Leontief and Ghosh 2

Paper: Two Interdependence Models Ping Chen, 4/13/2023

Demand Driven and Supply Constrained Input-Output

Models for Infrastructure Interdependence Analysis

Abstract

Unknown and unmanaged interdependence among infrastructure sectors could cause

severe problems and long lasting impacts on productivity and economic activity.

Understanding and evaluating the security of national infrastructure systems need

requires systematic and inclusive analysis. This paper reviews and examines the

interdependence among these critical infrastructures by investigating the supply chain

connections among them. In this paper, infrastructure interdependence related disruptions

have been classified into two types: demand driven and supply constrained. Two

economic input-output models that can be extended to address these two interdependence

related problems are introduced. As the demand driven problem based on the Leontief

economic input-output model has received much attention, this paper focuses on

reviewing and evaluating the counterpart of the Leontief model: the Ghoshian model,

which can be used to estimate the impact from constrained supply. Extensions of these

two models that can be applied in interdependence analysis are discussed in the paper. It

is found that various sectors can be characterized as either a typical supply or demand

sector according to their impact on the entire economy. The proposed method of

classifying these infrastructure sectors and the features of the typical supply and demand

sector are presented. At the end of the paper, we discuss the implications of having these

two types of models. They are suitable appropriate for the assessment of various

dependence related disruption problems. The combined application of these two models

enables a comprehensive analysis of the vulnerability of individual infrastructure sectors

and it facilitates the detection of sensitive sectors that are prone to the disturbance from

other infrastructure sectors and the sectors whose stable supply or demand are crucial for

the entire economy. The prioritization and optimization of resource allocation strategies

based on the output from these two models makes decision making and policy design

more rational.

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Key word: Interdependence Analysis, Economic Input-Output Model, Critical Infrastructure Sectors,

Demand Driven, Supply Constrained

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1. Introduction

Infrastructure systems are generally manmade systems that function collaboratively and

synergistically to produce and distribute a continuous flow of essential goods and

services that interact with people’s daily life and everyday economic activities [Heller

2002]. Critical infrastructures, such as those that supply water, oil and gas, power,

telecommunications, transportation, etc. are foundations of today’s society. They support

and maintain the economic operations and activities of our communities. Aside from

being productive and in high demand, the increased operational complexity and excessive

utilization of these infrastructure systems have made them more vulnerable than in the

past [Zimmerman 2001] [Haimes 2005(c)]. The reliability and safety of the services

provided by these infrastructure sectors are under threat of from many potential factors.

Little [2002] has identified a number of them: natural disasters, terrorist attacks, design

faults, excessively prolonged service lives, aging materials, and inadequate maintenance.

More diversified sources that can bring unexpected disruptions with large-scale and long-

term impacts also exist, such as a power outage, a labor strike, and so on.

To carry out the critical services that are needed, infrastructure systems themselves are

physically connected to each other to fulfill the requirement of the service/commodity

from one sector as a necessary input/aid to facilitate the production in another. As an

example, electricity is required in almost every economic sector and the rapid

development of the economy further intensifies this requirement. The increased buildup

of interdependencies can be found as the result of promoting convenient and efficient

services, such as the encouragement of the companies to incorporate information

technology in modern production processes under the pressure of intense competition and

rapidly increased demand. The consequence from this interdependence is that the

fluctuation of supply or demand in any sector which is part of an interconnected system

can disturb the normal production of others. Moreover, this effect could ripple through

their interconnections and increase the total impact. Interruptions in one infrastructure

sector can cascade to others. This has become an important factor that can cause critical

infrastructures to reduce their operational productivity and even fail to provide necessary

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services that are fundamental for economic vitality and sustainability. The U.S.

Department of Energy and the Office of Science and Technology Policy, for example,

underscored in their report, that “the issue of interdependencies among critical

infrastructures is a fundamental dimension of critical infrastructure protection”

[Zimmerman 2001]. Cascading failure has been identified as the main source of

vulnerability in critical infrastructure systems [Amin 2000]. To protect these sectors

effectively and efficiently, we need to first identify and understand these

interdependencies and, understand how the interdependence-induced disruptions get

spread and measure their impacts..

Research on interdependencies has been conducted mostly within the realm of qualitative

methods. Some research has attempted to quantitatively evaluate the interdependencies

among some of the sectors. For example, an agent-based Complex Adaptive System

(CAS) approach has represented the interactions among economic and societal factors

and the operation of several infrastructures by assuming each system as one agent

interacting with another and studying the behaviors and responses of these systems by

changing the connection conditions among them [Wildberger 1997]. In addition, Heal

and Kunreuther [2004] has introduced the concept of Interdependent Security (IDS) using

game-theoretic models as a way of investigating how interdependence affects individual

choices about security expenditures in interdependent systems. The advantage of these

approaches is that they can characterize multiple aspects of interdependencies. However,

because of the complexity of each pair of dependent infrastructure sectors, these models

can only include a limited number of infrastructure sectors. The ripple effects among the

collection of complete infrastructure sectors cannot be represented appropriately. “The

analytical capacities in understanding infrastructure interconnections and

interdependencies have not been developed to a point where their interactions can be

easily managed. One reason for the complexity of these interdependencies is the many

combinations and metrics used to characterize either the interactions or their impacts, and

analytical models to simulate these conditions have not yet been developed”

[Zimmerman 2001]

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According to [Paelinck and Nijkamp 1976], one way to measure the degree of

interdependence of various industries is through input-output tables. In measuring the

extent to which any one industry interacts with others, a distinction should be made

between two kinds of linkage effects, called the backward effects and the forward effects.

The distinction should be made based on the recognition of two mechanisms. First, the

input provision induces the attempt to supply. Tracking this input function back to the

original supplier constitutes a backward connection. Secondly, various products are

consumed to feed the demand of an upstream activity; this generates a forward

connection [Paelinck and Nijkamp 1976]. However, there have been very few continuing

attempts that integrate these two supply-demand effects. In this research, we are going to

investigate two modifications made on the economic input-output models to obtain

models that can evaluate interdependence and recognize both supply and demand

propagations within an interdependent economic network that is composed of a complete

collection of economic sectors including these infrastructure sectors.

The research presented here uses input-output transaction data based connections to

interpret the interdependencies among a large collection of various economic sectors. As

the sectors defined in the input-output tables tie each other together through their demand

and supply relations, this supply chain connection has evolved into an important linkage

that connects the critical infrastructure sectors to each other and could, as well, propagate

the damage of any of them to the others. Santos and Haimes [2004] have explored how to

use demand reduction derived impact to quantify their interdependency. However, his

study reviewed only the impact from the demand provision side, leaving the impact from

the supplier side untouched. As interdependence analysis is about the evaluation of the

impact from both the supply side and the demand side, this is an incomplete assessment

method. This paper presents another impact mechanism which is counterpart of his and

reveals the implications importance and vulnerability ofon the selected infrastructure

sectors by considering both of these two impact mechanisms.

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The paper is organized as follows: (1) introduction and explanation of two types of

dependence induced disruption problems; (2) introduction of two classical input-output

(I-O) models to lay the foundation for an economic loss and inoperability

interdependence model that are designed to address these two types of interruption

problems; (3) interpretation and comparison of the impacts derived from these two

models for assumed interruptions on selected infrastructure sectors; (4) identification and

characterization of two major types of infrastructure sectors: typical supply and typical

demand sectors; (5) identification of vulnerable infrastructure sectors and critical

infrastructure sectors; (6) discussion of potential applications of the proposed

interdependence model.

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2. Dependence Induced Disruption Problem Type

In a physically interconnected economy, each sector typically functions as both a supplier

and consumer. Therefore, dDemand and supply constitute the main forces that sustain the

normal operations of each individual sector. Material/Goods/Service moves from one

sector to the other. The consumer sector becomes the downstream side of the transaction;

the supplier becomes the upstream side of the transaction. The spread of interdependence

induced disruptions thereafter can be classified into two ways: either being borne by its

the downstream upstream sectors as the result of a disturbance applied onproduced at its a

supply sector or borne by itsthe downstream upstream sectors as the result of a

disturbance applied on itsproduced at a demand sector,. or a mixed effect of these two.

That isNamely, whatever the initial disruption cause is and whichever the initially

affected sector would be, the spread of disruptions has only two directions: forward

propagation from the upstream to the downstream; and backward propagation from the

downstream to the upstream. In other words, it is eitherThe former is a supply or a

demand-driven a supply constrained disruption. and the latter is a demand driven

disruption. Figure 1 shows these two types of disruption propagation processes where the

arrow indicates the direction of physical connection from the supply sector to the demand

sector. The starting end of the arrow represents the upstream sector of a supply demand

connection while the finishing end of the arrow represents the downstream sector. The

solid box represents the initially disturbed sector and the shaded box represents the sector

directly or indirectly affected after the initial disruption on the solid-box sector occurs.

The following details the classification of these two types of disruptions.Therefore, we

have two sets of flow here, one is the flow of the material, service, etc, which is always

from the upstream sector to the downstream sector; the other is the flow of disruptions. In

the demand driven disruption case, the disruption effects propagate from the downstream

sector to the upstream sector; in the case of supply constrained disruption, the disruption

effects propagate from the upstream sector to the downstream sector. Discussion after

this graph details and examplifies the classification of these two types of disruptions.

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Demand-driven Supply-constrained

Figure 1 Illustration of Two Dependence Related Disruption Type

1. Demand-driven Disruption: This type of indirect interruption is caused by changed

demand in a one sector and; the consequences of reduced demand are borne by its supply

sectors. For example, the 9/11 terrorist attack greatly reduced the confidence of travelers

in the safety of airlines; therefore, quite a few passengers changed their choice of travel

modes. Consequently, the supply sectors to the air transportation sector (e.g., petroleum

supply sector, etc) lost their production request from these airline companies and their

productivities output were reduceddropped even through there was increased demand on

other types of products / services for the same reason, i.e., the increased demand on its

substitutes, such as highway transportation services. The Other causes that can bring

about this changedemand-driven interruptions may include technology reformation,

reduced customer interests, etc. Sometimes, demand-driven disruption has support from

psychological belief, like the one statedexample in Haimes [2005(b)] that “psychological

factors mirror the physical destruction delivered by terrorism and other extreme

disasters”. Because humans serve as the final requester for all kindsconsumer of many

types of production activitiesoutputs, any factors that could affect human choice would

become a reason that the demand level of intermediate or final products is affected.

Technology reform could also bring higher demand in one sector and reduced interest in

other sectors. This type of disruption is related more to changes in physical requirements

instead of the psychological concerns. An example could be the technology change in

certain industries, such as requested from environmental inspection. The dis-

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Downstream Upstream UpstreamDownstream


encouragement of the public from using fossil fuels to generate electricity will

unavoidably inevitably force the power plants to choose renewable clean energy sources

or install innovative cleaning technologies. Such changes may cause the related fossil

fuel supply sectors to reduce their production, while at the same time driving up the

production level in these new technology providing sectors.

2. Supply-drivenSupply-constrained Disruption – Most of this type of disruptionThis

type of indirect disruptions is initially caused by reduced production in one sector, for a

variety of reasons; and the consequences are borne by the sectors that have direct or

indirect demand on the deficient supply sectors. Therefore, it may be more appropriate to

call it “supply constrained disruptions”. For example, the attack on a power plant could

possibly break down the production of other sectors whose operations can not continue

without electricity. This is because the demand on the affected sector won’t decrease

even though its service becomes unsecured or less reliable as people have less flexibility

of switching to an alternative product or service. The causes of such disruptions may

include system failure, natural disaster, etc, on the supply sectors. These kinds of chained

disruptions happen only when the output from the economic sectors is curtailed by a

reason that is not a result of reduced demand. For example, equipment failure, natural

disaster, accidental accidents, etc, which cause the reduction of production in the supply

sector and does not necessarily cause an immediate change in the demand for the services

or products from the demand sectors. What always happens is that tThe indirectly

affected sectors have planned demand and the disruptions are caused because their

production capacity is not ablecan not to be fully realized because ofdue to their inability

to acquire insufficient acquisition quantities of limited products or services from their

supply side. A terrorist attack could cause supply-drivensupply-constrained disruptions as

well as the demand driven disruptions..

Therefore, tThe question of evaluating infrastructure interdependence becomes howis

equivalent to estimate the impact of a disruption using calibrated, scalable measurement

through the interconnections among these infrastructure sectors. Two issues are raised

when evaluating the interdependence related impacts: (1) how to classify whether one

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propagated perturbation creates a demand-driven or supply-drivensupply-constrained

impact or both. Given both of them are possible to occur, which one should be addressed

first;; (2) how to estimate the direct and indirect impacts through the supply chain

induced due to some initial disruptions problems. Related to the first issue, we need to

identify the type of disruptions that could happen after a particular sector is exposed to an

initial interruption. As the connections among these sectors are determined by their input-

output relations, we need criteria to determine which sectors are prone to generate supply

drivensupply constrained impacts and which sectors are prone to generator demand

driven impacts. Related to the second issue, we need to compute the economic loss due to

a supply or demand interruption and take into account both direct and indirect effects.

The following sections will illustrate the insights that have been gained by employing

economic input-output data and economic input-output models to address these two

issues.

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3. Economic Input-Output (EIO) Data

The United States economic input-output (EIO) transaction data have been collected and

reported for over 50 years. EIO data are presented in the form of transactions measured

by dollar amount. These data describe the monetary transactions between various

economic sectors, defined according to a standard classification system developed by the

US Department of Commerce to categorize business activities. The Bureau of Economic

Analysis (BEA) publishes the transaction data covering two aspects: the Make table

depicts what commodities and how much of each commodity is produced by each

industry; the Use table explains what commodities and how much of each commodity is

consumed by each industry to implement its own production level. In this study, we

chose the 1997 commodity-by-industry Use table and industry-by-commodity Make table

as our base data set, which is the most recent benchmark collection of data available.

Benchmark tables are collected only every five years and released five years later than

the benchmark year. In the Use table, each row represents one distinct commodity and

each column represents one industry. Each cell entry represents the amount of the row

commodity that is bought and used by the column industry. In the Make table, each row

represents one distinct industry and each column represents one distinct commodity. Each

cell entry represents the amount of the column commodity that is made and sold by the

row industry. The 1997 data use a new classification system that is based on the North

American Industry Classification System (NAICS) 511 IO sectors are included in the

1997 data and they are defined according to this classification system. Among them,

eleven critical infrastructure sectors are identified for further study. Their NAICS code

number and sector name are listed in Table 2 Table 1.

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19 211000 Oil and gas extraction 30 221100 Power generation and supply

142 324110 Petroleum refineries391 481000 Air transportation 392 482000 Rail transportation 393 483000 Water transportation 394 484000 Truck transportation 396 486000 Pipeline transportation 412 514100 Information services 419 52A000 Monetary authorities and depository credit intermediation 468 7211A0 Hotels and motels, including casino hotels 470 722000 Food services and drinking places

Index NAICS Sector Name

Table 1 Infrastructure Sectors selected from 1997 EIO Table

The classification of demand-driven and supply-drivensupply-constrained disruptions

requires us to explain whether the sectors are prone to better classified as one of the two

disruption types. One way of doing so is to characterize each sector by comparing its

supply and demand features, which is whether or not these sectors contribute “more” as a

supplier or contribute “more” as a consumer. Here, the comparison could be based on

either the monetary value or the amount of consumers and suppliers among their entire

supply and demand transactions. The following is an experiment we conducted to

identify supply and demand sectors via the EIO Use and Make tables. Since the Use and

Make tables represent only the relationship between industry and commodity, to

investigate the inter-transactions from one industry to another industry, an industry-by-

industry transaction table is created using the following method: the commodity-by-

industry Use table is first normalized at each column by dividing each element in that

column by the total sum purchase made by that column sector; the industry-by-

commodity Make table is normalized at each row by dividing each element in that row by

the total sum of sales made by that row industry. The product of the normalized Make

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and Use tables return a normalized industry-by-industry matrix. This normalized

industry-by-industry matrix is different from the direct requirement matrix in that the

direct requirement matrix is the column normalized Use table and it doesn’t consider

which sectors the used commodities is made from. By integrating the Use table and Make

table, the portion of output that is produced from a supply sector to a demand sector is

determined. By multiplying this the industry-by-industry matrix with the total industry

output from each sector, we can obtain the industry-by-industry table. [Haimes 2005(a)]

adapted the same method to obtain the industry-by-industry input output table. There are

511 sectors included in the generated 1997 industry-by-industry table by using the Use

and Make tables. Among them, 12 sectors are special industry sectors, 13 are final uses

sectors; 3 are value added sectors. As these sectors don’t have clearly defined product or

service, they are excluded from the following classification analysis. Therefore, only 483

sectors are used for the classification purposeexercise.

Two criteria related to this industry-by-industry transaction table have been designed to

differentiate classify a sector into a typical supply sector from or a typical demand sector:

Criteria I: Number of connections. This criteria needs toC count the number of

different sectors that one particular sector buys from or sells to out of the 483 sectors

from Industry-by-Industry Transaction Table. If the total number of sectors buying

the product/service from this sector is higher than the amount of sectors it buys from,

this sector is classified as a supply sector, otherwise it is a demand sector;

Criteria II: Monetary value of transactions. This criteria needs to cCount the total

dollar value of the commodities one particular sector buys and sells from Industry-by-

Industry Transaction Table. If the total amount is higher from the purchase side, the

sector is recognized to be demand sector; otherwise it is a supply sector;

Table 2 shows the classification outcome for the infrastructure sectors under one of the

two criteria defined above, where “SUPPLY” indicates that the sector contributes more

as a supply sector than as a demand sector, or “DEMAND” otherwise under one of the

two criteria defined above. Overall, most of the infrastructure sectors are classified as

“SUPPLY” sectors. As an example of a supply sector, the power sector purchases from

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355 various sectors in a total amount of $79.7 Billion and sells to 479 sectors in a total

amount of $100.2 Billion. As there are more sectors requesting electricity and for a larger

amount of dollar value, we classify the power sector as a supply sector. Food services and

drinking is one example of a demand sector under Criteria II. The purchase and sale for

this sector in 1997 are $174.5 Billion and $57.3 Billion which has a larger amount dollar

value of input transactions than the output from its inter-sector transactions. The Air

Transportation sector is an example of a demand sector under Criteria II, also. The total

purchase and sale in this sector in 1997 is $65 Billion and $46.0 Billion, respectively, and

the amount of suppliers and demanders are 344 and 481 each. The Pipeline Transaction

sector is a special example of discrepancy between the classification under Criteria I and

Criteria II. Pipeline Transportation sector is classified as a demand sector under Criteria I.

There are 332 different sectors that make commodities or provide services for the

pipeline transportation industry and 194 sectors that use the service from this sector.

However, when the actual monetary transaction is taken into account, the actual sale from

this sector to these 194 demand sectors was $24.8 Billion in 1997, which is much higher

than the 18.8 Billion of purchases it made in 1997 from its supply sectors.

Suppliers Demanders ClassificationPurchase ($Million)

Sale ($Million)

Classification

19 211000 Oil and gas extraction 331 481 SUPPLY $54,137 $147,600 SUPPLY30 221100 Power generation and supply 355 479 SUPPLY $79,725 $100,210 SUPPLY

142 324110 Petroleum refineries 375 482 SUPPLY $140,090 $86,222 DEMAND391 481000 Air transportation 344 481 SUPPLY $65,012 $46,049 DEMAND392 482000 Rail transportation 353 482 SUPPLY $16,404 $25,529 SUPPLY393 483000 Water transportation 359 481 SUPPLY $14,947 $5,377 DEMAND394 484000 Truck transportation 341 482 SUPPLY $86,401 $109,760 SUPPLY396 486000 Pipeline transportation 332 194 DEMAND $18,771 $24,803 SUPPLY412 514100 Information services 348 477 SUPPLY $4,677 $6,535 SUPPLY419 52A000 Monetary authorities and depository credit intermediation 342 481 SUPPLY $92,607 $109,080 SUPPLY468 7211A0 Hotels and motels, including casino hotels 404 481 SUPPLY $20,789 $24,284 SUPPLY470 722000 Food services and drinking places 417 476 SUPPLY $174,510 $57,256 DEMAND

Amount of TransactionInd-by-Ind Transaction Table

Index NAICS Sector NameNumber of Connections

Suppliers Demanders ClassificationPurchase ($Billion)

Sale ($Billion)

Classification

211000 Oil and gas extraction 331 481 SUPPLY $54.1 $147.6 SUPPLY221100 Power generation and supply 355 479 SUPPLY $79.7 $100.2 SUPPLY324110 Petroleum refineries 375 482 SUPPLY $140.1 $86.2 DEMAND481000 Air transportation 344 481 SUPPLY $65.0 $46.0 DEMAND482000 Rail transportation 353 482 SUPPLY $16.4 $25.5 SUPPLY483000 Water transportation 359 481 SUPPLY $14.9 $5.4 DEMAND484000 Truck transportation 341 482 SUPPLY $86.4 $109.8 SUPPLY486000 Pipeline transportation 332 194 DEMAND $18.8 $24.8 SUPPLY514100 Information services 348 477 SUPPLY $4.7 $6.5 SUPPLY

52A000 Monetary authorities and depository credit intermediation 342 481 SUPPLY $92.6 $109.1 SUPPLY7211A0 Hotels and motels, including casino hotels 404 481 SUPPLY $20.8 $24.3 SUPPLY

722000 Food services and drinking places 417 476 SUPPLY $174.5 $57.3 DEMAND

Number of Connections Amount of TransactionNAICS Sector Name

Table 2 Classification of Supply Sector vs. Demand Sector based on Direct Transactions

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Looking atIn addition to the infrastructure classification result as shown in Table 2 more

closely, we see:, we have also compared the overall classification outcome by using these

two methods on the whole collection of economic sectors. Here is a summary of these

findings:

(1) Criteria I identified 321 supply sectors and 164 demand sectors; Criteria II identified

256 supply sectors and 229 demand sectors, there are a higher proportion of supply

sectors than demand sectors according to the above defined criteria;

(2) Criteria I identified 321 supply sectors and 164 demand sectors; Criteria II identified

256 supply sectors and 229 demand sectors, there are a higher proportion of supply

sectors than demand sectors according to the above defined criteria;

(3) Both of these classification methods show identify that most of these designatedthe

selected infrastructure sectors used in practice, i.e., those recognized in Table 1 are

supply sectors and. This is reasonable as we think that the services from these sectors are

fundamental for a large number of and varied number kinds of economic activities in

addition to the huge amount of requirement;

(4) Criteria I and II agree in most situations for classifying these infrastructure sectors.

For sectors which they disagree, The observation that there are a broader sectors have

identical classification outcomes by these two criteria partially attributes to the fact that a

typical supply sector will supply to a large number of sectors and the total dollar value of

these supplies are high and a typical demand sector have requirement from a large

number of supply sectors and the total dollar value of these supplies are high.

(5) Criteria I and II agree in most situations for classifying these infrastructure sectors.

For sectors which they disagree, the discrepancy comes in two types. Some of the sectors

consume a higher amount of products / services from a relatively small amount of

different suppliers, such as air transportation, petroleum refineries, water transportation

and food service sector, etc. Some of the sectors supply to a small amount of different

consumers but with a high amount of dollar values, such as pipeline transportation

service sector;

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Since there are a large number of sectors classified as supply sectors, it is important to

study the impact of losing the supply from these sectors as one part of interdependence

analysis. In the following sections, we will review the demand-driven impact model that

was studied by Haimes and propose its counterpart Ghosh model for studying the supply-

constrained impact.

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4. Economic Input-Output Models

As mentioned before, one apparent feature of supply chain connections is that the

influence of an initial perturbation on any sector can be spread to another other sectors

through direct and indirect linkages. As indirect effects are the major manners

mechanism tothat spread the initially disturbed services to other seemingly unrelated

sectors, it is important that an interdependence model is capable of exploring the indirect

impacts as well as the direct ones. There are two similar interdependence modeling

methods that use economic input-output data and take into account both the direct and the

indirect effect: the Leontief model and the Ghosh model. Both of these models were

originally created to study the degree of inter-connections among various economic

sectors.

Both models assume that the economy consists of nN interconnected economic sectors.

Each sector employs the output from part or all of these sectors, as well as additional

primary input, called value added value here, to satisfy the needs of the final demand and

intermediate requirements. The total output from each industry is composed of two parts:

the supply from that sector to the inter-industry activities, in addition to the supply to the

final demand, such as human consumptions. Similarly, the total input into each industry

is also composed of two parts: the input that is from the inter-industry activities, as well

as the supply from the primary input, or added value, such as labor input etc. The

summation of the supply from one sector contributed to the inter-industry activities,

together with their supply to the final demand, constitute the total output from that sector.

The inter-industry input going into that sector, together with the supply from the primary

input, or added value, constitute the total input into that industry. Table 3 depicts these

items, their names and their relationships through in an input-output table.

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1 2 3 n1 X11 X12 X13 X1n O1 c1 X1

(1)

2 X21 X22 X23 X2n O2 c2 X2(1)

3 X31 X32 X33 X3n O3 c3 X3(1)

n Xn1 Xn2 Xn3 Xnn On cn Xn(1)

I1 I2 I3 In

v1 v2 v3 vn GDP

X1(1) X2

(1) X3(1) Xn

(1)

Value Added or Primary Input (v)

Total Input Output (X)

Total Industry Input (XT)

Non-infrastructure

Output from Industry

Intermediate Input (I)

Intermediate Output (O)

Input to Industry

Infrastructure Non-infrastructure

Infrastructure

Final Output (c)

1 2 3 n 1 2 q1 X11 X12 X13 X1n O 1 c 11 c 12 c 1q X 1

(1)

2 X21 X22 X23 X2n O 2 c 21 c 22 c 2q X 2(1)

3 X31 X32 X33 X3n O 3 c 31 c 32 c 3q X 3(1)

n Xn1 Xn2 Xn3 Xnn O n c n1 c n2 c nq X n(1)

I 1 I 2 I 3 I n

1 v 11 v 12 v 13 v 1n

2 v 21 v 22 v 23 v 2n

p v 31 v 32 v 33 v 3n

X 1(1) X 2

(1) X 3(1) X n

(1)

Output from industriesInfrastructures Non-Infrastructures

Total Industry output (X)

Input to industries Exogenous Demand or Final Output (c)

Total Industry input (X T )

Infrastructures

Non-Infrastructures

Intermediate input (I)

Value Added or Primary Input (v)

Intermediate Ouput (O)

GDP

Table 3 Economic Input-Output Table Illustration

The variables used in the economic input-output table (Table 3) include:

n – The number of defined industries;

– Total output of industry i (i = 1, 2, …, n);

– Total input to industry j (j = 1, 2, …, n);

– Input of industry i to the production output of industry j (intermediate

consumption);

q – The amount of different category of final demand;

– Final demand (or final consumption) for industry i’s output in Final Demand

category k (k=1…q);

p – The amount of different category of primary input;

– Value added (or primary input) for industry j’s input in the category l of the added

value (l = 1…p);

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Input-Output analysis conducted on these transaction data creates a picture of a regional

or national economy describing flows to and from industries and institutions which can

be used to predict changes in overall economic activity as a result of trigger change in the

local or national economy. To facilitate the analysis, here are the assumptions for

performing the input-output analysis:

(1) The activities of these economic sectors are within an open static economic input-

output system that has a balanced input and output;

(2) Fixed proportions technology: each output is produced via a unique combination of

inputs. There is no substitution among inputs which can give us the same commodity as

output;

(3) The demand from sector j to sector i is proportional to the total input to sector j.

– Proportion of industry i’s input to j, with respect to total production output of

industry j;

(4) The supply from sector i to sector j is proportional to the total output from sector i.

– Proportion of industry i’s input to j, with respect to the total input from industry i;

(5) Constant returns to scale: doubling inputs doubles all outputs, no more and no less.

Furthermore, the following balance eEquation and suggests that the total output of

industry i is consumed either as intermediate consumption (i.e., ), or as final

consumption ( ); the total input to industry j is composed of inter-industry supply (i.e.,

) and the primary input ( ):

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The matrix format of the equation becomes

The Leontief model and Ghosh model are established using these input-output balance

equations. The solution of total industry input (output) X to the above equations and

forms the Leontief and Ghosh model respectively:

The Leontief model is a demand-oriented driven EIO model. Similarly, a supply-

drivensupply-constrained input-output model was formulated by Ghosh (1958) to first

describe certain aspects of centrally planned economies [Oosterhaven 1988]. Compared

with the Leontief model, the Ghoshian model does precisely the opposite. It starts with

the input identity and complements it with the assumption of fixed output coefficients,

also called allocation coefficients, which is symbolized by B here.

The following equationEquation shows the connection between the two sets of

coefficients where A (called the direct requirement matrix) is the coefficient matrix in the

Leontief’s model and B (called the direct supply matrix) is the coefficient matrix in the

Ghosh model and x

is the vector of the total output per industry. Also, the A or B matrix

can be acquired by normalizing the transaction matrix by column or row with regard to

the total output from each sector which was proposed by Oosterhaven [1988].

20


Another way of expanding the result of X can explain how the total impact is counted:

Where represents the direct requirement on each sector from the final demand c;

represents the first level indirect requirement and represents the second level

indirect requirement and so on. Where represents the direct supply to all the

sectors as an effect of primary input (value added), represents the first level indirect

supply and represents the second level supply and so on.

Following are two examples of performing Leontief and Ghosh input-outputIO analysis

on how the final demand and primary input drive the production and allocation in these

economic sectors.

According to the published 1997 US input-output benchmark transaction tabledata, to

produce $1 Million of electricity from the power generation and supply sector, $21,700 is

demanded from the petroleum refinery industry; $ 30,500 from the rail transportation

industry and $33,600 from the pipeline transportation industry as a direct input. An

example of running the Leontief model on the generation of $1 Million of electricity is

conducted through the EIO-LCA website [EIOLCA 2005]. The Economic Input-Output

Life Cycle Assessment software developed by Carnegie Mellon traces various economic

transactions and resource requirements for a particular product or service. The model

captures various manufacturing, transportation, and related requirements to produce a

product or service. The results are based upon the 491 by 491 sector direct requirement

matrix published by Department of Commerce, which includes around 483 commodities.

DoC’s 485x 485 commodity input-output model of the U.S. economy. Table 4 shows the

top 10 sectors and their output in dollar amount that are required to support the

generation of $1 Million of electricity through the total supply chain.

21


Sector Total Economic

($ Million)Direct Economic

(%)Direct Economic

($ Million)Total for all sectors 1.7300 79.8 1.3805

221100 Power generation and supply 1.0072 99.3 1.0001211000 Oil and gas extraction 0.0983 71.0 0.0698212100 Coal mining 0.0782 90.6 0.0709486000 Pipeline transportation 0.0336 93.2 0.0313482000 Rail transportation 0.0305 87.8 0.0267420000 Wholesale trade 0.0253 32.5 0.0082533000 Lessors of nonfinancial intangible assets 0.0232 3.0 0.0007324110 Petroleum refineries 0.0217 43.5 0.0094541100 Legal services 0.0200 75.7 0.0151531000 Real estate 0.0194 37.5 0.0073

NAICS

Table 4 Top 10 Sectors that are demanded for generating $1Million Power Supply

(Example Output from Leontief Model. Source: [EIO-LCA 2005])

By running the Ghosh model on the consumption of $1 Million of generated electricity, it

can be determined that the electricity will be allocated as follows: $23,000 to petroleum

refinery industry and $38,500 to the food service and drinking places, directly. Table 5

shows how the generation of $1.007 Million electricity is allocated to various sectors

through their supply chain. The total amount of allocation ($1.007 Million) is higher than

the original $1 Million because during the successive production processes, more demand

on electricity is generated. The top 10 sectors that acquire electricity directly or indirectly

are listed in Table 5 as well as the total amount of usage of electricity in that sector which

is computed from the Ghosh model and the 1997 EIO data.

22


Sector Total Economic

($ Million)Direct Economic

(%)Direct Economic

($ Million)Total for all sectors 2.0464 23.7 0.4851

221100 Power generation and supply 1.0072 99.3 1.0001531000 Real estate 0.0759 83.1 0.06314A0000 Retail trade 0.0656 69.5 0.0456722000 Food services and drinking places 0.0385 59.6 0.0229420000 Wholesale trade 0.0346 55.9 0.0194324110 Petroleum refineries 0.0230 36.2 0.0083550000 Management of companies and enterprises 0.0215 73.0 0.0157336300 Motor vehicle parts manufacturing 0.0201 26.8 0.0054336110 Automobile and light truck manufacturing 0.0187 9.1 0.0017622000 Hospitals 0.0181 46.0 0.0083

NAICS

Table 5 Top 10 Sectors that are supplied by $1Million Power Supply

(Example Output from Ghosh Model)

23


5. Extensions to Infrastructure Interdependence Model

An economic input-output model explains how the final demand drives the total output

and how the primary input is allocated into different industries’ production needs. It

demonstrates the economic connections among infrastructure sectors. However, to

evaluate infrastructure dependency, especially to estimate the dependency induced impact

explicitly and efficiently, we need a scalable measurement of the impact and need to

extend the original IO model to be able to assess these impacts.

Variations of the Leontief model have been applied in estimating the economic impact as

a result of demand-driven interconnections. One of the few attempts for creating such a

model is to estimate the demand reduction input-output inoperability due to terrorism of

interconnected infrastructures [Haimes 2004]. This model is developed to estimate the

terrorist related infrastructure vulnerability under the assumption that the loss of

confidence in the attacked infrastructure sector would bring loss of demand in that sector

and therefore bring production losses to the downstream supply sectors. It can be used to

estimate the accumulated losses among all economic sectors by assuming that the losses

could mount up among all these sectors following their input-output connections.

To assess interdependence oriented vulnerability, it is necessary to explore and measure

how disturbances of production in one infrastructure sector propagate to other sectors,

either as a result of naturally caused or human induced threat. The interdependence effect

occurs when an infrastructure disruption spreads beyond itself to cause appreciable

impact on other infrastructures, which in turn cause more effects on still other

infrastructures [Little 2002]. Therefore, estimation of the consequence of dependence

induced interruptions that is brought to one infrastructure sector from an initially

disturbed sector becomes a good measurement of the tightness of interdependence

between these two. Haimes [2004] introduced two measurements for quantitatively

describing the tightness of interdependency: economic loss and inoperability. Economic

loss is the monetary representation of lost production in the measured sector and

24


infrastructure inoperability is the ratio of the lost production capacity to its planned

production level. For example, an economic loss of $10,000 means that the lost

production level in the affected sector is equivalent to $10,000. 10% inoperability means

that 10% of the planned production capacity in the sector of interest is unavailable for

some reason. As economic loss is not indicative of the capacity of the sector’s real

production level, inoperability would be a better alternative assessment as it takes into

account whether that loss is significant compared to the planned production in that sector.

For example, a $1 Million loss would be significant for a plant having $2 Million of

planned production every year, but is not so significant for a plant having $200 Million of

planned production every year.

The demand-driven inoperability (economic loss) input-output model created by Santos

and Haimes [2004], the extension of the initial Leontief model, is used to estimate the

inoperability in all sectors after the initial shock and the model is given as below:

Where q is the accumulated inoperability vector; A* is the inoperability interdependency

matrix where the cell entry of row i, column j represents the inoperability that is brought

to sector i if we assume that sector j loses its complete productions and this value is

between 0 and 1; c* is the demand-side perturbation vector. The solution to the overall

impact on each sector is the following:

As an example of applying this inoperability interdependence model, suppose that we

have a system that is composed of four sectors: the power sector, the transportation

sector, the water and the telecommunication sector. Suppose that the A* matrix is

determined using Equation and the unexpected events in the transportation sector cause

their consumers to lessen their demand by 10%. We can set up the inoperability

25


interdependence equation as shown in Equation . By solving this equation, we can

acquire the supply chain induced total inoperability impact in each sector (q1, q2, q3, q4).

The solution for the above equation is (q1, q2, q3, q4) = (0.03, 0.13, 0.06, 0.03), which

means that when the demand on the service from the transportation sector is decreased by

10%, due to the supply chain connections among them determined by the A matrix in

Equation , the total loss of demand from the power sector, the transportation sector, the

water and the communication sector is around 3%, 13%, 6% and 3%, respectively.

Similarly, we can establish the extension of the Ghosh model that can be applied to

supply drivensupply constrained infrastructure interdependence problem. The supply

constrained interdependence model is derived similarly to the Ghosh input-output model:

Where, v* is a supply-side perturbation vector; B* is the supply-drivensupply-constrained

interdependency matrix; q is the accumulated inoperability vector. Therefore, the total

inoperability after the shortage of primary supply can be represented as

As an example of applying this supply constrained inoperability interdependence model,

suppose that the B* matrix is determined using Equation and the initial disruption in the

transportation sector causes it to lessen its available supply by 10%. We can set up the

inoperability interdependence equation as shown in . By solving this equation, we can

acquire the supply chain induced total inoperability impact in each sector (q1, q2, q3, q4).

26


The solution for the above equation is that (q1, q2, q3, q4) = (0.03, 0.12, 0.02, 0.01), which

means the when the supply of service from the transportation sector is decreased by 10%,

due to the supply chain connections among them determined by the B matrix in Equation

, the total loss of production from the power sector, the transportation sector, the water

and the communication sector is around 3%, 12%, 2% and 1%, respectively.

Although matrix A* in Equation and matrix B* in Equation have very similar format,

they share completely different meanings. For example, the second row and first column

in the A* matrix, which is 0.3, means that if 10% production in the column sector is

disabled, the row sector, which is a supply sector to the column sector, will lose its

productivity by 0.3*10%=3%. In contrast, the second row and first column in B* matrix,

which is 0.2, means that if 10% production in the column sector is disabled, the row

sector, as a demand sector of electricity, will lose its productivity by 0.2*10%=2%.

The B* matrix and A* matrix have to be created separately and they are not normally

equal to each other. Haimes [2005 (a)] proposed to compute the inoperability matrix A*

as:

That is, employing the original Leontief input-output model, but restating the final

demand in that model (c in Equation) as a decreased demand (c* in Equation) caused by

unexpected perturbations will return from the model the consequent resulting economic

loss (q in Equation), instead of necessary economic input (x in Equation), from all the

supply sectors measured in monetary value. By normalizing this monetary loss with

regard to the annual output of the supply sector gives us the inoperability that is

represented by a percentage number. Therefore, the inoperability matrix in Equation can

be represented by first retrieving the economic loss that is represented by the demand

27


sector’s inoperability and then normalized by the annual productivity of the supply sector

as shown in Equation. Similarly, to acquire the impact in the form of inoperability for the

supply constrained interdependence model, a new interdependence matrix B* needs to be

created which modifies the economic interdependence matrix with each sector’s as-

planned productivity, as:

According to Haimes [2004], the as-planned productivity, which is assumed to be equal

to the total output from each industry, is denoted as . creates a square matrix

which has all along its diagonal and zero on the off-diagonal positions. Each element bij

in the interdependence matrix B measures the economic loss in jth sector when the ith

sector loses its total output supply by $1 Million dollar. To gain the interdependence

matrix measured by inoperability B*, bij is normalized by a factor of where

represents the as-planned productivity from the supply sector (ith sector) and

represents the as-planned productivity from consumer sector (jth sector). Therefore, bij*

from the inoperability interdependence matrix B* measures the reduced productivity in jth

sector when the ith sector loses its productivity by 100%. We use these two

interdependence matrix to measure the impact in the following analysis.

28


6. Experiments: Demand Driven vs. Supply Constrained

Impact

The rest of this section describes an experiment to calculate the economic dependencies

among 12 infrastructure sectors using the extended Ghosh model. The 12 infrastructure

sectors considered are selected from Table 1. Compared with the original full economic

input-output model (Table 3), this experiment maintains only the input output

transactions among these infrastructure sectors and leaves the contribution inter-industry

transactions from related to these the non-infrastructure sectors as part of the new added

value (z) or the new final demand (e) (Table 6Error: Reference source not found). The

total input, output from each industry stays the same comparing with the full economic

input output model (Table 3). This 12 by 12 infrastructure sector matrix maintains the

intermediate transactions among these 12 sectors. The final demand and added value

parts of this matrix are higher than the ones in the original full scale EIO model because

the intermediate output from the non-infrastructure sectors is added to the final demand

and added value parts of that matrix. The total industry input (output) remains the same in

both the original full-scale EIO model and the reduced infrastructure sector only model.

Similar method has been used in Haimes [2004] to compare the impact from within the

12-sectors and within the full sectors. The direct requirement matrix is obtained from the

1997 EIO data set and the direct supply matrix is acquired through Equation .

29


1 2 3 n1 X11 X12 O 1' X13 X1n e 1' X 1

(1)

2 X21 X22 O 2 ' X23 X2n e 2 ' X 2(1)

I 1' I 2'

3 X31 X32

n Xn1 Xn2

z' z 1' z 2'

X 1(1) X 2

(1)Total Industry input (X T )

Intermediate Ouput (O)

Infrastructures

Intermediate input (I')

Value Added (z)

GDP

Exogenous demand (e)

Output from sectorsInfrastructures Non-Infrastructures

e'

Total Industry output (X)

Input to sectors

1 2 3 n1 X11 X12 O1

' X13 X1n c1 X1(1)

2 X21 X22 O2' X23 X2n c2 X2

(1)

I1' I2

'

3 X31 X32 X3(1)

n Xn1 Xn2 Xn(1)

Added Value (v)

v v1 v2

X1(1) X2

(1)

Output from Industry

New Added Value (z)

Infrastructure

Intermediate Input (I')

Total Industry Input (XT)

Non-infrastructure

GDP'

Total Input Output (X)

Infrastructure Non-infrastructureInput to Industry

Final Output (c)

New Final Demand (e)Intermediate Output (O')

Table 6 Infrastructure Only Economic Input-Output Model

The direct requirement matrix A for the infrastructure only economic input-output model

is obtained by column normalizing the industry-by-industry input output table (Table 6)

using the total industry input (XT ); the direct supply matrix B for the infrastructure only

economic input-output model is obtained by row normalizing the industry-by-industry

input output table (Table 6) using the total industry input (X). The direct requirement

matrix measured by inoperability (A*) and the direct supply matrix measured by

inoperability (B*) are obtained by using Equation and with the exception that is the

as-planned productivity only for these infrastructure sectors. Similar method has been

used in Haimes [2004] to compare the impact from within the 12-sectors and within the

full sectors.

The total impact, both supply-drivensupply-constrained and demand-driven impact,

measured by inoperability is computed. Figures 2 through 5 show the impact on these

selected sectors when the petroleum refinery industry, the power generation and supply

industry, the truck transportation industry and the water supply industry each has a 10%

loss of production (inoperability). The results of supply drivensupply constrained and

30


demand-driven impact within these selected infrastructure sectors are presented in two

tables: Table 7 and Table 8.

PowerSupplyWaterSupplyPetroRefineAirTrans RailTrans WaterTransTruckTransTelecom InformSci Monetary,etcHotels,etc Food, etcPowerSupply 10.00% 0.17% 0.12% 0.05% 0.01% 0.01% 0.02% 0.04% 0.04% 0.01% 0.17% 0.14%WaterSupply 0.00% 10.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.01% 0.00%PetroRefine 0.11% 0.09% 10.78% 0.85% 0.20% 0.15% 0.46% 0.00% 0.02% 0.01% 0.01% 0.02%AirTrans 0.01% 0.01% 0.03% 10.02% 0.01% 0.02% 0.04% 0.01% 0.12% 0.05% 0.02% 0.03%RailTrans 0.27% 0.01% 0.02% 0.02% 10.03% 0.01% 0.10% 0.00% 0.00% 0.00% 0.01% 0.02%WaterTrans 0.03% 0.00% 0.02% 0.01% 0.01% 10.01% 0.02% 0.00% 0.00% 0.00% 0.00% 0.00%TruckTrans 0.05% 0.03% 0.04% 0.03% 0.04% 0.02% 11.41% 0.01% 0.02% 0.00% 0.02% 0.10%Telecom 0.01% 0.13% 0.01% 0.21% 0.01% 0.03% 0.16% 11.92% 0.37% 0.06% 0.11% 0.06%InformSci 0.00% 0.00% 0.00% 0.01% 0.00% 0.00% 0.01% 0.00% 10.02% 0.00% 0.01% 0.00%Monetary,etc 0.10% 0.07% 0.09% 0.09% 0.08% 0.08% 0.09% 0.09% 0.09% 10.38% 0.12% 0.07%Hotels,etc 0.01% 0.01% 0.02% 0.01% 0.01% 0.01% 0.01% 0.01% 0.07% 0.04% 10.01% 0.02%Food, etc 0.08% 0.01% 0.03% 0.55% 0.01% 0.06% 0.02% 0.01% 0.12% 0.12% 0.04% 10.07%

Supply Sectors (Intial

Supply Reduction:

10%)

Affected Demand Sectors (Resulted Production Loss (%))

Table 7 Summary of Total Impact from 10% Supply Reduction in the Supply Sectors

PowerSupplyWaterSupplyPetroRefineAirTrans RailTrans WaterTransTruckTransTelecom InformSci Monetary,etcHotels,etc Food, etcPowerSupply 10.00% 0.00% 0.09% 0.03% 0.00% 0.00% 0.02% 0.05% 0.00% 0.01% 0.06% 0.23%WaterSupply 0.04% 10.00% 0.00% 0.01% 0.00% 0.00% 0.01% 0.08% 0.00% 0.02% 0.06% 0.10%PetroRefine 0.15% 0.00% 10.78% 0.65% 0.05% 0.02% 0.50% 0.01% 0.00% 0.02% 0.00% 0.04%AirTrans 0.02% 0.00% 0.04% 10.02% 0.00% 0.00% 0.06% 0.03% 0.01% 0.14% 0.01% 0.10%RailTrans 1.51% 0.00% 0.09% 0.05% 10.03% 0.00% 0.44% 0.02% 0.00% 0.01% 0.01% 0.17%WaterTrans 0.25% 0.00% 0.11% 0.07% 0.01% 10.01% 0.14% 0.00% 0.00% 0.00% 0.00% 0.02%TruckTrans 0.06% 0.00% 0.04% 0.02% 0.01% 0.00% 11.41% 0.02% 0.00% 0.01% 0.01% 0.20%Telecom 0.01% 0.00% 0.01% 0.09% 0.00% 0.00% 0.10% 11.92% 0.02% 0.07% 0.03% 0.07%InformSci 0.05% 0.00% 0.01% 0.11% 0.00% 0.00% 0.11% 0.08% 10.02% 0.06% 0.03% 0.07%Monetary,etc 0.06% 0.00% 0.04% 0.03% 0.01% 0.01% 0.05% 0.07% 0.00% 10.38% 0.02% 0.07%Hotels,etc 0.02% 0.00% 0.04% 0.02% 0.01% 0.00% 0.02% 0.02% 0.01% 0.20% 10.01% 0.07%Food, etc 0.05% 0.00% 0.01% 0.19% 0.00% 0.00% 0.01% 0.01% 0.00% 0.12% 0.01% 10.07%

Demand Sectors (Initial Demand Reduction: 10%)

Affected Supply Sectors

(Resulted Production Loss (%))

Table 8 Summary of Total Impact from 10% Demand Reduction in the Demand Sectors

Figure 2 illustrates that the loss of 10% productivity of refined petroleum would bring a

higher shock in the air transportation sectors as well as truck transportation sector (0.5-

0.6%), because both of them consume a large portion of the supplied gasoline in market.

The lack of enough gasoline would undoubtedly bring a significant impact to these two

industries. This is because according to the Ghosh model, the sectors which consume the

most part of the output from one sector would be affected significantly by the stable

output of that sector. By comparison, the decrease of 10% demand in the petroleum

sector will not cause too much impact on other sectors; the maximum shock appears in

the power generation sector, whose production will be affected by around 0.1%.

shows that the shock caused by a reduction of demand on electricity by 10% would bring

a large blow to the railway companies (over 0.25%) as the rail transportation sector

provides a large portion of its services to the transportation of fuels to the power

generation sector and it will lose this productivity if the power plants reduce their

production level. Meanwhile, the disruption in the supply of electricity will unavoidably

bring disturbances in the food services and drinking place by around 0.2% as these places

31


have a higher reliance on electricity supply. Besides this, the petroleum refinery plants,

hotel industries and telecommunication services will see a reduction in their

productivities from 0.05% to around 0.1% when they lose 10% of their electricity supply.

Figure 4 shows that the disruption of the supply of truck transportation sector’s service by

10% would cause the food service sector to be the one that is affected the most (0.15-

0.2%). However, the lost production demand in the truck sector will cause a loss of sale

in the Petroleum Refinery sector by 0.45%.

Impacts Comparison of 10% Petroleum Refineray Perturbation (Supply Driven vs. Demand Driven : Infrastructure Sectors)

0.00%

0.10%

0.20%

0.30%

0.40%

0.50%

0.60%

0.70%

0.80%

0.90%

PowerS

upply

Water

Supply

AirTra

ns

RailTra

ns

Water

Trans

Truck

Tran

s

Teleco

m

Info

rmSci

Mon

etary,e

tc

Hotels,

etc

Food, e

tc

Dependent Infrastructure Sectors

Inop

erab

ility

Supply Driven Impact

Demand Driven Impact

Figure 2 Supply vs. Demand Driven Impact: Petroleum Refinery Industry

Impacts Comparison of 10% Power Supply Perturbation (Supply Driven vs. Demand Driven : Infrastructure Sectors)

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

1.20%

1.40%

1.60%

Water

Supply

Petro

Refine

AirTra

ns

RailTra

ns

Water

Trans

Truck

Tran

s

Teleco

m

Info

rmSci

Mon

etary,e

tc

Hotels,

etc

Food, e

tc


Inop

erab

ility



Figure 3 Supply vs. Demand Driven Impact: Power Generation

32


Impacts Comparison of 10% Truck Transportation Perturbation (Supply Driven vs. Demand Driven : Infrastructure Sectors)

0.00%

0.10%

0.20%

0.30%

0.40%

0.50%

0.60%

PowerS

upply

Water

Supply

Petro

Refine

AirTra

nsRailT

rans

Water

Trans

Teleco

m

Info

rmSci

Mon

etary,e

tcHote

ls,etc

Food, e

tc


Inop

erab

ility



Figure 4 Supply vs. Demand Driven Impact: Truck Transportation

Here, in the supply-constrained example, each experiment treats the assumed disrupted

sector as a primary supply sector for the production in the demand sectors. That is, if the

demand sector loses their supply from the primary supply sector, even if they have stores

or uninterrupted supply from other sectors, that part of production won’t be implemented.

For example, Figure 3 assumes that power generation is the primary input to the

production of the petroleum refinery sector and therefore assumes that a10% reduction in

the electricity supply will cause the corresponding 0.1% reduction in the petroleum

refinery sector. Similarly, when the Leontief model was tested, it was assumed that the

power plant is the initially affected demand sector with its demand curtailed by 10%.

Therefore, all the sectors that supply the power sector will reduce their production

correspondingly, and the rail transportation sector would reduce their production by

around 0.25%, which means that the electricity sector is one of the largest clients of rail

transportation services and the loss of demand from this sector causes a reduction of

production by 0.25% in the railway sector.

33


7. Typical Supply Sector and Typical Demand Sectors

Section 3 presented two methods to classify supply and demand sectors based on how

much that sector purchases versus how much it sells, or the amount of suppliers versus

the amount of consumers. Both of them measure the direct supply and demand

connections of these sectors. However, as the interdependence model suggests, both

direct and indirect connections exist among these sectors; it could become a partial

conclusion to identify the major role of one sector by counting only the direct

connections. In this section, we will discuss other ways of classifying these sectors based

on the overall impact that could be produced through their direct and indirect

connections.

The results from the Leontief and Ghosh models could be very different as shown in

Figures 2 through 4. For instance, the initial disturbance on any sector as a demand sector

and as a supply sector could bring dramatically different impacts on other sectors.

Moreover, the comparison between the results of the Leontief and Ghosh models

indicates that some sectors behave more like “supply” sectors while others behave more

like “demand” sectors. The following is a simple methodology that can separate the

sectors as a typical demand sector or a typical supply sector by using the result from the

Leontief and Ghosh model and counting both direct and indirect dependencies. It can be

done by acquiring and comparing the total impact that the initially disturbed sector has as

a demand sector by collecting the output from the Leontief model, and as a supply sector

by collecting the output from the Ghosh model. If the total impact as a demand sector is

higher than the impact as a supply sector, that sector is said to behave more like a typical

“demand” sector; otherwise, it behaves like a typical “supply” sector. By applying this

criterion, we can perform a diagnosis on the critical infrastructure sectors that have been

identified. For example, from Figure 2, we see that, overall, the impact that the petroleum

sector has on other sectors as a supply sector would be muchis higher than it has as a

demand sector (Figure 2),, which implies that it functions more like a supply sector

rather than a demand sector.

34


Tables 7 and 8 compare the output (total impact) from the Leontief model and the Ghosh

model for each infrastructure sector which is assumed to be interrupted. Table 9 shows

the overall impact by assuming the initially lost economic value from each affected sector

is $1 Million, the total economic loss it could bring to the entire economy system is listed

and the classification is made based on the comparison of the output from the two

models. Each sector indicated in the “Sector Name” column is assumed to be the initially

disturbed sector. Depending on the types of chain disruption generated, two kinds of total

impact are listed in column (1) and column (2). Column (1) assumes that the initially

disturbed sector brings a demand-driven chain disruption, that is, the demand from that

sector decreases and the total impact among the entire economy system is computed;

column (2) assumes the initially disturbed sector brings a supply-drivensupply-

constrained chain disruption, that is, the supply from that sector decreases and the total

impact is computed. Table 10 shows the overall impact by assuming the production in

each infrastructure sector is reduced by 10% because of unstated reasons, the total

inoperability level over the whole system is listed and the classification is made. The

Leontief Input-Output matrix and the Ghosh matrix utilized here are derived from the

original full matrix with 511 sectors in total. Therefore, the impact is a summation over

these 511 sectors as well. Still, 485 sectors classification are conducted over 483 sectors.

with classification.

35


(1) (2) (3) (4)

Demand-Driven Total Impact

($Million)

Supply-Driven Total Impact

($Million)Classification

((2)-(1))/(1) (%)

19 Oil and gas extraction 1.951 5.076 SUPPLY 160%30 Power generation and supply 1.728 2.021 SUPPLY 17%

142 Petroleum refineries 2.791 2.341 DEMAND -16%391 Air transportation 2.071 1.726 DEMAND -17%392 Rail transportation 1.832 2.589 SUPPLY 41%393 Water transportation 2.151 1.524 DEMAND -29%394 Truck transportation 1.981 2.421 SUPPLY 22%396 Pipeline transportation 2.317 3.065 SUPPLY 32%412 Information services 1.727 2.110 SUPPLY 22%419 Monetary authorities and depository credit intermediation 1.435 1.601 SUPPLY 12%468 Hotels and motels, including casino hotels 1.505 1.651 SUPPLY 10%470 Food services and drinking places 2.106 1.292 DEMAND -39%

Index

(initial loss from individual infrastructure sector is $1 Million)

Sector Name

Total Economic Loss

Table 9 Infrastructure Sector Classification: demand sector vs. supply sector (by Total Economic Loss)

(1) (2) (3) (4)Demand-Driven Total Impact (%)

Supply-Driven Total Impact (%)

Classification((2)-(1))/(1)

(%)19 Oil and gas extraction 34.4% 136.8% SUPPLY 297%30 Power generation and supply 73.7% 120.8% SUPPLY 64%

142 Petroleum refineries 71.2% 110.0% SUPPLY 54%391 Air transportation 46.8% 44.9% DEMAND -4%392 Rail transportation 26.3% 45.0% SUPPLY 71%393 Water transportation 19.3% 19.0% DEMAND -2%394 Truck transportation 49.9% 161.5% SUPPLY 224%396 Pipeline transportation 21.4% 31.6% SUPPLY 48%412 Information services 13.8% 14.3% SUPPLY 4%419 Monetary authorities and depository credit intermediation 42.2% 88.7% SUPPLY 110%468 Hotels and motels, including casino hotels 22.1% 27.0% SUPPLY 22%470 Food services and drinking places 197.1% 44.2% DEMAND -78%

Index Sector Name

Total Inoperability

(initial inoperability from individual infrastructure sector is 10%)

Table 10 Infrastructure Sector Classification: demand sector vs. supply sector (by Total Inoperability)

36


Using economic loss as the measurement, 222 out of 483 sectors (46%) have been

classified as supply sectors. Using inoperability as the measurement, 199 out of 483

sectors (41%) have been classified as supply sectors. Among all the classifications, 320

out of 483 sectors, over 66%, have been classified into the same category by these two

classification methods (Table 11). As these classification methods consider the direct as

well as the indirect interconnections, it gives a slightly different classification outcome

from the method discussed in Section 3. However, out of 483 sectors, 250 sectors have

been assigned into the same category by both the methods discussed here and in Section

3. For the infrastructure sectors that are identified and studied in most of the research and

applications (as listed in Table 1), these classification methods identified that most

sectors are supply sectors. For sectors listed in Table 2 that have been classified as a

demand sector, the difference between the total demand-driven impact and supply-

drivensupply-constrained impact are relatively small. For example, in Table 9, the

average difference between these two impacts for the 8 sectors classified as demand

sector is around 40%, for the 4 sectors classified as supply sector is around 25.5%.

Overall, the supply change generated impact from these infrastructure sectors is much

higher than the demand change generated impact from these sectors. Therefore, the stable

supply of products/services from these infrastructure sectors is more critical for the

continuous development of the entire economy.

Number of Connections

Amount of Transactions Economic Loss Inoperability

Supply Sectors 321 256 222 199Demand Sectors 164 229 263 286Supply Sectors (%) 66% 53% 46% 41%

Supply Sectors 11 8 8 9Demand Sectors 1 4 4 3Supply Sectors (%) 92% 67% 67% 75%

7 117

320 424250

Agreed Classification

Direct Connection Measurement Total Connection Measurement(Ind-by-Ind Transaction) (Interdependence Model)

Infrastructure Sectors

Agreed Classification

Full Economic Sectors

Table 11 Classification Outcome Summary

Table 11 shows the number of supply sectors and demand sectors classified using

different classification methods and for different group of sectors (full economic sectors

and infrastructure sectors only). Identified supply sectors are around half of the entire

37


485483 economic sectors (i.e., 46% by economic loss measurement); however, this

proportion becomes much higher (75%) when considering only these infrastructure

sectors which are designated in critical infrastructure protection commission [PCCIP

1997]. From this perspective, we see again that most of these identified infrastructure

sectors function more like a supply sector than the other sectors. In another word, one of

the common characteristics of these infrastructure sectors is that they are critical supply

sectors for the entire economy.

The large amount of identified supply sectors indicates also the significance of applying

the extended Ghosh model to evaluate supply constrained impacts. Supply caused impact

has been less frequently studied than the demand driven impact. However, historical

experience shows that supply-constrained disruption problems occurred more frequently

than demand-driven disruptions. For example, 9/11 was a rare event, while a power

blackout or highway closure caused by an earthquake, etc has happened a lot. Therefore,

the extension of the Ghosh model and the application of it are much more significant.

Most of the existing definitions of infrastructure sectors are empirically constructed and

based entirely on people’s conceptual perception and various versions and changes have

to be made constantly. For example, in October 1997, a Report to the U.S. President

Commission on Critical Infrastructure Protection first narrowed down and selected eight

critical infrastructures “whose incapacity or destruction would have a debilitating impact

on our defense and economic security” [PCCIP 1997] which include telecommunications,

electric power systems, natural gas and oil, banking and finance, transportation, water

supply systems, government services, and emergency services. Later, this definition was

broadened and refined by the Critical Infrastructure Assurance Office (CIAO). Other

examples of sectors that have been classified as infrastructure sectors include

food/agriculture (production, storage, and distribution), numerous commodities (iron and

steel, aluminum, etc), the health care industry, and the educational system and so on. The

changes and various sources of definition show that the identification of an infrastructure

sector is not a trivial work and it is not so evident as well. The classification methods

proposed above are expected to bring a guide to help the policy makers to make a more

38


rational decision when they have to decide which infrastructures to protect as critical

infrastructures. For example, functioning as a major supply sector might be one of the

criteria for selecting a critical sector to protect with a high priority.

The large amount of identified supply sectors indicates also the significance of applying

the extended Ghosh model to evaluate supply constrained impacts. Supply caused impact

has been less frequently studied than the demand driven impact. However, historical

experience shows that supply-driven disruption problems occurred more frequently than

demand-driven disruptions. For example, 9/11 was a rare event, while a power blackout

or highway closure caused by an earthquake, etc has happened a lot. Therefore, the

extension of the Ghosh model and the application of it are much more significant.

39


8. Vulnerable Infrastructure Sectors and CriticalCrucial

Infrastructure Sectors

To quantitatively evaluate and compare the vulnerability and significance of different

economic sectors is not an easy task. The difficulty comes from how to measure the

vulnerability and the significance and how to set a uniform and scalable standard so that

they the characteristics of different sectors are comparable. The two interdependence

models discussed in the previous sections suggest a method of assessing the

interdependence induced consequences measured either by the lost economic revenue or

the unimplemented productivity that is propagated from one sector to the other. This

quantitative measurement enables us to evaluate the strength of the dependent

connections between any pair of sectors and solves the first issue. On the other hand,

eachEvery economic sector functions as both a supply and demand sector in the

interconnected economy network. As a consequence, each economic sector could suffer

from unexpected disruptions from any part of the whole system. On the other hand, and

the state of production in this sector itself could affect any other sector in the system as

well. In this section, an innovative method to compare and evaluate the vulnerability and

spot critical sectors among the infrastructure network is proposed and several examples

of applying this method to assess these economic sectors are provided.

To start the discussion, we first define two concepts terms that lay the foundation of our

investigation: vulnerability profile and influence profile. Figure 5 illustrates graphically

how to create the profile that describes the vulnerability of each economic sector from

due to the dependence on the other sectors and the influence of each economic sector on

the survivability of the others.. Assuming that there are a total of nN economic sectors

within an interconnected economy network and we are interested in learning the

vulnerability and influence of power generation sector. We assume that each sector from

this system has the same initial disruption, for example, the loss of 10% of its normal

production level, individually,individually; the power generation sector would therefore

could be impacted affected as a receiver of each of these impacts at each time every time.

40


The receiver could be either a demand sector of an upstream interrupted sector or a

supply sector of a downstream interrupted sector. The arrows in the graph show the

direction where the impact propagates. If it starts from It could start from aa supply sector

and ends at a demand sector and, creates a supply drivensupply constrained impact is

generated; . Ifit could also it starts from a demand sector and ends at a supply sector,

and creates a demand driven impact is generated. Assuming that a same amount of initial

disruption, for example 10% output loss is generated at each source sector individually

and these source sectors are direct or indirect supply sectors of the one of interest. , tThe

selected sector, i.e., the power generation sector, will thus be affected by by nN separate

supply constrained impacts. Above each supply chain link, there is a number indicating

the total impact undertaken by the sector of interest because of the loss of initial supply

from the sector indicated at the starting end of the arrow (Figure 5). Plotting these nN

impacts into one histogram, we obtain a “Supply Constrained Vulnerability Profile” for

this sector. Similarly, we can generate a “Demand Driven Vulnerability Profile” for that

sector by assuming that the initially disrupted sectors are demand sectors of the sector of

interest. The “Vulnerability Profile” depicts the level of impact and the frequency of this

that level of impact that the sector of interest would possibly experience.

Since there is very low probability that individual impact all happens at the same time,

the profile describes the worst case scenario of the vulnerability. SimilarlyBy the same

means, we can create an “Influence Profile” (Figure 6) for the sector of interest and it

defines how the reduced production of this sector would affect other sectors in the

system. It is literarily a histogram of the impact that the selected sector can bring to the

nN sectors in the system when a disturbance is initiated in this sector. Similarly, there are

two types of “Influence Profile”. If the sector of interest is considered as the direct or

indirect supply of the impact receiver sector, the histogram plot of these N impacts is

called a “Supply Constrained Influence Profile” of the source sector. A “Demand Driven

Influence Profile” of the source sector is generated if the source sector is a direct or

indirect supply sector of the impact receiver sector.

41


Figure 5 Generation Process of “Vulnerability Profile” and “Influence Profile”

42


Figure 6 Influence Profile

From the process, we canWe can see from the tellprocess of generating these profiles

that a sector which that is more vulnerable than the other sectors tends to have a

vulnerability profile that displays a higher frequency on the large impact. More losses

could be generated in this sector than other sectors under the same disruption scenarios.

Similarly, a sector which is more crucial than the other sectors tends to have an influence

profile that displays a higher frequency on the large impact.

As discussed before, supply-drivensupply-constrained impact and demand-driven impact

can be computed by the extended Ghosh and Leontief interdependence model. Economic

loss and inoperability can be used to measure the impact. The following subsections

discuss how we generate the profiles for each economic sector using these impact

measurements, with a particular interest on the infrastructure sectors identified from the

1997 Economic Input-output Account.

Interdependence Induced Sector Vulnerability Evaluation

Figure 7 is an example of the vulnerability profile of the power generation and supply

sector. Using 1997 economic input-output data at detailed level, 485483 sectors are

43


included in the investigated system. Two disruption types are identified and two

measurements are adoptedadapted. The profiles in Figure 7 (a) and (c) represents the

demand driven vulnerability of the power sector which illustrates how vulnerable the

power sector would be if there is fewer needless demand on the power supply. The

profiles in Figure 7 (b) and (d) represents the supply drivensupply constrained

vulnerability of the power sector. That is, how vulnerable the power sector would be if it

can not get enough supply that is needed for generating power. The impact in Figure 7 (a)

and (b) is measured by economic loss in at the power sector; the impact in Figure 7 (c)

and (d) is measured by inoperability. When economic loss is used as the measurement,

$0.1 Million initial loss is assumed to be applied initialized on each source sector; when

inoperability is used as the measurement, 10% of lost productivity is assumed. For

example, in Figure 7 (a), each of the N sectors are assumed to reduce their planned

production level by $0.1 Million, respectively. In total, there are N individual impacts

generated on the power supply sector due to less demand, directly or indirectly, on the

power supply. The histogram of these N total impacts on the power generation sector

becomes the “Demand Driven Vulnerability Profile” of the power sector measured by

economic loss. Similarly, in Figure 7 (d), each of the N sectors are assumed to reduce

their production level by 10%. In total, there are N individual impacts generated on the

power supply sector due to less supply, direct or indirect, to the production in the power

generation sector. This histogram of these N total impacts becomes the “Supply

Constrained Vulnerability Profile” of the power generation sector measured by

inoperability. The distribution of the computed impact value is highly skewed. The

impact presented in Figure 7 has been taken logarithmic transformation from the original

impact value. The distribution of the transformed impact values exhibits a shape which is

very close to a normal distribution. The approximated normal distribution is plotted over

the histogram. Therefore, the comparison of profiles of different sector can be simplified

by examining the characteristic values, such as the mean, variance of the approximated

normal distribution.

(b)

44


(a)

(c) (d)

Figure 7 Example: Vulnerability Profile of “Power Generation and Supply Sector”

Figure 8 are plots of the vulnerability profiles of all the infrastructure sectors identified in

Table 1. Profiles sitting at the right side of the graph represent sectors that are more

vulnerable than the sectors whose profiles sitting at the left side of the graph. We see

from Figure 8 (b) that when each of these 485483 sectors loses its production supply of

product/service by $0.1 Million, the telecommunication sector and the power supply

sector would suffer an overall greater loss than other infrastructure sectors. That is, these

two sectors are more vulnerable than other infrastructure sectors. Meanwhile, Figure 8

(ca) indicates that when the final demand on each of the 485483 sectors loses its

productivitydecreases by 10%$0.1 Million, the truck transportation sector would suffer a

relatively higher loss. As Since the same amount of dollar loss may indicates different

inoperability for different sector which is determined by the total output level of that

sector, adopting different measurement could result in identifying different vulnerable

45


sectors. For example, there is less discrepancy among the supply-constrained

vulnerability profiles measured by inoperability in Figure 8 (d).

Here, the initial disruption is measured by inoperability and 10% initial supply loss

cwould mean different dollar loss for economic sectors having different annual output

level. Telecommunication sector is highly vulnerable when the same amount of dollar

value loss occurs on all sectors and become indifferently vulnerable when the same

proportion of productivity is lost from all sectors.

(a) (b)

(c) (d)

Figure 8 Vulnerability Profiles of Infrastructure Sectors

46


Interdependence Induced Sector Influence Evaluation

Different from the vulnerability analysis, to evaluate the significance of these sectors, we

will assume that the evaluated sector, for example, the power generation and supply

sector, is the initially interrupted sector, and then detect how each sector in the system

can be affected and how significant is the impact. Figure 9 is the example of the

Influence Profile of the power generation and supply sector. Similarly, the impact in

Figure 9 (a) and (b) is measured by economic loss in the power sector; the impact in

Figure 9 (c) and (d) is measured by inoperability. The impact value is computed and

transformed using logarithm algorithm and plotted into this histogram. The shape of the

profile is close to a normal distribution and the approximated normal distribution is

plotted on the top of each histogram.

(a) (b)

(bc) (cd)

47


Figure 9 Example: Power Profile of “Power Generation and Supply Sector”

Figure 10 are plots of the influence profiles of the infrastructure sectors identified in

Table 1. The closer the influence profile is to the right side of the graph, the greater

impact this sector could bring to the whole economy if the provision from this sector is

severely disrupted. Comparing the supply-drivensupply-constrained influence profiles of

different sector measured by inoperability (Figure 10(d)), we see that the loss of 10%

productivity from truck transportation and power supply sector can generate an overall

higher impact than what can be caused by the disruption of provision in other

infrastructure sectors. That is, these two sectors are more influential and therefore crucial

for the stable development of the whole economy.

(a) (b)

(c) (d)

Figure 10 Influence Profiles (Infrastructure Sectors)

48

User, 05/16/06,

Change “Power profile” to “Influence Profile” in the plots.


Comparing Figure 10 with Figure 9, we see that the there are certain connections between

the influence profile and the vulnerability profile. Typically, a supply-constrained

vulnerability profile measured by economic loss (e.g., Figure 9 (b)) would have the same

curve shape as the demand-driven influence profile measured by inoperability (e.g.,

Figure 10 (c)). The idea behind this is that if a sector which is quite influential in terms of

the demand it has on the other sectors would be very vulnerable if the supply from all

these other sectors swing a lot. In general, we see that the supply to the

telecommunication sector and the power sector have a greater influence on the stable

production level in these two sectors. The supply from the truck transportation sector, as

well as power generation and supply sector, oil and gas extraction sector (Figure 10 (d))

has a greater influence on maintaining the stable operability of the entire economy

system.

Infrastructure Sector’s Profile

Another advantage of having these profiles is that we can obtain compare different types

of profile for the same sector and therefore diagnose determine the type and

characteristics of that sector. As an experiment, the vulnerability profile (demand-driven

and supply-drivensupply-constrained) and influence profile (demand-driven and supply-

drivensupply-constrained) of each infrastructure sector measured by inoperability has

been plotted into a single graph as shows in Figure 11.

(a) (b)

49


(c) (d)

(e) (f)

(g) (h)

(i) (j)

50


(k) (l)

Figure 11 Infrastructure Sector’s Vulnerability (Power) Profile measured by Inoperability

To distinguish recognize the major function of these infrastructure sectors, we can

compare the “supply drivensupply constrained influence profile” and “demand driven

influence profile” for each sector in Figure 11. It can be found that all most of the

selected infrastructure sectors have their supply drivensupply constrained influence

profile (dash blue) sit at the right side of their demand driven influence profile (dash

green). Thus, we can conclude that these sectors should be classified as an influential

supply sector as since the reduced provision from these sectors could bring a generally

higher impact than the reduced demand from these sectors. In other words, the supply

from these sectors is extremely crucial for maintaining the normal operation of the

overall economy systemnetwork.

Similarly, we can plot and compare the “demand driven vulnerability profile” and

“supply drivensupply constrained vulnerability profile” for each of the 12 infrastructure

sectors to detect where the vulnerability comes from for them. As a result, we find out

that infrastructure sector in general have a demand driven vulnerability profile that sits at

the right side of its supply drivensupply constrained vulnerability profile. That is, the

stable demand from the entire economic system on the products / services from these

infrastructure sectors is important for the healthy operation and production of these

infrastructure sectors and other sectors. In other words, a decreased demand on these

infrastructure sectors would have a higher impact on them than a decreased reduced

supply to these sectors.

51

User, 05/16/06,

Change “Power” to “Influence” profile…


Furthermore, as we compare the supply-drivensupply-constrained profiles of these

infrastructure sectors with other economic sectors, we see that the profiles of these

infrastructure sectors are sitting at the right side of these economic sectors’ profiles. That

is, the loss of the supply to these infrastructure sectors can bring a greater impact to these

infrastructure sectors than how the loss of supply impacts other sectors. The emphasis is

that keeping the stable and continuous supply of the required services / products to these

infrastructure sectors is extremely important.

To compare among these infrastructure sectors, the rank of the vulnerability and

influence of these selected infrastructure sectors according to the combination of different

measurements and disruption propagation modes are summarized in Tables 12 and 13.

The impact value is represented by the mean of the distribution of impact values after

taken logarithmic transformation. From the ranking results, we see that food and drinking

service sector would be more vulnerable than other infrastructure sectors as it needs

provisions from various sectors and in large amounts. Truck transportation, rail

transportation would be more vulnerable if the demand for these transportation services

decreases.

Value Rank Value Rank Value Rank Value Rank211000 Oil and gas extraction -6.40 3 -8.65 1 -8.79 7 -11.04 7221100 Power generation and supply -6.27 2 -9.39 5 -8.00 2 -11.18 10324110 Petroleum refineries -6.62 5 -9.42 6 -8.16 3 -11.02 6481000 Air transportation -7.32 6 -9.85 8 -8.21 5 -10.81 3482000 Rail transportation -7.59 8 -8.98 2 -9.52 9 -10.97 5483000 Water transportation -9.12 11 -10.06 10 -9.68 10 -10.69 2484000 Truck transportation -6.11 1 -9.00 3 -8.17 4 -11.12 8486000 Pipeline transportation -8.17 10 -9.23 4 -9.75 11 -10.87 4514100 Information services -9.50 12 -9.72 7 -10.89 12 -11.16 952A000 Monetary authorities and depository credit intermediation -6.48 4 -10.07 11 -8.37 6 -12.02 127211A0 Hotels and motels, including casino hotels -8.02 9 -10.03 9 -9.29 8 -11.36 11722000 Food services and drinking places -7.36 7 -10.95 12 -6.81 1 -10.46 1

NAICS Sector NameRank. Of Vulnerability Profile (mean of log distribution)

Demand-Driven Supply-DrivenTotal Economic Total Inoperability Total Economic Total Inoperability

Table 12 Vulnerability Ranks of Infrastructure Sectors

52


Value Rank Value Rank Value Rank Value Rank211000 Oil and gas extraction -11.04 7 -8.79 7 -8.65 1 -6.40 3221100 Power generation and supply -11.18 10 -8.00 2 -9.39 5 -6.27 2324110 Petroleum refineries -11.02 6 -8.16 3 -9.42 6 -6.62 5481000 Air transportation -10.81 3 -8.21 5 -9.85 8 -7.32 6482000 Rail transportation -10.97 5 -9.52 9 -8.98 2 -7.59 8483000 Water transportation -10.69 2 -9.68 10 -10.06 10 -9.12 11484000 Truck transportation -11.12 8 -8.17 4 -9.00 3 -6.11 1486000 Pipeline transportation -10.87 4 -9.75 11 -9.23 4 -8.17 10514100 Information services -11.16 9 -10.89 12 -9.72 7 -9.50 1252A000 Monetary authorities and depository credit intermediation -12.02 12 -8.37 6 -10.07 11 -6.48 47211A0 Hotels and motels, including casino hotels -11.36 11 -9.29 8 -10.03 9 -8.02 9722000 Food services and drinking places -10.46 1 -6.81 1 -10.95 12 -7.36 7

NAICS Sector NameRank. Of Power Profile (mean of log distribution)

Demand-Driven Supply-DrivenTotal Economic Total Inoperability Total Economic Total Inoperability

Table 13 Power Ranks of Infrastructure Sectors

53


9. Summary and Discussions

Discussions about infrastructure security and survivability require system-wide

comparisons and interdisciplinary approaches. Our consideration of survivability focuses

on large-scale economic implications of attacks or vulnerabilities on major infrastructure

sectors as defined by the Department of Commerce (DoC). The basic market

relationships between industries comprising the core service sector are identified by using

data from the DoC and the existing supply chain analysis models. Instead of relying on

generic and qualitative models, this research provided a quantitative approach to assess

interdependence risk between businesses within and dependent on the infrastructure

sectors and designed an innovative methodology for industries to better evaluate their

supply chains vulnerability in the event of market disruption. Specifically, we tackle this

problem from the following perspectives:

First, we introduced and established two interdependence models that can be used in

interdependency analysis. By utilizing two impact measurements: economic loss and

inoperability proposed by Haimes, this paper extends the Ghosh economic input-output

model to estimate the magnitude of supply constrained impact. When using a supply-

constrained interdependency model, a scarcity of a particular resource, say petroleum, is

viewed as initially constraining payments to labor, capital, and other value-added in

petroleum production industry, and subsequently decreasing the availability of petroleum

inputs to other industries. The interdependence risk has been identified by measuring the

magnitude of revenue losses due to economic shocks. The demand-driven

interdependence model can evaluate the loss of output derived from reduced interest or

request of a sector’s product/service. Supply constrained model is used to evaluate the

consequence on local or national economy from limited resources.

One advantage of having these interdependence models is that they can detect both the

direct and indirect impact from an initial disruption. Historical records show that the cost

of cascading failure is huge. According to the data from the North American Electric

54


Reliability Council (NERC), outage from 1984 to the present affects nearly 700,000

customers annually. Many of the outages were exacerbated by cascading effects [Amin

2000]. To estimate and envisage the impact more realistically, models that can evaluate

indirect impact are highly desired. Impacts of higher-order effects can be detected from

the model output. As [Little 2002] mentioned, how far these effects propagate, and how

serious they become, depends on how tightly coupled the infrastructure components are,

how potent the effects are, and whether or not countermeasures such as redundant

capacity are in place. The proposed interdependence enables the detection of not only

direct impact but also higher order dependence induced impacts.

Second, four methods have been recommended to classify one economic sector as a

typical supply sector or a demand sector. The classification is needed as we want to

understand the properties of different sectors and recommend appropriate models for

counting the potential risk of the sector. This is a necessary step before we start to

prioritize what kind of impact should be considered first after the disruption occurs in a

particular industry: the impact on its upstream sectors or the impact on its downstream

sectors. The classification results are generated according to the supply requirements and

demand needs from each sector and derived after comparison of the supply side

connection with demand side connection based on the number of players, the amount of

transactions or the impact acquired by different measurements.

Out of the roughly 500 sectors in the DoC model, only a few sectors have been identified

as critical infrastructure sectors. So far, there is no clear-cut and instructive definition of

infrastructure sector and the criteria for selection of infrastructure sectors has changed

over time. The research identified that most of the practically classified infrastructure

sectors are supply sectors in general. The study shows that these sectors are critical and

significant mostly because of their role as an important major supply sector and they

provide fundamental and critical service to the other sectors. We suggested in the paper

that functioning as a critical supplier should be set as a main criteria to identify the

critical infrastructure sectors. The result further reveals the importance to have a supply

constrained model to evaluate the significance of these infrastructure sectors.

55


The determination of a demand sector versus a supply sector enables us to predict wisely

the kind of disruptions that should be prepared for the potential disruptions of that sector:

its upstream sectors or its down stream sectors. With this knowledge in mind, we can

prepare strategically and tactically measures that are needed and can maximally mitigate

the total losses.

Third, assessing and comparing the survivability and vulnerability among economic

sectors in a systematic way has hardly been studied. With the increasing attention in the

United States on national security, there are many issues and agendas put forth that

identify vulnerabilities in our system. The resulting legislative push towards exposing

apparent problems, there is no obvious socially acceptable way to choose which

vulnerabilities should be addressed first. In this paper, we proposed and designed two

profiles: vulnerability profile and power profile to evaluate the vulnerability and

influence of individual economic sector, especially these infrastructure sectors. We

studied the properties and the response behavior of these sectors after disruption happens

as either a demand sector or a supply sector.

We created also sector profiles for each to summarize the resilience and security level of

each sector throughout the economy. Through the estimation of the fraction of direct and

total supply chain effects for all sectors, we separately created a ranking of the two types

of results to show which of these sectors are most pervasive throughout the economy, as

well as which are most dependent on other sectors. For example, we could show which

sectors use the most electricity, and also which sectors are most purchased to generate a

given amount of electricity.

The type of the model we proposed here represents the average production in a sector by

an average firm. So at the firm level, a financial service company could compare its own

infrastructure vulnerabilities with the average firm in the sector to guarantee that

emergency response plans and corporate disaster training fully incorporate the range of

vulnerabilities that exist. A similar analysis across all infrastructure and service sectors

would show the economic effect other sectors would feel due to a technological or

56


economic shock to national infrastructure. As crisis management is still predominantly a

local affair [Boin et al. 2003]. The assessment at the local level comparing with the

national level could be one criterion to determine whether special improvement is needed

in that company at local level. The individual firm should generate their own

vulnerability profile and compare with the average level of the sector it belongs to and

determine whether a higher level of security should be considered or a lower severity

security level be planned.

Overall, analysis of this kind can lead to new approaches to resource allocation for

investment, or build up redundancy to assure infrastructure capabilities. Using the data as

mentioned above allows us to address a wide range of potential policy questions. For

example, we could consider which portion of the service sectors should be given budget

priority for upgrading security. We could look at the economic dependencies of all other

sectors in the economy to see, for example, which of the infrastructure sectors, lead to the

most value added in the economy. Thus making investment for security upgrades in that

sector would have the largest prophylactic effect when considering the degree to which

potential negative economic shocks could be avoided. By estimating rankings of

vulnerability, companies within and dependent on the service sector can plan for

survivability. When viewed from a national security or survivability perspective, these

insights of how sectors depend on each other to create output will suggest policy or

management changes to improve the reliability of the supply chain. We can explore such

issues by considering alternatives and estimating the economic effects of such changes.

For example, we can consider the effects of making a $1 billion investment in improving

the security of the electricity grid to ensure better telecommunication connectivity.

57


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