Evaluation of Economic Impacts from Flood Damages Using Hybrid Input-Output Analysis

Flooding is a common issue in many countries and can cause extensive damage to residential areas, agricultural and livestock areas, and public facilities. These damages impact the local economy directly and create unexpected demand for goods and services. The consequences of flood damage are marked by the ambiguity of how it changes the production of local economies. For this reason, our study implements the use of the hybrid I-O analysis to evaluate the economic effects of flood damages. The flooding scenario in Kochi prefecture, Japan simulated from the inundation model was selected to demonstrate 10 the analysis. The influences of flood damages were divided into two stages, the garbage cleaning stage and the reconstructing stage; these two stages lead to the different scenarios based on the different activities. It was found that in total, flood damages could stimulate economic growth when the positive effect of reconstruction activities surpass the negative effect of garbage cleaning activities.

In addition, the cost of garbage cleaning works is estimated based on the total flood damages, about 8% of the total flood damages. This cost is spent on manpower and trucks that are necessary for clearing obstacles and cleaning garbage. The garbage cleaning cost emerges in an early stage soon after the flood struck the damaged area and the reconstruction cost appears thereafter. Therefore, the calculation will be presented in two steps and each step shows how each cost for garbage cleaning and reconstruction can be evaluated using hybrid input-output analysis. 5

Garbage Cleaning Sector in Physical Submatrix
It might be intriguing that we imagine the new activities that appeared from the flood damages as a new industry. It is a fact that floods destroy buildings, facilities, household furniture, and electrical appliances, resulting in additional demand for goods and services for garbage cleaning and reconstructing the damaged area [Li et al., 2013, Hallegatte, 2008. Since the garbage 10 cleaning service and reconstruction for flood damages do not exist in the existing economy, the new process of consuming resources and producing the product has to be set up in the I-O table. A virtual sector called the garbage cleaning sector is then added to the existing economy in response to the new activities. This sector consists of three processes including truck and other transportation use, manpower use, and garbage cleaning service. Trucks and manpower are the main resources which already existed in the local economy. If the resources in the local economy are limited, these two resources are cut-off from 15 the local economy to serve the demand for garbage cleaning activities. The truck is cut-off from the transportation sector directly. However, there is no manpower sector in the existing economy so we must create a new manpower sector especially for this purpose (section 4.2). The assumption has been made that the manpower required for the garbage cleaning activities is only the construction manpower which is likely to perform similar works. The manpower is then cut-off from the manpower row, where the construction sector is previously consumed. The garbage cleaning sector produces the garbage cleaning service 20 as a product and this product is provided in return to the local economy or the main sector that is affected by flood damage including the agricultural sector, public work sector, and household and government demand.

Manpower Row and Column Setting
The garbage cleaning activities likely require only manpower, excluding the materials or goods to accomplish the work.
Regarding the I-O table, the manpower sector's consumptions and products prior exist in the value-added and final demand. 25 Thus, we intend to migrate this manpower to the inter-industry region as the manpower sector to assess the impact of the manpower used for garbage cleaning activities (Table 2). where the total production (X) is the summation of each vector of input and output. The manpower is separated from valueadded directly to create a new row of the manpower sector. For the manpower sector column, we divide it from the final 5 demand column by the following equation: where X1 is the economic sector's total production, Z11 is the economic sector's goods that consumed by the economic sector, Z12 is the economic sector's goods that consumed by the manpower sector, f1 is the economic sector's final demand, Z21 is the manpower sector's goods that consumed by the economic sector, and VA1 is the value-added that consumed by the economic sector. By solving the above equation, the manpower sector's column is expressed by the following equation: 10 The manpower products that once belonged to the construction sector are now cut-off as the garbage cleaning demand. As a result, some negative and positive values present in the manpower consumption consuming column (Table 3).

Calculating Procedure of Hybrid I-O Analysis
The calculation procedure inside hybrid I-O analysis is separated into pre-process, intermediate-process, and post-process ( Fig.2). The pre-process is the first step for changing the economy's structure in response to the garbage cleaning activities including constructing P, Cu, Cd, and M, and utilizing a cut-off method to transfer the resources and products from M to Cu and Cd. The garbage cleaning sector purchases of goods and services from the economy for garbage cleaning purpose. This 5 action could be determined by the cut-off resources, where the resources in M are transferred to Cu. Then, the cost of removing the garbage and clearing space is responsible for the main affected sectors such as the agricultural sector and public work, and non-sectors such as the local government and households. It is certain that the government, private sector, and households unavoidably have to purchase the goods and services for resuming the condition of the city; otherwise, people could not continue their daily life. Therefore, the resources are purchased and utilised by the garbage cleaning sector for their activities, 10 while the burden cost is left to be paid by the affected economic sector and the final demand.
The intermediate process is to maintain the technical coefficient value after cut-offs. When the cut-off was made from M to Cu and Cd, the resources that input to the economic sectors are reduced equivalent to the cut-off portion and transfer to garbage cleaning input. The remaining input to the economic sectors affects the change of technical coefficient value. The technical 15 coefficient represents the trade ratio from one sector to another or it is the structure of the economy. The technical coefficient cannot be changed rapidly, but it is gradually changed due to technological advancement. To do this, we firstly separate M from the other submatrices. Then, we detach the row and column of the sector that is cut -off their products to Cd. Thus, this sector will not affect by the following process. Regarding the cut-off resources to Cu, the loss in the economic sector's input induce a loss in the total production. To maintain the existing economic structure, the technical coefficient before the cut-off 20 resources is used to recalculate with the reduced total production. After that, we reattach the row and column of the cut-off product sector. As a result, the loss through the economic sector regarding the necessary resources for garbage cleaning activities appears in the loss in total production. Finally, the post-process determines the rise of demand for additional goods and services initiated by the flood damages. The 25 reconstruction cost is used to purchase goods and services to resume the good condition of building structure, furniture, and household appliance, industrial equipment, and shop and company equipment to the operational condition. This expenditure is considered as the economic stimulant. For instance, Kochi prefecture residents buy their new furniture and appliances and repair their houses and garages. Private companies and shops also refurbish and redecorate the working space, while the government has to invest in maintaining all public facilities such as roads, bridges, and other utilities. Therefore, the additional 30 demand for reconstructing the facilities is placed on the related economic sector's final demand, which results in a benefit to the local economy [Okuyama, 2007].

Calculation Results and Discussion
The results from the calculation are presented in two steps: [1] the negative economic effect of garbage cleaning cost in the early stage, and [2] the total economic effect when the reconstruction cost is included, and this cost is considered a benefit to stimulate the growth of the local economy.

Negative Effect from Garbage Cleaning Activities 5
Flood damages initiate the loss in the economy's total production by acquiring the goods and services from manpower and transportation sectors for garbage cleaning. The garbage cleaning cost appears in the early stage of flood and must be paid by some economic sectors, households, and the government. Consequently, the demand for goods and services of some economic sectors temporarily decreases to meet the requirement for garbage cleaning activities. Regarding the calculation process, the technical coefficient pre-adjustment method is applied to firstly conserve the existing resource distribution ratio by keeping 10 the technical coefficient constant and secondly to examine the economic effect of resource shifting to the garbage cleaning activities. As a result of using the technical coefficient pre-adjustment method, the influence of the cut-off resources from the Yen). In total, the economy loses about -2,056 million Yen for garbage cleaning purposes. When the resource demand for producing the product of these sectors shrinks or is cut-off to the garbage cleaning sector, it simultaneously initiates the loss of the other economic sectors' resource demand for production.

Total Economic Impact Influenced by the Flood Damages
Flooding destroys houses, shops and companies, agriculture areas, public facilities, and the surrounding landscape. The 5 reconstruction cost must be spent to recover the damage from the flood. This cost is considered to be the factor for vitalising the economy because it initiates increasing demand for goods and services from some economic sectors. Households, private investment and the government have to spend their money on maintenance and renew their facilities. Regarding the calculation, the additional demand for goods and services is allocated to final demand in the hybrid I-O table.
10 Fig. 4 displays the total production of each economic sector influenced by the effect of both garbage cleaning and reconstructing activities by comparing with the existing total production of Kochi prefecture, in Japanese Yen. It appears that the manpower sector gains the highest benefit of about +9,858 million Yen in total production. Public work and business services also obtain significant gains at about +6,948 and +4,475 million Yen of total production respectively. Lumber, wood products and furniture, petroleum and coal, iron, steel and non-ferrous, precision machinery, construction, trading, and 15 transportation production also increase at least +2,000 million Yen. There is a major loss in the medical and healthcare sector of about -1,458 million Yen in total production, while personal services, public services, food and beverage, agricultural, and fishery also suffer minor losses.

Discussion
The garbage cleaning activities acquire the manpower and trucks from the economic sectors to perform the cleaning services.
The resources taken away by these activities initiate a loss in the related economic sectors, which results in a shrink of the economy's total production. On the contrary, the additional demand for reconstructing the damaged facilities mobilizes the growth of the economy. Many goods and services are needed by private investors, households, and governments, which 10 consequently increases the total production of related economic sectors. In summary, the flood damages inflict direct loss from garbage cleaning activities, resulting in -2,056 million Yen of depletion of the economy's total production, while the reconstruction cost stimulates economic growth by +52,670 million Yen. The total economy's production increases by 50,614 million Yen and accounted for 1.024% of the overall total production. Damages are an unfortunate loss, but from an economic productivity perspective, it is also an opportunity for economic growth. The use of hybrid I-O analysis leads to the new model adjustment as well as the new finding of economic impact characteristics from flood damages. The manpower sector is newly created in response to the demand for garbage cleaning services, which is added as an extended economic sector. In value-added, the manpower exists in the form of the income for labor that each sector has to pay to produce goods. This income is later paid back to the economy as demand for goods and services for household living, which is allocated in the final demand. In the hybrid I-O table, the manpower sector's row is cut-off directly 5 equivalent to the labor compensation in value-added, while the manpower sector's column is cut-off from the final demand following equation 5. Noticeably, some values in the manpower sector's column are found negative. A negative value in the I-O table signifies a byproduct and it is also similar to the negative value presented in the manpower sector's column. If one observes the definition of negative value in the manpower sector's row, the negative value means that the manpower sector did not consume the products, but it produces the product instead. Referring to equation 5, if the final demand at a specific row 10 is higher than the value-added in the column of the same sector, the value in the manpower's column becomes negative. If we recognise Z21+VA1 as a value-added and f1 as demand for that specific sector, Z21+VA1<f1 means that people consume the products more than their capability of producing value-added. Each industry has positive and negative values in the manpower column; therefore, the total amount of the manpower column is zero. In case there is a negative value at the specific sector in the ordinary I-O table, it is a byproduct. In the same case of the hybrid I-O table, practically it is a negative demand, which has 15 the same effect of by-product to fulfill the final demand. It means that a large number of f1 is allowed by the negative value in this specific sector.
Public work, business services, and manpower sectors are benefited the most from the additional demand for reconstruction.
The public work sector gains this benefit directly through increasing demand for reconstructing the public facilities. On the 20 other hand, the manpower sector and business service sector are induced by indirect demand for goods and services from the other economic sector's consumption. The products of these two sectors are the major requirement for the other economic sector, so an increase in demand for reconstruction significantly impacts the additional number of products required in the economy, and thus indirectly induces the manpower sector and business service sector.

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The structure of the hybrid I-O analysis also allows one to trace the resource use in each process. The resources from economy M to Cu for the garbage cleaning work, the process of utilizing resources of the garbage cleaning sector, as well as the product of the garbage cleaning sector that is fed back to the economy in Cd, can be visualised. Moreover, by the hybrid I-O method, the resources transfer from the economy to use in the new sector's process can be analyzed in both the physical unit and monetary unit. This advantage of unit transition leads to the finding of implementation on a unit price adjustment. When the 30 resource is cut-off from M and presents in Cu, the unit price of each resource can be individually adjusted regardless of the prior unit price. This price can represent the new price of the resource that the new sector purchases and further uses for their process of generating products. It is yet to be present in this study, but it is likely that the unit price for garbage cleaning cost https://doi.org/10.5194/nhess-2020-298 Preprint. Discussion started: 3 November 2020 c Author(s) 2020. CC BY 4.0 License.
is not equivalent to the existing price purchased by the prior sector. In that case, the advantage of hybrid I-O analysis of unit price adjustment could play an important role in assessing the flood damages.

Conclusions
In conclusion, this study presents the new concept of using the hybrid I-O analysis to evaluate the economic impacts of flood damages in the form of the new garbage cleaning sector. The flood damages are described through two new scenarios, the 5 garbage cleaning stage and the reconstructing stage, in which each scenario appears in a different period. The cost of garbage cleaning and reconstruction are recognised as significant factors to assess the economic impacts of flood damages. The flood damages stimulate economic growth where the positive effect of reconstruction activities is overthrown by the negative effect of garbage cleaning activities. The benefits to the local economy's total production are reflected by the additional total production of each economic sector. The study proves the usefulness of hybrid I-O analysis, not only for assessing the 10 economic sector, but also for adapting the analysis to other scenarios such as flooding. The use of the model could enhance the damage prediction and also enable the government and policymakers to find alternative solutions for mitigating damages.