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Li, J, Crawford-Brown, D, Syddall, M et al. (1 more author) (2013) Modeling imbalanced economic recovery following a natural disaster using input-output analysis. Risk Analysis, 33 (10). 1908 - 1923. ISSN 0272-4332

https://doi.org/10.1111/risa.12040

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Risk Analysis, Vol. 33, No. 10, 2013 DOI: 10.1111/risa.12040

Modeling Imbalanced Economic Recovery Followinga Natural Disaster Using Input-Output Analysis

Jun Li,1,∗ Douglas Crawford-Brown,1 Mark Syddall,1 and Dabo Guan2

Input-output analysis is frequently used in studies of large-scale weather-related (e.g., Hurri-canes and flooding) disruption of a regional economy. The economy after a sudden catastro-phe shows a multitude of imbalances with respect to demand and production and may takemonths or years to recover. However, there is no consensus about how the economy recov-ers. This article presents a theoretical route map for imbalanced economic recovery calleddynamic inequalities. Subsequently, it is applied to a hypothetical postdisaster economic sce-nario of flooding in London around the year 2020 to assess the influence of future shocks to aregional economy and suggest adaptation measures. Economic projections are produced by amacro econometric model and used as baseline conditions. The results suggest that London’seconomy would recover over approximately 70 months by applying a proportional rationingscheme under the assumption of initial 50% labor loss (with full recovery in six months), 40%initial loss to service sectors, and 10–30% initial loss to other sectors. The results also suggestthat imbalance will be the norm during the postdisaster period of economic recovery eventhough balance may occur temporarily. Model sensitivity analysis suggests that a propor-tional rationing scheme may be an effective strategy to apply during postdisaster economicreconstruction, and that policies in transportation recovery and in health care are essentialfor effective postdisaster economic recovery.

KEY WORDS: Disaster; dynamic inequalities; input-output analysis; London flooding; rationingschemes

1. INTRODUCTION

Some recent large-scale disasters such as the2003 heat wave that struck Paris and other Europeancities, the 2004 Indian Ocean earthquake leading tothe Asian tsunami, Hurricane Katrina in New Or-leans (USA) in 2005, Cyclone Nargis in Myanmarin 2008, and the 2008 Sichuan earthquake in China

1Department of Land Economy, Cambridge Centre for ClimateChange Mitigation Research (4CMR), University of Cambridge,19 Silver Street, Cambridge CB3 9EP, UK.

2School of Earth and Environment, University of Leeds, LeedsLS2 9JT, UK or Institute of Applied Ecology, Chinese Academyof Sciences, Shenyang, 110016, China.

∗Address correspondence to Jun Li, Gray Institute for RadiationOncology & Biology, Department of Oncology, University of Ox-ford, Old Road Campus Research Building, Off Roosevelt Drive,Oxford, OX3 7DQ, UK; [email protected].

show the urgency of understanding and then prepar-ing for such environmental hazards, including under-standing their impacts on the economy.(1) Researchindicates that economic losses caused by such eventshave been on the rise in last few decades.(2) With theconcentration of population and assets, metropolitanareas are particularly vulnerable to such disasters.

Temporal properties such as magnitude and du-ration of extreme climatic events determine the ex-tent of initial damage inflicted and have significantinfluence on the adaptive capacity of individuals,households, and therefore an economy.(3) The du-ration of an event, including the length of recov-ery, is very important in estimating economic costsof a climate-change-related disaster.(4,5) Studies(6–8)

have appeared in recent years in postdisaster eco-nomic modeling aiming to better understand the

1908 0272-4332/13/0100-1908$22.00/1 C© 2013 Society for Risk Analysis

Modeling Imbalanced Economic Recovery 1909

consequences of environmental disasters for a re-gional economy and to develop prevention and re-covery strategies.

The article presents a model for assessing theeconomic impacts of disasters, organized as follows.In Section 2, a literature review of recent devel-opment in risk damage valuation is presented. InSection 3, a series of dynamic inequalities are in-troduced to provide a theoretical basis for model-ing imbalanced economic recovery. Section 4 appliesthese inequalities to a hypothetical postdisaster eco-nomic scenario occurring in London around 2020. InSection 5, a U.K. multisectoral dynamic model isused to project predisaster economic conditions andprovide the main baseline data required by the sce-nario. Section 6 presents simulation results on pro-duction and demand inequalities. A sensitivity analy-sis is carried out in Section 7, which mainly focuses ondifferent disaster scales, rationing schemes, and al-ternative exogenous labor and household consump-tion recovery paths. Finally, Section 8 summarizesthe findings and proposes directions for further re-search. The case study and key assumptions are pro-vided in the Appendix.

2. RECENT DEVELOPMENT OF RISKDAMAGE VALUATION

A number of well-known modeling method-ologies, including computable general equilibrium(CGE), econometrics, and input-output (IO) anal-ysis, are frequently used to assess economic re-covery following damage. However, no distinct ad-vantages of any are evident across all applications.For example, CGE is considered to be overly opti-mistic on market flexibility and overall substitutiontendencies,(9) while IO analysis does not take intoaccount productive capacity and producer and con-sumer behaviors.(7) Econometric models are moreprevalent at the national level, while IO models arethe major tools of regional impact analysis.(10) More-over, econometric models, which are based on time-series data that may not include any major disas-ters, appear ill-suited for disaster impact analysis(1)

and cannot easily distinguish between direct and in-direct effects.(11) On the other hand, such models arestatistically rigorous, which can provide a basis forstochastic estimates and forecasting. IO analysis isgrounded in the technological relationships of pro-duction and provides a full accounting for all inputsinto production,(9) which is in contrast to some largeeconometric models that express quantities only in

terms of primary factors of production. Moreover, IOanalysis is a powerful tool to assess the economic ef-fect of a natural catastrophe at regional and sectorallevels through effects on intermediate consumptionand demand. Although IO analysis is mainly a modelof production, it is fully capable of analyzing demandby households and other institutions affected by adisaster.(12) Also, the simplicity of IO analysis and theability to integrate it with engineering models add toits popularity.

Existing literature(1,11,13–19) suggests that there isno generally accepted methodology for the repre-sentation of postdisaster economic development, andno uniform way in which economic agents will ad-just their actions during a period of economic im-balance. Steenge and Bockarjova(6,8) suggest an ap-proach by connecting a closed IO table with an eventaccounting matrix.(15) They assume that postdisas-ter economic recovery will have two steps to restorepredisaster conditions: the first is to reach “as fastas possible” the targeted output proportions and thesecond is to bring the economy back to the predisas-ter level of operation. However many situations havedemonstrated that an imbalance may persist during apostdisaster period, requiring that economic agentsadapt themselves in a dynamic manner. Moreover,the basic equation does not solve the dynamic, tem-poral change in the postdisaster economy.

Hallegatte(7) applies IO analysis to the land-fall of Katrina in Louisiana by taking into accountchanges in production capacity due to productivelosses and adaptive behavior in the aftermath of adisaster. However, the impacts of housing destruc-tion and labor constraints on production capacity areneglected, each of which critically influence the re-covery process. Haimes, Jiang, and Santos(17,20) pro-vide an alternative IO approach—the inoperabilityinput–output model (IIM)—to assess direct and in-direct economic impacts based on the demand-sideLeontief equation with perturbation and inoperabil-ity vectors. The term “inoperability” is used to con-note the level of a system’s dysfunction, expressed asa percentage of its “as-planned” production capacityavailable at any point in time. IIM has been featuredin economic interdependency analysis with differentapplications such as analysis of workforce disrup-tions caused by pandemics(21) and economic impactsof terrorism.(20) However, such an approach doesnot take into consideration supply bottlenecks(7) anddemand constraints. Moreover, it only captures pe-ripheral time-varying features (e.g., sector resiliencethrough a resilience coefficient matrix(21)) in its

1910 Li et al.

dynamic IIM,(22–24) while some more important time-varying features such as demand behavior adapta-tion, labor force change, and import and export dy-namics are not fully considered.

Von Neumann growth theory asserts that an im-balanced economic setting following a disaster willseek a return of balance between economic agentsbefore an economy can continue to grow.(8) How-ever, this is not entirely true empirically. A postdisas-ter economy often keeps an imbalanced state of de-velopment during the recovery period, as reflectedin the 2003 heat wave that struck Paris and otherEuropean cities, Hurricane Katrina in New Orleans,and the 2008 Sichuan earthquake in China. More-over, current studies rarely reflect the influence ofhypothetical future shocks to a regional economy,which is vital for decision planning.

Based on the stated strengths and limitations ofexisting methods and analyses, this article adopts anIO analysis linked to a macro-econometric model(the U.K. multisectoral dynamic model or MDM(25)),adding a temporal dimension to analyze changes ina regional economy and assess economic costs, vul-nerability, and resilience of the region during the pe-riod of recovery following a disaster. In the study,a monthly IO model is constructed through a se-ries of dynamic inequalities, followed by integratingthe IO model with an event accounting matrix toassess recovery of a postdisaster economy along animbalanced recovery route. The model is applied toassess London’s economic adaptability in the after-math of a hypothetical flooding event around 2020.The dynamics of final demand categories, labor forcerecovery, and import-export adjustments during thepostdisaster period in response to the inequalities aredeveloped.

3. THE BASIC DYNAMIC INEQUALITIES

This section presents an input-output basic dy-namic inequalities (BDI) model capable of assessingthe impact of a natural disaster at the level of a re-gional economy, accounting for interactions betweenindustries through demand and supply of intermedi-ate consumption of goods with circular flow—a set ofinputs that should be in balance, given certain restric-tions, with a set of outputs that subsequently becomea set of inputs in the next temporal round. No prioreconomic balance will be assumed during the periodof recovery in the model.

Regarding the mathematical symbols and for-mulae, matrices are represented by bold capital let-ters (e.g., X); vectors by bold lowercase (e.g., x), andscalars by italic lowercase (e.g., x); by default, vec-tors are column vectors, with row vectors being ob-tained by transposition (e.g., x′); a conversion froma vector (e.g., x) to a diagonal matrix is expressedas the bold lowercase letter with a circumflex (i.e.,x); and the operators “.*” and “./” are used to ex-press element-by-element multiplication and divisionof two vectors, respectively. The two operators canbe converted into mathematical expressions. For ex-ample, given two vectors x and y with nonzero ele-ments, the conversions are:

x. ∗ y = x × y (a)

x./y = (y)−1 × x. (b)

Assume a regional economy consisting of n in-dustries that exchange intermediate consumptiongoods and services in order to sustain the productionprocesses, and final demand categories that includefinal consumption goods and services for local house-hold, government, fixed investment, and export. Thiseconomy is struck by a natural disaster, which ini-tially damages household physical assets, industrialcapitals and stocks, and the transportation system,thereby affecting people traveling.

The input-output BDI model is derived froma standard IO model that reflects a detailed flowof goods and services between producers and con-sumers. All economic activities are assigned to pro-duction and consumption sectors. An economy withn sectors in the predisaster condition can be pre-sented in the following standard IO relationship:

x = Ax + f, (1)

where x represents sectoral production output, f rep-resents final demand, and A is matrix of the technicalcoefficients.

A standard IO model is a solely demand-driven,open model. In the postdisaster period, however, lim-itations in supplies become important constraints forproduction capacity. On the other hand, Leontiefclosed models allow for tracking the supply and de-mand of each individual good and those that are con-sidered as primary inputs such as labor in an openmodel. Let us introduce a labor constraint to Equa-tion (1):

[

A f/ l

l′ 0

]

(

xl

)

=

(

xl

)

(2)


or

Mq = q, where M =

[

A f/ l

l′ 0

]

and q =

(

xl

)

(3)with

l = l′x, (4)

where l is a scalar of total regional employment, whilel′ is a row vector of direct labor input coefficients.Equation (4) describes an economy in equilibriumwith a closed Leontief model, which is the so-calledbasic equation.(8) The left-hand side of Equation (3)stands for the totality of inputs, and the right-handside for the totality of outputs in the economy.

Let us introduce time dynamics and a damagefraction (i.e., event accounting matrix) into the equa-tions step by step, first:

xttd = (I − A)−1ft , (t > 0) (5.1)

or, xttd ≈ A

(

I − Ŵt)

x0 + ft , (5.2)

where in Equation (5.1) xttd simulates the degraded

total demand determined by final demand ft overtime, and t refers to a time step (in this article wedenote the predisaster time as t = 0, and t = 1 as thefirst period immediately after the disaster). In Equa-tion (5.2), xt

td is calculated based on the intermediatedemand met by the current production capacity andtotal final demand.3However, the equation needs tobe balanced between A (I − Ŵt ) x0 and ft .

In Equations (5.1) and (5.2), I is an n × n identitymatrix. The matrix Ŵ is the damage fraction matrix—an n dimensional diagonal matrix which changes withtime:

Ŵt =

⎛

⎜

⎝

γ t1 · · · 0...

. . ....

0 · · · γ tn

⎞

⎟

⎠. (6)

Meantime, let us introduce dynamics intoEquation (4):

xtl = lte./l, where lte =

(

1 − γ tn+1

)

l0e, (7)

where xtl simulates the degraded labor pro-

duction capacity, lte represents the employ-ment in sectors at time t, and the parameterγ t

i (0 ≤ γi ≤ 1; 1 ≤ i ≤ n + 1) indicates the frac-tion of the production capacity lost in industry i

3Under certain economic circumstances and assumptions, the A

matrix may also change over time, which is not considered in thisarticle.

(1 ≤ i ≤ n) as shown in Equation (6), or in labor(i = n + 1) at the time step t as shown in Equation(7). Here, we assume that the impact of employmentloss on each sector is equally distributed. Equa-tions (5) and (7) are constrained by the followingequations at each time step,

xttp = l(I − Ŵt )x0 (8)

Mq∗(t) = q∗(t), where q∗(t) =

(

x∗(t)

l∗(t)

)

(9)

q∗(t) =

(

x∗(t)

l∗(t)

)

← q(t) =

(

xttp|td|l

l ttp|td|l

)

, (10)

where xttp simulates the degraded total production.

Equation (9) refers to a balanced economy in aclosed model, while the balance (i.e., q∗(t)) can becalculated by Equation (10) through q(t). Here, weuse q∗(t) to represent a balanced total output andlabor force, distinct from q(t), which represents animbalanced input-output condition. xt

tp|td|l and l ttp|td|l

represent the balances of total output and laboras required between total production capacity, totaldemand, and labor production capacity at time step t.As there are constraints during the recovery betweenthese factors (e.g., the labor production capacity maynot meet or may exceed the capital production capac-ity), a balance is needed. There are many ways (rep-resented by the label “←” in Equation (10) to adaptq(t) to a balanced input-output condition. The articleintroduces two ways to achieve it in Section 4.5.

From the equations shown earlier, there exist afew inequalities at each time step. Let us consider acondition at time step t during the recovery. Then,the inequalities are as shown below:

⎧

⎪

⎨

⎪

⎩

xttd �= xt

tp

xttd �= xt

l

xttp �= xt

l

(11)

and

Mqtdeg �= qt

deg, (12)

where qtdeg represents the degraded total economic

output and the labor force within a closed modelat time t. The condition holds unless qt

deg is propor-

tional to q0, which is the case when the economy isshrinking proportionally in all sectors. Even thoughbalance or proportion may hold at some time steps,the dynamic inequalities may still appear at subse-quent time steps as total production capacity, final

1912 Li et al.

demand, and labor capacity vary disproportionately.In practice, the economy only has a “tendency” dur-ing the recovery period to move back toward predis-aster conditions.

The series of inequalities introduced is to pro-vide a general framework for modeling postdisastereconomic recoveries; they are not intended to givesolutions to simulate the dynamics of the specific fac-tors such as total production, final demand behav-iors, and labor recovery. In specific applications ofthe model, it is left to analysts to specify the dynamicsof these economic actors pertaining to specific post-disaster circumstances. Imports and exports duringthe disaster and recovery period are not only affectedby the severity of a disaster, especially reflected indamage to the transportation infrastructure, but alsoby disaster aid policies and actions. The followingsections implement the framework and also simulatethe dynamics of those economic factors mentionedearlier using a hypothetical case of storm damage inLondon in 2020.

4. MODELING THE RECOVERY OF LONDONAFTER FLOODING

Urban areas are spatial concentrations of vulner-ability to climate change. Here, let us assume thatLondon is stricken by a flooding incident from theRiver Thames around 2020, which may be causedby a combination of on-tidal flooding from theThames, fluvial flooding from tributaries that flowinto the river, and surface water flooding resultingfrom excessive rainfall. London’s economic structureis severely disrupted by the flooding, which is re-flected in labor and production capacity losses and fi-nal demand reductions. Details of the assumed dam-age magnitude are given in the following sections. Ifone views the economy as a system of circular flowinterrelations among production and consumption,then the interrelations are broken suddenly by the in-cident and a number of imbalances occur in the Lon-don economy’s supply-demand relationships duringthe period of recovery. This section focuses on mod-eling economic consequences of the hypothetical dis-aster, including the economic recovery process andthe possible response strategies based on the BDIframework introduced previously.

4.1. Modeling Process

In the modeling we assume that the labor re-covery path (expressed as lte) is defined exogenously.

The BDI model of London simulates the total fi-nal consumption adaptation process (expressed as ft )based on consideration of a long-term tendency backto the predisaster economic condition and a short-term tendency toward a balanced economy. House-hold demand usually accounts for more than half oftotal final demand. Let us assume that the house-hold consumption pattern changes during the dis-aster and subsequent recovery period, that house-hold demand will therefore have a sudden drop, andthat it will increase gradually thereafter but not ex-ceed the level of the predisaster condition. Immedi-ately following the disaster, households will switchtheir consumption patterns to focus on basic goodsand services such as food, water, clothing, and healthcare, for which government and civil society canusually ensure a sustainable supply even though lo-cal production may not be sufficient. We also in-troduce a distinction between sectors according towhether the substitution of local production by ex-ternal providers is or is not possible (e.g., one cannotsubstitute an external provider for electricity or localtransportation).

In the study, the recovery process is modeled ona monthly basis with three computational steps ateach time interval. First, labor loss is captured bythe percentage of labor not available for traveling,the percentage of labor delayed for work becauseof transport damage and corresponding hours of de-lay in travel. The labor production capacity— xt

l —iscalculated based on Equation (7). The capital pro-duction capacity—xt

tp—during recovery is capturedby the damage demand through the magnitude oflocal production. It corresponds to dynamic Equa-tion (8). Then, the production capacities of surviv-ing labor and capital are compared with the currenttotal demand—xt

td—resulting from the final demandchange, allowing determination of how much couldbe locally produced based on constraints between thethree factors (reflected in Equations (9) and (10)).A rationing scheme (either a proportional rationing,or a priority system, or a mix of these) is applied tothe intermediate consumption and a new total pro-duction is calculated. Third, if the three elements(new total production capacity; total demand and la-bor production capacity; and predisaster total pro-duction) are met, the economy has recovered fromthe postdisaster conditions; otherwise, a new total de-mand is calculated based on the new total final de-mand adjustment (corresponding to Equation (5)).Then the three steps repeat with a new time stepand the labor and capital production capacities arerecalculated. A detailed diagram for the recovery,


with components such as the final demand behavioradjustment equation and import availability compu-tation, is given in Fig. A1. The following subsectionsare further illustrations of essential components in-volved in the modeling process.

4.2. Reconstruction Demands

Let us consider that the flooding occurs att = 0, and thereafter the economy recovers grad-ually over time (t = 1, 2, . . . ). In this example,the disaster causes an amount of industrial cap-ital damage—d1

cap—and households, housing and

equipment damage—d1hh (in sectors). Let us assume

that these damages will all be repaired or replacedthroughout the entire postdisaster period. Repair ofthis damage will lead to additional demands—f1

rec:

f1rec = d1

cap + d1hh. (13)

Here, d1cap and d1

hh are damages immediately after theflooding and are n × 1 vectors. The Leontief equationcan be rewritten in terms of the damages for industryi as:

x1 (i) =∑

j

A (i, j) x1 ( j) +

⎧

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎩

f1hh (i)

f1gov(i)

f1cap (i)

f1exp (i)

f1rec(i).

(14)

As shown in the equation, industry i con-sists of two sets of demand: intermediate de-mand and final demand. The final demand—f1—consists of household consumption—f1

hh, governmen-tal expenditures—f1

gov, fixed capital formations—f1cap,

exports—f1exp— and the reconstruction demand—

f1rec, which is zero prior to the disaster.

4.3. Labor and Production Capacity

The BDI model’s focus is on simulating how theeconomy meets core tasks such as fulfillment of con-sumer demand. In the aftermath of a disaster, indus-tries may be unable to produce enough to satisfy thedemand due to (i) insufficient production capacitycaused by the loss of capital, (ii) insufficient interme-diate supply from other industries, or (iii) insufficientprimary inputs such as the loss of labor, as reflectedby Equations (5.1), (7), and (8). A disaster may af-fect these categories differently. For example, flood-ing could cause labor loss. In this case, a firm’s pro-

duction capacity decreases due to lack of a primaryinput—the workforce—to perform production activi-ties. Alternatively, the major loss may be from indus-trial capital damage rather than labor. The differencecauses the inequalities over time as shown in Equa-tions (11) and (12).

Labor shortage in the postdisaster period is oneof the important supply constraints for economic re-covery. In the postdisaster period, the labor produc-tion capacity reduction caused by the loss of life andtime delay for work-related travel is captured by xt

l

and lte. Let us assume every laborer works for 8 × 22hours per month. If the amount of extra hours foreach laborer spent on traveling in the month i of thepostdisaster replaces working hours and is capturedby oi, and the percentage of labor affected is pi, thenthe relative percentage of labor loss in the month isidentified by pi ×oi /(8 × 22). Here we assume thatthe labor loss and additional travel time are providedexogenously, and that they return to the predisastercondition linearly within six months (see Table A1).Then the labor production capacity can be calculatedbased on Equation (7).

The maximum production capacity of industryi is set equal to the predisaster total output x0 (i).Production capacity is decreased immediately afterthe flooding. The degraded capacity x1

deg (i) serves asan initial condition for economic recovery resultingfrom the repair or replacement of productive capitaland stock. Let us assume the capital remaining willfunction fully and is determined by the amount ofsurviving productive capital in percentage terms, rep-resented here by the matrix Ŵ as shown in Equation(8). The production capacity increases both throughlocal production and imports at each time step, whichis again influenced by the rationing strategy selectedby actors.

In the study, the “overproduction” effect is notmodeled because that effect usually happens in man-ufacturing sectors, while London’s economy is domi-nated by service sectors. For this exercise, we assumethat the disaster will not influence the labor pro-ductivity of an industry, although it may lead to theloss of employment due to the reduced productioncapacity.

4.4. Rationing Scheme

When industries have limited capacity, unableto fulfill both intermediate and final consumptiondemand, a rationing scheme is applied to prioritizethe allocation of commodities. In the present

1914 Li et al.

modeling, two different rationing schemes are con-sidered: a “priority” scheme and a “proportional”scheme. Here let us assume priorities are distributedbetween categories of “Intermediate Demand—∑

j A (i, j) x ( j),” “Final Demand for Industriesand Households Reconstruction—frec(i),” “House-holds Demand—fhh (i),” “Governmental Demand—fgov (i),” “Fixed Capital Formation—fcap (i),” and“Exports—f exp (i),” and that priority for allocationof production is always given to intermediate de-mand for both schemes. This assumption is justi-fied by the fact that in reality business-to-businessrelationships are usually deeper than business-to-household relationships, and so a business often fa-vors business clients over household clients.(7)

If an industry has satisfied the intermediate de-mand of other industries, the remaining productionwill be distributed among frec(i), fhh (i), fgov (i), andf exp (i) in proportion to the predisaster allocationin the case of proportional rationing, or prioritizedand assigned to them in a sequence (defined exoge-nously) in the case of the priority scheme. The pro-portion is calculated based on two equations:

(

xttp − A ∗ xt

tp

)

. ∗ f0k.

/

⎛

⎝

f0k

∑

+ ftrec

⎞

⎠ , (15.1)

(

xttp − A ∗ xt

tp

)

.∗ ftrec.

/

⎛

⎝

f0k

∑

+ ftrec

⎞

⎠ , (15.2)

where k refers to the subscripts hh, gov, cap, and exp;(

xttp − A ∗ xt

tp

)

refers to the production left after sat-

isfies the intermediate demand; and∑f0

k refers to thetotal final demand in the predisaster period. Equa-tion (15.1) calculates the proportions distributed tothe household, government, capital formation, andexport, respectively, while Equation (15.2) calculatesthe actual consumption due to reconstruction overtime.

The priority scheme distributes the remainingproduction based on a prior sequential set of pref-erences. For example, if one sets a priority rank-ing as “Final Demand for Industries and HouseholdsReconstruction—frec(i)” > “Households Demand—fhh (i)” > “Governmental Demand—fgov (i)” >

“Fixed Capital Formation—fcap (i)” > “Exports—f exp (i),” then goods will be distributed so as to satisfythe reconstruction demand first. Any goods left overwill then be used to satisfy households’ demand, andso on in order of declining preference.

In the following sections of the modeling, theproportional rationing scheme has been extensivelyused. Only in the sensitivity test are other rationingschemes applied. The justification of this choice is il-lustrated in the sensitivity analysis section.

4.5. Consumption Behavior, Import, and Recovery

In the modeling, consumption demand for lux-ury goods is assumed to be halved immediately af-ter the disaster (see the sectoral detail in TableA2, expressed by vector µ0). The recovery processis influenced both by the long-term tendency togo back to the predisaster economic condition andshort-term tendency towards a balance between to-tal production capacity and total demand at the cur-rent time step. The short-term tendency represents anoise factor to the long-term recovery. The dynamichousehold consumption recovery equation is givenbelow:

fthh = (µ0 + s ∗ dt

1 + r ∗ dt2). ∗ (V ∗ c0), (16)

where (µ0 + s ∗ dt1 + r ∗ dt

2) models the recovery ofhousehold demand damage (a parameter vector sim-ilar to the EAM, Ŵt ) over time, vector c0, and matrixV represent the predisaster total household expen-diture on products and a converter between prod-ucts (shown in Table A2) and industrial sectors, re-spectively. Here dt

1 and dt2 represent the long-term

tendency and short-term tendency influencing recov-ery. Parameters s and r are influential factors withinranges [0, 1]. In the article dt

1 is simulated based onthe assumptions that household consumption has a10% recovery rate for each month, and dt

2 is calcu-lated as a gap percentage; that is, the total demandminus total production capacity compared againstthe total demand at each time step.

In regard to imports, it is assumed that commodi-ties from other regions are always available for pro-vision and that the maximum rate of import is equalto the import quantities in the predisaster condition.There is no constraint on types of goods and servicesimported, except in regard to goods and services thatare not suitable for import (e.g., utilities and trans-portation). The justification for such an assumptionis that authorities will prioritize the supply of goodsand services to the disaster region if there is an emer-gency, while supplies from utility sectors (e.g., elec-tricity) are usually provided locally, making it infea-sible to have large-scale adjustments to these lattergoods and services over the time scale of disasterrecovery.


However there are no data or experimental stud-ies on how households or companies react to produc-tion shortages by turning to external producers. Herewe assume that if the degraded production capacityfor industry i cannot satisfy final demand, householdswill seek imports. When the degraded production ca-pacity for industry i can satisfy both intermediate andfinal demand due to the reconstruction effort, cus-tomers will return to their initial suppliers. However,in the modeling, imports are also constrained by thetotal “importability capacity,” calculated as the prod-uct of the import amount in the predisaster time pe-riod and the percentage of the transportation sector’srecovery by that time period. The import mt in sec-tor and final demand categories at time step t is cal-culated as below:

mt =

(

q∗(t)tran

q0tran

∗ m0

)

. (17)

Here q∗(t)tran

q0tran

∗ m0 refers to the importability capacity at

time step t, where q0tran and q

∗(t)tran are the predisaster

and postdisaster (at time step t) total capacities fortransport of goods and services by the transport sec-tor obtained from vectors q0 and q∗(t), respectively.The subscript “tran” refers to aggregate transporta-tion by land, sea, and air.

Decisions to return to the predisaster conditionscan be complex and varied. Here, let us suggest twoways of adapting toward a balanced input-outputcondition (i.e., a balanced Equation (3) reflecting in-equality (12)) at each time step for the next round ofeconomic recovery. One approach is simply to adopta minimal production balance between labor produc-tion capacity, industry production capacity, and totalfinal demand. The second is to return to the balanceat the end of each time step by an adjustment policythrough changes in import and export in three steps:

� First, let us keep sector i’s degraded productionoutput—qt

deg (i)—constant in time and causeother sectors j to adjust accordingly in propor-tion to the balanced economic condition in thepredisaster period as shown in the equation:

rt ( j) =x0( j)

x0 (i)× qt

deg (i) , (18)

where x0( j)/x0(i) is the ratio of production in sectorj to sector i in this predisaster time. In this case, r isa column vector that describes the amount of goodsand services required in every sector so that the dis-

rupted economy is balanced by keeping the degradedoutput of industry i—qt

deg (i)—unchanged. For eachsector, a corresponding vector r is produced.

� Second, compare the amount of im-ports/exports generated based on the cal-culation of rt with the value of imports/exportsat the postdisaster time t. If any sector withinrt exceeds the limit of import/export for thatsector (constrained by transportation sectors),that vector rt is ignored; otherwise, it is retainedin the model as a possible candidate for rt if thefollowing conditions hold:

(rt (i) − qtdeg (i)) < �ft

imp (i) , where

(rt (i) − qtdeg (i)) > 0;

or |rt (i) − qtdeg (i) | < �ft

exp (i) where

(rt (i) − qtdeg (i)) < 0,

(19)

where �ftimp and �ft

exp are available capacities of cur-

rent imports and exports, respectively, and |rt (i) −

qtdeg (i) | will be met in an IO table either through

import or export. The comparison is to check ifthe import/export values (i.e., |rt (i) − qt

deg (i) |) arepractical for the currently available capacity to de-liver imports/exports. Further, because utility ser-vices are assumed to be provided locally, any possi-ble vectors rt requiring changes in these sectors areremoved.

� Finally, one may opt for one of the possible vec-tors rt left or their average as the return to a bal-anced production pattern.

However, the procedure has various constraints.For example, imports and exports are limited by theavailability of transportation in the postdisaster pe-riod; therefore, again there is only a tendency to-wards economic balance. In the modeling the firstapproach to returning to balance is adopted, while asensitivity analysis can be conducted in the future byapplying the two different economic balance optionsand comparing results.

5. DATA

5.1. U.K. Multisectoral Dynamic Model

For this article, the U.K. multisectoral dynamicmodel—MDM(25)—was used to produce the IO ta-ble components consisting of Leontief coefficients,

1916 Li et al.

0

2

4

6

8

10

12

14

1 A

gri

cult

ure

etc

2 C

oa

l

3 O

il &

Ga

s e

tc

4 O

the

r M

inin

g

5 F

oo

d,

Dri

nk &

To

b.

6 T

ext.

, C

loth

. &

Le

ath

7 W

oo

d &

Pa

pe

r

8 P

rin

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g &

Pu

bli

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arm

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14

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sic

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tals

15

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tal

Go

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s

16

Me

ch.

En

gin

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rin

g

17

Ele

ctro

nic

s

18

Ele

c. E

ng

. &

In

stru

m.

19

Mo

tor

Ve

hic

les

20

Oth

. T

ran

sp.

Eq

uip

.

21

Ma

nu

f. n

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ctri

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s S

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ply

24

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ter

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26

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28

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tels

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rin

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nd

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nsp

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etc

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ter

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nsp

ort

31

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Tra

nsp

ort

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un

ica

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ns

33

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nk

ing

& F

ina

nce

34

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35

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mp

u�

ng

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rvic

es

36

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f. S

erv

ice

s

37

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er

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s. S

erv

ice

s

38

Pu

bli

c A

dm

in.

& D

ef.

39

Ed

uca

�o

n

40

He

alt

h &

So

cia

l W

ork

41

Mis

c. S

erv

ice

s

42

Un

all

oca

ted

Mil

lio

n p

ou

nd

s

Predisaster

Fig. 1. Monthly industrial outputs in the predisaster period around 2020.

final demand categories, and total outputs specific toLondon’s economy around 2020. Due to the lack ofseasonal and monthly production data for London,we assume that London has an identical monthly pro-duction pattern as the U.K. national average. Sec-toral details of industrial monthly outputs of Lon-don’s economy around 2020—in terms of a constantprice at the 2003 level before the disaster—are shownin Fig. 1.

5.2. Event Accounting Matrix

In Section 3, a flooding event matrix Ŵ measuredby the proportion of production capacity loss for theBDI model was introduced. The degraded produc-tion capacity can be calculated from surviving pro-ductive capital and stock. Such information is usu-ally estimated by a flooding damage function, whichis highly dependent on the particular scale and tim-ing of a disaster event. In this article, a hypotheticalflooding event accounting matrix with 42 sectors andlabor loss for London’s economy around 2020 is in-troduced in Table I.

Table I contains two sets of information relatedto direct damage to London’s economy: (i) capitalloss or damages in sectoral detail, which can be in-terpreted as the reduction of industrial productioncapacity as a proportion of predamage capacity, and(ii) labor loss. In this table, labor is taken to be themost vulnerable; that is, 50% of labor in London is

unable to provide inputs to economic production im-mediately after the disaster for this scenario. The ser-vice sectors in London are assumed to be the nextmost affected by the flooding as most of them arecurrently located close to both sides of the Thames,while the utility sectors are assumed to be resilientbecause they are located in the remote rural area, rel-atively far from the river and outside flood plains.

6. RESULTS

The model produces the estimated temporal evo-lution of total output in London’s economy aroundthe year 2020 from the time of the flooding shock(t = 0) to the time of full economic recovery. All val-ues displayed in the figures of the article are in mil-lion pounds per month, with a constant price at 2003levels. Fig. 2 shows the monthly inequalities betweentotal production capacity, total demand, and the la-bor production capacity during the period of eco-nomic recovery. The economic imbalance due to theinequalities during the postdisaster period persists,although balance between these factors may occuroccasionally during the period of recovery. The la-bor production capacity recovery is set exogenouslyand is assumed to recover fully in six months. Thetotal production capacity and total demand recover-ies are modeled endogenously. The total productioncapacity recovery is constrained by capital recovery.The variation shown in the total demand curve is


Table I. Event Matrix Ŵ0—The Entries Show the Initial Percentage Loss in Productive Capacity in Each Sector and in Labor ImmediatelyFollowing the Flooding

1 Agriculture, etc. 30% 12 Rubber & Plastics 20% 23 Gas Supply 10% 34 Insurance 40%2 Coal 10% 13 Non-Met. Min. Prods. 20% 24 Water Supply 10% 35 Computing Services 40%3 Oil & Gas etc 10% 14 Basic Metals 20% 25 Construction 30% 36 Prof. Services 40%4 Other Mining 10% 15 Metal Goods 20% 26 Distribution 40% 37 Other Bus. Services 40%5 Food, Drink, & Tob. 20% 16 Mech. Engineering 20% 27 Retailing 40% 38 Public Admin. & Def. 40%6 Text., Cloth., & Leath 20% 17 Electronics 20% 28 Hotels & Catering 40% 39 Education 40%7 Wood & Paper 20% 18 Elec. Eng., & Instrum. 20% 29 Land Transport, etc. 40% 40 Health & Social Work 40%8 Printing & Publishing 20% 19 Motor Vehicles 20% 30 Water Transport 40% 41 Misc. Services 40%9 Manuf. Fuels 20% 20 Oth. Transp. Equip. 20% 31 Air Transport 40% 42 Unallocated 40%10 Pharmaceuticals 20% 21 Manuf. Nes. 20% 32 Communications 40% Labor 50%11 Chemicals nes 20% 22 Electricity 10% 33 Banking & Finance 40%

0 10 20 30 40 50 60 703

3.5

4

4.5

5

5.5

6

6.5

7

7.5x 10

4

month

Capacity in t

ota

l

Total production

Total demand

Labor production capacity

Fig. 2. The total production inequalities between different factorsduring the recovery.

caused by the simulation of consumer consumptionbehavior in the postdisaster period (see Equation(16): in the London case study we take the parame-ter r as a random variable with range [0, 1]). From thelevel of damage as shown in Table I, London’s econ-omy recovers in 70 months (about six years). Fig. 3shows an unequal recovery of final demand. The solidblue line at the top (colors visible in online version)refers to the predisaster total final demand; the greencurve with star marker represents the total final de-mand recovery in the postdisaster period, whose vari-ation is consistent with the total production requiredby final demand shown in Fig. 2; the red line with plusmarker in Fig. 3 shows the final demand met by con-strained local production alone; the black line withcircle marker in Fig. 3 shows the final demand metby constrained local production plus constrained im-ports. The difference between the green curve and

0 10 20 30 40 50 60 701.6

1.8

2

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6x 10

4

month

tota

l final dem

and

Final demand of predisaster

Final demand met by production

Final demand met by import+production

Final demand of postdisaster

Fig. 3. The total final demand inequalities between different fac-tors.

the black curve at each time step reflects the fact thatproduction does not meet final demand all the waythrough the postdisaster recovery period (partly dueto the rationing scheme including a bottleneck(7)),but is narrowed gradually.

In the modeling the proportional rationingscheme involving a bottleneck is adopted; selec-tion is justified in the following sensitivity analysis.Fig. 4 shows a comparison of total production be-fore adopting a bottleneck based on the Hallegattemethod(7) and after a bottleneck is applied duringthe recovery period. It shows how much effect thebottleneck may bring. It can be seen from the fig-ure that there is a significant impact at the beginningperiod—when the rationing scheme and bottleneckbalance the intermediate production—while the in-fluence fades as intermediate demand is satisfied byproduction over time.

1918 Li et al.

0 10 20 30 40 50 60 703

3.5

4

4.5

5

5.5

6

6.5

7

7.5x 10

4

month

tota

l pro

duction

Imbalanced Total Production

Production After Rationing Scheme

Fig. 4. The distortion of proportional rationing scheme with bot-tleneck to the total production during the recovery.

7. SENSITIVITY ANALYSIS

The variations in model inputs, model algo-rithms, and consumption behavior may have a largeeffect on the model results. The magnitude of thesevariations can be evaluated using systematic sensitiv-ity analysis, in which range values, different param-eters of equations, algorithms, and assumptions canbe applied. In this study, several aspects of model-ing variations, such as the scale of disaster, rationingscheme strategies, Leontief matrix, and consumptionbehaviors, are investigated.

� Modeling different scales of disaster without

changing households’ consumption pattern and

rationing scheme. Here a smaller-scale floodingevent with 10% direct loss to all industry sec-tors and a larger-scale flooding event with 70%direct loss to all industry sectors are modeled.Results are shown in Figs 5 and 6.

The two figures show similar recovery paths fortotal production capacity and total demand, with thelabor production capacity recovery path being speci-fied exogenously. The recovery durations for the twomodeled cases are 43 months and 126 months, re-spectively. While in the second case the direct loss isseven times higher than the first, the recovery periodis almost trebled.

� Modeling with different rationing schemes. Inthe model, one can employ either the pro-

0 5 10 15 20 25 30 35 40 453

3.5

4

4.5

5

5.5

6

6.5

7

7.5x 10

4

month

Capacity in t

ota

l

Total production

Total demand


Fig. 5. Unequal recovery given 10% direct loss.

0 20 40 60 80 100 120 1402

3

4

5

6

7

8x 10

4

month

Capacity in t

ota

l

Total production

Total demand


Fig. 6. Unequal recovery given 70% direct loss.

portional scheme or a priority scheme andadjust the order of priority between house-hold demand and industry reconstruction needswhile keeping all other assumptions unchanged.Fig. 7 shows the results of a simulation withthe priority as “Intermediate Demand” > “Fi-nal Demand for Reconstruction” > “House-holds Demand” > “Governmental Demand” >

“Fixed Capital Formation” > “Exports.” Sucha priority arrangement is justified by the factsthat business-to-business relationships are oftendeeper and favored over business-to-householdrelationships;(7) reconstruction and actions to


0 10 20 30 40 50 60 703

3.5

4

4.5

5

5.5

6

6.5

7

7.5x 10

4

month

Capacity in t

ota

l

Total production

Total demand


Fig. 7. The recovery based on the damage demand prior scheme.

0 200 400 600 800 1000 1200 1400 1600 18003

3.5

4

4.5

5

5.5

6

6.5

7

7.5x 10

4

month

Capacity in t

ota

l

Total production

Total demand


Fig. 8. The recovery based on the final demand prior scheme.

return the economy back to the predisastercondition are considered a priority by theauthorities; government consumption alwaysgives priority to household consumption in apostdisaster situation; and exports are rankedlowest because customers from other regionsmay easily switch to other suppliers and com-modities when short of imports from the disas-ter region. Fig. 8 shows the results of a simula-tion with an alternative priority scheme to dis-tribute goods to households, government, andexports prior to reconstruction efforts. The re-sult demonstrates that in this latter situation theeconomy recovers very slowly if at all (>1,727

0 10 20 30 40 50 602.5

3

3.5

4

4.5

5

5.5

6x 10

4

month

Capacity in t

ota

l

Total production

Total demand


Fig. 9. The total production recovery using alternative assump-tions.

months). The reason is that economic produc-tion capacity and final demand are determinedby the restoration of industrial capital. As pro-duction in the aftermath of a disaster does notsatisfy both the intermediate demand and finalconsumption, a prior allocation for reconstruc-tion leading to capital recovery is needed. Theapproximate recovery periods in Fig. 2 (propor-tional scheme), 7, and 8 are 70, 65, and >1,727months, respectively. The difference between aproportional scheme as shown in Fig. 2 and apriority scheme with reconstruction having toppriority as shown in Fig. 7 is not significant,which demonstrates that a proper proportionalscheme applied to the demand for production,reconstruction, household, and other demandsis highly recommended to policymakers in a dis-aster recovery situation. The scheme may givea fairer goods allocation. The lack of recoveryshown in Fig. 8 suggests that a reconstructionpolicy that brings business back to work quicklyis essential for the recovery.

� Modeling with a regional matrix, alternative la-

bor, and household recovery paths. We next testcombinations of three alternative factors: a re-gional Leontief matrix A, an alternative exoge-nous labor recovery path, and household con-sumption recovery path, with other parts ofthe model left unaltered. Results are shown inFigs. 9 and 10. As discussed previously, themodel assumes that London’s economy has the

1920 Li et al.

0 10 20 30 40 50 601.6

1.8

2

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6x 10

4

month

tota

l final dem

and

Final demand of predisaster

Final demand met by production

Final demand met by import+production

Final demand of postdisaster

Fig. 10. The final demand recovery using alternative assumptions.

same industrial structure as the national econ-omy and therefore the U.K. matrix A is adoptedduring the modeling. However, a London tech-nical coefficient matrix may be estimated basedon the estimated regional supply percentage;that is, the percentage of the total required out-puts from each sector that could be expectedto originate within London region, through theequation:(26)

pi = (xi − ei ) / (xi − ei + mi ) , (20)

where xi , ei , and mi refer to the total regional out-put, the export, and the import of each sector i of theregion, respectively. Then, the regional matrix A isestimated as (in the case of London the number ofsectors is 42):

A∗ = P A=

⎛

⎜

⎝

p1 · · · 0...

. . ....

0 · · · pn

⎞

⎟

⎠

⎛

⎜

⎝

a11 · · · a1n

.... . .

...an1 · · · ann

⎞

⎟

⎠.

(21)Labor recovery is still assumed to start from the

same initial degree of damage, but the path is sub-stituted with an s-shape. It assumes that recovery ofthe labor rate is slow for the first few months, fol-lowed by a sharp increase as people have adaptedto the postdisaster situation, and then a leveling-off as the labor force has fully adapted. The alteredhousehold consumption recovery is assumed to befulfilled in six months with the same starting pointas shown in Table A2, but the path is set to in-crease 10% in every following month for degraded

consumption rates until the predisaster level isreached.

From the figures mentioned earlier, the recoveryprocess is complete at the 59th month, demonstrat-ing shorter recovery duration in comparison to the 70months shown in Fig. 2. The large influence of the al-tering factors is reflected by the shape change in thetotal production and final demand recovery curves,which also show similar s-shapes. This demonstratesthat labor recovery has been playing an essential rolein the simulated recovery of London’s economy. Aslabor recovery relies heavily on transportation andhealth care provision, policies emphasizing these sec-tors should be a top priority for authorities in a post-disaster period.

8. CONCLUSIONS

This article proposes a framework for modelingan imbalanced economic recovery process in a post-disaster period using IO analysis. Labor, capital, andfinal demand are among the major constraints thatinfluence and distort an economic balance and recov-ery; that is, the imbalance between them is a drivingfactor along the pathway of recovery for an affectedeconomy. A series of dynamic inequalities is devel-oped as a theoretical basis for the modeling, based onwhich economic conditions following a hypotheticaldisaster occurring in London around 2020 are takenas a scenario to assess the influence of future shockson a regional economy. The model simulates recon-struction demand, labor, and capital recovery, con-sumption behavior and imports constrained by ra-tioning schemes, connected through the IO table anddriven by the inequalities between them, influencedby short-term economic rebalance and long-term re-covery tendencies.

Along with the framework, a macroeconomet-ric model—MDM—is used to project the baselineconditions at the time of the disaster. The modelingresults show that London’s economy recovers withthe reconstruction complete in 70 months (about sixyears) by applying a proportional rationing schemeunder the assumption of 50% labor loss (with fullrecovery in six months), 40% initial loss to servicesectors, and 10–30% initial loss to other sectors. Theinequalities and results also suggest that the imbal-ance during a postdisaster period will persist, al-though balance may occur temporarily during the re-covery period.

There are large variations in results caused by se-lection of data, behavioral assumptions, and model


methodologies. The article studies several aspects ofmodeling variations including the scale of disaster,rationing scheme strategies, the Leontief matrix em-ployed, and household consumption behaviors. Themodeling on different scales of disaster provides acomparison of recovery trajectories and durations;the modeling on different rationing schemes suggestsa proportional scheme may be a proper strategy usedfor rapid postdisaster economic recovery with a fairbalance between final demand actors; the modelingon an estimated regional matrix shows that the influ-ence on recovery time is minimal under current as-sumptions and data applied; the modeling with dif-ferent labor recovery paths demonstrates that priorpolicies in transportation recovery and health careare essential in postdisaster economic recoveries.

One further extension of the model is in thearea of economic agents and primary factors dynam-ics simulation. For example, in the postdisaster pe-riod labor productivity is likely to change. If peopletake longer time traveling to work, they may chooseto nonetheless complete their required work assign-ments or tasks; this would reduce the influence oftransportation loss on economic production. More-over, the framework needs to be further justified byapplying real disaster scenarios data; a comprehen-sive sensitivity analysis on key parameters of the dy-namic inequalities might then be conducted. In addi-tion, endogenizing the flooding damage function todetermine surviving productive capital and stock isrecommended when feasible.

ACKNOWLEDGMENTS

This research is part of the ARCADIA projectfunded by the U.K. Engineering and Physical Sci-ences Research Council (EPSRC). The authors aregrateful to Professor Jim Hall of Oxford Univer-sity for helpful advice and discussion and to theanonymous reviewers who provided constructivecomments. This research is part of the ARCADIAproject funded by the U.K. Engineering and Phys-ical Sciences Research Council (EPSRC). The au-thors are grateful to Professor Jim Hall of OxfordUniversity for helpful advice and discussion and tothe anonymous reviewers who provided constructivecomments. Dabo Guan would also like to give hissincere thanks to the Natural Science Foundation ofChina (71250110083) for the full support.

APPENDIX

Initialization

(Reading in Damages and London

Predisaster Economic Conditions)

Computing the Labour Production

Capacity Recovery at Step (t),

Computing the Industrial Production

Capacity Recovery at Step (t),

Balance Between Current

Total Production Capacity, Total Demand

and Labour Production

Computing the Consumption Behaviour

Change at Step (t),

Computing the Total Demand at Step

(t),

, (t > 0)

Yes

No

End

t = t + 1

Computing the Import Availability at

Step (t), - mainly used by box 4

1

2

3

4

5

6

7

Fig. A1. Modeling imbalanced economic recovery following aLondon flooding event around 2020 using input-output analysis.The diagram, which has been described in Section 4.1, is the mod-eling process for the London case study based on the generalframework developed in Section 3 (mainly Equations (1)–(12)).In the London case the framework is further enriched based on adefined scenario and further assumptions by simulating labor forcerecovery (box 2 of Fig. A1), rationing scheme (box 4), consump-tion behavior change (box 5), and imports dynamics (box 7), etc.Here the solid lines form a recovery circle within a time step (i.e.,a month).

1922 Li et al.

Table A1. The Assumption of Labor Recovery of All Sectors inLondon Case, lte

Month 1 SectorsLoss recovery in percentage term 0.5Travel delay: number of hours per day (o1) 3% of labor affected of delaying (p1) 10%

Month 2

Loss recovery in percentage term 0.6Travel delay: number of hours per day (o2) 2% of labor affected of delaying (p2) 8%

Month 3


Month 4


Month 5

Loss recovery in percentage term 0.9Travel delay: number of hours per day (o5) 0.5% of labor affected of delaying (p5) 1%

Month 6

Loss recovery in percentage term 1Travel delay: number of hours per day (o6) 0% of labor affected of delaying (p6) 0%

Note: Here two scenarios are given: the labor capacity recovery iseither based on the loss recovery in percentage terms directly or,more specifically, calculated according to “% of labor affected ofdelaying” × “Travel delay: number of hours per day” × 22/(8 ×

22). In the London flooding scenario modeling, the first one isused.

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Table A2. Reduced Household Consumption Demand Immediately After the Disaster in Fraction of Predisaster Levels, µ0

1 Food 1 14 Gas 0.5 27 Petrol & oil 0.5 40 Educational services 0.52 Nonalcoholic drinks 1 15 Coal & coke 0.5 28 Running costs(m/v) 0.5 41 Catering services 0.53 Beer 0.5 16 Other fuels 0.5 29 Rail travel 0.5 42 Accommodation servs 0.54 Spirits 0.5 17 Furniture & carpets 0.5 30 Buses & coaches 0.5 43 Personal care 0.55 Wine, cider & perry 0.5 18 Household textiles 0.5 31 Air travel 0.5 44 Personal effects nec 0.56 Tobacco 0.5 19 Household appliances 0.5 32 Other travel 0.5 45 Social protection 0.57 Clothing 0.5 20 Tableware & hh utens 0.5 33 Communications 0.5 46 Insurance 0.58 Footwear 0.5 21 Tools & equipment 0.5 34 AV, photo, &info eq 0.5 47 Financial servs nec 0.59 Actual rents (hsg) 0.5 22 Gds & servs hh maint 0.5 35 Other durables 0.5 48 Other services nec 0.510 Imputed rents (hsg) 0.5 23 Medical products 1 36 Other recreational eq 0.5 49 Expenditure abroad 0.511 Maintenance of hsg 0.5 24 Out-patient services 1 37 Rec & cultural servs 0.5 50 Foreign tourists exp 0.512 Water & dwel. serv 0.5 25 Hospital services 1 38Newspapers & books 0.5 51 NPISH final exp 0.513 Electricity 0.5 26 Purchase of vehicles 0.5 39 Package holidays 0.5 52 Unallocated 0.5


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