Cost-Benefit Analysis of Adaptation to Beach Loss Due to Climate Change in Japan

To measure economic effects of changes in environmental quality caused by climate change in Japan, we estimate beach loss damage costs in Japan and in each prefecture and evaluate the economic effectiveness of hypothetical adaptation measures to restore sandy beaches. For analyses, we use a computable general equilibrium model (CGE) that integrates a utility function with environmental quality factors as an independent variable derived from a recreation demand function in a travel cost method (TCM). We use future projections of beach loss rates in 2081–2100 based on ensemble-mean regional sea-level rise (SLR) for four Representative Concentration Pathway (RCPs) scenarios (RCP2.6, RCP4.5, RCP6.0, and RCP8.5). The main findings of our study are presented as follows. (1) In 2081–2100, beach loss damage costs were estimated respectively as 398.54 million USD per year for RCP2.6, 468.96 (m.USD/year) for RCP4.5, 494.09 (m.USD/year) for RCP6.0, and 654.63 (m.USD/year) for RCP8.5. (2) For all RCPs, six prefectures for which the cost–benefit ratio exceeds 1.0 were Kanagawa, Osaka, Hyogo, Hiroshima, Saga, and Kumamoto. Our hypothetical adaptation measure of an artificial beach enhancement is expected to be quite effective as a public works project in these prefectures.


Introduction
According to the fifth Assessment Report (AR5) published by the IPCC [1], the medium-term and long-term countermeasures are expected to accommodate the possible impacts of climate change. The Ministry of the Environment (MOE) in Japan has discussed planning for a climate change adaptation policy. Some research projects in Japan such as S-8 [2] have forecast climate change effects by region and provide support for adaptative countermeasures. Assessment of climate change effects and the effectiveness of adaptation measures based on nationwide and regional climate change projection are needed.
Numerous attempts have been undertaken to evaluate the economic effects of climate change. Their evaluation methods are classifiable into two approaches: A partial equilibrium approach and a general equilibrium approach. The former method includes a travel cost method (TCM) and a contingent valuation method (CVM). These methods have been applied in some studies to quantify the economic value of the natural environment and ecosystems and the value of statistical life. Since these methods are partial equilibrium approaches, however, economic effects of changes in natural environment by climate change and environmental conservation policies on the whole economy cannot be captured. On the other hand, the latter method has a computable general equilibrium (CGE) analysis. Since a computable general equilibrium model explicitly formulates an objective function in economic agent, direct effects of climate change on economic activities of agent can be captured. In addition, since a CGE model treats all markets in the economy, indirect effects of climate change on the entire economy through changes in the behavior of agents can be captured. Using a CGE model, however, to measure the economic effects of climate change on the natural environment and ecosystems, formulation of the effects on them and estimation of their parameters in a model are necessary. As described above, numerous studies of economic evaluation of climate change have separately been analyzed by two approaches. Therefore, comprehensive assessments in a general equilibrium framework must be made through explicit linkage between a partial equilibrium approach and a general equilibrium approach.
By applying a recreation demand function to a general equilibrium model, for water reallocation issues in Nevada in the United States, Seung et al. [3] analyzed the effects of water reallocation on some recreation sectors and the agriculture sector. However, since the recreation demand function used in their study does not account for the generalized transportation cost, it is not consistent with a utility function. Ciscar et al. [4] comprehensively evaluated the economic and physical effects of climate change on the natural environment, ecosystem, and human society in Europe by treating four sectors as physical effect terms: Agriculture, coastal zone, flood, and tourism. Although their study produced estimates of respective physical effects from projected climate data under conditions of socioeconomic scenarios, and evaluated the projected economic effects by the economic model, it has no theoretical consistency between estimates of physical effect terms and economic models. In a general equilibrium analysis of waste problems in Japan, Miyata [5] derived a utility function consistent with a pre-formulated demand function from solving the integrability problem, and integrated externalities such as waste into a CGE model. For the sandy beach loss caused by climate change, Sakamoto and Nakajima [6] and Nakajima and Sakamoto [7] developed a CGE model that has a utility function consistent with a recreation demand function in a travel cost method by solving the integrability problem. Then, we extend the mode of describing the framework by Nakajima and Sakamoto [7] to simulate more realistic climate change scenarios.
In Japan, although numerous studies such as those of Mimura et al. [8] and Udo et al. [9] have been made of the physical effects of sea level rise and the beach loss caused by climate change, little is known about the economic effects of beach loss and adaptation strategies against climate change. From Table 1, Ohno et al. [10] and Sao et al. [11] evaluated recreation values for a sandy beach in Japan using a travel cost method. The former used beach loss rates calculated by Mimura et al. [8] and estimated the prefectural damage cost of a sandy beach. The latter used beach loss rates by Udo et al. [9], and evaluated not only the prefectural damage cost but also the effect of adaptation measures to restore a sandy beach. Since both studies were based on a partial equilibrium approach, they were unable to treat effects on prices and income caused by changes in environmental quality attributable to climate change. On the other hand, Sakamoto and Nakajima [6], Nakajima and Sakamoto [7], and Sao et al. [11] estimated beach loss damage costs attributable to climate change using a CGE model incorporating a utility function consistent with a recreation demand function in the travel cost method. However, since these studies used future projections by Mimura et al. [8], their economic assessments of beach loss became outdated. Although Sao et al. [11] evaluated adaptation measures for beach loss, their CGE model in these studies had only three goods: Composite goods, gasoline, and an expressway used to visit a sandy beach for recreation. As one might expect, their model framework was quite unrealistic.  Therefore, we sought to measure economic effects of changes in environmental quality attributable to climate change in Japan. Results were obtained using a CGE model that integrates a utility function with environmental quality factors as an independent variable derived from a recreation demand function in a travel cost method (TCM), we aim to estimate the damage cost of beach loss in each prefecture and in Japan and to evaluate the economic effectiveness of hypothetical adaptation measures to restore sandy beaches.

Structure of Economic Model
We use the 2005 Input-Output table for Japan by MIC [15] as the reference dataset. Table 2 shows 30 sectors that we aggregated in our model. Economic influences comprise household, a production sector, an investment sector, government, and exports and imports.
2.1.1. Household Figure 1 shows the consumption structure of household in our computable general equilibrium (CGE) model, where index R is used as household consumption for visiting a sandy beach and index H is used as household consumption excluding that for visiting a sandy beach. The set of all affordable bundles that satisfy a consumer's budget constraint is derived from solving the basic problem of utility maximization. Then, consumption of the petroleum and coal products and transportation for visiting a sandy beach depends on a recreation demand function that incorporates travel cost (the petroleum and coal price, the price of goods and services supplied by the transport sector, and the value of time) and the sandy beach area. For details of derivation of utility function consistent with recreation demand function and definition of goods for visiting a sandy beach, see Appendices A and B.  Figure 1 shows the consumption structure of household in our computable general equilibrium (CGE) model, where index R is used as household consumption for visiting a sandy beach and index H is used as household consumption excluding that for visiting a sandy beach. The set of all affordable bundles that satisfy a consumer's budget constraint is derived from solving the basic problem of utility maximization. Then, consumption of the petroleum and coal products and transportation for visiting a sandy beach depends on a recreation demand function that incorporates travel cost (the petroleum and coal price, the price of goods and services supplied by the transport sector, and the value of time) and the sandy beach area. For details of derivation of utility function consistent with recreation demand function and definition of goods for visiting a sandy beach, see Appendix A and Appendix B.  Figure 2 shows that all production functions in the domestic production sector are assumed to have a nested function style. For the first step, labor and capital are aggregated into composite production factor using a Cobb-Douglas production function. As the second step, to produce the gross domestic output for the j-th production sector, the composite production factor is combined with intermediate inputs using a Leontief production function. In addition, the Cobb-Douglas production function allows us to describe substitution between labor and capital , while the Leontief production function does not between intermediate inputs and composite production factor [16].   Figure 2 shows that all production functions in the domestic production sector are assumed to have a nested function style. For the first step, labor L j and capital K j are aggregated into composite production factor VA j using a Cobb-Douglas production function. As the second step, to produce the gross domestic output Y j for the j-th production sector, the composite production factor is combined with intermediate inputs using a Leontief production function. In addition, the Cobb-Douglas production function allows us to describe substitution between labor L j and capital K j , while the Leontief production function does not between intermediate inputs X ij and composite production factor VA j [16]. J. Mar. Sci. Eng. 2020, 8, x 5 of 18 Figure 2. Structure of the production sector.

Government Sector and Investment Sector
The government sector and investment sector are assumed to have behaviors modeled by Hosoe et al. [16]. The government earns revenues from an income tax, production tax, and indirect tax. Then, the government spends them on purchases of goods proportionately with the constant expenditure share. The structure of investment sector is the same as that of the government sector. In accordance with Hosoe et al. [16], the investment agent collects funds from the household, the government, and the foreign sector. Then, this virtual agent purchases investment goods proportionately with a constant share.

Export and Import
In accordance with Hosoe et al. [16], Figure 3 portrays the structure of the substitution between imports and domestic goods and that of the transformation between exports and domestic goods. Regarding imperfect substitution between imports and domestic goods, we adopt Armington's assumption [17]. The i-th Armington-composite-good-producing sector aggregates domestic goods and imports into composite goods using a constant elasticity of substitution (CES) function. However, gross domestic output is transformed into domestic goods and exports using a constant elasticity of transformation (CET) function. Both parameters of elasticity of transformation and elasticity of substitution are assumed to be 2.0 exogenously.

. Government Sector and Investment Sector
The government sector and investment sector are assumed to have behaviors modeled by Hosoe et al. [16]. The government earns revenues from an income tax, production tax, and indirect tax. Then, the government spends them on purchases of goods proportionately with the constant expenditure share. The structure of investment sector is the same as that of the government sector. In accordance with Hosoe et al. [16], the investment agent collects funds from the household, the government, and the foreign sector. Then, this virtual agent purchases investment goods proportionately with a constant share.

Export and Import
In accordance with Hosoe et al. [16], Figure 3 portrays the structure of the substitution between imports and domestic goods and that of the transformation between exports and domestic goods. Regarding imperfect substitution between imports and domestic goods, we adopt Armington's assumption [17]. The i-th Armington-composite-good-producing sector aggregates domestic goods D i and imports IM i into composite goods Q i using a constant elasticity of substitution (CES) function. However, gross domestic output Y i is transformed into domestic goods D i and exports EX i using a constant elasticity of transformation (CET) function. Both parameters of elasticity of transformation σ DEX and elasticity of substitution σ DIM are assumed to be 2.0 exogenously. assumption [17]. The i-th Armington-composite-good-producing sector aggregates domestic goods and imports into composite goods using a constant elasticity of substitution (CES) function. However, gross domestic output is transformed into domestic goods and exports using a constant elasticity of transformation (CET) function. Both parameters of elasticity of transformation and elasticity of substitution are assumed to be 2.0 exogenously.

Scenario of Adaptation Measure for Restoring Sandy Beach
For hypothetical adaptation measures related to beach loss, we assume that after erosion of coastal areas caused by the sea-level rise, the coastal area can be restored to its earlier state by implementation of adaptation measures such as a public works project using artificial beach enhancement. From considerations of data availability and comparison with earlier studies, we chose to use an average adaptation cost per unit area assumed by Sao et al. [12] for the scenario of adaptation measures for restoring sandy beaches. Sao et al. [12] collected data including those of 92 public works in 33 prefectures related to artificial beach enhancement, and assumed the average adaptation cost per unit area as 215.96 USD/m 2 from available data for sandy beaches. However, since few public works projects are limited to artificial beach enhancement and since these projects include costs of protecting land unrelated to sandy beaches, it is noteworthy that the average adaptation cost that we assumed might be overestimated.
Finally, to estimate beach loss damage costs and to evaluate the economic effectiveness of hypothetical adaptation measures to restore sandy beaches, we measure the benefit as equivalent variation. For details of the definition of benefit, see Appendix C.  Figure 5 and Table 5 present prefectural damage costs because of the projected beach loss in four RCPs in 2081-2100. For any RCPs, damage costs of four prefectures (Okinawa, Kanagawa, Niigata and Hyogo) accounts for about 40% to about 45% of the total damage cost to Japan. As shown in Table 5, for RCP2.6, damage costs of these four prefectures were estimated respectively as 22.        Figure 6 and Table 6 show prefectural damage costs per unit area attributable to beach loss in four RCPs in 2081-2100. Prefectures for which the damage cost per unit area is high were Kanagawa, Niigata, Toyama, Fukui, Kyoto, Osaka, Hyogo, Wakayama, Okayama, Hiroshima, Saga, Kumamoto, and Okinawa. Especially, damage costs per unit area in prefectures in western Japan or along the Inland Sea tend to be higher. For RCP2.6, damage costs per unit area to the tenth highest prefecture were Saga, Kumamoto, Kanagawa, Osaka, Hiroshima, Hyogo, Okayama, Okinawa, Fukui, and Toyama in order from the highest, estimated as 138.47 USD per unit area to 723.26 (USD/m 2 ). For RCP8.5, damage costs per unit area to the tenth prefecture were Kanagawa, Saga, Kumamoto, Osaka, Okayama, Hyogo, Toyama, Hiroshima, Kyoto, and Wakayama, estimated as 178.34 to 765.76 (USD/m 2 ).

Economic Effects of Beach Loss
(a) RCP2.6 (b) RCP8.5    For uncertainty assessment, we calculated 21 beach loss scenarios in 2081-2100 using 21 CMIP5 models. For RCP4.5, damage costs were estimated respectively as an average of 491.06 million USD/year, a minimum of 385.72 (m.USD/year), and a maximum of 739.50 (m.USD/year). In addition, Figure 7 shows prefectural damage costs per unit area using 21 CMIP5 models. As shown in Figure 7, although results of Kanagawa and Toyama have a large variance, those of many other prefectures have a small variance. Figure 8 and Table 6 show cost-benefit ratios of adaptation policies for RCP2.6, for RCP4.5, for RCP6.0, and for RCP8.5 in 2081-2100. Prefectures in red in Figure 8 and shaded values in Table 6 have cost-benefit ratios larger than 1.0, i.e., the benefit from adaptation measures exceeds the cost because of beach loss. As described above, we assumed 215.96 USD/m 2 of the average cost per unit area as the adaptation cost to restore a sandy beach. The higher the future temperature becomes, the more numerous the prefectures for which adaptation measures are cost-effective become. Especially in four prefectures along the Inland Sea, which are Osaka, Hyogo, Okayama, and Hiroshima, our hypothetical adaptation measure as a public works project of artificial beach enhancement is quite effective.   Figure 8 and Table 6 show cost-benefit ratios of adaptation policies for RCP2.6, for RCP4.5, for RCP6.0, and for RCP8.5 in 2081-2100. Prefectures in red in Figure 8 and shaded values in Table 6 have cost-benefit ratios larger than 1.0, i.e., the benefit from adaptation measures exceeds the cost because of beach loss. As described above, we assumed 215.96 USD/m 2 of the average cost per unit area as the adaptation cost to restore a sandy beach. The higher the future temperature becomes, the more numerous the prefectures for which adaptation measures are cost-effective become. Especially in four prefectures along the Inland Sea, which are Osaka, Hyogo, Okayama, and Hiroshima, our hypothetical adaptation measure as a public works project of artificial beach enhancement is quite effective.

Discussion
We compare the results of beach loss damage costs attributable to climate change with those of earlier studies. As shown in Table 1, Ohno et al. [10], Sakamoto and Nakajima [6], Nakajima and Sakamoto [7], and Sao et al. [11] used the future projection of beach loss calculated by Mimura et al. [8] and estimated the damage costs of sandy beach because of the sea level rise from 30 to 100 cm. These earlier studies estimated damage costs of the sea level rise as 247 to 832 (m.USD/year). It is apparent that the results of our study are slightly lower than those of earlier studies. Especially, although differences between results of Ohno et al. [10] and our study are larger, it is likely that these results became overestimated since Ohno et al. [10] formulated damage costs of beach loss by a proportional relation between the frequency of visiting the sandy beach for recreation and the sandy beach area.
Sao et al. [12] and Nakajima et al. [13] used the future projection of beach loss by Udo et al. [9] and respectively estimated damage costs for RCP2.6 and RCP8.5. Sao et al. [12] estimated them as 254-284 (m.USD/year) in 2031-2050 and 426-494 (m.USD/year) in 2081-2100. One reason for the difference between results reported by Sao et al. [12] and those of our study is that our general equilibrium approach reflects price changes and income changes that are not considered in the definition of consumer surplus derived from the partial equilibrium approach. Consequently, it is apparent that beach loss damage costs in our study are slightly lower than those found in earlier studies.

Discussion
We compare the results of beach loss damage costs attributable to climate change with those of earlier studies. As shown in Table 1, Ohno et al. [10], Sakamoto and Nakajima [6], Nakajima and Sakamoto [7], and Sao et al. [11] used the future projection of beach loss calculated by Mimura et al. [8] and estimated the damage costs of sandy beach because of the sea level rise from 30 to 100 cm. These earlier studies estimated damage costs of the sea level rise as 247 to 832 (m.USD/year). It is apparent that the results of our study are slightly lower than those of earlier studies. Especially, although differences between results of Ohno et al. [10] and our study are larger, it is likely that these results became overestimated since Ohno et al. [10] formulated damage costs of beach loss by a proportional relation between the frequency of visiting the sandy beach for recreation and the sandy beach area.
Sao et al. [12] and Nakajima et al. [13] used the future projection of beach loss by Udo et al. [9] and respectively estimated damage costs for RCP2.6 and RCP8.5. Sao et al. [12] estimated them as 254-284 (m.USD/year) in 2031-2050 and 426-494 (m.USD/year) in 2081-2100. One reason for the difference between results reported by Sao et al. [12] and those of our study is that our general equilibrium approach reflects price changes and income changes that are not considered in the definition of consumer surplus derived from the partial equilibrium approach. Consequently, it is apparent that beach loss damage costs in our study are slightly lower than those found in earlier studies. Table 7 shows the number of prefectures for which the cost-benefit ratio exceeds 1.0 in the adaptation scenarios using 215.96 and 182.76 USD/m 2 as the average cost per unit area. Although the number of cost-effective prefectures between Sao et al. [11] and Sao et al. [12] is significantly different, Sao et al. [12] described that the difference between these studies resulted from the average adaptation cost per unit area. As described above, for the possibility that the average adaptation cost per unit area (215.96 USD/m 2 ) that Sao et al. [12] assumed could be overestimated, we compared the effects of two adaptation costs. In both adaptation scenarios, the number of prefectures for which adaptation measures were cost-effective in our results was almost identical for all RCPs. Consequently, it is apparent that the results of our study are more robust than those of earlier studies. In addition, six prefectures for which the cost-benefit ratio exceeds 1.0 for all RCPs have a large damage cost despite the small area of their beaches. In other words, we consider the higher damage cost per unit area to be the reason why hypothetical adaptation measures are economically efficient. Unit: The number of cost-effective prefectures. Figure 9 portrays effects of two adaptation measures of RCP8.5 in 2081-2100. As described above, we demonstrated that the higher the future temperature becomes, the greater the number of prefectures for which adaptation measures are cost-effective. From Figure 9, the lower adaptation cost makes adaptation measures in Kyoto more effective. Additionally, one assumes that the adaptation cost becomes much lower, then we can say that adaptation measures in Niigata, Wakayama, Fukui, and Okinawa are potentially cost-effective. Therefore, it is apparent that the lower the average adaptation cost per unit becomes, the more numerous prefectures for which the adaptation measures are cost-effective become. Especially, in some prefectures along the Inland Sea such as Osaka, Hyogo, Okayama, and Hiroshima, our hypothetical adaptation measure of a public works project of an artificial beach enhancement is quite effective.

Conclusions
To assess the economic effects of changes in environmental quality caused by climate change in Japan, we used a computable general equilibrium model that integrates a utility function with environmental quality factors as independent variables derived from a recreation demand function

Conclusions
To assess the economic effects of changes in environmental quality caused by climate change in Japan, we used a computable general equilibrium model that integrates a utility function with environmental quality factors as independent variables derived from a recreation demand function in a travel cost method. Results show the estimated damage costs of beach loss in Japan and in the respective prefectures. We evaluated the economic effectiveness of hypothetical adaptation measures to restore sandy beaches. The findings obtained from this study are presented below.

1.
Higher future temperatures will cause higher damage costs of sandy beaches. In 2081-2100, we estimated damage costs as 398.54 million USD per year for RCP2. 6 For all RCPs, six prefectures for which the cost-benefit ratio exceeds 1.0 were Kanagawa, Osaka, Hyogo, Hiroshima, Saga, and Kumamoto. 3.
Higher future temperatures will bring high numbers of prefectures for which adaptation measures are cost-effective. Especially for four prefectures along the Inland Sea, which are Osaka, Hyogo, Okayama, and Hiroshima, our hypothetical adaptation measure of an artificial beach enhancement is expected to be quite effective as a public works project.
Further examinations can be expected to support further discussion. First, since we were unable to treat the adaptation cost endogenously, we will incorporate endogenous adaptation costs into our CGE model and evaluate the effectiveness of some adaptation measures. Secondly, since we evaluated only the recreation value (use value) estimated using TCM, we expect to develop a CGE model incorporating evaluation methods of non-use values.