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date: 15 November 2018

# Benefit-Cost Analysis of Economic Resilience Actions

## Summary and Keywords

Economic resilience, in its static form, refers to utilizing remaining resources efficiently to maintain functionality of a household, business, industry, or entire economy after a disaster strikes, and, in its dynamic form, to effectively investing in repair and reconstruction to promote accelerated recovery. As such, economic resilience is oriented to implementing various post-disaster actions (tactics) to reduce business interruption (BI), in contrast to pre-disaster actions such as mitigation that are primarily oriented to preventing property damage. A number of static resilience tactics have been shown to be effective (e.g., conserving scarce inputs, finding substitutes from within and from outside the region, using inventories, and relocating activity to branch plants/offices or other sites). Efforts to measure the effectiveness of the various tactics are relatively new and aim to translate these estimates into dollar benefits, which can be juxtaposed to estimates of dollar costs of implementing the tactics. A comprehensive benefit-cost analysis can assist public- and private sector decision makers in determining the best set of resilience tactics to form an overall resilience strategy.

# Introduction

The proliferation of research on resilience has focused increasingly on its measurement in recent years. This includes many studies of its ability to reduce property damage and/or business interruption (see, e.g., Barker & Santos, 2009; Hallegatte, 2008; Kajitani & Tatano, 2009; Rose, Oladosu, & Liao, 2007a; Rose & Wei, 2013). It also includes many studies to construct a resilience index, primarily at the community level (see, e.g., Cutter, 2016; Cutter, Burton, & Emrich, 2010; Rose & Krausmann, 2013; Sherrieb, Norris, & Galea, 2010). However, very few of these studies by themselves are sufficient for policy making from a risk management standpoint, because they lack one or more of the following measurements for resilience as a whole or in terms of various tactics or strategies to achieve it: effectiveness of resilience, benefits of resilience (in monetary terms), or costs of resilience.

This article develops a benefit-cost analysis (BCA) framework for economic resilience, examines complications of its implementation and derives illustrative benefit-cost ratios for some major resilience tactics. The focus is on resilience at the microeconomic level (i.e., individual businesses, households, government institutions) to reduce business interruption (BI) losses following a disaster. The definition of resilience has been restricted to actions that can be taken after a disaster strikes to reduce BI, because this is more in keeping with the essence of the term resilience, whose etymological origin is “to bounce back” (see also Alexander, 2013; Klein, Nicholls, & Thomalla, 2003). This is done also because pre-disaster actions to reduce the costs of disasters, commonly referred to as mitigation and primarily intended to reduce property damage, have been extensively analyzed in general and with regard to BCA (see, e.g., Lave & Balvanyos, 1998; MMC, 2005; Rose et al., 2007b; Schulze Brookshire, Hageman, & Tschirhart, 1987).

The article lays the groundwork for examining resilience by defining BI and examining its prominence in disaster risk management. Economic resilience is defined, and what economists term a production function framework is established for its analysis. This is followed by the presentation of an operational metric of resilience previously developed by the author (Rose, 2004; Rose, Oladosu, Lee, & Beeler Asay, 2009), which facilitates BCA. Attempts to measure resilience thus far and identify some of the major shortcomings these measurement efforts are then summarized. The next section develops a conceptual framework for BCA of resilience, followed by an exposition of how benefits and costs can be measured utilizing prior studies and data in the more general literature. The focus is primarily on the demand (customer) side of resilience rather than on the supply (provider) side because the former includes a much larger set of resilience options. The article concludes with a comparison of resilience and mitigation benefit-cost ratios (BCRs), discussion of the limitations of the analysis, and some guidelines for future research.

Until the last decade, natural hazard loss estimation, developed primarily by engineers, focused on property damage, with any other disaster costs generally considered “indirect,” or “secondary.” However, economists and other social scientists have broadened this framework (see, e.g., Tierney, 1997) into what has become known since the beginning of this century as “economic consequence analysis,” a major emphasis of which is that disasters incur other major types of costs to society that are no less important (Rose, 2015). Property damage represents a reduction of the capital stock and generally takes place at a given point in time. However, the capital stock itself does not directly affect the well-being of the citizenry; instead it is the flow of goods and services (including government services) produced from the capital stock that does so. Rather than just taking place at a point in time, these flow losses begin when the disaster strikes and continue until a business or the economy has recovered or has reached an alternative goal, typically referred to as a “new normal.” Flow losses are typically measured in terms of gross domestic product (GDP), personal income, profits, and employment, but in general are referred to as business interruption (BI).

In fact, both direct stock and flow losses have indirect counterparts. Indirect stock losses include ancillary fires or toxic releases. Indirect flow losses refer to ripple, or multiplier, general equilibrium, or macroeconomic effects, up and down the supply chain. Recent events have brought direct and indirect flow losses to the fore.1 For example, Rose et al. (2009) estimated that the BI losses, from the September 11, 2001, World Trade Center attacks, were more than $100 billion, or four times the property damage, and the vast majority of the BI losses were of an “off-site” nature associated with a behavioral response (a “fear factor”) manifesting itself in an almost two-year decline in air travel and related tourism.2 In terms of another example, because BI continues until an economy has recovered, the many analysts that use the pre-disaster level of economic activity as a reference point would consider this loss type, stemming from Hurricane Katrina, as continuing to this day.3 Actions that take place before an event, typically referred to as mitigation, reduce the frequency and magnitude of property damage. Of course, they also have the effect of reducing potential BI, but resilience is another way to reduce these latter types of losses, even after the disaster has struck. # Defining Economic Resilience Below, economic resilience is defined, and some fundamental considerations for compiling a Resilience Index are set forth. Following Rose (2007) and Rose et al. (2009), this begins with basic definitions and their relation to more general concepts of resilience and definitions in related fields. These comparisons have indicated that there are commonalities and differences across various fields, especially with regard to the essence of the definitions.4 In general, static resilience refers to the ability of the system to maintain a high level of functioning when shocked (see, e.g., Holling, 1973). Static economic resilience is the efficient use of remaining resources at a given point in time. It refers to the core economic concept of coping with resource scarcity, which is exacerbated under disaster conditions. In general, dynamic resilience refers to the ability and speed of the system to recover (see, e.g., Pimm, 1984). Dynamic economic resilience is the efficient use of resources over time for investment in repair and reconstruction. Investment is a time-related phenomenon—the act of setting aside resources that could potentially be used for current consumption to re-establish productivity in the future. Static economic resilience does not completely restore damaged capacity and is, therefore, not likely to lead to complete recovery. Of course, recovery is a multi-faceted activity. It is not as simple as, for example, just automatically rebuilding a school or bridge destroyed by an earthquake, hurricane, or armed attack. Note that the definitions are couched in terms of functionality, typically measured in economics as the flow of goods and services, such as gross domestic product (GDP), or broader measures of human well-being, as opposed to property damage. Note also, for both static and dynamic resilience, “ability” implies a level of attainment will be achieved. Hence, the definitions of economic resilience are contextual—the level of function has to be compared to the level that would have existed had the ability been absent. This means a reference point must be established. In the case of static economic resilience it refers to the case where resilience is entirely absent. In the case of dynamic resilience it refers to the normal recovery path, where no special resilience is implemented.5 Further discussion of this oft-neglected point is provided below. Another important distinction is between inherent and adaptive resilience. The former refers to aspects of resilience already built into the system, such as the availability of inventories, excess capacity, substitutability between inputs, and contingent contractual arrangements accessing suppliers of goods from outside the affected area (imports). Resilience capacity can be built up through these means and is then accessed after the disaster. Adaptive resilience arises out of improvisation under stress, such as Draconian conservation otherwise not thought possible (e.g., working many weeks without heat or air conditioning), changes in the way goods and services are produced, and new contracting arrangements that match customers who have lost their suppliers with suppliers who have lost their customers. The approach to resilience emphasized in this article delves deeper into economic considerations than does other work, such as the classic framework presented by Bruneau et al. (2003), by summarizing the research exploring the important dimensions of economic resilience, offering an operational metric better suited to it, enumerating resilience tactics (actions) and their characteristics, and spelling out the steps necessary to undertake a benefit-cost analysis to develop an optimal resilience strategy. # An Operational Metric Following Rose (2004, 2009), an admittedly crude but operational metric of resilience is provided. Direct static economic resilience (DSER) refers to the initial resilience effectiveness at level of the individual firm or industry (micro and meso levels) and corresponds to what economists refer to as “partial equilibrium” analysis, or the operation of a business or household entity itself.6 However, it can also apply to the initial effect of a resilience tactic at the macro level. Total static economic resilience (TSER) refers to sum of all effects stemming from the resilience action on the economy as a whole and would ideally incorporate what is referred to as “general equilibrium” effects, which would potentially include all of the price and quantity interactions in the economy, macro-aggregate considerations, and the broader ramifications of fiscal, monetary, and security policies related to the disaster. At the macro level, an example of DSER would be the direct effect of government keeping interest rates low to stimulate investment (such as the policy initiative after 9/11), while TSER would be the economy-wide effect of this policy. An operational measure of DSER is the extent to which the estimated direct output reduction deviates from the likely maximum potential reduction given an external shock, such as the curtailment of some or all of a critical input. In essence, DSER is the percentage avoidance of the maximum economic disruption that a particular shock could bring about. A major measurement issue is what should be used as the maximum potential disruption. For ordinary disasters, a good starting point is a linear, or proportional, relationship, as, for example, between an input supply shortage and the direct disruption to the firm or industry. Note that, while a linear reference point may appear to be arbitrary or a default choice, it does have an underlying rationale. A linear relationship, such as the use of fixed input coefficients in a linear production functions, connotes rigidity, the opposite of the “flexibility” connotation of static resilience defined in this article. Analogously, the measure of TSER is the difference between a linear set of total (direct and indirect) effects, which implicitly omits resilience, and a non-linear outcome, which incorporates the possibility of resilience. These reference points would be best established through the use of the simplest macro modeling approach—input-output (I-O) analysis, a linear model of all purchases and sales between sectors of an economy, based on the technological relationships of production (Rose, 1995). I-O characterizes a brittle economy exhibiting a minimum of resilience (see, e.g., Zoli & Healey, 2012). The definition is illustrated with the following case study by Rose et al. (2009), who estimated the national and regional economic impact of the September 11, 2001, terrorist attack on the World Trade Center (WTC). The researchers refined some available data indicating that more than 95% of the businesses and government offices operating in the WTC area survived by relocating—the vast majority to mid-town Manhattan or across the river to Northern New Jersey. Had all of these firms gone out of business, the potential direct economic loss in terms of GDP would have been$43 billion, the estimated value of the economic activity generated by business and government occupants of the World Trade Center. Relocation after 9/11 was facilitated by the on-going 2001 recession and the existence of extensive spare office space in general and of excess capacity in neighboring branch offices. However, relocation was not immediate, taking anywhere from a few days to as long as eight months for the vast majority of firms. Rose et al. (2009) calculated this loss in GDP at $11 billion. The researchers were then able to apply the resilience definition, provided in this section, to estimate that the effectiveness of relocation as a resilience tactic in the aftermath of the 9/11 attacks was 72% ($43 billion minus $11 billion, divided by$43 billion). This study highlights the importance of excess capacity as a resilience tactic. This more intensive use of resources is also the theme of the recovery in the current “Great Recession” in the U.S. and other countries, as employment recovery significantly lags the recovery of output. The experience of New York City thus signals a significant change in approaches to disaster recovery, which has typically emphasized prompt rebuilding. Coupled with stronger requirements for mitigation, and hopefully some general accumulated wisdom, economies are recovering less by reflex action and more by intelligent planning (see also Chang & Rose, 2012; Vale & Campanella, 2005).

For the most part, TSER refers to off-site considerations. These would include infrastructure interdependence, supply-chain interactions, community and institutional systems, and features of the economy of the entire region or nation, including the influence of fiscal and monetary policy. Clearly, Federal Reserve Bank policies, of providing $100 billion for interbank loans in the immediate aftermath of 9/11, and keeping interest rates low for a much longer period, greatly helped to reduce the potential losses of this disaster (Rose & Blomberg, 2010). Note also, while DSER can be directly empirically measured (e.g., every firm is aware of the amount of electricity it purchases directly), TSER cannot as readily be measured, primarily because of its complexity arising from the many rounds of interdependencies (e.g., the firm does not know how much electricity its direct and indirect suppliers and customers use).7 # Economic Theory Underpinnings ## Production Functions Economists have developed sound theories to explain the workings of most aspects of the economy. Theories are abstractions by definition, but they serve the purpose of providing a consistent framework of analysis that focuses on fundamental causal relationships. One such body of knowledge is known as production theory—how firms (businesses) operate. At the core is the concept of the production function, or how firms combine various inputs to generate their products. Specification of these functions provides insight into the combination of inputs and their productivity, substitution between inputs, and how input relationships with outputs vary according to scale. Various “functional forms” are available, the most ideal of which allow for a variety of possibilities in these key relationships. Production functions have been refined over time to include a variety of determinants other than basic generalized inputs of labor, capital, and natural resources. This first included intermediate inputs, infrastructure, inventories, spatial considerations, and management characteristics, and then environmental inputs. More recently, it has included behavioral considerations, which are especially important when considering resilience. These focus primarily on human factors such as perceptions and motivations. In empirical work, analysts have utilized sophisticated production functions, such as the constant elasticity of substitution (CES), translog, and Generalized Leontief to analyze resilience (see, e.g., Rose & Liao, 2005). More rigid constructs, such as the fixed-coefficient (absence of substitution among inputs), or Leontief production function, are applicable for short-run analyses (generally less than 3 or 6 months). The generalized production function approach is presented in the following implicit form:8 $Display mathematics$ where A = technology K = capital L = labor N = natural resources M = materials (intermediate goods) I = infrastructure V = inventories E = environment (use of the environment for waste disposal)9 S = spatial considerations (location) G = management B = behavior (information processing, perceptions, biases) Other microeconomic units have similar bodies of theory. The theory of consumer choice is the counterpart of production theory in a number of ways. It is typically based on utility functions, with properties similar to production functions but measured in terms of a subjective valuation of individual well-being (utility), or various expenditure functions that are less abstract because they are based on spending patterns. Production theory has been extended to consumers with the advent of the household production function approach—households use a combination of inputs, including their own time, to produce household goods and services. For example, households combine raw food, water, energy, and time to produce meals. Application to disasters as discussed by Rose and Oladosu (2008), illustrates this in terms of a “boil water” decree, where households use contaminated water, energy, and time to produce potable water. This approach is especially useful in analyzing the value of some “non-market” inputs. Government operations typically are modeled by two approaches. One is a simple model of providing goods and services—often just shifting their level of mix exogenously. At the other extreme are behavioral theories, which focus on non-economic motivations (often cynical views of the bureaucracy), such as getting re-elected, rather than operating so as to maximize efficiency of resource utilization or service provision for their constituency. However, it is not unreasonable to expect governments, at least in the United States, to be more attentive to their constituencies in a crisis and to be more inclined to optimize utilization of scarce resources, in part because such actions are highly visible and will help them get re-elected. ## Resilience in a Production Function Context Resilience options for businesses on the demand (customer) side are summarized in Table 1 following Rose (2009) and Rose and Krausmann (2013). The table lists each major category of resilience, provides examples, and specifies a prior action that can be taken to enhance it. The table also specifies the extent to which the resilience category is inherent and adaptive. In addition, the applicability of the type of resilience to factors of production is specified in terms of the letters: capital (K), labor (L), infrastructure (I), materials (M), as well as for the output (Q) that they produce. Finally, obstacles to the implementation of each type of resilience are listed. Capital letters associated with each of these inputs or outputs represent a strong relationship, while lower-case letters represent a weak one. The same convention is used to denote the strength of inherent or adaptive resilience, which is denoted by the letter X. For example, a firm can readily import all inputs except infrastructure services and physical capital, which are more limited because of their stationary nature. Factories cannot readily be relocated, but equipment can be; thus, these variables are relevant to relocation resilience, but are limited and hence connoted by lower case letters. Another example is that inherent conservation is primarily already accounted for by maximizing behavior, but it is included as at least weak, because not all firms actually optimize their production relationships before a disaster strikes. For instance, in Table 1, the first category is Conservation. Examples include automated controls to monitor the flow of inputs (e.g., water) to help reduce non-essential uses. Prior action can be taken to promote resilience by closing systems to promote recycling, such as in the re-use of circulating water. Conservation is only minimally inherent because economists typically assume that most inherent conservation options are currently being maximized. Thus, the remaining conservation options pertain to adaptive applications. All inputs—capital, labor, infrastructure services, and materials—can be conserved. The major obstacle is necessity of the input into the production process. Similar explanations are provided for other resilience options for the case of business customers. There are analogous resilience options on the business supplier side as well. These include a different set of resilience categories in several cases, such as delivery logistics, which refers to the fact that suppliers must deliver their products to customers. Examples include shoring up the network of wholesale and retail trade, contingency contracts with transportation companies, and planning exercises. The rubric for prior action is “broadening the supply chain.” These actions are strong at both the inherent and adaptive levels. As with most cases of supply-side resilience, they are applicable primarily to output. The major obstacle in implementing many supplier-side resilience tactics is the condition of the transportation network. Table 1. Resilience Options: Business (Customer-Side) Category Prior Action Inherenta Adaptivea Applicabilityb Obstacles Conservation Close system to promote recycling x X K, L, I, M Necessity Automated controls Reduce non-essential use Input Substitution Enhance flexibility of system X X K, L, I, M Specialization Back-up generators Cross-training Import Substitution Broaden supply chain X X k, L, i, M Transportation Mutual aid agreements Re-routing of goods Inventories (Stockpiles) Enhance; protect X x k, L, i, M Storage capacity Fuel supplies Labor pool Excess Capacity Build and maintain X x K Obsolescence System redundancy Factor-in risk Input Isolation Reduce ependence on critical inputs X X K, l, I, M Integrated process Decrease dependence Segment production Relocation Arrange for facilities in advance x X K, L, I, M Coordination Back-up data centers Physical move Production Recapture Arrange long-term agreements X X Q Capacity Information clearinghouse Restarting procedures Technological Change Increase flexibility x X K, L, I, M, Q Lack of ingenuity Change processes Alter product characteristics Management Effectiveness Train; Increase versatility X X k, L, m Pressure Emergency procedures Succession/continuity Source: Based on the author’s judgement. Notes: a Capital X indicates the resilience tactic is strongly inherent or adaptive, while lower-case x indicates it is weakly inherent or adaptive. b Capital letters associated with each input or output represent a strong relationship, while lower-case letters represent a weak one. The production theory framework reflects mainstream economics but has its limitations (e.g., assuming maximizing behavior and a limited number of explanatory factors). It is intended as a starting point and can be enhanced by incorporating features of the behavioral theory of the firm (e.g., non-optimizing behavior and other managerial considerations) and bounded rationality in general (considerations of limited time horizons, limited information, and limited ability to process it). This is accomplished by adding the managerial variable explicitly to the production function. # Conceptual Framework for Benefit-Cost Analysis To make prudent resource management decisions, one must consider the cost of each resilience tactic as well as its effectiveness, which represents the gains from implementing it; in our case this gain is the BI prevented. One tactic might be capable of reducing more than twice the BI losses of another, but if it costs 10 times as much to implement, the former is not the better option. Cost-effectiveness analysis is based on the ratio of this gain to a unit increase in cost. Benefit-cost analysis (BCA) is a generalization of this principle over a broad range of levels and is not restricted to a linear proportional relationship, as is cost-effectiveness. More subtly, though, the concept of “benefits” in BCA opens the door to consider benefits to society as a whole and not just a single entity, be it business, household, or government agency. This becomes important if there are significant spillover effects in either the implementation of or the gains from resilience.10 Note the relationship between the aforementioned framework in relation to the production theory approach presented in the section “Economic Theory Underpinnings.” The ordinary business enterprise, or firm, would seek to maximize its profits, which would be equal to its revenues minus expenditures. The relationship between business revenues and societal benefits as just defined is equivalent if there are no spillover effects. At the same time, analysis of profit maximization can be simplified when converted to cost minimization for a given level of output (or its dual, output maximization given a level of cost). The revenue term drops out and only the output level is left to analyze. Moreover, this equivalence is further promoted when there is a fixed relationship between output and revenue, as in the case of the perfectly competitive firm, whose marginal revenue function is constant. ## Cost-Effectiveness A general overview of cost considerations proceeds as follows. Many resilience tactics are adaptive, meaning they involve improvisation after the disaster strikes. Most adaptive conservation more than pays for itself when it represents a productivity improvement, such as an increase in energy efficiency (producing the same amount but with less energy). A more general definition of conservation (reducing the amount of an input irrespective of its effect on output) can incur net positive costs.11Input substitution requires a small penalty for using a less optimal input combination. Import substitution involves an increase in costs from utilizing higher-cost sources and/or increasing transportation distances. Relocation can be somewhat expensive if it involves a physical move; however, increasing the role of telecommunications, and the prospects for working in cyberspace and telecommuting, have significantly decreased this cost. Production rescheduling involves the payment of overtime wages. Some resilience tactics are primarily inherent, i.e., they already exist or can be enhanced relatively inexpensively during the process of building resilience capacity. They then simply await their utilization once the disaster strikes. Input and import substitution have inherent counterparts as well. The cost of inventories is just the carrying charge and not the value of the inventories themselves, which simply replace resources that would have been paid for otherwise. Excess capacity involves a similar cost, though some excess capacity is often planned in order to enhance business flexibility or to accommodate downtime for maintenance; these aspects should not be charged to disaster resilience. Production isolation, instances where some production activities are separated from the need for one or more inputs, is inherent in the system, and should likewise not be charged to resilience unless it is expressly done for that purpose. Emergency Planning Exercises take relatively little time and incur relatively low costs. Once the cost per unit of effectiveness, expressed in percentage terms or in terms of dollars of net revenue from business interruption loss prevention, is determined the options should be ranked from lowest cost to highest, as depicted in the stylized example in Figure 1. The result is an increasing marginal cost curve (a step-function thus far). The limit of this function would be the maximum percentage or dollar amount of resilience possible. Note that since most conservation more than pays for itself, the function begins in the negative cost range. The cost of each resilience tactic is affected by the context in which it is implemented. First, for any given tactic, its cost is not likely to be constant over the range of application (effectiveness). Nearly all economic processes eventually exhibit diminishing returns, resulting in a marginal cost relationship that increases at an increasing rate. For example, there might be several conservation options, likely with different costs, which can then be ranked form lowest to highest cost. Import substitution would be another example, where increasing amounts would need to be brought in from longer distances, or even higher cost suppliers at the same distance. Diminishing returns are also likely applicable in the cases of relocation and technological change. This consideration provides a rationale for fitting a curve through the step function, as is done in Figure 1. Note also that the total cost of achieving any target level of resilience is reflected by the area under the marginal cost (MC) curve; it represents the mathematical integration of the first-derivative (marginal term) to yield the total. The context in which the disaster strikes and resilience is implemented also has an influence on the effectiveness side. Relevant factors include the disaster type, magnitude, and recovery duration, as well as background conditions relating to the economy, such as its economic health at the time of the disaster and its geographic location. For example, inventories are finite and more likely to run out in disasters for which the duration of recovery is long. Production recapture also erodes over time, as customers begin to seek other suppliers. Excess capacity is dependent on the business cycle. For example, one reason that relocation was so effective after the World Trade Center attacks was because New York City was in the throes of a recession, which then provided a great deal of vacant office and manufacturing space (see Rose, 2009, for a further analysis of the potential changes in resilience as recovery progresses). In addition, obstacles to implementation, such as those listed in the last column of Table 1, can inhibit the effectiveness of the various tactics. Click to view larger Figure 1. Benefit-cost analysis of resilience. ## Benefit-Cost Analysis of Resilience Resilience can be couched in a benefit-cost analysis (BCA) framework by bringing its rewards formally into the picture. For purposes of simplification, one can think of the benefits as the net revenue of business interruption losses that are prevented. At first this might best be represented by a horizontal marginal benefit (MB) curve, reflecting equal additional increments of benefits for each percentage increase in resilience. For example, if potential BI losses are$1,000,000 in net revenue terms, then each percentage of resilience has a marginal benefit of $10,000. In this case, the marginal benefit function is constant by definition.12 If the horizontal axis of Figure 1 were measured in terms of physical units of production, then it could be non-linear. The optimal level of resilience would be at the point at which the marginal cost and marginal benefit curve intersect.13 Even without a precise numerical example, one can draw some insights from the example. All cost-saving resilience options would be taken, because they yield guaranteed net benefits. Also, given the relatively low cost of many of the tactics, at least in some of their initial applications, it is likely that a fairly high level of resilience would be chosen. Additional considerations relating to important characteristics of resilience tactics should be noted. One pertains to whether a given tactic yields benefits only to an individual business or whether these benefits apply more broadly. Nearly all of the micro-level resilience tactics discussed thus far, with a focus on the customer-side, have limited spillover effects. However, the opposite is true for resilience tactics on the supplier-side. An example is that of redundancy, such as the presence of a back-up water pipeline system. In this case, the benefits are not simply limited to maintaining revenue to the supplier, but apply to avoiding business interruption for all its customers. Thus, while redundant systems are relatively much more expensive than the resilience options just discussed, their benefits are much more widespread. In fact, they basically exhibit something akin to “public goods” benefits, when these benefits are non-excludable (i.e., the benefits of any quantity supplied are the sum of all of the many utilizations of that quantity, where no single utilization detracts from another), such as in the case of storm barrier, which could protect all inhabitants of a community against both storm surge and sea-level rise. When beneficiaries of the mitigation can be excluded, such as the case of utility services, the characterization is that of a “club good”, but again the benefits should be summed across all utilizations. A further consideration needs to be taken into account on the cost side for redundant system, as well as some demand-side tactics, such as inventories or back-up equipment. Rose (2009) makes the case that customer-side resilience tactics need not be implemented until the disaster strikes, which would appear to give them a cost advantage over mitigation and supplier-side tactics such as redundancy. However, most forms of inherent resilience, such as inventories and back-up equipment, are in place whether or not the disaster strikes. While they lack the flexibility that other customer-side tactics have, there is a positive ramification of this—they exist to protect against many threats over the course of their lifetime. Thus, their cost-effectiveness is much higher than if one considers only a single threat. The MB function in our analysis can readily be adjusted for these features by incorporating all of these benefits of implementing the given resilience tactic and also considering a distribution of threats for which it reduces BI losses. The larger the number of customers served by a water utility with a redundant system, the greater the benefits of redundancy. Likewise, the more threats a stockpile protects against, the greater its benefits. These points are illustrated in relation to a tactic such as redundancy in Figure 1. The MB curve discussed thus far, MB1, would be raised significantly if one takes into account that it protects against a distribution of threats (see, e.g., MB2). On the other hand, one would have to multiply the benefits by the probability of their occurrence, which would put downward pressure on the MB curve. It is not known a priori whether the net effect would be a higher or lower MB curve than MB1. Also, the fact that benefits of a redundant system accrue beyond simply the electric or water utility providing the service and extend to all of their customers would significantly increase the overall benefits. Implicitly, the MB curve has been defined thus far in terms of the rewards to the entity implementing this resilience tactic—the electric or water utility. However, the gains to all the customers are likely to be much greater; in essence, these gains would be the net revenue losses prevented by this resilience tactic, and thus likely to be at least an order of magnitude larger than the benefits to the utility itself.14 The latter essentially represents a type of social benefit of implementing the resilience tactic. This is what is illustrated by MB2 in Figure 1, which is significantly higher than MB1, though not drawn to scale.15 One further ramification of this situation is the difference between the private optimum and social optimum, as well as the associated motivations. The utility’s decision to implement this resilience tactic would be based on its own private marginal benefits, while, from the standpoint of society, it would be best to implement a higher level (the classic “public goods” optimal resource allocation problem). This raises public policy issues related to how to induce behavior consistent with the best interests of society as a whole. This is achieved more readily in the cases of government-owned or -run utilities. For investor-owned utilities, subsidies or some form of regulation would be required. # Empirical Analysis Each individual firm would know much of the data needed to estimate static economic resilience at the micro level, so survey research would be ideal.16 Prior studies can be adapted in the meantime to derive ballpark estimates and to identify conceptual issues in developing a benefit-cost analysis framework and formulating survey questions. There are actions that can be taken before the disaster to increase resilience capacity, such as lining up back-up locations, keeping excess capacity in good working order, etc., but their effectiveness is difficult to measure. A more general approach to improving resilience capacity is to impart greater flexibility into structures and procedures (Zolli & Healy, 2012), but this is especially hard to quantify. However, most resilience tactics have been or can more readily be estimated in terms of their BI loss reduction capabilities, including conservations of scarce inputs, input and import substitution, build-up of inventories, or stockpiles, purchase of back-up electricity generators, emergency management drills, relocation and production recapture (Rose, Oladosu, Liao, 2007a; Kajitani & Tatano, 2009; Rose & Wei, 2013).17 In contrast to the above, benefit-cost analyses of mitigation tactics and strategies are legion both in the academic literature (see, e.g., Lave & Balvanyos, 1998; Schulze, Brookshire, Hageman, & Tschirhart, 1987), and for practical purposes (e.g., FEMA requires BCA’s be performed for all proposals submitted for Hazard Mitigation Grant Program [HMGP] funds). Nearly every one of these studies to date, however, has merely evaluated benefits in terms reduced property damage. One exception is the Mitigation Saves study of the HMGP program covering grants from the period 1993–2003 (MMC, 2005, Rose et al., 2007b). That study relied primarily on FEMA’s hazard mitigation loss estimation methodology, HAZUS (see, e.g., FEMA, 2013), to estimate probability distributions of damages that could be prevented for various threats by various mitigation options (e.g., building codes, flood-proofing, burying power lines underground, safe rooms). The grants were primarily devoted to public sector projects relating to the operation of public buildings and infrastructure. Therefore, most of the analyses did not apply to BI, and there exists no good unit of measure for evaluating flow losses to public sector activities. However, there were a few cases, such as grants for burying power lines and otherwise protecting electricity and water systems, where direct and indirect BI was estimated. These estimates were included in the total benefits of these grants along with the avoidance of property damage, fatalities, and historical and environmental damage. Only in the case of wind-related damages does BI represent more than 10% of the total, but, again, this study dealt only tangentially with business operations. The study is noted here primarily for potential future utilization of its general methodology and estimation techniques for analogous analyses of post-disaster resilience. Benefit-coat ratios estimated by MMC (2005) and Rose et al. (2007b) for major threats are presented below for later comparison with those presented for resilience: Earthquakes – 1.8; Floods – 5.0; Hurricanes and tornadoes – 3.9; Other – 4.8. ## Estimates of Resilience Effectiveness, Benefits, and Costs Examples of some of the basic data for the calculation of benefit-cost ratios (BCR) relating to resilience to electric power disruptions are summarized in Table 2 and are based on simulation studies by Rose, Oladosu, and Liao (2007a). An electric utility has been chosen as an example because it can represent either a private business or a government operation.18 The table identifies alternative tactics (options) electricity customers can use to reduce the impacts to the power outage. Each entry in the first numerical column measures the percentage reduction in BI/GI that each tactic can provide in the aftermath of a power disruption, that is, the estimate of resilience potential. Note that resilience is not additive across all tactics (indicators), as there is some overlap; hence, total resilience is not the simple sum of the column entries in Table 2. Table 2. Relative Prominence of Resilience Factors for Electric Power Outages in Los Angeles Resilience Factor Overall Effectiveness (%) Benefits (billion$)a

Costs (billion$)b Benefit-Cost Ratio Adaptive Electricity Substitution 5.5 0.81 0.16 5.06 Electricity Conservation 5.5 80 –0.08 to +0.08 Undefined to +10 Electricity Isolation 15.1 2.21 0 Undefined Distributed Generation 20.4 2.99 0.60 4.98 Production Rescheduling 77.1 11.30 2.71 4.17 Total 86.0 12.61 3.39 to 3.55 3.55 to 3.72 Sources: Columns 1 and 2: Rose, Oladosu, andLiao(2007a); Column 3: Author’s judgement. Notes: a Converted to billions of 2015 dollars of gross output (sales revenue). b Column sums exceed totals because of overlap in resilience tactic effects. In essence, the entries in Table 2 denote the effectiveness of the various resilience tactics.19 Although an emphasis is usually placed on costs and benefits, effectiveness measures the extent to which the tactics can be applied, and represents a fundamental step in the analysis. Turning now to the costs of various options, the reader is first referred back to Table 1.20 On the customer-side, there are relatively more widespread and less expensive options. The benefits and costs of the tactics are discussed as well in Table 2, in turn. First, note that total losses from the two-week power outage are$14.6 billion in gross output (sales revenue), updated to 2015 dollars. The 86% reduction potential of resilience would reduce this by $12.61 billion. Essentially, the second column translates resilience effectiveness into dollar benefits. Increased (adaptive) inter-fuel substitution21 has the potential to increase the elasticity of substitution between electricity and various fuels by 10%, and would result in a decrease of BI of 0.81 billion. We have assumed that this improved capability to switch to other fuels still comes with a 20% cost penalty as an upper bound. Unlike other inputs, conservation of electricity is a very limited option—Rose and Liao (2005) and Rose, Oladosu, and Liao(2007a) estimate it to be 5% based on a refinement of survey data by Tierney (1997). However, a good deal of conservation is in the category of energy efficiency, which means it can be attained at a cost savings (negative cost). Therefore, a range of cost estimates of plus/minus 10% of the dollar benefits has been entered in the table. Inventories (customer storage) are not a major option in the case of electricity. Electricity isolation, which pertains to those aspects of the production process that do not require electricity in the first place, differs by sector, ranging from levels of 70% in various transportation-related sectors to zero percent in various manufacturing sectors (ATC, 1991). However, this is inherent resilience, and the cost is effectively zero. On-site alternatives to centralized electricity delivery, or distributed generation (micro-grid electricity generation, solar panels or back-up electricity generators) differ by location, but for the City of Los Angeles values ranged from 10% in most sectors to 50% in sectors with very large firms (e.g., petroleum refining), sensitive production processes (e.g., semi-conductors), or where implementation is relatively easy (e.g., security brokers). The incremental costs of most distributed generation alternatives (tactics) are relatively modest, and some may be cost-saving. Still, a cost of 20% of the benefits of this tactic has been entered as an upper bound. Production rescheduling (recapture) also differs by sector, with very high rates for those sectors whose deliveries are not time-sensitive (e.g., durable manufacturing) and low rates for those whose are (e.g., hotels and restaurants) (FEMA, 2013; Rose & Lim, 2002). The analysis also assumed that a two-week outage would not cause any permanent change in customer-supplier relationships. The majority of the cost of production recapture can readily be calculated in terms of overtime pay, which represents the cost entry of$2.71 billion in Table 2.

## Estimation of Benefit-Cost Ratios

One is now able to derive a ballpark benefit-cost ratio for resilience to electricity power disruption. The methodology can be followed for other interruptions of business or government activity as well. Taking the ratio of total benefits to total costs, and using an average of the range for electricity conservation, yields an overall BCR of 3.63. Resilience BCRs for individual tactics can be calculated in a like manner by dividing the Table 2 entries in numerical column 2 by the corresponding entries in numerical column 3. This makes many individual resilience tactics and overall resilience to the electricity disruption threat competitive with some of the mitigation options evaluated in the Mitigation Saves Study (MMC, 2005).

At the same time, these estimates must be tempered by several considerations, such as the fact that mitigation benefits carry over to decades of a useful life of a mitigation project, and most resilience options pertain to risk reduction only on a one-shot basis. Hence, to render the BCRs for these two risk reduction strategies comparable, three adjustments are needed.

First, BCRs of tactics that build up inherent resilience capacity prior to disasters (e.g., increased inventories or stockpiles of critical materials, purposeful construction of excess capacity, back-up equipment) need to be calculated for their entire useful life. This would be analogous to what is done for mitigation BCRs and would mean calculating the flow of future benefits from say, portable electricity generators, and discounting them; the ensuing BCR would be at least several times the annual BCR for this tactic (though the useful life of inherent resilience tactics is not as likely to be as lengthy as the useful life of mitigation tactics such as building codes, levees, and buyouts of property in flood plains).

Second, BCRs for the capacity building resilience tactics put into place before the disaster need to be adjusted for the probability of occurrence of a disaster. On the other hand, (post-disaster) adaptive resilience tactics maintain the strong advantage over mitigation and pre-disaster resilience of not requiring to be adjusted by probabilities of occurrence, which are known because the disaster has in fact happened.

Third, most resilience tactics applied to the customer side represent ways of coping by a business/government/household to disruption of the supply of critical inputs, as well as to coping with damage to operating facilities. Thus, they pertain to reducing losses across various threats; in contrast, most mitigation measures are threat specific (building codes, levees, warming systems). This essentially increases the BCRs associated with resilience in relation to those associated with mitigation.

Note that BCRs have been provided for the select case of an electric utility disruption, which are comparable in magnitude to those of mitigation (MMC, 2005). Additional estimation has been performed for two other resilience tactics in a recent study by Rose, Ganderton, Eyer, Wei, von Winterfeldt, and Bostic. (2016). Studies were done for selected sectors including: light manufacturing in general, food/drug/chemical manufacturing, metal processing, high technology, and administrative services. The BCRs for production recapture for disruptions lasting up to three months ranged from 4.4 to 19.2. BCRs for relocation ranged from 6 to 274 (the implicit BCRs for relocation following 9/11 were also very high, as noted in Rose et al., 2009).

# Conclusion

This article has presented a conceptual framework for the benefit-cost analysis of economic resilience to disasters. Resilience here is confined to actions implemented after disasters have taken place; however, resilience capacity, as a process, can be enhanced prior to disasters. Measurement begins with the specification of the operational metric that measures resilience effectiveness. This is then translated into costs and benefits of various resilience tactics, adapting previous studies and data available from the literature. The resilience estimates presented are admittedly very crude and are intended only for the purpose of illustration. Still they provide useful insights into critical aspects that need to be measured and provide some ballpark estimates of the importance of post-disaster resilience.

Several studies have indicated that resilience can be more cost-effective than mitigation in some cases, even when one considers the returns to mitigation to include not only reduction in BI but also reductions in property damage and fatalities. The main reasons that resilience tactics have higher BCRs than many mitigation tactics is that the former are often relatively inexpensive to begin with and also do not have to be multiplied by probabilities of occurrence. No such adjustment for the probability of occurrence is applicable to post-disaster resilience, such as relocation and production recapture, because these tactics are not implemented until the event has actually taken place.

The various empirical and simulation studies cited above, as well as the calculations presented in this article, are generally biased towards estimating resilience and mitigation at their maximum effectiveness. This is not always the case due to perception problems and other manifestations of bounded rationality, as well as implementation and administrative obstacles. BCRs for both these approaches to risk reduction need to be adjusted downward to take these factors into account.

This article has endeavored to illustrate some of the major issues involved in measuring resilience for risk management purposes. The study is also intended to serve as a foundation for more formal theoretical analyses and for the formulation of survey questions to collect primary data from businesses, to obtain the most accurate estimates of economic resilience.

# Acknowledgment

The research contained in this paper was supported by a grant from the U. S. National Science Foundation and contracts from the Critical Infrastructure Resilience Institute and the Federal Emergency Management Agency. The author wishes to thank his colleagues Phil Ganderton, Jonathan Eyer, and Dan Wei, for their collaboration on the FEMA study, in which the author explored some of the key issues of benefit-cost analysis of resilience that are further refined in this paper. The author also thanks and anonymous reviewer and Section Editor of the Encyclopedia for their helpful comments. He also acknowledges the valuable help of Noah Miller and Joshua Banks in developing empirical measures of the benefits and costs of selected resilience tactics, and Jonathan Eyer, Lee White and Noah Miller for comments on the final manuscript.

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## Notes:

(1.) The economic classification system just described for analyzing the cost of disasters is now well developed. It is embodied in major studies such as the Mitigation Saves report (MMC, 2005), and three National Research Council reports over the last dozen years (NRC, 2005, 2011, 2012).

(2.) In the analysis, we confine our attention to direct BI (see, e.g., Rose, 2015).

(3.) Others prefer the reference point to be a “new normal,” referring to a more viable level of economic activity for New Orleans, for example, whose economy was in decline before the disaster. The new normal, however, poses greater measurement challenges for BI.

(4.) These definitions of economic resilience capture the essence of definitions across disciplines, which generally are: actions that maintain function and accelerate recovery (see also Cutter, 2016; Holling, 1973; Martin & Sunley, 2014; Pimm, 1984; Tierney, 2007). See also the in-depth comparisons of various definitions in Rose (2007, 2017).

(5.) Complete absence of dynamic resilience would imply no recovery, so we use “normal” recovery for a meaningful reference point.

(6.) Chang and Shinozuka (2004) offer a similar definition, but not expressed in percentage terms. The percentage approach facilitates comparisons across resilience tactics and their applications.

(7.) The definitions and metrics developed by the author (see, e.g., Rose, 2004, 2009; Rose & Liao, 2005; Rose et al., 2009) are widely cited and used in analyzing and measuring resilience. See, e.g., Hallegatte (2014); Hu, Xie, Li, Xu, Ji, and Wu (2014); Kajitani and Tatano (2009); Reggiani (2013), Shi, Jin, and Seeland (2015) with regard to static economic resilience, and, e.g., Xie, Li, Wu, and Hao (2014) and Todo, Nakajima, and Matous (2015) with regard to dynamic economic resilience.

(8.) Production functions differ according to their explicit form, which involves a precise mathematical specification. The specifications combine various properties of the production function (such as returns to scale, relative input productivity, and ease of substitution among inputs) and mathematical properties that have some more subtle economic implications, such as additivity and separability of inputs. The technology term is incorporated in various manners depending on the explicit production function specification. It is often postulated as affecting the entirety of inputs uniformly or individually, in both cases representing a type of “productivity” parameter.

(9.) This refers to pollution. Positive inputs from the environment are included via the natural resources input.

(10.) BCA refers to the assessment of all relevant benefits and costs of a deliberate course of action. In its broadest form, BCA is typically applied to public policy and public actions, such that the relevant aspects include benefits and costs to society as a whole, including joint-product benefits and externalities, both market and non-market (see, e.g., Boardman, Greenberg, Vining, & Weimer, 2011). As such, it typically applies to decisions made by government agencies on the part of their constituents (society as a whole in their jurisdiction). The term BCA, however, is often applied to calculations of individual businesses and households regarding investment and other resource allocation decisions. In these cases the relevant costs are typically just private costs, for instance, those incurred or received only by the decision maker. In this article, we use the term BCA broadly to include both private and public sector decision making. Most of the principles of BCA are relatively straightforward, and we only elaborate on them when they are complicated and relevant to issues discussed in this article.

(11.) Conservation often involves the installation of energy-saving equipment. When this more than pays for itself, an energy efficiency improvement has taken place.

(12.) For example, economies of scale would actually increase the marginal benefits successively as resilience is carried out, counter to the more standard downward-sloping marginal benefit curve. Net revenue would also increase if fixed costs are significant. Working in the opposite direction, however, would be factors such as keeping the business open at some minimum level for the sake of its public image. The most significant factor affecting the MB curve, however, would be on the gross revenue side. The perfectly competitive firm could sell as much of its product as needed at a constant price to maximize profits, which is essentially at a constant marginal revenue. However, firms in imperfectly competitive markets would face a declining marginal revenue curve, putting pressure on the net revenue function to decline as well.

(13.) This condition holds even for an increasing marginal benefit curve, as long as its slope is flatter than the marginal cost curve.

(14.) The order-of-magnitude estimates stem from a simple back-of-the-envelope calculation. Electricity and water inputs represent less than 5% each on average of total production costs of nearly all businesses in the economy. Assuming that rates of return (or profit rates in general) are reasonably equal across all business enterprises, again on average, this means that net revenue losses are more than 20 times higher for the economy than for the utility supplier. Moreover, this number increases when indirect (multiplier or general equilibrium) effects are taken into account.

(15.) Strictly speaking, only resilience tactics that have this characteristic (mainly supply-side ones) would have their MB segments raised. This would make for a likely non-monotonically increasing or decreasing MB curve and would complicate the identification of an optimum.

(16.) Other data sources would need to be accessed for the extension to the meso (market, sector) and macro (community, regional economy) levels. U.S. Department of Commerce data and data from commercial sources, such as Dun and Bradstreet, would be prime candidates.

(17.) The definitions of economic resilience in this article reflect two separate types of decisions relating resilience. Static resilience typically pertains to expenditures on goods and services to promote resilience in the current year. Dynamic resilience, on the other hand, pertains to investment in assets (setting aside current consumption or profits to increase resilience or productivity in future years), such as expenditures on repair and recovery. There is an intermediate case that refers to enhancing inherent static resilience capacity, such as purchasing back-up electricity generators and building-up inventories of critical materials. As in dynamic resilience, this decision is time-related, and a discount rate must be applied because the dollar value of benefits in the future is less valuable than those benefits received today because of the deferral of the gains (often referred to as the time-value of money). The choice of the discount rate can be complicated, but we simply assume here that it is equivalent to the interest rate for a given risk category prevailing in the market at the time the investment decision is being made.

(18.) The counterpart pertaining to loss of government services would be referred to as government interruption (GI). While data on BI are extensive, data on GI are not. Government activity is often measured in terms of expenditures or sometimes on a net basis in terms of employee compensation. However, these measures might be reconsidered. When government goods and services are not provided, some adjustments might be needed. Provision of some government activities might simply be delayed to a later date. Also, some revenue might be shifted to other purposes. We note two fruitful approaches. One is case studies of the costs of state and local GI (see e.g., Minnesota Management and Budget, 2011). Another is to use private-sector analogues. There are numerous studies of the reduction in GDP stemming from electricity outages, and even those related to privately owned electric utilities are applicable to the case of municipal electric utilities.

(19.) The tactics and their effectiveness would serve as individual indicators in the compilation of a resilience index (Rose, 2017; Rose & Krausmann, 2013). The relative effectiveness of the various resilience tactics could serve as weights in developing the index. Most studies to date have simply assumed equal weight across indicators.

(20.) Several resilience tactics are available on the supplier side as well (see, e.g., Lave, Apt, & Morgan, 2005). However, these are dominated by relatively expensive options, such as spare transformers, as well as less expensive options, such as expediting service restoration (basically dynamic economic resilience in the form of recovering more quickly).

(21.) The existing substitution possibilities represent inherent resilience, and the increased substitution possibilities (increased elasticity of substitution values) represent adaptive resilience.