National Land Structure and Disaster Vulnerability
Ryoji ISHII & Daisuke FUKUDA TSU, Tokyo Institute of Technology
Geotectonic lines
(This is the first result and your comments are highly appreciated)
2
BackgroundNational land structure (i.e population distribution) and disaster riskJapan faces the higher risk of natural disasters
Tokyo metropolitan area • 3.6% of the land area• 27.5% of the population• 31.9% of GDP
Centralized national land structure improves productivity (economics of agglomeration)
Centralized national land structure may lead to higher disaster vulnerability
Magni-tude
Capital loss(billion JPY)
Great Hanshin-Awaji Earthquake in 1995 M7.3 9,900
Great East Japan EQ. in 2011 M9.0 16,000
~ 25,000
Tokyo Metropolitan EQ. (estimate) M7.3 66,000
Examine the relationship between the disaster vulnerability and the national land structure (to be centralized? or de-centralized?)
Trade-off
3
Background
Direct impacts– Capital losses, human losses
Spatially-indirect impacts– Decrease in production due to the suspension of providing
intermediate goods in other regions
Temporally-indirect impacts– Lower productivity continues for a while until the full restoration
“Disaster vulnerability”
Characteristics of the natural disaster
The natural disaster is stochastic event.
Necessary to model how the impact spread across regions over time when a disaster occurs.
Necessary to model stochastic property of the disaster.
4
Concept of “Economic Resilience”
[Source] Ron Martin (2010) “Regional economic resilience, hysteresis and recessionary Shocks,” Journal of Economic Geography.
Disaster
GDP or Social welfare
Objective
5
To develop the stochastic dynamic multi-regional macroeconomic model to analyze the fundamental relationship between national land structure and disaster vulnerability
※ National land structure is defined by … Population distribution (Total population is fixed) Disaster risk Topological relationship of regions
Centralized Decentralized
Exogenously given andFixed in the model
60% of population
20% 20%
33% ofpopulation
33% 33%
Ex. three regions
6
Modelling methodology: DSGE-based approach
• DSGE = Dynamic Stochastic General Equilibrium– Macroeconomic (i.e. dynamic) model with microeconomic foundations – Consider “stochastic shocks” on productivity
Ex: RBC (Real Business Cycle) model by Kydland & Prescott (1982)– Many extensions and applications
(e.g. textbooks by Heer et al. (2009); Den Haan et al. (2011))
• Application in disaster analysis– Barro (2006, QJE): non-gaussian shocks of rare disaster– Schmitt-Grohé & Uribe (2004, JEDC); Andreasen (2012, RED):
effects of rare disasters and uncertainty shocks on risk premia– Segi et al. (2011, JSCE): risk-sharing rule of disaster in multi-regional
economy– Our study: “vulnerability” analysis within multi-regional DSGE framework.
7
Multi-regional Economic system at time-step
Population
Capital
D Capital
Representativehousehold
Goods
Region
Infrastructure
InfrastructureProduction technology
Time
Consumption
Investment
Capital
Transfer
Infrastructure
Productiontechnology
Investment
𝐾 𝑗 , 𝑡𝑁 𝑗
𝐾 𝐴𝐷𝑗 ,𝑡
𝑣 𝑗 ,𝑡
𝐼𝐺 ,𝑡
𝐼 𝑗 , 𝑡
𝐶 𝑗 ,𝑡
𝐾 𝑗 , 𝑡+1
𝑢𝑖 ,𝑡𝑢 𝑗 ,𝑡
Other Regions
Time Time
8
Multi-regional Economic system at time-step
Population
Capital
Region
Infrastructure
Time Other Regions
Time
Setup At the start of time , each region has its own
production capital. Capitals have been accumulated from the past. The national economy has a common infrastructure
for all regions. Population of each region is fixed and does not
change over time. Also, people are supposed not to change their residential regions.
𝐾 𝑗 , 𝑡𝑁 𝑗
Time
9
Multi-regional Economic system at time-step
Population
Capital
D
Region
Infrastructure
Infrastructure
Time
𝐾 𝑗 , 𝑡𝑁 𝑗
𝐾 𝐴𝐷𝑗 ,𝑡
A natural disaster occurs stochastically before the regions conduct their production activities.
Damages from the natural disaster is defined as a ε% reduction of production capital in the affected region and of the infrastructure, respectively.
Natural disaster
𝑣 𝑗 ,𝑡
Other Regions
Time Time
Capital
10
Multi-regional Economic system at time-step
Population
Capital
D Capital
Goods
Region
Infrastructure
InfrastructureProduction technology
Time
Productiontechnology
𝐾 𝑗 , 𝑡𝑁 𝑗
𝐾 𝐴𝐷𝑗 ,𝑡
Each region produces goods by using their own production capital, local labor, and the infrastructure.
Production technology
𝑣 𝑗 ,𝑡
Other Regions
Time Time
11
Multi-regional Economic system at time-step
Population
Capital
D Capital
Goods
Region
Infrastructure
InfrastructureProduction technology
Time
Consumption
Investment Transfer
Investment
Productiontechnology
𝐾 𝑗 , 𝑡𝑁 𝑗
𝐾 𝐴𝐷𝑗 ,𝑡
𝐼𝐺 ,𝑡
𝐼 𝑗 , 𝑡
𝐶 𝑗 ,𝑡
𝑣 𝑗 ,𝑡
Other Regions
Time Time
A single homogenous good is used for the consumption and the investment.
Goods are transferred freely across regions (i.e. no transport cost).
Goods market
12
Multi-regional Economic system at time-step
Population
Capital
D Capital
Representativehousehold
Goods
Region
Infrastructure
InfrastructureProduction technology
Time
Consumption
Investment Transfer
Investment
Productiontechnology
𝐾 𝑗 , 𝑡𝑁 𝑗
𝐾 𝐴𝐷𝑗 ,𝑡
𝐼𝐺 ,𝑡
𝐼 𝑗 , 𝑡
𝐶 𝑗 ,𝑡
𝑣 𝑗 ,𝑡
𝑢𝑖 ,𝑡𝑢 𝑗 ,𝑡
Other Regions
Time Time
Representative households incur utility according to their consumption level.
Representative household
13
Multi-regional Economic system at time-step
Population
Capital
D Capital
Representativehousehold
Goods
Region
Infrastructure
InfrastructureProduction technology
Time
Consumption
Investment
Capital
Transfer
Infrastructure
Investment
Productiontechnology
𝐾 𝑗 , 𝑡𝑁 𝑗
𝐾 𝐴𝐷𝑗 ,𝑡
𝐼𝐺 ,𝑡
𝐼 𝑗 , 𝑡
𝐶 𝑗 ,𝑡
𝐾 𝑗 , 𝑡+1
𝑣 𝑗 ,𝑡
𝑢𝑖 ,𝑡𝑢 𝑗 ,𝑡
Other Regions
Time Time
Capital stock and infrastructure are accumulated by investment.
But, adjustment costs are required for investment. They are defined as a function of capital stock and investment.
Capital accumulation
14
Dynamical economic system
Instantaneoussocial welfare
Instantaneous social welfare
The social welfare is given by the linear sum of the utilities of all regions (i.e. Benthamite-type social welfare function).
The social planner determine the sequence of control variables to maximize the objective function.
The objective function is the expected present value of the social welfare for all time horizons.
Economic system at time
Economic system at time
Sequence of control variables:
15
Dynamical economic system
The social planner’s problemEconomic system at time
Economic system at time
Balance of goods flow
Capital accumulation
Natural disaster
Instantaneoussocial welfare
Instantaneous social welfare
16
Social welfare
Time
𝑊∗
0
Disaster vulnerability
Quantifying disaster vulnerability
Steady state– The condition that capital does not
change between time t and t+1 and disaster doesn’t occur while that.
Consumption
Capital
Steady state𝑆∗(𝐾∗ ,𝐶∗)
Natural disaster
𝑆 ′ (𝐾 ′ ,𝐶 ′ ) Restoration path– the dynamic process returning to the
original steady state after the disaster
Disaster vulnerability– Spatial and temporal widespread
impact of the natural disaster
Disaster happens
– The area surrounded by the restoration curve and the social welfare at the steady state.
17
Results of Numerical Simulations
Case.1 Case.2
Case.3
National land structure (exogenously changed) Population distribution Disaster risks fixed Topological relationship
Infrastructure (its usability varies with topology)
Parameters
High risk Low riskSame risk level
Circular arrangement Linear arrangement
All the regions have the same likelihood of disaster and the equivalent capital-loss ratio.
Asymmetric risk level across regions.
Effects of network topology
Results: Case.1 (two regions)
To avoid catastrophic impact, decentralized national land structure might be desirable.
The same disaster risk in all regions
50%
50%
A disaster in Region 1A disaster in Region 2
Decentralization would have the effects of reducing disaster vulnerability.
At the 50% population share of Region 1, the nation has the highest social welfare.
Region 1 Region 2Same risk level
Maximum value of vulnerability
All the regions have the same likelihood of disaster and ratio of capital loss
Results: Case.2 (two regions)Asymmetry in disaster risk level across regions
41%
20%
A disaster in Region 1A disaster in Region 2
At the 41% of population share of Region 1, the nation has the highest social welfare.
Desirable national land structure in terms of maximizing social welfare or avoiding disaster vulnerability are different.
To avoid catastrophic impact, on the other hand, 20% of population share of Region 1 is optimal (least vulnerability).
Region 1 Region 2
High risk Low risk
Region 2 has the lower disaster risk.
Results: Case.3 (three regions)Difference in topological relationship of regions
In both arrangements, decentralized national land structure is desirable.
If the accessibility to the infrastructure is low, national land structure might have a high disaster vulnerability.
Region 1
Region 2 Region 3
circulararrangement
a disaster in Region 1
a disaster in Regions 2,3
lineararrangement
a disaster in Region 1a disaster in Regions 2,3
Region 1Region 2 Region 3
Circular arrangement
The disaster vulnerability per welfare in the linear arrangement is higher than that in the circular arrangement.
Linear arrangement
21
Conclusion
Consideration of – inter-regional trade, multiple goods cases, population mobility,
agglomeration economy …– Reconsideration of “vulnerability” concept within economic framework
The centralized national land structure would have high disaster vulnerability than decentralized one.
In the case of asymmetric disaster-risk level across regions, the desirable national land structure either in terms of social welfare or disaster vulnerability might be different.
Infrastructure would have the effect of equalizing the disaster vulnerability across regions.
If there is the difference in the usability to the common infrastructure , the disaster vulnerability might increase (i.e. topological effects).
Current findings
Lots of works to do!
22
Thank you for your kind attention.