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 Please do not cite or distribute.Comments are welcomed and encouraged.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 justing@econ.berkeley.edu.

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