The National Flood Insurance Program was established in 1968 as a federally administered insurance program to reduce costs to the federal government for flood recovery and allocate recovery costs among potential disaster relief beneficiaries. Participants purchase flood insurance through participating property insurance providers which receive a haircut of the premium for overhead costs and passes the remainder to the Federal Emergency Management Agency. This paper outlines a model to measure the net social benefits attributable to the insurance component of the NFIP. Development of this model provides the baseline for further economic and social analysis of the NFIP

A E Boardman

D A Moss

James P. Howard, II

M A Rumsey

R Chetty

R H Frank

S Farrow

W H Desvousges

Howard II., James P.

Munich Personal RePEc Archive

MPRA
Munich Personal RePEc Archive
Measuring the impacts of the national
flood insurance program
James P. Howard II.
University of Maryland Baltimore County
22. March 2012
Online at http://mpra.ub.uni-muenchen.de/37758/
MPRA Paper No. 37758, posted 30. March 2012 13:56 UTC
Electronic copy available at: http://ssrn.com/abstract=2021204
Running head: MEASURING THE IMPACTS OF THE NFIP 1
Measuring the Impacts of the National Flood Insurance Program
James P. Howard, II
University of Maryland Baltimore County
The Eleventh William and Mary Graduate Research Symposium
23 March 2012
Author Note
The author can be contacted at jh@jameshoward.us or howard5@umbc.edu.
Electronic copy available at: http://ssrn.com/abstract=2021204
MEASURING THE IMPACTS OF THE NFIP 2
Measuring the Impacts of the National Flood Insurance Program
Introduction
The National Flood Insurance Program (nfip) was established in 1968 as a federally
administered insurance program to reduce costs to the federal government for flood
recovery and allocate recovery costs among potential disaster relief beneficiaries (Rumsey,
2010, pp. 56, 62). Participants purchase flood insurance through participating property
insurance providers which receive a haircut of the premium for overhead costs and passes
the remainder to Federal Emergency Management Agency (fema). This paper outlines a
model to measure the net social benefits attributable to the insurance component of the
nfip. Development of this model provides the baseline for further economic and social
analysis of the nfip.
The Social Surplus Model
A benefit-cost analysis (bca) requires a determination of whose costs and benefits
count in the analysis. First is consumers, who purchase insurance through the nfip.
Second is producers, who sell flood insurance plans on behalf of the nfip. Third is the
federal government, which manages the program. Fourth is third parties affected broadly
by externalities, such as environmental impacts.
A bca methodology typically defines the net social benefit as the summed benefits
minus the summed costs. This model uses an alternative approach which analyzes the
change in the social surplus attributable to a program (Boardman, Greenberg, Vining, &
Weimer, 2010, p. 62). The social surplus (S) is the sum of the consumer surplus (C), the
producer surplus (P ), government surplus (G), and the external surplus (E), each of which
have their own definitional components:
S = C + P +G+ E (1)
MEASURING THE IMPACTS OF THE NFIP 3
In addition, the incremental shift in social benefit due to a policy change is,
∆S = ∆C +∆P +∆G+∆E. (2)
The consumer surplus measures the net benefit due to consumers from acquiring
goods and services in the market. In general, the consumer surplus represents the net
amount consumers are willing to spend for a given good or service minus the actual price
paid (Frank, 2006, pp. 160–162). In the case of the nfip, it is assumed that consumers
would be unable to purchase flood insurance through the private market if the federal
program did not exist, as was the case prior to enactment of the National Flood Insurance
Act of 1968 (nfia). The case case, where nfip provides insurance to consumers is
represented by C∗ and the alternative, where the nfip no longer provides service is
represented by C ′. Based on this, the total change in consumer surplus due to the nfip is:
∆C = C∗ − C ′. (3)
In the event the nfip did not exist, it is reasonable to assume the government would make
payments to those affected by flood disasters on an ad hoc basis. This was the stance of
the Congress prior to the enactment of the nfia (Moss, 1999). In this case, such ad hoc aid
is represented by a. Therefore,
C ′ = a. (4)
To calculate the consumer surplus due to the nfip, it is necessary to find the
willingness-to-pay (wtp) for insurance services (w), to estimate the premium payments
consumers are likely to pay for flood insurance through the nfip (ω), and to find the
difference between the two. In a given year, this would be given by
C∗ = w − ω. (5)
MEASURING THE IMPACTS OF THE NFIP 4
Combining the equations for C∗ and C ′ with equation 3 yields a final form for ∆C:
∆C = C∗ − C ′
= (w − ω)− a
= w − ω − a. (6)
This final equation, 6, shows the complete change in the consumer surplus is represented
by the willingness to pay for flood insurance minus the premiums actually paid to the
insurance fund and the estimated ad hoc disaster aid the government may sponsor.
The producer surplus measures the net benefit due to producers and their suppliers
from providing goods and services to the market. In this analysis, the principal producer is
the federal government. However, the surplus change due to governmental activity is better
considered as part of the government surplus. Therefore, the producer surplus is limited to
insurance companies providing administrative services to the nfip.
It is assumed that consumers would be unable to purchase flood insurance if the
program did not exist, because it is assumed private insurers would not provide flood
insurance. The base case, where the nfip provides insurance to consumers is represented
by P ∗ and the alternative, where the nfip no longer provides service is represented by P ′.
Based on this, the total change in producer surplus due to the nfip is:
∆P = P ∗ − P ′. (7)
Because it is assumed no producer would enter a hypothetical open market for flood
insurance, then P ′ = 0. In the case where the nfip is extant and being serviced by
individual insurance companies, a simple multiplier (φ) is applied to the value ω,
representing the gross industry revenue from servicing nfip programs on behalf of fema.
However, the producer surplus is only the profit to the insurance industry for providing
administrative services, which is only a portion of that revenue. Therefore, the gross
revenue will be multiplied by an estimate for insurance industry profitability which is
MEASURING THE IMPACTS OF THE NFIP 5
represented by pi. As a result, P ∗ represents the producer surplus across the entire industry
due to the nfip. The estimate for the producer surplus is:
P ∗ = φωpi. (8)
Using these estimates for the producer surpluses in each case leads to an estimate for the
net change in the producer surplus due to the nfip:
∆P = P ∗ − P ′
= φωpi − 0
= φωpi. (9)
The government surplus measures the benefits and costs due to the government as part of
a policy change. The government of the United States, through the National Flood
Insurance Fund (nfif), sees inflows and outflows directly stemming from the program.
Continuing the assumption program participants would be unable to purchase flood
insurance if the program did not exist, The base case, where the nfip provides insurance to
consumers is represented by G∗ and the alternative, where the nfip no longer provides
service is represented by G′. Based on this, the total change in the government surplus due
to the nfip is:
∆G = G∗ −G′. (10)
Prior to the nfia, the government provided ad hoc disaster assistance to flood victims.
Because it is assumed the government would compensate the victims of flooding, per C ′,
the government surplus must balance this in the case where the nfip did not exist.
Therefore, G′ = −a.
In the existing case of the nfip, represented by G∗, government experiences inflows in
the form of premium payments from program participants. It experiences outflows from
claims payments made to policyholders after a flood event. Therefore, G∗ = ω − κ and the
MEASURING THE IMPACTS OF THE NFIP 6
complete equation for the net change in the government surplus is:
∆G = G∗ −G′
= ω − κ+ a. (11)
Finally, the external surplus is the sum of benefits and costs due to third parties caused by
the actions of consumers, producers, and the government. Like the other surpluses, the
change in external surplus is the difference between the external surplus with the nfip, E∗,
and the case where the nfip did not exist, E ′:
∆E = E∗ − E ′. (12)
In the case the nfip did not exist, the government is likely to give disaster relief aid and
this may cause some beneficiaries to rebuild in environmentally sensitive areas. Therefore,
the environmental impact, β, must be accounted for. In addition, there is the externality of
the impact of taxation required to pay for ad hoc payments in C ′. This impact is a
multiplier, m, against the revenue to pay for the ad hoc payments, a. This externality is
known to be a negative externality. As a result,
E ′ = β −ma. (13)
In the case where the nfip does exist, the interactions are more complex. There are no
producer nor consumer surplus, but there is an environmental impact of the nfip funding
redevelopment in environmentally sensitive areas and there is ongoing debate about
whether the existence of the nfip may create inefficient use of the floodplain. This
environmental impact, B, must also be accounted for. As a result, E∗ = B and:
∆E = E∗ − E ′
= B − β +ma. (14)
It is possible other externalities exist, however, given the data available from fema
regarding the nfip, it is not currently possible to identify or estimate them in this analysis.
MEASURING THE IMPACTS OF THE NFIP 7
Using equation 2, the consumer, producer, government, and external surplus
estimates are combined to provide the net social surplus given by the nfip:
∆S = ∆C +∆P +∆G+∆E
= (w − ω − a) + (φωpi) + (ω − κ+ a) + (B − β +ma)
= w + φωpi − κ+B − β +ma. (15)
Beginning with equation 15, several variables must be resolved to calculate the net social
surplus for the insurance component of the nfip. Finding the wtp is a complex matter,
that differentiates between the ex ante and ex post values for the wtp. The ex post value
represents how much an insured is willing to pay for insurance after an event and is
equivalent to the expected amount received in response to an insurance claim. Because
insurance policies are normally rolled over from year to year and policyholders are not
likely to make a claim each year, the expected amount due to policyholders due to claims is
the long run average over the lifetime of the policy.
The ex ante value is the amount an insured is willing to pay before a claim is made
and is generally believed to be greater than the ex post value, based on the value of
smoothing any large changes in wealth (Farrow & Scott, 2011). While the ex post value is
simpler to find based on existing data, the ex ante estimate better represents the value
insurance program participants place on participation.
Research by Farrow and Scott shows the expected ex ante estimates of wtp for flood
insurance is 15 percent greater than the known ex post values for Baltimore, Maryland.
The analysis behind this was limited to Baltimore, a city built on a major body of water.
However, if this estimate reflects the national wtp for flood insurance, calculating the ex
ante wtp is no more difficult than finding the ex post wtp, represented by κ here:
w = (1 + e)κ. (16)
This estimate is, however, of limited purpose and is ripe for additional analysis through
sensitivity analysis.
MEASURING THE IMPACTS OF THE NFIP 8
The estimate for the ad hoc disaster aid, a must also be estimated. The best estimate
for it derives from the impetus behind the nfia, to relieve pressure on the federal budget
for disaster aid. As a result, it is possible to assume that the ad hoc disaster aid is replaced
by the claims against the program following a flood event. Therefore, a = κ is the best
estimate for ad hoc disaster aid if the nfip were not available.
Finally, it is necessary to estimate B and β, the environmental impacts in the
external surplus. Because B and β are both the environmental damages caused by the
rebuilding in sensitive areas and because the funding for those damages are presumed
equal, though derived from different sources, it is reasonable to assume the environmental
impacts would also be equal. Therefore, B = β and B − β = 0.
Beginning with equation 15, this allows the value of ∆S to be further simplified:
∆S = w + φωpi − κ+B − β +ma
= (1 + e)κ+ φωpi − κ+mκ
= κ+ eκ+ φωpi − κ+mκ
= κ(e+m) + φωpi (17)
Equation 17 includes six variables necessary for calculating the net change in social surplus
due to the nfip. Values for κ and ω can be estimated from historical nfip financial data
available from fema. Estimates for pi can be calculated using historical insurance industry
profitability data. The variable m is provided directly by
Office of Management and Budget (1992, p. 13).
The next variable to estimate is φ, representing the percentage of the premium
earned by the insurance companies participating in the Write Your Own (wyo) program
for administering the nfip. This percentage is defined in regulations governing the wyo
program to be 15 percent with a potential 2 percent bonus for meeting certain targets for
administration and sales. Because the value of φ is fixed within a single narrow band only
2 percent wide, this analysis will select the midpoint of the band, 16 percent, as the
MEASURING THE IMPACTS OF THE NFIP 9
baseline for analysis.
The variable e, representing the additional sum policyholders are willing to pay prior
to a flood event for coverage has been researched by Farrow and Scott and estimated to be
15 percent.
Conclusion
Equation 17 provides a simple theoretical model for analyzing the net social benefits
of the nfip insurance component. On its face, it provides a single number. More broadly,
this model when combined with a model for analyzing the Flood Mitigation Assistance
(fma) component, provides the net social benefits of the nfip as a whole. This model can
also be applied both prospectively and retrospectively, leading to net social benefits both
historically and moving forward.
Relying on a series of assumptions, listed in table 2, the broad economic model,
including some variables that cannot be estimated, is reduced to a final form using six
variables with estimates readily available from nfip financial data or the literature through
benefits transfer (Desvousges, Johnson, & Banzhaf, 1998). Consequently, the reduced form
model is an attempt to find a sufficient statistic for the nfip’s insurance component
(Chetty, 2009), and starting point to more complex analyses of the nfip. Because
information on premiums and claims are available at the state and county level from fema,
analytical granularity can be reduced. This encourages jurisdictional level analysis of
distributional impacts of the program. In addition, by relaxing the assumptions made in
the model, such as the equivalence of environmental impacts or estimates of the ex ante
adjustment to the wtp for flood insurance, it is possible to perform break-even analysis,
adapt other estimates of the values to the model, or search for optimal values through
Monte Carlo simulation. Finally, this model forms the basis for analyzing proposed changes
to the nfip or new disaster insurance programs.
MEASURING THE IMPACTS OF THE NFIP 10
References
Boardman, A. E., Greenberg, D. H., Vining, A. R., & Weimer, D. L. (2010). Cost-benefit
analysis: concepts and practice (4th ed.). Pearson series in economics. Upper Saddle
River, NJ: Prentice Hall.
Chetty, R. (2009). Sufficient statistics for welfare analysis: A bridge between structural and
reduced-form methods. In K. J. Arrow & T. F. Bresnahan (Eds.), Annual review of
economics (Vol. 1, pp. 451–487). Palo Alto, California: Annual Reviews.
Desvousges, W. H., Johnson, F. R., & Banzhaf, H. S. (1998). Environmental policy analysis
with limited information: Principles and applications of the transfer method.
Cheltenham, UK: Edward Elgar.
Farrow, S., & Scott, M. (2011). Estimating the ex-ante willingness to pay for flood
protection. (presented at the Association of Environmental and Resource Economists
summer workshop)
Frank, R. H. (2006). Microeconomics and behavior (6th ed.). Boston: McGraw-Hill Irwin.
Moss, D. A. (1999). Courting disaster? the transformation of federal disaster policy since
1803. In K. A. Froot (Ed.), The financing of catastrophe risk (Chap. 8, pp. 307–355).
Chicago: University of Chicago Press.
Office of Management and Budget. (1992, October). Guidelines and discount rates for
benefit-cost analysis of federal programs (tech. rep. No. A-94). Washington.
Rumsey, M. A. (2010, May). Beyond bigger and better: gilbert white and america’s new
approach to floodplain management. (Master’s thesis, Mississippi State University,
Starkville, MS).
MEASURING THE IMPACTS OF THE NFIP 11
Variable Description
a Amount of ad hoc disaster aid payments
B, β Estimates of environmental impacts
C Consumer surplus
κ Claims made against the nfip
E External surplus
e The ex ante adjustment for wtp
G Government surplus
φ wyo fees to insurers
m the marginal excess tax burden (metb)
P Producer surplus
ω Premiums paid to the nfip
pi Profit ratio for the insurance industry
S Net social surplus
w willingness-to-pay for flood insurance
Table 1
Variable list included in social surplus
MEASURING THE IMPACTS OF THE NFIP 12
Assumption Explanation Impact
a = κ nfip claims are equal to the expected
amount of ad hoc aid granted in the
absence of the nfip
Limits prospective benefits of nfip
B = β Environmental damages caused by
ad hoc flood recovery is the same
as environmental damages caused by
nfip-funded recovery
Environmental damages are not con-
sidered
pi’s value Insurers make a profit on administra-
tive services and the profit ratio on
that service is the same as the gen-
eral industry profitability
Ties the producer surplus to general
insurance profitability
φ’s value Property insurance provides receive
administrative fees equal to mean po-
tential fees
Reduced by the narrow band (2%)
for potential fees
e’s value The estimate for ex ante wtp for the
City of Baltimore is transferable na-
tionwide
This may be significantly different
from the nationwide wtp for flood
insurance due to specific regional fac-
tors affecting local behavior
Table 2
Simplifying Assumptions Contained Within the Model


Measuring the impacts of the national flood insurance program

Munich RePEc Personal Archive

MPRAMunich Personal RePEc ArchiveMeasuring the impacts of the nationalflood insurance programJames P. Howard, IIUniversity of Maryland Baltimore County22. March 2012Online at http://mpra.ub.uni-muenchen.de/37758/MPRA Paper No. 37758, posted 30. March 2012 13:56 UTCElectronic copy available at: http://ssrn.com/abstract=2021204Running head: MEASURING THE IMPACTS OF THE NFIP 1Measuring the Impacts of the National Flood Insurance ProgramJames P. Howard, IIUniversity of Maryland Baltimore CountyThe Eleventh William and Mary Graduate Research Symposium23 March 2012Author NoteThe author can be contacted at jh@jameshoward.us or howard5@umbc.edu.Electronic copy available at: http://ssrn.com/abstract=2021204MEASURING THE IMPACTS OF THE NFIP 2Measuring the Impacts of the National Flood Insurance ProgramIntroductionThe National Flood Insurance Program (nfip) was established in 1968 as a federallyadministered insurance program to reduce costs to the federal government for floodrecovery and allocate recovery costs among potential disaster relief beneficiaries (Rumsey,2010, pp. 56, 62). Participants purchase flood insurance through participating propertyinsurance providers which receive a haircut of the premium for overhead costs and passesthe remainder to Federal Emergency Management Agency (fema). This paper outlines amodel to measure the net social benefits attributable to the insurance component of thenfip. Development of this model provides the baseline for further economic and socialanalysis of the nfip.The Social Surplus ModelA benefit-cost analysis (bca) requires a determination of whose costs and benefitscount in the analysis. First is consumers, who purchase insurance through the nfip.Second is producers, who sell flood insurance plans on behalf of the nfip. Third is thefederal government, which manages the program. Fourth is third parties affected broadlyby externalities, such as environmental impacts.A bca methodology typically defines the net social benefit as the summed benefitsminus the summed costs. This model uses an alternative approach which analyzes thechange in the social surplus attributable to a program (Boardman, Greenberg, Vining, &Weimer, 2010, p. 62). The social surplus (S) is the sum of the consumer surplus (C), theproducer surplus (P ), government surplus (G), and the external surplus (E), each of whichhave their own definitional components:S = C + P +G+ E (1)MEASURING THE IMPACTS OF THE NFIP 3In addition, the incremental shift in social benefit due to a policy change is,∆S = ∆C +∆P +∆G+∆E. (2)The consumer surplus measures the net benefit due to consumers from acquiringgoods and services in the market. In general, the consumer surplus represents the netamount consumers are willing to spend for a given good or service minus the actual pricepaid (Frank, 2006, pp. 160–162). In the case of the nfip, it is assumed that consumerswould be unable to purchase flood insurance through the private market if the federalprogram did not exist, as was the case prior to enactment of the National Flood InsuranceAct of 1968 (nfia). The case case, where nfip provides insurance to consumers isrepresented by C∗ and the alternative, where the nfip no longer provides service isrepresented by C ′. Based on this, the total change in consumer surplus due to the nfip is:∆C = C∗ − C ′. (3)In the event the nfip did not exist, it is reasonable to assume the government would makepayments to those affected by flood disasters on an ad hoc basis. This was the stance ofthe Congress prior to the enactment of the nfia (Moss, 1999). In this case, such ad hoc aidis represented by a. Therefore,C ′ = a. (4)To calculate the consumer surplus due to the nfip, it is necessary to find thewillingness-to-pay (wtp) for insurance services (w), to estimate the premium paymentsconsumers are likely to pay for flood insurance through the nfip (ω), and to find thedifference between the two. In a given year, this would be given byC∗ = w − ω. (5)MEASURING THE IMPACTS OF THE NFIP 4Combining the equations for C∗ and C ′ with equation 3 yields a final form for ∆C:∆C = C∗ − C ′= (w − ω)− a= w − ω − a. (6)This final equation, 6, shows the complete change in the consumer surplus is representedby the willingness to pay for flood insurance minus the premiums actually paid to theinsurance fund and the estimated ad hoc disaster aid the government may sponsor.The producer surplus measures the net benefit due to producers and their suppliersfrom providing goods and services to the market. In this analysis, the principal producer isthe federal government. However, the surplus change due to governmental activity is betterconsidered as part of the government surplus. Therefore, the producer surplus is limited toinsurance companies providing administrative services to the nfip.It is assumed that consumers would be unable to purchase flood insurance if theprogram did not exist, because it is assumed private insurers would not provide floodinsurance. The base case, where the nfip provides insurance to consumers is representedby P ∗ and the alternative, where the nfip no longer provides service is represented by P ′.Based on this, the total change in producer surplus due to the nfip is:∆P = P ∗ − P ′. (7)Because it is assumed no producer would enter a hypothetical open market for floodinsurance, then P ′ = 0. In the case where the nfip is extant and being serviced byindividual insurance companies, a simple multiplier (φ) is applied to the value ω,representing the gross industry revenue from servicing nfip programs on behalf of fema.However, the producer surplus is only the profit to the insurance industry for providingadministrative services, which is only a portion of that revenue. Therefore, the grossrevenue will be multiplied by an estimate for insurance industry profitability which isMEASURING THE IMPACTS OF THE NFIP 5represented by pi. As a result, P ∗ represents the producer surplus across the entire industrydue to the nfip. The estimate for the producer surplus is:P ∗ = φωpi. (8)Using these estimates for the producer surpluses in each case leads to an estimate for thenet change in the producer surplus due to the nfip:∆P = P ∗ − P ′= φωpi − 0= φωpi. (9)The government surplus measures the benefits and costs due to the government as part ofa policy change. The government of the United States, through the National FloodInsurance Fund (nfif), sees inflows and outflows directly stemming from the program.Continuing the assumption program participants would be unable to purchase floodinsurance if the program did not exist, The base case, where the nfip provides insurance toconsumers is represented by G∗ and the alternative, where the nfip no longer providesservice is represented by G′. Based on this, the total change in the government surplus dueto the nfip is:∆G = G∗ −G′. (10)Prior to the nfia, the government provided ad hoc disaster assistance to flood victims.Because it is assumed the government would compensate the victims of flooding, per C ′,the government surplus must balance this in the case where the nfip did not exist.Therefore, G′ = −a.In the existing case of the nfip, represented by G∗, government experiences inflows inthe form of premium payments from program participants. It experiences outflows fromclaims payments made to policyholders after a flood event. Therefore, G∗ = ω − κ and theMEASURING THE IMPACTS OF THE NFIP 6complete equation for the net change in the government surplus is:∆G = G∗ −G′= ω − κ+ a. (11)Finally, the external surplus is the sum of benefits and costs due to third parties caused bythe actions of consumers, producers, and the government. Like the other surpluses, thechange in external surplus is the difference between the external surplus with the nfip, E∗,and the case where the nfip did not exist, E ′:∆E = E∗ − E ′. (12)In the case the nfip did not exist, the government is likely to give disaster relief aid andthis may cause some beneficiaries to rebuild in environmentally sensitive areas. Therefore,the environmental impact, β, must be accounted for. In addition, there is the externality ofthe impact of taxation required to pay for ad hoc payments in C ′. This impact is amultiplier, m, against the revenue to pay for the ad hoc payments, a. This externality isknown to be a negative externality. As a result,E ′ = β −ma. (13)In the case where the nfip does exist, the interactions are more complex. There are noproducer nor consumer surplus, but there is an environmental impact of the nfip fundingredevelopment in environmentally sensitive areas and there is ongoing debate aboutwhether the existence of the nfip may create inefficient use of the floodplain. Thisenvironmental impact, B, must also be accounted for. As a result, E∗ = B and:∆E = E∗ − E ′= B − β +ma. (14)It is possible other externalities exist, however, given the data available from femaregarding the nfip, it is not currently possible to identify or estimate them in this analysis.MEASURING THE IMPACTS OF THE NFIP 7Using equation 2, the consumer, producer, government, and external surplusestimates are combined to provide the net social surplus given by the nfip:∆S = ∆C +∆P +∆G+∆E= (w − ω − a) + (φωpi) + (ω − κ+ a) + (B − β +ma)= w + φωpi − κ+B − β +ma. (15)Beginning with equation 15, several variables must be resolved to calculate the net socialsurplus for the insurance component of the nfip. Finding the wtp is a complex matter,that differentiates between the ex ante and ex post values for the wtp. The ex post valuerepresents how much an insured is willing to pay for insurance after an event and isequivalent to the expected amount received in response to an insurance claim. Becauseinsurance policies are normally rolled over from year to year and policyholders are notlikely to make a claim each year, the expected amount due to policyholders due to claims isthe long run average over the lifetime of the policy.The ex ante value is the amount an insured is willing to pay before a claim is madeand is generally believed to be greater than the ex post value, based on the value ofsmoothing any large changes in wealth (Farrow & Scott, 2011). While the ex post value issimpler to find based on existing data, the ex ante estimate better represents the valueinsurance program participants place on participation.Research by Farrow and Scott shows the expected ex ante estimates of wtp for floodinsurance is 15 percent greater than the known ex post values for Baltimore, Maryland.The analysis behind this was limited to Baltimore, a city built on a major body of water.However, if this estimate reflects the national wtp for flood insurance, calculating the exante wtp is no more difficult than finding the ex post wtp, represented by κ here:w = (1 + e)κ. (16)This estimate is, however, of limited purpose and is ripe for additional analysis throughsensitivity analysis.MEASURING THE IMPACTS OF THE NFIP 8The estimate for the ad hoc disaster aid, a must also be estimated. The best estimatefor it derives from the impetus behind the nfia, to relieve pressure on the federal budgetfor disaster aid. As a result, it is possible to assume that the ad hoc disaster aid is replacedby the claims against the program following a flood event. Therefore, a = κ is the bestestimate for ad hoc disaster aid if the nfip were not available.Finally, it is necessary to estimate B and β, the environmental impacts in theexternal surplus. Because B and β are both the environmental damages caused by therebuilding in sensitive areas and because the funding for those damages are presumedequal, though derived from different sources, it is reasonable to assume the environmentalimpacts would also be equal. Therefore, B = β and B − β = 0.Beginning with equation 15, this allows the value of ∆S to be further simplified:∆S = w + φωpi − κ+B − β +ma= (1 + e)κ+ φωpi − κ+mκ= κ+ eκ+ φωpi − κ+mκ= κ(e+m) + φωpi (17)Equation 17 includes six variables necessary for calculating the net change in social surplusdue to the nfip. Values for κ and ω can be estimated from historical nfip financial dataavailable from fema. Estimates for pi can be calculated using historical insurance industryprofitability data. The variable m is provided directly byOffice of Management and Budget (1992, p. 13).The next variable to estimate is φ, representing the percentage of the premiumearned by the insurance companies participating in the Write Your Own (wyo) programfor administering the nfip. This percentage is defined in regulations governing the wyoprogram to be 15 percent with a potential 2 percent bonus for meeting certain targets foradministration and sales. Because the value of φ is fixed within a single narrow band only2 percent wide, this analysis will select the midpoint of the band, 16 percent, as theMEASURING THE IMPACTS OF THE NFIP 9baseline for analysis.The variable e, representing the additional sum policyholders are willing to pay priorto a flood event for coverage has been researched by Farrow and Scott and estimated to be15 percent.ConclusionEquation 17 provides a simple theoretical model for analyzing the net social benefitsof the nfip insurance component. On its face, it provides a single number. More broadly,this model when combined with a model for analyzing the Flood Mitigation Assistance(fma) component, provides the net social benefits of the nfip as a whole. This model canalso be applied both prospectively and retrospectively, leading to net social benefits bothhistorically and moving forward.Relying on a series of assumptions, listed in table 2, the broad economic model,including some variables that cannot be estimated, is reduced to a final form using sixvariables with estimates readily available from nfip financial data or the literature throughbenefits transfer (Desvousges, Johnson, & Banzhaf, 1998). Consequently, the reduced formmodel is an attempt to find a sufficient statistic for the nfip’s insurance component(Chetty, 2009), and starting point to more complex analyses of the nfip. Becauseinformation on premiums and claims are available at the state and county level from fema,analytical granularity can be reduced. This encourages jurisdictional level analysis ofdistributional impacts of the program. In addition, by relaxing the assumptions made inthe model, such as the equivalence of environmental impacts or estimates of the ex anteadjustment to the wtp for flood insurance, it is possible to perform break-even analysis,adapt other estimates of the values to the model, or search for optimal values throughMonte Carlo simulation. Finally, this model forms the basis for analyzing proposed changesto the nfip or new disaster insurance programs.MEASURING THE IMPACTS OF THE NFIP 10ReferencesBoardman, A. E., Greenberg, D. H., Vining, A. R., & Weimer, D. L. (2010). Cost-benefitanalysis: concepts and practice (4th ed.). Pearson series in economics. Upper SaddleRiver, NJ: Prentice Hall.Chetty, R. (2009). Sufficient statistics for welfare analysis: A bridge between structural andreduced-form methods. In K. J. Arrow & T. F. Bresnahan (Eds.), Annual review ofeconomics (Vol. 1, pp. 451–487). Palo Alto, California: Annual Reviews.Desvousges, W. H., Johnson, F. R., & Banzhaf, H. S. (1998). Environmental policy analysiswith limited information: Principles and applications of the transfer method.Cheltenham, UK: Edward Elgar.Farrow, S., & Scott, M. (2011). Estimating the ex-ante willingness to pay for floodprotection. (presented at the Association of Environmental and Resource Economistssummer workshop)Frank, R. H. (2006). Microeconomics and behavior (6th ed.). Boston: McGraw-Hill Irwin.Moss, D. A. (1999). Courting disaster? the transformation of federal disaster policy since1803. In K. A. Froot (Ed.), The financing of catastrophe risk (Chap. 8, pp. 307–355).Chicago: University of Chicago Press.Office of Management and Budget. (1992, October). Guidelines and discount rates forbenefit-cost analysis of federal programs (tech. rep. No. A-94). Washington.Rumsey, M. A. (2010, May). Beyond bigger and better: gilbert white and america’s newapproach to floodplain management. (Master’s thesis, Mississippi State University,Starkville, MS).MEASURING THE IMPACTS OF THE NFIP 11Variable Descriptiona Amount of ad hoc disaster aid paymentsB, β Estimates of environmental impactsC Consumer surplusκ Claims made against the nfipE External surpluse The ex ante adjustment for wtpG Government surplusφ wyo fees to insurersm the marginal excess tax burden (metb)P Producer surplusω Premiums paid to the nfippi Profit ratio for the insurance industryS Net social surplusw willingness-to-pay for flood insuranceTable 1Variable list included in social surplusMEASURING THE IMPACTS OF THE NFIP 12Assumption Explanation Impacta = κ nfip claims are equal to the expectedamount of ad hoc aid granted in theabsence of the nfipLimits prospective benefits of nfipB = β Environmental damages caused byad hoc flood recovery is the sameas environmental damages caused bynfip-funded recoveryEnvironmental damages are not con-sideredpi’s value Insurers make a profit on administra-tive services and the profit ratio onthat service is the same as the gen-eral industry profitabilityTies the producer surplus to generalinsurance profitabilityφ’s value Property insurance provides receiveadministrative fees equal to mean po-tential feesReduced by the narrow band (2%)for potential feese’s value The estimate for ex ante wtp for theCity of Baltimore is transferable na-tionwideThis may be significantly differentfrom the nationwide wtp for floodinsurance due to specific regional fac-tors affecting local behaviorTable 2Simplifying Assumptions Contained Within the Model

Measuring the impacts of the national flood insurance program

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