Methodologies

Within the economics literature an intense debate exists regarding which methodology should be used in the analysis of natural disasters. The conversation is derived from the influence that assumptions, data and referenced theories have on the results (^{Okuyama, 2007}; ^{Greenberg et al., 2007}). Among the most widely applied methodologies are econometric models, the IO model and the applied general equilibrium model (AGE). All of the alternatives seek to rectify the weaknesses that have emerged when natural disasters are subjected to analysis.

On one hand, the statistical rigorousness of econometric models allows for making predictions about the impact of natural disasters. Still, the application of this type of analysis requires historical information about natural disasters in the regional environment, a fact which complicates the implementation of these sorts of tools, given the scarcity of data during the time period and for the region. Another related problem concerning the data is that it does not distinguish between direct and indirect losses generated by natural events. Consequently, the lack of adequate data for the analysis limits the applicability of econometric models (^{Cochrane, 2004}; ^{Greenberg et al., 2007}; ^{Hallegatte and Przyluski, 2010}; ^{Li et al., 2013}; ^{Okuyama, 2007} and ²⁰⁰⁹).

On the other hand, the circular flow of the economy in equilibrium is the basis for IO models, which are made up of inter-industrial transaction tables for the whole economy. This information is then organized in matrices. When learning about transactions between economic agents, it is possible to evaluate the indirect effects through the value chain. One advantage of using this methodology is that it requires less calibration of parameters as compared to other methodologies; another advantage is that IO matrices can be regionalized. The foregoing allows for regional analyses, and for the calculation of indirect losses from natural disasters. Nonetheless, disadvantages in the application of this methodology include the fact that they constitute a static model based on a function of production for fixed proportions and fixed prices, and that it does not consider input substitution or imports (^{Cole, 2003}; ^{Greenberg et al., 2007}; ^{Okuyama, 2007} and ²⁰⁰⁹; ^{Rose, 2004}).

As opposed to the limitations of IO models, EGA models seek to reduce the rigidity related to supply restrictions, price changes, nonlinearity and the substitution of input and imports. The disadvantage is that they increase considerably the number of parameters with an exogenous calibration. In the analysis of natural disasters, the problem is that EGA models assume that the economy is in equilibrium at all times, which is in fact impossible to sustain in the case of a negative natural phenomenon (^{Cole, 2003}; ^{Greenberg et al., 2007}; ^{Okuyama, 2007} and ²⁰⁰⁹; ^{Rose, 2004}).

Applications of the IO model

The decision to study the impact of hurricane Alex with the IO model is based on its capacity to undertake a regional analysis (the state of Nuevo León), to calculate the indirect effects and to measure damages in a scenario of economic disequilibrium provoked by a weather event.

Before explaining the IO model as applied to this case study, some studies that adopt this model and apply it to the topic of natural disasters will be reviewed. Natural disasters provoke economic disequilibria in the IO model that ^{Steenge and Bockarjova (2007)} incorporate using an accounting matrix of the event’s damages (AMED). The main diagonal of an AMED shows the damaged proportion of each sector’s productive capacity. As such, disequilibria and possible bottlenecks after a negative natural phenomenon are accounted for using the AMED, in addition to recuperation.

Another adaptation of the model consists of including an analysis of goods and services substitution by way of imports (^{Bockarjova et al., 2004}; ^{Steege and Bockjarjova, 2007}). A further contribution of the IO model was developed by ^{Hallegatte (2008)}, who added a temporal dimension, with the goal of studying the recuperation process. This model is called the regional adaptive input-output model (RAIOM). For the analysis of the recuperation process, this model considers bottlenecks in production that are caused by natural disasters, and the adaptive behavior of consumers and producers before the event. However, a weakness of this model is the fact that it excludes restrictions in productive labor capacity from the analysis, and likewise with losses of residential capital (^{Li et al., 2013}).

^{Li et al. (2013)} seek to make up for the limitations of the RAIOM by taking into account restrictions in production caused by damages from a natural disaster, including those caused to the labor force. Another element of ^{Li et al.’s (2013)} model is the incorporation of damage to residential capital. The RAIOM covers desirable characteristics for the analysis of natural disasters, given that it includes the analysis of damages to capital and industry work, and it incorporates economic disequilibria that result from the event, as well as bottlenecks in the economic supply of the affected economy.

Recently, ^{Mendoza-Tinoco et al. (2017)} developed the so-called “flood footprint,” which is an analytical framework for the evaluation of damages, both of the flooded region and of those economic systems which are interconnected on a broader scale. The methodology builds on what is developed by ^{Li et al. (2013)}.

The present article applies ^{Mendoza-Tinoco et al.’s (2017)}methodology (refer to the article for a more detailed explication of the model), and in addition it broadens the methodology so as to include a capital matrix, which provides consistency to the transition from a stock variable (industrial capital) and a flow variable (production), during the process of recovery. Finally, changes in final demand are explained by modeling the adaptive behavior of consumers.

Recovery processes after a disaster

An economy may be considered recovered once the labor capacities and industrial production are in equilibrium and the value of the total demand and production regain their level previous to the disaster. The method of using the remaining resources, to reach conditions before the disaster, is modeled following the rationing diagram.

The first step is to determine the production capacity available in each period following the disaster. In the context of Leontief production functions, productive capacity is determined by the minimum of each productive, capital and labor factor, as is demonstrated below:

Second, the level of restricted production capacity is compared to the total demand, to determine the allocation strategy of the remaining resources, and for reconstruction planning. The rules for this process constitute what is called the rationing diagram, which is described below.

Total economic impact

Lastly, the total economic impact of event (tec), is the sum of direct costs (va _dir) and indirect costs (va _ind) generated during each period of the recovery process, as expressed in equation (11). Costs are measured in terms of value added, which in the case of direct damages, is equal to the cost of replacement, at market price. This makes up the total recovery demand frec0. On the other hand, the indirect cost is calculated as the accumulation of differences between the level of production before the disaster (x ⁰) and the restricted production after the disaster in each period (Xtpt), which is equal to the term (Tx0-∑txtpt), where T is the time estimated for the economy’s recovery.

Economic data

The economic variables that need corresponding data are the following: capital stock, household stock, final demand, employment and the level of inter-industrial commerce. The information is required at a regional level (for the state of Nuevo León), and when not available at that scale, statistical techniques are used as a way to regionalize the data.

Capital stock, employment and final demand (or GDP) are available at a regional level. The first two variables were obtained from the Economic Census of 2014, by the National Institute of Statistics and Geography [Spanish INEGI]; the GDP was obtained from the Bank of Economic Information (BEI), while household stock was obtained at the national level from the 2010 Population and Household Census by INEGI. Lastly, the interindustrial transactions that were used are found in the national input-output matrix (IOM) for 2008. As part of the methodology, Flegg´s coefficient technique for increased localizations was used to regionalize the technical coefficient matrix, starting from the regional employment in relation to the national employment. The distribution of final regional demand for household costs, governmental costs, capital formation, and exports and imports, follows the same distribution as the national.

Information on damages

The model requires information on damages to industrial capital, residential capital and infrastructure. Additionally, information is needed regarding impacts to the workforce´s productive capacity, as well as changes to final demand.

Statistics for damages to physical capital were obtained from the Characteristics and socioeconomic impact of main disasters that occurred in the Mexican republic during 2010 report (^{CENAPRED, 2014}), which also gives an account of the damages to social sectors (households, health, education and hydraulic infrastructure) of $7.275 billion MXN; economic infrastructure (highways, electricity production, navy and urban)of $13.356 billion MXN; productive sectors (agriculture, livestock and aquaculture, commerce and services) of $706 million, and the environment. For the industrial sectors, a distribution of damages based on the size of each industry within the regional economy was performed. This distribution can be consulted in column 5 of table A1 of the Appendix, in which event’s damage vector is designated.

As concerning impacts to the productivity of the workforce and household consumption, the novel character of this methodology establishes the need for data that is sometimes not available, as was the case for the effects of hurricane Alex. To resolve this situation, an analysis of various cases was performed based on the values of other variables. In the case of impacts to the workforce, the reported proportion of population affected was considered with respect to the total regional population, a proportion which was applied directly to the PEA proportion in Nuevo León. It is also assumed that this population suffered delays of one hour for transportation to their jobs during the first month, which then decreased linearly for six months until reaching zero. This parameter adds uncertainty which can be overcome by undertaking a sensibility analysis, which determines the stability of the model and tests the solidity of the scenario’s data.

Meanwhile, the changes in final demand for households follow psychological patterns, as has been observed following a disaster, when the population decreases consumption of nonbasic goods, showing prevention behavior. In this regard, it was assumed that such a decrease applies only to the affected population; an estimate of a 20% decrease in non-basic goods is given, with a linear recuperation of five months. A sensibility analysis was performed with respect to this parameter as well.

The cases under consideration are: a) impacts to industrial capital without impacts to the workforce or final demand; b) impacts on industrial capital with impacts on the workforce (disequilibria in productive factors); c) impact to industrial capital and final demand; and d) impact to industrial capital, the workforce, and final demand. In these cases, impacts on residential capital are also considered.

Total economic costs to the state of Nuevo León

The entity’s GDP in 2010 was $855 billion MXN (in 2009 prices), which represents approximately 0.73% of the national GDP for that year. Additionally, around 1,234,000 employees were registered in the region, which makes up about 0.6% of the total workforce in Mexico.

According to the present analysis, Nuevo León’s economy took around 20 months to recover after the natural phenomenon’s occurrence. Within the proposed methodological framework, recovery is reached with the economy reaches equilibrium again, and when the production level is the same as before the disaster. The quantification of the total economic loss rises to $27.423 billion MXN, which would amount to 3.2% of the state’s GDP for that year.

Figure 1 shows the composition of damages by category. Direct economic losses (which are made up of damages to industrial capital, the city’s infrastructure and to homes) represent 2.3% of the regional annual GDP ($21.500 billion MXN), of which 95% correspond to industrial and infrastructure damages. Indirect economic loss -which is the sum of all production flows that are not performed as a consequence of disruptions to productivity- represents an additional loss, equivalent to 1% of the state’s GDP ($5.922 billion MXN). This means that indirect damages were 28% higher than direct costs.

Source: prepared by the authors based on the model’s results.

Figure 1 Distribution of damages by category (in millions of Mexican pesos) 

Economic recovery

This section describes the trajectories of economic variables which are involved in the recovery process, such as recovery of the productive capacity of industry, the participation of imports in recovery, and the dynamics of final demand that include demand for reconstruction.

Figure 2a shows the indirect damaged accumulated during the recovery process, and is calculated as the distance between the final demand satisfied by the available production during a period and at a level preceding the disaster. It can be seen that the initial decrease of the productive capacity is 2% compared to the value added in Nuevo León. This figure also shows the rapid initial recovery, especially during the first five months, a period when the economy recovered approximately 95% of the damaged productive capacity. However, the shape of the recovery curve is influenced by the rationing diagram chosen for the model, within which inter-industrial demand and recovery demand are prioritized above the rest of the final demand. The results indicate that for period (month) 15, the production level was basically the same as before the disaster; yet, disequilibria in the markets do exist, and accordingly the process continues until period 20.

Source: prepared by the authors based on the model’s results.

Figure 2 Dynamics of economic variable during the recovery process 

Figure 2b then shows the dynamics of recovery of the productive capacity of capital, and its interaction with total productive capacity. Delays in production in following the recovery pace of industrial capital is due to secondary effects caused by disequilibria across production chains in each industry. Figure 2c illustrates the disequilibria between supply and demand. Finally, figure 2d demonstrates the contribution of imports to the recovery process.

Sectoral analysis

One of the advantages of the methodology being used here is that, given that it is circumscribed in the IO analysis, a sectoral analysis of the results is possible, which allows for a look at how the effects of the shock to the economy are distributed across production chains. This element of the methodology becomes useful for planning in flood risk management, in addition to adjustment policy.

Figure 3 presents the distribution of economic impact in the 19 productive sectors, divided into direct and indirect damages. The damages, in particular direct ones, are concentrated in sectors related to infrastructure, i.e. that of Electricity, Gas and Water, and the Transportation sector. These two sectors concentrate 81% of the event’s total damage, which for direct damages represents 93%, though only 39% as regards indirect damages.

Source: prepared by the author based on the results of the model.

Figure 3 Sectorial distribution of economic impact 

Additionally, it can be observed that the remaining sectors were affected primarily by indirect damages, despite not having been reached directly by the effects of the hurricane.

Direct losses in the sector with highest damage, that of Electricity, Gas and Water, represent 57% of the total direct economic losses; while the sector with the next highest direct damages (Transportation and Storage) make up 36% of the rubric.

Regarding the sectors with highest indirect damage, that of Transportation and Storage sees the highest concentration, with 31% of total indirect damages. Following it is the manufacturing industry sector, whose indirect losses are 22% of the total.

It is worth noting that the Transportation and Storage sector and that of Education are found to be among the three most affected sectors in each category, even though the proportion of indirect damages is much higher for Education (58%) than for Transportation and Storage (20%).

Figure 4 allows for a more detailed analysis of the distribution of direct and indirect damages by sector, independently of their amounts. This makes it possible to know which of the sectors were found to be proportionally more affected in an indirect way. It is especially the Service sectors, which are at the end of the production chain, that turn out to be the most indirectly affected-such as the Commerce, Business Support and Professional Services sectors. The proportion of indirect damages in primary sectors such as Agriculture and secondary, such as Manufacturing, is notable. The foregoing can be explained as a result of high levels of damage to energy and transportation infrastructure.

Source: prepared by the author based on the results of the model.

Figure 4 Proportional distribution of damages 

Case and sensibility analyses

Here, the effect of impacts to workers and possible changes to households’ final demand are analyzed. To do this, hypothetical values were used, based on possible scenarios and in line with information from reports on damages caused by hurricane Alex in Nuevo León. Nonetheless, information on these variables is scarce, especially in the form that the model requires, such that various scenarios were considered for its implementation.

In the case of impact to the workforce, the proportion of people affected with respect to the total population was taken and applied to the total working population for impacts that caused delays in transportation of up to two hours during the first month. A linear recuperation was modeled for five months.

For the case of changes to household consumption, the total portion of the affected population was taken into account. A 20 % decrease in their consumption of non-basic products during the first month. A linear recuperation was modeled over five months.

The parameters under consideration are conservative and based on reported data. Nonetheless, a sensibility analysis was performed for the parameters in order to prove the model’s stability and the solidity of the results. The sensibility analysis considered the variation of the parameters to be +/- 10% with respect to the initial values.

From figure 5a to 5b the values of different variables across the recovery process are shown. The error bars calculate the standard deviation for each point across time. The sensibility analysis applies for the case in which the workforce is affected, but not the final demand. In that case, the average value of indirect costs is $6.086 billion MXN, with a standard deviation of +/- $80 (+/- 1.3%) million MXN, which represents an additional 3% than when not considering the decrease in productivity because of impacts to the workforce.

Source: Prepared by the authors based on results from the model.

Figure 5 Analysis of damages due to impacts to the workforce 

Figure 6 shows, on the other hand, the effect of changes to final demand, but without variation of the workforce and with respect to indirect damage variables (see figure 5a), for total production, given the changes in behavior of final consumers (see figure 5b), the evolution of final demand (see figure 5c), and the evolution of value added under this scenario (see figure 5d). The results show average indirect damages of a total of $6.172 billion MXN, with a standard deviation of +/- $15 million (+/- 0.3%) MXN, and an increase of 4% as compared to the base scenario.

Source: prepared by the authors based on the results of the model.

Figure 6 Analysis of damages by impacts to final demand 

Finally, a global sensibility analysis was performed. That is, varying all of the parameters at the same time (for workforce and household final demand). The results show average indirect damages of a total of $6.636 billion MXN, with a standard deviation of $96 million (+/- 1.5%) MXN, which represents 7% compared to the base scenario. A summary of the results can be seen in table 1, where the damage increase index (DII) indicates how much indirect economic cost was implied by each damage monetary unit to the productive (or industrial) capital.