Review on Energy Resilience

Inoperability Input-Output Modeling of Disruptions to Interdependent Economic Systems

INOPERABILITY INPUT-OUTPUT MODELING OF DISRUPTIONS TO INTERDEPENDENT ECONOMIC SYSTEMS

Joost R. Santos*

Research Assistant Professor, Department of Systems and Information Engineering, and Center for Risk Management of Engineering Systems, University of Virginia, Charlottesville, VA 22904

Received 27 April 2005; Accepted 17 August 2005, after one or more revisions Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/sys.20040

ABSTRACT

In this study, the Inoperability Input-Output Model (IIM) is deployed for assessing the impacts of disruptive events on interconnected economic systems. The IIM is based on Wassily Leontief’s input-output model which is capable of describing the ripple effects of disruptions to interdependent systems. Besides describing economic impact in financial terms, the “inoperability” metric is also used in the IIM to quantify the percentage of a system’s production that is affected relative to the desired level. To analyze the magnitude and extent of system linkages, an interdependency matrix based on the North American Industry Classification System (NAICS) is constructed. The study highlights four key features of the IIM. First, demand patterns in the aftermath of such events are modeled and analyzed using available sector-based performance data. Second, the NAICS-based capital flow data re- leased for the first time in 2003 by the US Bureau of Economic Analysis enable applying a dynamic IIM to describe the temporal behavior of economic impacts associated with disrup- tive events. Third, a discussion on utilizing other sources of data, such as consumer confidence for forecasting system-specific demand disruptions, is presented. Fourth, a visualization tool is presented for conducting a multi-criteria ranking of the most-affected systems using both economic loss and inoperability metrics. Ultimately, the study offers insights on describing the sensitivity of economic systems to various classes of disruptions. In the broader perspec- tive, this can provide guidance toward policymaking activities. © 2006 Wiley Periodicals, Inc. Syst Eng 9: 20–34, 2006

Key words: inoperability input–output model; regional analysis; terrorism; homeland security; multi-criteria decision analysis

Regular Paper

*E-mail: [email protected].

Systems Engineering, Vol. 9, No. 1, 2006 © 2006 Wiley Periodicals, Inc.

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1. INTRODUCTION

Any systems engineering process requires the compre- hensive documentation and accounting of interdepend- encies among its elements (or sub-systems). To achieve the as-planned functionality (or normative scenario) of a system, it is important to understand the ripple effects associated with a direct disruption to a particular sub- system (or a set of sub-systems), and how such ripple effects can adversely impact the “health” of the overall system. In order to quantify the adverse effects of a given disruption, the use of performance metrics is vital, measured relative to the system’s predefined nor- mative scenario.

Systems engineering is commonly associated with the development, operation, and maintenance of tech- nological systems (e.g., aerospace, transportation, tele- communication, and computer systems). However, this paper focuses on the US economy as a large-scale system of systems comprised of interdependent indus- try sectors (e.g., banking, transportation, trade, and service sectors). It emphasizes the importance of inter- dependency analysis in the context of interconnected economic systems. No literature survey on interdepen- dency analysis is complete without mentioning the Input-Output (I-O) Model [Leontief, 1951a; 1951b], for which Wassily Leontief received the 1973 Nobel Prize in Economics. The I-O model is useful for study- ing the effects of consumption shocks on interdepend- ent economic systems.

The previously developed Inoperability Input-Out- put Model (IIM) [Haimes and Jiang, 2001; Santos and Haimes, 2004] was formulated on the basis of Leon- tief’s model, which attempts to predict the resulting economic losses and inoperability suffered by individ- ual sectors resulting from a direct disruption to a par- ticular sector (or a particular set of sectors). The current study revisits the IIM, provides extensions, and offers new features such as:

(i) using the North American Industry Classifica- tion System (NAICS) as applied to the most recent I-O tables (year 2003);

(ii) adding a dynamic capability using the capital flow data;

(iii) providing insights on how other data sources such as consumer confidence indices can be em- bedded in the IIM for structuring demand pertur- bation inputs; and

(iv) validating IIM results versus previously publish- ed 9/11 economic loss estimates and presenting a visualization tool for conducting multi-criteria analysis.

Today, economic sectors in the US (and the entire global economy) are highly interdependent—making them more vulnerable to natural and human-caused disruptive events. Such events not only disrupt the “business-as-usual” production levels of the affected systems, but they also lead to a variety of economic losses such as demand reductions. Interdependency analysis applies to ripple effects triggered by various sources of disruptions, including terrorism, natural ca- lamities, and accidents, among others. However, this paper specifically applies interdependency analysis to quantify economic losses due to terrorism-induced de- mand degradations. Efforts to deter terrorist attacks and mitigate their consequences are vital to address current high-priority national goals and homeland security con- cerns in the US. (See, for example, Executive Order 13260 [2002].)

Psychological factors mirror the physical destruc- tion rendered by terrorism and other extreme disasters. A comprehensive survey of the psychological effects of various types of disasters is documented by Norris et al. [2002]. Empirical studies such as those conducted by Susser et al. [2002] and Galea et al. [2002] specifically show the significance of post-traumatic stress disorder (PTSD) in the aftermath of the September 11, 2001 (or “9/11”) attacks. This paper postulates that fear can cause the public to reduce its consumption of the goods/services produced by an attacked system. For example, public apprehension on air transportation pur- suant to 9/11 caused a dramatic reduction in the demand for outputs of the airline transportation and other air- line-dependent systems [FAA, 2002]. These retrench- ments and changes in demand can have compelling economic ramifications, in addition to structural and human losses.

This article implements the IIM to analyze terror- ism’s impact on interconnected economic systems. The IIM’s risk assessment capabilities can help to identify the critical systems in the US that are in most need of protection—given specific input scenarios surrounding the nature and extent of a possible terrorist attack. Therefore, the IIM can guide the generation of risk management policy options. The remainder of the arti- cle is organized as follows. Section 2 presents the IIM and background discussions on Leontief’s I-O model. Section 3 enumerates and describes the databases for implementing the IIM, including other potentially use- ful data for estimating effects of disruptive events on consumption. Section 4 presents a demonstration of the IIM model and a dynamic extension using capital flow data for assessing the effects of the September 11, 2001 attacks. Finally, Section 5 provides the summary and conclusions of the study.

INOPERABILITY INPUT-OUTPUT MODELING OF DISRUPTIONS TO INTERDEPENDENT ECONOMIC SYSTEMS 21

2. INOPERABILITY INPUT-OUTPUT MODEL

2.1. Background: Leontief Input-Output Model

Wassily Leontief was awarded a Nobel Prize in Eco- nomics in 1973 for what became known as the Input- Output (I-O) Model for Economy [Leontief, 1951a; 1951b]. Miller and Blair [1985] provide a comprehen- sive introduction of the model and its applications. Leontief’s I-O model describes the equilibrium behav- ior of both regional and national economies [Lahr and Stevens, 2002; Liew, 2000; Isard, 1960]. The I-O model is a useful tool in economic decisionmaking processes used in many countries [Miller et al., 1989]. Leontief’s I-O model presents a framework that is capable of describing the interactive nature among economic sys- tems. Extensions and current frontiers on I-O analysis can be found in Lahr and Dietzenbacher [2001] and Dietzenbacher and Lahr [2004]. It is worth noting that the traditional use of input-output analysis for estimat- ing the effects of economic shifts (e.g., changes in consumption) has been extended to other applications such as disaster risk management, environmental im- pact analysis, and energy consumption, among others. Various studies for estimating losses pursuant to disas- ters have employed traditional I-O analysis and ex- tended approaches such as computable general equilibrium models. Rose and Liao [2005] conducted a case study of water supply disruption scenarios in Port- land using computable general equilibrium (CGE) to account for resilience factors (e.g., substitution and conservation) that business sectors typically consider in order to minimize the potential losses. (Note that Rose [2004] states that CGE is an extension rather than a replacement of the traditional I-O model). Cho et al. [2001] identified the I-O model as a useful tool for estimating the economic costs associated with major earthquakes in urban areas. Lenzen et al. [2004] imple- mented a multi-region environmental input-output analysis to determine CO2 multipliers based on interna- tional trade data for commodities that emit greenhouse gas by-products. Alcántara and Padilla [2003] devel- oped an I-O-based methodology that considers energy demand elasticities for determining the key sectors that are involved in the final consumption of energy.

The formulation of the basic Leontief I-O model is shown in Eq. (1). The notation xi refers to the total production output of industry i. On the other hand, the Leontief technical coefficient aij indicates the ratio of the input of industry i to industry j, with respect to the total production requirements of industry j. Thus, given n industries, aij can tell the distribution of inputs con-

tributed by various industries i = 1, 2, . . . , n to the total inputs required by industry j. Finally, the notation ci refers to the final demand for the ith industry—the portion of industry i’s total output for final consumption by end-users (i.e., the excess of all intermediate con- sumptions by various industries j = 1, 2, . . . , n).

x = Ax + c ⇔ {xi = ∑ j

aijxj + ci} Wi (1)

2.2. Inoperability Input-Output Model (IIM)

Based on Leontief’s work, Haimes and Jiang [2001] developed the Inoperability Input-Output Model (IIM) for interconnected systems. One of the metrics offered by the IIM is inoperability, which is defined as the inability of a system to perform its intended functions. In the IIM, inoperability can denote the level of the system’s dysfunction, expressed as a percentage of the system’s intended production level. Inoperability can be caused by internal failures or external perturbations, which negatively affect the delivery of a system’s in- tended output. The IIM was later expanded by Santos and Haimes [2004] to quantify the economic losses triggered by terrorism and other disruptive events to economic systems (or industry sectors). The analysis of economic impacts associated with such events is made possible through the economic I-O data published by the Bureau of Economic Analysis (BEA) [1998]. The formulation of the IIM is as follows:

q = A*q + c* (2)

The details of model derivation and an extensive discus- sion of model components are found in Santos and Haimes [2004]. In a nutshell, the terms in the IIM formulation in Eq. (2) are defined as follows:

• c* is a demand-side perturbation vector expressed in terms of normalized degraded final demand (i.e., “business-as-usual” final demand minus ac- tual final demand, divided by the “business-as- usual” production level);

• A* is the interdependency matrix that indicates the degree of coupling of the industry sectors. The elements in a particular row of this matrix can tell how much additional inoperability is contributed by a column industry to the row industry; and

• q is the inoperability vector expressed in terms of normalized economic loss. The elements of q represent the ratio of unrealized production (i.e., “business-as-usual” production minus degraded production) with respect to the “business-as- usual” production level of the industry sectors.

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Previous IIM-based works on infrastructure interde- pendencies and risks of terrorism include Haimes [2002; 2004], Haimes and Horowitz [2004], Jiang and Haimes [2004], and Haimes et al. [2005a; 2005b]. Other quantitative research on modeling terrorism risks have emerged in the recent years because of the sus- tained threats to homeland security. Apostolakis and Lemon [2005] proposed the use of graph theory for modeling infrastructure interconnectedness and em- ployed the multi-attribute utility theory for setting pri- orities to vulnerabilities. Paté-Cornell and Guikema [2002] employed the probabilistic risk analysis (PRA), decision analysis, and game theory for prioritizing vul- nerabilities and their associated countermeasures. Bier and Abhichandani [2003] proposed a game-theoretic approach to model how defenders and offenders deter- mine the optimal strategies to achieve their respective objectives of protecting or destroying a system.

2.3. Practical Uses of the IIM

The IIM provides a computation base for risk-impact analysis that utilizes I-O data from the US Department of Commerce. One of its divisions, the Bureau of Eco- nomic Analysis (BEA), is responsible for documenting the transactions of approximately 500 producing and consuming sectors within the economy. Through the direct use of the detailed national I-O tables published by BEA, the IIM benefits from the agency’s intensive data-collection efforts and resource base. In addition, the Regional Input-Output Multiplier System (RIMS II) can be utilized for conducting regional-level analysis. The IIM framework can provide a foundation for eco- nomic impact and sensitivity analysis that can guide policymaking activities for mitigating the highly uncer- tain outcomes of disruptive events.

Given that BEA data provides each producing sec- tor’s requirement or support from other sectors (i.e., production inputs such as products and services), IIM is capable of:

• estimating the impact of initial disruptions to a sector (or group of sectors) to other “external” sectors;

• assessing the propagating impacts of disruptive events for various regions; and

• presenting various perspectives of impact, in- cluding inoperability and economic loss, which can provide insights for risk management.

2.4. Assumptions and Limitations of the IIM

The IIM formulation retains several assumptions from the original Leontief structure. Many assumptions re- main unchanged in order to capitalize on the vast BEA

databases that were designed specifically for the equi- librium, deterministic, and linear model. To optimally understand and interpret analysis results, it is important to address the underlying model assumptions:

• Equilibrium Assumption. Equilibrium implies that industry inputs and outputs will balance with the final consumption of the sectors’ outputs. In the long run, such a condition is evidently true. However, during the transient times following scenarios that impose large and widespread de- mand perturbations, non-equilibrium conditions could dominate. In such cases, the IIM results would not accurately reflect the real economic effects. Therefore, it is necessary to consider a substantially long period of time to satisfy the equilibrium assumption.

• Deterministic Assumption. At the core of Leon- tief’s model and the IIM is the technical coeffi- cient matrix A, derived from BEA’s databases. These equilibrium data define deterministic guidelines for sector interactions based on as- sumptions of constant technology and economic structure. Hence, the constant values that define the relationships between sectors are time-invari- ant and deterministic. The BEA generates the comprehensive I-O data every five years because of the intensive data collection effort required and also because economic momentum does not cause the technical coefficients to deviate dra- matically from year to year.

• Linear Assumption. The BEA decomposes the US economy into about 500 sectors whose out- puts contribute to the inputs required by other sectors. Each element in this matrix gives a con- stant, linear value that represents the contribu- tions to one sector, say j, from any other sector, say i, which is proportional to the output of sector j. There are obvious examples where this assump- tion is valid. For example, if sector i is tire pro- duction and sector j is automobile production, then the value of tires used by sector j would naturally increase linearly with the value of auto- mobiles produced. On the other hand, there are also cases, perhaps less obvious, where the linear- ity assumption may not be valid. As production increases proportionally, producers seek to in- crease efficiency through resource-sharing, among other measures, to consume fewer pro- duction requirements. Addressing nonlinearity (e.g., assigning a range of values to technical coefficients) would require substantially longer data-collection time and higher cost.

INOPERABILITY INPUT-OUTPUT MODELING OF DISRUPTIONS TO INTERDEPENDENT ECONOMIC SYSTEMS 23

There are complexity issues that need to be consid- ered in the analysis of large-scale systems. Bar-Yam [1997] identifies several manifestations of complexity such as nonlinearity, nonreducibility and interconnect- edness. Rinaldi et al. [2001] highlight the complex adaptive nature of interdependent infrastructures. Al- though the current paper recognizes the limitations of the I-O method in capturing the complexity of large- scale systems, it can provide a reasonable framework for assessing the impacts of disruptive events to inter- dependent economic systems. In particular, the 9/11 case study presented in the paper has a substantially long duration of effects (i.e., more than one year), and it is assumed that the presence of “noisy” transient behaviors among the interacting economic sectors have already smoothened out for the time horizon of interest. Also, the I-O data collection of the BEA for a large group of sectors already consumes immense time and resources, hence the benefit-to-cost ratio of collecting higher-fidelity data to address complexity is assumed to be insignificant in the context of 9/11 macro-scale modeling.

3. DATA SOURCES FOR ANALYSIS OF ECONOMIC DISRUPTIONS

3.1. Bureau of Economic Analysis (BEA) Data

The BEA publishes the national economic I-O accounts [BEA, 1998]. These are a series of tables depicting the production and consumption of commodities (i.e., goods and services) of various sectors in the US econ- omy. The detailed national tables are composed of hundreds of industries, organized according to the Standard Industry Classification (SIC) or more re- cently, the North American Industry Classification Sys- tem (NAICS) codes.

In the original Leontief model formulation, each industry is assumed to produce a distinct commodity. The term commodity in this article refers to the output of an industry, which can take the form of goods or services. Realistically, it is possible that a given industry can produce more than one commodity. On the other hand, a given commodity may not be a unique output of a given industry. The BEA recognizes that assuming a one-to-one correspondence between an industry and commodity is generally not true. The BEA makes a distinction between an industry and a commodity in its published I-O data via the make and use matrices (e.g., Lawson [1997]).

3.2. Coefficients of Production (The “Make” Matrix)

The make matrix is an industry-by-commodity matrix. It would show the monetary values of the different column commodities produced by the different row industries. Table I shows partial entries of the make matrix data for the 2003 US economy. For example, the crop and animal production (CROP) industry produced $215,977 million and $6,037 million worth of crop and animal production (CROP) and forestry, fishing, and related activities (FRST) commodities, respectively, in 2003.

3.3. Coefficients of Consumption (The “Use” Matrix)

The use matrix on the other hand is a commodity-by- industry matrix. It would show the monetary values of the different row commodities consumed by the differ- ent column industries. Sample data from the use matrix is depicted in Table II. For example, the crop and animal production (CROP) commodity was used by several industries as follows: $61 million by the crop and animal production (CROP) industry; $1,842 million by the forestry, fishing, and related activities (FRST) in-

(Based on http://www.bea.gov/bea/pn/Annual_IOMakeUse.XLS, accessed March 31, 2005.)

Table I. Partial Make Matrix for 2003 US Economy, in Millions of Dollars

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dustry; $496 million by the oil and gas extraction (OILG) industry, and so on.

3.4. Technical Coefficient Matrix

Note that neither the make nor the use matrix represents an industry-by-industry matrix of transactions. This matrix, denoted by A in standard Leontief model for- mulation, is called the technical coefficient matrix. It would show the input of industry i to j, expressed as a proportion of the total production inputs to industry j. BEA does not typically publish the elements of the A matrix because this task is left to the analyst. The A matrix can be established from the make and use matri- ces using various assumptions (e.g., commodity-tech- nology assumption (CTA) and industry-technology assumption (ITA); see Guo et al. [2002]). One approach is carried out by first normalizing the values of the make and use matrices and then multiplying the resulting normalized matrices.

3.5. Capital Flow Matrix A capital flow matrix published by the BEA describes how capital commodities (e.g., equipment, software, and structures) are distributed throughout sectors in the economy. An excerpt of a capital flow matrix is shown in Table III. For example, this table indicates that the crop and animal production (CROP) industry invested $13,127 million worth of capital commodities pro- duced by the machinery manufacturing (MACH) in- dustry. A normalized version of the capital flow data would give rise to the capital coefficient matrix, denoted by B in the standard dynamic I-O formulation.

3.6. Regional Input-Output Multiplier System (RIMS II) Regional decomposition enables a more focused and hence a more accurate analysis of interdependencies for regions of interest in the United States. The Regional I-O Multiplier System (RIMS II) division of the BEA

(Based on http://www.bea.gov/bea/pn/Annual_IOMakeUse.XLS, accessed March 31, 2005.)

(Based on http://www.bea.gov/bea/newsrel/capitalflownewsrelease.htm, accessed March 31, 2005.)

Table III. Partial Capital Flow Matrix for 1997 US Economy

Table II. Partial Use Matrix for 2003 US Economy, in Millions of Dollars

INOPERABILITY INPUT-OUTPUT MODELING OF DISRUPTIONS TO INTERDEPENDENT ECONOMIC SYSTEMS 25

[1997] is responsible for releasing multipliers for vari- ous regions in the United States. Empirical tests suggest that regional multipliers can be used as surrogates for time-consuming and expensive surveys without com- promising accuracy [Brucker et al., 1990]. With the availability of national use and make matrices, analysts can convert and localize the national data according to the region of interest. The RIMS II utilizes location quotients derived from personal income data and wage- and-salary data to regionalize the national technical coefficient matrix (i.e., the A matrix). A location quo- tient indicates how well an industry’s production capac- ity satisfies the regional local demand. In addition, as the value of an industry’s location quotient tends to 1, its relative concentration in the region approaches that of the national level. RIMS II issues a series of multi- pliers for various sectors of a specified region, gener- ated via the region’s location quotients. Some examples are as follows:

• Output Multiplier—gives the change in a sector’s production output resulting from a $1 change in the demand for that output.

• Earnings Multiplier—gives the change in a sec- tor’s workforce earnings resulting from a $1 change in the demand for that sector’s output.

• Employment Multiplier—gives the change in a sector’s number of workers resulting from a $1 million change in the demand for that sector’s output.

3.7. Other Data Sources

Consumption behavior in the aftermath of disruptive events can be modeled and analyzed using measures of consumer confidence. The two most popular indices of consumer confidence are those released by the Confer- ence Board (http://www.conference-board.org) and the University of Michigan’s Survey of Consumers (http://www.sca.isr.umich.edu). These agencies pub- lish results derived from their analyses of consumer responses to an interview questionnaire. For example, they publish a time series of the values of consumer confidence representing the public’s beliefs (i.e., expec- tations) on the strength of the economy. The trajectory of the consumer confidence index can be used to fore- cast changes in consumption. In other words, changes in consumer expectations on the economy typically correlate to changes in gross domestic product (GDP); see Howrey [2001].

Consumption patterns in the aftermath of disruptive events may also be predicted using web-based fact sheets on post-traumatic stress disorder (PTSD). Exam- ples of these websites include the National Center for Post-Traumatic Stress Disorder, which maintains a

comprehensive database of literature pertaining to the psychological effects of various types of disruptive events (see, for example, Norris et al. [2002]). Such events translate to a variety of public behavior effects such as a low-morale work environment (hence, affect- ing productivity), and in terms of consumption, nega- tive impacts on spending are generally observed (e.g., decrease in demand for directly-affected and discretion- ary sectors).

4. CASE STUDY

4.1. Scenario Description

The case study described in this article is an ex post analysis of the September 11, 2001 (or “9/11”) attack on the United States. Although many sectors of the economy were affected initially by this disruptive event, this economic loss estimation focuses on those sectors that suffered the largest demand reductions. The study uses integrated information derived from I-O matrices (make, use, and capital flow), supported with data pub- lished by the Federal Aviation Administration [2002] and Ernst and Young [2002]. It considers a 33.2% reduction in passenger enplanements and a 19.2% re- duction in hotel occupancy. These demand-reduction percentages are then used as inputs to the IIM. The 59-sector NAICS classification scheme is utilized, which can be found in Table IV. (Note that in addition to the NAICS sector definitions, this table contains other information that will be discussed further in the “Dynamic Multipliers” section.)

4.2. Inoperability and Economic Loss Rankings

Demand-side inoperability (or inoperability, for brev- ity) is one type of metric that results from the IIM analysis. It represents the percentage gap between a sector’s “business-as-usual” and current levels of pro- duction due to demand reductions caused by a disrup- tive event. Using the initial demand reductions of 33.2% and 19.2% to the air transportation and accommodation sectors, respectively, the resulting ripple effects throughout the entire set of US economic sectors are calculated. In terms of the inoperability metric, the resulting top 10 most-affected sectors are shown in Figure 1: (i) Air transportation; (ii) Accommodation; (iii) Oil and gas extraction; (iv) Other transportation and support activities; (v) Petroleum and coal products manufacturing; (vi) Administrative and support serv- ices; (vii) Other transportation equipment manufactur- ing; (viii) Pipeline transportation; (ix) Rental and leasing services and lessors of intangible assets; and (x) Information and data-processing services.

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While the inoperability metric quantifies the non- achievement of a target production level, it is also meaningful to express the resulting impact of a demand reduction in terms of monetary values. Examples of questions that can be raised from Figure 1 are as fol- lows: How much economic loss is associated with a 33.49% inoperability of the air transportation sector? 19.38% inoperability of the accommodation sector? 2.99% inoperability of the oil and gas extraction sector? and so on. Such questions can be answered by ranking the economic losses as depicted in Figure 2. The top 10 sectors with the highest economic losses resulting from demand reductions in the air transportation and accom- modation sectors are as follows: (i) Air transportation; (ii) Accommodation; (iii) Administrative and support services; (iv) Professional, scientific, and technical services; (v) Petroleum and coal products manufactur- ing; (vi) Other transportation and support activities; (vii) Oil and gas extraction; (viii) Food services and drinking places; (ix) Real estate; and (x) Wholesale trade.

4.3. Multi-Criteria Evaluation Analysis

Integrating the inoperability and economic loss metrics offers additional insights into the IIM analysis. Specifi- cally, these metrics generate different sector rankings, which may be attributable to the sectors’ different pro- duction scales. For example, a $1 million economic loss in one sector (“Sector X”) is lower compared to a $10 million economic loss in another sector (“Sector Y”). However, “Sector X” can have a larger inoperability value than “Sector Y” if the ideal production levels are $5 million and $1 billion, respectively. This would lead to a 20% inoperability for “Sector X” ($1 million/$5 million) versus a 1% inoperability for “Sector Y” ($10 million/$1 billion). Therefore, both the IIM metrics of inoperability and economic loss need to be considered when conducting sector risk assessments because they yield different criticality rankings of sector effects. The effects can either be prioritized in terms of the magni- tude of monetary loss versus the “normalized” loss relative to a sector’s total production. Logically, differ-

Table IV. Dynamic Multipliers for the 59-Sector Classification Scheme for Three Time Lags

(continued)

INOPERABILITY INPUT-OUTPUT MODELING OF DISRUPTIONS TO INTERDEPENDENT ECONOMIC SYSTEMS 27

ent sets of priority sectors are generated depending upon the type of objective being considered (i.e., mini- mizing inoperability versus minimizing economic loss).

The case study results in Figures 1 and 2 show that the inoperability and economic loss metrics yield dif- ferent top 10 rankings of most-affected sectors. The sector rankings can be integrated into a multi-criteria evaluation matrix that is capable of encapsulating the results from both the inoperability and economic loss metrics. In Figure 3, the sector impacts are arranged according to three types of zones, namely the top 10, top 20, and top 30 zones. For example, the top 10 zone is generated by taking those sectors that belong to the top 10 rankings of both metrics. Referring again to Figure 3, the “intersection” of the top 10 sectors gener- ated from these metrics constitutes the top 10 zone. This includes: air transportation; accommodation; oil and gas extraction; other transportation and support activi-

ties; petroleum and coal products manufacturing; and administrative and support services.

Multi-criteria trade-off analysis can allow policy- makers to view the effects of terrorist attacks in different perspectives, which can provide decision-making in- sights to reduce the likelihood of a successful terrorist attack (e.g., hardening of vulnerable sectors and provid- ing redundancies to tightly-coupled sectors). In particu- lar, visual aids, such as the one presented in Figure 3, can give information on the most-likely sectors to suffer the largest effects (i.e., economic loss and inoperabil- ity). When multiple scenarios are considered (in addi- tion to the air transportation and accommodation sector scenario considered in the current case study), a more holistic comparison of the resulting rankings of critical sectors can be performed, which to some extent can provide guidance on generating courses of actions to reduce the likelihood and adverse effects of a suc- cessful attack.

Table IV. (continued) Dynamic Multipliers for the 59-Sector Classification Scheme for Three Time Lags

(d(k) is the multiplier for lag k and p(k) is the corresponding % relative to the total dynamic multiplier (I–A–B)–1)

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Figure 2. Sectors most affected in terms of 1-year economic losses given demand reductions in air transportation and accommodation sectors.

Figure 1. Sectors most affected in terms of inoperability given demand reductions in air transportation and accommodation sectors.

INOPERABILITY INPUT-OUTPUT MODELING OF DISRUPTIONS TO INTERDEPENDENT ECONOMIC SYSTEMS 29

4.4. Dynamic Input-Output Analysis

A dynamic form of the I-O model is discussed in Miller and Blair [1985]. In discrete form, the mathematical formulation of the dynamic model with time-invariant technical and capital coefficient matrices is as follows:

x(k) = Ax(k) + c(k) + B[x(k + 1) – x(k)] (3)

where k is a time index, x is the total production, A is the technical coefficient matrix, c is the final demand, and B is the capital coefficient matrix. This dynamic model converges to the static equation when the differ- ence between the outputs approaches zero for two suc- cessive periods.

The economic loss estimates provided in Figure 2 are underestimated because they capture only the losses

for the year following the 9/11 catastrophe. In addition, these estimates do not include other costs such as emer- gency response, costs for repairing the physical damage and cleanup, and equity losses (e.g., from stock market drops), among others (see related discussions in Center for Contemporary Conflict [2002]). The losses for sub- sequent years can be estimated via the concept of dy- namic multipliers. Liew [2000] derives a total multipliers formula (t) that includes a capital coefficient component to reflect losses that are accumulated over several production lags (measured in years). Denoting a vector of ones by i′ = [1 1 … 1] and a conformable identity matrix by I, we have:

t = i′(I – A – B)–1 (4)

Figure 3. Sectors most affected in terms of inoperability and economic losses resulting from demand reductions in the air transportation and accommodation sectors. (See Table IV for descriptions of abbreviated sectors.)

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The above vector of total multipliers can be decom- posed into a series of dynamic multipliers (d(k)) for various production lags k as follows:

d(0) = i′(I – A)–1 (5a)

d(1) = i′(I – A)–1B(I – A)–1 = d(0)B(I – A)–1 (5b)

I

d(k) = d(k – 1)B(I – A)–1 Wk > 0 (5c)

The first-ever NAICS-based capital flow data for the US (which is useful for generating the B matrix) was released by the Bureau of Economic Analysis in Sep- tember 2003. The capital flow data can indicate to some extent the degree of sector dependence on capital com- modities (investment in structures, equipment, or soft- ware on which other sectors are dependent).

To generate the B matrix, it is necessary to first conduct a compatibility mapping of the sector classifi- cations used in the capital flow data with those used in the A matrix. This mapping process enables the forma- tion of an adjusted capital flow data, which involves aggregating the lower-resolution capital sectors to match any of the 59 industry sectors utilized in the A matrix. (As one example, uranium, radium, and vana- dium ore mining capital sectors are subsets of the mining except oil and gas industry sector.) The resulting B matrix is then established by normalizing the entries along the jth column of the adjusted capital flow data (for all j) with the total production output of the corre- sponding column sector (i.e., the notation xj in Eq. (1)).

Using Eqs. (5a)–(5c), Table IV shows the temporal decomposition of the 59-sector dynamic multipliers over five periods. On the average, roughly 80% of the demand-reduction impacts are expected to be realized during the first year, while the remaining 20% of the impacts are spread over the remaining years following

a disruptive event. The demand-reduction scenarios in the 9/11 case study are those that initially render direct disruptions to the air transportation and accommoda- tion sectors. Figure 4 depicts the evolution of the dy- namic multipliers for these sectors over five time lags. For both sectors, the majority of the total impacts are realized within the first three years: about 70% of the impacts occur during the first year, about 25% during the second year, and about 5% during the third year.

Applying the same demand-reduction scenarios to the air transportation and accommodation sectors de- scribed earlier in this section, Figure 5 shows the top 10 sectors most affected in terms of 5-year economic losses. When compared to the first-year losses in Figure 2, several observations can be made. First, additional economic losses amounting to $50 billion ($158–$108 billion) are expected to be realized after the first year. Second, the rankings of the most-affected sectors are different (e.g., the wholesale trade sector which was initially ranked #10 in Figure 2 is raised to #8 in Figure 5). Third, three sectors that were not in the first year’s top 10 highest economic losses (computer and elec- tronic product manufacturing, other transportation equipment manufacturing, and construction) are now part of the 5-year top 10 highest economic losses. This result is not surprising because these three sectors pro- duce capital outputs that have relatively low replace- ment frequencies; this explains the somewhat delayed economic losses.

4.5. Discussion

The 9/11 case study was intended as an ex post analysis for model validation purposes. It is worth noting that the economic loss estimates are in the same ballpark of a previously published estimate by the Government Accountability Office [GAO, 2002:3]: “…while all the metropolitan areas in the country sustained losses of about $191 billion.”

Figure 4. Dynamic multipliers for the air transportation and accommodation sectors.

INOPERABILITY INPUT-OUTPUT MODELING OF DISRUPTIONS TO INTERDEPENDENT ECONOMIC SYSTEMS 31

Although economic loss estimates of the 9/11 at- tacks have been published previously, the IIM analysis offers additional perspectives on the event and results beyond the scope of other studies. An additional feature offered by the IIM is its capability of showing the distributions of economic losses according to different sectors using the 59-sector NAICS classification scheme. Typically, economic loss estimates are publish- ed in highly aggregated values that would comprise only broad sector categories. Hence, validating the sec- tor rankings obtained here is difficult to perform due to the insufficient level of sector details in other published estimates. Nevertheless, an ex post analysis can be conducted through comparisons of the actual total out- put data of each sector after year 2001 with the corre- sponding data before 2001 (Note: the case study performed here assumed that 9/11 just took place). For example, one can compare the difference in the total output of each sector for year 2002 and year 2000 using t h e B u r e a u o f E c o n o m i c A n a l y s i s d a t a [http://www.bea.gov/bea/dn2/i-o_annual.htm, date ac- cessed July 29, 2005]. Such analysis will reveal the sectors with greatest losses post 9/11 as follows: Com- puter and electronic products; Securities, commodity contracts, and investments; Machinery; Motor vehi- cles, bodies and trailers, and parts; Petroleum and coal products; Chemical products; Oil and gas extraction; Electrical equipment, appliances, and components;

Primary metals; and Air transportation. When com- pared to Figure 3 results, the majority of these sectors have been included in the ranking of the most-affected sectors in terms of economic losses. In addition, one of the equipment-producing sectors such as Computer and electronic products, which has not been ranked in Fig- ure 3, has been captured using the dynamic IIM ap- proach (see Figure 5).

5. SUMMARY AND CONCLUSIONS

The study highlights the importance of assessing eco- nomic interdependencies to identify the sectors that are most sensitive to the adverse effects of a disruptive event. Through the IIM, an I-O based framework ana- lyzed the negative demand effects of the 9/11 catastro- phe on the air transportation and accommodation sectors, and also the ripple effects to other sectors in the economy. The IIM analysis reveals the most-affected sectors through inoperability and economic loss met- rics, which can be used to prioritize sectors for planning and evaluating potential policy actions to manage the adverse effects of disruptive events. The resulting rank- ings produced by the IIM metrics can differ, hence motivating the development of a multi-criteria visuali- zation tool to introduce the importance of trade-off analysis.

Figure 5. Sectors most affected in terms of 5-year economic losses, given demand reductions in air transportation and accommodation sectors.

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Several useful databases can be fused to form input scenarios for the I-O computations. These include pas- senger enplanement data published by the Federal Avia- tion Administration and hotel occupancy data from research agencies such as Ernst and Young. Addition- ally, post-traumatic stress disorder data and consumer confidence surveys can be used to create perturbation inputs to the IIM, especially for disruptive events that are impending or have just recently taken place. The Bureau of Economic Analysis data sets (e.g., make, use, and capital flow tables) are primarily utilized to gener- ate the coefficient matrices that serve as engines for the inoperability and economic loss calculations. Although this article considers only one particular IIM input scenario, it is possible to incorporate parametric analy- sis to determine the sensitivity of sector rankings to different values of demand reductions. For example, one can tweak the air transportation demand-reduction value while fixing that of the accommodation sector (and vice versa) to determine the “tipping points” where changes in rank start to occur (i.e., each sector has a different set of linkages to other sectors).

The IIM can serve as a tool for forecasting any future impacts of 9/11. The US economy may still be suffering from some remaining effects, which can be potentially quantified via a dynamic I-O framework. The 9/11 case study presented here serves as a demonstration of the IIM. A similar approach can be customized for model- ing other disruptive events that can potentially cause prolonged demand reductions (e.g., the effect of the Severe Acute Respiratory Syndrome (SARS) epidemic on global tourism).

Although we have identified useful features of an I-O based framework for analyzing disruptive events, it is also necessary to carry out supplementary analyses that deal with other important modeling aspects and dimensions. A holistic 9/11 impact analysis study re- quires estimating losses other than those resulting from demand reductions. For example, I-O analysis may not be appropriate for estimating the physical losses that reduce the production capacity of sectors (e.g., de- stroyed structures and equipment necessary for produc- tion) (see discussions in Oosterhaven [1988]). Also, not all disruptive events entirely result in demand reduc- tions. Clearly, 9/11 has triggered increased spending on defense, intelligence, and other activities related to homeland security.

In conclusion, the IIM is a useful tool for identifying and managing the sectors that are critically affected by disruptive events. When used in combination with other tools, a more powerful and robust analysis can be performed to address other modeling issues beyond its current capabilities. Therefore, a more detailed effort to

integrate I-O models with other tools deserves contin- ued research attention.

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Joost R. Santos received his Ph.D. degree in Systems and Information Engineering from the University of Virginia (2003). To date, he is a Research Assistant Professor at UVa’s Center for Risk Management of Engineering Systems, where he is actively involved in various projects dealing with risk analysis and optimization of complex large-scale systems. He has led several risk management studies commissioned by agencies such as the Department of Homeland Security, Virginia Department of Transportation (VDOT), National Science Foundation, and NASA. He is a primary author or key contributor to more than 10 technical reports and peer-reviewed journal articles. Prior to his Ph.D. studies at UVa, he served for four years (1995–1999) as a faculty member of the University of the Philippines, College of Engineering. He worked as a staff in the Corporate Planning Division of the Philippine National Oil Company (1994). He obtained his Master’s (1997) and Bachelor’s (1994) degrees in Industrial Engineer- ing at the University of the Philippines (Diliman Campus).

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