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Measuring Natural Risks in the Philippines: Socioeconomic Resilience and Wellbeing Losses

Abstract

Traditional risk assessments use asset losses as the main metric to measure the severity of a disaster. Here, an expanded risk assessment is proposed based on a framework that adds “socioeconomic resilience” — that is, the ability of affected households to cope with and recover from disaster asset losses — and uses “wellbeing losses” as its main measure of disaster severity. Using a new agent-based model that represents explicitly the recovery and reconstruction process at the household level, this risk assessment provides new insights into disaster risks in the Philippines. Its first conclusion is the close link between natural disasters and poverty. On average, estimates suggest that almost half a million Filipinos per year face transient consumption poverty due to natural disasters. Nationally, the bottom income quintile suffers only 9% of the total asset losses, but 31% of the total wellbeing losses. As a result of the disproportionate impact on poor people, the average annual wellbeing losses due to disasters in the Philippines is estimated at US$3.9 billion per year, more than double the asset losses of US$1.4 billion. The second conclusion is the fact that the regions identified as priorities for risk-management interventions differ depending on which risk metric is used. While cost-benefit analyses based on asset losses direct risk reduction investments toward the richest regions and areas, a focus on poverty or wellbeing rebalances the analysis and generates a different set of regional priorities. Finally, measuring disaster impacts through poverty and wellbeing impacts allows the quantification of the benefits from interventions like rapid post-disaster support and adaptive social protection. While these measures do not reduce asset losses, they efficiently reduce their wellbeing consequences by making the population more resilient.

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Notes

  1. 1.

    In geographical terms, the current version of the FIES is representative only at the regional level. An updated FIES, expected in 2019, will make it possible to perform the same analysis at the provincial level.

  2. 2.

    Comprehensive asset loss estimates are a direct output of the AIR catastrophe model, a probabilistic model of natural hazards and their interactions with, or impacts on, insurable assets. Starting from event simulations with localized intensity calculations, the AIR model estimates damages and expected losses, taking into account the best available exposure data and policy conditions (Guin and Saxena 2000; Grossi and Kunreuther 2005). However, this analysis is specifically interested in the impacts of disasters on household assets, consumption, and welfare. One issue we face is the difference between the Gross Domestic Income (GDI) derived from national accounts and the aggregated household consumption (AHC) calculated from household surveys. As is well known, the latter tend to report lower incomes and consumption than national accounts (Deaton 1997). In this analysis, we work based on the AHC. Therefore, the expected losses in Table 1 have been scaled by AHC as a fraction of the nominal regional productivity (GRDP), a factor of 0.43 on average (cf. Table 7).

  3. 3.

    AHC is the total household consumption in each region, as reported in FIES.

  4. 4.

    We also note that post-disaster income losses should be observable using high-frequency panel surveys in areas recovering from disasters.

  5. 5.

    Here, the unit of analysis is the households. It would be useful to do it at the individual level, to uncover intra-household distributional effects, linked to gender or age. In the absence of within-household data, we make the strong assumption that pre-disaster consumption and disaster losses are distributed equally per capita within each household.

  6. 6.

    More precisely, the impact on wellbeing is equivalent to a 193 billion decrease in consumption that would be optimally shared across households in the country and across time. Or it is equivalent to a 193 billion decrease in consumption that would be equally shared across households in the country, if all households had the same income (i.e. if all inequality had disappeared).

  7. 7.

    Socioeconomic resilience is independent of asset losses, except for a threshold effect that occurs when households fall into extreme poverty, and are unable to reconstruct at all. Resulting wellbeing losses can approach infinity, but the effect is rare enough that resilience results are robust against the inclusion or exclusion of these households in this analysis. This will not be true in all countries or contexts, and particularly in the poorest, least developed cases.

  8. 8.

    This estimate is significantly lower than that from the Unbreakable report, and cannot be directly compared, considering the difference between the models. The difference is explained by the improved consideration of distributional impacts (using the full survey instead of only two categories of households) and the explicit representation of the reconstruction pathway. The difference confirms the need to model the reconstruction pathway in a dynamic manner and to include the impact of short-term consumption drops.

  9. 9.

    It is also possible to look at different subgroups in the country or at the regional scale (e.g., per occupation, head of household gender, household size, ethnic background or religion, social transfer enrollees), within the limits of the representativeness of the household survey.

  10. 10.

    A more complete description of the response to Yolanda is provided in the Shock Waves report (Hallegatte et al. 2015).

  11. 11.

    Here, we report expected asset losses from the 100-year wind event in the Eastern Visayas (a product of the DFCRM, scaled to match AHC), and this represents 45% of the reported US$1.4 billion in losses to Yolanda in the Eastern Visayas. The total value includes damage from precipitation flooding and storm surge (not included in this example), as well as the assets that account for the difference between AHC and nominal GRDP.

  12. 12.

    Progressive taxation, social insurance-like systems, existing program enrollments and conditionalities, and more complex alternatives can also be modeled.

  13. 13.

    It is important to note that even if the amount of post-disaster support is equal to asset losses, it does not fully cancel wellbeing losses: indeed, post-disaster support maintains consumption, but consumption losses are larger than asset losses. This result is consistent with intuition: even if people are immediately given in cash the cost of rebuilding their houses and replacing their assets, they would still experience wellbeing losses during the reconstruction period, since assets and houses cannot be replaced instantaneously.

  14. 14.

    This is a serious limit in a country where international remittances have reached more than 8 percent of the gross national income in 2017, and where remittances have been shown to support post-disaster recovery (Le De et al. 2013; Yang and Choi 2007).

  15. 15.

    In some countries, it may be necessary or preferable to infer household income from expenditures, whether because incomes are not reported, because consumption is more stable over time, or because the official poverty statistics are calculated from consumption rather than income.

  16. 16.

    Similarly, the services provided by other assets (e.g., air conditioners, refrigerators) could be added as an additional income that can be threatened by natural disasters.

  17. 17.

    Administrative costs are not included in the assessment of the cost of the programs. When household data do not include the transfers, then transfers from social programs can be modeled on the basis of the actual disbursement rules that qualify households for participation in each program (eg, PMT score, household number of dependents or senior citizens, employment status, etc.).

  18. 18.

    Although we assume a flat tax, the model is capable of handling more complicated tax regimes, including progressive taxation.

  19. 19.

    Since general spending of the government is not explicitly represented in the income ih, the effective capital stock estimated here \(k_{h}^{eff}\) is net of the resources used to finance this general spending through taxes.

  20. 20.

    Where higher resolution household and disaster loss data are available, it is of course possible to expand Equation 8 to the provincial or sub-regional level.

  21. 21.

    In exceptional cases where fa exceeds an upper threshold of 0.95, or 95% of households affected, the exposure is capped at 95% and the vulnerability vh is increased to match the asset losses from the AIR model.

  22. 22.

    This is equivalent to assuming that the government budget is always balanced and that inter-household transfers respond instantaneously to income changes. Other changes in government spending, tax rates, and remittances are represented through the third term of the equation, \({\Delta } i_{h}^{PDS}\), see below.

  23. 23.

    In addition to the loss of monetary income, this includes the loss in virtual income if the housing services provided by their home or their asset (fridge, fans, air conditioning systems) is also lost.

  24. 24.

    Even though natural capital “rebuilds itself,” people may have to reduce consumption to allow for accelerated growth.

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Acknowledgments

The authors wish to recognize the work of many colleagues who contributed to this report, including Artessa Saldivar-Sali, Lesley Jeanne Y. Cordero, Adrien Vogt-Schilb, Mook Bangalore, and the World Bank country office in Manila. They also thank the teams at the Philippines’ National Economic and Development Authority and the Philippine Statistics Authority for their contribution to the development of the model and its application to the Philippines. All errors, interpretations, and conclusions are the responsibility of the authors.

Author information

Correspondence to Brian Walsh.

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Global Facility for Disaster Reduction and Recovery (GFDRR), World Bank Group

Technical Appendix — Methodology and model description

Technical Appendix — Methodology and model description

This section explains the methodology and describes the model used to translate asset losses into wellbeing losses. The code of the model is freely available, and the reader is invited to refer to the code for the implementation of the principles and equations presented in this section. The household survey data cannot be made available directly, as they need to be requested from the statistical agency of the Philippines.

In all applications, the model assumes a closed national economy. In terms of disaster risks, this means that 100% of household income is derived from assets located inside the country, and that post-disaster reconstruction costs can be distributed to non-affected taxpayers throughout the country, but not outside its borders.Footnote 14

This report picks up and develops the analytical machinery of the original Unbreakable report. Its primary innovation is in its use of the Family Income & Expenditure Survey (FIES) to disaggregate expected asset losses among representative households, resulting in a measurement of asset losses, poverty impacts, and wellbeing losses by income quintile and region in the country. While the remainder of this report offers a detailed description of the methodology we highlight three ways in which this iteration of the Unbreakable analysis is an extension of previous work (Hallegatte et al. 2016; Hallegatte et al. 2018):

  • Based on national data, the original model could not give insight into spatial heterogeneities in hazard, exposure, or asset vulnerability. This shortcoming limited the practical value of the Unbreakable framework to inform funding decisions at actionable level of spatial detail. The present analysis is based on hazard- and asset class-specific exceedance curves at the provincial level, even though the spatial resolution of the analysis is limited by the representativeness of the available household survey.

  • The original analysis, used most recently to generate national-level indicators for 149 countries in Hallegatte et al. (2018), divided the population of each country into “poor” and “non-poor” groups. National averages for the characteristics of each group (e.g., income and asset vulnerability; access to early warning and financial institutions; social protection receipts, etc.) are used to estimate their respective asset and wellbeing losses and socioeconomic resilience. Consequently, it was not possible to examine the characteristics that influence socioeconomic resilience within quintiles. In the new iteration, we can examine income and expenditures data for more insight into how best to help the poor cope with disasters.

  • Formerly, the model assumed exogenously that all households recover at the same pace when they are affected by a disaster. In its current iteration, the model explicitly represents disaster reconstruction dynamics at the household level using an agent-based approach in which each household acts rationally to minimize its wellbeing losses. This optimization specifies each household’s reconstruction and savings expenditure rate, assuming households optimize the fraction of income they dedicate to repairing and replacing their assets. For instance, people close to the subsistence level cannot set aside much of their income to rebuild their assets without experiencing large wellbeing losses, and may therefore take longer to recover. In extreme cases, they may even be trapped in poverty, generating large wellbeing losses going well beyond the few years that follow a disaster (Carter and Barrett 2006; Dercon and Porter 2014). The model also provides a better assessment of wellbeing losses by distinguishing between short-lived deep consumption losses, and more persistent but shallower impacts.

Pre-disaster situation

Population & weighting

The pre-disaster situation in the country is represented by the households described in the Family Income and Expenditure Survey (FIES). We use a per capita weighting (ωh), such that summing over all households in the survey or in an administrative unit (Nh) returns the total population (P):

$$ P = \sum\limits_{h = 0}^{N_{h}}\omega_{h} $$
(1)

One essential characteristic of each household is its income (ih). As defined by the FIES, ih combines primary income and receipts from all other sources, including the imputed rental value of owner-occupied dwelling units, pensions and support, and the value of in-kind gifts and services received free of charge. The data recorded in the survey are assumed to capture the household’s permanent income, which is smoothed over fluctuations in income and occasional or one-off expenditures.Footnote 15 It is important to note that the value of housing services provided by owner-occupied dwelling is included in the income data, so that the loss of a house has an impact on income (even though it would not affect actual monetary income).Footnote 16

Social transfers, taxation, and remittances

The enrollment and value of social transfers (\(i_{h}^{sp}\)) are listed in FIES, and the total cost (\(\mathcal {C}_{sp}\)) of these programs to the government is given by a simple sum:Footnote 17

$$ \mathcal{C}_{sp} = \sum\limits_{h=0}^{N_{h}}\omega_{h} i_{h}^{sp} $$
(2)

All incomes reported in FIES are assumed to be reported net of the income tax that finances general spending of the government (for infrastructure and other services) and of an additional flat income tax that finances social programs (rate = \(\delta _{sp}^{tax}\)). The rate \(\delta _{sp}^{tax}\) can be estimated with the following equation:Footnote 18

$$ \sum\limits_{h=0}^{N_{h}}\omega_{h} i_{h}^{sp} = \sum\limits_{h=0}^{N_{h}}\omega_{h} i_{h}\frac{\mathcal{C}_{sp}}{\sum \omega_{h} i_{h}} = \sum\limits_{h=0}^{N_{h}}\omega_{h} i_{h}\delta_{sp}^{tax} $$
(3)

Note that, since ih includes \(i_{h}^{sp}\), income from social programs is treated as taxable in the model. A similar approach is used to derive the tax rate (\(\delta ^{tax}_{pub.}\)) to fund post-disaster reconstruction of public assets.

Remittances and transfers among households play a very important role for people’s income. Some of these transfers are within a family or a community, while others are international. The FIES provides estimates of the amount received, but it is of course impossible to represent the bilateral flows of resources among households. For this reason, remittances are modeled like an additional social protection scheme: the transfers received from friends and family are added to the social transfers, and it is assumed that these transfers come from a single fund, in which all households contribute proportionally to their income (like a flat tax). Under these assumptions, remittances can be aggregated with social protection and redistribution systems. This is of course a simplification, especially in that it does not account from international remittances, which have been shown to play a role after disaster (Yang and Choi 2007).

Income, capital, & consumption

Household income is equal to the sum of the social transfers and domestic and international remittances, plus the value generated by a household’s effective capital stock (\(k_{h}^{eff}\)), less the flat tax at the rate \(\delta _{sp}^{tax}\).Footnote 19

$$ i_{h} = i_{h}^{sp} + (1-\delta_{sp}^{tax}) \cdot k_{h}^{eff} \cdot {\Pi}_{k} $$
(4)

In practice, the household’s effective capital stock (\(k_{h}^{eff}\)) is estimated based on the income and transfers reported in the FIES, and the tax level \(\delta _{sp}^{tax}\) that would balance the budget:

$$ k_{h}^{eff} \cdot {\Pi}_{k} = \frac{\overbrace{i_{h}-i_{h}^{sp}}^{\mathrm{Income~from~assets}}}{\underbrace{1-\delta_{sp}^{tax}}_{\mathrm{Gross~of~taxes}}} $$
(5)

All household income not from transfers is assumed to be generated by household effective assets, including some assets not owned by the household (like roads and factories). Some of the assets represented by \(k_{h}^{eff}\) are private (\(k_{h}^{prv}\)), such as equipment used in family business or livestock; some assets are public (\(k_{h}^{pub}\)), such as road and the power grid (and possibly the environment and natural capital); and some assets are owned by other households (\(k_{h}^{oth}\)), but still used to generate income by the household, such as factories.

In the absence of data on different capital stocks, we use the AIR loss modeling results to calibrate the model. The AIR catastrophe model describes expected asset losses in 15 separate asset categories: all private assets are grouped together, while public assets, including transport, health, education, and utility infrastructure are reported individually. For each household, we distribute \(k_{h}^{eff}\) to private (\(k_{h}^{prv}\)) and public (\(k_{h}^{pub}\)) using the fraction of private to total asset losses in the region, assuming that (1) the ratios of the different capital categories are similar for all households, and (2) the vulnerability of each household’s public assets is given by the vulnerability of its private assets.

The productivity and vulnerability of these assets to various hazards can vary, so it is useful to disambiguate among them as much as the data allow. In addition, these distinctions are important to understand the consumption and wellbeing losses that follow a disaster, since the liability for reconstruction varies: households rebuild their own assets (unless they carried private insurance); the national, regional, or provincial taxpayers rebuild public assets; and other privately-held assets are reconstructed by private business owners or corporations.

Precautionary savings

Precautionary savings play a key role in managing disasters, but there is no estimate of these savings in the FIES. Also, although the FIES provides information on both income and consumption, the difference between income and consumption is highly variable and negative for many households (aggregate consumption greater than reported income), making it an uncertain indicator of savings at the household level. Instead, we calculate the average gap (income less consumption) by region and decile. We then assume that each household maintains one year’s surplus as precautionary savings: separate from their productive assets, and available to be spent on recovery or consumption smoothing.

Household versus nominal regional GDP

Based on this definition of each household’s income and assets, we note that the total capital stock (K) of any country is given by a sum over the effective capital of all households, and the portion of national GDP from household consumption (hhGDP) as reported in the FIES is given by the product of K and the average productivity of capital (πk).

$$ K = \sum\limits_{h=0}^{N_{h}} \omega_{h} k_{h}^{eff} $$
(6)

Table 7 on the following page lists the aggregated household income (AHI) and the nominal GDP (GRDP) for each region of the Philippines. Overall, the incomes reported in FIES represent 43% of the nominal GDP, subject to significant regional variations. In order to compensate for this discrepancy, and ensure that our parameters and variables are consistent, we decided to work in the FIES reference. To do so, we scale expected asset losses in each region (based on the AIR catastrophe model (Deanna 2017)) by the ratio of the asset value calculated from the FIES to the total asset value in the AIR model. In other terms, we do not use the asset losses in PDP or US$ from the AIR model. Instead, we calculate the damage ratio or the ratio of losses to total asset values in the AIR model, and then apply the damage ratio to the assets \(k_{h}^{eff}\) calculated from the FIES data.

Table 7 Aggregate household income (AHI), calculated at the regional level from the 2015 FIES, versus nominal regional productivities (GRDP). Both values are expressed in billions of US$ per year

In the following sections, we will trace the impacts of disasters on household assets and wellbeing through the following steps:

  1. 1.

    Disasters result in losses to households’ effective capital stock (\({\Delta } k_{h}^{eff}\)).

  2. 2.

    The diminished asset base generates less income (Δih).

  3. 3.

    Reduced income contributes to a decrease in household consumption (Δch), but households affected by a disaster must further reduce their consumption to finance the repair or replacement of lost and damaged assets.

  4. 4.

    Household consumption losses are used to calculate wellbeing losses (Δwh).

One of the limits of the study is that we treat every event as independent, assuming that disasters affect the population as described by the 2015 FIES, and that two disasters never happen simultaneously (or close enough to have compounding effects).

Asset losses

The model starts from exceedance curves, produced by AIR Worldwide, which provide the probable maximum (asset) loss (PML) for several types of natural disasters (earthquakes, tsunamis, tropical cyclones, storm surges, and fluvial and pluvial flooding), each administrative unit in the country, and various frequencies or return periods. We make the simplification that a disaster affects only one region at a time, so that total losses in the affected region are equal to national-level losses.

For each region, the input data detail the total value of assets lost due to hazards as well as the frequency of each type of disaster over a range of magnitudes. Magnitudes are expressed in terms of total asset losses (L). For example, the curves specify “An earthquake that causes at least $X million in damages in Y region is, on average, expected to occur once every Z years.”

When distributed at the household level, the losses Lin the affected region can be expressed as follows:

$$ L = {\Phi}_{a} \cdot K = \sum\limits_{h=0}^{N_{h}} \omega_{h} f_{a_{h}} k_{h}^{eff} v_{h} $$
(7)

Setting aside for the moment the probability of a disaster’s occurrence (the “Hazard” component of Fig. 1 on page 6), Eq. 7 expresses total losses (L) in terms of total exposed assets (K) and the fraction of assets lost when a disaster occurs (Φa). In the rightmost expression, losses are expressed as the product of each household’s probability of being affected (\(f_{a_{h}}\), the “Exposure” component of Fig. 1 on page 6), total household assets (\(k_{h}^{eff}\)), and asset vulnerability (vh, cf. Section “Asset vulnerabilities” on page 53).

We make one important simplifying assumption, imposed by the data that are available: we assume that households are either affected or not affected; and, if they are affected, they lose a share vh of their effective capital \(k_{h}^{eff}\), with vh a function of household characteristics, independent of the local magnitude of the event. In case of a flood, one household is flooded or not, and if it is flooded, the fraction of capital lost will depend on the type of housing and other characteristics of the households and on a random process — but the losses do not depend on the local water depth or velocity. Similarly, an earthquake will affect a subset of the population who will experience building damages that depends on luck and the type of building — but the model does not take into account the ground motion at the location of the household. While this is of course a crude approximation, it is made necessary by the uncertainty on the exact localization of households in the FIES. With this approach, a bigger disaster is a disaster that affects more people, not a disaster that affects people more.

Household exposure

On the right side of Eq. 7 on the previous page, \(f_{a_{h}}\) is an expression of household exposure to each disaster. If we had perfect knowledge of each household’s exposure – for example, super high-resolution flood maps overlaid with the coordinates of every household (including those represented only implicitly in FIES) – we could assign a value of 0 or 1 to \(f_{a_{h}}\) for each household and each event.

Lacking this information, we interpret household exposure as the probability for any given household to be affected by the disaster when it occurs, and we assume that this probability is determined by household localization (at the highest resolution available) and characteristics. If the localization of a household in the FIES is known through the district, for instance, then the likelihood of one household to be flooded can be estimated by the fraction of the area of the district that is within the flood zone. Or, if population density maps are available and reliable, by the fraction of the population of the district living within the flood zone. This assumes that there is no relationship between income and exposure within a district. If poor people are found to be systematically more likely to be flooded, it is possible to introduce a “poverty bias” in the form of a higher probability of being affected for household with lower income. We do not have strong evidence that it is the case in the Philippines, and reviews suggest that such a bias is far from universal (see a review in Hallegatte et al. (2016) and Erman et al. (2018)).

We therefore assume that the odds of being impacted by a given disaster are the same for all households in each administrative region. As a result, we can move \(f_{a_{h}}\) out of the sum and drop the “h” subscript to indicate it is no longer household-specific (but it remains region-specific):Footnote 20

$$ L = {\Phi}_{a} \cdot K = f_{a} \sum\limits_{h=0}^{N_{h}} \omega_{h} k_{h}^{eff} v_{h} $$
(8)

This assumption also allows us to make a critical conceptual shift: if exposure is constant for all households in a given area, then we can reinterpret exposure (fa) as the fraction of each household affected by a given disaster. After each disaster, of course, every household will be in exactly one of only two possible states: either it suffered direct impacts, or it escaped the disaster. On average, however, we can adopt a probabilistic approach by bifurcating each household in the FIES into two instances: affected and non-affected. We introduce this split in such a way that the total weight of each household (as well as asset losses at the household and provincial levels) remains unchanged:

$$ \omega_{h} = \omega_{h_{a}} + \omega_{h_{na}} \left\{\begin{array}{ll} \omega_{h_{a}}~~=~f_{a}\cdot\omega_{h} & \text{affected households}\\ \omega_{h_{na}} = (1-f_{a})\cdot\omega_{h} & \text{non-affected households} \end{array}\right. $$
(9)

Asset vulnerabilities

The model assigns to each household a vulnerability (vh), which describes the fraction of assets lost when a household is affected by a disaster. Again, this fraction does not depend on the local intensity of the hazard. Vulnerabilities are based on categorical, qualitative information on the construction and condition of each domicile. Households are grouped into three categories: fragile, moderate, and robust, with associated vulnerabilities as described in Table 8 on the following page.

Table 8 Asset vulnerability categories

The right-most column in Tab. 8 indicates the fraction of assets lost when a household is affected by a disaster. Each category includes a smearing factor (± 20% for the moderate and fragile categories, ± 40% for robust dwellings). This randomness recognizes a degree of irreducible uncertainty, including the fact that actual losses depend not only on whether a household is affected, but also on many situational factors (e.g., for floods, water depth and velocity; for earthquakes, local soil conditions) and some random factors. For each household, a value is chosen at random within the indicated range, allowing for variation as plotted in Fig. 11 on the next page.

Fig. 11
figure11

Household asset vulnerability (vh), constructed from qualitative wall and roof descriptions in the FIES 2015 from the Philippines

This method of assigning asset vulnerabilities involves a critical, simplifying assumption: the condition of each dwelling is assumed to be a direct proxy for the vulnerability of all assets that generate income for the household. This vulnerability factor is applied not just to household (private) assets, but also the assets that a household does not own, but from which it derives income (e.g., roads, utilities, factories, agriculture, and other infrastructure). In other words, the model assumes that the vulnerability of assets not owned by a household but which it still uses to generate income is well-described by the condition of their private assets—for example, that the roads used by people who live in makeshift dwellings are not paved, and equally vulnerable to being destroyed as is their home. This assumption avoids significant increases in data requirements—indeed, global data on the vulnerability of infrastructure are not available—and is necessary to avoid overly-complex representations of economic interactions between each household and assets held in common.

Early warning systems

When available, we incorporate data on the presence of early warning systems in affected regions. This reflects the assumption that early warning systems allow exposed households to move, reinforce, or otherwise protect their most fragile or valuable assets, thus reducing their vulnerability to disaster. Using the same assumption as in the Unbreakable report (Hallegatte et al. 2016), we assume that households who receive a warning are able to reduce their vulnerability by 20%, relative to identical households without access to early warning systems, by moving valuable items (from important papers to car or motorbikes) and implementing other mitigating measures (e.g., boarding windows, sandbagging doors).

Summary of asset losses and calibration

Returning to Eq. 7 on page 51, total losses in each region are defined as the losses suffered by each household, times that household’s likelihood of being directly affected by a disaster when it occurs. As mentioned in the previous section, losses include all assets that produce an income for the household—even those that are not owned by the household. If the vulnerability of all asset types is assumed to be linked to the vulnerability of the household’s private assets (Fig. 12):

$$ L = \sum\limits_{h=0}^{N_{h}} \omega_{h} \cdot f_{a} \cdot {\Delta} k_{h}^{eff} $$
(10)

where:

$$ {\Delta} k_{h}^{eff} = v_{h}\cdot(k_{h}^{prv}+k_{h}^{pub}+k_{h}^{oth}) $$
(11)

The calibration of fa and vh depends on the availability of hazard data. Here, we start from results from the AIR catastrophe model, which provides an estimate of L in each region and each possible event (different hazards, different return periods). The value of vh is based on the damage function from 1 on page 54, and is independent of the intensity of the hazards. Then, the number of affected people (or, equivalently, the probability for households to be affected) fa is calibrated such that the estimated losses are consistent with the AIR estimate.Footnote 21

Fig. 12
figure12

When disasters occur, affected household reconstruct its assets at the optimal rate while staying out of subsistence, as described in “Private asset reconstruction” on page 61. Here, we illustrate the reconstruction process for a household that suffers \({\Delta } k^{eff}_{0} = {\Delta } k^{prv}_{0} + {\Delta } k^{pub}_{0}\) in losses at time t=to, and reconstructs with period τh= 2.1 years

Income Losses

To represent the longitudinal impacts of a disaster, it is not sufficient to consider the initial aggregate and distributional asset losses: one needs to explore the impacts on income and consumption, not only assets. Further, one needs to consider the dynamics of these impacts, not only the initial shock. The same asset losses do not cause the same effects if reconstruction and full recovery can be completed in a few months, compared with a case where various constraints make the recovery span years. To investigate this issue, asset losses are assumed from this point to be time-dependent: \({\Delta } k_{h}^{eff} \rightarrow {\Delta } k_{h}^{eff}(t)\). When it is possible, the time variable is omitted below for simplicity and readability.

Initial asset losses decrease throughout the reconstruction and recovery process as houses, infrastructure (i.e., roads and electric lines), and natural assets are repaired, replaced, and regrown. However, we assume that the income these assets had generated for each household is diminished unless and until they are repaired. This includes the value households derive from their domicile; their appliances, vehicles, and livestock; and the infrastructure they use to commute to work or market. In this way, asset losses translate to income losses. Further, the reconstruction process is not free: households and governments have to invest in the reconstruction, at the expense of consumption (for households) or budget reallocation and increased taxes (for government). The objective of the model is to represent these processes, in order to estimate their longitudinal impacts on consumption, wellbeing, and poverty.

It is important to note that the model assumes that households and governments aim at returning to the pre-disaster situation. It is well known that reconstruction can be used to “build back better” (for instance with more resilient building and infrastructure, but also with more efficient and productive assets); see (Hallegatte et al. 2018). And the reconstruction process is sometimes transformative for an economy (Hallegatte and Vogt-Schilb 2016). However, measuring the impact of a disaster as the cost of returning to the pre-disaster situation is non-ambiguous and objective, making shocks comparable even when the reconstruction leads to a different end point.

$$ {\Delta} i_{h} = (1-\delta_{sp}^{tax}) \cdot {\Pi}_{k} \cdot {\Delta} k_{h}^{eff} + {\Delta} i_{h}^{sp} $$
(12)

Post-disaster income losses are described by Eq. 12 on the preceding page. The first term specifies direct losses, while the last two terms incorporate secondary and indirect impacts on household income, beyond the income losses resulting directly from a disaster. Each of these links between asset and income losses will be treated separately in this section.

Direct income losses

The definition of \(k_{h}^{eff}\) includes all assets used by a household to generate income, including the value of owner-occupied dwellings that are generating “virtual” income in the form of housing services. The first term in Eq. 12 on the previous page represents the post-tax reduction in income due to the loss of assets, assuming that the income loss is simply proportional to the asset loss.

$$ {\Delta} i_{h} = \underbrace{(1-\delta_{sp}^{tax}) \cdot {\Pi}_{k} \cdot {\Delta} k_{h}^{eff}}_{\mathrm{Direct~losses}} + {\Delta} i_{h}^{sp} $$
(13)

For instance, in the absence of social transfers, a pastoralist losing 3 of 10 goats would see her income reduced by 30 percent. A factory worker working in a factory losing half of its machinery would experience a 50 percent loss in income. Hallegatte and Vogt-Schilb (2016) provides the theoretical basis for this linear relationship, in spite of decreasing returns on capital, based on imperfect substitutability of assets. Direct income losses are partially offset by the social transfers tax (\(\delta _{sp}^{tax}\)), assuming that households’ tax burden is directly proportional to their asset base.

Social transfers

The second term in Eq. 12 on the preceding page, \({\Delta } i_{h}^{sp}\), represents the change in social transfers due to the decrease in tax revenue. As discussed above, these transfers include also remittances, which are modeled as an additional social protection scheme. Households’ asset losses directly reduce their income, and as a result the tax they pay and the financial transfers they make to other households.Footnote 22 Based on Eq. 3, it is easy to verify that the reduction in transfers is proportional to national asset losses, and these losses are fully diversified at the national level:

$$ {\Delta} i_{h}^{sp}(t) = \frac{L(t)}{K}\cdot i_{h}^{sp} $$
(14)

We include explicit time dependence in Eq. 14 to indicate that social transfers recover to pre-disaster levels throughout the recovery and reconstruction process. Total asset losses L(t) is inclusive of all asset classes, irrespective of ownership (private, public, and other). These assets are rebuilt independently, and at different rates. Therefore, social transfers tend to recover even for households that are unable to recover their direct income losses through private asset reconstruction.

Importantly, the fact that the assets used by households to generate an income have different ownerships introduces interactions across households, with each household benefiting from a rapid recovery of the others. For instance, poor people benefit from a more rapid recovery of asset-rich households, if it allows them to re-open shops and factories earlier, thereby protecting jobs and increasing income of workers. Similarly, a rapid recovery of tax payers helps governments restore social transfers and rebuild public assets.

In Eq. 15, we update Eq. 12 on page 57 to reflect the structure of \({\Delta } i_{h}^{sp}\). In Eq. 16, we show that the aggregate loss in income is equal to the average productivity of capital multiplied by the total asset losses. Note that the final term, \({\Delta } i_{h}^{PDS}\), is omitted in Eq. 16, since we have not yet discussed its funding mechanism, but costs and revenue sum to zero for all PDS systems independently (Fig. 13).

$$ {\Delta} i_{h}(t) = (1-\delta_{sp}^{tax}) \cdot {\Pi}_{k} \cdot {\Delta} k_{h}^{eff} + \frac{L}{K}\cdot i_{h}^{sp} + {\Delta} i_{h}^{PDS} $$
(15)
$$ \sum\limits_{h=0}^{N_{h}}\omega_{h} {\Delta} i_{h} = \sum\limits_{h=0}^{N_{h}}\omega_{h} \Big((1-\delta_{sp}^{tax}) \cdot {\Pi}_{k}{\Delta} k_{h}^{eff} + \frac{L}{K}i_{h}^{sp}\Big) = {\Pi}_{k}L $$
(16)
Fig. 13
figure13

After being affected by a disaster, each household reconstructs its assets at the optimal rate, while avoiding falling below the subsistence line, as described in “Private asset reconstruction” on the next page. Here, we illustrate consumption losses through the reconstruction process for a household that suffers \({\Delta } k^{eff}_{0} = {\Delta } k^{prv}_{0} + {\Delta } k^{pub}_{0}\) in losses at time t=to, and reconstructs with period τh= 2.1 years

Consumption losses

After their capital has been diminished by a disaster, households are able to generate less income and, therefore, can sustain a lower rate of consumption.Footnote 23 Ideally, this decrease in income and consumption is not permanent, as households usually repair the damages to their dwelling, replace lost assets such as fridges and furniture, and rebuild their asset base (for instance regrowing their livestock).

Because assets do not rebuild themselves, affected households will also have to forego an additional portion of their income (\({\Delta } c_{h}^{reco}\)) to fund their recovery and reconstruction.Footnote 24 Total consumption losses, then, are equal to income losses plus reconstruction costs, less savings and post-disaster support (together represented by Sh), as indicated by Eq. 17 (Fig. 13):

$$ {\Delta} c_{h} = {\Delta} i_{h} +{\Delta} c^{reco}_{h} - S_{h} $$
(17)

Total reconstruction costs are equal to the reduction in consumption needed to rebuild their asset stock, plus the increase in taxes needed for the government to rebuild public assets such as roads and water infrastructure. The contribution of reconstruction costs to consumption losses at each moment depends on the ownership of the damaged assets, and on the reconstruction rate. These two dimensions will be discussed next.

Consumption losses due to reconstruction costs vary by asset type (i.e., private, public, or other):

  1. 1.

    Affected households pay directly and entirely the replacement of the lost assets that they owned (Δkprv).

  2. 2.

    All households pay indirectly and proportionally to their income for the replacement of lost public assets through an extraordinary tax (Δkpub)

  3. 3.

    Households do not pay for the replacement of the assets they use to generate an income but do not own (such as the factory where they work; Δkoth).

Private asset reconstruction

In the event of a disaster, affected households lose productive assets, which directly reduces their income. Household-level consumption losses do not end there, however, as the destroyed assets do not rebuild themselves. Rather, affected households will have to increase their savings rate–that is, avoid consuming some fraction of their post-disaster income–to recover these assets. Assuming each household pursues an exponential asset reconstruction pathway, we calculate a reconstruction rate for each household that maximizes its wellbeing over the 10 years following the disaster while avoiding bringing consumption below the subsistence level (if possible). If the households cannot avoid having consumption below the subsistence line (for instance because consumption is below the subsistence level even without repairing and replacing lost assets), then we assume that reconstruction takes place at the pace possible with a saving rate equal to the average saving rate of people living at or below subsistence level in the Philippines (according to the FIES).

To model each household’s recovery, we assume that disaster-affected households rebuild their lost assets exponentially over some number of years (τh) after the shock, where τh specifies the number of years each household takes to recover 95% of initial asset losses. τh is related to reconstruction rate λh as follows:

$$ \tau_{h} = ln\big(\frac{1}{0.05}\big)\cdot \lambda_{h}^{-1} $$
(18)

Given these assumptions for the response of each affected household to a disaster, the asset losses at time t after a disaster (occurring at time to) are given by:

$$ {\Delta} k_{h}^{eff} \rightarrow {\Delta} k_{h}(t) = {\Delta} k_{h}^{eff} \cdot e^{-\lambda_{h}\cdot t} $$
(19)

In order to rebuild at this rate, the reconstruction costs to household consumption are given by:

$$ {\Delta} c^{reco}_{h}(t) = -\frac{d}{dt} \Big({\Delta} k_{h}(t)\Big) = \lambda_{h} \cdot {\Delta} k_{h}(t) $$
(20)

In the above equation, we have introduced a negative sign in order to keep this contribution to consumption losses positive, in accordance with our convention.

To calculate for each household a reconstruction rate that maximizes its wellbeing, we plug Eq. 17 on the previous page into the canonical definition of wellbeing:

$$ W = \frac{1}{1-\eta}\times \int\Big[c_{h} - {\Delta} c_{h}(t)\Big]^{1-\eta}\cdot e^{-\rho t}dt $$
(21)

Expanding these terms (and omitting social transfers and taxes for simplicity), we arrive at the following equation, where λh is the optimal reconstruction rate for each household:

$$ W = \frac{k^{eff}_{h}}{1-\eta}\times {\int}_{t=0}^{10}\Big[{\Pi} - ({\Pi}+\lambda_{h})\cdot ve^{-\lambda_{h} t}\Big]^{1-\eta}\cdot e^{-\rho t}dt $$
(22)

This integral cannot be solved analytically, but we know that each household will maximize its wellbeing if it chooses a reconstruction rate (λh) such that \(\frac {\partial W}{\partial \lambda } = 0\):

$$ \frac{\partial W}{\partial \lambda} = 0 = {\int}_{t=0}^{10}\Big[ {\Pi} -({\Pi}+\lambda_{h})\cdot ve^{-\lambda t}\Big]^{-\eta}\Big(t({\Pi}+\lambda_{h})-1\Big)\cdot e^{-t(\rho+\lambda)}dt $$
(23)

We use this expression to determine the value of λh numerically. We note again that the optimum depends only on productivity of capital (π), asset vulnerability (v), and future discount rate (ρ), while dependence on initial assets and absolute losses has dropped out of the expression.

Figure 14 on the following page displays the full distribution of reconstruction times τh, for two 50-year hurricanes, affecting either the NCR region or the Bicol region. In the case of the NCR region, most households can recover rapidly, in 2 to 3 years, and only a few households take more than five years to fully rebuild their asset base. In the case of Bicol, with much higher poverty rates, reconstruction is much longer, with a significant fraction of households needing more than five years to rebuild their asset base. This result is consistent with the idea of a poverty trap (see, e.g, Carter and Barrett (2006)) and with the observation that poor households sometimes need a long time to get back to their pre-disaster situation (Dercon and Porter 2014; de Janvry et al. 2006; Caruso 2017). It may also provide a theoretical explanation for the long-term consequences on incomes and growth that have been identified in the literature (Hsiang and Jina 2014).

Fig. 14
figure14

Optimal reconstruction time distribution and mean for disaster-affected households in NCR (red histogram) and Bicol (blue) after a 50-year hurricane event. Reconstruction time is calculated for each household after each disaster, and characterizes the disaster recovery pathway that minimizes wellbeing losses individually for each household

In addition, households must maintain consumption above a certain level to meet their essential needs. To reflect this, we use the following heuristic: if a household cannot afford to reconstruct at the optimal rate without falling into subsistence (i.e. if \(\big (i_{h} - {\Delta } i_{h} - \lambda _{h} {\Delta } k_{h}^{eff} \big )\Big |_{t=t_{0}} < i_{\text {sub}}\)), then the household reduces its consumption to the subsistence line less the regional savings rate for households in subsistence (\(R_{sav}^{sub}\)), and uses the balance of its post-disaster income to reconstruct. Its consumption remains at this level until its reconstruction rate reaches the optimum. This leads to an initial reconstruction rate equal to \(\lambda _{h} = \frac {1}{\Delta k_{h}^{priv}}\cdot \big (i_{h}-{\Delta } i_{h}-i_{\text {sub}}+R_{sav}^{sub}\big )\Big |_{t=t_{0}}\).

Public asset reconstruction

When disasters occur, we assume that the government borrows externally to finance the cost of public asset reconstruction, in order to speed recovery and minimize the financial burden on affected households. Eventually, the government recovers these costs through a tax, but only when recovery is complete. Through this mechanism, all households throughout the country share the cost of public asset reconstruction in the affected area.

$$ i_{h}\cdot\delta^{tax}_{pub} = \underbrace{\Big[{\Pi}_{k} k_{h}^{eff}(1-\delta^{tax}_{sp})+i_{h}^{sp}\Big]}_{\mathrm{pre-disaster~income}}\cdot \underbrace{\frac{\sum\omega_{h} v_{h} k_{h}^{pub}}{K}}_{\mathrm{fractional~public~losses}} $$
(24)

Note that Eq. 24 represents a distribution of the costs of rebuilding public assets to both affected and non-affected households. Like the tax to fund social protection programs, it should be understood as a universal tax with a flat rate (\(\delta _{pub}^{tax}\)) that is by construction proportional to pre-disaster household income.

Because this is conceived as a one-time tax to fund reconstruction, public asset reconstruction costs are not spread across the duration of the reconstruction (in contrast to income lost due to the destruction of public assets, which does last for years after the disaster). Therefore, all of the time-dependence has been eliminated in Eq. 24, which indicates our assumption that the government does not collect the special tax at any point during recovery, but rather covers the cost of public asset reconstruction for the duration of reconstruction and collects taxes to fund this process many years later, after full recovery.

Savings and post-disaster support

The final term in Eq. 17 on page 61, Sh, represents households’ precautionary savings, increased by post-disaster support, potentially including cash transfers to affected households, increases in social protection transfers, help through informal mechanisms at the community level, potential increases in remittances, and other exceptional cash transfers to households following a disaster. When available, these resources help households to smooth their consumption over time, or decrease consumption losses.

In “Savings and post-disaster support”, we discussed one example of a post-disaster support system in which all Filipinos affected by a disaster receive a uniform payout, which is equal to 80% of the asset losses suffered by the poorest quintile. In this and other systems, the value of this PDS in included in Sh, along with any savings the household may have had before the disaster. In more realistic applications, these benefits can also accrue to non-affected households: for example, due to targeting errors in post-disaster support systems. Like the cost of public asset reconstruction, the cost of all exceptional post-disaster transfers is distributed among all households, including those in unaffected regions, long after reconstruction is complete (cf. “Public asset reconstruction” on page 64). Similarly, the rebuilding of the savings of affected households is assumed to take place far in the future, when reconstruction is complete and affected households’ incomes are back to their pre-disaster levels.

Optimal consumption of savings and post-disaster support

As illustrated by the gray shaded region in Fig. 13 on page 60, each household uses its savings, plus any post-disaster support it receives to smooth its consumption. More specifically, each household spends its liquid assets to establish a floor, or offset the deepest part of its consumption losses. The floor each household is able to afford is a function of the value of its income losses, savings and post-disaster support, and reconstruction rate, as well as of the average productivity of capital. Having assumed an exponential recovery with rate λh and a total value of savings \(S^{tot}_{h}\), we can determine the level of this floor (γ) and the time at which the household’s savings are exhausted (\(\hat {t}\)) by solving the following coupled equations:

$$ S^{tot}_{h} + \gamma \hat{t} = \frac{k_{h}^{eff} v_{h}}{\lambda_{h}}\Big({\Pi} + \lambda_{h} \Big)\Big[1-e^{-\lambda_{h} \hat{t}}\Big] $$
(25)
$$ \gamma = k^{eff}_{h}\Big[{\Pi}-v_{h}({\Pi}+\lambda_{h})e^{-\lambda_{h} \hat{t}}\Big] $$
(26)

As with the reconstruction rate, this optimization cannot be completed in a closed form without resorting to series expansions, so we combine Eqs. 25 and 26 into Eq. 27, and numerically find the value of γ that satisfies this equation:

$$ 0 = k^{eff}_{h} v_{h} \big({\Pi} + \lambda_{h}\big)\Big[1-\upbeta \Big] + \gamma ln\big(\upbeta\big) - \lambda_{h} S^{tot}_{h} $$
(27)

where \(\upbeta = \gamma \cdot (k^{eff}_{h}v_{h}({\Pi }+\lambda _{h}))^{-1}\)

Importantly, we assume here that the provision of PDS and savings do not accelerate reconstruction pace, since the utilization of these resources is determined only after the rate of reconstruction is determined. This is a simplification that allows the two questions (rate of reconstruction and utilization of savings and PDS) to be solved sequentially, making it easier to solve the model.

Wellbeing losses

A $10 reduction in consumption affecting a rich household does not impact welfare or threaten health and wellbeing as much as the same loss would affect a poor household. Welfare economics theory quantifies this difference by evaluating the utility (w) derived from a given level of consumption. Here, we use a simple constant relative risk aversion (CRRA) utility function:

$$ w = \frac{c^{1-\eta}}{1-\eta} $$
(28)

The value of η, representing the elasticity of the marginal utility of consumption, is important to the modeling of the wellbeing losses; it represents both the risk aversion and the aversion to inequality in a society and is linked to preferences and values. It describes how $1 in consumption loss affects differently poor and non-poor people. Implicitly, it sets distributional weights, i.e. the weight attributed to poor people vs. the rest of the population in the aggregation of costs and benefits in an economic analysis (Fleurbaey and Hammond 2004). In this study, we use a standard value of 1.5. Higher values give more importance to poor people, lead to higher estimates of wellbeing losses, and make it relatively more important to use policy instruments targeted towards poor people to reduce wellbeing risks.

In order to determine the wellbeing losses that accumulate to each disaster-affected household during the reconstruction period (defined as the time for consumption to return to its pre-disaster level), we calculate wellbeing as the future-discounted time integral over 10 years after a disaster.

$$ {\Delta} W_{h} = \frac{c_{h^{o}}^{1-\eta}}{1-\eta}~{\int}_{0}^{\infty}{\Big[}{\Big(}1-\frac{\Delta c_{h}(t)}{{c_{h}^{o}}}e^{\lambda_{h}t}{\Big)^{1-\eta}-1}{\Big]}e^{-\rho t}dt $$
(29)

Note that the integral evaluates to 0 when Δch = 0. For all other values of \(0~<~{\Delta }~c_{h}~<~{c_{h}^{o}}\), Eq. 29 has to be evaluated numerically. To balance the need for precision with computational limitations, Eq. 29 on the preceding page is evaluated within the model with tmax = 10 years and dt = 1 week.

$$ {\Delta} W_{h}^{\mathbf{reconstruction}} = \frac{c_{h^{o}}^{1-\eta}}{1-\eta}~\sum\limits_{t = 0}^{t_{max}}dt\times{\Big[}{\Big(}1-\frac{\Delta c_{h}(t)}{{c_{h}^{o}}}e^{-\lambda_{h}t}{\Big)^{1-\eta}-1}{\Big]}e^{-\rho t} $$
(30)

We have assumed that the reconstitution of household savings and the taxes that fund public asset reconstruction and post-disaster support are widely distributed and far in the future, so that they reduce consumption but only after reconstruction is complete. Therefore, we assume that the wellbeing impact of using savings and PDS-related taxes can be estimated using the marginal utility of consumption of each household:

$$ {\Delta} W_{h}^{\mathbf{long-term}} = \frac{\partial W}{\partial c}{\Delta} c = c_{h}^{-\eta}\times\Big(i_{h}\cdot \delta^{tax}_{pub} + {\Delta} S^{tot}_{h}\Big) $$
(31)

Total wellbeing losses one household are equal to the sum of the loss along the reconstruction path and the long-term losses:

$$ {\Delta} W_{h} = {\Delta} W_{h}^{\mathbf{reconstruction}} + {\Delta} W_{h}^{\mathbf{long-term}} $$
(32)

Then, the total wellbeing losses are calculated by summing over all households, using the number of individuals in the household as weight:

$$ {\Delta} W = \sum\limits_{h = 0}^{N_{h}}\omega_{h} {\Delta} W_{h} $$
(33)

Finally, we translate ΔW from an expression of utility back into an “equivalent consumption loss” (ΔCeq) by determining the value of the consumption loss that an imaginary individual earning the national mean income would have to suffer in order to experience wellbeing losses equivalent to each “real” individual’s losses. This final step allows us to express wellbeing losses, like asset losses, in currency units and as a percentage of national or regional GDP.

We derive ΔCeq as follows:

$$ {\Delta} C_{eq} = \frac{\Delta W}{W^{\prime}} $$
(34)

where:

$$ W^{\prime} = \frac{\partial W}{\partial c}{\Bigg|_{c_{avg.}}} =\frac{\partial}{\partial c} \Bigg(\frac{c^{1-\eta}}{1-\eta}\Bigg){\Bigg|_{c_{avg.}}} = c_{avg.}^{-\eta} $$
(35)

The result ΔCeq is the metric we use to measure the wellbeing impact of a disaster (or of risk) on the population. It is a measure — expressed in domestic currency — of the wellbeing loss due to a disaster. If a disaster causes 1 in wellbeing losses, it means that its wellbeing impact is equivalent to a 1 decrease in the consumption of the average Filipino (i.e. a hypothetical individual with a consumption level equal to the average consumption in the Philippines).

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Walsh, B., Hallegatte, S. Measuring Natural Risks in the Philippines: Socioeconomic Resilience and Wellbeing Losses. EconDisCliCha (2020). https://doi.org/10.1007/s41885-019-00047-x

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Keywords

  • Natural risks
  • Resilience
  • Risk assessment
  • Welfare
  • Philippines