
Research classifies each US county as belonging to a primary radio and television media
market. There are 210 unique designated media markets (DMAs).32 33 Column (3) of
Table 3 estimates flood insurance take-up in the year of a PDD flood in communities not
part of a Presidential Disaster Declaration, but that are in the same media market as other
communities hit by a PDD flood. Flood insurance take-up is 2.3% higher in media neighbor
communities in the year of nearby PDD flood relative to the year before the flood. This
point estimate is statistically significant at the 1% level and of a similar magnitude as the
take-up for geographic neighbors.
Columns (4) and (5) of Table 3 estimate a version of equation (1) that considers both
30The adjacent county file, Contiguous County File, 1991, was created by The Inter-University Consor-tium for Political and Social Research (www.icpsr.umich.edu). The Contiguous County File, 1991 includescounties that share a boarder, are connected by a major road, or are connected due to “significant economicties”. I only consider those counties that share a boarder.
31I would like to thank Juan Carlos Suarez Serrato for creating and sharing the datafile that lists all UScounties and the 10 closest counties as measured by Euclidean distance between county centroids. I use the5 closest counties as the definition of a centroid neighbor in this paper. I experimented with definitions thatused the closest county and the closest 3, 5, and 10 counties respectively. Using the 5 closest counties is thedistance definition that had the greatest statistical power.
32I would like to thank James Snyder for sharing the DMA data. Synder and Stromberg (2010) use thesedata to estimate how press covered effects citizen knowledge, politicians’ actions, and policy. The data werefirst collected and used by Ansolabehere and Snowberg (2006) and Ansolabehere and Gerber (unpublishedmanuscript).
33The primary media market can change over time for a county. Nielson Media Research released newcounty DMA classifications in 1980, 1990, and 2000. For those counties that change media markets overtime, I assume that a county is in a media market until the year the new DMA data are released.
26
adjacent neighbors and media neighbors. Interestingly, there is no effect on take-up of
being a geographic neighbor after controlling for whether a community is in the same
media market. The point estimate for insurance take-up for communities in the same
media market remains virtually unchanged.34.
When I estimate the preferred specification of equation (1) the pattern of results be-
comes even more clear. Columns (6)-(10) of Table 3 estimate the same event study spec-
ifications, but control for state specific time trends. The geographic neighbor coefficients
are no longer significant (columns 6 and 7), while the media coefficient remains unchanged
(column 8). The event study specifications of columns (9) and (10) include both geo-
graphic neighbor and median neighbor impulse response functions. Homeowner take-up in
communities in adjacent counties is economically small (around 1%) and not statistically
significant. Take-up in communities that are in the same media market, but not hit by
the flood, increase to about one third the magnitude of take-up in communities in PDD
counties.
Table 3 taken together with the estimates from Column (5) of Table 2 imply that
homeowners update their beliefs over future flooding if they live in a community hit by
a flood or if they are in the same media market as a community hit by a flood. Should
expand a bit more here.
4 Economic Framework: Insurance Model and Two Alter-
native Learning Models
In this section I present a simple flood insurance model and two alternative homeowner
flood probability learning processes. The goals are twofold. First, provide an economic
framework to interpret the empirical results from the last section. Second, outline two
theories of learning and belief formation that have been used in the literature. Section V.
presents evidence as to which theory of learning best describes observed flood insurance
take-up.
34The results are very similar if I estimate equation (1) with the media neighbor variable and the centroidneighbor variable.
27
4.1 Insurance Model
Each year homeowners purchase the level of flood insurance that maximizes their expected
utility given their belief about the probability of a flood.
maxqictEt[u(qict, wi, li, r, pict)] = pict ∗ u(wi− li− rqict + qict) + (1− pict) ∗ u(wi− rqict) (2)
qict is the level of flood insurance selected by homeowner i in community c in year t. There
are four parameters. The parameter of interest is pict, the homeowner belief of the yearly
flood probability in time t. wi is homeowner wealth and li is the amount of flood damage
conditional on being hit by a flood. r ∈ (0, 1) is the dollar rate per $1 of flood insurance.
Each homeowner chooses the level of insurance, q∗ict, that maximizes expected utility at the
end of the calender year after observing whether there is a flood and updating beliefs pict.
f(qict, wi, li, r, pict) ≡ pict(1−r)(wi− li−rqict+qict)∗u′− (1−pict)r ∗u′(wi−rqict) = 0 (3)
Equation (3) defines f() as an implicit function equal to the first order condition for the
homeowner flood insurance problem. q∗ict solves the implicit function. wi, li, r are all
constant parameters. The insurance rate is set by the federal government and to a close
approximation is fixed in real dollars. An assumption of this paper is that homeowner beliefs
over flood damages are fixed. Figure 3b provides evidence that county level flooding costs
are constant from 1969-2007. In the next subsection I discuss implications if homeowners
update over both the probability of a flood and damages conditional on a flood.
Homeowner wealth, in contrast to the assumption of this paper, is certain to vary over
time. In particular, in a year of a flood, those homeowners without flood insurance are
likely to have a negative shock to their wealth.
If a homeowner’s belief over future flooding increases, then the utility maximizing level
of flood insurance will increase. The comparative static,∂q∗ict∂pict
> 0, by the implicit function
theorem, provided u′ > 0 and u′′ < 0.35 Figure 7a plots q∗ict as a function of pict for a
35By the Implicit Function Theorem (IFT) we can write∂q∗ict∂pict
= − ∂f/∂pict∂f/∂q∗ict
, where f is equation (3). Note
that to apply the IFT two conditions on f must hold. First, equation (3) must be continuously differentiableat (q∗ict, pict), given the values of the fixed parameters wi, li, r. Second, ∂f/∂q∗ict 6= 0 at (q∗ict, pict). I assume
28
representative homeowner living in community c in time t. q∗ict is plotted on the vertical
axis with a horizontal line at q∗ict = 0. pict ∈ [0, 1] is plotted along the horizontal line and
increases as you move towards the right. p̄ic is the cutoff value of pict such that q∗ict = 0.
If the belief over future flooding in year t is greater than p̄ic, then homeowner i living in
community c will purchase flood insurance for that calender year. p̄ic varies by homeowner
depending on the parameters wi, li, r, and each homeowner’s level of risk aversion. The
assumptions over the homeowner utility function (u′ > 0 and u′′ < 0) give the q∗ict(pict)
function its upward sloping concave-up shape.
I observe flood insurance count data aggregated at the community level. Figure 7b
shows the relationship between the number of community level flood insurance policies and
beliefs over future floods. On the vertical axis is the number of flood insurance policies in
the community: Qct =∑I
i=1 1(q∗ict > 0) =∑I
i=1 1(pict > p̄ic). The horizontal line plots
flood probabilities. Similar to 7a, each homeowner’s q∗ict(pict) can be plotted in Figure 7b.
I have plotted this function for three homeowners in the community.
For ease of exposition, let’s first assume that all homeowners in each community are
impacted by a flood in the same way and use the same learning process when adjusting
beliefs over future floods. If this were the case, then pict = pct so that each year, everyone in
the community shares the same flood belief. The dashed vertical line in Figure 7b represents
a hypothetical (universally shared) flood belief for each homeowner in the community. pct is
greater than the flood insurance cutoff point for homeowners 1 and 2, but not for homeowner
3. Homeowners 1 and 2 will purchase flood insurance. It is important to emphasize that
although each homeowner’s belief of a flood is the same, that q∗ict(pict) varies for each
homeowner.
Figure 7b helps to clarify two points. First, I assume in this paper that there is a contin-
uous range of homeowner insurance cut-off points (p̄ic) in each community. In other words,
for a change in pct there will be a marginal homeowner just willing to purchase (if dpict > 0)
or fail to renew an insurance policy (if dpict < 0). Second, although other researchers have
noted an increase in the average level of community wide insurance coverage among policy
holders after a flood, this doesn’t necessarily follow from the assumptions of this paper
that these two conditions hold.
29
(Michel-Kerjan and Kousky 2008). There are two effects of an increase in community flood
beliefs (a shift of the dotted line to the right): (i) existing policy holders will purchase more
insurance, and (ii) new “marginal” homeowners will decide to purchase insurance. The av-
erage level of flood insurance (conditional on having insurance) in a community depends on
the composition of these two effects. For example, if the curvature of the q∗ict(pict) functions
is relatively flat, or if there are many new policy holders, then the average level of insurance
(conditional on having insurance) may decrease. The curvature of q∗ict(pict) is relatively flat
for less risk averse homeowners. There will be more new homeowners purchasing flood
insurance in high density cutoff regions along the horizontal interval.
The interpretation of the community aggregated insurance policy count data is similar
if we relax the strict assumption that all homeowners in the same community perceive each
flood the same when updating beliefs. Homeowners in a community likely consider flooding
information differently depending on where their home was located in the community and
if their home is hit by the flood. Under this more realistic view, each homeowner would
have individual specific beliefs over future flooding. We could adjust figure 7b so that there
is a dashed vertical line specific to each homeowner.
4.2 Homeowner Learning Models
One of the conclusions from the event studies of Section III is that homeowners react to a
new flood by purchasing flood insurance. I model the observed take-up in flood insurance as
the utility maximizing decision from an annual homeowner insurance purchasing problem.
The underlying assumption is that homeowners use the information implicit in a new flood
event to update their expectation over the probability of future flood hit. In other words,
the changing homeowner beliefs towards future floods is driving the dynamics of insurance
take-up after a flood. In the next Section I provide evidence in support of this assumption.
This subsection presents two models of homeowner learning.
Floods potentially provide new information for homeowners about their underlying flood
risk. Standard (neo-classical) economic models assume fully “rational” economic agents. In
the context of flooding, this implies that homeowners would use the Beta-Bernoulli Bayesian
30
learning model to synthesize existing information and update beliefs.36 In this model, large
yearly regional floods, yt, are distributed Bernoulli where the probability of a flood in a
given year for community c is: P (yt = 1) = p. Each community’s yearly flood draw is
assumed to be independently drawn from a stationary flood distribution with parameter p.
The probability of a flood in a given year, p, is assumed to be distributed Beta(α, β)37. The
first two moments of p ∼ Beta(α, β) are E[p] = αα+β and V ar[p] = αβ(α+ β)2)(1 + α+ β).
I assume that homeowners observe whether there is a flood in a given year and update
their expectation of a future flood. The conditional mean and variance are:
E[p|St, t] =St + α
t+ α+ β(4)
V ar[p|St, t] =(St + α)(t− St + β)
(t+ α+ β)2(1 + α+ β + t)(5)
t is the number of yearly observations (time periods) St =∑t
s=1 ys is the number of
observed floods. α and β are fixed parameters from the Beta distribution. The parameters
α and β determine the initial belief over flooding. Homeowners use the conditional flood
expectation equation to update this belief each year. One property of the Beta-Bernoulli
Bayesian model is that over a sufficiently long period of time the conditional flood expecta-
tion will converge to the empirical mean. The longer the observed time period then the less
relevant are the starting parameters in forming the conditional expectation. For example,
the Beta-Bernoulli Bayesian model predicts that flood insurance take-up in older commu-
nities after a flood would be less than the take-up in newly settled communities. The older
communities have decades (or centuries) of historical flood data, while the newly settled
communities do not.
An important assumption of the Beta-Bernoulli Bayesian model that deserves highlight-
ing is the assumption that each community’s underlying flood probability distribution is
stationary. In this model, each flood observation is considered to be an independent draw
from a fixed (but unknown) distribution. As discussed in Section IIb, Figure 3b provides
36The discussion of the Beta-Bernoulli statistical model closely follows Card (2010).37The Beta distribution is the conjugate prior for the Bernoulli distribution (DeGroot 1970) and used in
most Bernoulli Bayesian models for convenience.
31
support that per county flooding in the US–although variable from year to year–is constant
over the period 1969-2007.
Recent empirical studies in a range of economic settings lend support to Bayesian learn-
ing. These include: employer learning of employee productivity (Farber and Gibbons 1996,
Altonji and Pierret 2001, Lange 2007, Ichino and Moretti 2009), physician own skill learning
(Johnson 2010). NEED A COUPLE OF SENTENCES HERE ABOUT THESE
The study most similar to this paper is Davis (2004). Davis (2004) models homeowner
learning of location specific cancer risk. Homeowners are assumed to take Bernoulli draws
from a location-specific cancer risk distribution with an unknown cancer risk parameter.
An unusually large number of leukemia cancer cases were diagnosed in Churchill County,
a sparsely populated county in Nevada, in the early 2000’s. This “cancer cluster” was
widely publicized in local and national media. Davis shows that the increase in cancer
diagnoses in this county are associated with a contemporaneous decline in home property
values. This evidence is consistent with a Beta-Bernoulli Bayesian learning model where
updated homeowner beliefs about their location-specific cancer risk are then reflected in
their willingness to pay for housing.
The Bayesian learning model does not fit the data well in other settings. These include
financial investment decisions (Ulrike and Nagel 2010) and Palm (book date?). Evidence
in support of this theory of learning includes a recent empirical study on investment de-
cisions and past stock market returns (Ulrike and Nagel 2010). The same historical stock
market return data are available to all investors. However, the authors find that individu-
als most likely to have personal experience with low stock market returns invest less in the
stock market.
Alternative theories of learning have been developed to explain these patterns of ob-
served behavior. Many of these theories have their roots in the field of psychology. One
prominent theory of learning stresses the importance of first hand experience in interpret-
ing information. A large class of choice ‘reinforcement’ models “assumes that strategies are
‘reinforced’ by their previous payoffs, and the propensity to choose a strategy depends in
some way on its stock of reinforcement.”38
38Quote from Camerer and Ho (1999), p828; Camerer and Ho (1999) also synthesize previous research
32
Choice reinforcement models highlight two types of deviations from the learning process
assumed in the Beta-Bernoulli Bayesian model. The first difference is that individuals, when
provided with the exact same information, will form different beliefs based on their previous
experience. The second difference is that individuals may discount past information. If the
underlying distribution is assumed to be stationary (as is the case of flooding in this paper),
then discounting past information is inconsistent with the Beta-Bernoulli Bayesian model.
One interpretation of homeowner discounting when the underlying flood distribution is
stationary is that homeowners “forget”.
In addition to the Beta-Bernoulli Bayesian model, this paper considers a second learning
model that incorporates two of the salient features of the reinforcement models: (1) the
importance of first hand experience, and (2) the possibility of “forgetting”. The model
I consider is a simplified version of the ‘experience-weighted attraction’ (EWA) learning
model proposed by Camerer and Ho (1999).
Camerer and Ho (1999) were among the first to recognize that ‘reinforcement’ models
and ’belief-based’ models, such as the Beta-Bernoulli Bayesian model, could be synthe-
sized into a single modeling framework. The Camerer and Ho introduce the EWA model
to describe player learning in noncooperative games. Their model has three parameters.
The first parameter (δCH) allows each player to weigh the payoffs from past periods in the
game differently depending on whether the player chose the strategy associated with the
payoffs. This parameter discounts the information implicit in past payoffs when updating
future beliefs if the payoff did not come from a strategy chosen by the player. The second
parameter (φCH) discounts all information from past periods, while the third parameter
(ρCH) discounts the number of periods. The difference in interpretation between these two
parameters is a bit subtle. Camerer and Ho explain that these two parameters “combine
cognitive phenomena like forgetting [φCH ] with a deliberate tendency to discount old ex-
perience [ρCH ]”.39 Finally, it is important to note that Camerer and Ho consider a larger
set of belief-based models where the underlying distribution isn’t necessarily stationary.40
that uses ‘reinforcement’ models in a game theoretic setting. IS THERE A RESOURCE THATSUMMARIZES ‘REINFORCEMENT’ MODELS MORE GENERALLY?
39Camerer and Ho (1999), p83940Setting φCH = ρCH and ρCH < 1 is consistent with these non-stationary belief-based models.
33
I refer to the simplified version of the Camerer and Ho EWA model used in this paper as
the EWA Beta-Bernoulli model. The EWA Beta-Bernoulli model introduces one additional
parameter, δ, into the conditional expectation and conditional variance updating equations
of the Beta-Bernoulli Bayesian model. Nevertheless, introducing δ is appealing for two
reasons. First, given that the flood insurance data in this paper are aggregated at the
community level, the single parameter δ provides a parsimonious way to incorporate both
the importance of first hand experience and the possibility of forgetting into the model.
Second, this model has the appealing feature of reducing to the Beta-Bernoulli Bayesian
model when δ = 1.
The conditional mean and variance updating equations under the EWA Beta-Bernoulli
model are given by equations (6) and (7).
E[p|S′t] =S′t + α
t′ + α+ β(6)
V ar[p|S′t] =(S′t + α)(t
′ − S′t + β)
(t′ + α+ β)2(1 + α+ β + t′)(7)
t′
=∑t
s=1 δt−s is the number of yearly observation “equivalents”. S
′t =
∑ts=1 ysδ
t−s are
weighted flood observations. δ ∈ [0, 1] is a weighting parameter.
The data I observe and the event study estimation results in section III are aggregated
at the community level. The conditional flood expectation equations (3) and (6) both
model individual homeowner learning of the probability of future floods. If all homeowners
update using Equation (3), then aggregating to the community level changes the unit of
observation from an individual, i, to a representative individual in community c. Aggregat-
ing to the community level provides two interpretations of δ if some or all of a community’s
homeowners use equation (6) to update beliefs.
If all of the homeowners use equation (6), then we can interpret δ as a measure of
“forgetting” in the community. All homeowners discount past flood information, so δ in
the community level equation is the average amount of “forgetting”. On the other hand,
if some homeowners update according to equation (6) and other homeowners update using
equation (3), then when we aggregate to the community level, δ becomes a weighting
34
parameter between individuals using the two different updating equations. Following the
logic of the reinforcement learning literature and the modeling of Camerer and Ho, those
homeowners who don’t have first hand experience with floods will discount past flood
information. Those homeowners with first hand experience do not discount the past flood
information (i.e. δ = 1).
5 Testing the Two Learning Models
This section uses the two learning models and the complete history of Presidential Disaster
Declaration floods to generate a time series of flood probabilities for each community. I
then compare the simulated homeowner beliefs over future flooding under each learning
model with the observed take-up of flood insurance. The EWA Beta-Bernoulli learning
model consistently fits the data better than the Beta-Bernoulli model.
5.1 Generating Homeowner Flood Beliefs
I use equations (3) and (6) to generate county-level homeowner flood beliefs using the
complete 50 year time series of Presidential Disaster Declaration floods. To determine the
starting values for the county-level α and β parameters I make the following assumptions:
I assume that the realized Presidential Disaster Declarations over the 50 year period from
1958-2007 approximates the true national distribution of large county-level floods. The
representative homeowner in 1958 knows the national county flood probability distribution,
but doesn’t know where his county is located in this distribution. Therefore, in 1958 the
representative homeowner assumes that he is in the mean county from the national county
flood distribution.41
Under the above assumptions, I derive the starting values by matching the first two
moments of the empirical county flood probability distribution of the 50 year Presidential
Disaster Declaration history to the first two moments of the Beta Distribution. This gives
two equations and two unknowns (the parameters α and β). Matching the first two mo-
ments: α = 2.87 and β = 21.87. I use the same sample of US counties in matching these
41Davis (2004) uses similar assumptions to determine homeowner initial beliefs over the probability ofbeing diagnosed with cancer.
35
moments (N=2704) as are included in the baseline 1980-2007 event study regressions.42
Figure 8 shows the empirical distribution of yearly county-level PDD flood probabilities
from 1958-2007. On top of this empirical distribution I plot the probability density func-
tion from the Beta Distribution when the parameter values are α = 2.87 and β = 21.87. [I
still need to create this figure]
The two event study panels are 1980-2007 and 1990-2007. I use data on PDD floods
before the first year of the event study panels as a “burn in” period. During which time flood
beliefs, based only on the initial parameters α and β, adjust in response to observed PDD
floods. The longer the history of flooding information used to generate flood beliefs, the
less relevant are the values of the initial parameters in determining updated flood beliefs.43
To generate a county level time series of yearly flood probabilities using the EWA Beta-
Bernoulli homeowner learning model (equation 6) I must also specify a value for δ. I use
a two step process to determine the best fitting δ. First, I use equation 6 to generate 15
separate flood probability time series for each county under the initial starting values α =
2.87 and β = 21.87, PDD flood data from 1958-2007, and δ = 0.85,0.86,...,1.00. Second, I
select the time series of flood probabilities, pct(δ), that minimizes the mean square error of
equation (8).44
lnqct = βtlnpct(δ) + αc + γt + εct (8)
Equation (8) is the same as event study estimating equation (1), except that here I
replace the event time dummy variables with log flood probability. The dependent variable,
lnqct, is the log flood policies per person for community c in year t. The independent variable
42The empirical moments are the same if I use the slightly larger number of counties included in the1990-2007 panel.
43I plan to test the sensitivity of the starting values by using other starting value assumptions including:(i) Matching the moments of regional distributions (rather than the national distribution), and (ii) use eachcounty’s 50-year empirical mean as the first moment. Approach (i) assumes that homeowners know thecounty flood probability distribution for their region (e.g. Southeast US), but not where in this regionaldistribution their county is located. Approach (ii) assumes that homeowners know the “true” county floodprobability in 1957 as approximated by the 1958-2007 empirical mean (pi1957 = α
α+β). Changing the
numerical values of α and β, while keeping pi1957 fixed is analogous to changing the degree of certainty thathomeowners have over their initial beliefs. I plan to generate updated flood beliefs using several pairs ofvalues of α and β to represent different levels of homeowner certainty.
44This two step process is equivalent to a single estimation procedure using non-linear least squares whereI minimize over both βt and δ simultaneously, except that I only consider 15 values for δ in the range δ =0.85,0.86,...,1.00. I do not estimate δ to the 3rd decimal place.
36
of interest is the EWA Beta-Bernoulli flood probability, pct(δ). The flood probabilities are
specific to a community, but vary only at the county level. αc is a community fixed effect.
γt is a calender year fixed effect. εct is a stochastic error term. I estimate equation (8) on
the same two panels of communities as the in section III. In some specifications of equation
(8) I replace γt with state by year fixed effects.
A δ = .95 best fits equation (8) using the 1990-2007 panel of communities. This is
true regardless of whether equation (8) is specified with year or state by year fixed effects.
Similarly, a δ = .91 best fits equation (8) using the 1980-2007 panel (under both fixed effect
specifications). I focus on the simulated probabilities from the 1990-2007 panel. This panel
has a longer “burn in” period. I observe PDD floods for 32 years before the first year of the
panel. The 1990-2007 also has the advantage of using the more precise PDD community
hit variable.
5.2 Comparing the Learning Models
I first compare the two hypothesized homeowner learning models by observing how the
simulated Beta-Bernoulli and EWA Beta-Bernoulli (δ = .95) evolve after a PDD flood.
In order to do this, I estimate equation (1) using the log simulated probabilities as the
dependent variable (instead of log insurance take-up). Figure 10a graphs the Beta-Bernoulli
simulated probability event time coefficients in the left panel. In the right panel are the
flood insurance take-up coefficients from the same event study specification (copied from
Figure 4a). I scale the vertical axis of each panel so that they are the same. There is a
6.2% change in the Beta-Bernoulli probability in the year a community is hit by a PDD
flood. Ten years after a flood, there is still a statistically significant 3.2% increase in the
belief of a future flood, relative to the year before a PDD flood hit. The change is flood
beliefs is 2.4% and statistically significant for the pooled coefficient for 11-17 years after a
flood.
The left hand panel of Figure 10b plots the event time coefficients from estimation of
equation (1) with the EWA Beta-Bernoulli probabilities as the dependent variable. There
is a 9.6% jump in the EWA Beta-Bernoulli probability in the year of a PDD flood hit.
Ten years after a flood the flood belief point estimate is 2.4% and statistically significant.
37
The point estimate for the pooled 11-17 event year coefficient is 1.0% and not statistically
significant.
Figures 10a and 10b suggest that homeowner learning model that allows for “forgetting”
better fits the observed take-up in flood insurance, given the assumption over the initial
conditions and the 32 year “burn in” period. The percent change in simulated probabilities
under the EWA Beta-Bernoulli model (δ = .95) is zero at the end of the 1990-2007 panel
event study. In contrast, the percent change in the (classical) Beta-Bernoulli model is
statistically significant for the entire time period.
Next, I compare take-up in communities when the PDD flood is “unexpected”. To de-
termine if a flood is “unexpected”, I observe the percent change in the simulated probability
in the year of a flood relative to the year before a flood. I then classify each flood as an
above or below median expectation flood by whether the percent change is above or below
the median relative to all other county-flood years. I do this for both homeowner learning
models. Figure 11a displays the simulated (classical) Beta-Bernoulli probabilities and flood
insurance take-up response functions after above and below median expectation floods.
The left panel graphs event time probability coefficients, while the right panel graphs flood
insurance take-up. The set-up for Figure 11b is the same except that simulated EWA Beta-
Bernoulli probabilities are used to determine if a flood is “unexpected”, and are plotted in
the left panel.
In both Figures 11a and 11b the probability and take-up impulse response functions for
the more “unexpected” (above median percent change) floods lie above that of floods that
were less of a surprise. Again, as in figures 10a and 10b, the EWA simulated probabilities
appear to better match the observed pattern of take-up. [NEED TO ELABORATE,
BUT ALSO EXPLAIN THAT GRAPHS NOT CONCLUSIVE]
6 Conclusion
Still to come: Conclusion, Bibliography, Data Appendix
38
Table 1: Community Flood Insurance Statistics and Flood Map Characteristics
Year 1980 1990 2007
Panel A: Community Flood Policy Statistics
Policies Per 1,000 Persons 20 (2) 20 (2) 32 (4)Yearly Premium per Holder 237 (191) 464 (403) 656 (562)Yearly Pay Out per Holder 1,372 (185) 2,306 (401) 2,425 (243)Pay Out per Claim 10,335 (4,721) 15,448 (7,669) 19,017 (9,689)
Panel B: Community Policies Per 1,000 Persons
Communities < Median 100 Year Flood Plain 7 (1) 4 (1) 8 (2)Communities > Median 100 Year Flood Plain 21 (2) 22 (2) 35 (4)
Flood Map Designation 100 Year 100-500 Year Outside Flood Plain
Panel C: % Communities by Flood Designation
Percent of Community 14 (8) 87 (77) 4 (0)
Sample of Communities All < Median 100 Yr > Median 100 Yr
Panel D: % Communities “Hit” by a PDD
Percent “Hit” (receiving Public Assistance) 32 29 35
39
(1) (2) (3) (4) (5) (6)
hyr_m11_17 -0.0209 -0.0346 -0.0428 -0.01 -0.0225 -0.0241
hyr_m10 -0.0062 0.0075 0.0067 -0.0072 -0.0019 -0.022
hyr_m9 -0.0074 -0.0035 -0.0316 -0.0144 -0.0137 -0.0503
hyr_m8 0.016 0.0724 -0.0089 0.0024 0.0024 -0.0199
hyr_m7 0.0007 0.0138 0.0011 0.0049 0.0025 -0.0009
hyr_m6 0.0181 0.0216 0.0311 0.0138 0.0141 0.0153
hyr_m5 0.0211 0.0264 0.0386 0.0107 0.0076 0.0223
hyr_m4 0.029 0.023 0.047 0.0147 0.015 0.0264
hyr_m3 0.0157 0.0097 0.0389 0.0047 0.003 0.0164
hyr_m2 0.0183 0.0271 0.0425 0.0174 0.0223 0.0240*
hyr 0.1038*** 0.0680*** 0.1082*** 0.0791*** 0.0683*** 0.0711***
hyr_p1 0.1080*** 0.0769*** 0.1217*** 0.0914*** 0.0748*** 0.0863***
hyr_p2 0.1235*** 0.0866*** 0.1147*** 0.0837*** 0.0699*** 0.0781***
hyr_p3 0.1006*** 0.0746*** 0.0986*** 0.0705*** 0.0565*** 0.0701***
hyr_p4 0.0931*** 0.0576*** 0.0946*** 0.0753*** 0.0559*** 0.0796***
hyr_p5 0.0714*** 0.0382** 0.0728*** 0.0707*** 0.0505*** 0.0753***
hyr_p6 0.0573*** 0.0298** 0.0632*** 0.0625*** 0.0500*** 0.0735***
hyr_p7 0.0566*** 0.0371** 0.0691*** 0.0568*** 0.0497*** 0.0628***
hyr_p8 0.0561*** 0.0304* 0.0570** 0.0594*** 0.0488*** 0.0501***
hyr_p9 0.0143 -0.0069 0.0196 0.0321** 0.0224 0.0331*
hyr_p10 -0.0088 -0.0239 0.0038 0.0227 0.0106 0.0262
hyr_p11_p17 -0.0126 -0.0139 0.0231 0.0132 0.0236 0.0435**
dyear 0.0399*** 0.0179**
dyear event time dummies X X
Com FE X X X X X X
Year FE X X X
State*Year FE X X X
Observations 191,970 191,970 101,034 191,970 191,970 101,034
Communities 10,665 10,665 5,613 10,746 10,746 5,613
Table 2. Event Time Regression for Panel 1990-2007
40
Table 3
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
disaster county 0.0933*** 0.0932*** 0.0971*** .0974*** .0978*** .0598*** 0.0597*** .0724*** 0.0725*** .0736***
adjacent neighbor 0.0162* 0.0286 0.0256 0.0105 -0.007 0.0106
centroid (5 closest) nbr 0.0196* 0.0077
media neighbor .0234*** .0224** .0251*** .0266*** .0293*** .0333***
adjacent*media nbr -0.0174 -0.0227
event time dummies X X X X X X X X X X
community FE X X X X X X X X X X
Year FE X X X X X
State*Year FE X X X X X
Observations 265,412 265,412 265,412 265,412 265,412 265,412 265,412 265,412 265,412 265,412
Communities 9,479 9,479 9,479 9,479 9,479 9,479 9,479 9,479 9,479 9,479
R-squared 0.1504 0.1504 0.1505 0.1505 0.1505 0.2038 0.2038 0.2039 0.2039 0.2039
41
42
43
44
45
46
47
48
49
50