• Economic impacts;
  • input-output model;
  • natural disasters;
  • reconstruction


  1. Top of page
  2. Abstract
  9. References

Estimates of the cost of potential disasters, including indirect economic consequences, are an important input in the design of risk management strategies. The adaptive regional input-output (ARIO) inventory model is a tool to assess indirect disaster losses and to analyze their drivers. It is based on an input-output structure, but it also (i) explicitly represents production bottlenecks and input scarcity and (ii) introduces inventories as an additional flexibility in the production system. This modeling strategy distinguishes between (i) essential supplies that cannot be stocked (e.g., electricity, water) and whose scarcity can paralyze all economic activity; (ii) essential supplies that can be stocked at least temporarily (e.g., steel, chemicals), whose scarcity creates problems only over the medium term; and (iii) supplies that are not essential in the production process, whose scarcity is problematic only over the long run and are therefore easy to replace with imports. The model is applied to the landfall of Hurricane Katrina in Louisiana and identifies two periods in the disaster aftermath: (1) the first year, during which production bottlenecks are responsible for large output losses; (2) the rest of the reconstruction period, during which bottlenecks are inexistent and output losses lower. This analysis also suggests important research questions and policy options to mitigate disaster-related output losses.


  1. Top of page
  2. Abstract
  9. References

Natural disasters have multiple impacts. Beyond their direct impacts on human lives and assets, they also perturb the functioning of the economic system, leading to additional losses, often referred to as indirect losses or higher order losses.[1-5] Evidence from past disasters shows that indirect effects can represent a significant—or even dominant—share of total losses.[6-8] And modeling exercise results are consistent with these findings, highlighting in particular the role of key infrastructure and services.[9, 10] In a cost-benefit framework for risk management, additional costs from indirect losses can be an important justification for more ambitious risk mitigation measures. As suggested by Haimes,[11, 12] risk management cannot be designed and implemented if these secondary effects are not accounted for, and a system (or holistic) view is needed. Better risk assessment—and particularly for indirect impacts—thus appears as a requirement for better risk management.

Investigating indirect economic impacts has, however, a second justification, also directly connected to risk management. It would be too costly—or even impossible—to protect against all risks. A hazard that exceeds protection capacity and triggers a disaster is thus always possible. In such a case, the overall cost of the disaster will depend on the ability of the economic system to cope with the shock at minimum cost, and to recover quickly from it—that is, on the resilience of the economic system. Beyond their focus on direct impacts—human losses, asset destructions—risk management policies can thus reduce risk by targeting and reducing indirect and secondary impacts, through an increase in system resilience. But doing so would require a much better understanding of the origin of these indirect losses. Identification of critical infrastructure to prioritize action [13, 14] is, for instance, a major input in systemic risk management. More generally, a better understanding of the mechanisms of disaster secondary impacts would help define effective risk management strategies.

This article contributes to the research on risk assessment tools that are better able to account for indirect losses and secondary impacts, and to represent the mechanisms that explain them. Even though uncertainty in the matter is very large, it is expected that better tools would allow to explore the determinants of indirect losses, to include them in risk assessment—even in crude ways—and to design specific policy actions to mitigate them.

In the present analysis, indirect losses are defined as output losses, that is, losses from reduced economic value added. These indirect losses can be added to direct economic losses (i.e., the value of the damages to assets that need to be repaired or replaced).[5] For instance, the volcanic eruption in Iceland in 2010 did not cause any asset losses (no direct losses), but it interrupted air transport for a week and reduced the output of the entire air transport sector.1 A damaged factory after a hurricane cannot produce until it is rebuilt or repaired. A hurricane, therefore, causes direct losses (the damages to the factory) and indirect losses (the loss of output before the factory is repaired); the same level of direct losses can lead to various levels of indirect losses, depending on how fast reconstruction can be completed. Businesses may stop producing as a result of lifeline interruptions (water, electricity, communication) or because transportation issues make it impossible for workers or customers to access their workplace.[6-8, 15] Finally, business perturbations may also arise from production bottlenecks through supply chains and intermediate consumption.[16]

As mentioned in Hallegatte,[17] these ripple effects can be labeled “backward” or “forward.” Backward ripple effects arise when the impact propagates from clients to suppliers, that is, when a business cannot produce, and thus reduces its demand to its suppliers, reducing their own activity (even in the absence of direct damages). Forward ripple effects arise when the impact propagates from suppliers to clients, that is, when a business cannot produce and thus cannot provide its clients with inputs needed for their own production process.

This article focuses on these interindustry interactions and on their role in natural-disaster aftermaths. It proposes a new version of the ARIO model, which was first presented in. Ref. 17. This new version is better able to represent production bottlenecks through the taking into account of inventories and production dynamics. Section 'EXISTING MODELING APPROACHES' summarizes existing tools to assess output losses due to natural disasters and highlights their shortcomings. Section 'THE ARIO-INVENTORY MODEL' presents the new version of the model (ARIO-inventory) and explains how it answers some of the identified needs. Section 'RESULTS ON HURRICANE KATRINA' presents a case study on Louisiana and the landfall of Katrina, and sensitivity analysis. Section 'CONCLUSION' provides some concluding remarks.


  1. Top of page
  2. Abstract
  9. References

Postdisaster interindustry ripple effects have been the topic of intense research.[18-21, 3, 22, 23, 9, 10] In these studies, the economy is described as an ensemble of economic sectors that interact through intermediate consumptions.

Some models are based on the input-output (IO) linear assumption,[24] 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.[19, 21, 25, 22, 23, 26, 27] In this framework, producing one unit in the automotive industry requires a fixed amount of energy, water, steel, financial services, transport, etc. Even though the IO model is originally a demand-driven model,[28, 3] it has been used to model disasters, which are largely supply-side shocks. Extensions of IO models have been used to include supply constraints and production dynamics within IO-model disaster assessments.[22, 23] The IO approach is based on the idea that, over the short term, the production system is fixed, and that local production capacity is constrained by existing capacities, equipment, and infrastructure. This approach assumes that the nonaffected capital cannot increase its production to compensate for lost production from affected capital. Only imports from outside the affected region and postponement of some nonurgent tasks (e.g., maintenance) can create a limited flexibility over the short term.

Other models are based on the computable general equilibrium (CGE) framework, which assumes that changes in relative prices balance supply and demand.[10, 29] In this framework, there is no rationing in the economic system. A disaster-caused destruction of production capital in a sector translates into a reduction in the production of the corresponding commodity, and into an increase in its price. This increase in price leads in turn to a reduction in its consumption, restoring the equality between demand and the reduced production. Moreover, in CGE models based on Cobb-Douglas or constant elasticity of substitution production functions, the production technology is not fixed and short-term input substitution is possible: if an input is scarce, production can be carried out using less of it, and more of other inputs.

Because of socioeconomic inertia, transaction costs, and antigouging legislation,[30] adjustment through prices appears unlikely in disaster aftermath. In postdisaster situations, little change in prices has been observed, except in the construction sector. But prices and elasticity in CGE can also be seen as an artificial way of modeling flexibility. In that case, prices in the model should be considered as proxies for scarcity, more than actual observable prices. The CGE-model flexibilities (the signaling effect of prices, reduction in demand, and substitution in the production process) smooth any exogenous shock and mitigate disaster consequences.

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[29]). It is also likely that CGE models are optimistic, even in the long run, because prices cannot adjust perfectly and instantaneously, and because technical limits to substitution are not adequately represented in production functions.

Natural disasters and their reconstruction phases are medium-term events, spanning from the first hours of the shock to years of reconstruction after large-scale events. Some authors have looked for intermediate approaches to natural disaster modeling, trying to find a common ground between IO and CGE. Rose and Liao[10] and Rose et al.[29] use a CGE framework, but with a lower substitution elasticity to take into account the fact that substitution is more limited over the medium term than over the long term. Other authors have developed IO models that address previous IO-model shortcomings by introducing explicit supply constraints and production flexibility.[22, 23] In Ref. 17, an IO model is complemented by a flexibility in IO coefficients. These coefficients are modeled dynamically, assuming they vary in response to scarcity indicators (namely, the ratio of production over total demand), to represent additional hours by workers, increased capacity, and the increased use of imports when local production is impaired.

Modelers face three main difficulties in representing the economic consequences of natural disasters. The first one is the representation of network-shaped industries (electricity, water, transport) in a more explicit manner, to take into account their specificities. Gordon et al.,[8] Cho et al.,[31] and Tsuchiya et al.,[15] among others, go in this direction.

The second difficulty lies in the aggregation level of these models, in which economic sectors, that is, thousands of businesses located in different places, are treated as a unique producer. Taking into account the multiplicity of producing units, their location, and their explicit supply chains would allow for a much more realistic representation of natural disaster consequences and for the accounting of intraindustry interactions, which is impossible with sector-scale models. Several papers investigate this issue and propose modeling approaches to account for these effects.[21, 32-35, 16]

The third difficulty is related to the role of inventories, production dynamics, and the representation of supply shortages.[22, 23, 36, 37] Some inputs are absolutely necessary for production, and a short interruption can cause significant perturbation in production. Examples are electricity, water, fresh goods, and all other goods that are required for production and cannot be stocked. Other inputs are also necessary for production, but they can be stocked, and a short interruption in supply does not create large difficulties. An example is steel and tires for automakers, which are indispensable but stockable. Finally, other inputs are not absolutely necessary for production, and reasonably long interruptions can be managed. This is the case, for instance, of many business services, education, and professional training and—to a certain extent—maintenance.

Inventories matter because they influence bottlenecks in the production system. They introduce an additional—and critical—flexibility into the system. MacKenzie et al.[27] find very different impacts of the 2011 Japanese earthquake and tsunami, depending on whether inventories are included or not in the analysis. Investigating inventories is also interesting because modern production organization tends to reduce the use of inventories with production-on-demand and just-in-time delivery. Added to other trends (e.g., outsourcing, reduction in the number of suppliers), these changes may make each production unit more dependent on the ability of its suppliers to produce in due time the required amount of intermediate goods. As a result, these changes may increase the overall vulnerability of the economic system to natural disasters, in a tradeoff between robustness on the one hand, and efficiency in normal times on the other hand.[16]

This article proposes a modified version of the ARIO model described in a previous paper[17] to account for inventory effects in the production system. This version also appears more satisfying than the previous version in the way it models production bottlenecks and the impact of input scarcity on the production system.


  1. Top of page
  2. Abstract
  9. References

The ARIO model is the adaptive regional input-output model. This model has been used on Louisiana and New Orleans to investigate the cost of Hurricane Katrina in 2005, on Copenhagen to assess the risks from coastal floods in a climate change context,[38] on the Sichuan region to assess the cost of the 2008 Wenchuan Earthquake,[39] and—in a slightly modified version—to assess flood risks and climate change impacts in Mumbai.[40]

In its initial version, the model has a one-month time step, and no inventories. The new version presented here has a one-day time step and introduces an inventory dynamics, which is not present in classical IO models.2

The modeling strategy is inspired by Levine and Romanoff,[41-44] who introduced the sequential interindustry model (SIM) framework to evolve from the classic static IO model to a dynamic model. Doing so requires the introduction of inventories and specific demand dynamics, and has been used already in disaster assessment.[22, 23, 36, 37]

3.1. Model Principles and Equations

Production in each economic sector depends on (i) observed demand, which depends on the orders it receives from its clients (households and other sectors); (ii) input availability, which depends on supplier production and the level of inventories; and (iii) its own internal production constraints (i.e., productive capital). In this version, labor is not considered as a possible constraint. The following description only describes changes with respect to the model presented in the previous paper.[17]

We assume that Y is the output vector of the different sectors and A is the IO matrix, that is, the matrix that describes the quantity each sector is providing (or, equivalently, purchasing) to other sectors. The coefficient inline image is the consumption of commodity j by the production process of sector i. The production is used to satisfy the demand for intermediate goods and final demand. The equilibrium equation is then:

  • display math(1)

where C is the vector of final demands and Y the equilibrium production. Classically, the optimal production is:

  • display math(2)

where Y0 would be the production if production capacities were not bounded and without inventory constraints. In the present model, however, each sector production capacity will be taken into account, and the impacts of inventories and input availability on demands will be modeled.

3.1.1. Inventories and Demand Model

We define inline image as the total demand to the jth sector at the time t. It includes household final demand, government consumption, business investments, and interindustry demands (i.e., intermediate consumption demand). Each sector produces commodities by drawing from their commodity inventories. They have then to order new inputs to their supplying sectors in order to restore their inventories. The inventory levels at the end of each time step are used to determine the demands to supplying sectors.

We assume that the ith sector has an inventory inline image of the commodity produced by the jth sector. Some commodities, for instance, those produced by the manufacturing sector, can be stocked, while it is almost impossible to stock electricity. For simplicity, nonstockable goods—like electricity—are modeled assuming that their inventories cannot be larger than what is needed to produce during three days.3 It means that, if electricity or water is shut down, production in the affected area will be stopped only a few days later. This is not perfect, but it significantly simplifies the model. Also, it can be interpreted as the flexibility from the use of generators, batteries, and small water reservoirs in case of lifeline interruptions.

The demand from the ith sector to the jth sector is designed to restore the inventory inline image to a target level inline image, equal to a given number of days inline image of intermediate consumption, at the production level needed to satisfy total demand (or the maximum production, considering existing production capacity). The target inventory level is given by the following equation:4

  • display math(3)

where inline image is the production capacity of the ith sector, as defined by Equation (6).

The orders inline image from the ith sector to the jth sector j then reads:

  • display math(4)

The parameter inline image is the model time step (i.e., one day). The variable inline image is the actual production of sector i (see Equation (11)). So, inline image is the amount of commodity j that has been used in the production process of the sector i during the current time step. The first term of the RHS of Equation (4) represents thus simply the orders needed to compensate for the current consumption of commodity j by sector i. The second term of the RHS of Equation (4) represents the orders that make the inventory converge toward its target value, that is, toward inline image days of target consumption. The parameter inline image is the characteristic time of inventory restoration, which is assumed identical in all sectors (except for nonstockable commodities). The influence of this parameter will be analyzed in Section 'Sensitivity Analysis'

This modeling provides the total demand directed toward each sector j for the next time step, that is, at inline image, by adding all demands from individual sectors, plus final demand inline image, reconstruction demand inline image, and exports inline image,

  • display math(5)

The modeling of inline image, inline image, and inline image is detailed in Ref. 17. This modeling of demand makes it possible to represent backward ripple effects: if a sector produces less, then Equation (4) shows that it will demand less from its suppliers, thus reducing their own production.

3.1.2. Production Model

In the absence of supply-side constraint, each sector i would produce at each time step t the exact level of demand inline image. But production can be lower than demand either (i) because production capacity is insufficient or because (ii) inventories are insufficient as a result of the inability of other sectors to produce enough (forward propagation). The production capacity of each sector depends on its stock of productive capital (e.g., factory, equipments), and on the direct damages to the sector capital (e.g., a sector that suffer from disaster damages can produce less).

The capacity and supply constraints are described by the following relationships:

  1. Limitation by production capacity. Independently of its suppliers, the production capacity inline image of the ith sector reads:

    • display math(6)

    where inline image is the pre-event production of this sector, assumed equal to the normal production capacity. The variable inline image is the reduction in productive capacity due to the disaster, directly because of the disaster (e.g., the volcano ash case) or through capital destructions. Like in the previous version of the model, we assume that if a disaster reduces the productive capital of the industry i by x%, then the production capacity of this industry is also reduced by x%,

    • display math(7)

    where inline image is the stock of productive capital in sector i, and inline image the amount of damages to this sector-productive capital. The variable inline image is the overproduction capacity; its modeling is the same as in Ref. 17 and is recalled in Section 'Overproduction Capacity'.

    In absence of an inventory constraint, the production in sector i would be:

    • display math(8)
  2. Limitation by supplies. Production can also be limited by insufficient inventories. It is assumed that if inventories are lower than their required levels, then production is reduced. Each supplying sector j creates an additional constraint if the corresponding inventory is lower than a share ψ of its required level inline image, which is given by:

    • display math(9)

    where inline image is the required consumption flux of commodity j to produce the level of production the previous time step.5 If the inventory is lower than the required level, it is assumed that production is reduced following:

    • display math(10)

    The actual production inline image is given by the minimum of all sectoral constraints:

    • display math(11)

    This modeling follows the same principles as Barker and Santos,[36, 37] but aims at taking into account the heterogeneity in disaster losses and impacts: when a sector production is reduced by x% by disaster losses, it is unlikely that all production units have their production reduced homogenously by x%. Instead, as shown by Tierney,[7] impacts are heterogeneous and a few businesses are likely to be responsible for most of the decrease in production. In the same way, when a sector inventory is lower than its optimal value, it is likely that the inventory of some businesses are very low or even empty, causing production problems, while other businesses have their inventories at normal levels and can keep producing normally.

    If this model, setting inline image amounts to assuming that a reduction by x% in a sector inventory (w.r.t. to the required inventory level) represents a homogenous situation in which all businesses have an inventory reduced by x% and can keep producing until the sector inventory inline image is empty. In such a situation, an inventory shortage by x% (with respect to the required level) leads to no production reduction until inline image; in the latter case, production has to stop.

    Setting inline image amounts to assuming that a reduction by x% in a sector inventory (w.r.t. to the required inventory level) represents a heterogeneous situation in which x% of the businesses have an empty inventory and stop producing, while other businesses are at (or above) their required inventory level and can keep producing. To represent such a situation, an inventory shortage by x% (with respect to the required level) leads to a reduction by x% in production.

    The choice of ψ is therefore a crucial one that represents assumptions about scales and heterogeneity in the economic system and in disaster direct impacts. First, the choice of ψ may be different if one models a small economy that is entirely affected by the event (ψ would then be low), or a large economy that finds one of its regions affected (ψ would then be larger). Second, this choice depends on the economic structure.[16] If all businesses are connected to all businesses, all business inventories would be reduced equivalently after a shock, and inline image. If businesses have only one supplier in each other sector, and if the disaster creates heterogeneous impacts, then the impact on inventory will be very heterogeneous and ψ will be close to one. Considering the importance of this parameter, a sensitivity analysis is carried out in Section 'Sensitivity Analysis'.

The vector inline image is the vector of actual production by each sector, taking into account the two production constraints. These constraints then propagate into the economy: if a sector reveals itself unable to produce enough to satisfy the demand, it will both (i) ration its clients and (ii) demand less to its suppliers. These two effects, forward and backward ripple effects, affect the entire economy.

3.1.3. Overproduction Capacity

The overproduction capacity is modeled with the variable inline image (see Equation (6)). This modeling assumes that when production is insufficient, the variable inline image increases toward a maximum value αmax, with a characteristic time inline image:

  • display math(12)

The term inline image is a scarcity index.6 This modeling implies that overproduction capacity can increase up to αmax, in a time delay inline image, in response to production shortages. When the situation is back to normal, this overproduction capacity goes back to one, with the characteristic time inline image,

  • display math(13)

where inline image is the overproduction capacity before the disaster, assumed equal to one.

3.1.4. Market Modeling, Rationing Scheme, and Inventory Dynamics

When a sector is not able to produce enough to satisfy the demand, and in the absence of an optimal price response to restore the production-demand equality like in a CGE model, producers have to ration their clients. To model this effect, it is necessary to introduce a rationing scheme.

In our framework, in absence of market equilibrium, demand can be larger than actual production (see Equation (11)):

  • display math(14)

where inline image is the normal final demand, inline image is the reconstruction demand, and inline image is the export demand. From these different demand and supply, the actual sales and purchases must be balanced, however,

  • display math(15)

Some agents, therefore, must be rationed.[45] The rationing scheme gives the sales and purchases of each agent, depending on the demands and supplies of all the agents. In the present case, since we are interested in disasters, there is only underproduction and the suppliers can sell all their production while clients may only get a fraction of their demand. Assumptions on rationing are extremely important: to maximize economic output, households should be rationed before other industries. Indeed, when an industry is rationed by $1, it cannot create value and the loss in output is larger than $1; when a household is rationed by $1, the output loss is only $1. In an optimal world, therefore, the rationing scheme should prioritize other industries, and this is what was modeled in Ref. 17.

In practice, however, doing so can be impossible because an economic sector produces heterogeneous goods destinated either to final demand or to other industries. If businesses are highly specialized, there is no flexibility in the system: if one business cannot produce, households will be rationed if the business produces commodities for households and other businesses will be rationed if the business produces commodities for intermediate consumption. And even for homogeneous goods, it is not always possible to prioritize other businesses: when a road is destroyed by a hurricane, it cannot be used by either businesses or households, and the capacity of the transport system is reduced equally for final and intermediate demands.

We thus assume that businesses are highly specialized and we introduce a proportional rationing scheme:[45] if a sector reduces its production by x%, then households and other industries receive only inline image% of what they demand.7

For interindustry demands, it means that

  • display math(16)

And for final demands:

  • display math(17)
  • display math(18)
  • display math(19)

Since each sector order depends on the demand it observes (see Equation (4)), there is flexibility in the use of production in this model: sectors in which the demand is higher also demand more to other sectors, and receive therefore a larger quantity of supply as a result of the proportional rationing.

In the model, the actual sales of sector i to sector j, that is, inline image, are those that increase inventories of the sector j from one time step to the next one,

  • display math(20)

where the term inline image is the increase in inventory thanks to purchases from the supplier i, and the last term is the decrease in inventory due to the commodity consumption needed to produce the amount inline image.

3.1.5. Rest of the Model

The rest of the model is unchanged compared with Ref. 17, with two important exceptions. First, the housing sector was considered separately from the IO table and the other economic sectors in Ref. 17; in the new version, losses in the housing sector are included in the IO matrix, within the sector “finance, insurance, real estate, rental, and leasing.” Second, the flexibility of the economic system is modeled by the inventories, and the dynamics of the IO table coefficients and of the final demand is not present anymore in the new version. This means that the inventory modeling potentially represents more than the effect of inventories, but also the use of imports, flexibility in the production system (e.g., the possibility to delay maintenance), and the possibility of rescheduling production. This choice makes it easier to calibrate the model: what is needed is information about how long a sector can keep producing when another sector reduces its production. For instance, one could survey businesses, asking how long they can manage an interruption in utility services (probably a very short duration), an interruption in manufacturing goods supplies (probably a few weeks), or an interruption in construction-sector services (probably several years).


  1. Top of page
  2. Abstract
  9. References

To investigate the behavior of the model and the role of inventories, we apply it to the landfall of Hurricane Katrina in Louisiana in 2005. This experiment is not meant to reproduce precisely the post-Katrina dynamics, since many major mechanisms are missing in the model, including the massive migration outside the affected area and the large infusion of external funding (especially from the federal U.S. government). Instead, its objective is to analyze the model dynamics and get a better understanding of the role of inventories and heterogeneities in postdisaster situations.

4.1. Data and Parameters

Economic data are the same as in Ref. 17, with two major differences. First, as already stated, the housing service is now included in the table. Second, new estimates of the amount of productive capital in each sector have been produced. In Ref. 17, a unique ratio of sector productive capital to sector value added was used in all sectors. In this new version, U.S.-scale data on the amount of private and government capital, from the Bureau of Economic Analysis, are used to assess national-sector-scale ratios of productive capital to value added. These ratios are then used for Louisiana, assuming that the structure of each economic sector is similar in Louisiana and in the United States as a whole. These ratios are reproduced in Table I.

Table I. Ratios of Productive Capital to Value Added in the 15 Sectors of the Louisiana Economy, and Direct Losses Caused by Hurricane Katrina (see text for details)
 RatioDirect Losses
 Capitalfrom Katrina
Sectorto VA(US$m)
Agriculture, forestry, etc.2.9262
Mining and extraction5.115,000
Wholesale trade0.6404
Retail trade1.11,027
Transportation and warehousing2.75,000
Finance, insurance, real estate, etc.6.922,000
Professional and business services0.5408
Educational services, health care, etc.1.11,053
Arts, recreation, accommodation, etc.1.2769
Other services, except government1.2364

No data are available on the distribution of damages to productive capital among sectors. The Congressional Budget Office produced estimates in broad categories: 17–33 billion US$ in housing; 5–9 US$ in consumer durable goods; 18–31 US$ in the energy sector; 16–32 US$ in other private-sector businesses; 13–25 US$ for the government. Taking the conservative side of these estimates, these losses were distributed among the different sectors according to their respective size to assess productive capital losses in each sector. Housing losses and consumer durable goods were included in the financial and real estate sector; energy sector losses were distributed in the utilities and mining and extraction sectors ($5 billion and $15 billion, respectively); government losses were distributed in the energy, transport, and government sectors; other private-sector losses were distributed in all other sectors, following their respective productive capital. All losses are reproduced in Table I. Aggregated direct losses amount to $63 billion, and are significantly lower than estimates used in the previous paper[17] ($107 billion).

Parameter values are presented in Table II. The large uncertainty in all of these values must be acknowledged, and a sensitivity analysis on these parameters is provided in Section 'Sensitivity Analysis'.

Table II. Parameter Values
inline image100%
inline image1 year
inline image90 days
inline image30 days

4.2. Impacts of Inventories on the Cost of Katrina

The total cost of Katrina in Louisiana is lower in this new model version, with output losses amounting to $11 billion. In the previous paper,[17] the estimate was $42 billion. One fraction of the difference arises from including housing losses in the IO table (instead of a separate treatment), from changes in the loss distribution, from using different parameters, and from the change in rationing scheme, which introduces production bottlenecks in the economic systems. But most of the change arises from more optimistic estimates of direct losses ($63 billion vs. $107 billion of direct losses) and from the the introduction of sector-scale capital-to-VA ratios (in Table I): since capital-to-VA ratios are large in highly affected sectors, the change from economy-wide capital-to-VA ratios to sector-scale ratios is mitigating final output losses.

The dynamic effects are represented in Fig. 1. Just after the shock, the production is reduced by the decrease in production capacity due to destruction of productive capital (equipment, factories, infrastructure, etc.), but without sectoral interactions. Rapidly, however, sectoral bottlenecks are responsible for a drop in production that lasts about eight months. The manufacturing sector becomes first a bottleneck for the economic system and reduces the total economic output of all other sectors. This is due—in part—to the increase in demand in this sector, driven by reconstruction needs. In response to this underproduction, the production capacity of the manufacturing sector starts to increase. After about 10 months, the manufacturing sector stops being the main bottleneck, and the transportation sector becomes the limiting factor of the economic system, until about one year after the shock.


Figure 1. Dynamics of value added (VA) losses in Lousiana after Hurricane Katrina, as estimated by ARIO-inventory.

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The recovery and reconstruction period is thus distributed in two periods: during the first year, there are large output reductions due to reduced production capacity and cross-sectoral forward ripple effects; after that, and until full reconstruction, output losses are much lower and are only due to the reduction in production capacity (with no remaining forward ripple effects).

After about two years, total output is larger than before the disaster, due to the combined effect of higher demand (linked to reconstruction) and increased capacity (linked to the overproduction capacity). Compared with the previous model,[17] reconstruction is carried out more rapidly, in less than five years.

In this assessment, indirect losses include gains in reconstruction sectors (especially the construction sectors) and large losses in other sectors. There are winners and losers in disaster aftermath, and the aggregate loss is not a good proxy for welfare and economic losses at the sector, business, and household levels (see also Section 'Total Amount of Direct Losses').

4.3. Sector Production and Bottlenecks

To get a better understanding of the model dynamics, it is interesting to focus on a few sectors and investigate their behavior. In this section, we focus on the agriculture and construction sectors; see Fig. 2. These sectors are chosen because their dynamics are different and they illustrate possible constraints to production.


Figure 2. Dynamics of production in the agriculture sector (left-hand side panel) and the construction sector (right-hand side panel), and the role of demand, production capacity, and inventory constraints. Where actual production is below capacity and demand, it is because inventories are binding. The figure shows that different constraints are binding at different stages of the reconstruction period.

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In the agriculture sector, demand (the dashed red line (colors visible in online version)) is significantly reduced by the disaster (because other industries cannot produce and reduce their purchase of agricultural goods), but the decrease in production capacity is larger than the decrease in demand. Production (the dotted blue line) is first constrained by production capacity (the straight black line), which is directly reduced by disaster losses. Thanks to reconstruction and the overproduction capacity process, however, this limit increases over time. After a few months, inventories become the binding constraint when insufficient supplies from the manufacturing sector cause a reduction in agricultural production. In that case, actual production is below production capacity and below demand (the dotted line is below the straight and the dashed lines). In practice, the manufacturing sector has a reduced production capacity because of disaster-related capital losses and sees an increased final demand because of reconstruction needs. As a consequence, it cannot satisfy all demands and it rations all sectors, including the agriculture sector, which in turns reduces its production. Reconstruction in the manufacturing sector progressively reduces this constraint, which is replaced after about a year by a constraint from the transportation sector, until it disappears about 12 months after the shock. At that point, the reduced production capacity in the agricultural sector again becomes the binding constraint, until the system returns to its initial conditions.

In the construction sector, demand becomes very large after the disaster because of reconstruction needs. At first, production capacity in the construction sector is the main constraint on production: equipment and capital are lacking to satisfy the demand. Then, production capacity increases in view of this large demand (thanks, for instance, to imports of equipment), and is no longer the binding constraint. After a few months, inventories become the binding constraint on production. As in agriculture, the manufacturing sector and then the transportation sector supplies become insufficient, thereby reducing the construction-sector output. After four years, however, reconstruction is almost completed and reconstruction demand starts to decrease. Demand in the construction sector then becomes lower than production capacity and inventory capacity (both of which have increased significantly over the years), and the construction sector is then in an overproduction situation. At that time, demand becomes the binding constraint, until production capacity and inventories return to their predisaster levels.

4.4. Sensitivity Analysis

Uncertainty in natural disaster economic losses is extremely large, and many important mechanisms are not well understood. For this reason, models cannot be trusted without a careful analysis of the robustness of their results. To do so, we carry out a sensitivity analysis on the model's most important parameters. Beyond an estimate of result robustness, this analysis can help us understand what are the most important drivers of disaster economic losses and provide insights into future research needs.

4.4.1. Production Reduction Parameter ψ

As explained in Section 'Production Model', the parameter ψ describes how production is reduced when inventories are insufficient. It would be equal to zero if all disaster impacts were homogeneous and if all businesses in a sector produced substituable goods and services. It would be equal to one if disaster impacts were completely heterogeneous (a few businesses suffer from most of the losses) and if businesses produced nonsubstituable goods and services, even within a given sector. Fig. 3 shows that model results are extremely sensitive to this parameter, which is not surprising since the ability to substitute for affected production is key for economic robustness. In particular, if ψ is low enough (here lower or equal than about 0.7), substitution is sufficient to make it possible for all sectors to satisfy interindustry demands, and there is no cross-sector forward ripple effect. The only binding constraint in this situation is thus the reduced production capacity due to disaster damages. It ψ is larger, then substitution does not allow to satisfy interindustry demand and total losses soar.


Figure 3. Dynamics of production in the Louisiana economy, for five values of the parameter ψ, which depends on heterogeneity in the production system.

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This extreme sensitivity shows what is most important for future research, namely, an assessment of how the remaining production from nonaffected businesses can be directed to the most productive uses. The possibility to do so depends largely on how one business production can be replaced by another business production and on the existence of signals to affect production to the most productive uses. In a general equilibrium framework, one could assume that prices could play this latter role, but their ability to do so can be questioned over the short term. In the absence of an efficient price signal, it is an open question what alternative signal could convey this information, considering how complex it is to determine an optimal use of resources.

4.4.2. The Time of Inventory Restoration inline image and the Target Inventory Level inline image

Inventory parameters are also extremely important in determining output losses (see Fig. 4). Sensitivity analysis shows that output losses decrease with the target inventory level in days of demand (inline image) in the stockable sectors (90 days in the reference simulation). Output losses decrease to $7.5 billion for a target inventory level larger than or equal to 120 days: in this case, there is no cross-sectoral forward ripple effects, and reduction in production capacity is the only cause for losses (this case is comparable with the case with inline image). On the opposite, the modeled economy collapses if the initial and target inventories are only of 30 days. This result suggests (i) that there is a threshold in the amount of losses the economy can cope with in the absence of external support and (ii) limited inventories increase the vulnerability of the economy to exogenous shocks like natural disasters. The collapse occurs when all sectors have consumed their input inventories and cannot keep producing, making it in turn impossible for their client sectors to produce. This type of collapse is common with ecological systems. The same type of result is found with inline image. Output losses are lower with rapid inventory restoration (i.e., lower inline image), and the system collapses if inline image is too large.


Figure 4. Dynamics of production in the Louisiana economy, for five values of the parameters inline image, which describe the size of inventories (left-hand side panel), and for five values of the parameter inline image, the characteristic time of the inventory restoration (right-hand side panel).

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This extreme sensitivity can appear surprising. In fact, it is closely related to the modeling of the rationing process. With proportional rationing, indeed, what a sector receives depends on how much it demands. This is why this scheme can be manipulated: by exaggerating its demand, an economic actor can obtain more. In the model, interindustry demands and final demand compete for scarce output, and final demand increases because of reconstruction needs. If inline image is small, then interindustry demands increase rapidly as soon as inventories are below their target level, and sectors capture more of the available production (and consumption gets less) than with a large inline image. So, the parameter inline image also describes the possibility to concentrate available production toward interindustry demands (at the expense of final demand). With a small inline image, more of the production is channeled toward sectors with highest demand (at the expense of consumption), thereby helping maintain production.

4.4.3. Total Amount of Direct Losses

All previous simulations were carried out using an estimate of direct losses from Hurricane Katrina in Louisiana. There is, however, a large uncertainty in direct loss estimates, and this uncertainty needs to be taken into account. Even more importantly, it is useful to assess the model sensitivity to direct losses, to estimate whether different mechanisms work for different types of disasters. It is very likely that small and large disasters do not lead to comparable economic responses and consequences. This assumption is supported by previous modeling work[17] that found a nonlinear dependency of indirect losses with respect to direct losses: aggregated indirect losses were negligible for direct losses lower than $50 billion and increasing nonlinearly beyond this threshold.

This assumption is also supported by econometric analysis. Econometric analyses at a national scale have indeed reached different conclusions on the impact of disasters on growth. Some researchs[47, 48] suggest that natural disasters have a positive influence on long-term economic growth, probably thanks to both the stimulus effect of reconstruction and the productivity effect (the embodiment of higher productivity technologies thanks to capital replacement; see Hallegatte and Dumas[49]). Others[50-54] suggest exactly the opposite conclusion, that is, that the overall impact on growth is negative. As suggested by Cavallo and Noy[55] and Loayza et al.,[56] the difference between both conclusions may arise from different impacts from small and large disasters, the latter having a negative impact on growth while the former enhance growth. Investigating model response for small versus large disasters may help understand this difference.

To do so, simulations were carried out with “scaled” disasters, that is, disasters with the same sectoral distribution of direct losses, but different levels of aggregate losses. In the left-hand side panel of Fig. 5, simulations are carried out with disasters causing losses between 10% and 150% of Katrina losses. The simulations show that for “small” losses (direct losses lower than or equal to 50% of Katrina), output is reduced by direct losses, but is not affected by cross-sectoral interactions (thanks to the substitution assumed possible with the parameter inline image). For larger losses, output is affected both by reduction in production capacity and by cross-sectoral interactions. It can be seen in the figure that the reduction in output increases rapidly with direct losses.


Figure 5. Simulations for different amounts of direct losses (left-hand side panel) and VA changes (total, in the construction sector, in the other sectors) as a function of the total amount of direct losses (right-hand side panel).

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This reduction is confirmed by the right-hand side panel of Fig. 5, which shows the direct losses (in red) and the total indirect losses (in blue) (as a function of direct losses). The nonlinearity identified in the previous model version[17] is still present with this new model version. For direct losses amounting to $95 billion, the model estimates output losses about $80 billion, to be compared with only $11 billion output losses for $63 billion of direct losses (i.e., output losses are multiplied by 7 for direct losses increased by 50%). For disaster causing more than $100 billion, output losses also exceed $100 billion.

To help interpret the figure, value added changes in the construction sector are separated (in light blue) from the other sectors (in purple). In the construction sector, there are gains (i.e., increase in value added) for small-enough disasters (up to about $110 billion of direct losses), and losses for larger disasters. This result suggests that, for small disasters, the construction sector benefits from higher demand and can increase production; for large disasters, the construction sector cannot benefit from the higher demand because cross-sectoral ripple effects constraint its production (e.g., need for transportation and materials). This difference may explain—at least partly—why different econometric studies found positive and negative impacts of disasters on growth.


  1. Top of page
  2. Abstract
  9. References

In the debate between IO models, which do not allow any flexibility in the economic system, and CGE models, which assume that substitution and markets make the economic system highly adaptive, this article proposes a middle-ground solution. Based on an IO structure, the ARIO-inventory model explicitly represents production bottlenecks and input scarcity, models flexibility in production capacity in case of scarcity (measured with an explicit scarcity index whereas CGEs use the price as a scarcity indicator), and introduces inventories for additional flexibility in the production system. This modeling strategy makes it possible to distinguish between (i) essential supplies that cannot be stocked (e.g., electricity, water) and whose scarcity can paralyze all economic activity; (ii) essential supplies that can be stocked at least temporarily (e.g., steel, chemicals), whose scarcity creates problems only over the medium term; and (iii) supplies that are not essential in the production process (e.g., some business services) and whose scarcity is problematic only over the long run and are therefore easy to replace with imports. Since prices and substitution play a large role over the longer run, one major limit of this model is the assumption of fixed IO coefficients and the use of a scarcity index over both the short and long terms. These assumptions appear acceptable in the immediate disaster aftermath, but are more questionable over the entire reconstruction period. Ideally, a model should be able to represent the continuum between the short term, with fixed technologies and sticky prices, and the long term, with technological substitution and market mechanisms. Also, the model focuses on production and available consumption, but cannot assess explicit welfare losses without modeling consumer utilities.

Using this model, we estimate the output losses due to Katrina at around $11 billion, for direct losses of approximately $63 billion. More interesting than this numerical estimate, which is found to be extremely sensitive to many model parameters, the model identifies two periods in the disaster aftermath: the first year during which cross-sectoral forward ripple effects, that is, production bottlenecks, are responsible for a larger loss of output, and the rest of the reconstruction period, during which output losses are much lower and bottlenecks are inexistent.

Sensitivity analysis identifies parameters that require a precise calibration and additional work, possibly at the sector scale. Heterogeneity and substitution capacity are key parameters in disaster assessments. The model reaches quite different results depending on whether or not sectors are supposed to be homogeneous, implying that production reduction in one factory can be compensated by production in other factories (modeled through ψ in the model). Another question is the potential for intraindustry interactions, which are difficult to account for without an explicit representation of supply chains, such as in Ref. 16. Also, the possibility of targeting more of the remaining production toward other industries (instead of final demand) reduces losses (modeled through inline image in the model). In the same way, focusing existing production toward reconstruction (instead of “normal” demand) accelerates reconstruction and reduces total losses. But the possibility to do so depends on the homogeneity in produced goods and services within each sector (e.g., is it possible to divert the manufacturing-sector production dedicated to final consumers to another industry?). Differentiating final consumption and interindustry consumption in different sectors in the model would be a good solution to solve this problem, and this change will be done in a follow-up model version.

More generally, determining the optimal distribution of goods and services is indeed extremely difficult since it requires taking into account all supply chains and business relationships in the economic system, that is, a perfect knowledge of the economic network. One possibility is to assume that prices include all existing and necessary information and make it possible to optimize the use of remaining production capacities; this assumption drives results from CGE models. Over the short term, however, prices are unlikely to include all information. Prices cannot play this role because they are influenced by many mechanisms. Natural disasters are indeed situations of abnormal solidarity and assistance, and different economic, governance, and political processes take place. For instance, price increases that reflect real scarcity will appear socially unacceptable in disaster aftermath, as shown by the recent multiplication of (quite popular) antigouging laws in U.S. states. Moreover, as mentioned by Rapp,[30] antigouging regulations can make economic sense because of (i) imperfections in how prices are determined, especially in disaster aftermath, and their response asymmetry; (ii) damages to the payment system in affected areas that can paralyze consumer markets. More research is needed on the role that prices play in channeling production toward its most efficient use, and on the other processes that influence rationing (e.g., the role of existing long-term business relationships, decisions by public authorities). Assessing the efficiency of these information-transfer mechanisms is crucial to assess disaster consequences.


  1. Top of page
  2. Abstract
  9. References

The authors want to thank Nicolas Naville and Fanny Henriet for their assistance in this research, and Patrice Dumas, Celine Guivarch, Julia Kowalewski, and three anonymous referees for their comments on a previous version of this article. This research is supported by the European Community's Seventh Framework Program (FP7/2007-2013) through the WEATHER project (

  1. 1

    In fact, some of this output interruption has only been postponed.

  2. 2

    The model is available upon request to the author of this article.

  3. 3

    A model with a time step of one day cannot reproduce mechanisms with time scales shorter than a few days.

  4. 4

    In this equation, and in the following ones, variables depend on the time step t, which is omitted for simplicity.

  5. 5

    The required level of inventory inline image and the target level of inventory inline image are different. The former represents the amount of input necessary to produce (see a discussion of its impact on production below), while the latter represents orders to replenish inventories. The former takes into account constraints on other supplies, not the latter.

  6. 6

    In CGE models, scarcity information is included in prices, which drive substitution and other economic responses. Here, there are explicit scarcity indexes that drive all economic responses, including longer work hours and the replacement of impaired local production with imports.

  7. 7

    The problem of this rationing procedure is than it can theoretically be manipulated: an agent can declare a higher demand to increase his transactions. We assume that sectors declare their true demand, that is to say, the amount of intermediate good they actually need to satisfy their own demand. The rationing can also be modeled in a linear programming framework in which the objective is to maximize the regional output, as suggested in Cochrane,[46] but such an optimal distribution of resources represents a best-case scenario.


  1. Top of page
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