metadata: authors: 0: author: Hallegatte,Stephane
count: World
docna: 0: docna: The indirect cost of natural disasters and
            an economic definition of macroeconomic resilience
docty: Policy Research Working Paper
subtopic: Urban Housing and Land Settlements,Urban Governance and Management,Urban Housing,Hydrology,Municipal Management and Reform,Natural Disasters
teratopic: Macroeconomics and Economic Growth
abstracts: cdata!: The welfare impact of a disaster does
            not depend only on the physical characteristics of the event
            or its direct impacts in terms of lost lives and assets.
            Depending on the ability of the economy to cope, recover,
            and reconstruct, the reconstruction will be more or less
            difficult, and the welfare effects smaller or larger. This
            ability, which can be referred to as the macroeconomic
            resilience of the economy to natural disasters, is an
            important parameter to estimate the overall vulnerability of
            a population. Here, resilience is decomposed into two
            components: instantaneous resilience, which is the ability
            to limit the magnitude of the immediate loss of income for a
            given amount of capital losses, and dynamic resilience,
            which is the ability to reconstruct and recover quickly. The
            paper proposes a rule of thumb to estimate macroeconomic
            resilience, based on the interest rate (a higher interest
            rate decreases resilience and increases welfare losses), the
            reconstruction duration (a longer reconstruction duration
            increases welfare losses), and a “ripple-effect” factor that
            increases or decreases immediate losses (negative if enough
            idle resources are available to cope; positive if
            cross-sector and supply-chain issues impair the production
            of non-affected capital). An optimal risk management
            strategy is very likely to include measures to reduce direct
            impacts (disaster risk reduction actions) and measures to
            reduce indirect impacts (resilience building actions).
repnme: repnme: The indirect cost of natural disasters and
            an economic definition of macroeconomic resilience
display_title: The indirect cost of natural
            disasters and an economic definition of macroeconomic resilience
listing_relative_url: /research/2015/07/24744802/indirect-cost-natural-disasters-economic-definition-macroeconomic-resilience
topicv3: Water m1326522 137,Land and Housing m1327648 817,Earthquake m1503308 3154,Hurricane m1503314 3179,Flood m1503315 3216
publishtoextweb_dt: 2015-07-02T00:00:00Z
historic_topic: Macroeconomics and Economic Growth
no_of_pages: 40
author_keys: 0: author_key: 1103816
model_extractions: WPS7357 Policy Research Working Paper 7357 The Indirect Cost of Natural Disasters and an Economic Definition of Macroeconomic Resilience _Stephane Hallegatte_ Finance and Markets Global Practice Group & Global Facility for Disaster Reduction and Recovery July 2015
Policy Research Working Paper 7357

# **Abstract**

The welfare impact of a disaster does not depend only on the physical characteristics of the event or its direct impacts in terms of lost lives and assets. Depending on the ability of the economy to cope, recover, and reconstruct, the reconstruction will be more or less difficult, and the welfare effects smaller or larger. This ability, which can be referred to as the macroeconomic resilience of the economy to natural disasters, is an important parameter to estimate the overall vulnerability of a population. Here, resilience is decomposed into two components: instantaneous resilience, which is the ability to limit the magnitude of the immediate loss of income for a given amount of capital losses, and dynamic resilience, which is the ability to reconstruct and recover quickly. The paper proposes a rule of thumb to estimate macroeconomic resilience, based on the interest rate (a higher interest rate decreases resilience and increases welfare losses), the reconstruction duration (a longer reconstruction duration increases welfare losses), and a “ripple-effect” factor that increases or decreases immediate losses (negative if enough idle resources are available to cope; positive if cross-sector and supply-chain issues impair the production of non-affected capital). An optimal risk management strategy is very likely to include measures to reduce direct impacts (disaster risk reduction actions) and measures to reduce indirect impacts (resilience building actions).

This paper is a product of the Disaster Risk Financing and Insurance Program (DRFIP), a partnership of the World Bank’s Finance and Markets Global Practice Group and the Global Facility for Disaster Reduction and Recovery, with funding from the UK Department For International Development. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at shallegatte@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **The Indirect Cost of Natural Disasters and an Economic Definition of Macroeconomic Resilience**<sup>**12**</sup>

## Stephane Hallegatte

The World Bank Climate Change Group – Office of the Chief Economist <u>shallegatte@worldbank.org</u>

**Keywords:** natural disaster, resilience, economic losses, welfare **JEL:** D60, E22, Q54

1 This article benefited from inputs from Valentin Przyluski and from comments and suggestions from Mook Bangalore, Paolo Bazzurro, David Bevan, Laura Bonzanigo, Sebastian Boreux, Daniel Clarke, Sebastian von Dahlen, Patrice Dumas, Marianne Fay, Ulf Narloch, Ilan Noy. James Orr, Richard Poulter, Adam Rose, Rae Rosen, Julie Rozenberg, Tse‐Ling The, Adrien Vogt‐Schilb, and the participants to the conference “Managing the Risk of Catastrophes—Protecting Critical Infrastructure in Urban Areas,” organized by the Federal Reserve Bank of New York. It has been developed as a background paper for the “Sovereign DRFI impact appraisal project”, funded by UKaid, The World Bank, the Disaster Risk Financing and Insurance Program, and the Global Facility for Disaster Reduction and Recovery (GFDRR). This analysis serves as a basis for a companion piece that includes a discussion of micro‐level resilience (Hallegatte, 2014).

2 This research has been completed as part of a series of papers developed under the Sovereign Disaster Risk Financing and Insurance Impact Appraisal project. The project is led by the World Bank Disaster Risk Financing and Insurance Program and funded through a cooperation between the UK Department for International Development (DFID) and the Global Facility for Disaster Reduction and Recovery (GFDRR).
# **1 Introduction**

From an economic perspective, a natural disaster can be defined as a natural event that causes a perturbation to the functioning of the economic system, with a significant negative impact on assets, production factors, output, employment, or consumption. There are multiple formal definitions. The Center for Research on the Epidemiology of Disasters (CRED) at the Catholic University of Louvain defines a disaster as a natural situation or event which overwhelms local capacity and/or necessitates a request for external assistance.<sup>3</sup> When it happens, however, the perturbation affects the economic system in a way that goes beyond the loss of assets and the monetary expenditures to replace damaged property. Additional consequences include the loss of output and production, rationing in some sectors, loss of employment and tax revenues, etc.

Even though the most immediate consequences of natural disasters are obviously the fatalities and casualties they cause, the economic consequences need to be accounted for to assess the disaster impact on the population’s well‐being and welfare.

This paper discusses the economic consequences of natural disasters. It summarizes the most important mechanisms that determine the cost of disaster, and explains why the direct economic cost, i.e. the value of what has been damaged or destroyed by the disaster, is not a sufficient indicator of disaster seriousness and why estimating indirect losses is crucial. Then, it discusses the methodologies and the models that are able to measure indirect losses and proposes a simple rule of thumb to take them into account when time and resources do not allow for a full modeling exercise. Finally, the paper discusses the tools that are available to increase the resilience of the economic system, i.e. to make it better able to recover and reconstruct and to reduce the indirect consequences of disasters.

Throughout this paper, boxes will present an application of the methodologies on one case study conducted in an OECD project, on flood risk in Mumbai.<sup>4</sup> The study investigates the vulnerability to heavy precipitations of the city of Mumbai, a rapidly‐growing coastal city in a developing country. The complete study is available in (Ranger et al., 2011), and a longer version with a survey of the slum dwellers affected during the 2005 floods in Mumbai is in (Hallegatte et al., 2010).

# **2 The economic cost of a disaster**

## **2.1 Defining the economic cost of extreme events**

Defining the economic cost of a disaster poses different theoretical and practical challenges. After each large‐scale disaster, media, insurance companies and international institutions publish numerous assessments of the “cost of the disaster.” These various assessments are based on different

> 3 For a disaster to be listed in the EM‐DAT database, at least one of the following criteria should be met: (i) 10 or more people are reported killed; (ii) 100 people are reported affected; (iii) a state of emergency is declared; (iv) a call for international assistance is issued.

> 4 The study was carried out by a consortium including the OECD, Risk Management Solutions, CIRED, Météo‐France, NATCOM PMC, and the Indian Institute for Technology Bombay at Mumbai, and published in Ranger et al. (2011).

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methodologies and approaches, and they often reach quite different results. In the US, for instance, a systematic analysis by (Downton and Pielke, 2005) showed that loss estimates differ by a factor of 2 or more for half of the floods that cause less than $50 million in damages. These discrepancies are in part due to technical and practical problems, but also to the multi‐dimensionality in disaster impacts and their large redistributive effects and the fact that the boundary of assessment dependent on the purpose of the assessment.<sup>5</sup> But the purpose of these assessments is rarely specified, even though different purposes correspond to different perimeters of analysis and different definitions of what a cost is.

This confusion translates into the multiplicity of words to characterize the cost of a disaster in published assessments: direct losses, asset losses, indirect losses, output losses, intangible losses, market and non‐ market losses, welfare losses, or some combination of those. It also makes it almost impossible to compare or aggregate published estimates that are based on many different assumptions and methods.

# **2.1.1 Direct and indirect costs**

Many authors have discussed typologies of disaster impacts (e.g., Cochrane, 2004; Lindell and Prater, 2003; Pelling et al., 2002; Rose, 2004). These typologies usually distinguish between direct and indirect losses. Direct losses are the immediate consequences of the disaster physical phenomenon: the consequence of high winds, of water inundation, or of ground shaking. Typical examples include roofs that are destroyed by high winds, cars destroyed and roads washed away by floods, and injuries and fatalities from collapsed buildings. Direct losses are often classified into direct market losses (for goods that can be bought on a market, such as cars and buildings) and direct non‐market losses (for what cannot be bought on a market, like human lives and ecosystems). Indirect losses (also labelled “higher‐order losses” in Rose, 2004) include all losses that are not provoked by the disaster itself, but by its consequences; they span over a longer period of time than the event, and they affect a larger spatial scale or different economic sectors. They include some additional losses to assets (e.g., when an earthquake causes a fire or a toxic spill that damages assets) and effects on flows (e.g., through macroeconomic effects).

Here, instead of the direct/indirect typology, we use an alternative (and complementary) terminology. Like in (NRC, 2013, 2011; Rose et al., 2007b), we distinguish between _asset losses_ (i.e., the _stock_ of assets that is reduced), and _output losses_ (i.e., a reduction in an income _flow_ ). Output losses include different categories that often overlap:

- _Business interruptions_ (the interruption in production during the event);

- _Production losses directly due to asset losses_ (because damaged or destroyed assets cannot produce, during a period that is much longer than the event itself);

- _Supply‐chain disruptions_ (when lack of input or reduced demand is responsible for a reduction in production from a production site that is not directly affected);

> 5 For instance, an analysis can be carried out at national scale to estimate the impact on macroeconomic aggregates (e.g., GDP, tax revenues) and at local scale to estimate local welfare losses and the need for support. The latter will not include potential benefits outside the affected areas; the former will include them.

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- _Macro‐economic feedbacks_ (e.g., the impact of reduced final demand because consumers and businesses suffer from a reduced income, and the effect of lost tax revenue on public demand);

- _Long‐term adverse consequences on economic growth_ (e.g., due to changes in risk perception (including over‐reactions) that can drive investors and entrepreneurs out of the affected area);

- _Increased production from the “reconstruction boom”_ that acts as a stimulus for the economy.

Note that these output losses include household production, not only production by the productive and commercial sectors. For instance, the reduction in housing service (a service produced by houses and dwellings) is considered as an output loss, as are all services from other household assets (e.g., appliances).

_The impact on poverty or inequalities_ is also sometimes included in the indirect losses. The landfall of Katrina on New Orleans has renewed attention on the larger weather vulnerability of the poorest communities within a country, and on the inequality‐widening effect of disasters (Atkins and Moy, 2005; Tierney, 2006). Rodriguez‐Oreggia et al. (2009) show that municipalities affected by disasters in Mexico see an increase in poverty by 1.5 to 3.6 percentage points. Often, the poorest have little to lose in a disaster and the impact on their welfare is therefore invisible in aggregated economic statistics. If the aim of the assessment is to look at welfare impacts, focusing only on economic aggregates can be misleading.

Some of these impacts can be captured using classical economic indicators, such as Gross Domestic Product (GDP). There are however several issues when using GDP change as an indicator for output losses. A first question deals with the spatial scale: for large countries, the scale of the event and the scale of GDP measurement are very different, and a large shock for local populations can hardly be visible on national GDP. It does not mean, however, that welfare impacts are negligible. Second, GDP does not include non‐ market production and household production and therefore cannot capture a significant share of output losses. With a broader definition of output, it is possible to include at least some non‐market and non‐ commercial impacts. Third, GDP is known to be a poor proxy for welfare because it does not capture wealth (e.g., stocks of assets) and does not account for inequality and distributional effects (Fleurbaey, 2009).

# **2.1.2 Assessing indirect losses: Defining a baseline**

A first difficulty in disaster indirect cost assessment lies in the definition of the baseline scenario. The cost of the disaster has indeed to be calculated by comparing the actual trajectory (with disaster impacts) with a counterfactual baseline trajectory (i.e., a scenario of what would have occurred in the absence of disaster). This baseline is not easy to define, and several baselines are often possible. Moreover, in cases where recovery and reconstruction do not lead to a return to the baseline scenario, there are permanent (positive or negative) disaster effects that are difficult to compare with a non‐disaster scenario.

For instance, a disaster can lead to a permanent extinction of vulnerable economic activities in a region, because these activities are already threatened and cannot recover, or because they can move to less risky locations. In that case, the disaster is not a temporary event, but a permanent negative shock for a region. Also, reconstruction can be used to develop new economic sectors, with larger productivity, and lead to a final situation that can be considered more desirable than the baseline scenario. This improvement can be seen as a benefit of the disaster. It is however difficult to attribute unambiguously 4
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vulnerability curves), these damage ratios are estimates at 5–15% for residential properties, 15–35% for commercial properties, and 10–30% for industrial properties. In the absence of data on infrastructure, a constant ratio of infrastructure to non‐infrastructure losses is introduced. Based on previous events in various world cities, this ratio is taken at 40% (i.e., where there is $1 of non‐infrastructure losses, there is $0.40 of infrastructure losses).

From this, the analysis can then provide an estimate of the direct economic losses that corresponds to various probability of occurrence, expressed in terms of return periods. For instance, the losses due to the 50‐yr return period flood are estimated between $210 and $570 million.

To complete this analysis with information on how these losses are distributed in the population and especially on the poorest, a survey was conducted with informal dwellers affected by the 2005 floods. It was found that the aggregated losses they suffered from are about $250 million (for total losses due to the 2005 flood of about $2 billion), but the relative impact on their savings and consumption was extremely large, with average capital losses of the same order of magnitude than their average total savings (in other terms, their savings were totally wiped out by the event).

For instance, hurricanes in 1806 and 1807 participated in the shift that occurred at la Réunion – a French island in the Indian Ocean – from coffee to sugar cane production. Indeed, it takes about 5 years for a coffee plant to start producing usable fruits. When the hurricanes hit, the need to start producing again as soon as possible drove farmers to plant sugar cane, an annual crop that can be harvested in a year. Moreover, coffee production was then considered more vulnerable to wind damages than sugar cane. But sugar cane production also has a different economic vulnerability to other stresses such as changes in food markets, consumer tastes, and agricultural subsidies. Therefore, it is difficult to assess whether the shift from coffee to sugar cane should be considered as a cost of the hurricanes (if sugar cane eventually reveals less profitable than coffee) or as a benefit (if sugar cane is more profitable than coffee). The final outcome depends on many other factors that can hardly be predicted at the time of the disaster.

This baseline issue – very common in economics – is not easy to deal with, and different scholars have used different techniques. (Coffman and Noy, 2011) use two nearby islands to assess the impact of hurricane Iniki. Since the hurricane affected only one island, the other can be used as a “control”, i.e. as a proxy for the economic condition of the affected island if it had been spared. But such convenient control is not always available, making it necessary to construct the counterfactual, for instance using modelling tools (DuPont and Noy, 2012).

# **2.2 Output losses and their drivers**

Damages to assets make them unable to produce: a damaged factory cannot build cars, a damaged road cannot be used, and a damaged house cannot be inhabited. The first step in an assessment of output losses is to estimate how much output is lost because of these direct asset losses.

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# **2.2.1 From asset losses to output losses**

Economic theory states that, at the economic equilibrium and under certain conditions, the value of an asset is the net present value<sup>6</sup> of its expected future production. In this case, the annual loss of output is equal to the value of the lost capital multiplied by the marginal productivity of capital (which is equal to the interest rate, increased by the depreciation rate). Assuming this equality is always verified, the output loss caused by capital loss is simply equal to the value of the lost asset, and summing the two is a double count.

Figure 1 illustrates this point in a scenario in which no reconstruction takes place: in that case, the production that is lost because of the disaster is equal to the value of the lost assets.<sup>7</sup> In estimates of disaster consequences, _what is referred to as “asset loss” is the replacement value of the capital_ . To have the equality of asset loss and output loss, a double equality needs to be verified: replacement value has to be equal to market value; and market value has to be equal to the net present value of expected output.

<!-- Start of picture text --> Production<br>DISASTER<br>Baseline production<br>(no disaster)<br>“discounted” area = value of lost<br>assets<br>Actual production (with disaster<br>and no reconstruction)<br>Time<br><!-- End of picture text --> _Figure 1. Production as a function of time, without disaster or in a scenario with disaster and no reconstruction. In the latter case, the discounted value of the lost production (from the disaster to the infinity) is equal to the value of lost assets. The production decrease is equal to the value of lost assets multiplied by the interest rate._

> 6 Note that the net present value is the sum of the production, discounted to account for the fact that production far in the future has less value than more immediate production.

> 7 Note also the baseline issue: maintaining unchanged production requires investments to maintain the capital stock; the lower production level post‐disaster is possible with a reduced investment level, thereby creating a benefit. This is taken into account by the fact that the marginal productivity of capital used to calculate asset value should include the depreciation rate.

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In a theoretical and optimal economy at equilibrium – these two equalities are valid. First, if the market value of an asset is lower (resp. larger) than the net value of its output, then investors will buy more (resp. sell) more of this asset to capture the difference in value, making asset price increase (resp. decrease). Second, if market value were higher (resp. lower) than replacement value, then investors would increase (resp. decrease) the amount of physical capital to restore the equality between market and replacement value (assuming decreasing returns). In a realistic setting, however, these two assumptions are not always verified. The reasons why asset values and output losses can differ are discussed below.

_The economy is not at its optimum._ For the replacement value and the market value to be equal, the economy needs to be at its optimum, i.e. the amount of capital is such that its return is equal to the (unique) interest rate. This is not always the case especially in sectors affected by disasters. In some sectors, expectations can be heavily biased (e.g., in the housing market) and markets distorted, leading to large differences between capital returns and interest rate. This is also unlikely for infrastructure and public assets. Since these assets are not exchanged on markets, they have no market prices. Moreover, they are not financed by decisions of private investors using financial returns, but by government decisions through a political process taking into account multiple criteria (e.g., land‐use planning objectives). Furthermore, output losses need to be estimated from a social point‐of‐view. The equality between market value (for the owner) and expected output (for the society) is valid only in absence of externalities. Some assets that are destroyed by disasters may exhibit positive externality. It means that their value to the society is larger than the value of the owner’s expected output. Public goods have this characteristic, among which most infrastructures, health services, education services.

An example is provided by the San Francisco Oakland Bay Bridge, which is essential to economic activity in San Francisco and had to be closed for one month after the Loma Prieta earthquake in 1989. Its replacement value has no reason to be equal to the loss in activity caused by the bridge closure, because the bridge production is not sold on a market, the bridge has no market value, and the social return on capital of the bridge is unlikely to exhibit decreasing returns and is likely to be much higher than the interest rate. Another example is the health care system in New Orleans. Beyond the immediate economic value of the service it provided, a functioning health care is necessary for a region to attract workers (what economists call a “positive externality”). After Katrina’s landfall on the city, the lack of health care services made it more difficult to reconstruct, and the cost for the region was much larger than the economic direct value of this service.

_The shock is large (“non‐marginal” in economic terms)._ The equality of asset value and output is valid only for marginal changes, i.e. for small shocks that do not affect the structure of the economy and the relative prices of different goods and services. The impact is different for large shocks. Most assets have “decreasing returns”, i.e. their productivity decreases with the total amount of asset. For instance, if there are one million cars in a city, the loss of one car is a marginal shock, and the output of this car should be equal (at the optimum) to the production cost of a car. But in practice, some cars have a larger productivity than others: some cars are driven 1,000 km per year while others are driven 80,000 km per year; clearly the latter car is more productive than the former. In economic theory, the least productive car – i.e. the one that is driven the shortest distance per year – has an output equal to the production cost of cars. All the other ones have a higher productivity. As a result, the destruction of one car – assuming the least 8
productive one is destroyed – leads to an output loss equal to the replacement cost of the car. But the destruction of many cars will affect cars with various productivity levels, and leads to an output loss that is larger than the replacement value of these cars. Moreover, the equality of asset value and output depends on the assumption that the destructions affect the least productive assets only. In the previous example, it is assumed that if one car is destroyed, then it is the least productive (i.e. the one that is driven the shortest distance per year). Or equivalently, it is assumed that the owner of the destroyed car will instantaneously buy the least used car to its owner (which makes sense because the former makes a more efficient use of the car than the latter).

To account for these effects, it is more realistic to assess the loss of output as the value of lost assets multiplied by the average productivity of capital, instead of the marginal productivity. Using classical production function and parameters, this approximation leads to output losses equal to approximately three times the value of lost assets; see details in (Hallegatte et al., 2007), and Appendix A.

Asset and output losses are often estimated assuming unchanged (pre‐disaster) prices, which is valid only for marginal shocks. One can assume that if a house is destroyed, the family who owns the house will have to rent another house at the pre‐disaster price. In other terms, the value of the housing service provided by the house can be estimated by the rental cost of a similar house before the disaster. But this assumption is unrealistic if the disaster causes more than a small shock. In post‐disaster situations, indeed, a significant fraction of houses may be destroyed, leading to changes in the relative price structure. In this case, the price of alternative housing can be much higher than the pre‐disaster price, as a consequence of the disaster‐related scarcity in the housing market. For large shocks, estimating the value of lost housing service should take into account the price change. Compared with an assessment based on the pre‐ disaster prices, it can lead to a significant increase in the assessed disaster cost. The same reasoning is possible in all other sectors, including transportation, energy, water, health, etc.

In extreme cases, there may be rationing, i.e. the price cannot clear the market and supply is not equal to demand. This is because markets are not at equilibrium in disaster aftermath). The « If I can pay it, I can get it » assumption is not valid in post‐disaster situations (e.g., there is no available house for rent at any price, there is no qualified worker to repair a roof). In these situations, therefore, the welfare impact of lost production cannot be estimated as the product of lost produced quantity and pre‐disaster prices. Providing an unbiased estimate requires an assessment of the disaster impact on prices and taking into account rationing. Appendix B provides details.

Post‐disaster price inflation (also referred to as “demand surge”) is especially sensible in the construction sector, which sees final demand soar after a disaster. For instance, Figure 2 shows the large (and persistent) increase in wages for roofers in an area heavily affected by hurricane losses in Florida in 2004.

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<!-- Start of picture text --> Annualized wage change in Miami, FL<br>20.00%<br>All occupations<br>Roofers<br>15.00%<br>10.00%<br>5.00%<br>0.00%<br>-5.00%<br>Aug-03 Oct-03 Dec-03 Feb-04 Apr-04 Jun-04 Aug-04 Oct-04 Dec-04 Feb-05 Apr-05 Jun-05 Aug-05 Oct-05 Dec-05 Feb-06 Apr-06 Jun-06 Aug-06 Oct-06<br><!-- End of picture text --> _Figure 2: Roofer wages in an area where losses have been significant after the 2004 hurricane season in Florida. Data from the Bureau of Labor Statistics, Occupational Employment Surveys in May 03, Nov 03, May 04, Nov 04, May 05, May 06, May 07._

# **2.2.2 “Ripple effects”**

Output losses are not only due to forgone production from the assets that have been destroyed or damaged by the event. Assets that have not been affected by the hazards can also be revealed to be unable to produce at the pre‐event level because of indirect effects, sometimes referred to as “ripple effects”. This is particularly the case for infrastructure and utility services (electricity, water and sanitation, gas, etc.). In past cases, it has been shown that the loss of utility services had larger consequences than direct asset losses, both on households (McCarty and Smith, 2005) and on businesses (Gordon et al., 1998; Tierney, 1997).

(McCarty and Smith, 2005) investigated the impact of the 2004 hurricane season on households in Florida, and find that among the 21% of the households who were forced to move after the disaster, 50% had to do so because of the loss of utilities (e.g., they had no running water). In only 37% of the cases, the main reason was structural damages to the house. (Tierney, 1997) and (Gordon et al., 1998) investigate the impact of the Northridge earthquake in 1994 in Los Angeles; they find also that loss of utility services and transport played a key role. Tierney surveys the reasons why small businesses had to close after the earthquake. The first reason, with 65% of the answers (several answers were possible), is the need for clean‐up. After that, the five most important reasons are loss of electricity, employee unable to get to work, loss of telephones, damages to owner’s or manager’s home, and few or no customers, with percentages ranging from 59% to 40%. All these reasons are not related to structural damages to the business itself, but to offsite impacts. (Gordon et al., 1998) ask businesses to assess the earthquake loss due to transportation perturbations, and find that this loss amounts to 39% of total losses. (Kroll et al., 1991) find comparable results for the Loma Prieta earthquake at San Francisco in 1989: the major problems for small business were customer access, employee access, and shipping delays, not structural 10
damages. Utilities (electricity, communication, etc.) caused problems, but only over the short term, since these services have been restored rapidly; only transportation issues have led to long lasting consequences. (Rose and Wei, 2013) investigate the impact of a 90‐day disruption at the twin seaports of Beaumont and Port Arthur, Texas, and find that – even in the absence of other losses – regional gross output could decline by as much as $13 billion at the port region level (and that specific actions to cope with the shock can reduce these impacts by nearly 70%).

In theoretical terms, this effect arises from the fact that the capital is non‐homogeneous and capital components are not perfectly substitutable. As a result, the consequences of disaster capital losses depend not only on the amount of capital that is lost, but also on which type of capital is lost. If the stock of capital consists of an ensemble of capital categories that have some complementarity, then the destruction of one component may reduce the productivity of other components and thus have an impact that is larger than what could be expected from the analysis of one component only (see Appendix A). One extreme example is the case of a road that is built out of a series of segments between point A and B: if one segment is destroyed, then the road is not usable and the other segments become useless. The output loss due to the destruction of one segment cannot be estimated based on the analysis of one segment, but requires an analysis of the entire system (the road). The same is true – at various degrees – of the entire economic system: the loss of one component can affect the other component and lead to losses that are higher (or lower) than the value of the asset loss suggests depending on the substitutability.

Output losses are also due to complex interactions between businesses. Business perturbations may indeed also arise from production bottlenecks through supply‐chains of suppliers and producers.<sup>8</sup> These ripple‐effects can be labelled “backward” or “forward”:

- Backward ripple‐effects arise when the impact propagates from clients to suppliers, i.e. when a business cannot produce, and thus reduces its demand to its suppliers, reducing their own activity (even in absence of direct damages).

- Forward ripple‐effects arise when the impact propagates from suppliers to clients, i.e. when a business cannot produce and thus cannot provide its clients with inputs needed for their own production.

The output losses due to a disaster depend on the characteristics of the firm‐to‐firm networks (Henriet et al., 2012), such as the average number of suppliers that firms have, or the shape and structure of the connection between firms. These results suggest that modern economies, with global supply chains, limited number of suppliers and small stocks, may be more vulnerable to natural disasters than traditional, close economies. But the model used in (Henriet et al., 2012) is too simple for providing realistic assessment of disaster costs, and detailed information on real‐world economic networks is not available. The impact of disasters on supply chains are tragically illustrated by the recent Tohoku‐Pacific earthquake in Japan, and its wide consequences on industrial production and exports, especially in the auto industry.

> 8 These ripple effects can even take place within a factory, if one segment of the production process is impossible and therefore interrupts the entire production.

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As an example, The Economic Times, an Indian newspaper, reports that “ _Japan's Toyota Motor will cut production at its Indian subsidiary by up to 70% between April 25 and June 4 due to disruption of supplies.”_ When capital cannot produce because of a lack of input (e.g., electricity, water), several options are available: input substitution, production rescheduling, mobilization of existing idle resources, and longer work hours can compensate for a significant fraction of the losses (Rose et al., 2007a). Loss of output in the affected area and during the disaster aftermath could thus be compensated by increased production outside the affected area (e.g., when another region capture the market shares lost by the affected region) or later (e.g., when production is rescheduled after basic services are restored). Even within the affected area, output losses from destroyed capital can be compensated by increased production from factories and production units that did not suffer from losses and had idle capacity before the event (which depends on the pre‐existing situation, see next section).

These mechanisms can damp output losses, and can especially reduce the crowding‐out effects of reconstruction on normal consumption and investment. But their ability to do so is limited, especially when losses are large. In case of large disasters, output losses will be largely dependent on two characteristics of the economy: the adaptability and flexibility of its production processes; and its ability to channel economic production toward its most efficient uses.

# **2.2.3 Stimulus effect**

Disasters lead to a reduction of production capacity, but also to an increase in the demand for the reconstruction sector and goods. Thus, the reconstruction acts in theory as a stimulus. However, as any stimulus, its consequences depend on the pre‐existing economic situation, such as the phase of the business cycles and the existing of distortion that lead to under‐utilization of production capacities.

If the economy is efficient and in a phase of high growth, in which all resources are fully used, the net effect of a stimulus on the economy will be negative, for instance through diverted resources, production capacity scarcity, and accelerated inflation. If the pre‐disaster economy is depressed, on the other hand, the stimulus effect can yield benefits to the economy by mobilizing idle capacities.

Economies in recession are more resilient to the effects of natural disasters (see a model based analysis in Hallegatte and Ghil, 2008). This result appears consistent with empirical evidence. For instance, the 1999 earthquake in Turkey caused direct destructions amounting to 1.5 to 3% of Turkey’s GDP, but consequences on growth remained limited, probably because the economy had significant unused resources at that time (the Turkish GDP contracted by 7% in the year preceding the earthquake). In this case, therefore, the earthquake may have acted as a stimulus, and have increased economic activities in spite of its human consequences. In 1992, when hurricane Andrew made landfall on south Florida, the economy was depressed and only 50% of the construction workers were employed (West and Lenze, 1994). The reconstruction needs had a stimulus effects on the construction sectors, which would have been impossible in a better economic situation (e.g., in 2004 when four hurricanes hit Florida during a housing construction boom).

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The stimulus therefore exists only if there is idle capacity in the economy, i.e. some distortions in the economic system. In developing countries, where capital is scarce and (unskilled) labor abundant, it is unlikely that large idle capacity exist, except during recessions. However, many developing country economies are plagued with large distortions that sometimes lead to excess investments in capital. In that latter case, it is possible that idle capacity is available and that the reduction in capacity due to a disaster has no impact.

The stimulus benefits may be considered as a positive outcome of disasters, but they should not. Indeed, the same stimulus benefits could be captured in the absence of a disaster, through a standard stimulus policy, and without the negative welfare and human impacts that come with disasters. For instance, output may be stimulated by the reconstruction of many houses destroyed by a hurricane; but the same output generation is possible by building new and better housing or by retrofitting existing building to make them more energy efficient, without the need for any destruction. The possibility of a stimulus effect would only reflect the fact that pre‐existing economic policy is inappropriate, and this could be corrected independently of a disaster. So, it would be improper to attribute this positive effect to the disaster itself.

# **2.2.4 Non‐linearity in output losses**

There are three main reasons why output losses are likely to increase non‐linearly with the size of the disaster (and the amount of destruction):

- First, all economies have idle capacities (e.g., factories that do not produce as much as they technically can, and workers who could and sometime wish to work more hours). If lost production by affected capital is small enough to be fully compensated by increased production from non‐ affected idle capacity, then there is no output loss (Albala‐Bertrand, 2013). As a result, output losses appear only if direct losses are larger than a given threshold that depends on the pre‐ existing economic situation.

- Second, the “ripple effects” from infrastructure to firms and households and across firms are also likely to increase with the number of affected firms (and the individual loss of output) (Henriet et al., 2012).

- Third, the reconstruction capacity is always limited by financial and technical constraints and it makes rebuilding after a large scale disaster much longer than after a small one (Benson and Clay, 2004). In other terms, the duration of the shock increases with its amplitude. As a result, the output losses – that depend on the magnitude of the shock and its duration – will increase more than proportionally with direct losses.

The amount of damages can be a misleading indicator of the reconstruction duration. The 10 billion euros of reconstruction expenditures after the 2002 floods in Germany correspond to 10 days of total German investments. But reconstruction has been spread out over more than 3 years, suggesting that only a small fraction of investments can be dedicated to reconstruction (even though the return on investment from reconstruction should theoretically be higher than other investments, as suggested in Appendix A), because of financial and technical constraints.

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A model‐based investigation of this issue using the Adaptive Regional Input‐Output (ARIO) model (Hallegatte, 2008; Hallegatte, 2014) concludes that total losses due to a disaster affecting Louisiana increase nonlinearly with respect to direct losses when direct losses exceed $50 billion (see Figure 3). When direct losses are lower than $50bn, aggregated indirect losses are close to zero (even though the aggregation hides important disparities among sectors and among social categories). Beyond $50 billion of direct losses, indirect losses increase nonlinearly. When direct losses exceed $200 billion, for instance, total losses are twice as large as direct losses. For risk management, therefore, direct losses are insufficient measures of disaster consequences.

<!-- Start of picture text --> 400<br>350<br>300<br>250<br>200<br>150<br>100<br>50<br>0<br>‐50<br>0 100 200 300<br>Direct losses (US$b)<br>Indirect losses (US$b)<br><!-- End of picture text --> _Figure 3: The direct losses – output losses as a function of direct (asset) losses, in Louisiana for Katrina‐ like disasters of increasing magnitude._ The output losses due to a hazard (and the resulting welfare impact) do not depend only on the physical intensity of the natural event, but also on the coping capacity of the affected human system. Physical measures of disaster intensity (e.g., in m/s for windstorm) or even measures of direct losses (e.g., the number and value of destroyed and damaged buildings) are very poor proxies of the real economic cost of a disaster. A corollary is that natural disasters can have significant macroeconomic impacts, when they are larger than the (context specific) economic coping capacity. Moreover, it means that reducing natural disaster impacts on welfare can be done through an increase of the coping capacity, to make reconstruction faster and more efficient and limit output losses.

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# **2.3 Assessing indirect losses**

## **2.3.1 Measuring indirect losses using econometric analyses**

Econometrics analyses have been used to measure output losses, understood as reduction in GDP following a disaster, but they reach contradictory conclusions (see great reviews in Dell et al., 2013; Kousky, 2014). Albala‐Bertrand (1993) and Skidmore and Toya (2002) suggest that natural disasters have a positive influence on long‐term economic growth, probably thanks to the stimulus effect of reconstruction (section 2.2.3) and possibly the replacement of damaged capital with more recent technologies (on this “productivity effect”, see also critical discussions in Benson and Clay, 2004; Hallegatte and Dumas, 2009). Others, like (Hochrainer, 2009; Jaramillo, 2010; Noy and Nualsri, 2007; Noy, 2009; Raddatz, 2009) suggest that the overall impact of disasters on growth is negative. At local scale, (Strobl, 2010) investigates the impact of hurricane landfall on county‐level economic growth in the US and shows that a county that is stuck by at least one hurricane over a year sees its economic growth reduced on average by 0.79 percentage point (and increased by only 0.22 percentage point the following year). On Vietnam, (Noy and Vu, 2010) investigate the impact of disasters on economic growth at the province level, and find that lethal disasters decrease economic production while costly disasters increase short‐term growth.

The lack of consensus on the impact of disasters on GDP is likely to arise from different impacts from small and large disasters, the latter having a negative impact on growth while the former enhance growth, and from different impacts from different types of disasters. For instance, (Felbermayr and Gröschl, 2013) find that disasters in the top decile in terms of magnitude lead on average to a 3 percent reduction in GDP growth. The loss is only 1.5 percent for disasters in the top 15% percentile, and 0.8% for disasters in the top 20%. For smaller disasters, no impact can be detected. The type of disaster also matters: (Loayza et al., 2012) find that droughts reduce GDP growth by 1.7 percentage point, while floods increase GDP by 0.5% (possibly because floods enrich soils and increase agricultural productivity).

## **2.3.2 Modeling indirect losses**

Many scholars have used economic models to estimate output losses. Many different models have been used, but the most common are Input‐Output (IO) or Calculable General Equilibrium (CGE) models. In these models, the economy is described as an ensemble of economic sectors, which interact through intermediate consumptions. These models however describe differently how these different sectors interact with each other, and how they react to shocks.

Some models are based on the Input‐Output (IO) linear assumption (Leontief, 1951), in which the production of one unit in one sector requires a fixed amount of inputs from other sectors, and in which prices do not play any role. These include (Bockarjova et al., 2004; Haimes and Jiang, 2001; Stéphane Hallegatte, 2014; Hallegatte, 2008; Okuyama, 2004; Okuyama et al., 2004; Santos and Haimes, 2004). Other models are based on the Calculable General Equilibrium (CGE) framework, which assumes that changes in relative prices balance supply and demand in each sector (Rose and Liao, 2005; Rose et al., 2007a).

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Economic losses caused by a disaster are smaller in a CGE setting than in an IO setting. It is often considered that IO models represent the short‐term economic dynamics, in which production technologies are fixed and prices cannot adjust. CGE models, on the other hand, represent the long‐term dynamics, in which flexibility in production processes and markets allow for an adjustment of the economic system. In reality, it is likely that IO models are pessimistic in their assessment of disaster output losses, because there is flexibility even over the short term (for instance, maintenance can be postponed; workers can do more hours to cope with the shock; production can be rescheduled, see (Rose et al., 2007a)). It is also likely that CGE models are optimistic, even in the long run, because prices have stickiness and cannot adjust perfectly, and because substitution has technical limits that are not always adequately represented in production functions.

Considering the sensitivity of model results to many parameters, and the limitation of existing tools, it is fair to admit that models are useful tools to explore the indirect consequences of disasters but cannot estimate precisely the total economic cost of a disaster.

# **2.3.3 Rule of thumb**

In the framework presented here (see details in Appendix A and B), one dollar of direct loss in productive capital translates into a decrease in instantaneous (annualized) output that equal to the average productivity of capital, that is about three times the interest rate (i.e. the marginal productivity of capital, r), possibly increased by a factor (1+ that represents ripple‐effects: The parameter  represent the “ripple‐effects” through the supply chain and infrastructure interruption effects (see Section 2.2). It represents the lost production from capital that is not affected by the event, and depends on the ability of the economic system to (1) mobilize existing idle capacity (which depends on the existence of idle capacity); (2) adjust production network to compensate for damaged production units (e.g., producers find new suppliers and clients rapidly), (3) channel remaining production toward its most productive uses (including reconstruction needs), (4) increase imports to compensate for unavailable supplies. It is likely to be close to zero for relatively limited disasters, and to increase for large‐ scale events. It is lower (and possibly negative) if the pre‐existing economic situation is depressed, with under‐utilization of production capacity.

In the absence of convincing models or even theory, it can be recommended to take =0, keeping in mind that we are disregarding some potentially important effects. In very specific cases, different values could be used, for instance a ‐20% value if the shock occurs during a recession with large idle resources (e.g., the landfall of hurricane Andrew in Florida in 1992), or a +20% if the transport sector is heavily affected, creating large‐scale supply‐chain issues (or in case of power generation issues such as in Japan after the 2011 earthquake and tsunami).

As shown in Appendix C, assuming that output losses are reduced to zero exponentially, and that 95% of the losses are repaired in N years, total _non‐discounted_ output losses ����∆� are equal to: 16
With discounting at a rate r, the net present value of output losses is<sup>9</sup> : The parameter N is the reconstruction period and it can often be estimated by experts based on past experience. Note that the reconstruction time is not the time when the observed GDP or output returns to its pre‐disaster value, but is much longer. Indeed, the GDP and output is affected by other mechanisms, including increase in labor productivity, other investments, and possibly the “stimulus effect” of the disaster. But the stimulus effect should not be accounted in disaster consequences (see Section 2.2.3), since it corresponds to benefits that could have been captured in the absence of the disaster, through a classical stimulus policy.

Taking on example of a disaster that make capital losses equal to $500 million, in a country with a 10% interest rate, with a reconstruction period that is likely to span over 3 years would lead to (non‐ discounted) output losses equal to $225 million (i.e. 45% of direct capital losses). In the context of figure 3 (hurricanes on Louisiana), this rule of thumb reproduces model results perfectly, assuming that losses lower than $50 billion can be repaired in one year, and that losses amounting to $100, $150, $200, and $250 billion can be repaired in 5, 10, 12, and 15 years, respectively.

# **2.4 From output losses to welfare losses**

Losses in economic output do not affect directly people welfare; for them, what matters most is consumption. It is thus important to investigate how output losses translate into consumption losses. And since capital and output losses partly interact, it is incorrect to simply sum them to estimate welfare losses.

Consider first a scenario in which all losses are repaired instantaneously by reducing consumption and directing all the goods and services that are not consumed toward reconstruction investments (this is a scenario where reconstruction capacity is infinite). In this theoretical scenario, there is no output loss since all asset damages are instantaneously repaired, and N=0 in Eq. (2‐3). There are however consumption losses, since consumption has to be reduced to reconstruct, and this reduction is equal to the reconstruction value (i.e. the replacement cost of damages capital). In that case, consumption losses are thus simply equal to the value of lost assets (i.e., direct losses).

Consider now another scenario with no reconstruction, in which output losses are permanent (like in Figure 1) and all losses in output are absorbed by a reduction in consumption (but no share of income is used for reconstruction). In that case, consumption losses are equal to output losses (with no reconstruction), and N is equal to infinity in Eq. (2‐3). The loss in consumption is thus equal to (1+)K/. Consumption losses and welfare losses are thus larger than the value of lost assets in a no‐reconstruction scenario.

> 9 The variable noted with x� are the net present value of the future fluxes of x�t� .

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In the instantaneous reconstruction scenario, consumption losses are equal to the share of consumption needed to repair and rebuild, i.e. to direct losses. In the no‐reconstruction scenario, consumption losses are equal to output losses, i.e. larger than direct losses.<sup>10</sup> As a result, consumption (and welfare) losses are magnified when reconstruction is delayed or slowed down.<sup>11</sup> And in all realistic scenarios where reconstruction takes some time (from months for small events to years for large‐scale disasters), welfare losses are larger than direct losses.

The actual welfare losses are thus the sum of the net present value of reconstruction cost (i.e. direct capital cost) and the net present value of indirect (output) losses. The reconstruction phase, and the economic recovery pace, will ultimately determine the final welfare cost of the natural disasters. If reconstruction is done over N years with investments equal to K/N, the present value of consumption losses is equal to: Note the two extreme cases: ‐ As N tends toward zero, ∆�� tends to K.

‐ As N tends toward the infinity (no reconstruction), ∆�� tends to (1+)K/.

And if we approximate this equation further, we get: So in that case, aggregate consumption losses are equal to capital losses, increased by a factor Γ that depends on a few parameters:

- the _interest rate_ , as the welfare impacts of disasters will be higher in countries where capital is scarce and the interest rate (and the marginal productivity of capital) is high;

- the _decreasing return_  in the production function, which is also equal to the share of profits in national income;

- an _instantaneous resilience_ , i.e. the ability to limit the magnitude of the immediate loss of income for a given amount of capital losses, that is given by the parameter .

- a _dynamic resilience_ , i.e. the ability to reconstruct and recover quickly, that is given by the variable N.

> 10 The reality is more complex that what has been described here because not all output losses are translated into consumption losses. In practice, the loss in output changes the terms of the inter‐temporal investment‐ consumption trade‐off and translates into ambiguous instantaneous changes in consumption and investment. But the main conclusions of the analysis are not affected by this complexity.

> 11 The fact that rapid reconstruction is better for welfare than slow reconstruction – or equivalently, that reconstruction has a return that is much higher than that of “normal investments” and the interest rate – explains why reconstruction is usually a priority and crowds out consumption and other investments in the affected region.

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Taking again the example of a disaster that makes capital losses equal to $500 million, in a country with a 10% interest rate, with a reconstruction period that is likely to span over 3 years, the discounted loss of consumption is $606 million, which is 21% larger than asset losses.

# **Box 2 – Indirect flood losses in Mumbai**

The ARIO model is then used to assess the output impact that would be caused by different floods, accounting for the characteristics of the Mumbai region economy. In particular, the model accounts for the financial constraints that can make it very difficult for poor households to finance the reconstruction, and can thus slow down the recovery significantly. In the model, the 2005 floods – that caused direct losses amounting to about $2 billion – led to indirect losses amounting to $425 million, i.e. 18% of direct losses (see figure). In the model, reconstruction is carried out over a 12 months period.

<!-- Start of picture text --> 4000<br>3000<br>2000 July 2005 event<br>1000<br>0<br>0 2000 4000 6000 8000<br>Direct losses (million USD)<br>Indirect losses (million USD)<br><!-- End of picture text --> _Figure. Relationship between direct losses due to an event and indirect losses (productive sectors plus housing sector), with the July 2005 event highlighted._ This number evaluated through a significant modeling exercise is broadly consistent with the rule of thumb proposed below and the fact that most of the reconstruction occurred in one year. With a marginal productivity of capital of 12.5% in Mumbai, the rule of thumb for the 2005 event would give: Of course, aggregated numbers hide the very large heterogeneity in indirect losses. As already mentioned, informal dwellers suffered from losses that were on average equal to their total savings, suggesting that their ability to invest has been strongly affected. Many of them also report forced reduced consumption, including of food. However, dwellers with stable jobs in the service sector reported only a few days of lost work.

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# **3 Reducing disaster losses through higher resilience**

The previous section demonstrates that welfare losses will depend on the amount of direct losses, but also on the ability of the economic system to recover and reconstruct (represented by the reconstruction period length, _N_ ). This ability can be referred to as the _macroeconomic resilience_ of the affected economy. As discussed in Section 2.2, reconstruction investments – and thus the reconstruction speed – are constrained by a series of constraints. These constraints reduce the economic resilience and increase welfare costs. Relaxing them can therefore increase resilience and reduce total disaster losses. This section reviews a few policies to do so.

One source of friction is that consumers, firms and public organizations need time to direct high amounts of money to reconstruction activities. This constraint is crucial in developing economies (Benson and Clay, 2004). Insurance can of course play an important role in helping finance reconstruction (see next section), but access to credit is also extremely important. The second source of friction is linked the capacity of the economic system to produce enough to satisfy reconstruction needs. Finally, one constraint to reconstruction is linked to the limited ability of the government to finance reconstruction, directly when public assets are affected and indirectly through the support the government provides to private actor to help them rebuild.

## **3.1 Insurance benefits**

Insurance is useful for several reasons. First, it spreads the risk among customers, over space, and over time. By doing so, it replaces rare and large losses by regular and small payments. If economic agents are risk averse, they prefer smooth and regular losses to an unknown and potentially large loss, and insurance increases welfare.

Second, most economic agents are not aware of the risk they are facing (World Bank, 2013, Chapter 2). If insurance premiums are risk‐based (which is not the case in most of the world), they provide an accessible measure of the level of risk. This signaling effect can help households and businesses make smarter choices (e.g., settling in lower‐risk areas), and be an incentive to risk‐mitigation actions (e.g., by reducing insurance premium if homeowners invest in flood‐mitigation). The signaling effect of risk‐based insurance premium should not be overstated, however. In many places, it would be too small to trigger significant behavioral changes.

But most importantly, insurance claims support the affected population after a disaster, reducing immediate welfare losses and consumption reductions, and allowing a faster and more efficient reconstruction (by relaxing financial constraints, see (Benson and Clay, 2004)). Faster reconstruction means that overall output losses are reduced.<sup>12</sup> Also, reconstruction needs and lost output and income have a strong impact on households, firm, and public agency budgets, especially in developing countries,

> 12 In Mumbai, our survey shows that loans was almost absent in the 2005 recovery and reconstruction. An improved access to credit (especially for the underprivileged) could help during the post‐disaster period; e.g. the government guaranteeing reconstruction loans.

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forcing them to reduce consumption (or non‐reconstruction‐related investments). The reduction in consumption can then have second‐order consequences on other businesses that will see reduced demand and may respond by cutting on production and employment, magnifying the negative impact of the shock further (and affecting firms and households that have not been directly affected).

A last benefit of insurance is linked to the predictability of post‐disaster support. Government support is often necessary to some extent (for instance, after Katrina, the U.S. Federal government partly replaced insurance for households that had no flood insurance). But when it is ad hoc, government support creates inefficient uncertainty for economic actors (e.g., because, after an event, they cannot known the exact scope of the government support they will receive) and can lead to moral hazard (e.g. if households know that they will be compensated by government, they will have little incentive to reduce their own risks or to pay for insurance). International support (grants or goods provided to affected people) can help reconstruction, but (in addition to the moral hazard issue) is very volatile and unpredictable.

# **Box 3 – The current and potential effect of insurance in Mumbai**

We can use the ARIO model to investigate the benefits of insurance by exploring the sensitivity of indirect losses to the insurance penetration rate (γ) assumed in the model. In ARIO, the insurance penetration affects the response to the shock through two mechanisms: first, if the insurance penetration of households is low, they have to pay for their reconstruction (either directly, or by getting into debt and then paying off later), and reduce their consumption to so. Second, if the insurance penetration of firms is low, firms have to pay for reconstruction, reducing their profits. As a portion of these profits normally goes to local households, this affects the household budget, also reducing their consumption.

The box figure illustrates the effect of insurance penetration<sup>13</sup> on the household’s budget, for a July 2005 like flood estimated using the ARIO model. Three scenarios are included: (i) γ=0, equivalent to the absence of insurance system, but with an access to credit; (ii) the current value of flood insurance penetration estimated by RMS (γ=0.08 for households, γ=0.15 for firms); and (iii) γ=1, representing the situation where all the reconstruction is paid for by insurance. Where the budget is positive in the figure, it can be interpreted as the additional savings of households, and where negative it represents debt. When insurance penetration is large, households make savings after the disaster. This occurs because in this case, households are rationed and consume less than what they would like to and as a result, they involuntarily save money. Variations in household budget affect the local demand, as households in debt reduce their consumption. This decrease in demand affects local production. Total output losses is reduced from $455 million in the absence of insurance to $425 million with the current insurance penetration to $265 million if all losses are covered by insurance.

> 13 It is important to note that our “insurance penetration rate” does not represent the fraction of the total amount of houses that is insured (as is often done), but the fraction of the total value of goods that is insured (never equal to one in the real world, because of ceilings or deductibles).

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<!-- Start of picture text --> 100<br>0<br>-100<br> = 1 (full insurance)<br>-200<br>RMS estimates<br>-300  = 0.08 (households)<br> = 0.15 (businesses)<br> = 0 (no insurance)<br>-400<br>0 12 24 36 48 60 72 84 96 108 120<br>Time (months)<br>Household budget change (USD)<br><!-- End of picture text --> _Figure. Household Budget as a function of time, for 3 different penetration rates. Note : γ=0 (no insurance), current value estimated by RMS (γ=0.08 for households and γ=0.15 for businesses) and γ=1 (reconstruction is entirely paid by the insurance system)._ In sum, insurance yields macroeconomic (at the aggregated output level) and microeconomic benefits (at the household level). Microeconomic benefits include in particular the avoidance of increased poverty and inequality, the avoidance of the reduction in food intake (observed for about 40% of households in Mumbai after the 2005 floods), and facilitation and acceleration of reconstruction. Even though they are difficult to estimate in monetary terms, all these benefits should be taken into account, e.g. in the cost‐ benefit analysis of the implementation of a micro‐insurance scheme.

# **3.2 Increase in reconstruction capacity**

Another source of friction is that the sectors involved in reconstruction activities have skills, equipment, access to material, and organizational capacities adapted to the normal state of affairs and cannot face huge increases in demand. After the French storms in 1999 or after the explosion in a chemical plant in Toulouse in 2001, reconstruction took several years largely because roofers and glaziers were not numerous enough.

Indeed, over short timescales, local production capacity is highly constrained by existing capacities, equipment and infrastructure. Only imports from outside the affected region and postponement of some non‐urgent tasks (e.g., maintenance) can create a limited flexibility over the short‐term. Over the longer term and the entire reconstruction period, which can stretch over years for large‐scale events, the flexibility is much higher: relative prices change, incentivizing production in scarce sectors; equipment and qualified workers move into the affected region, accelerating reconstruction and replacing lost capacities; 22
and different technologies and production strategies can be implemented to cope with long‐lasting scarcities.

Large economic losses can be avoided with increased flexibility in the construction sector production capacity. The flexibility depends heavily on the pre‐event conditions; for example, if idle capacities are present (e.g. unused equipment) they can be mobilized to cope with the disaster (Hallegatte and Ghil, 2008; West and Lenze, 1994), whereas if capacities are fully used then no additional capacity can be mobilized. The flexibility of the construction section could be enhanced through:

- Enabling qualified workers to settle down temporarily in the affected region (e.g. by providing working permit or helping workers to find accommodation).

- Organizing and sharing reconstruction resources among regions, states or cities and setting super‐ national policies to ensure reconstruction capacity is adequate to cope with possible disasters.

- Empowering governments to mobilize their workers (e.g., soldiers) and equipment to speed up reconstruction.

Past disasters illustrate the barriers to efficient reconstruction and suggest good practices. For instance, in the Katrina aftermath, many qualified workers from the entire U.S. moved to New Orleans to help reconstruct the city and capture higher construction‐sector wages. Most of these workers, however, had to leave the area rapidly because they could not find proper accommodation or because of insufficient public services. Providing housing to temporary workers, therefore, seems to be extremely important to speed up reconstruction. Also, these workers left the region because the reconstruction of many buildings was delayed by legal problems, either due to delays in insurance claim payments or to the slow approval of building permits. For reconstruction to be as effective as possible, therefore, it seems that all administrative and legal issues must be solved rapidly, to benefit for the mobilization of internal and external resources.

# **3.3 Increase in public expenditures**

Government with fiscal space or insurance or other risk sharing mechanisms will be able to increase public expenditure to deal with the disaster. The benefits from doing so will depend on how these resources are spent and used.

The first element is of course the management of the emergency situation. Resources are necessary to (i) maintain the functioning of the national and local authorities (civil servant salaries need to be paid, for instance); (ii) provide emergency services to the population, for instance through in‐kind support (food, temporary shelters, drugs and medical services, etc.).

Over the long‐term and the whole reconstruction phase, a few elements have to be taken into account. The reconstruction is a period of supply‐side constraints in the sectors involved in reconstruction (especially the construction sector), so increasing public reconstruction expenditure may crowd out private reconstruction efforts (by firms and households) and increase prices for all. This may or may not happen, depending on (1) which reconstruction tasks are concerned (there is less crowding out between 23
highway and housing reconstruction than between public buildings and housing reconstruction), (2) the situation of the construction sector and the available worker skills.

# **Box 4 – Enhancing reconstruction capacity in Mumbai**

The ARIO model also allows us to assess the benefits of sets of policies that aim to accelerate reconstruction. We find that, for the July 2005 event, the indirect effect of the disaster on the local economy can vary by a factor of 4 (see box figure), depending on the amplitude and quickness of response of the construction sector. Of course, the ability to reconstruct impacts mostly the reconstruction duration and through it the rule of thumb proposed in Section 2.3.3.

<!-- Start of picture text --> 0.8<br>{120% ; 3 months }<br>No overproduction<br>0.7<br>{ 120% ; 6 months }<br>0.6<br>0.5<br>0.4<br>0.3<br>0.2<br>0.1<br>{ 150% ; 6 months }<br>0<br>{ 150% ; 3 months }<br>-0.1<br>0 2000 4000 6000 8000<br>Direct losses (million USD)<br>Ratio indirect losses / direct losses<br><!-- End of picture text --> _Figure. Indirect losses to direct losses ratio, as a function of the amount of direct losses, for four sets of adaptation parameters (the first parameter describes the amount of additional production that is possible, and the second parameter the time it takes to increase production to this level)_ Public resources can be used to increase supply‐side capacity in the reconstruction sector – for instance by supporting the migration of workers in the affected areas with temporary housing and the rapid provision of basic services. It can also focus on restoring transport infrastructure to facilitate the import of reconstruction materials, equipment, and skilled workers, and more generally of rationed goods and services.

Public resources can also be used to help private actors reconstruct and rebuild, especially where insurance penetration is low. The goal is to accelerate reconstruction (but using private actors to determine priorities) and mitigate the needed reduction in consumption (see previous section). More generally, they can support the population through classical safety nets, in particular to help it cope with 24
lost income. Moreover, they can help the affected population import (possibly at a higher costs) goods and services that are not produced locally (e.g., through a reduction in import tariffs).

These different aspects can be combined, for instance using cash‐for‐work programs in which the affected population gets paid for reconstruction work. This approach combines demand‐ and supply‐side benefits and is very likely to maximize the welfare benefits.

# **4 Macroeconomic resilience and risk management policies**

This analysis shows that the welfare cost of a disaster does not depend only on either the physical characteristics of the event or its direct impacts. Depending on the ability of the economy to cope, recover and reconstruct, the reconstruction will be more or less difficult, and its welfare effects smaller or larger. This ability, which can be referred to as the _macroeconomic resilience_ of the economy to natural disasters, is an important parameter to estimate the overall vulnerability of a population. Here, resilience is recomposed into two components: _instantaneous resilience_ , i.e. the ability to limit the magnitude of the immediate loss of income for a given amount of capital losses; and _dynamic resilience_ , i.e. the ability to reconstruct and recover quickly.

This paper proposes to assess the total discounted consumption loss of a disaster through the following relationship: Where _r_ is the interest rate (a higher interest rate decreases resilience and increases consumption losses),  is the share of profit in the production function (and a measure of decreasing returns), _N_ is the reconstruction duration (a longer reconstruction duration increases losses), and  is the factor that increase or decrease immediate output losses and is negative if enough idle resources are available and positive if ripple‐effects impair production of non‐affected capital.

After a disaster, it is easy to estimate N, and r and  are also known. The parameter is more difficult to estimate, and can be taken at zero as a first‐order estimate, except in very specific situations.

To reduce the negative impact of natural disasters on population welfare, a first approach is to reduce the direct impacts on the economic systems, using for instance better coastal protections and stricter building norms. But another approach consists of reducing indirect losses through an increase in the resilience of the socio‐economic system, using for instance insurance schemes or government support to the affected population.

An optimal risk management strategy is very likely to include measures targeting direct impacts (disaster risk reduction actions) and measures targeting indirect impacts (resilience building actions); see an example in Figure 4. For instance: 25
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aggregate level. The benefits from insurance, for instance, arise probably more from such micro‐benefits than from the macro‐effects discussed earlier (even though the latter is not negligible and should not be overlooked). The macro‐level concept of economic resilience presented here should thus be completed with other aspects regarding the ability of firms to cope (see a framework to define firm resilience in Rose and Krausmann, 2013) and the ability of household to cope (see for instance Adger et al., 2002; Morris et al., 2002). Hallegatte (2014) builds on this work to propose a more comprehensive economic resilience indicator, taking into account the macro‐level as described here and additional micro‐level effects (including the role of inequalities and social protection).

# **5 References**

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# **6 Appendix A: The use of classical production function leads to underestimating output losses**

There are several possible biases resulting from disaster modelling using classical production function (Hallegatte et al., 2007). Production functions are classically used in economics to relate the inputs and the outputs of a production process. Often, the production function takes as inputs the amount of labor used in the production process (referred to as L) and the amount of capital (i.e., the value of all equipment used in the process, referred to as K), and gives the value of the production (expressed as Y): Y = f(L,K) . (A1) Disasters mainly destroy the stock of productive capital and a natural modelling option to represent their consequences is to consider that they reduce instantaneously the total productive capital (K0 → K0 − ΔK). Figure A1 illustrates several ways of assessing the impact on production. The figure represents the production Y as a function of capital K. The production function is the blue line linking the origin of the graph to the point A. It is assumed that the pre‐disaster situation is the point A, with capital K0 and production Y0.

The impact on production can be estimated using the marginal productivity of capital, i.e. the interest rate at the optimum. This case is shown in Figure A1 as the point B. Point B is estimated using the orange line, which is the tangent to the production function at point A; its slope is the marginal productivity of capital (i.e., how much more production do I get if I increase capital by one unit). The production Y1 is given by the orange line at the X‐coordinate K0 – ΔK, and is the estimated residual production if the output loss is estimated by multiplying the value of the lost capital ΔK by the interest rate. It is also what is done when the net present value of all output losses is assumed to be equal to the value of lost assets.

The impact on production can also be estimated using the full production function, and decreasing the amount of capital from K0 to K0 – ΔK. This is what is shown by the point C in the figure. The point C gives the value of production Y2 given by the production function, i.e. f(L, K0 – ΔK). This option, however, amounts to assuming that only the least‐productive capital has been affected. Obviously, this is not the case: when a disaster hits, it destroys the capital indiscriminately, not only the least efficient capital.

Because of decreasing returns in the production function, using a classical production function amounts to assuming that capital destructions affect only the less efficient capital. In a Cobb–Douglas setting (Y=AL<sup>λ</sup> K<sup>μ</sup> ), indeed, the after‐disaster production would be Y2=AL<sup>λ</sup> (K0−ΔK)<sup>μ</sup> . Since μ is classically estimated around 0.3, an x% loss of equipment would reduce the production by a factor (μ x), i.e. approximately (0.3 x) % (see figure below).

To account for the fact that disasters affect the capital independently of its productivity, Hallegatte et al. (2007) propose to modify the Cobb–Douglas production function by introducing a term ξK, which is 31
the proportion of non‐destroyed capital. This new variable ξK is such that the effective capital is K=ξK∙K0, where K0 is the potential productive capital, in absence of disaster. The new production function is In Figure A1, the new production function is the red line and the new production Y3 is given by the point C’.

With these assumptions, the decrease in output from a disaster is not equal to the value of lost assets multiplied by the marginal productivity of capital anymore. Instead, output losses are equal to the value of lost assets multiplied by the average productivity of capital, which is 1/� times larger than the marginal capital productivity. With classical values for � , it means that output reduction at the time of shock ( �� ) is about 3 times larger than what is suggested by the market value of damaged assets. As result, production losses are then given by:

# Production

<!-- Start of picture text --> A<br>Y<br>0<br>B<br>Y<br>1<br>Y0<br>Y<br>2 C<br>Y<br>3 C’<br>O<br>K0‐K K0 Capital<br><!-- End of picture text --> _Figure A1. Production with respect to productive capital for different modelling assumptions._ Another bias arises from the aggregation of many different types of capital within only one variable – capital K – in economic models. If the function f(L,K) is replaced by a function with two types of capital f(L,K1,K2), the impact of disasters can change dramatically. In particular, because of decreasing returns in K1 and K2, the impact of a given loss K=K1+K2 depends on how losses are distributed across the two capitals. The loss in output is larger if all losses affect one type of capital, compared with a scenario where the two capitals are more homogeneously affected. As a result, disaster loss estimates can be 32
Y = [Min(@,Ky,a@2K2)]" K = Ky + K ak, = azK> Kj _~ ~~(—_)aj~~ k Y Q1+a2 oY . ~~aK~~ i+6 ~~—~~ k=x ~~(4)(Y~~ A) A=_ ~~[=|~~ <u>aA1a2</u> Y
<!-- Start of picture text --> Y = [a;kj]”<br>= = yalKY"*<br>oe (8) G+)<br><!-- End of picture text --> AY (to) = ~~“r~~ AK
This parameter also depends on other – more micro – considerations regarding the ability of firms to cope with shocks (see a framework to define firm resilience in Rose and Krausmann, 2013).<sup>16</sup> As such, the parameter  is linked to the concept of _“static resilience_ ” proposed by (Rose, 2013, 2009). He defines it as follows: _“Static resilience refers to the ability of an entity or system to maintain function when shocked. This is related in turn to a fundamental economic problem—how to efficiently allocate the resources remaining after the disaster. It is static because it can be attained by various means, such as conservation, input substitution, relocation, etc., that increase capacity to produce in subsequent time periods._ ”

# **7 Appendix B. Quantity and prices in disaster aftermaths**

Figure B1 is a classical quantity‐price plot, showing the long‐term demand and supply curves for a goods or service aggregated at the macroeconomic level. The green line is the demand curve: it shows how the quantity demanded by consumers decreases when the price increases. The blue curve is the pre‐disaster (long‐term) supply curve: it shows how the quantity produced increases with the price (or, equivalently, the price asked by producers to produce a given quantity). The point A is the intersection of demand and supply and shows the price and quantity that clear the market (at that point, supply equals demand). The economic “surplus” is the area ADE. The consumer surplus is the upper area (AFE) and the producer surplus the bottom area (AFD).

The red line is the short‐term supply curve after the disaster: because of damages, production cannot exceed Q1, and the supply curve becomes vertical at this level (whatever the price consumers are ready to pay, producers cannot produce more than Q1). If the market clears, the new equilibrium is reached at point B, where the quantity is reduced to Q1 and the price increases to p1.

In classical economic reasoning, the move from A to B is reducing the pre‐disaster surplus ADE to the area BCDE. In other terms, the surplus loss is ABC. But this would be correct only if firms were deciding to reduce production from Q0 to Q1 _and to reduce the expenditure needed to produce Q0_ . If firms decided to reduce investment and production capacity from Q0 to Q1, they would reduce their sales from p0Q0 to p1Q1, and reduce their production expenses from the area ODAQ0 to the area ODCQ1.

> 16 Note that these ripple‐effects can be particularly large when critical infrastructure (e.g., electricity networks) is affected. An extreme case is when terrorist attacks target critical infrastructure, see (Rose et al., 2007a); in this case,  can be extremely high, much higher than for natural disasters.

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<!-- Start of picture text --> Price p<br>E Supply curve<br>(post‐disaster)<br>Supply curve<br>(pre‐disaster)<br>B<br>p1 A<br>p0 F<br>Demand curve<br>pC C<br>D<br>O<br>Q1 Q0 Quantity Q<br><!-- End of picture text --> _Figure B1. Supply and demand curves in the pre‐ and post‐disaster situations._ When a disaster hits, however, the sales are reduced from p0Q0 to p1Q1, but the expenses are not reduced from the area ODAQ0 to the area ODCQ1. This is because firm expenses have three components: intermediate consumptions, capital expenses, and labor. The reduction in intermediate consumptions translates into a loss of output for another firm, so at the macroeconomic level, a reduction in intermediate is not a gain. Reduction in labor expenditures is also a loss for workers, so it should not be counted at the macroeconomic level (unless, workers can find instantaneously another job, which is mostly not the case in disaster contexts). Finally, when a disaster reduces the production capacity from Q0 to Q1, it does not do so by reducing capital expenses, but by damaging existing capital. If a firm at a loan to pay for its capital (factory, equipment, etc.), the capital is destroyed but the loan is still there. In other terms, the capital expenditures are not reduced by the disaster.

So to assess the disaster impact on welfare over the short‐term, it makes sense to consider the area Q0ABQ1 (and not the area ABC as in classical long‐term welfare analysis). If the price is unchanged, then the impact can be estimated as p0Q (i.e. the loss of output). If the price change is significant, then it is necessary to take it into account, but it is challenging because the shape of the form Q0ABQ1 is complex. A linear assumption would simply be: (p0 + p1) Q/2.

36
to <u>t—to</u> AY(t) = ~~——r~~ 1 ~~+~~ dKe _f-toNis <!-- Start of picture text --> Production<br>DISASTER<br>Baseline production<br>(no disaster)<br>l+a_orN :<br>— AK —<br>Lt 3<br>1l+a<br>—raAk ;<br><!-- End of picture text --> <!-- Start of picture text --> (with disaster) .<br>to to +N Time<br>Time when 95%<br>of damages are<br>repaired<br><!-- End of picture text --> exp(—3) ~ AY(N) = 0.05 AY(t,) AY = ~~14a TN~~ u 2
not accounted for in disaster consequences since it corresponds to benefits that could have been captured in the absence of the disaster, through a classical stimulus policy.

The length of the reconstruction period will depend on many characteristics of the affected economy, including (1) the capacity of the sectors involved in the reconstruction process (especially the construction sector); (2) the flexibility of the economy and its ability to mobilize resources for reconstruction (e.g., the ability of workers to move to the construction sector, see Hallegatte, 2008); (3) the openness of the economy and its ability to access resources (e.g., skilled workers and materials for reconstruction); (4) the financial strength of private actors, households and firms, and their ability to access financial resources for reconstruction, through savings, insurance claims, or credit; and (5) the financial strength of the public sector and its ability to access financial resources to reconstruct (see the very thorough analysis of financing options in developing countries in Mechler, 2004).<sup>19</sup> With discounting at a rate r, the net present value of output losses is<sup>20</sup> :

> 19 Specific instruments such as contingent credit lines help with reconstruction financing. See for instance on the World Bank’s Cat‐DDO, http://treasury.worldbank.org/bdm/pdf/Handouts_Finance/CatDDO_Product_Note.pdf.

> 20 The variable noted with x� are the net present value of the future fluxes of x�t� .

38