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A quick method for assessing economic damage caused by natural disasters: an epidemiological approach.

Abstract In the aftermath of any natural disaster, a quick assessment of economic damage is called for, without which recovery planning and fiscal budgeting is impossible. What is customarily done as damage accounting is to use some aggregation by parts method, which is predisposed to commit double counting, omission, and bureaucratic inconsistencies. As an alternative, we propose to work with a social epidemiological model. First, we present a result by means of a log linear model which shows evidence of hazard factors and vulnerability factors at work. We then simplify the model by deleting the variables that are not significant in a linear formulation. Lastly, we give our estimate of economic damage for the case of the North East Japan Earthquake and Tsunami of March 11, 2011 and alert that the true damage may well be the double of government's estimate.

Keywords Direct economic damage * Natural disaster * Epidemiological model

JEL 3 * 15 * 29 * 31


Japan is a natural disaster prone country. Figure 1 compares the top 10 countries in terms of the occurrences of natural disaster per 100,000 square kilometers of land territory for the period 1990-2010. Japan ranks number two after the Philippines. Among the high income countries, however, Japan stands at the top by the same metric.


In any occurrence of a natural disaster, it is imperative, as well as academically challenging, to assess the value of economic damage involved. From a practical point of view, assessment needs to be done in the midst of an on-going emergency, where time is the most scarce resource of all. In retrospect, it must be conducted in order to search for possible policy measures for future mitigation.

However, as Cochrane (2004, pp.290-291) says in relation to the 9/11 incident in New York, 2001, "Loss accounting, as currently practiced, is problematic for several reasons." He goes on to say that" ... most problems stem from double counting, failure to identify clearly an accounting stance, ignoring non-market losses, confusion as to whether post-disaster economic trends are a product of the event or some other unrelated factor, and the employment of too limited a time frame."

Thus, the purpose of this paper is to present a simple epidemiological model for assessing economic damage, which is applicable to any event or natural disaster. The method comprises an alternative to the common accounting practice of aggregation by parts.

In the next section, we will explain what is commonly done in Japan regarding the economic damage measurement. In the section following that, we will present a social epidemiological model of hazard and vulnerability leading to economic damage. We will then examine the data availability and select variables to be used for estimation. Finally, we will present the fixed effect estimation result.

In the section after that, we will propose yet another model of a simple equation, which is convenient for a quick estimation. By applying this method to calculate the damage of the North East Japan earthquakes and tsunami of March 11, 2011 (the Tohoku earthquake), we conclude that the true direct economic damage may well be the double of government's estimation.

Measurement of Post-Disaster Economic Damage: The Common Practice

The Fire and Disaster Management Agency (FDMA) of the Japanese government has been compiling statistics regarding natural disasters based on reports filed by 47 prefectures. (1) The FDMA classification of disaster damage is shown in Table 1. All types of damage are reported in physical units except economic damage.
Table 1 FDMA classification of Natural disasters damage

Damage           Type of damage                      Unit

Human damage     dead                                person

                 missing                             person

                 injured               seriously     person

                                       injured       person

                 affected population   affected      household

                                       affected      person

Building damage  housing damage        totally       building

                                       half          building

                                       partially     building

                                       inundated     building
                                       above floor

                                       inundated     building
                                       below floor-

                 non-housing           public        building

                                       other         building

Others           rice field destroyed                ha

                 rice field flooded                  ha

                 fruit and vegetable                 ha
                 patch destroyed

                 fruit and vegetable                 ha
                 patch flooded

Public           public                school        campus
infrastructure   infrastructure

                                       bridge        bridge

                                       river         site

                                       landslide     site

Transportation   railway blocked                     site

                 ship                                ship

Economic damage                                      thousand

Data is compiled on a yearly basis, and it covers the period 1995-2007. Hence, we have a cross section of 47 prefectures and 24 types of damage each year, and the data runs over 13 years now, which is enough to configure a panel data.

However, there is a critical flaw in the economic damage data. (2) In order to calculate this number, FDMA adds up numbers compiled by prefectures. Prefectures are interested only in damage inflicted on infrastructure, public buildings, and agriculture and fishery facilities, (3) and they report just that. Hence, the government data on economic damage excludes damage done to an important segment of the economy: the private sector. This is a serious omission, since disasters that hit urban areas bring about more damage to residential houses, condominiums, commercial buildings, and office buildings than to public infrastnicture. (4) This means that we must augment the FDMA data to cover all direct economic damage prior to our analysis.

An Epidemiological Analysis of Economic Damage

Conceptual Framework

We start from a conceptual framework: economic damage is a product of hazard and the community's vulnerability factors. (5) Measurement of the magnitude of hazard is usually done in terms of some physical unit. For example, a number in Richter magnitude scale is commonly used to represent the energy released in the case of earthquakes. In case of meteorological disasters, precipitation, or wind velocity, the Saffir-Simpson category scale is used.

However, when dealing with all natural disasters as we are doing here, we need to find some social index that represents the scale and frequency of disasters that hit the area in a year. This is an empirical question to which we will try to give our answer in the next section.

Regarding the vulnerability factors, we note Weichselgartner (2001, p.89) who indicated that the concept of vulnerability includes pre-existing characteristics of the community, such as preparedness and prevention, and the post-disaster response and recoverability. Again, we will give our empirical answer to the question: what are the proper indices for preparedness, prevention, and response?

Epidemiological Model and Data

We employ the following epidemiological model:

ln([]) = [[alpha].sub.0] + [[alpha].sub.1] ln([]) + [[alpha].sub.2] ln([])+ [[alpha].sub.3]ln([]) + [[beta].sub.1] ln(Under []) + [[beta].sub.2] ln([])+ [[beta].sub.3] ln([]) + [[beta].sub.4]1n([]) + [[beta].sub.5] ln([]) + [[beta].sub.6] ln([]) + [[beta].sub.7] ln([]) + [u.sub.i] + [[theta].sub.t] + [[epsilon]],

where In stands for the natural logarithm, [theta], is a time fixed effect for year t (t=19952007), [u.sub.i] is a fixed effect for prefecture i (1=1,2,...,47) and [[epsilon]] the error tem. We will apply this model to the fixed effect estimation by panel data consisting of 47 prefectures and 13 years.

All variables are scaled to the size of prefectures as is summarized in Table 2. Edamage, for example, is the direct economic damage caused by natural disasters divided by the gross regional product of the prefecture involved. As noted above, the FDMA numbers for economic damage do not include damages done to the private sector. We, therefore, augment the FDMA figures by adding the economic damage of buildings caused by natural disasters taken from the Building Destruction Statistics compiled by the Ministry of Land, Infrastructure, Transport and Tourism.
Table 2 Variables and statistics

Factors        Index           Variables  Description

Dependent      damage          Edamagc    direct damage/gross
variable                                  regional product

Hazard         magnitude of    Dead       number of dead or
               major disaster             missing

               magnitude of    Hdamage    number of houses
               minor disaster             partially
                                          number of housing
                                          units in

               frequency of    HQ         number of times
               disasters                  disaster head
                                          quarters are set
                                          up/number of cities

                                          and townships
Vulnerability  preparedness    Stocks     sum of social and
                                          private stocks per

               prevention      Under 15   number of people
                                          under 15 years of

               response        Recovery   5 year average of
                                          ratios of recovery
                                          expenditures to
                                          total public
                                          investments in

Another amendment we made to the FDMA data concerned the Niigata prefecture in 2004 and 2007. In these years, Niigata was hit by middle-sized earthquakes. However, we found that economic damages from the earthquakes are not reflected in the FDMA numbers. We added the publicly known damage numbers to the statistics.

Hazard and Vulnerability Variables

As for the data for hazard factor, we chose to use: 1) the number of dead or missing persons per prefectural populations (Dead); 2) the ratio of partially destroyed houses to the total number of housing units in prefecture (Hdamage); and 3) the number of times local emergency headquarters are set up divided by the number of cities and townships in the prefecture (HQ).

Clearly, the variable Dead represents the extent to which disasters are deadly. The Hdamage variable is to complement Dead in measuring the magnitude and frequency of less severe disasters. The ratios of buildings totally destroyed or half destroyed have a strong correlation with the Dead variable. This indicates that when a disaster kills people, the disaster also brings about building devastation. (6)

Each time a sizeable disaster hits a locality, its government is mandated to set up a local emergency headquarter. Hence, the number of such headquarters indicates how many significant disasters hit the prefecture in a year.

We also decided to use three variables as indices of vulnerability: I) the sum of social and private capital stocks per capita compiled by the Cabinet Office (Stocks), 2) the ratio of population 15 years old and under in the total local population (Under15), and 3) the ratio of post disaster recovery expenditures to the total public investments in the prefecture (Recovety).

The variable Stocks is used as a preparedness variable, since it is expected that the local community in which capital stocks are heavily accumulated is relatively well prepared for disaster, and inversely, perceived infrequency of disaster may be the reason for such accumulation.

The prevention factor is reflected in the variable Under15 which is an indication that the community is inhabited by younger families. It is known that communities with relatively young population are resilient against natural disasters. Researches point to several factors for this observation. It is easier for younger generations to take quick actions in the wake of disaster than older generations. Moreover, community events like religious festivals and school events of sports and culture promoted by younger families solidify local social capital, which contributes to sharing information, emergency supplies, and shelters in emergency.

The variable Recovery corresponds to response. Toya (2009) has shown that the post-disaster public investment made in the previous year contributes to reducing disaster damage in the current year. Thus, the volume of expenditures which local government invested in the post-disaster recovery program in the past is expected to reduce economic damage in the current year.

We must hasten to add, however, that we have tried other variables as candidates for the prevention variable. Data is available for gross prefectural product, population 65 year and over, savings per household, unemployment rate, the ratio of flood and forest control investments in the total local public expenditures, and population density. However, none of these variables showed statistical significance in our estimate.

We also rejected the ratio of houses constructed before 1981, when the building code was strengthened against disaster risks, because our estimate suggested the existence of of unit root problem. (7)

Estimation Result

The result of our epidemiological estimation is summarized in Table 3. The three hazard variables, Dead, Hdamage, and HQ, are all statistically significant at the 1 % level. The result shows clearly that heavier economic damage is brought about when there are more human casualties, more house destructions, and more emergency headquarter setups. We may take it that these three variables are fair indices for the hazard factor.
Table 3 Fixed effect estimation

Dependent variable:

R-sq: within             0.495        prefecture   47

Between                  0.234              year   13

Overall                  0.002           sample:  611

Hazard                    Dead         0.107 ***

                       Hdamage         0.170 ***

                            HQ         0.126 ***

Vulnerability         Under 15        -9.731 ***

                        Stocks          -6.543 *

                      Recovery    L1    -0.164 *

                                  L2       0.081

                                  L3      -0.183

                                  L4       0.101

                                  L5  -0.285 ***

Year                            1995     dropped

                                1996   -0.583 **

                                1997      -0.430

                                1998      -0.140

                                1999       0.389

                                2000      -0.489

                                2001       0.890

                                2002      -0.789

                                2003      -0.824

                                2004      -0.424

                                2005      -1.426

                                2006      -1.004

                                2007      -1.081

Cons                                       0.341

Significance level:
***:1 %, **:5 %, *

                         cocf.              Prob

F-test                    9.87             0.000

Hausman                  245.5             0.000

BP-LM                     83.5             0.000

Hcttcst                   3387             0.000

Serial                   0.014             0.905

Among the vulnerability variables, Under 15 shows the same significance level as hazard variables and its effect is negative on economic damage. Stocks is significant at the 10 % level, and it contributes to the mitigation of economic damage. The Recovery variables show an intriguing pattern of influence; recovery expenditures of 1 and 5 year vintage work negatively on economic damage.

Also, some tests results are shown in Table 3. Our F test, Hausman test, and Breush Pagan Lagrange multiplier (LM) test support the fixed effect model. Since heteroskedasticity is suspected by Wald test, this estimation is conducted by hetero-skedasticity consistent estimation by White. As for possible serial correlation, we performed the Lagrange multiplier (LM) test, which rejected the existence of First order Autoregressive Process, AR(1), serial correlation.

Some Discussion

Our results support the basic hypothesis that economic damage caused by natural disaster can be explained by the magnitude and frequency of hazard occurrences and social vulnerability factors. We found that the proportion of the population under 15 years, the existence of per capita public and private capital stocks, and the level of past post-disaster recovery expenditures all contribute positively to the reduction of vulnerability.

In particular, the elasticity of damage reduction with respect to the young generation ratio and per capita private and public capital stocks are noteworthy: a 1 % increase in the young generation ratio will lead to a reduction of damage per gross regional product by 9.7 %, and a 1 % increase in the per capita stocks reduces the damage by 6.5 %.

It is commonly believed that a reinforcement of social infrastructure, an installation of a stricter building code, and a stronger system of command and control in an emergency are effective measures for damage reduction from the engineering perspective. However, our results show that attracting a young population, promoting economic growth, and accumulating private, as well as public capital stocks, should also be a crucial strategy for disaster mitigation. Post-disaster recovery efforts in previous years work also to reduce economic damage in the current year.

A Damage Estimation for the Tohoku Earthquake

Choice of Variables

Finally, we would like to present our estimation of economic damage caused by the earthquake and tsunami which hit the Tohoku region on March 11, 2011. We notice first that the model in the previous section is not convenient for a forecasting purpose, since the result is too sensitive to a small perturbation in the estimated coefficients of log variables. (8)

Thus, we tested a model without log transformation. We found that some of the variables whose statistical significance was verified in the log linear model lost their significance. HQ and Stocks and Recovery and year dummies turned out to be not statistically significant at the 10 % confidence level. We are thus led to a model consisting only of hazard variables and fixed effect of prefectures. This model is useful in on-going emergency situations, because it only requires the basic and minimum amount of information about variables whose values are publicized on a daily basis in many cases.

The result is shown in Table 4. In order to adjust for the effect of prefecture dummies, we did an Least Square Dummy Variable (LSDV) estimate. In Table 4, only the coefficients of dummies for the affected prefectures are shown.
Table 4 LSDV estimation


LSDV estimation

R-sq             0.7977      prefecture   47

                                   year   13

                                sample:  611

Hazard           Dead        298468.600

                 H damage   1360.474 **


                 Hokkaido         0.910

                 Aomori        2.853 **

                 Iwatc          5049 **

                 Miyagi       (dropped)

                 Yamagata         1.603

                 Fukushima      2.027 *

                 ibaragi          0.010

                 Tochigi          1.703

                 Gunma            0.915

                 Chiba            0.009

                 Tokyo            0.103

cons             Kanagawa        -0.041

significance level: ***:1%, **:5%, * 10%

Estimated Economic Damage

We then performed out-of-sample predictions. We applied the result above to the current Tohoku disaster. Data for the Dead variable was taken from the Police Agency's daily report as of September 9, 2011 and divided by the prefecture population in 2009. The Hdamage data was also taken from the Policy Agency's daily report and divided by the number of housing units in prefectures reported in the House and Land Survey 2008.

Substituting these values to the variables in the estimated equation in Table 4, we obtained the economic damage as a ratio to gross prefectural product. Finally, we multiplied the number by gross prefectural product 2007 to obtain our estimate of economic damage for each affected prefecture. Table 5 summarizes the fatalities and housing destructions for 12 prefectures and estimated total economic damage for the affected prefectures.
Table 5 Estimated damage for Tohoku

Prefecture   Dead or missing   Buildings partially    Estimated damage
             (persons)         destroyed (buildings)  (million yen)

Hokkaido                   1                       7             1,134

Aomori                     4                     107            18,805

lwatc                  6,348                   6,974         7,409,008

Miyagi                11,640                 149,856        14,482,443

Yamagata                   2                       0             2,328

Fukushima              1,844                 134,905         4,311,176

Tokyo                      7                     257            13,016

lbaraki                   25                 154,839         2,094,745

Tochigi                    4                  62,803           939,688

Gunma                      1                  16,150           202,756

Chiba                     22                  30,099           326,387

Kanagawa                   4                     279             6,844

Total                 19,902                 556,276        29,808,330

As of September 6, 2011

Concluding Remarks

Many organizations and research groups rushed to give their estimates of economic damage after 3/11. The Cabinet Office said their latest estimate came down to 16.9 trillion yen from 25 trillion yen, including damage on buildings, lifeline facilities, social infrastructure and agriculture, and forestry and fishery facilities.9 However, how they came up with this number is in the black box.

Inada et al. (2011, pp.1-9) estimated the direct damage done to housing units, social infrastructure, plant and equipment, automobiles, and ships and inventory at 17.8 trillion yen, and the indirect loss on Japan's GDP at 6 trillion yen. They applied the same damage rate to all kinds of stocks in the affected regions as a convention.

The Development Bank of Japan (2011) published yet another estimate. They estimated damage in the seaboard and inland areas separately and came up with the direct damage at 16 trillion yen for the four heaviest damaged prefectures combined. Hayashida et. al. (2011, pp.1-25) noted that almost all preceding estimates on direct damage fall in the range of 14 to 18 trillion yen and presented simulations as to the future course of regional economies.

However, when it comes to assessment of direct damage, all studies utilized one form of aggregation by parts or other. There has been no effort made so far to employ epidemiological models as we reported above. Furthermore, our estimate lies on the higher end of the scenarios these estimates draw. This result alone suggests the need for further studies that should lead to a widely accepted method of estimation.

After all, what is more pertinent is not who wins in the guessing game, but to learn what factors, natural and social, give rise to economic damage of the magnitude that comes to 6 % of GDP. A disaster-prone country must be equipped with as quick a method of disaster damage assessment as a preparedness measure for post-disaster reconstruction. We hope our research has made a modest contribution.

Acknowledgment This work was supported by 2011 Research Grant from Kampo Financial Group.


Cabinet Office (2011). Press release on damage estimate of the Great East Japan Earthquake (in Japanese), June 24. (

Cavallo, E., Powell, A., & Becera, 0. (2010). Estimating the direct economic damage of the earthquake in Haiti. Economic Journal, 120(546), F298-F312.

Cochrane, H. (2004). Economic loss: myth and measurement. Disaster Prevention and Management, 1.3(4), 290-296.

Development Bank of Japan (2011). Assessment of economic damage on private and public stocks caused by the Tohoku Earthquake (in Japanese), News Release, April 28.

Hayashida, H., Hamagata, S., Nakano, K., Hitomi, K., & Hoshino, Y. (2011). Macroeconomic impacts of the Tohoku earthquake: an assessment by means of the CRIEPI macrocconometric model (in Japanese). Discussion Paper 11024, Socio-Economic Research Center, Central Research Institute of Electric Power Industry, 1-25.

Inada, Y., Irie, Y., Shima, A., &. Toizumi, T. (2011). The Tohoku earthquake's impacts on the Japanese macrocconomy (in Japanese), KISER Report No.6, April 12,1-9.

Toya, H. (2009). The mitigation effect on disaster damage by preventive policy measures: a panel analysis based on prefectural data (in Japanese). In Report on a system of anti-disaster policies with economics perspective, Cabinet Office, No.44, June, 67-89.

United Nations Development Programme (2004). Reducing disaster risk: a challenge for development. i-xii+ 146.

Weichselgartner, J. (2001). Disaster migigation: the concept of vulnerability revisited. Disaster Prevention and Management, 10(4), 85-94.

(1.) Prefectures are subnational jurisdictions governed by publicly elected governors, which are comparable to the states in the United States.

(2.) It docs not include the indirect damage of lost business and employment opportunities either, which are outside the scope of our investigation here.

(3.) The reason for their bias can be found in two laws; "Law of National Government Finance on the Disaster Recovery of Public Facilities" and "Disaster Recovery Expenditures on Agriculture, Forestry, and Fishery Facilities." In order to obtain national government funding, local governments, including prefectures, need to present damage estimates of the relevant facilities as soon as possible.

(4.) In case of the Kobe earthquake of 1995, the private sector damage came to 60% of the total damage.

(5.) This formulation or its variations are frequently used in the United Nations publications. See, for example, UNDP (2004, p.100).

(6.) The Fukushima nuclear power plant accidents pose a serious problem, for there is no reported casualty among the inhabitants and no physical destruction in the vicinity, yet the inconvenience and economic losses incurred by the dislocated people are enormous.

(7.) Houses that were built before 1981 were subject to a more lenient building code than afterwards.

(8.) Cavallo et al. (2010) also focused on the relationship between the human damage and the direct economic damage in disasters. They used a log linear model to predict the direct economic damage of the earthquake in Haiti. However, they came up with a wide range for prediction, which is, basically, an unavoidable consequence of log linear models.

(9.) Cabinet Office (2011).

An earlier version of the paper was presented at the 72nd International Atlantic Economic Conference in Washington D.C. The author wishes to thank the chair of the session and other participants for helpful discussions.

Int Adv Econ Res (2012) 18:417-427

Published online: 13 July 2012

[c] International Atlantic Economic Society 2012

M. Hayashi ([??])

Asia Pacific Institute of Research, Osaka, Japan


DOI 10.1007/s1 1294-012-9367-y
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Author:Hayashi, Mampei
Publication:International Advances in Economic Research
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Date:Nov 1, 2012
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