Evaluating Dynamic, Regional, and Economic Impacts of the Tokai Earthquake

Abstract

Natural disasters result in economic losses. In this study, a dynamic spatial computable general equilibrium model is constructed to investigate the negative economic impacts of an earthquake. In our model, Japan is subdivided into 47 regions, which are all connected by transportation networks. The model is of a decentralized economy with utility-maximizing consumers and value-maximizing firms in a dynamic context. The model embodies both spatial and dynamic aspects, i.e., commodity flows among regions and the dynamics of regional investments. The model is calibrated for the 47 regions’ economies using a multi-regional input–output table for Japan. We estimate the impacts of a hypothetical earthquake, which is expected to occur in the near future, on the regional economy (taking the Tokai region of Japan as a case study). The simulation results show both dynamic and spatial economic impacts before and after an earthquake. This study suggests that the economic impacts of such a disaster should be evaluated based on both ex-ante and ex-post criteria.

Appendix

Production function (j ∈ I ∪ M, r ∈ R)

$$ {Y}_j^r\left({K}_j^r(t),{L}_j^r(t),{\mathbf{X}}_j^r(t)\right)=\min \left\{\frac{V_j^r(t)}{a_{Vj}^r},\frac{X_{1j}^r(t)}{a_{1j}^r},\frac{X_{2j}^{\mathrm{r}}(t)}{a_{2j}^r},\cdots, \frac{X_{\overline{I}j}^r(t)}{a_{\overline{I}j}^r}\right\} $$

$$ {V}_j^r(t)={A}_j^r{K}_j^r{(t)}^{\upalpha_r^j}{L}_j^r{(t)}^{1-{\upalpha}_r^j} $$

${a}_{ij}^r$ is the input coefficient and ${a}_{Vj}^r$ is the value added ratio. ${V}_j^r(t)$ denotes the value added function. ${A}_j^r$ is the production-efficiency parameter . ${\alpha}_r^j$ is the expenditure allocation ratio for capital.

Investment function (j ∈ I ∪ M, r ∈ R)

$$ {\Delta K}_j^r\left({\mathbf{Z}}_j^r(t)\right)=\min \left\{\frac{Z_{1j}^r(t)}{\upphi_{1j}^r},\frac{Z_{2j}^r(t)}{\upphi_{2j}^r},\cdots, \frac{Z_{\overline{I}j}^r(t)}{\upphi_{\overline{I}j}^r}\right\} $$

Utility function (r ∈ R)

$$ {U}^r\left({\mathbf{C}}^r(t)\right)=\prod \limits_{i\in \mathrm{I}}{C}_i^r{\left(\mathrm{t}\right)}^{\beta_i^r},\kern0.5em \sum \limits_{i\in \mathrm{I}}{\beta}_i^r=1 $$

${\beta}_i^r$ is the household expenditure allocation ratio for goods i.

Investment Cost function (i ∈ I, j ∈ I ∪ M, r ∈ R)

$$ {G}_{ij}^r\left({Z}_{ij}^r(t)\right)={G}_{ij}^r\left({\upphi}_{ij}^r{\Delta K}_j^r(t)\right)={\upphi}_{ij}^r\cdot {c}_{Kj}\Delta {K}_j^r{(t)}^{\upomega_j}\kern1em \left({\upomega}_j>1\right) $$

c K _j and ω _j are the parameters for the cost function.

Asset function (j ∈ I ∪ M, r ∈ R)

$$ {\Phi}_j^r\left({K}_j^r\left(\overline{T}+1\right)\right)={\eta}_j^r{K}_j^r\left(\overline{T}+1\right). $$

${\eta}_j^r$ is the parameter for the assent function.