Discussion Paper Series

2012-03
Public and Private Mitigation for Natural Disasters in Japan
Kazuyuki Iwata, Yutaka Ito and Shunsuke Managi

October 5, 2012

Discussion Papers can be downloaded:
http://www1.tcue.ac.jp/home1/c-gakkai/dp/dp12-03

1

Public and Private Mitigation for Natural Disasters in Japan

Kazuyuki Iwata 1*, Yutaka Ito 2 and Shunsuke Managi 2

1

Faculty of Regional Policy, Takasaki City University of Economics, Japan

2

Graduate School of Environmental Studies, Tohoku University, Japan* Corresponding author.
Fax +81-27-344-7590
E-mail address: iwata.kazuyu@gmail.com

Abstract
An increasing number of studies analyze the relationship between natural disaster damage andincome levels, but they do not consider the distinction between public and private disastermitigation. This paper empirically distinguishes these two types of mitigation using Japanese
prefectural panel data from 1975 to 2007. Our results show that public mitigation rather thanprivate mitigation has contributed to mitigating the total damage resulting from natural
disasters. Our estimation of cost-benefit ratios for each prefecture confirms that the mitigation
efforts of urban prefectures are less effective than those of rural prefectures in focusing on
frequent and small disasters. Hence, the national budget for their mitigation investments andsupport must shift from urban prefectural governments to rural governments. Furthermore, tolessen the damage resulting from extreme catastrophes, policy makers should invest in
improved mitigation infrastructures when faced with a high probability of disasters.

Keywords: public mitigation; natural disaster; cost-benefit ratio; urbanization;
JEL Classification:

H54, Q54, R53

2

1. Introduction
Natural disasters have caused tremendous damage throughout the world. In March 2011, a
9.0-magnitude earthquake struck Japan and resulted in more than 20,000 people consideredeither dead or missing. The 2004 Indian Ocean tsunami that was caused by an earthquake
killed approximately 230,000 people in Southeast Asia. More than 60,000 people were victimsof the 2008 Sichuan earthquake in China. These examples show that natural disasters cause
massive losses in many countries. 1 In addition, climate change is expected to lead to anincrease in extreme weather events and thus result in further damage (IPCC, 2007).
Unlike for other externalities, such as crime and pollution, we cannot control thenumber of natural disasters because they occur exogenously. Therefore, disaster damage
reduction activities (i.e., mitigation) are important. The anticipation of and response to natural
disasters require advances in the use of effective mitigation activities. Two countermeasures
are addressed in this study: public mitigation and private mitigation.
The first countermeasure is public mitigation. To prevent or mitigate the damage
incurred as a result of natural disasters, governments have an important role in providing
disaster prevention infrastructures, such as dams, levees and flood control basins. The second
countermeasure is private mitigation. Households can choose between several self-protection
strategies, such as moving to less risk-prone areas, investing in building reinforcement orpurchasing insurance based on their income (Smith et al., 2006).2
There is accumulating evidence regarding the relationship between fatalities/damage
from disasters and mitigation measures. For example, using data from 73 countries from 1980
to 2002, Kahn (2005) finds that countries with high gross domestic product (GDP) per capita
suffer fewer deaths from natural disasters compared with countries with low GDP per capita.
Similarly, using data from 151 countries from 1960 to 2003, Toya and Skidmore (2007) reveals
that the economic damage resulting from disasters in wealthy countries is less than the damage
incurred in poor countries. Kellenberg and Mobarak (2008) show that the relationship between
GDP per capita and death tolls is an inverted U-shape, which is similar to the environmental

1

The economic loss and death toll resulting from 335 natural disasters in 2009 were approximately $41.3 billionand 10,655 people, respectively (Vos et al., 2010).
2
See Kousky et al. (2006) for a discussion of the theoretical relationship between private investment andgovernmental protection.

3

Kuznets curve hypothesis (Grossman and Krueger, 1995). 3 These previous studies indicatethat an increase in GDP per capita in developed countries leads to a decrease in natural disasterdamage.
These studies apply GDP per capita do not explicitly distinguish public and private
mitigation. Anbarci et al. (2005) suggest separating public and private mitigation measures for
future studies. We distinguish these two measures using Japanese prefecture-level data. These
data enable us to examine the reduction effects of public and private mitigation on disasterdamage.
There is an additional advantage to using Japanese prefectural data. Unlike
cross-country analysis, these data allow differences in detailed socio-economic and physicalconditions to be incorporated into the examination of relationships. For example, geographicalconditions, such as the absolute value of latitude and elevation, are key determinants of thedamage that results from disasters (Kahn, 2005). Therefore, the geographical characteristics ofFlorida and Illinois in the United States clearly differ despite the location of these two states inthe same country.
Furthermore, most previous studies have restricted their attention to medium- andlarge-scale natural disasters using the Emergency Events Database (ED-MAT) 4 (Kahn, 2005;
Toya and Skidmore, 2007; Kellenberg and Mobarak, 2008) or to earthquakes based on the
National Geophysical Data Center (NGDC)’s Significant Earthquake Database5 (Anbarci et al.,2005; Escaleras et al., 2007) 6, but no previous studies have considered all types and scales ofnatural disasters due to the lack of data. The Fire and Disaster Management Agency in Japan
provides all types of natural disaster damage data for each prefecture in its official statistics.
Thus, we collect data pertaining to catastrophes (or large-scale specific disasters) andsmall-scale and infrequent disasters.
An increase in the number and intensity of natural disasters is likely in Japan(Guha-Sapir et al., 2004). However, there is considerable variation in the levels of disasterdamage at the prefectural level. For instance, the total economic damage from 1975 to 2007 in
3

In addition, Anbarci et al. (2005) show that GDP per capita and inequity have negative and positive influences on
fatalities resulting from disasters based on their analysis of 269 earthquakes from 1960 to 2002. Escaleras et al.
(2007) obtain the same results in line with the literature.
4
The ED-MAT is provided on the website of the Centre for Research on the Epidemiology of Disasters:
http://www.emdat.be/.
5This database is published on the NGDC’s website: http://www.ngdc.noaa.gov/ngdc.html.
6
Many studies have focused on measuring the effects of specific catastrophes, such as the Great Hanshin-Awaji
Earthquake in Japan in 1995 (Hyogo Prefecture, 2008), Hurricane Andrew in 1992 (West and Lenze, 1994;
Hallstrom and Smith, 2005), and Hurricane Katrina in the United States in 2005 (Baade et al., 2007).

4the Hyogo prefecture was about US$ 81.4 billion as evaluated in 2007. This damage wasprimarily caused by the Great Hanshin-Awaji Earthquake (GHAE). 7 However, the damage
during the same period in the Kanagawa prefecture was only $500 million.
Mitigation requires cost-effective implementation from economic perspective. Thereis wide variation in public mitigation measures among prefectures during our study periods.
The public mitigation measures in this study represent disaster prevention infrastructure in
mountains, rivers, and seashores (the detailed explanation will be provided in section 2)..For
example, public mitigation per capita ranges from $1,807 to $21,696 per person in 2007 (seeFigure 1). Public mitigation per income also varies; these measures range from 4.7 to 124.1%
in 2007 (see Figure 2). Consequently, if there are large differences in the efficiency of public
mitigation measures among prefectures, these differences could result from varying levels of
economic damage because the economic damage is highly related to population density.
Therefore, we also estimate the cost-benefit ratios of public mitigation and compare theseratios among prefectures. A more detailed discussion of our reasons for considering prefectural
population density for the cost-benefit ratio is provided in Appendix 1.

20000
15000
10000
5000
0

Public mitigation per capita (unit:dollar)

Figure 1. Public Mitigation Per Capita by Prefecture in 2007

0

2000

4000

Population Density (unit:person per square kilometer)

Note: Obs.=46.

7

The GHAE caused 6,437 deaths and 43,792 injuries in 1995.

5

6000

100
50
0

Public Mitigation Per Income (unit:percent)150

Figure 2. Public Mitigation Per Income by Prefecture in 2007

0

2000

4000

6000

Population density (unt:person per square kilometer)

Note: Obs.=46.

Ideally, if governments are aware of the true risks of prefectural disasters, such as theannual probability of a large earthquake occurrence, they can construct proper mitigation
measures according to those risks. Then, when sufficient long-term data reflecting the exact
risks are available, no difference among the efficiency of prefectural mitigation should beobserved (however, we cannot obtain such data). If the measured cost-benefit ratios show
significant variation between prefectures, it is considered that some prefectures provide their
mitigation measures inefficiently as an ex-post judgment. Though there is indeed a limitationin our estimation due to the unknown true disaster risks, our ex-post evaluation of disastercountermeasures is valuable for policymakers.
Typically, analysts report the collection of more taxes in wealthy urban areas, butsome of the collected tax is used for less wealthy rural regions as part of the national tax policy.
Thus, the total social infrastructure is less sufficient in urban areas than in rural areas.
Therefore, these expenditures must be allocated more toward urban regions (Yamano and
Ohkawara, 2000). However, public mitigation which is a part of social infrastructure has notbeen evaluated from the ex-post viewpoint. Therefore, we estimate the efficiency levels andprovide a discussion regarding the allocation of public mitigation measures between rural andurban prefectures.
6This paper is organized as follows: Section 2 describes the empirical framework. Sections 3
and 4 present our data set and estimation results. Section 5 provides the estimated cost-benefit
ratios for each prefecture and a discussion regarding the efficiency of disaster prevention
measures. Section 6 provides the conclusion.

2. Empirical Model
2.1. Natural Disaster Damage

The benefits generated by public mitigation (prevention measures) are divided into threecomponents (Ministry of Land, Infrastructure, Transportation and Tourism (MLITT), 2004):
reductions in human capital loss, physical capital loss, and psychological loss. Human capital
loss refers to the number of deaths, as well as missing and injured people, caused by natural
disasters.
Physical capital loss consists of primary and secondary economic damage based on
the duration of a natural disaster. Primary economic damage is the direct destruction of public
or private infrastructure, such as roads, buildings or houses, and products that may include
crops or goods. Secondary economic damage represents the indirect economic loss arisingfrom primary economic damage, such as stagnation in logistics. Due to the lack of data sources,
we obtain only primary economic damage data.
Psychological loss is the human anxiety that results from natural disaster occurrences.
There are several approaches to measuring reductions in psychological loss, including thecontingent variation method. However, it is difficult to obtain data pertaining to the number ofpeople who experience anxiety as a result of natural disasters. Therefore, our data do notinclude psychological loss. This paper focuses on the human capital loss and physical capital
loss associated with primary economic damage. Therefore, the levels of natural disasterdamage defined in this paper are lower than the actual levels of damage.
Suppose that human capital damage (HDM) is composed of deaths (including
missing people) and minor/major injuries. The total damage, TDMit, in year t in prefecture i isdefined as the summation of the economic damage (EDM) and HDM, as shown in equation (1).
Let ND be the number of deaths, and NMI and NMA be the number of minor and major injuriescaused by natural disasters. In addition, let VSL be the value of a statistical life, and OCMI and
OCMA be the opportunity costs for minor and major injured people, respectively.
7

TDM it = HDM it + EDM it
HDM it = NDit ⋅ VSLit + NMI it ⋅ OCMI it + NMAit ⋅ OCMAit(1)

In this paper, it is necessary to determine the value of a statistical life and the opportunity costs.
We use data from previous studies to generate these parameters using the following procedure.
There is abundant literature pertaining to the value of a statistical life in the UnitedStates (Viscusi and Aldy, 2003). However, there is minimal literature regarding this topic forJapan. One representative study includes the estimates provided by Tsuge et al. (2005), in
which the value is approximately $2.5 million, as evaluated in 2007. We established this value
as the value of a statistical life in Japan.
In addition, considering the differences in the substantial price levels between years
and between income levels among prefectures, we set DEFt as the GDP deflator and INCt as
the average income per capita in year t. Then, we calculate the value of a statistical life, as
evaluated in 2007, by year and by prefecture using the following formula.

VSLit = 2.5 (million dollar ) ×

DEF2007 INC it
×
DEFt
INC t

(2)

We consider the loss of time required to completely recover from the damage as theopportunity cost for the injured. People suffering minor and major injuries due to an
earthquake have an average recovery time of 8.8 and 55.6 days, respectively (Non-Life
Insurance Rating Organization of Japan, 2001). Therefore, the opportunity costs, OCMI and
OCMA, can be calculated based on the loss of income during hospitalization as follows.

OCMI it = 8.8 × INCit / 365(3)

OCMAit = 55.6 × INCit / 365
2.2. Damage Function

The public mitigation measures in this study include the social infrastructure associated withthe protection of mountains, rivers, and seashores. The information pertaining to this social
8infrastructure is provided by the Cabinet Office (2007). The social infrastructure of mountains
and rivers represent infrastructures for flood control and sand prevention, such as dams, levees,
and groins. Alongshore, bulwarks and wave-dissipating blocks are types of social
infrastructure. 8
Public mitigation is intuitively expected to reduce natural disaster damage. Private
mitigation may also reduce damage because wealthier people can afford to invest in
self-protection activities, such as reinforcing their homes and moving to areas in which thenatural disaster risks are low (Smith et al., 2006).
Furthermore, we are certain that the extent of damage also depends on the following
three factors. The first factor is the social factor. If two massive earthquakes with the same
scale occur in highly and sparsely populated prefectures at the same time, ceteris paribus, mostof us intuitively expect that the number of injured people is larger in the highly populated
prefecture than in the sparsely populated prefecture. Therefore, factors relating to social
structure, such as population, affect the extent of damage that may be incurred.
According to Kahn (2005), the second issue is the geological factor. For instance,high tide does not occur in inland prefectures. People who live in prefectures without
volcanoes do not suffer damage from volcanic explosions. Thus, the geographicalcharacteristics of prefectures also influence the extent of damage that may be incurred.
Finally, the climate factor includes temperatures and rainfall amounts. Prefecturesthat experience heavy snow and rain are likely to face snow disasters, torrential rain, andsubsequent landslides. Because these disasters cannot be completely captured by the geologicalfactors, we incorporate the climate factors as determinants of the damage function.
Previous studies, such as Kahn (2005), Anbarci et al. (2005), Toya and Skidmore(2007), Escaleras et al. (2007), and Kellenberg and Mobarak (2008), have used GDP per capita
as a proxy because high-income people are able to prevent damage (i.e., private mitigation)
and/or wealthier governments can provide more effective disaster prevention projects (i.e.,
public mitigation). However, income level, which is actually a form of private mitigation, is
not a sufficient variable with which to capture public mitigation efforts because publicauthorities invest in and construct disaster mitigation stocks in consideration of the society,
8

The Cabinet office (2007) provides the social capital information regarding mountains, rivers, and seashores byprefecture only for 5 years. Therefore, we regress the capital in terms of year and squared year for each prefecture,and then we predict the missing values of social capital. The quadratic form is applied because the adjusted
R-squares are approximately 0.99 in all estimations.

9whereas private households do not have significant incentives to help unknown people in theirsociety. In fact, the correlation between the income per capita (i.e., private mitigation) and the
public mitigation stock per capita is only 0.32 in our dataset. Therefore, this study separates
private and public mitigation measures using two different variables.
We estimate the damage function using equation (4). The dependent variable is thetotal damage per GDP, and the independent variables are the public mitigation stock (PPS) per
capita, the income per capita (private mitigation) and the other control vector (X), as
previously discussed. We convert all variables into logged values to consider the potential
non-linear relationships between damage and mitigation.

ln(

INC it
PPS it
TDM it) = α 1 ln() + α 2 ln() + X it β'+ µ i + ε it
POPit
POPit
GDPit

(4)

where α1, α2 and β are the parameters to be estimated, and μ and ε are the unobserved
prefectural specific effect and error terms, respectively. To avoid endogeneity of residential
choice problem on the population density, we use lagged population density in the estimation,
similar to Wagner(2010).
The control vector X refers to the social, geological, and climate factors. We set the
population density as a social factor. To account for geological factors, we apply the average
degree of slant, the coastal length and the number of active volcanoes. The annual rainfall
amount, maximum temperature, annual snow accumulation, number of approaching typhoons,and dummy for earthquakes with an intensity greater than 5 are applied for the climate factors.
The threshold intensity of 5 is chosen because earthquakes that exceed this threshold not only
affect human activity but also damage houses, the ground and lifelines, which are defined by
the Meteorological Agency in Japan.
For the other determinants, we incorporate two dummy variables to control for theextreme effects of the GHAE and catastrophes. The dummy for GHAE is one in the 1995
Hyogo prefecture. Another dummy variable of one is used for catastrophes if there has been acatastrophe claiming more than 100 lives.
3. Data Sources

10Our dataset includes Japanese prefectural panel data from 1975 to 2007, except for the
Okinawa prefecture. 9 The data sources for each variable are as follows. Information regarding
human and economic damage was obtained from the annual White Book on Fire Service inJapan published by the Fire and Disaster Management Agency. The white book reports thenumber of fatalities and injured people and the primary economic damage by year and byprefecture.
The amount of disaster prevention infrastructure stock in the form of public
mitigation is obtained from the Cabinet Office (2007). We obtained population and income
information from the annual Basic Resident Register Population Survey and the Annual Reporton Prefectural Accounts published by the Japan Geographic Data Center and by the Cabinet
Office, respectively. Data pertaining to the geographical characteristics for each prefecture
were obtained from the Survey of the Land Area for Shi, Ku, Machi, and Mura of Japan and
Digital National Land Information published by the Japan Map Center and by MLITT for the
information regarding prefectural areas and regarding the coast length and average degree ofthe slant, respectively. The climate data were obtained from the Japan Meteorological Agency’s
website database.
The descriptive statistics for each variable are shown in Table 1, including
decompositions of the natural disaster damage. The sample size of the dataset in our estimationis 1,457 (that is, 32 years multiplied by 46 prefectures minus 15 missing values because weemploy first-year lagged population density).
The mean of the total damage per GDP is approximately 0.590%. Dividing this value
into economic damage and human damage, we find that the mean of economic damage per
GDP is 0.582%, which is up to 95% of the total damage. However, human capital damage
accounts for only 5% of the total damage. Hence, most natural disaster damage results fromdirect physical destruction. The contribution ratio of human capital damage to total damage
increases as the applied value of a statistical life increases. However, even if the value of astatistical life doubles, the economic damage still constitutes a significant portion of the natural
disaster damage. Therefore, it is important for governments to place greater emphasis on
preventing economic losses that result from natural disasters.

9

There are 47 prefectures in Japan. A prefecture is roughly equal to a county in the United States.
11

Table 1. Descriptive statistics and data sources
variables
Total damage per GDP
Damage Human capital damage per GDP
Economic damage per GDP
Public Preparation per capita
Preparation
Self Preparation per capita
Social Population density
Average degree of slant
Geological Length of shore
number of active volcano
Annual rainfall
Maximum temperature
Climate Snow accumulation
number of approaching typhoon
Dummy for earthquake withmore than intensity 5
Dummy for catastrophes
Other
Dummy for GHAE

maximu
unit
mean
s.d.
minimum
Sourcempercent
0.590
1.954 1.18E-06
59.20 White Book on Fire Service in Japan0.302
011.08 White Book on Fire Service in Japan
percent
0.028
percent
0.562
1.694 7.88E-07
48.12 White Book on Fire Service in Japan
0.612
21.70 Cabinet Office (2007)$1,000/person
5.373
3.593
38.28 Annual Report on Prefectural Accounts$1,000/person
19.41
4.487
10.22464.37 5878.35 Basic Resident Register Population
person/square km
593.54 1035.45
6.900
27.80 Digital National Land Information
degree18.73
4.947
663.39800.55
0 4139.30 Digital National Land Information
km
2.017
3.112
0
16.00 Japan Meteorological Agency
529.73555.50 4383.00 Japan Meteorological Agencymm1602.3629.10
40.90 Japan Meteorological Agency
Celsius degree
35.69
1.640
88.92
165.330 1263.00 Japan Meteorological Agency
cm
2.951
1.762
0
10.00 Japan Meteorological Agency
0.085

0.279

0

1.00 Japan Meteorological Agency

0.004
0.001

0.064
0.026

0
0

1.00 White Book on Fire Service in Japan
1.00 White Book on Fire Service in Japan

Note: Obs.=1457. Monetary values are converted into U.S. dollars as evaluated in 2007.

12

4. Estimation Results
Table 2 presents the results of estimating the damage function, i.e., equation (4). The
dependent variable is the logged total damage per GDP (TDM/GDP). We provide several
specification results for the robustness check and a comparison with the results from previous
studies.
Model 1 and models 2 through 4 represent the estimation results with and without
prefectural fixed effects, respectively. To capture the unobserved prefectural specific effects,
we use fixed effects estimator in model 2 to 4. In addition to fixed effects, an endogenous
problem is considered in models 3 and 4. In the structure of equation (4), the income per capita
is endogenous rather than exogenous because both sides of equation (4) contain the income
variable. To avoid the endogenous problem, we employ an instrumental variable estimator, inwhich the current income per capita depends on the previous value and the previous disasterdamage levels. We apply the number of dead and missing people as the damage level. In
addition, we conduct the serial test for autocorrelation introduced by Wooldridge (2010), andwe find evidence of an autocorrelation. Therefore, the heteroscedastic and autocorrelationconsistent standard errors are used in models 3 and 4. In model 4, one independent variable,
logged public mitigation per capita, is excluded to enable a comparison of the estimation
results of previous studies.
Let us discuss the results from models 1 through 4, in which the independent variable
is the total damage per GDP. The overidentification tests indicate that model 3, in which theprefectural fixed effects and endogeneity of income are included, is the most feasible result.
Although both public and private mitigation are statistically significant and negative in model
1, public mitigation is not significant when we consider the prefectural fixed effects in models
2 and 3. Even when we consider the endogeneity problem in model 3, the coefficient of public
mitigation is significantly negative, but that of private mitigation is not. Therefore, private
mitigation has no robust influence on the reduction of the total natural disaster damage.
However, private mitigation may not be observed accurately on the basis of income
level. There is one survey in Japan reported by Kobe Shinbun (2011). Two prefectures arecompared: Hyogo prefecture, where the GHAE occurred in 1995, and Shizuoka prefecture,
where there is a high probability that a large earthquake will occur within 30 years. The results
show that the residents of the Hyogo prefecture undertook greater measures to prepare for a13

large earthquake than those in the Shizuoka prefecture. This evidence demonstrates that theextent to which people protect themselves depends on their past experience, and income levels
may not accurately reflect the extent of individual mitigations for private mitigation. As aresult, the expectation that wealthier people can reduce disaster risks in various ways (seeSmith et al. (2006) regarding the United States) may not be relevant in Japan.
Furthermore, when we eliminate public mitigation from the determinants as in model4, private mitigation is significantly useful for reducing disaster damage. This result is
consistent with the results from previous studies. Therefore, we can conclude that the income
per capita used in the literature cannot capture both types of mitigation and that public
mitigation has an important role in decreasing disaster damage. Therefore, in examining therelationship between disaster mitigation and damage, we must place strong emphasis on the
differences between public and private mitigation.
The coefficients of population density and length of shore for the other determinants
are significantly negative. Therefore, sparsely populated (rural) and inland prefectures arelikely to face more natural disaster damages 10. Pluvial areas are also likely to suffer greater
damage because the coefficient for these areas is positive at a 1% significance level. Although
the dummies for large earthquakes and the number of approaching typhoons have significant
positive effects on the levels of damage, the number of active volcanoes does not have asignificant robust effect.

10

The natural disaster damages in this paper include not only human damages but also economic damages. In
addition, the damages are divided by prefectural GDP. Therefore, the results are not surprising though we intuitively
suppose that coastwise prefectures are likely to suffer more human damages caused by tsunami.

14

Table 2. Estimation results for the damage function: the independent variable is logged total damage per GDP (DMG/GDP)
Dependent Variables
Independent Variables
logged Public Mitigation per capita
logged Private Mitigation per capita
logged Population Density-1
logged Average Degree of Slantlogged Length of Shore
logged Annual Rainfall
logged Maximum Temperaturelogged Snow Accumulation
Number of Active Volcanoes
Dummy for Large Earthquake
Number of Approaching Typhoons
Dummy for Catastrophes
Dummy for GHAE
Constant
Adjusted/Centered R-squared
F value (P-value)
Overidentification Test (P-value)
Municipal Fixed Effects
Endogeneity

Model 1
Coef.
S.E.
-0.306 0.117 ***-2.820 0.309 ***-1.107 0.132 ***-0.071 0.158-0.006 0.003 *1.090 0.122 ***-0.825 0.816-0.003 0.003
0.006 0.015
0.247 0.141 *0.176 0.021 ***2.126 0.344 ***5.421 0.373 ***1.204 3.333
0.567
147.71 (0.00)
NoNo

ln(TDM/GDP)
Model 2Model 3
Coef.
S.E.
Coef.
S.E.
-1.096 0.200 ***-1.069 0.194 ***-0.517 0.506-0.595 0.527-2.311 0.525 ***-2.284 0.547 ***-0.451 0.591-0.463 0.621-0.097 0.018 ***-0.097 0.019 ***2.188 0.160 ***2.188 0.152 ***-0.711 0.807-0.709 0.823-0.004 0.004-0.004 0.004-0.075 0.035 **-0.073 0.037 *
0.328 0.125 ***0.327 0.106 ***0.117 0.019 ***0.117 0.017 ***2.219 0.386 ***2.216 0.484 ***4.977 0.432 ***4.986 1.182 ***-10.107 6.019 *-9.864 5.802 *
0.697
0.708
61.83 (0.00)
61.83 (0.00)
0.01 (0.91)
Yes
Yes
No
Yes

Model 4
Coef.
S.E.
-3.236 0.211 ***-2.001 0.551 ***-1.674 0.590 ***-0.121 0.019 ***2.182 0.154 ***-1.093 0.831-0.004 0.004-0.034 0.037
0.258 0.107 **0.123 0.018 ***2.156 0.490 ***5.303 1.196 ***6.512 5.078
0.701
60.83 (0.00)
0.16 (0.69)
Yes
Yes

Note: Obs.=1457. When the length of shore and snow accumulation are converted into logged values, we add them to 10-10 to avoid a zero problem. In models 1 and 2, robust
standard errors are used. Heteroscedastic and autocorrelation consistent standard errors are used in models 3 to 4.

15

5. Cost-Benefit Ratio From the Results
5.1. Derivation of Cost-Benefit Ratio
In this section, we estimate the cost-benefit ratios of public mitigation for each prefecture using
the predictions of the estimated damage functions. The estimation results of model 3 are used
for our computations. If prefectures did not invest in mitigation against disasters, the natural
disaster damage would be greater than the actual damage because the coefficient of public
mitigation in model 3 is significant and negative. Therefore, the benefits derived from publicprevention measures are defined as the difference between the damage levels with and without
the investments for mitigation.
Using the estimated coefficients in model 3, we predict the total benefits evaluated in
2007, TB, derived from the public mitigation measures for each prefecture as follows:2007
 PTDM it|without − PTDM it|with 
TBi = ∑ 
(1 + ir ) t −2007
t =1975 (5)where PTDMit|without and PTDMit|with denote the predicted total damage with and without the
public mitigation investments, respectively. The social interest rate is ir.
Without public mitigation investments, the disaster prevention stocks of prefecture i,
PPSi, do not increase any more than the baseline, PPSi,1975. Instead, the baseline stocks annuallydepreciate at the rate of dr. Hence, we calculate the public mitigation stocks without any
investments and then predict PTDMit|without by applying the estimated coefficients.
In contrast, the total cost of prefecture i, TCi, is a summation of the annual disasterprevention investments. Thus, we calculate the total costs for each prefecture, as evaluated in2007 (see equation (6)). The 2007 investment is eliminated from the equation because it does
not become the 2007 stock by the beginning-of-period method.

2006
 PPSit +1 − PPSit × (1 − dr ) 
TCi = ∑ 
(1 + ir ) t −2007
t =1975 (6)

For calculation, we assume that both the social interest rate and the depreciation rate
are 4% (MLIT, 2004). Based on equations (5) and (6), we calculate the cost-benefit ratios, CBR,for each prefecture as follows in equation (7).
16

CBRi = TBi / TC i

(7)5.2. Estimated Cost-Benefit Ratio
Figure 3 describes the estimated cost-benefit ratios, CBR, for each prefecture. The horizontal
and vertical axes represent population density and cost-benefit ratio, respectively. The
cost-benefit ratios in prefectures with a high population density (urban) are clearly lower than in
prefectures with a low population density (rural) (see Appendix 1, which explains why weconsider population density and its relation to the ratio). When the logged ratios are regressedon the logged population densities as the simple log-log linear regression, the coefficients of thedensity are significant and negative. Hence, public mitigation in rural prefectures, in which the
population density is low, is more efficient than in urban prefectures.

0

2

4

6

Figure 3. Estimated Cost-Benefit Ratios by Prefecture02000
Municipalities

4000

6000

fitting curve

Note: Obs.=46. The X and Y axis denote population density and cost-benefit ratio, respectively. The ratio for the
Hyogo prefecture is 14.94. The fitting curve is CBR=(Population Density) -0.91 * exp4.75.

Demonstrating the differences between rural and urban prefectures more clearly, Table
3 shows the average cost-benefit ratios by prefectural population density. The average ratio of
all 46 prefectures is 1.15. The number of prefectures in which the estimated ratios are more than
one is 13, which is approximately 28% of the 46 prefectures in Japan.
17

By sorting the 46 prefectures by population density, we label the top 5 and bottom 5
prefectures as “high population density” and “low population density,” respectively. The
average ratio of sparsely populated prefectures reaches 1.27; thus, the ratios are more than one.
Hence, most rural prefectures with a low population density construct cost-effective public
mitigation measures for natural disasters. In contrast, the average ratio of urban prefectures witha high population density is only 0.05; thus, the ratio is much less than one. Therefore, public
mitigation measures are not cost-effective in urban prefectures. The null hypothesis in which theaverage ratios of the two groups, the highly and sparsely populated prefectures, are not different
from each other is rejected at a 1% significance level.
Table 3. Estimated Cost-Benefit Ratios by Population Density
average of prefectures with high population density
average of 46 prefectures
average of prefectures with low population density

Cost-Benefit Ratio
0.05
1.15
1.27

Note: “high population density” refers to the top 5 prefectures: Tokyo, Osaka, Kanagawa, Saitama and Aichi, which
are located in Japanese metropolitan areas. “low population density” refers to the bottom 5 prefectures: Hokkaido,
Iwate, Akita, Shimane and Kochi.

This result has two implications. First, we confirm that only 28% of the prefectures
have provided cost-effective disaster prevention works. However, there is a wide gap between
the cost-benefit ratios of urban and rural prefectures. The ratios of urban prefectures are small,and the ratios of rural prefectures are large. Therefore, the results imply that urban prefectures
likely need to reduce or reassess their investments to improve their social surplus.
Second, it is often argued that public infrastructures are too small in urban areas incomparison with rural areas in Japan (Yamano and Ohkawara, 2000). However, our results
suggest that some specific public infrastructures in urban prefectures, such as disasterprevention works, may be an excessive investment even though public infrastructures may be
excessively small as a whole.
5.3. The Case for Extreme Catastrophes

Although we consider that the frequent occurrences of both catastrophes and small-scaledisasters, unlike in previous studies, here the damage resulting from catastrophes isincomparably larger than others. Japan has experienced two catastrophes since 1975: the GHAE
in 1995 and the Higashi-Nihon Earthquake in 2011 (which is outside of our study period). In
this section, we discuss these catastrophes using cost-benefit ratios.
18

The Hyogo prefecture suffered the GHAE in 1995. Table 4 presents the costs, benefits,
deaths and economic damage in the Hyogo prefecture from 1975 to 2007. Although the total
cost-benefit ratio is 14.94, the ratio decreases to only 0.33 when we exclude the 1995 data. Thus,
it is clear that a terrible catastrophe dramatically increases the ratio. If the Hyogo prefecture had
known of the GHAE prior to its occurrence, the prefecture could have reduced death tolls andeconomic damage by constructing more public mitigation measures.
Table 4. Estimated Cost-Benefit Ratios of the Hyogo Prefecture
CostBenefit
Ratio
unit
Hyogo
14.94
Hyogo (only 1995)
14.61
Hyogo (exclude 1995) 0.33

BenefitCost

million dollar
1146806 76776
1121658 76776
25149 76776

Death Injuries HDM
persons
6497 40731
6281 39488
216
1243

EDM TDM

million dollar
17756 81413 #####
17264 74974 #####
492
6439 6932

Note: HDM, EDM and TDM denote human capital loss, primary economic destruction and total damage as a result of
natural disasters. The units of benefit, cost, EDM, HDM and TDM are represent in millions of U.S. dollars as
evaluated in 2007. Deaths include missing persons.

The greatest earthquake and tsunami recorded, the Higashi-Nihon Earthquake,occurred in Japan’s Tohoku area on March 11, 2011. Three prefectures in the area continue tosuffer from tremendous damage. 11 In January 2011, the governmental Headquarters ofEarthquake Research Promotion under the Ministry of Education, Culture, Sports, Science andTechnology released a forecast stating that the probability of a huge earthquake occurring within
30 years in the Tohoku area with a magnitude of approximately 8.0 would be 99%. The public
forecast underestimated the magnitude of the earthquake (the actual earthquake was 9.0 in
magnitude), and extensive damage was generated.
The total cost-benefit ratios of the three prefectures in the area from 1975 to 2007 arepresented in Table 6. Viewing the ratios of the three prefectures, we observe that the ratio for the
Miyagi prefecture is less than one, whereas the ratios are more than one for the other prefectures.
Although the population density of the Miyagi prefecture was 341 people per square kilometerin 2007, the density of the Iwate and Fukushima prefectures were 90 and 152 people per square
kilometer, respectively. Again, we observe the trend in which the ratio of prefectures with a highpopulation density is lower than those with a low population density.
A brief estimation of the damage incurred from the Higashi-Nihon Earthquake is also
shown in Table 6. The death toll as of June 1, 2011, including missing and injured people, isprovided by the governmental National Police Agency. In the Miyagi prefecture, the earthquake
11

These three prefectures are the Iwate, Miyagi and Fukushima prefectures on the Pacific Coast.

19

generated 14,000 deaths and 3,000 injuries. The human damage resulting from the earthquake iscalculated using income per capita and the value of a statistical life for the prefectures in 2007.
To determine the levels of economic damage, we referred to Goldman Sachs reports, which
estimate that the amount of damage was approximately $164.8 billion, as evaluated in 2007.
Based on the assumption that only these three prefectures suffered economic damage, we assign
the value of $164.8 billion to the three prefectures based on the scale of human damage.
How effective were the public mitigation measures in the prefectures in terms ofalleviating the damage caused by the catastrophe? We must estimate the damage that would
have occurred as a result of the Higashi-Nihon Earthquake if there had been no investment inpublic mitigation. We estimate the benefit derived from the mitigation in the catastrophe using
the following procedure. It is assumed that the 2011 values of determinants (e.g., public andprivate mitigation, population, and snow accumulation) are identical to those of 2007. In
contrast to the previous estimation, we add the three samples for the Miyagi, Iwate andFukushima prefectures in 2011 to the observations in Tables 1 to 4 (that is, 1,457). We thenincorporate three dummies of the Higashi-Nihon Earthquake for the Miyagi, Iwate andFukushima prefectures as the determinants. Using 1,460 observations, we again estimate thedamage function and then predict the damage with and without public mitigation.
The updated cost-benefit ratios that reflect the earthquake are presented at the bottomof Table 5. The ratios dramatically increase in the three prefectures; this result is consistent withthe effect of the GHAE in the Hyogo prefecture. Even in the Miyagi prefecture, in which theratio is below one before the earthquake, the ratio increases to 61.66 after the 2011 data areconsidered. Therefore, we conclude that a catastrophe is associated with significantly improved
benefits.
As previously mentioned, the Higashi-Nihon Earthquake was forecasted by theJapanese government. Considering this fact and our results, we recommend that the threeprefectures in the Tohoku area should increase their investments in mitigation because they areaware of the high probability of earthquake occurrences. In particular, the extent of public
mitigation in the Miyagi prefecture should be approximately more than 60 times the current
level; however, the calculation of optimal investments must reveal the marginal benefits andcosts of public mitigation measures. Therefore, the governments in areas in which catastrophes
are forecasted with a high probability should invest in and construct their mitigation measuresmore aggressively.
Regarding the countermeasures designed to mitigate extreme catastrophes that occur
once every several hundred years, is the cost-benefit approach applicable to an extreme event?
Tol (2003) discusses whether the cost-benefit analysis is an applicable tool with which to
manage the global warming problem and concludes that cost-benefit analysis is beneficial if the20uncertainties (that is, variances in both cost and benefit) are finite. For natural disasters, it isprobable that the variances in both cost and benefit are finite even in an extreme event, such as
the GHGE. Hence, it is appropriate to apply the cost-benefit approach for public mitigation
against disasters.
Table 5. Effects of the Higashi-Nihon Earthquake in the Three Prefectures
CostBenefi Benefit Cost Deaths Injuries HDM EDM TDMtmillion dollar
persons
million dollar
from 1975 to 2005
139
9648
9787
73
484
Iwate
1.60 62087 38915
110
546
234
9674
9908
Fukushima 1.42 73030 51309
190
80 12051
6833
7023
Miyagi0.44 18940 43474
Higashi-Nihon Earthquake
Iwate
7390
166 12451 48365 60816
236 3736 14512 18248
Fukushima
1983
14273
3459 26234 ###### ######
Miyagifrom 1975 to 2005 + Hibashi-Nihon Earthquake
650 12590 58013 70603
Iwate
39.57 ####### 38915 7463
Fukushima 10.16 521307 51309 2093
782 3970 24186 28155
Miyagi61.66 ####### 43474 14353 15510 26424 ###### ######
Note: The quick estimation deaths (including missing people) and injuries were the values announced by the National
Police Agency in June 1, 2011. In calculating HDM of Tohoku Earthquake, recovery time for opportunity cost is
assumed to be 33.2 days, which is average time of 8.8 and 55.6 days for minor and major injuries, respectively.

Notably, our analysis might underestimate benefits for the following two reasons. The
first concerns the analytic period considered in this paper. After new disaster prevention
infrastructures are constructed, approximately 20% of them function for more than 40 years
because our depreciation rate is assumed to be 4%. Therefore, the public mitigation measuresconstructed in 2006 will be maintained after 2007. It is desirable to predict and expand the data
set to obtain an accurate value of the benefits observed after 2007. Thus, the estimated benefits
in this paper are under-evaluated.
Second, the natural disaster damage defined in this paper excludes secondary
economic damage and psychological damage due to the lack of a suitable reference. Secondary
economic damage is likely to be greater in urban prefectures than in rural prefectures. In
addition, if the extent of human anxiety for people in urban areas does not differ from that inrural areas, then the amount of psychological damage in urban areas would be greater than inrural areas. These omitted types of damage may close the cost-benefit ratio gap between therural and urban prefectures, but there are still large gaps between rural and urban areas. Future
research should consider these two concerns.
21

6. Conclusion
Natural disasters are among the most important externalities that we must confront because
extreme events, such as massive earthquakes and hurricanes, generate a tremendous number ofdeaths and severe economic destruction. We cannot control the probabilities of disasteroccurrences; in contrast, we can control the other externalities derived from our economic
activities. Furthermore, disasters may have significant effects on governmental electricity andenvironmental policies throughout the world. For example, the 2011 Higashi-Nihon Earthquake
in Japan recently resulted in more than 20,000 dead and missing people. This earthquake halted
the generation of electricity from nuclear power plants and caused radioactive leaks. The
earthquake will likely cause significant changes in future Japanese environmental policies.
Because we must discuss mitigation policies against natural disasters, studies
examining natural disasters from the economics viewpoint have been conducted. Although mostprevious studies have examined the relationship between development and disaster damage,they have not explicitly treated governmental roles as disaster protection works providers. This
paper is the first study to examine the relationship between public/private mitigation anddisaster damage and consider public and private mitigation separately.
Focusing only on Japan, in which many natural disasters (e.g., earthquakes, typhoons,gales, high tides) occur every year, we are able to incorporate detailed information into our
econometric model. Therefore, a variety types and scales of natural disasters and climate andsocio-economic conditions are considered in the analysis.
The previous studies in the literature show that wealthier countries tend to suffer lessdamage and that economic growth is a good countermeasure with which to decrease disasterdamage. However, using Japanese prefectural data from 1975 to 2007, we find that public
mitigation has a key role in mitigating the total disaster damage from the viewpoint of efficiency.
We also found that the private mitigation (economic growth) effect is limited.
Additionally, we revealed a wide gap between the efficiency levels of public
mitigation measures among prefectures despite evidence that these measures are capable of
mitigating the damage incurred. In particular, the effects of public mitigation in urban
prefectures are smaller than those in rural prefectures.
This result highlights four important implications. First, people may not richly
recognize the natural disaster risks of the areas in which they live. If people were aware of thetrue risks, private mitigation measures should effectively reduce disaster damage because many
people could afford to invest in self-protection measures, such as house reinforcement, based on
their income levels, as shown in the literature.
Second, governments must effectively and efficiently construct disaster prevention22

infrastructures based on natural disaster risks because public mitigation can reduce the damage
incurred from disasters. In addition, informing residents regarding these risks is also crucial tobridging the asymmetric information gap between governments and residents.
Third, urban prefectures should reassess their public mitigation measures. Despite thelow number of disaster occurrences, the cost-benefit ratios of public mitigation measures inurban prefectures are small due to excessive investments (the cost is excessively large) or
ineffective mitigation measures (the benefit is excessively small). In either case, urban
prefectures must reconsider their public mitigation measures to improve their social welfare.
Finally, prefectures that have a high probability of suffering massive earthquakes in
the near future should construct more aggressive prevention infrastructures. In Japan, except for
the Tohoku area, there are several areas in which large earthquakes are expected to occur with ahigh probability. To protect our society in a more cost-effective manner, we must accumulate
economic studies pertaining to disaster prevention.

Acknowledgements
We appreciate useful comments from Hajime Katayama. This study was supported by the
Grant-in-Aid for Young Scientists (B) of the Japan Society for the Promotion of Science(23730223).

Appendix 1. Performance Analysis of Prefectures
In general, there is smaller per capita damage in urban areas because large cities historicallytend to be constructed in areas with lower disaster risks. Figures A1 and A2 support this claimby showing higher levels of damage per capita and damage per income in rural areas in terms of
population density. Therefore, we expect that there could be a clear difference in the cost-benefit
ratios over population density. We determine whether we can expect more damage in areas withlower population density by applying a nonparametric data envelopment analysis (DEA).
DEA is an effective data analysis tool because it does not require a specific function
form and allows us to easily view the DEA scores. In this paper, we consider simple
input-output combinations in which more labor, public mitigation stocks and other social
infrastructure stocks are the inputs for producing income as a positive output and reducing
disaster as an undesirable output. Chen et al. (2011) and Barros et al. (2011) developed andprovided an application that measures overall and undesirable output (disaster) scores. The
technical inefficiency score is an indicator between 0 and 1 that indicates the extent to which
prefectures suffer damage as a result of natural disasters. Therefore, smaller scores indicate
23.0025
.002
.0015
.001
.0005
0

Total Damage Per Capita (unit:million dollar)

Figure A1. Total Disaster Damage Per Capita by Prefecture from 1975 to 2007

0

2000

4000

6000

Population Density (unit:person per square kilometer)

Obs.=1503. The values of total disaster damage per capita in 1995 in the Hyogo prefecture and in 1983 in the
Shimane prefecture are 0.0170 and 0.0047, respectively.

15
10
5
0

Total Damage Per Income (unit:percent)20

Figure A2. Total Disaster Damage Per Income by Prefecture from 1975 to 2007

0

2000

4000

6000

Population Density (unit:person per square kilometer)

Obs.=1503. The values of total disaster damage per income in 1995 in the Hyogo prefecture and in 1983 in the
Shimane prefecture are 73.4 and 38.3, respectively.

24with linear fitting curves. These results show that lower population density areas are associatedlower levels of natural disaster damage. Figure A3 provides the technical inefficiency resultswith high technical inefficiency scores; thus, rural prefectures suffer more disaster damage per
input. Therefore, we intend to consider the differences of cost-benefit ratios by various
population density ranges.
Figure A3. Nonparametric Results (left: constant return to scale, right: variable
return to scale)
Constant Return to Scale

0

0

.2

.2

.4

.4

.6

.6

.8

.8

1

1

Variable Return to Scale

0

2000

4000

6000

0

2000

pop_aallMunicipalities

4000

6000

pop_aallFitting Curve

Municipalities

Fitting Curve

Note: Obs.=1503. The vertical axis is the technical inefficiency score for disasters based on the DEA.

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The Society of Regional Policy, Takasaki City University of Economics
1300, Kaminamie-machi, Takasaki-city, Gunma 370-0801 Japan+81-27-344-6244
c-gakkai@tcue.ac.jp
http://www1.tcue.ac.jp/home1/c-gakkai/dp/dp12-03
28