National Land Structure and Disaster Vulnerability

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)

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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

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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.

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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

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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

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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.

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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

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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.


Time

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Population

Capital

D

Region

Infrastructure

Infrastructure

Time



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

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Population

Capital

D Capital

Goods

Region

Infrastructure


Time




Each region produces goods by using their own production capital, local labor, and the infrastructure.

Production technology

𝑣 𝑗 ,𝑡

Other Regions

Time Time

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Population

Capital

D Capital

Goods

Region

Infrastructure


Time

Consumption

Investment Transfer

Investment




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

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Population

Capital

D Capital


Goods

Region

Infrastructure


Time

Consumption

Investment Transfer

Investment




𝐼𝐺 ,𝑡

𝐼 𝑗 , 𝑡

𝐶 𝑗 ,𝑡

𝑣 𝑗 ,𝑡


Other Regions

Time Time

Representative households incur utility according to their consumption level.

Representative household

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Population

Capital

D Capital


Goods

Region

Infrastructure


Time

Consumption

Investment

Capital

Transfer

Infrastructure

Investment




𝐼𝐺 ,𝑡

𝐼 𝑗 , 𝑡

𝐶 𝑗 ,𝑡

𝐾 𝑗 , 𝑡+1

𝑣 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

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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


Sequence of control variables:

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Dynamical economic system

The social planner’s problemEconomic system at time


Balance of goods flow

Capital accumulation

Natural disaster

Instantaneoussocial welfare

Instantaneous social welfare

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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.

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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

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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!

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Thank you for your kind attention.

National Land Structure and Disaster Vulnerability

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