From Direct Losses to Indirect Losses

Different actors in climate change risk management process are interested in different types of information. City planners and flood protection designers are mainly interested in landfall probabilities; insurers focus on average annual direct losses and probabilities of exceeding a given level of damages. But national and local governments, when they perform cost-benefit analyses to assess the desirability of new infrastructure, cannot consider only direct losses. The communities they represent, indeed, suffer not only from direct loss but from total losses, which include many indirect effects including production losses during the recovery and reconstruction periods (see, e.g., Tierney, 1995; Pielke and Pielke, 1997; Lindell and Prater, 2003; Hallegatte et al., 2007b).

Direct cost can be amplified (i) by spatial or sectoral propagation into the rest of the economic system over the short-term (e.g., through disruptions of lifeline services) and over the longer term (e.g., sectoral inflation due to demand surge, energy costs, insurance company bankruptcy, larger public deficit, or housing prices that have second-order consequences on consumption); (ii) by responses to the shock (e.g., loss of confidence, change in expectations, indirect consequences of inequality deepening); (iii) by financial constraints impairing reconstruction (e.g., low-income families cannot finance rapidly the reconstruction of their home); and (iv) by technical constraints slowing down reconstruction (e.g., availability of skilled workers, difficulties in equipment and material transportation, difficulties in accommodating workers).

To measure the impact of these effects, Hallegatte et al. (2007b) introduced the Economic Amplification Ratio (EAR), which measures the ratio between the overall economic cost and the direct loss due to a disaster. While this ratio is less than one for small-scale disasters, EAR is found, using a simple model, to increase dramatically for large-scale disasters like the New Orleans floods. This increase arises mainly from propagation effects between sectors or regions, and from the addition to capital replacement costs of the production losses during the reconstruction phase. For example, if a $1 million plant is destroyed and immediately rebuilt, the loss is equal to $1 million; if its reconstruction is delayed by one year, the total loss is the sum of the replacement cost and of the value of one year of production. For housing, the destruction of a house with a one-year delay in reconstruction has a total cost equal to the replacement cost of the house plus the value attributed to inhabiting the house during one year. The value of such production losses, in a broad sense, can be very high in some sectors, especially when basic needs are at stake (housing, health, employment, etc.).

To carry out cost-benefit analyses in a fair way, indirect losses must be estimated in spite of the difficulties to do so. A model able to provide an assessment of a fraction of these indirect losses will now be proposed and applied, as an illustration, on the landfall of Katrina on Louisiana. This case study illustrates how indirect losses can be estimated, and how difficult this assessment is.

Assessing Indirect Losses Case Study on Katrina and Louisiana

The assessment of the total cost of disasters is the topic of intense research (e.g., Rose et al., 1997; Brookshire et al., 1997; Gordon et al., 1998; Cochrane, 2004; Okuyama, 2004; Rose and Liao, 2005; Greenberg et al., 2007). In this literature, however, nobody pretends to reproduce all the mechanisms involved in disaster aftermaths. In the present article, only two types of indirect effects are accounted for: (i) the propagation effect between sectors; (ii) the reconstruction duration and the production loss during this period.

Many models used to assess disaster consequences are based on Input-Output (IO) models, which are powerful tools to assess how a shock, on one or several sectors, propagates into the economy through intermediate consumption and demand.

In Hallegatte (2008a), a modified IO model has been proposed: the Adaptive Regional Input-Output (ARIO) model, which is based on IO tables and a hybrid modelling methodology, in the spirit of Brookshire et al. (1997). This dynamic model takes into account changes in production capacity due to productive capital losses and adaptive behaviour in disaster aftermaths. Importantly, the model takes as an assumption that the Louisiana economy will eventually return to its pre-storm situation. Of course, the uncertainty in results is still very high and the model results must be considered only as indicators of the disaster seriousness.

As an illustration, this model is applied to the landfall of Katrina on Louisiana. Following the classification by the Bureau of Economic Analysis, the Louisiana economy is constituted of 15 sectors: (1) Agriculture, forestry, fishing, and hunting; (2) Mining; (3) Utilities; (4) Construction; (5) Manufacturing; (6) Wholesale trade; (7) Retail trade; (8) Transportation and warehousing; (9) Information; (10) Finance, insurance, real estate, rental, and leasing; (11) Professional and business services; (12) Educational services, health care, and social assistance; (13) Arts, entertainment, recreation, accommodation, and food services; (14) Other services, except government; and (15) Government. From the U.S. Input-Ouput tables, a regional one for the state of Louisiana is built. Sector losses due to Katrina have been evaluated by the Committee on the Budget U.S. House of Representatives, and are reproduced in Figure 5.

From these sectoral losses, the model simulates the reconstruction of the region, as shown in Figure 6. In its upper panel, this figure provides the evolution of the ''regional economic production", i.e. the sum of the value added by all sectors of the economy. In the bottom panel, one can see that the model predicts a reconstruction period of about 10 years.

Comparisons with available data in Louisiana are proposed in Hallegatte (2008a). The orders of magnitude reproduced by this model are realistic, with an instantaneous production reduction of 8 percent after the shock, and a production

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Fig. 5 Sector-per-sector estimated losses due to Katrina in Louisiana

0 24 48 72 96 Time (months)

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Fig. 6 Louisiana output variation, in percent of pre-Katrina output (upper panel); and reconstruction needs in U.S.$ billion (bottom panel)

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Fig. 6 Louisiana output variation, in percent of pre-Katrina output (upper panel); and reconstruction needs in U.S.$ billion (bottom panel)

loss over the four last months of 2005 of 2.8 percent of annual Gross State Product. This production loss underestimates the observed growth loss, which is close to 4.5 percent according to BEA data when exogenous growth is removed. This underestimation is likely to arise from the model inability to reproduce the New Orleans disorganization in the months following Katrina, which is caused by lifeline interruptions, bankruptcy, and supply-chain issues. Additionally, the political and practical issues linked to the reconstruction of New Orleans are not taken into account.

This model also provides the evolution of the production of each sector over time, as shown in Fig. 7. This figure shows (i) the generalized decrease in production following the event (the horizontal dark region); (ii) the large increase in

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Fig. 7 Louisiana output variation, sector per sector (X-axis) as a function of time in quarter (Y-axis), in percent of pre-Katrina output. Dark colors show decrease in production; light colors show increase in production

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Fig. 7 Louisiana output variation, sector per sector (X-axis) as a function of time in quarter (Y-axis), in percent of pre-Katrina output. Dark colors show decrease in production; light colors show increase in production production in the construction sector (sector #4) caused by the large demand for reconstruction, and the subsequent production increase in the sectors that are large suppliers of the construction sector (e.g., the retail trade sector, sector #7). The sum of these production losses (positive and negative) over the entire reconstruction period is estimated at $28 billion.

Also, the model provides an assessment of the "production loss'' in the housing sector. Indeed, the decrease in housing services because of damaged houses and buildings has to be taken into account. The model, because it reproduces the reconstruction period and duration, can assess the total loss in housing service production. In the Katrina's case, the model estimates this loss at $19 billion. As a consequence, the total production loss (sector production plus housing services) is estimated at $47 billion, i.e. 44% of direct losses. Total losses, i.e. the total production loss plus the part of production that has to be dedicated to reconstruction instead of normal consumption, are estimated around $154 billion. The Economic Amplification Ratio, the ratio of total losses to direct losses, is, therefore, equal to 1.44.

Importantly, this model cannot capture all indirect losses. For instance, it does not assess which portion of customer demand will be satisfied and which fraction will be rationed. Such an assessment is not easy, because customers will be more or less able to turn to external producers, depending of the category of goods and services that is considered. If customers are rationed, there is an additional loss that is not included in the present analysis. Also, it is essential to repeat that the model assumes that the economy will return to its initial situation, which is not automatic. In the New Orleans case, it is even quite unlikely. It is difficult to do better, however, because the final state will depend on political choices that cannot be modelled. Finally, this model does not include losses outside the affected region

(e.g., through higher energy prices in the New Orleans case), and social and psychological costs, which are nevertheless very important (e.g., disruption of social networks, psychological trauma, loss of cultural heritage).

But the most interesting aspect of this model is the fact that it allows to relate various amount of direct losses to the corresponding total losses. Figure 8 shows that, for the same sectoral structure than Katrina (shown in Fig. 5), total losses are increasing nonlinearly with total aggregated direct losses. When direct losses are below U.S. $40b, indirect losses are negative. It means that, for most disasters, the response of the economic system damps the shock and limits the economic consequences. But when direct losses exceed U.S. $40b, the economic system is not able to react efficiently any more. Indeed, a larger disaster causes more damages and reduces production capacity in the sectors involved in reconstruction. Because of the interplay of these mechanisms, the Economic Amplification Ratio (EAR), the ratio of total losses to direct losses, increases with the size of the disaster. For a disaster like Katrina, with about $100 billion direct losses, the EAR is found equal to 1.44. For a disaster with $200 billion direct losses, this ratio reaches 2.00, with total costs twice as large as direct costs.

This relationship between direct losses and indirect losses has been estimated for the state of Louisiana in 2005, and for the consequences of Katrina. Of course, results would be different for different states, for instance because the production capacity of the construction sector would be different. Results would also be different for different disasters, for instance because affected sectors would not be the same.

Fig. 8 Indirect losses as a function of direct losses, for a disaster with the same sectoral structure than Katrina. The equation in black is the polynomial regression of indirect losses to direct losses, for this case study

Regardless, results would be different if considering an economy in 2030 or 2080, as needed to assess climate change impacts. It seems out of reach, however, to predict how IO tables will change over several decades. Considering the huge uncertainty that would surround any attempt to do so, it seems reasonable to use the present IO table, possibly scaled to account for economic growth, assuming that all sectors will growth at the same rate. In the present analysis, however, we assess how future hurricane risks would impact the present-day economy, disregarding the impact of economic growth. This assumption corresponds to the suppression of the right-hand arrow in Fig. 1, from the top box on scenarios to the bottom box on indirect impacts. Even though this method is not satisfying, it is the only one available: one can doubt it will soon be possible to project IO tables over decades with enough accuracy to perform this type of analysis on future economies.

In the following, in spite of these large uncertainties, the nonlinearity in total losses is assumed valid for all regions and all disasters, and the Katrina's case is used as a benchmark to provide a first-order estimate of how the changes in direct losses suggested in Section 4 could translate into changes in total losses.

Assessing Indirect Losses

Using a polynomial regression on the relationship between direct and indirect losses calculated for Louisiana and Katrina, one can assess the total losses due to the 3000 synthetic tracks created by the Emanuel's model (see Section 3 and 4). In the present climate, averaged direct losses were estimated at 1578 million U.S.$ per landfall and 980 million U.S.$ per track. These values translate into averaged total losses estimated at 1426 million U.S$ per landfall and 885 million U.S$ per track. These values are lower than direct losses only, because the economic system is able to limit total losses and make them lower than direct losses for the weakest hurricanes, which constitute the large majority of hurricanes. Indeed, indirect losses are positive only for hurricane causing direct losses in excess of $40b, and only 8 landfalls cause such losses in the 3000 synthetic tracks created for the present climate. The taking into account of indirect effects leads, therefore, to a reduction in the mean annual economic losses due to hurricanes.

In the modified climate, since hurricane intensity is increased according to the Emanuel's model, total losses are larger than in the present climate: the model estimates averaged total losses at 2272 million U.S.$ per landfall and 1448 million U.S.$ per track. When considering indirect losses, the Emanuel's model suggests, therefore, that a 10-percent increase in potential intensity would translate into a 59 percent increase in total economic losses.

Like in Section 4, when were considered only direct losses, the most worrying result concerns the very rare, most intense hurricanes. According to the present analysis, with all its drawbacks including the use of a single hurricane model, a 10-percent increase in potential intensity would double the likelihood of a hurricane landfall causing more than $50 billion of damages in the U.S.

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