Effects of restoration measures from the east Japan earthquake in the Iwate coastal area: application of a DSGE model

Abstract

Restoration investment after an earthquake and tsunami can improve regional production, but effects of investment emerge differently in production, investment and consumption. Conventional economic models cannot reproduce such chronological nonconformity among economic indices. This study aims to analyze whether the dynamic stochastic general equilibrium (DSGE) model can duplicate the chronological restoration path and nonconformity, and quantifies the efficiency of the restoration measures, such as restoration investment with fund transfer and rebuilding subsidy, in the Iwate coastal region, where the east Japan earthquake hit. The analytical results are as follows: (1) consumption after the earthquake follows a hump-shaped path, where peak point of consumption was delayed from production peak, but then recovered; (2) private investment and labor demand decrease by more than self-restoration does when the restoration measures end; and (3) restoration investment with fund transfer and rebuilding subsidy improves the economy by accelerating the reconstruction of damaged capital stocks, and the benefits of these two measures outweigh their respective costs. These findings show that the influence of an unforeseen and disastrous earthquake can be explained well by the forward-looking decisions on consumption and savings (equal to investment) endogenizing in the DSGE model.

Appendix

This section explains how to derive the equations relating to the production sector under monopolistic competition. These explanations are based on Torres (2013). Similar documents can be found in Eguchi (2011).

The final good is produced by a representative firm by aggregating the continuing of intermediate goods. This firm maximizes profits, Π, subject to the production function:

$$ \begin{aligned} \mathop {\hbox{max} }\limits_{{Y_{j,t} }} \;\varPi_{t} = P_{t} Y_{t} - \int_{0}^{1} {P_{j,t} Y_{j,t} {\text{d}}j} \hfill \\ {\text{s}} . {\text{t}} .\quad Y_{t} = \left[ {\int_{0}^{1} {Y_{j,t}^{{^{{\frac{\xi - 1}{\xi }}} }} {\text{d}}j} } \right]^{{\frac{\xi }{\xi - 1}}} , \hfill \\ \end{aligned} $$

(7)

where Y _t and Y _j,t are the final good production and intermediate goods production, respectively, differentiated by j at time t; P _t and P _j,t are the price of the composite final good and the prices of intermediate goods, respectively; and ξ(> 1) is the elasticity of substitution across intermediate goods. This method used to aggregate the intermediate goods is the Dixit–Stiglitz aggregator.

The first-order condition derives the following equation:

$$ Y_{t} = \left( {\frac{{P_{t} }}{{P_{j,t} }}} \right)^{ - \xi } Y_{j,t} \quad \forall \;j. $$

(8)

Each intermediate good j is assumed to be produced by only one firm, and optimizes production costs, as:

$$ \begin{aligned} \mathop {\hbox{min} }\limits_{{L_{j,t} ,K_{j,t} }} \;{\text{Cost}} = W_{t} L_{j,t} + R_{r} K_{j,t} + \varPhi_{j} \hfill \\ {\text{s}} . {\text{t}} .\quad Y_{j,t} = A_{t} K_{j,t}^{{\alpha_{1} }} Z_{j,t}^{{\alpha_{2} }} L_{j,t}^{{\alpha_{3} }} , \hfill \\ \end{aligned} $$

(9)

where Φ are fixed costs and assumed to be constant. The first-order conditions of the above problems derive the following equations:

$$ W_{t} = \lambda_{t} (1 - \alpha )Y_{j,t} /L_{j,t} , $$

(10)

$$ R_{t} = \lambda_{t} \alpha Y_{j,t} /K_{j,t} , $$

(11)

where λ _t shows the Lagrange parameter and represents the shadow price of a change in the ratio of the use of capital and labor services.

The monopolistic firm determines the optimal price for the intermediate good they produce. The profit maximization problem to be solved is:

$$ \mathop {\hbox{max} }\limits_{{P_{j,t} }} \quad \pi_{j,t} = P_{j,t} Y_{j,t} - W_{t} L_{j,t} - R_{t} K_{j,t} . $$

(12)

Using Eqs. (8), (10), and (11), the above maximization problem can be defined as

$$ \mathop {\hbox{max} }\limits_{{P_{j,t} }} \quad \pi_{j,t} = P_{j,t} \left( {\frac{{P_{j,t} }}{{P_{t} }}} \right)^{ - \xi } Y_{t} - \lambda_{t} \left( {\frac{{P_{j,t} }}{{P_{t} }}} \right)^{ - \xi } Y_{t} . $$

(13)

The conditions $\frac{{\partial \pi_{j,t} }}{{\partial P_{j,t} }} = 0$ derive the following relation as:

$$ P_{j,t} = \frac{\xi }{\xi - 1}\lambda_{t} P_{t} . $$

(14)

In the steady state, the price of final good, P _t , corresponds to the prices of the intermediate goods, P _j,t . If all intermediate firms are assumed identical, the following equation is obtained:

$$ \lambda_{t} = \frac{\xi - 1}{\xi }. $$

(15)

Hence, the wage rate and rental rate under the monopolistic situation in intermediate production is given as:

$$ W_{t} = \frac{\xi - 1}{\xi }(1 - \alpha )A_{t} K_{j,t}^{{\alpha_{1} }} Z_{j,t}^{{\alpha_{2} }} L_{j,t}^{{\alpha_{3} - 1}} $$

(16)

$$ R_{t} = \frac{\xi - 1}{\xi }\alpha A_{t} K_{j,t}^{{\alpha_{1} - 1}} Z_{j,t}^{{\alpha_{2} }} L_{j,t}^{{\alpha_{3} }} . $$

(17)

These equations are used for the model as Eqs. (M1) and (M2).