metadata: authors: 0: author: Gascoigne,Jon
1: author: Baquie,Sandra
2: author: Vinha,Katja Pauliina
3: author: Skoufias,Emmanuel
4: author: Calcutt,Evie Isabel Neall
5: author: Kshirsagar,Varun Sridhar
6: author: Meenan,Conor
7: author: Hill,Ruth
count: Africa
docna: 0: docna: The Welfare Cost of Drought in Sub-Saharan Africa
docty: Policy Research Working Paper
abstracts: cdata!: This paper quantifies the impact of
            drought on household consumption for five main
            agroecological zones in Africa, developing vulnerability (or
            damage) functions of the relationship between rainfall
            deficits and poverty. Damage functions are a key element in
            models that quantify the risk of extreme weather and the
            impacts of climate change. Although these functions are
            commonly estimated for storm or flood damages to buildings,
            they are less often available for income losses from
            droughts. The paper takes a regional approach to the
            analysis, developing standardized hazard definitions and
            methods for matching hazard and household data, allowing
            survey data from close to 100,000 households to be used in
            the analysis. The damage functions are used to quantify the
            impact of historical weather conditions on poverty for eight
            countries, highlighting the risk to poverty outcomes that
            weather variability causes. National poverty rates are
            1&#x2013;12 percent higher, depending on the country,
            under the worst weather conditions relative to the best
            conditions observed in the past 13 years. This amounts to an
            increase in the total poverty gap that ranges from US$4
            million to US$2.4 billion (2011 purchasing power parity).
display_title: The Welfare Cost of Drought in
            Sub-Saharan Africa
listing_relative_url: /research/2024/01/34247621/welfare-cost-drought-sub-saharan-africa
topicv3: Poverty m1326687 695,Drought m1503313 3162
publishtoextweb_dt: 2024-01-29T00:00:00Z
dois: 10.1596/1813-9450-10683
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
no_of_pages: 49
author_keys: 0: author_key: NA
1: author_key: 1767911
2: author_key: 435289
3: author_key: 177660
4: author_key: 1717790
5: author_key: 810339
6: author_key: NA
7: author_key: 663673
model_extractions: Policy Research Working Paper 10683

# The Welfare Cost of Drought in Sub-Saharan Africa

_Jon Gascoigne Sandra Baquie Katja Vinha Emmanuel Skoufias Evie Calcutt Varun Kshirsagar Conor Meenan Ruth Hill_ Poverty and Equity Global Practice January 2024 A verified reproducibility package for this paper is available at http://reproducibility.worldbank.org, click **here** for direct access.
Policy Research Working Paper 10683

# **Abstract**

This paper quantifies the impact of drought on household consumption for five main agroecological zones in Africa, developing vulnerability (or damage) functions of the relationship between rainfall deficits and poverty. Damage functions are a key element in models that quantify the risk of extreme weather and the impacts of climate change. Although these functions are commonly estimated for storm or flood damages to buildings, they are less often available for income losses from droughts. The paper takes a regional approach to the analysis, developing standardized hazard definitions and methods for matching hazard and household data, allowing survey data from close to 100,000 households to be used in the analysis. The damage functions are used to quantify the impact of historical weather conditions on poverty for eight countries, highlighting the risk to poverty outcomes that weather variability causes. National poverty rates are 1–12 percent higher, depending on the country, under the worst weather conditions relative to the best conditions observed in the past 13 years. This amounts to an increase in the total poverty gap that ranges from US$4 million to US$2.4 billion (2011 purchasing power parity).

This paper is a product of the Poverty and Equity Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at rhill@worldbank.org. A verified reproducibility package for this paper is available at http://reproducibility.worldbank. org, click **here** for direct access.

<!-- Start of picture text --> TRANSPARENT<br>ANALYSIS<br>G<br>R E<br>N<br>S<br>I P<br>Y E<br>K A<br>C A<br>R P<br>LI R<br>O E<br>O C<br>W R<br>H<br>S<br>P<br><!-- End of picture text --> _The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# The Welfare Cost of Drought in Sub-Saharan Africa

Jon Gascoigne (Centre for Disaster Protection) r Sandra Baquie (World Bank) r Katja Vinha (Consultant) r Emmanuel Skoufias (National University of Singapore and World Bank) r Evie Calcutt (World Bank) r Varun Kshirsagar Consultant) r Conor Meenan (Centre for Disaster Protection) r Ruth Hill (World Bank and Centre for Disaster Protection)<sup>1</sup> Originally published in the Policy Research Working Paper Series on January 2024. This version is updated on July 2025. To obtain the originally published version, please email prwp@worldbank.org.

JEL Codes: Q54, I32 Project Code: P177432 Keywords/topics: Shocks and vulnerability to poverty, drought

> 1 r indicates randomized author order using the American Economic Association author randomization tool, https://www.aeaweb.org/journals/policies/random-authororder/search?RandomAuthorsSearch%5Bsearch%5D=XxSZtJmQOh5k.

This paper started as a result of a conversation with Jon Gascoigne in early 2020. Jon understood better than any of us the need for a multidisciplinary team to understand how to model the welfare impacts of drought. Collaborating across disciplines can be a challenge, and negotiating those discussions requires good grace, humility, a strong focus on relationship, and a genuine interest in understanding another’s view and expertise. Jon exemplified these characteristics in all of his work, and true to form, brought them to this project too. We think it is very fitting that the randomization tool placed him as first author on this paper early in its drafting. We are saddened he didn’t get to see the final product and to know just how grateful we all were to him and the example he set us.

We thank Stefanie Brunelin and Odyssia Ng for being part of the early conversation on this paper and we thank Bhavin Thakrar and Paul Wilson for working on parts of the simulations data exercise.
# 1. Introduction

Climate disasters reverse gains and limit progress in efforts to reduce poverty. Global extreme poverty is increasingly concentrated in Sub-Saharan Africa (SSA) where drought is a major risk, a risk that is increasing in many parts of the continent because of climate change. Investments to reduce the impact of drought on welfare are thus essential to poverty reduction efforts in the region. Quantifying the welfare needs that arise when climate shocks occur is an important part of targeting investments to reduce their impact (Clarke and Dercon 2016). This requires vulnerability or damage functions that relate losses in welfare to climate conditions (Auffhammer 2018). While these are widely available for the impact of floods and cyclones on buildings, this is not the case when it comes to quantifying the impact of drought on household consumption in Sub-Saharan Africa.

This paper pilots a regional approach to estimating vulnerability functions for drought and consumption using methods widely employed in the microeconomic literature (Dell, Jones, and Olken 2014). The analysis uses survey data from close to 100,000 households across nine countries and five livelihood zones, allowing considerable variation in climatic conditions to be utilized in estimation. The result is stable estimates that are not driven by any one climate event. We find that consumption is reduced by 10-20 percent in the worst weather observations in our surveys (corresponding to about a 1 in 10-year drought event). We use the estimated vulnerability functions and the full hazard distribution in each household location to calculate the risk drought poses to welfare outcomes. The results indicate that risk is large. Poverty is 1–12 percent higher under the worst weather conditions relative to the best conditions observed in the past 13 years. This amounts to an increase in the total national poverty gap that ranges from US$4 million to US$2.4 billion (2011 PPP) across countries. To our knowledge, these are the first crosscountry estimates of the poverty impact of drought in Africa.

There are several ways in which damage functions for rainfall deficits have been estimated in the climate economics literature. Auffhammer (2018) provides a review and examples of the approaches applied to US farm incomes. The one used for estimating the impact of extreme weather events uses observed data to identify the causal impact of weather changes on outcomes of interest (Dell, Jones, and Olken 2014). Data on hazards are matched to household observations in survey data using information on the geographic location of a household, and a fixed effects regression is run to identify the impact of weather in determining economic outcomes.

Although not undertaken with the purpose of estimating vulnerability functions, several studies have used this method to estimate the impact of drought on welfare. For example, in Africa, Hill and Porter (2017) look at the impact of a water requirement satisfaction index (WRSI) on consumption and poverty, and Hill and Mejia-Mantilla (2017) look at the impact of WRSI on household income and consumption in Uganda. In Malawi, Baquie and Fuje (2020) look at the impact of rainfall on consumption and poverty. Wineman, Mason, Ochieng and Kirimi (2019) examine the relationship between rainfall and income, calorie consumption and poverty in Kenya. Baez, Kshirsagar and Skoufias (2019) look at the impact of rainfall defined dry spells on nutrition outcomes. Outside Africa, Kochhar and Knippenberg (2023) look at the impact of NDVI, rainfall and temperature on consumption and poverty in Afghanistan. Studies that use estimated impacts of drought to predict the welfare cost of other weather events include Hill and Porter (2017), Porter and White (2016), Kochhar and Knippenberg (2023).<sup>2</sup> This study uses the same methods as these papers but takes a regional approach (as in Baez, Kshirsagar and Skoufias 2019) with the objective of developing robust estimates of the relationship between drought conditions and consumption that is not specific to one context or event. This relationship can then be used to predict the impact of drought for other events or locations. The estimates presented in this paper are within the range of results found in country-specific papers. For example, a moderate (about a 1 in 10 year) drought is predicted to reduce consumption by 15 percent and 9 percent in Uganda and Ethiopia, akin to the 10 percent loss we estimate for crop cultivating households in maize and highland zones in this paper.

> 2 Anttila-Hughes and Sharma (2015) take the same approach for storms.

2
Taking a regional approach requires the use of standardized hazard definitions and methods for matching hazard and household data. This is done by considering the main hazard measures and techniques used in comparable country studies, and systematically assessing the choice of hazard, the hazard-household matching approach, and the functional form used in analysis. Specifically, we use gridded historical data on precipitation, vegetation, evapotranspiration, and soil moisture, using measures such as the Normalized Difference Vegetation Index (NDVI), the Standardized Precipitation Evapotranspiration Index (SPEI), and WRSI. These measures reflect the hazard to livelihoods from lack of rain in different ways. Some are direct measures of climate conditions (e.g., precipitation, soil moisture, and SPEI), others aggregate climate data through crop models (WRSI), and others measure vegetation outcomes (NDVI). The gridded hazard measures are then merged to harmonized household surveys from nine countries (Ethiopia, Lesotho, Malawi, Mauritania, Mozambique, Niger, Nigeria, Zambia, and Zimbabwe) with location coordinates for either the household or the community. The surveys used are the ones that are also used for official poverty estimates. A consistent approach to temporal matching was used to take into account the timing of the survey and agricultural seasons. Different approaches to spatial merging were tested.

There are important methodological insights from the analysis that emerge. First, we find that soil moisture and greenness measures provide more consistently reliable results than evapotranspiration or rainfall measures. This is an important finding given most of the extant literature is based on evapotranspiration or rainfall metrics. Second, we find that a linear specification performs adequately for the types of moderate shocks that are well-represented in the survey data used. Third, we find that a hazard measure based on 20 km or 50 km radius around each household performs better than those that use smaller radii, perhaps because a larger radius allows local market effects to also be considered.

The relationship between hazard measures and welfare outcomes is estimated separately for different livelihood zones across SSA. Separate estimation provides needed flexibility, given that drought conditions manifest themselves differently across livelihood zones. Important differences in impacts between agroecological zones and between land and livestock owners are observed. However, the downside of a regional approach is a limited ability to explore the heterogeneity of impacts across households in detail without significant investments in data harmonization, and we leave additional work on the heterogeneity of impacts as something to explore further in future analysis.

There are limitations to the analysis undertaken that should be borne in mind when interpreting results. First, estimates capture the direct impact of local drought conditions and not impacts beyond the local area, such as those that might arise from disruption of markets or price impacts. The degree to which this is a concern depends on the relative importance of direct and indirect impacts. The evidence is mixed on this. Hallegatte et al. (2016) suggest food prices are an important channel of the welfare impacts of climate change. However, Artuc et al. (2023) model trade between locations and find the main impact is the direct production effect, not the impact on prices. To the extent this is the case the local estimates presented in this paper may be quite close to aggregate impacts.

Secondly, the empirical estimates are subject to “survivor bias” in that consumption is only measured for households still in existence after the shock has occurred. If households move or disintegrate (perhaps due to the death of one or more household members) because of drought conditions, the estimated impacts could be over or underestimated. This is much more likely to be the case for severe drought conditions, whereas those that are captured in our surveys tend to be less extreme events that are unlikely to cause movement or disintegration of households.

This brings us to the third potential source of bias in the results. Although the analysis uses survey data across many weather conditions in the analysis, there are very few observations in the survey data that experience drought conditions below two standard deviations from the mean. This limits the degree to which non-linearities can be estimated. It also means there is limited empirical support for predicting the welfare costs of extreme events.

A final source of bias comes from measurement error in the hazard data. Although care was taken to use the best available data and match hazard and household data carefully, any measurement error in the hazard variable will attenuate the estimated coefficients, thereby underestimating the welfare impacts. Additional uncertainty is 3
present given the distribution of hazards is changing over time with climate change and historical data forms the basis of all simulations presented in this paper.

The models built in this paper are an important first step toward constructing vulnerability or damage functions as used in the catastrophe risk modeling literature, and can inform disaster response planning and financing. However, these limitations mean that care is needed in interpreting the results of the analysis. We envisage that the set of tools developed herein will provide the basis for refining the analysis as more data become available, and expanding coverage to other regions. Accompanying this paper is code designed to extract a large set of potential shock measures and determine which of these are consistent with changes in the welfare measures (outof-sample). The modular code used is intended to be transparent, to aid in replicability, and to be available for others to improve upon. The goal is to encourage both learning and common standards, which in turn contribute to the implementation of drought-responsive policies that are objective and transparent.

The paper is structured as follows. Section 2 presents the empirical framework for assessing the relationship between welfare and hazards in rural areas where rainfall-dependent agricultural production is dominant, and where rainfall deficits (droughts) thus may have very serious welfare consequences. It sets out the approach used to estimate the vulnerability function and an exceedance probability curve that describes the welfare losses likely to occur because of rainfall deficits of increasing severity. Section 3 discusses in detail the historical hazard database and the household survey data used, the merging of the hazard data to the household survey data, and the specifications used for the hazard measures. Section 4 presents estimates of vulnerability functions. Section 5 shows how these vulnerability functions can be used to project welfare losses and presents some exceedance probability curves. Section 6 offers some conclusions.

# 2. An Empirical Framework for an Ex Ante Assessment of the Welfare Costs of Drought

A catastrophe risk modeling framework uses three components to generate an ex ante assessment of the costs of a catastrophe: hazard, exposure, and vulnerability function. Hazards capture data on the possible weather outcomes that may occur in a given place, such as possible tropical cyclones. Exposure captures what could be affected by the hazard in that location, such as the number and type of buildings. A vulnerability function provides an estimate of the cost of damage that will occur as a result of a given hazard and a given exposure. In the example of tropical cyclones and buildings, it would indicate the cost of damage for a given windspeed affecting a given type of building. Combining the three components allows development of a probabilistic impact curve, which indicates how the cost of hazard varies with the probability of the hazard for a specific place, given the expected hazards and the exposed assets.

This section of the paper shows how this framework can be applied to generate a probabilistic impact curve for drought in SSA. For drought in SSA, the hazard is rainfall deficits during the growing season. As noted in the introduction, there are different ways of measuring this hazard, and the next section discusses the relevant data in more detail, including the time period for which historical data are available and use of the data to generate an estimate of the probability distribution of hazards in the near future.

Exposure in the current case is not about physical infrastructure and its location and characteristics, but about households that may be impacted differently by rainfall deficits depending on their location and characteristics. The data on households are also described in more detail in the next section.

The vulnerability function in this case is the income or welfare losses among households engaged in different livelihoods, which result from lower yields, lower demand for labor, and increased prices that may result from that. The rest of this section focuses on the estimation of the vulnerability function and how it is used to derive a probabilistic impact curve. The estimation of the vulnerability function is widely present in the microeconometric literature, even though it is not referred to as such or used for generating estimates of probabilistic impact.

4
2.1. Estimating a vulnerability function Household welfare at any given time may be summarized in general by the function below: hk k hk , (1) ff where hk denotes the measure of welfare (in the current analysis, log of per capita expenditures hkk hkk P hk of WW = ff(RR , XX , EE ) + εε household h in locality or cluster ,), k is the measure of the hazard at time at the level of the geographic cluster WW , denotes household observable characteristics, denotes an observable variable summarizing the EE environment of households, and κκhk RR is an error term summarizing the influence of all unobservable factors on tt hkk hkk welfare. κκ<sup>3</sup> For the purposes of this study, welfare is measured by the monetary value of total consumption XX EE expenditures or food and non-food consumption. εε<sup>4</sup> The main objective of a vulnerability function is to summarize the relationship between the level of and the level of . If the function were known a priori it would be simple to plug in values for and to determine the value of the welfare outcome . In the absence of information on the function , methods need to be WW employed to estimate it. RR ff RR, XX, EE WW ff This necessity gives rise to a fundamental trade-off between the prediction accuracy and the interpretability of the model used (James et al. 2013). For example, machine learning methods, such as random forests, bagging, boosting, and support vector machines, treat as a black box. None of these methods is especially concerned about the exact form and interpretability of the function , provided that it yields accurate predictions for the welfare outcome. ff ff On the other hand, approximating the function with the average value of the welfare outcome hk conditional on specific values of the explanatory variables , and — i.e., hk k = or the conditional expected function (CEF)—is typically easier to interpret and is useful for deeper ff WW kk 1hkk hkk hkk insights into the causal relationship between hazard and welfare (Angrist and Pischke 2009). These advantages, RR , XX EE ff(rr, xx, ee) = EE(WW |RR = rr, XX hkk xx, EE however, may come at the expense of predictive accuracy (in-sample or out-of-sample). = ee),<sup>5</sup>

With these considerations in mind, we adopt the CEF approach for estimating vulnerability functions. To keep the analysis simple and tractable, the approach begins with an ad hoc specification of the controls used in the regression model, using a linear approximation to the CEF that is extended to a nonlinear specification for the hazard and allowing for the potential heterogeneity of the hazard’s impacts on welfare based on some easily and commonly observable household characteristics and environmental features. For any given welfare measure h , a log linear approximation to equation (1) above yields hk 0 1 2 k 1 hk , (2) WW where denotes region- or district-level fixed effects and hkk hkk denotes country-survey year effects. The districtkk kk WW = ββ + ββ XX + ββ RR + γγ EE + μμ + ττ + εε level fixed effects control for fixed spatial characteristics, whether observed or unobserved, and thus disentangle kk kk the hazard measure from many possible sources of omitted variable bias. The year effects μμ ττ further control for any common trends and thus help ensure that the relationships of interest are identified from idiosyncratic local kk ττ

> 3 The elements of X can include the age and education level of the household head; the ethnicity, religion, total number, age, and gender composition of household members; ownership of assets such as livestock, phone, radio, TV, etc.; and characteristics of the household residence, including type and quality of water and sanitation facilities, main source of energy, and type of floor and material of construction for walls and roof.

4 Focusing on non-monetary dimensions of welfare such as the height for age z score of children (HAZ) or the weight for height z-score (WHZ), Skoufias et al. (2023) explore an alternative specification of the vulnerability function that allows consideration of the effects of hazards through the income as well as the environmental channels. In this specification, exposure to weather-related hazards may affect the value of agricultural income earned (the income channel), as well as the health status of household members (environmental channel).

5 In data-constrained environments like the ones we study, complex (black-box) machine learning models are unlikely to provide the gains in accuracy that justify the loss in interpretability.

5
shocks. Thus the empirical approach is very much in line with the strong identification properties of the weathershock approach summarized by Dell, Jones, and Olken (2014). It should be noted that with district fixed effects, , included in the specification, the coefficients 1 can be estimated only if the values of vary within districts. kk Otherwise, the use of the district dummies will absorb the effects of these environmental factors. μμ hkk γγ EE The impact of drought on consumption expenditures is the cumulative effect of a household’s crop loss and a series of entitlement failures in a local economy that are triggered by this initial loss (Sen, 1981; Deveraux, 2007). Devereux (2007) characterizes a sequence of four entitlement failures: first, production fails as a result of the rains failing; then labor markets fail as households are less and less able to find work opportunities on other farms or in off-farm activities; then commodity markets fail as grain prices increase and prices of liquid assets decrease. Finally, transfers fail as households cannot rely on the support of others in their network who face the same constraints in meeting everyday basic needs. The formulation outlined here is agnostic as to how rainfall is impacting consumption. However, the spatial measure of drought used and the necessity of incorporating district fixed effects focuses the analysis more on picking up production failures and failures in the immediate labor and commodity local market in which the drought is measured. The impact of drought through commodity markets that span a larger geographic area or transfer networks over a larger geographic space will not be picked up. If higher levels of k indicate rainfall sufficiency, it is anticipated that 2 > 0 such that lack of rainfall and droughts have a negative effect on welfare (especially when a monetary welfare measure is used, such as consumption expenditures per adult equivalent). RR ββ̂ The extent to which hazards experienced by households in the sample are associated with sufficiently significant declines in their welfare depends in part on the degree to which there is variability in the exposure to and intensity of the shocks experienced. For example, if the value of k is the same for all in the sample and not just for those within a given cluster, then there is no way to identify the parameter 2 . Hence, it is critical to derive estimates of 2 based on data that include significant variability in RRk . This task is a particular challenge when analyzing the impact of drought because these events are spatially correlated and not localized. Increasing the number of years ββ and the number of countries included increases the variation in ββ̂ RR k . For this reason, the analysis prioritizes inclusion of countries where multiple rounds of survey data were available. In addition, by estimating this relationship at the level of the livelihood zone and not the country, the analysis increases the number of years and RR variation in hazards available.

Based on the general but unknown function _f_ , the effect of exposure to the hazard on welfare depends on the specific values of the determinants of welfare summarized by the variables k , and , i.e., <u>hk</u> = k d <u>( k hk hk )</u> ddWW k ~~.~~ The linear specification in regression equation (2) assumes a constant effect of the hazard on RR , XXhkk EEhkk ddRR RR =rr,XX =xx,EE =ee welfare (i.e., ddRR <u>hk</u> = 2 ) that is independent of the level of the hazard and of specific household characteristics k ddWW and environmental factors . It is important to relax this assumption in two ways: first, by allowing the ddRR ββ impact of the hazard to vary by the size of the hazard deviation; and second, by allowing the impact of the hazard hkk hkk XX to vary by characteristics of the household. EE To explore the functional form of the hazard, several different approaches were adopted. Two approaches were visual: a simple plot of welfare against hazard and a binned scatterplot of the residualized welfare against the residualized hazard. Another approach estimated linear, quadratic, and cubic hazard specifications, as well as the best fractional polynomial specification, and compared the fit and plotted residuals.<sup>6</sup> A final approach explored further nonlinearities with step and piecewise linear functional forms. This involved segmenting the continuous hazard distributions into 5 (or 10) bins for use as a set of indicator variables to capture the hazard intensity. Results for linear, quadratic and cubic specifications are shown. Parsimonious specifications that best described the underlying relationship, especially in hazard range where 90 percent of the observed events occurred, were used for the simulations.

> 6 In Stata, the _binscatter2_ command was used to visualize the overall relationship between hazard and welfare. The _fp_ and _fp plot_ commands were used to explore the fit and residuals of different polynomial specifications.

6
It is important to bear in mind that sensitivity tests for the specification of the vulnerability function are based on the hazards and extreme events contained within the sample used to estimate the vulnerability function. A maintained assumption is that the functional form estimated based on the observed and probably limited set of historic events is also valid for extrapolated events outside the range of the sample. As King and Zeng (2006) point out, extreme counterfactuals that are far from the range of hazards contained in the estimation sample are more likely to be model dependent and thus quite misleading. This is because different model specifications (e.g., linear versus quadratic) may yield comparable losses within the limited range of the estimation sample, while in reality the welfare losses may be very different for extreme hazard values that are beyond the range of the estimation sample. Some of these concerns are addressed in section 5 of the paper.

The impact of the hazard is allowed to vary by characteristics of the household by estimating a model that includes interaction terms of the hazard with specific household characteristics and/or some or all environmental characteristics, as in equation (3): hk 0 1 2 k 3 ) + 1 2 k hk 1hkk kk (3) 1hkk WW = ββ + ββ XX + ββ RR + ββ (RR ∗XX In this specification, it is expected that hkk hkk kk kk 3 > 0 for a household characteristic or asset that mitigates the negative γγ EE + γγ (RR ∗EE ) + μμ + ττ + εε impact of the shock on welfare (e.g., irrigated land) (or 4 > 0 for an environmental characteristic that mitigates the negative impact of the shock on welfare). Among a number of characteristics that were tried, two were ββ̂ consistently significant across specifications: land for cropping livelihood zones and tropical livestock units (TLUs) γγ� for pastoral livelihood zones. We present results by land ownership and TLUs as appropriate, but future work should include other characteristics.

Acknowledging the costs of some out-of-sample predictive accuracy, we opted for the benefits of a simple (or adhoc) specification that allows for a more systematic and transparent comparison of the differences in estimates resulting from the hazard measure used, the specification of the functional form of the vulnerability function, and the potential heterogeneity of impacts. Country-level applications building on the findings of this study would benefit from the adoption of data-driven shrinkage or regularization methods such as Lasso, that are known to improve out-of-sample predictive accuracy.

# 2.2. Estimating an exceedance probability curve

A common way to communicate risk—as calculated by combining data for hazard and exposure (value at risk) with vulnerability functions—is via exceedance probabilities (EPs) and their inverse measure, return periods. An EP curve describes the probability that various levels of loss will be exceeded, in this case the welfare loss that will occur because of rainfall deficits of increasing severity. Another way to understand the EP is to consider its inverse measure: return period = 1/(exceedance probability). For example, a loss with an annual exceedance probability of 1 percent, which means that there is only a 1 percent chance of facing a worse loss, is equivalent to a loss that gives a return period of 1 in 100 years. A longer return period suggests a lower probability that the impact from an extreme hazard will occur in any single year.

For each hazard value in a given location, the loss is estimated using the vulnerability function and the characteristics of the households in the exposure data. To generate an EP curve, losses are ranked and combined with the probability of these drought events occurring. This calculation can be based on historical information (“as if” such events were to happen again today with current exposures) or many thousands of years of simulated/synthetic events. This paper focuses on the consumption losses that occur for below-average years, and it estimates an EP curve for both total consumption losses and consumption losses that push people into poverty or push those who were already poor further into poverty (i.e., that increase the poverty gap). Section 5 describes how this is done in practice and presents these curves.

Catastrophe risk modeling has developed in the insurance and reinsurance sector over the past 30 years in response to potential insolvency-inducing events, such as Hurricane Andrew in 1992 in the US. Such analytics exploit increasing geographical data that captures exposure value at risk, predominantly the built environment, as 7
well as improved representation of hazards. Investment in research and technology in the field has been driven by the inadequacies of the historical record, mainly insurance claims data, for extreme events, and specifically by the inability of these data to robustly capture the statistics of catastrophic loss on insured portfolios. Unlike automotive or health claims, which are numerous and lend themselves to more reliable curve fitting for frequency and severity distributions, the small number of records of low-frequency and high-severity loss-making events do not provide sufficient evidence for such actuarial analysis. . While EP curves can be constructed from 20 years of observed historical loss data, they are limited to low-return-period estimation, are highly erratic and sensitive to data addition, and almost certainly underestimate loss levels, especially when considering average annual loss (Verisk 2013). Such records are rarely representative, especially in the extreme tail of the EP curve, which has few if any points to define it and is of primary importance to insurers and reinsurers. That is, history is not a good predictor of all possible future events.

Moreover, in low-income regions of the world, there is often acute data scarcity around historical evidence of natural hazards. The resulting short time series of hazards hampers the estimation of the EP curve. The increasing availability of remotely sensed weather information from satellites has helped provide global coverage for hazardrelated data sets that now range from 10 years to 40 years in length. The range of variables inferred from satellite data has also expanded to include new ones such as soil moisture, as new sensors come online and provide reliable training and validation data.

A key component of catastrophe modeling is developing statistical and physics-based methodologies, which vary by hazard type, to extend limited historical catalogs of events to many thousands of years of probabilistic events in order to adequately capture frequency, extreme severities, and full geographical location. This process is computationally intensive, and great care must be taken to ensure that resultant event sets are constrained by observed physical processes; for example, definition of hazard parameter distributions of climatological characteristics must maintain spatial and temporal correlations. Model calibration and validation against historical information are a valuable check, but inevitably assumptions are required on data processing and sampling steps, ideally supported by academic reference (ABI 2011). Though the event-by-event loss calculations of catastrophe modeling are computationally intensive, especially for hazards that demand high geographic resolution (which can be less than 10 m for flood), these calculations also allow differing aspects of model uncertainty to be quantified and communicated.<sup>7</sup> Only such a large time series of synthetic but nevertheless realistic events can generate enough samples of losses to robustly define the remote tail of EP curves that are of interest to the insurance industry, such as 1-in-100-year and 1-in-250-year return periods. Taking such a probabilistic loss perspective also ensures the EP is smoothed out by having many thousands of data points. For the purposes of this paper, a 10,000-year stochastic catalog of synthetic simulations was generated across Malawi at a spatial resolution of 0.05° and dekadal temporal resolution for several hazard variables (including soil moisture).<sup>8</sup> These 10,000 years of hazard events are all potential versions of what could happen in the next 12 months and can be combined with vulnerability and exposure information to estimate longer return period tail behaviors) to get a fuller risk perspective. This step requires making assumptions about the relationship between hazard and impact, using historical data as a starting point. In a data-scarce environment, it can be very hard to validate the performance of the vulnerability function in the tails. This paper is a starting point, and more investigation is required.

As noted above, these 10,000 years of hazard events reflect events that are likely to occur under current (and near-current) climate conditions, rather than forecasting climate conditions 100 years (for example) in the future. In this way catastrophe models differ significantly from general circulation models/global climate models (GCMs), 7 LMA (Lloyd’s Market Association), “Understanding Uncertainty in Catastrophe Modelling for Non-Catastrophe Modellers,” <u>https://www.lmalloyds.com/lma/readfile.aspx?iDocumentStorageKey=cc44f6be-b83f-4cf9-903ce802c1f312a8&iFileTypeCode=PDF&iFileName=Understanding%20uncertainty%20in%20cat%20modelling%20for% 20non-cat%20modellers.</u> 8 Given the computational requirements to generate such a stochastic catalog, this exercise was completed for only one country.

8
as they have been built to answer different questions about risk. Such simulated hazard event sets focus upon a primary damage discriminator, such as wind speed for storm or ground shaking for earthquake, which is subsequently translated into impact on exposure through damage functions describing vulnerability.

A criticism of catastrophe models is that they are not forward looking regarding climate change.<sup>9</sup> Since the consequences of climate change are already present, however, any recent historical record for atmosphericrelated natural hazards comprises a climate change signal, alongside other potential modalities, such as the El Niño–Southern Oscillation (ENSO). Model sensitivity to these climate aspects can be explored in a catastrophe modeling environment and considered as another dimension of uncertainty. In recent years, “climate conditioning” of catastrophe models for differing time horizons and emissions scenarios (such as in Bates [2023]) has received much attention and is an active research frontier, attracting many new entrants to natural hazard risk modeling (see Fielder et al. 2021). Model adjustment can range from a simple shifting of event frequencies in stochastic hazard tables to much fuller incorporation of and alignment with GCM approaches. It must be remembered that there may be considerable uncertainty around future climate patterns (such as rainfall across the Sahel), and it may be challenging to adequately parameterize them without suggesting inappropriate levels of exactitude. Scenario modeling is one typical approach under high uncertainty. Additionally, exposure and vulnerability components of risk (such as urbanization, informal settlements, and flooding) can change much faster than climate trends. Since this work increasingly falls under financial regulation and disclosure regimes (e.g., NGFS 2022), explicit climate modeling for catastrophic risks will see much growth in the near future, with translation of approaches to low-income regions through use of underlying global data sets. This paper’s analysis focuses on past and current weather patterns and does not include an estimation of future changes due to global warming.

# 3. Data on Hazards and Welfare

## 3.1. Hazard data

For the analysis described in this paper, we constructed a database of historical hazard data for all SSA using remotely sensed satellite data and indices that were reputable and publicly available and that had high levels of spatial and historical coverage. The considered hazard variables include rainfall, vegetation cover, evapotranspiration, soil moisture, and the WRSI. Given there is no single definition of drought, these hazard data were used to develop different measures of climatic conditions as a proxy for drought. These measures range from simple ones based on the amount and timing of precipitation during the growing season in a defined area, to more complex composite measures combining precipitation with other information capturing the impact of increased temperatures on water availability and agricultural stress at a location. Appendix B provides more details on all the drought measures considered and the sources of the data.<sup>10</sup> Table 3.1 provides a brief overview of the measures used in the analysis. These measures by and large focus on the first three months of the growing season.

**Table 3.1. Summary of range of hazard measures derived from remotely sensed data**

|**Data type **|**Source**|**Hazard measures**|
|---|---|---|
|Rainfall|CHIRPS global rainfall data set from US<br>Geological Survey (NASA)|Standardized anomaly of cumulative<br>rainfall (based on the first three months of<br>thegrowingseason)|
|Vegetation<br>(greenness)|NDVI product of MODIS vegetation<br>indices|NDVI standardized anomaly (based on the<br>average over the first three months of the<br>growingseason)|
|Evapotranspiration|SPEI generated by the Climatic Research<br>Unit of the Universityof East Anglia|Level of three-month SPEI at the end of the<br>first three months of thegrowingseason|

9 See for example Purdy (2021).

10 A workshop was held at the beginning of the work described in this paper to ensure the right measures were included (in addition to those summarized in appendix B).

9
|Soil moisture|Soil Water Index from Copernicus Global<br>Land Service|Soil moisture standardized anomaly (based<br>on the average over the first three months<br>of thegrowingseason)|
|---|---|---|
|Availability of water<br>for crops|FEWS NET|End of season WRSI as anomaly (as a ratio<br>of the WRSI to the median historical WRSI)|

_Source:_ World Bank.

_Note:_ CHIRPS = Climate Hazards Group InfraRed Precipitation with Station; FEWS NET = Famine Early Warning Systems Network; MODIS = Terra Moderate Resolution Imaging Spectroradiometer; NASA = National Aeronautics and Space Administration; NDVI = Normalized Difference Vegetation Index; SPEI = Standardized Precipitation Evapotranspiration Index; WRSI = Water Requirement Satisfaction Index.

The historical coverage of the data differs. In general, the analysis uses data from the period 2000/01 to 2019/20 at dekadal or monthly intervals to reflect the shocks faced within the context of a changing climate. For example, the NDVI data utilized are a product of the MODIS (Terra Moderate Resolution Imaging Spectroradiometer) satellites and are available for February 2000 and after. However, the precipitation data are from the CHIRPS (Climate Hazards Group InfraRed Precipitation with Station) global rainfall data set and are available from 1981. Only the soil moisture data cover a shorter period, starting in 2007. Despite the limited history, however, soil moisture data are rapidly proving useful in estimating drought conditions, and they have a memory effect that rainfall data lack.

The hazard data were extracted at a uniform grid resolution of 0.05° by 0.05° (about 5 km by 5 km near the equator) and a crop coverage mask (Copernicus Global Land Cover Layers, 2019) was applied to exclude hazard values in areas that would not affect crop yields. Data on seasonal timing were taken from the UN Food and Agriculture Organization (FAO) for each country. To aggregate the hazard data to an appropriate geographic unit for merging with the welfare data, additional data were incorporated in the data set, including country and administrative area boundaries from the World Bank Group, Global Administration Areas (GADM), and Global Administrative Unit Layers (GAUL) of the FAO.

The standardized anomaly measure is defined as _(level – mean for local area)/standard deviation_ for the local area, where the mean and standard deviation for the local area are calculated based on the 20 years of hazard data, or the maximum data available in the case of soil moisture. The local area is defined by aggregating the data for a 20 km buffer of the household location or for the administrative area if the former is not available.

The unconditional correlation between different hazard measures is not particularly high. Table 3.2 presents results for each livelihood zone used in the analysis. The independent variation across these hazard measures highlights their capture of different atmospheric conditions; hence the difficulty of identifying a measure capturing drought events well. But as the analysis will show, in a regression framework the results are more consistent across most hazard measures (with some exceptions). This suggests that despite capturing different atmospheric conditions, the hazard measures are reasonably effective at capturing situations making households worse off.

10
**Table 3.2. Unconditional correlation between different hazard measures by livelihood zone**

|||**Ma**|**ize**|||**Highl**|**and**||**R**|**oots and**|**lowland**|**s**|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
||Total||||Total||||Total||||
||<br>seasonal<br>rainfall<br>|Soil<br>moistu|re<sup>SPEI</sup>|NDVI|<br>seasonal<br>rainfall|Soil<br>moistur|e <sup>SPEI </sup>|<sup>NDVI</sup>|<br>seasonal<br>rainfall|<br>Soil<br>moisture|<sup>SPEI</sup>|NDVI|
|Soil moisture|0.43||||0.49||||0.00||||
|SPEI|0.47|0.26|||0.44|0.28|||0.30|0.12|||
|NDVI|0.48|0.63|<br>0.32||0.32|0.51|0.18||0.22|0.43|0.07||
|WRSI|0.21|0.13|<br>0.12|0.16|0.22|0.15|0.18|0.11|0.15|-0.11|0.01|0.02|
||||**Pastoral**|||||**Ag**|**ropastora**|**l**|||
||Total seas<br>rainfal|onal<br>l|Soil<br>moisture|SPEI|<br>NDVI|To|tal seas<br>rainfall|onal<br> <br>|Soil<br>moisture|SPEI|NDVI||
|Soil moisture|0.46||||||0.32||||||
|SPEI|0.45||0.23||||0.51||0.39||||
|NDVI|0.57||0.54|0.28|||0.33||0.60|0.31|||
|WRSI|0.29||0.09|0.24|<br>0.26||0.26||-0.11|0.17|0.10||

_Source:_ World Bank. _Note:_ NDVI = Normalized Difference Vegetation Index; SPEI = Standardized Precipitation Evapotranspiration Index; WRSI = Water Requirement Satisfaction Index.

# 3.2. Hazard simulations data

For the analysis, we asked Verisk’s AIR Worldwide (AIR) to produce 10,000-year drought-related stochastic catalogs of synthetic simulations for Malawi at a spatial resolution of 0.05° and dekadal temporal resolution. Stochastic catalogs are designed to provide a view of hazard that goes beyond the data available in the historical record. AIR used historical data on rainfall to produce three such catalogs: for precipitation, soil moisture, and vegetation index.

To generate the stochastic catalogs, AIR used data similar to that used by the World Bank team in generating the historical hazard time series. CHIRPS data were used for precipitation; the Soil Water Index at a depth of 40 cm from the Copernicus Global Land Service was used for soil moisture; and the NDVI for vegetation cover was from MODIS. The resulting catalogs were validated by comparing the synthetic time series with the historical data in Malawi. The validation results show that the catalogs preserve the intrinsic properties in terms of spatial and temporal correlations, produce a realistic view of hazard, and are consistent with historical observations while allowing for the creation of new extremes.

For the purposes of this paper, the approach was tested using the stochastic catalog for soil moisture in Malawi. Further details on the methodology used to generate the 10,000-year catalog and the validation conducted are in appendix C.

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# 3.3. Welfare data

The main welfare measures examined are constructed from household consumption surveys. To provide a comparable measure of welfare across countries, the aggregate that is used for national poverty measures and that forms the basis for global poverty measurement is used. Consumption aggregates are converted into 2011 purchasing power parities (PPPs) for this analysis.<sup>11</sup> We selected nine countries representing geographic variation in SSA for the analysis of the relationship between droughts and monetary welfare (consumption). They include Ethiopia in Eastern Africa; Mauritania, Niger, and Nigeria in Western Africa; and Lesotho, Malawi, Mozambique, Zambia, and Zimbabwe in Southern Africa. For five of these countries data are available for multiple years. The countries, years, and outcome measures used in analysis are listed in Table 3.3. To allow for ease of matching rainfall patterns to consumption in the first analysis, the selected countries are all from parts of the continent where there is a clear main season of production. Selection was also designed to include countries that had multiple survey rounds that could be pooled for analysis and that would provide sufficient numbers for analysis across livelihood zones.

The empirical analysis is carried out by livelihood zone, which entails pooling these countries and estimating like areas of production within them. The zones used are those defined in Dixon et al. (2019). They allow for the required level of analysis. The authors provide gridded data for the livelihood zones estimated for 2015, which is within our analysis period. We further aggregated the zones estimated for 2015 into five zones. Table 3.4 indicates how the countries included match to the livelihood zones used in the analysis. Table 3.5 reports descriptive statistics for the variables used in the analysis by country and survey year.

**Table 3.3. Household surveys and welfare measures included in the analysis**

|**Country (years)**|**Welfare measure**|
|---|---|
|Ethiopia (2010/11, 2014/15)|Total expenditure per adult equivalent<br>Food expenditure per adult equivalent<br>Nonfood expenditureper adult equivalent|
|Lesotho(2017/18)|Total expenditureper capita|
|Malawi (2010/11, 2016/17,<br>2019/20)|Total expenditure per capita<br>Total food expenditure per capita<br>Total nonfood expenditure per capita<br>Household dietary diversity: based on 12 food categories<br>Household food consumption score: based on food types consumed and<br>frequencyof consumption in a seven-day period(maximum 120)|
|Mauritania(2014,2019/20)|Total expenditureper capita|
|Mozambique (2014)|Total expenditure per capita<br>Total food expenditure per capita<br>Total nonfood expenditureper capita|
|Niger (2018)|Total expenditure per capita<br>Total food expenditure per capita<br>Total nonfood expenditureper capita|
|Nigeria(2011,2013,2016)|Total expenditureper capita|
|Zambia(2015)|Total expenditureper capita|
|Zimbabwe(2017)|Total expenditureper capita|

_Source: World Bank._

> 11 In most countries, the aggregates take spatial variation in prices into account and where this is done, this is retained. In addition, if the consumption aggregate used for national poverty measurement uses per adult equivalent instead of per capita, this is also retained. This makes the aggregate different from the ones reported in the World Bank’s Poverty and Inequality Platform.

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**Table 3.4. Matching of household surveys to livelihood zones**

||Ethiopia|Lesotho|Malawi|Mauritania|Mozambique|Niger|Nigeria|Zambia|Zimbabwe|Total|
|---|---|---|---|---|---|---|---|---|---|---|
|Maize mixed|2,913|377|26,172|0|2,610|0|0|5,580|12,614|50,266|
|Highland|10,651|2,444|0|0|227|0|29|0|1,695|15,046|
|Roots and<br>lowland|0|0|0|0|0|0|5,705|0|0|5,705|
|Agropastoral|0|0|0|0|0|2,315|2,278|0|0|4,593|
|Pastoral|0|0|0|11,463|0|2,178|0|0|0|13,641|

_Source: World Bank. Note:_ Livelihood zones are generated from Dixon et al. (2019). Agropastoral and pastoral regions in Ethiopia are not included in the analysis. Pastoral includes pastoral and arid pastoral oasis farming systems. Highland includes highland perennial and highland mixed farming systems. Roots and lowland combines root and tuber crop, cereal root crop, and humid lowland tree crop farming systems.

**Table 3.5. Descriptive statistics for variables by** **<u>year and country</u>**

|**Year**|**Country**|**Average per**<br>**capita**<br>**consumption**<sup>**a**</sup><br>**(2011 US$ PPP)**|**Share of**<br>**households**<br>**with land**<br>**ownership**<sup>**b**</sup>|**Share of**<br>**households**<br>**with**<br>**educated**<br>**head**<sup>**b**</sup>|**Share of**<br>**households**<br>**with**<br>**female**<br>**head**|**Share of**<br>**households**<br>**interviewed**<br>**during the lean**<br>**season**|**Share of**<br>**households**<br>**in locations**<br>**considered**<br>**remote**|
|---|---|---|---|---|---|---|---|
|2011|Ethiopia|950|0.98|0.37|0.15|0.34|0.68|
|2016|Ethiopia|1,227|0.96|0.38|0.17|0.35|0.69|
|2017|Lesotho|1,281|0.79|0.16|0.39|0.48|0.44|
|2010|Malawi|590|0.94|0.45|0.20|0.42|0.21|
|2016|Malawi|543|0.90|0.47|0.27|0.58|0.19|
|2019|Malawi|498|0.90|0.50|0.29|0.42|0.22|
|2014|Mauritania|1,782|0.44|0.36|0.27|0.96|0.54|
|2019|Mauritania|1,755|0.42|0.36|0.33|0.00|0.55|
|2014|Mozambique|626|0.96|0.49|0.22|0.12|0.67|
|2018|Niger|869|0.88|0.06|0.13|0.42|0.16|
|2011|Nigeria|738|0.82|0.46|0.08|0.55|0.19|
|2013|Nigeria|873|0.84|0.43|0.08|0.54|0.19|
|2016|Nigeria|859|0.84|0.46|0.06|0.54|0.19|
|2015|Zambia|486|0.89|0.65|0.18|0.67|0.72|
|2017|Zimbabwe|950|0.68|0.47|0.34|0.40|0.69|

_Source: World Bank. Notes_ : a. Or per adult equivalent consumption, depending on the country. b. See appendix B, table B.2 for country-specific definitions used.

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_Note:_ Squares represent the 5 km by 5 km grids for which the hazard measures are available; the (starred) centroid of the square represents the household or cluster location; shaded squares represent the grids used to spatially aggregate the hazard measure for a 10 km radius (darker shade) and a 20 km radius (lighter shade) around the household’s location.

The results presented in this paper are based on matching a household’s geographic location with a spatially aggregated hazard measure within a 20 km radius. In the absence of any GPS data at the household or cluster level, the hazard measures are aggregated to the geographic or closest administrative level that is coded in the household survey. We chose the level of spatial aggregation so as to provide a roughly consistent area of spatial aggregation for surveys where matching was done using GPS data and administrative data.

Initial analysis suggested that this level of spatial aggregation was appropriate. We compared the sensitivity of the relationship between welfare and hazard measures aggregated using different radii in the case of Malawi, a country that has GPS coordinates for surveyed households and multiple years of data. The statistical significance of results increased for radii of up to 20 km and then started to decrease again with larger radii, suggesting that a radius of 20 km is able to reflect the local shock to a household’s crop yields and is also large enough to capture some localized impacts on prices and wages in the local market area. However, as shown in section 4.2, for the full data set a larger geographic area it is not clear that 20 km works better in every setting, and there is very little difference between the results across aggregating radii.

# 3.5. Using standardized anomalies for analysis

The hazard measures generated are in levels as well as standardized anomalies (z-scores).<sup>13</sup> The latter assume that differences in the level of the hazard from the historic average (i.e., level changes) matter not in an absolute sense but in proportion to an area’s usual variation. Welfare measures are only partly affected by the relation between hazards and crop yields and are the outcome of various ex ante and ex post risk-coping strategies developed by households over the years for the purpose of reducing income fluctuations and/or protecting their level of welfare (e.g., consumption). Hence the extent to which the experienced hazard deviates from what households expect (i.e., the historic mean value of the hazard) appears to be a better specification than the actual level of the hazard. Thus it is anticipated that the specification of shocks as standardized anomalies (in standard deviation units or z- scores) is likely to yield more sensible welfare impact estimates than those obtained using the level of the hazard (i.e., rainfall in millimeters). In the case of droughts, a positive anomaly means the hazard experienced was less severe than the historical mean, and a negative anomaly means it was more severe.

When analysis of the specification of the hazard level as a level includes enough years of welfare data, controlling for fixed effects at some spatial level (e.g., district level) transforms the hazard and all other control variables as deviations from the mean (Dell, Jones, and Olken 2014). In cases such as ours, where the sample of welfare data contains a limited number of observations over time, this is not the case, and it is preferable to use a full time series of hazard data prior to regression analysis to generate a standardized anomaly.<sup>14</sup> 13 Some hazard measures such as the WRSI cannot be expressed as a standardized anomaly because by construction they are top coded (for example, the top value of WRSI is 100 percent). However, WRSI can be expressed as an anomaly (i.e., the ratio of current value with the mean or median).

14 Consider, for example, a cross-sectional household data set with three survey rounds and an identifier for the same districts (or clusters, though that is less likely) in each round. Using fixed effects for districts (clusters) transforms all the variables as deviations from the sample district (cluster) mean over all the household observations across the years in the same district (cluster) within the sample. With three survey rounds over the 20-year period analyzed, the district-specific sample mean of any given hazard measured is likely to differ significantly from the district mean estimated over a 20-year period. As a consequence, estimates of the welfare impacts of shocks are likely to differ significantly depending on whether the analysis uses the specification of the 15
Another advantage offered by the standardization of the deviation from the local mean is that it offers the opportunity to gauge the magnitude of the shock experienced across a variety of geographic contexts. We use z- scores for the hazard anomalies, which means that in addition to being differenced from the mean, the hazard variable is scaled by the standard deviation. This approach assumes that changes in the hazard matter not in an absolute sense, but in proportion to an area’s usual variation. This assumption is useful in taking some production and livelihood differences into account across space. A 3 mm decrease in rain does not have the same impact in wet and dry regions. Considering variations relative to an area’s usual variation is more important when there is no control for this in the hazard measure being used, e.g., total rainfall, soil moisture. It is arguably less important when using an outcome measure that already takes crop choice into account, such as NDVI or WRSI.

Table 3.6 presents the means and standard deviations for the hazard variables used in the analysis. The means indicate lower than average years for many of the hazards across the livelihood zones. The standard deviations highlight substantial variation around these means. It is this variation that the analysis exploits.

**Table 3.6. Mean and standard deviation of hazards used in the analysis**

|**Hazard variable**|**Maize**|**Highland**|**Roots**|**Pastoral**|**Agropastoral**|
|---|---|---|---|---|---|
|||**Growin**|**g season**|||
|Soil moisture|-0.312|-0.322|-0.293|0.098|-0.359|
||(0.929)|(1.126)|(0.769)|(1.086)|(1.000)|
|NDVI|-0.284|-0.349|-0.472|0.334|0.058|
||(0.949)|(1.038)|(0.923)|(1.046)|(0.955)|
|SPEI|0.111|-0.345|-0.600|0.367|0.067|
||(0.721)|(0.820)|(0.850)|(0.834)|(1.183)|
|Rainfall|0.035|-0.378|-0.291|0.417|-0.002|
||(1.135)|(1.170)|(0.909)|(0.980)|(1.183)|
|WRSI|99.050|98.860|99.339|101.488|100.866|
||(9.785)|(9.789)|(2.118)|(11.026)|(10.109)|
|**Rai**|**ny season(us**|**ed inpastoral**|**and agropast**|**oral specificatio**|**ns)**|
|Soil moisture||||0.693|0.610|
|||||(0.497)|(0.173)|
|NDVI||||0.396|0.161|
|||||(1.038)|(0.852)|
|Rainfall||||0.205|0.334|
|||||(0.942)|(0.826)|

# _Source:_ World Bank.

_Note:_ NDVI = Normalized Difference Vegetation Index; SPEI = Standardized Precipitation Evapotranspiration Index; WRSI = Water Requirement Satisfaction Index. Countries and surveys included are: Ethiopia (2011, 2016), Lesotho (2017), Malawi (2010, 2016, 2019), Mauritania (2014, 2109/20), Mozambique (2014), Niger (2018), Nigeria (2011, 2013, 2016), Zambia (2015), and Zimbabwe (2017).

hazard as a level along with the fixed effects method or it uses the specification of the hazard as a standardized anomaly from the local normal (over the 20-year period). In fact, in the extreme case in which only one crosssectional round of survey data is available, then the specification of the hazard as a standardized anomaly is the only sensible option, since in this instance, use of the level of hazard with the fixed effects for districts (for example) would simply express the hazard as a deviation from the district mean of the hazard values experienced in the same survey round by other households in the survey.

16
# 4. Results

## 4.1. Main results

Tables 4.1 to 4.3 show results for continuous measures of hazard anomalies for the three cropping livelihood zones of maize, highland, and roots and lowland. Each table shows results for linear, quadratic, and cubic measures of soil moisture, vegetation (NDVI), evapotranspiration (SPEI), total seasonal rainfall, and WRSI; notes to each table indicate which countries and years are included. The impact of the hazard is estimated and presented separately for households with and without land to reflect the difference in the degree to which households are likely to be impacted by the hazard.<sup>15</sup> There are three important conclusions from these results. First, not all measures perform equally well at capturing the occurrence of the shock, to the extent that welfare is positively and significantly correlated with good weather conditions and negatively affected by weather shocks for households with land. Of the four measures, soil moisture and NDVI appear to give more precise and consistent results across specifications, with soil moisture offering the most consistent results across livelihood zones. SPEI, total seasonal rainfall and WRSI provide much less consistent results. Total seasonal rainfall often provides counterintuitive results, as does SPEI in some specifications. WRSI is often not significant.

Second, although nonlinearities are known to be present in the relationship between weather and agricultural production, we do not observe a consistent nonlinear pattern across regression results. This could simply reflect the fact that we are looking at the relationship between weather and consumption rather than agricultural production where non-linear effects are well established (e.g., Lobell, Schlenker and Costa-Roberts 2011). It could also reflect the fact that non-linearities are already part of the index construction in some cases. For example, WRSI weights losses in rainfall differently based on when they occur and NDVI, by capturing vegetation should, already capture the non-linear impact of weather conditions on yields. Another reason for not observing a consistent non-linear pattern could be that we have few household survey observations at extreme values of the anomaly which is where observations would be needed to pick up non-linear effects.

In the maize livelihood zone some nonlinearity is present: there is a stronger relationship between hazard anomalies and welfare in the middle of the distribution (where anomalies and therefore welfare changes are smaller) and a smaller impact of anomalies on welfare at the tails of the distribution. A steeper relationship is also observed in the quadratic and cubic specification for the roots and lowland livelihood zone, but no tapering off for negative values (Figures 4.1 and 4.2). Despite being significant in this case, the squared and cubic terms do not indicate much nonlinearity in the relationship. Nonlinearities are much more important when using the total rainfall measure; this makes sense because this measure does not reflect any nonlinear relationship between rainfall and crop production in how it is constructed. In these cases, the nonlinearity indicates a larger impact on welfare as the anomaly becomes bigger and more negative, and a smaller impact on welfare as the anomaly becomes more positive, even turning negative for very large values of total rainfall that may reflect waterlogging and flooding.

Third, for soil moisture negative impacts are felt for both landed and landless households with no consistent pattern of who is most affected. For the highlands and NDVI measures in roots and tubers livelihood area, there is a strong and significant impact on landed households, but little impact on landless households. Overall, though given the relatively similar impact in many specifications it suggests that using weather variation in a 20km radius includes the impact of the weather on immediate labor markets.

15 The term “hazard” as used here includes the full distribution of the weather anomaly used—that is, positive and negative events, not just events that cause welfare losses according to the definition of hazard.

17
**Table 4.1. Results for maize livelihood zone**

|||**Soil moistu**|**re**||**NDVI**|||**SPEI**||**Total**|**seasonal rain**|**fall**||**WRSI**||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
||(1)|(2)|(3)|(4)|(5)|(6)|(7)|(8)|(9)|(10)|(11)|(12)|(13)|(14)|(15)|
|**Landed h**|**ouseholds**|||||||||||||||
|Hazard|**0.055*****|**0.059*****|**0.119*****|**0.024****|**0.034*****|**0.071*****|0.019|0.019|**0.062*****|-0.019|-0.017|0.012|0.001|0.012|-0.015|
||**[3.852]**|**[4.097]**|**[4.792]**|**[2.122]**|**[2.755]**|**[4.120]**|[1.616]|[1.547]|**[2.843]**|[-1.570]|[-1.407]|[0.701]|[0.685]|[1.169]|[-0.433]|
|Hazard<sup>2</sup>||**0.022***|0.011||**0.020*****|-0.001||0.003|-0.004||**-0.022*****|**-0.015****||-0.000|0.000|
|||**[1.831]**|[0.839]||**[2.807]**|[-0.082]||[0.243]|[-0.250]||**[-3.021]**|**[-1.964]**||[-1.162]|[0.653]|
|Hazard<sup>3</sup>|||**-0.028*****|||**-0.021*****|||**-0.021*****|||-0.011**|||-0.000|
||||**[-2.954]**|||**[-3.814]**|||**[-2.600]**|||[-2.205]|||[-0.863]|
|**Landless**|**households**|||||||||||||||
|Hazard|**0.043****|**0.038***|0.032|0.013|**0.030***|**0.077****|**-0.028****|**-0.041****|0.071|**-0.045*****|**-0.042*****|**-0.075****|**-0.003*****|0.000|-0.016|
||**[2.239]**|**[1.844]**|[0.875]|[0.801]|**[1.696]**|**[2.441]**|**[-2.006]**|**[-2.249]**|[1.550]|**[-3.161]**|**[-3.128]**|**[-2.526]**|**[-3.064]**|[0.056]|[-0.422]|
|Hazard<sup>2</sup>||0.002|0.004||**0.029****|0.005||-0.022|**-0.039****||**-0.033****|**-0.039****||-0.000|0.000|
|||[0.101]|[0.181]||**[2.189]**|[0.347]||[-1.305]|**[-2.213]**||**[-2.114]**|**[-2.571]**||[-0.444]|[0.374]|
|Hazard<sup>3</sup>|||0.007|||**-0.023****|||**-0.041*****|||0.012|||-0.000|
||||[0.399]|||**[-2.352]**|||**[-2.917]**|||[1.215]|||[-0.406]|
|Obs.|50,266|50,266|50,266|50,242|50,242|50,242|50,266|50,266|50,266|50,266|50,266|50,266|48,506|48,506|48,506|
|R-sq|0.362|0.363|0.364|0.358|0.358|0.359|0.361|0.361|0.361|0.361|0.362|0.362|0.370|0.371|0.371|

_Source:_ World Bank.

_Note:_ NDVI = Normalized Difference Vegetation Index; SPEI = Standardized Precipitation Evapotranspiration Index; WRSI = Water Requirement Satisfaction Index. Results are from a weighted regression such that each household is assigned its survey-specific population weight. Countries and years included are Ethiopia (2011, 2016), Lesotho (2017), Malawi (2010, 2016, 2019), Mozambique (2014), Zambia (2015), and Zimbabwe (2017). Dependent variable is the log of per capita (or adult equivalent) consumption. Other variables included and not shown are education of household head, gender of household head, whether the household location is remote, agroecological zone indicators, whether the household was surveyed during the lean season, survey year, country, country x survey year, and administrative fixed effects for district (Ethiopia. Lesotho, Malawi) and province (Mozambique, Zambia, Zimbabwe). Robust t-statistics are shown in parenthesis. Significance level: * = 10 percent, ** = 5 percent, *** = 1 percent. When variable is significant the coefficient and standard error are in bold font.

18
**Table 4.2. Results for highland livelihood zone**

|||**Soil moistur**|**e**||**NDVI**|||**SPEI**||**Tot**|**al seasonal ra**|**infall**||**WRSI**||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
||(1)|(2)|(3)|(4)|(5)|(6)|(7)|(8)|(9)|(10)|(11)|(12)|(13)|(14)|(15)|
|**Landed h**|**ouseholds**|||||||||||||||
|Hazard|**0.045*****|**0.044*****|**0.044***|**0.020***|0.017|0.025|**0.041****|0.001|**-0.049***|**0.030****|0.017|0.031|**0.003***|0.017|0.065|
||**[4.495]**|**[4.350]**|**[1.653]**|**[1.649]**|[1.154]|[1.382]|**[2.426]**|[0.060]|**[-1.649]**|**[2.575]**|[1.172]|[1.307]|**[1.782]**|[1.332]|[0.902]|
|Hazard<sup>2</sup>||-0.004|-0.004||-0.003|-0.013||**-0.055*****|**-0.041****||**-0.017***|**-0.021***||-0.000|-0.001|
|||[-0.427]|[-0.333]||[-0.338]|[-0.917]||**[-3.940]**|**[-2.496]**||**[-1.895]**|**[-1.813]**||[-1.147]|[-0.783]|
|Hazard<sup>3</sup>|||-0.000|||-0.005|||**0.024****|||-0.005|||0.000|
||||[-0.007]|||[-0.853]|||**[2.153]**|||[-0.694]|||[0.699]|
|**Landless**|**households**|||||||||||||||
|Hazard|-0.005|-0.006|-0.030|-0.002|-0.027|-0.026|0.020|-0.011|0.031|0.017|0.016|0.042|0.002|0.021|0.111|
||[-0.214]|[-0.231]|[-0.533]|[-0.063]|[-0.565]|[-0.556]|[0.765]|[-0.294]|[0.600]|[0.747]|[0.622]|[0.876]|[1.046]|[1.368]|[1.577]|
|Hazard<sup>2</sup>||-0.002|-0.000||-0.023|-0.024||-0.031|**-0.111****||0.001|-0.009||-0.000|-0.001|
|||[-0.100]|[-0.002]||[-0.852]|[-0.496]||[-1.080]|**[-2.233]**||[0.062]|[-0.358]||[-1.303]|[-1.425]|
|Hazard<sup>3</sup>|||0.010|||-0.001|||**-0.051***|||-0.009|||0.000|
||||[0.523]|||[-0.045]|||**[-1.746]**|||[-0.625]|||[1.308]|
|Obs.|15,046|15,046|15,046|15,046|15,046|15,046|15,046|15,046|15,046|15,046|15,046|15,046|12,159|12,159|12,159|
|R-sq|0.265|0.265|0.265|0.260|0.260|0.261|0.261|0.266|0.268|0.262|0.263|0.263|0.258|0.259|0.259|

_Source:_ World Bank.

_Note:_ NDVI = Normalized Difference Vegetation Index; SPEI = Standardized Precipitation Evapotranspiration Index; WRSI = Water Requirement Satisfaction Index. Results are from a weighted regression such that each household is assigned its survey-specific population weight. Countries and years included are Ethiopia (2011, 2016), Lesotho (2017), Mozambique (2014), and Zimbabwe (2017). Dependent variable is the log of per capita (or adult equivalent) consumption. Other variables included and not shown are education of household head, gender of household head, whether the household location is remote, whether the household was surveyed during the lean season, survey year, country, country x survey year, and administrative fixed effects for district (Ethiopia. Lesotho) and province (Mozambique, Zimbabwe). Robust t-statistics are shown in parenthesis. Significance level: * = 10 percent, ** = 5 percent, *** = 1 percent. When variable is significant the coefficient and standard error are in bold font.

19
**Table 4.3. Results for roots and lowland livelihood zone**

|||**Soil moistur**|**e**||**NDVI**|||**SPEI**||**Tot**|**al seasonal rai**|**nfall**||**WRSI**||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
||(1)|(2)|(3)|(4)|(5)|(6)|(7)|(8)|(9)|(10)|(11)|(12)|(13)|(14)|(15)|
|**Landed h**|**ouseholds**|||||||||||||||
|Hazard|**0.152*****|**0.092*****|**0.136*****|**0.069*****|**0.092*****|**0.091*****|**0.082*****|**0.063***|0.027|**0.069*****|**0.036***|0.022|0.019|**-1.337*****|-3.865|
||**[8.123]**|**[3.668]**|**[4.314]**|**[4.269]**|**[4.214]**|**[3.038]**|**[2.634]**|**[1.785]**|[0.527]|**[3.406]**|**[1.766]**|[0.744]|[1.360]|**[-2.927]**|[-0.237]|
|Hazard<sup>2</sup>||**-0.07*****|**-0.149*****||0.022|0.023||-0.017|0.013||**-0.041*****|**-0.036*****||**0.007*****|0.033|
|||**[-2.801]**|**[-4.316]**||[1.496]|[1.419]||[-0.715]|[0.379]||**[-3.894]**|**[-3.504]**||**[2.967]**|[0.196]|
|Hazard<sup>3</sup>|||**-0.051*****|||0.001|||0.023|||0.005|||-0.000|
||||**[-2.668]**|||[0.092]|||[0.999]|||[0.839]|||[-0.154]|
|**Landless**|**households**|||||||||||||||
|Hazard|**0.166*****|**0.154*****|**0.165*****|0.036|0.013|-0.001|0.027|0.112|0.022|0.021|0.015|-0.010|**0.050****|**-2.006****|11.437|
||**[3.698]**|**[3.391]**|**[2.970]**|[0.971]|[0.236]|[-0.016]|[0.442]|[1.254]|[0.209]|[0.543]|[0.429]|[-0.148]|**[2.281]**|**[-2.266]**|[0.441]|
|Hazard<sup>2</sup>||-0.032|-0.037||-0.018|0.005||0.069|**0.167***||-0.008|-0.010||**0.011****|-0.126|
|||[-0.579]|[-0.571]||[-0.486]|[0.097]||[1.264]|**[1.677]**||[-0.323]|[-0.370]||**[2.335]**|[-0.476]|
|Hazard<sup>3</sup>|||-0.007|||0.014|||0.077|||0.010|||0.000|
||||[-0.157]|||[0.466]|||[1.373]|||[0.600]|||[0.514]|
|Obs.|5,705|5,705|5,705|5,705|5,705|5,705|5,705|5,705|5,705|5,705|5,705|5,705|2,206|2,206|2,206|
|R-sq|0.175|0.179|0.182|0.157|0.158|0.158|0.154|0.155|0.157|0.156|0.160|0.160|0.107|0.115|0.115|

_Source:_ World Bank.

_Note:_ NDVI = Normalized Difference Vegetation Index; SPEI = Standardized Precipitation Evapotranspiration Index; WRSI = Water Requirement Satisfaction Index. Results are from a weighted regression such that each household is assigned its survey-specific population weight. One country, Nigeria, is included for years 2011, 2013, and 2016. Dependent variable is the log of per capita (or adult equivalent) consumption. Other variables included and not shown are education of household head, gender of household head, whether the household location is remote, whether the household was surveyed during the lean season, survey year, country, country x survey year, and zone fixed effects. Robust t-statistics are shown in parenthesis. Significance level: * = 10 percent, ** = 5 percent, *** = 1 percent. When variable is significant the coefficient and standard error are in bold font.

20
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Tables 4.4 and 4.5 show results for pastoral and agropastoral areas respectively. The choice of hazard and functional form is influenced by in-depth work undertaken on Mauritania (Hill and Vinha 2022), one of the pastoral countries in the sample. This work highlights the importance of using Tropical Livestock Unit (TLU) ownership as a way of distinguishing between household types. It also highlights the importance of including households living in areas classified as urban, as many of these households were found to have significant TLU ownership. Also, given that especially many of the pastorals are in locations without growing season per se, the hazards are constructed over the whole rainy season. The results for pastoral areas show that poor weather impacts consumption much more strongly for households with fewer animals. Those with more animals are able to smooth their consumption in the face of poor weather. The results for agropastoralists are harder to interpret. The same pattern of worse impacts for households with fewer animals holds for agropastoralists, but weather shocks appear positive for landless households. Only results for NDVI are shown, but no measure provided sensible results. Further work, and probably additional data, are needed to better model and understand the impact of weather shocks on agropastoralist welfare in Sub-Saharan Africa, including considering cumulative impacts of rainfall losses across seasons and temperature impacts on cattle.

**Table 4.4. Results for pastoral zone in Western Africa**

|||**NDVI**<br>||**S**<br>|**oil moisture**<br>||**Tota**<br>|**l seasonal rai**<br>|**nfall**<br>|
|---|---|---|---|---|---|---|---|---|---|
||**(1)**|**(2)**|**(3)**|**(4)**|**(5)**|**(6)**|**(7)**|**(8)**|**(9)**|
|**No TLU**||||||||||
|Hazard|**0.069****|**0.065*****|**0.130*****|**0.120*****|0.050|0.014|0.014|0.019|0.111|
||**[2.463]**|**[2.966]**|**[3.510]**|**[2.809]**|[0.929]|[0.157]|[0.518]|[0.667]|[1.632]|
|Hazard<sup>2</sup>||0.004|**0.056***||0.079|0.022||-0.008|0.025|
|||[0.126]|**[1.832]**||[1.304]|[0.313]||[-0.227]|[0.662]|
|Hazard<sup>3</sup>|||**-0.037*****|||0.059|||**-0.049***|
||||**[-2.782]**|||[0.681]|||**[-1.659]**|
|**Few(less**|**than 2.1) TL**|**U**||||||||
|Hazard|**0.087*****|**0.065*****|**0.120*****|**0.110*****|**0.072****|**0.060**|**0.073****|**0.078****|**0.156****|
||**[2.899]**|**[3.656]**|**[4.102]**|**[2.841]**|**[2.378]**|**[1.233]**|**[2.432]**|**[2.579]**|**[2.552]**|
|Hazard<sup>2</sup>||0.024|**0.062*****||0.047|0.030||-0.013|0.005|
|||[1.049]|**[2.891]**||[1.185]|[0.506]||[-0.658]|[0.235]|
|Hazard<sup>3</sup>|||**-0.028*****|||0.016|||**-0.040***|
||||**[-3.379]**|||[0.375]|||**[-1.914]**|
|**Many (m**|**ore than 2.1)**|**TLU**||||||||
|Hazard|0.020|0.022|-0.011|0.016|**0.087****|0.078|0.001|0.009|0.028|
||[1.008]|[1.074]|[-0.382]|[0.433]|**[2.355]**|[1.592]|[0.047]|[0.330]|[0.520]|
|Hazard<sup>2</sup>||-0.009|-0.019||**-0.076***|-0.090||-0.027|-0.021|
|||[-0.954]|[-1.352]||**[-1.895]**|[-1.538]||[-1.522]|[-1.153]|
|Hazard<sup>3</sup>|||**0.013***|||0.013|||-0.005|
||||**[1.867]**|||[0.264]|||[-0.284]|
|Obs.|13,641|13,641|13,641|13,641|13,641|13,641|13,641|13,641|13,641|
|R-sq|0.417|0.418|0.422|0.415|0.416|0.416|0.415|0.415|0.416|

_Source:_ World Bank.

_Note:_ NDVI = Normalized Difference Vegetation Index; TLU = Tropical Livestock Unit. Results are from a weighted regression such that each household is assigned its survey-specific population weight. Countries and years included are Mauritania (2014, 2109/20) and Niger (2018). Dependent variable is the log of per capita (or adult equivalent) consumption. Other variables included and not shown are education of household head, gender of household head, whether the household location is remote, whether the household was surveyed during the lean season, survey year, country, country x survey year, and administrative fixed effects. Robust t-statistics are shown in parenthesis. Significance level: * = 10 percent, ** = 5 percent, *** = 1 percent.

23
**Table 4.5. Results for agropastoral zone in Western Africa**

|||**NDVI**||
|---|---|---|---|
||**(1)**|**(2)**|**(3)**|
|**Landed ho**|**useholds**|||
|**No TLU**||||
|Hazard|-0.046|-0.047|-0.031|
||[-0.817]|[-0.843]|[-0.329]|
|Hazard<sup>2</sup>||-0.002|-0.001|
|||[-0.068]|[-0.025]|
|Hazard<sup>3</sup>|||-0.009|
||||[-0.224]|
|**Few(less t**|**han 2.1) TLU**|||
|Hazard|**0.052***|**0.052***|0.064|
||**[1.658]**|**[1.693]**|[1.240]|
|Hazard<sup>2</sup>||0.022|0.022|
|||[1.034]|[0.970]|
|Hazard<sup>3</sup>|||-0.006|
||||[-0.292]|
|**Many (mor**|**e than 2.1) TLU**|||
|Hazard|0.039|0.039|-0.010|
||[0.908]|[0.906]|[-0.192]|
|Hazard<sup>2</sup>||-0.010|-0.008|
|||[-0.235]|[-0.215]|
|Hazard<sup>3</sup>|||0.032|
||||[1.044]|
|**Landless ho**|**useholds**|||
|Hazard|**-0.212*****|**-0.214*****|0.112|
||**[-3.393]**|**[-3.553]**|[0.453]|
|Hazard<sup>2</sup>||0.018|0.023|
|||[0.265]|[0.352]|
|Hazard<sup>3</sup>|||-0.186|
||||[-1.391]|
|Obs.|4,593|4,593|4,593|
|R-sq|0.132|0.133|0.137|

_Source:_ World Bank.

_Note:_ NDVI = Normalized Difference Vegetation Index. Results are from a weighted regression such that each household is assigned its survey-specific population weight. Countries and years included are Niger (2018) and Nigeria (2011, 2013, 2016). Dependent variable is the log of per capita (or adult equivalent) consumption. Other variables included and not shown are education of household head, gender of household head, whether the household location is remote, whether the household was surveyed during the lean season, survey year, country, country x survey year, and administrative fixed effects. Robust t-statistics are shown in parenthesis. Significance level: * = 10 percent, ** = 5 percent, *** = 1 percent.

# 4.2. Exploring different areas over which to aggregate the hazard data

Initial analysis suggested that a 20 km level of spatial aggregation of hazards was appropriate. This radius is able to reflect the local shock to a household’s crop yields and may be large enough to capture some localized impacts on prices and wages in the local market area. We tested this level of aggregation again at the end of the analysis for all countries and found that the level of spatial aggregation made very little difference. In some specifications taking a 24
larger level of spatial aggregation increases the estimated impact of the shock—although not significantly—without affecting statistical significance (table 4.6). In future work it would be interesting to explore much larger areas of aggregation if this is possible (i.e., if enough variation in the hazard is left and GPS data are available) to see if this affects the results.

**Table 4.6. Results for different areas of spatial aggregation of hazard data**

||**Maize(GPS**<br>|**coordinate c**<br>|**ountries only)**<br>|**2**<br>|**0 km radius**<br>||<br>|**50 km radius**<br>||
|---|---|---|---|---|---|---|---|---|---|
||**10km**|**20km**|**50km**|**Maize**|**Highland**|**Roots**|**Maize**|**Highland**|**Roots**|
|**Landed h**|**ouseholds**|||||||||
|Hazard|0.066***|0.075***|0.086***|0.055***|0.045***|0.152***|0.056***|0.045***|0.154***|
||[4.252]|[4.608]|[4.765]|[3.852]|[4.495]|[8.123]|[3.722]|[4.495]|[8.487]|
|**Landless**|**households**|||||||||
|Hazard|0.109***|0.112***|0.123***|0.043**|-0.005|0.166***|0.045**|-0.004|0.159***|
||[4.165]|[4.212]|[4.451]|[2.239]|[-0.214]|[3.698]|[2.276]|[-0.176]|[4.017]|
|Obs.|34,824|34,739|35,212|50,266|15,046|5,705|50,739|15,060|5,856|
|R-sq|0.138|0.137|0.133|0.362|0.265|0.175|0.357|0.260|0.177|

_Source:_ World Bank.

_Note:_ Results are from a weighted regression such that each household is assigned its survey-specific population weight. Dependent variable is the log of per capita (or adult equivalent) consumption. The hazard variable used is the soil moisture index. Other variables included and not shown are education of household head, gender of household head, whether the household location is remote, agroecological zone indicators, whether the household was surveyed during the lean season, survey year, country, country x survey year, and administrative fixed effects for district. Robust t-statistics are shown in parenthesis. Significance level: * = 10 percent, ** = 5 percent, *** = 1 percent.

# 4.3. Exploring food and nonfood consumption impacts separately

Four of the nine countries (Ethiopia, Malawi, Mozambique, and Niger) had separate aggregates of food and nonfood consumption in the data sets available for analysis. We conducted the same analysis separately on food and nonfood consumption for these countries to assess whether the main impact was on food consumption or whether households protected food consumption by reducing nonfood consumption; the latter result is found, for example, in Kochhar and Knippenberg (2023) using a similar method. Tables 4.7 and 4.8 present results for the maize and highland livelihood zones respectively. Results are shown using just the soil moisture variable. For both livelihood zones, the impacts of the hazard variables on food consumption are larger than impacts on nonfood consumption. Nonfood consumption is impacted only among landed households. Further work with data from additional countries would be informative in understanding whether this pattern holds.

25
**Table 4.7. Food and nonfood consumption, maize livelihood zone (soil moisture)**

||Total consu|mption, all c<br>zone|ountries in|Total cons<br>disagg|umption, co<br>regated info|untries with<br>rmation|Fo|od consumpti|on|Non|food consum|ption|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
|Landed h|ouseholds||||||||||||
|Hazard|**0.055*****|**0.059*****|**0.119*****|**0.058*****|**0.060*****|**0.131*****|**0.081*****|**0.082*****|**0.158*****|**0.037***|**0.041****|**0.101*****|
||**[3.852]**|**[4.097]**|**[4.792]**|**[3.731]**|**[3.900]**|**[4.681]**|**[4.754]**|**[4.680]**|**[5.581]**|**[1.903]**|**[2.168]**|**[2.751]**|
|Hazard<sup>2</sup>||**0.022***|0.011||**0.024***|0.012||0.011|-0.002||**0.030***|0.019|
|||**[1.831]**|[0.839]||**[1.753]**|[0.809]||[0.729]|[-0.152]||**[1.758]**|[1.009]|
|Hazard<sup>3</sup>|||**-0.028*****|||**-0.032*****|||**-0.035*****|||**-0.027***|
||||**[-2.954]**|||**[-3.041]**|||**[-3.740]**|||**[-1.902]**|
|Landless|households||||||||||||
|Hazard|**0.043****|**0.038***|0.032|**0.060*****|**0.053***|0.063|**0.093*****|**0.100*****|**0.112****|0.028|0.009|0.029|
||**[2.239]**|**[1.844]**|[0.875]|**[2.593]**|**[1.910]**|[1.161]|**[3.942]**|**[3.610]**|**[2.121]**|[0.950]|[0.255]|[0.407]|
|Hazard<sup>2</sup>||0.002|0.004||0.005|0.002||0.022|0.018||-0.013|-0.019|
|||[0.101]|[0.181]||[0.195]|[0.071]||[0.739]|[0.546]||[-0.384]|[-0.515]|
|Hazard<sup>3</sup>|||0.007|||-0.002|||-0.003|||-0.008|
||||[0.399]|||[-0.067]|||[-0.125]|||[-0.269]|
|Obs.|50,266|50,266|50,266|31,671|31,671|31,671|31,671|31,671|31,671|31,671|31,671|31,671|
|R<sup>2</sup>|0.362|0.363|0.364|0.363|0.363|0.365|0.281|0.281|0.284|0.387|0.388|0.389|

_Source:_ World Bank.

_Note:_ Results are from a weighted regression such that each household is assigned its survey-specific population weight. Countries and years included are Ethiopia (2011, 2016), Malawi (2010, 2016, 2019), and Mozambique (2014). Dependent variable is the log of per capita (or adult equivalent) consumption. Other variables included and not shown are education of household head, gender of household head, whether the household location is remote, agroecological zone indicators, whether the household was surveyed during the lean season, survey year, country, country x survey year, and administrative fixed effects for district (Ethiopia. Lesotho, Malawi) and province (Mozambique, Zambia, Zimbabwe). Robust t-statistics are shown in parenthesis. Significance level: * = 10 percent, ** = 5 percent, *** = 1 percent.

26
**Table 4.8. Food and nonfood consumption, highland livelihood zone (soil moisture)**

||Total consu|mption, all co<br>zone|untries in|Total consu<br>disaggr|mption, coun<br>egated inform|tries with<br>ation|Foo|d consumptio|n|Non-|food consum|ption|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
|Landed h|ouseholds||||||||||||
|Hazard|**0.045*****|**0.044*****|**0.044***|**0.044*****|**0.043*****|0.044|**0.054*****|**0.052*****|0.037|**0.042*****|**0.043*****|**0.060***|
||**[4.495]**|**[4.350]**|**[1.653]**|**[4.402]**|**[4.227]**|[1.600]|**[4.547]**|**[4.168]**|[1.195]|**[3.365]**|**[3.413]**|**[1.720]**|
|Hazard<sup>2</sup>||-0.004|-0.004||-0.005|-0.005||-0.010|-0.005||0.004|-0.001|
|||[-0.427]|[-0.333]||[-0.515]|[-0.422]||[-1.038]|[-0.420]||[0.395]|[-0.086]|
|Hazard<sup>3</sup>|||-0.000|||-0.000|||0.006|||-0.007|
||||[-0.007]|||[-0.040]|||[0.520]|||[-0.558]|
|Landless|households||||||||||||
|Hazard|-0.005|-0.006|-0.030|-0.012|-0.012|-0.053|0.013|0.012|-0.080|-0.026|-0.025|-0.016|
||[-0.214]|[-0.231]|[-0.533]|[-0.441]|[-0.450]|[-0.740]|[0.454]|[0.408]|[-1.218]|[-0.718]|[-0.685]|[-0.153]|
|Hazard<sup>2</sup>||-0.002|-0.000||-0.013|-0.009||-0.014|-0.002||-0.008|-0.012|
|||[-0.100]|[-0.002]||[-0.578]|[-0.384]||[-0.530]|[-0.091]||[-0.275]|[-0.365]|
|Hazard<sup>3</sup>|||0.010|||0.015|||0.035|||-0.004|
||||[0.523]|||[0.696]|||[1.624]|||[-0.117]|
|Obs.|15,046|15,046|15,046|10,877|10,877|10,877|10,877|10,877|10,877|10,868|10,868|10,868|
|R<sup>2</sup>|0.265|0.265|0.265|0.268|0.268|0.268|0.333|0.334|0.334|0.228|0.228|0.228|

_Source:_ World Bank.

_Note:_ Results are from a weighted regression such that each household is assigned its survey-specific population weight. Countries and years included are Ethiopia (2011, 2016) and Mozambique (2014). Dependent variable is the log of per capita (or adult equivalent) consumption. Other variables included and not shown are education of household head, gender of household head, whether the household location is remote, whether the household was surveyed during the lean season, survey year, country, country x survey year, and administrative fixed effects for district (Ethiopia, Lesotho) and province (Mozambique, Zimbabwe). Robust t-statistics are shown in parenthesis. Significance level: * = 10 percent, ** = 5 percent, *** = 1 percent.

27
=B +BX R (R Zz =W (R ((R ~~DD|~~
|Maize(GS)|32%|29%|23%|36%|
|---|---|---|---|---|
|Highland(GS)|23%|27%|33%|29%|
|Roots and lowland(GS)|9%|7%|42%|23%|
|Agropastoral(RS)|35%|28%||28%|
|Pastoral(RS)|40%|36%||27%|

_Source:_ World Bank.

_Note:_ NDVI = Normalized Difference Vegetation Index; SPEI = Standardized Precipitation Evapotranspiration Index; GS = growing season; RS = rainy season.

To assess whether the extreme values of the hazards are within or outside the range of hazards experienced by households within the districts and years used, we assessed the percentage of households in a given livelihood zone that experienced a hazard value more than two standard deviations lower than the mean or more than three standard deviations lower than the mean. The results for soil moisture for maize, highland and roots and lowland livelihood zones and for NDVI for agropastorals and pastorals are shown in table 5.2. Assessing the common support between the range of possible hazards and those used in estimating coefficients 2 and 3 can help address concerns regarding the plausibility of the welfare impact predictions that use the fixed effects estimates. In sum, while moderate deviations in rainfall are well reflected in the data used to estimate 2 and 3 , more extreme deviations are less well reflected in the ββ̂ ββ̂ data. ββ̂ ββ̂

**Table 5.2. Share of households with an extreme hazard outcome for soil moisture**

|**Livelihood zone**|**Hazard z-score < -3**|**Hazard z-score < -2**|**Negative hazard z-score**|
|---|---|---|---|
|Soil moisture (GS)||||
|Maize|0|0.01|0.63|
|Highland|0|0.05|0.64|
|Roots and lowland|0|0.03|0.63|
|NDVI (RS)||||
|Agropastoral|0|0.00|0.40|
|Pastoral|0|0.01|0.38|

_Source:_ World Bank. _Note:_ GS = growing season; RS = rainy season. We generated the alternate draws of the hazard distribution, k , a in two ways. The first used the historical weather distribution to select k for all households. This provided a first assessment of what an EP curve would look like but is based on a limited set of historical data points—in the case of soil moisture, only 13 years of data. The second way RR used the data set of 10,000 possible weather simulations for Malawi developed by the risk modeling firm AIR, which RR was based on the historical pattern of rainfall in Malawi. This catalog is available only for Malawi but suggests the degree of precision that modeling the weather offers as compared to using historical weather data. The generated k are used with parameter estimates from tables 4.1 to 4.5 to simulate what consumption would be for each household under these weather conditions. Once consumption has been simulated for a given draw of the weather, variables that describe the simulated consumption distribution can be generated. We focus particularly on: (i) RR the poverty headcount rate—the share of households whose simulated consumption falls below the extreme poverty line of $1.90—and (ii) the total poverty gap—the difference between consumption and the $1.90 poverty line added up for all households whose consumption falls below the poverty line.

The increase in the poverty rate and total poverty gap for eight of the nine countries included in this analysis are shown in figures 5.1 and 5.2. Niger was not included given the low percentage of the population in livelihood zones for which there are robust results. Each country comprises more than one livelihood zone, so each country draws on more than one set of parameter estimates. For the simulation results, the linear relationship is used with the soil moisture hazard for countries with growing season. For Mauritania we use the rainy season NDVI. The linear model was chosen 29
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revealed the limits of using standardized data sets in seeking to understand the heterogeneity of drought impacts across household types.

We find that consumption is reduced by 10-20 percent in the worst weather observations in our surveys (corresponding to about a 1 in 10-year drought event). We use the estimated vulnerability functions and the full hazard distribution in each household location to calculate the cost drought poses to welfare outcomes. The results indicate that risk is large. Poverty is 1–12 percent higher under the worst weather conditions relative to the best conditions observed in the last 13 years. This amounts to an increase in the total national poverty gap that ranges from US$4 million to US$2.4 billion (2011 PPP) across countries. Estimates are more precise for countries with a large share of production in maize, highland and pastoral areas. Potential biases in estimating impacts mean this is likely an underestimate of the true cost.

The cost of weather shocks on welfare provides an indication of the size of the increased need that would need to be met by adaptive social protection systems or access to financial services. The cost of weather shocks on consumption could be reduced by investments in adaptation policies such as soil management and tree cover or by other adaptive farming techniques. Investments in development that enable households to switch into less rainfall-dependent economic activities, either when droughts occur or as part of broader structural transformation, would also reduce the welfare cost of drought. Further work is needed to estimate how different investments would reduce the welfare cost of drought. This type of work is needed to help prioritize investments.

Statistical analyses that rely only on observed historical data are generally limited by their short observation periods. In the context of drought risk, patterns and severity of future drought events might differ from what has been observed historically. Stochastic data sets provide a synthetic view of all events that could occur in a given year, together with their likelihood of occurring. These data sets typically allow for a more reliable analysis of drought risk, especially for events that occur less frequently. Use of a stochastic data set for Malawi showed how such an analysis can be carried out, but further work is needed to produce and use more reliable analyses of spatial and temporal correlations of drought hazard. A further extension of this work would incorporate climate trends into the analysis of welfare impacts in order to estimate the costs of longer-run welfare impacts (Baquie and Foucault 2023).

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- Hill, Ruth, and Carolina Mejia-Mantilla. 2017. With a Little Help: Shocks, Agricultural Income, and Welfare in Uganda. Policy Research Working Papers. The World Bank. https://doi.org/10.1596/1813-9450-7935.

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# Appendix A. Exposure Data

The exposure data layers are static inputs for the drought/welfare modeling exercise that are fixed in analysis, unlike hazard components. These exposure data layers contain information relating to various spatial characteristics as set out in table A.1.

**Table A.1. Information on exposure data**

|**Data set**|**Description**|**Source and shape files**|**Citation**|
|---|---|---|---|
|Uniform<br>Resolution Grid<br>(URG)|A country x, y grid (w|here extents are buffered to 2° from countr|y boundary).|
|World Bank –<br>country<br>administrative<br>boundaries|World Bank–approved administrative<br>boundaries (Admin0) (and polygons) including<br>international boundaries, disputed areas,<br>coastlines,and lakes.|https://datacatalog.worldbank.org/datas<br>et/world-bank-official-boundaries|World Bank Basemap Collection,<br>February 2020.|
|GADM – Database<br>of Global<br>Administrative<br>Areas (Admin0–<br>Admin6)|GADM is a database of the location of the<br>world's administrative areas (boundaries).<br>Administrative areas in this database include<br>countries, counties, departments, etc. and cover<br>every country in the world. For each area some<br>attributes are provided, including the name and<br>in some cases variant names.|https://biogeo.ucdavis.edu/data/gadm3.<br>6/gadm36_shp.zip|Global Administrative Areas. 2012.<br>GADM database of Global<br>Administrative Areas, version 2.0.|
|GAUL – Global<br>Administrative<br>Unit Layers<br>(Gaul0–Gaul1)|Information is provided at two spatial levels:<br>national (Gaul0) and subnational (Gaul1). The<br>reference spatial layers are derived from the<br>GAUL data set, implemented by the UN Food<br>and Agriculture Organization (FAO) within the<br>CountrySTAT and Agricultural Market<br>Information System(AMIS) projects.|https://data.europa.eu/euodp/en/data/<br>dataset/jrc-10112-<br>10004/resource/609a472e-7e26-4b63-<br>8003-17298cb45e2a<br>https://mars.jrc.ec.europa.eu/asap/files/<br>gaul1_asap.zip|Europa.EU<br>http://data.europa.eu/eli/dec/2011/8<br>33/oj.|
|Crop coverage –<br>Copernicus Global<br>Land Cover Layers|Mapped crop coverage data layer (2019<br>vintage).|https://land.copernicus.eu/global/produ<br>cts/lc|Buchhorn, M., B. Smets, L. Bertels, B.<br>De Roo, M. Lesiv, N.-E. Tsendbazar, M.<br>Herold, and S. Fritz. Copernicus Global<br>Land Service: Land Cover 100m:<br>Collection 3: epoch 2019: Globe 2020.|
|Population – GHS-<br>POP R2019A|This spatial raster data set depicts the<br>distribution of population, expressed as the<br>number ofpeopleper cell.|https://ghsl.jrc.ec.europa.eu/ghs_pop20<br>19.php|GHS population grid multi-temporal<br>(1975–1990–2000–2015).|

36
|Travel Time to<br>Markets –<br>International Food<br>Policy Research<br>Institute (IFPRI)|The data set includes five data layers<br>representing travel time to the nearest market<br>of five sizes (population of 20,000, 50,000,<br>100,000, 250,000, and 500,000) respectively, on<br>five arc-minute grids (~9 km) across SSA (2016-<br>01-29).|https://dataverse.harvard.edu/file.xhtml<br>?persistentId=doi:10.7910/DVN/YKDWJD<br>/UFOGZS&version=2.2|HarvestChoice, International Food<br>Policy Research Institute (IFPRI). 2016.<br>“Travel Time to Markets in Africa<br>South of the Sahara.”<br>https://doi.org/10.7910/DVN/YKDWJD<br>,Harvard Dataverse,V2.|
|---|---|---|---|
|Global Agro-<br>Ecological Zones<br>(GAEZ)|GAEZ generates large databases of (i) natural<br>resource endowments relevant for agricultural<br>uses; (ii) spatially detailed results of individual<br>land utilization type assessments in terms of<br>suitability and attainable yields; (iii) spatially<br>detailed results of estimate/actual yields of main<br>food and fiber commodities for all rain-fed and<br>irrigated cultivated areas; and (iv) spatially<br>detailed yield and production gaps, also for main<br>food and fiber commodities.|http://pure.iiasa.ac.at/id/eprint/13290|Fischer, G., F. O. Nachtergaele, S<br>Prieler, E. Teixeira, G. Toth, H. van<br>Velthuizen, L. Verelst, and D. Wiberg.<br>2012._Global Agro-Ecological Zones_<br>_(GAEZ v 3.0)—Model Documentation_.<br>Laxenburg, Austria: IIASA<br>(International Institute for Applied<br>Systems Analysis) and Rome, Italy:<br>FAO.|
|Livelihood zones|Map of farming systems in Africa in 2015. The<br>farming systems analysis integrates an extensive<br>range of spatial data, administrative statistics,<br>assessment reports, and expert knowledge in<br>order to update the African component of the<br>2001 FAO/World Bank farming systems analysis.<br>Data sources include GAEZ FAO/IIASA, FAOSTAT,<br>and HarvestChoice.|Personal copy of data from Christopher<br>M. Auricht(https://auricht.com/)|Dixon, John, Dennis P. Garrity, Jean-<br>Marc Boffa, Timothy O. Williams,<br>Tilahun Amede, Christopher Auricht,<br>Rosemary Lott, and George Mburathi,<br>eds. 2019._Farming Systems and Food_<br>_Security in Africa: Priorities for Science_<br>_and Policy Under Global Change._<br>Routledge.(See figure 2.2b.)|

_Source:_ World Bank compilation.

# Appendix B. Hazard Data

**Table B.1. Information on hazard data**

||**ERA5**|**CHIRPS**|**SPEI**|**WRSI**|**SWI10**|**NDVI**|
|---|---|---|---|---|---|---|
|**Hazard**<br>**measure**|Precipitation<br>(modeled)|Precipitation|Evapotranspiration|Availability of water for<br>crops|Soil moisture|Vegetation<br>(greenness)|
|Full name|European Centre for<br>Medium-Range<br>Weather Forecasts<br>(ECMWF) Reanalysis<br>5th Generation|Climate Hazards Group<br>InfraRed Precipitation<br>with Station data|Standardized<br>Precipitation-<br>Evapotranspiration<br>Index|Water Requirement<br>Satisfaction Index|Average of Soil Water<br>Index over a 10-day<br>period|Normalized<br>Difference Vegetation<br>Index|

37
|Description|ERA5 climate<br>reanalysis gives a<br>numerical<br>description of the<br>recent climate,<br>produced by<br>combining models<br>with observations.<br>Total precipitation is<br>the accumulated<br>liquid and frozen<br>water, comprising<br>rain and snow, that<br>falls to the Earth’s<br>surface. It is the sum<br>of large-scale<br>precipitation and<br>convective<br>precipitation.|The CHIRPS data<br>archive is a quasi-<br>global (50S–50N)<br>gridded 0.05°<br>resolution times series<br>covering precipitation<br>from 1981 to near-real<br>time.|The SPEI is a multi-<br>scalar drought index<br>based on climatic data.<br>It is a ratio of actual to<br>potential<br>evapotranspiration.|This spatially explicit<br>index is an indicator of<br>crop performance<br>based on the<br>availability of water to<br>the crop during a<br>growing season.|The Soil Water Index<br>quantifies the<br>moisture condition at<br>various depths in the<br>soil. It is mainly driven<br>by precipitation via<br>the process of<br>infiltration. Various t-<br>values are available: 1,<br>5, 10, 15, 20, 40, 60,<br>100. The T- value<br>simulates the<br>infiltration time into<br>deeper soil layers and<br>hence indicates<br>qualitatively the depth<br>of the SWI estimate.<br>T40 was selected as<br>being generally<br>representative, based<br>on expert advice.|The Terra Moderate<br>Resolution Imaging<br>Spectroradiometer<br>(MODIS) Vegetation<br>Indices Monthly<br>(MOD13C2) Version<br>6.1 product provides<br>a vegetation index<br>value at a per pixel<br>basis. The NDVI is<br>referred to as the<br>continuity index to<br>the existing National<br>Oceanic and<br>Atmospheric<br>Administration<br>Advanced Very High<br>Resolution<br>Radiometer (NOAA-<br>AVHRR)-derived<br>NDVI.|
|---|---|---|---|---|---|---|
|Temporal<br>coverage|1979 to present|1981 to near-real time<br>precipitation time<br>series|1901–2018|2000–2021|2007–2021|2000–2021|
|Spatial coverage|Global|Global|Global|Regional|Global|Global|
|Resolution|Reanalysis: 0.25°<br>(~28 km)|0.05° (~5.5 km)|0.5° (~5.5 km)|0.1° (~11 km)|0.1° (~11 km)|0.5° (~5.5 km)|
|Output<br>information|24-hour aggregation<br>since the beginning<br>of the forecast|mm/per unit of time|Z-values, monthly|WRSI per raster cell;<br>current WRSI data give<br>range of 0–100 percent<br>of total|An index describing<br>the relation between<br>surface soil moisture<br>and profile soil<br>moisture as a function<br>of time(percent)|Vegetation density,<br>monthly|
|Data set source|https://cds.climate.c<br>opernicus.eu/cdsapp<br>#!/dataset/reanalysi|https://data.chc.ucsb.e<br>du/products/CHIRPS-<br>2.0/africa_dekad/tifs/|https://spei.csic.es/|https://edcftp.cr.usgs.g<br>ov/project/fews/dekad<br>al/|https://land.copernicu<br>s.eu/global/products/s<br>wi|https://lpdaac.usgs.g<br>ov/products/mod13c<br>2v061/|

38
||s-era5-single-<br>levels?tab=overview|||https://earlywarning.us<br>gs.gov/fews/product/1<br>28|||
|---|---|---|---|---|---|---|
|Data set<br>reference/citati<br>on|Hersbach, H., B. Bell,<br>P. Berrisford, G.<br>Biavati, A. Horányi, J.<br>Muñoz Sabater, J.<br>Nicolas, C. Peubey,<br>R. Radu, I. Rozum, D.<br>Schepers, A.<br>Simmons, C. Soci, D.<br>Dee, and J.-N.<br>Thépaut. 2018.<br>“ERA5 Hourly Data<br>on Single Levels<br>from 1979 to<br>Present.” Copernicus<br>Climate Change<br>Service (C3S) Climate<br>Data Store (CDS).|Funk, C.C., P. J.<br>Peterson, M. F.<br>Landsfeld, D. H.<br>Pedreros, J. P. Verdin,<br>J. D. Rowland, B. E.<br>Romero, G. J. Husak, J.<br>C. Michaelsen, and A.<br>P. Verdin. 2014. “A<br>Quasi-Global<br>Precipitation Time<br>Series for Drought<br>monitoring.” US<br>Geological Survey Data<br>Series 832, ftp://chg-<br>ftpout.geog.ucsb.edu/<br>pub/org/chg/products/<br>CHIRPS-<br>2.0/docs/USGS-<br>DS832.CHIRPS.pdf.|Sergio M. Vicente-<br>Serrano, Instituto<br>Pirenaico de Ecología,<br>Zaragoza, Spain.<br>Santiago Beguería,<br>Estación Experimental<br>de Aula Dei, Zaragoza,<br>Spain.|Verdin, J., and R. Klaver.<br>2002. “Grid-cell-based<br>Crop Water Accounting<br>for the Famine Early<br>Warning System.”<br>_Hydrological Processes_<br>16 (8): 1617–30. DOI:<br>10.1002/hyp.1025.|Copernicus Service<br>information 2018.|Didan, K. 2021.<br>MODIS/Terra<br>Vegetation Indices<br>Monthly L3 Global<br>0.05Deg CMG V061<br>[data set]. NASA<br>EOSDIS Land<br>Processes DAAC.<br>Accessed 2021-06-24<br>from<br>https://doi.org/10.50<br>67/MODIS/MOD13C2.<br>061.|
|Additional<br>information/<br>notes||||Range of WRSI values:<br>< 50: Failure<br>50–60: Poor<br>60–80: Mediocre<br>80–95: Average<br>95–99: Good<br>99–100: Very Good<br>0: N/A<br>The following values<br>are flags (and not<br>specific WRSI values in<br>the normal range 0–<br>100):<br>253: No start (late)<br>254: Yet to start|||

39
_Source:_ World Bank compilation.

Table B.2. Definitions used for household descriptive variables from country surveys

|**Country**|**Land ownership (0 if none, 1 if any)**|**Education**|
|---|---|---|
|Ethiopia|Ownership of land plots|Literacy|
|Lesotho|Ownership or cultivation of land|Level: primary complete|
|Malawi|Land area cultivated|Can read and write|
|Mauritania|Hectares owned|Literacy|
|Mozambique|Number of plots|Can read and write|
|Niger|Land area cultivated|Level: any|
|Nigeria|Land area cultivated|Level: primary complete|
|Zambia|Land area cultivated|Level: primary complete|
|Zimbabwe|Ownership of any arable land|Level: primary complete|

# _Source:_ World Bank.

_Note:_ Country-specific definitions for land ownership and education are based on survey information.

40
# Appendix C. Hazard Simulations

The Centre for Disaster Protection and the World Bank asked Verisk’s AIR Worldwide (AIR) to develop a series of stochastic catalogs of relevant climate variables in Malawi. These would support the ongoing effort to develop a standardized approach to ex ante estimation of the welfare impacts of moderate and severe droughts in SSA, complementing the ongoing empirical analysis. The catalogs would allow a forward-looking assessment of possible future events that goes beyond the reliance on the history of past events (i.e., would allow a more robust probabilistic view of future events).

AIR’s methodology, data sources (table C.1), data validation, and results are set out in Blanchard and Sousa (2021) and summarized below, with extracts largely taken directly from the paper.

## **Developing the Stochastic Catalogs for Malawi**

Under the scope of this project, AIR developed stochastic catalogs of three drought-related variables for Malawi— precipitation, soil moisture, and vegetation index.

The 10,000-year stochastic catalog produced for each variable includes 10,000 samples of annual time histories for the variable of interest, which all reflect conditions that are likely under the current (and near-current) climate.

**Table C.1. Data sets used to generate the stochastic catalogs**

|**Variable**|**Description**|**Data set**|**Resolution,**<br>**frequency,**<br>**period covered**|**Source**|
|---|---|---|---|---|
|Atmospheric<br>moisture|Atmospheric<br>reanalysis of the<br>global climate|ECMWF Reanalysis<br>v5 (ERA5)|0.25°, three-<br>hourly, 1979–<br>2018|ECMWF|
|Precipitation|Atmospheric<br>precipitation<br>estimates from<br>rain gauge and<br>satellite<br>observations|CHIRPS 2.0|0.05°, dekadal<br>(10-day), 2000–<br>2020|CHIRPS|
|Soil moisture|Soil Water Index<br>(SWI) at a depth of<br>40 cm|SWI10-40|0.1°, dekadal,<br>2007–present|Copernicus Global<br>Land Service|
|Vegetation index|Normalized<br>Difference<br>Vegetation Index|MOD13C2 Version 6|0.05°, monthly,<br>2000–2020|MODIS|

_Source:_ Blanchard and Sousa 2021.

_Note:_ CHIRPS = Climate Hazards Group InfraRed Precipitation with Station; ECMWF = <mark>European Centre for Medium-Range Weather Forecasts;</mark> MODIS = Terra Moderate Resolution Imaging Spectroradiometer.

The approach is based on random sampling of stochastic perturbations of historical data to generate stochastic realizations of precipitation values over Malawi. The stochastic catalogs of NVDI and SWI are then derived from the stochastic precipitation catalog.

More specifically, the 10,000-year stochastic precipitation catalog has a spatial resolution of 0.05° and dekadal temporal resolution. It was developed using random sampling of stochastic perturbations of atmospheric moisture data (ERA5 [( <mark>European Centre for Medium-Range Weather Forecasts)</mark> Reanalysis v5]) between 1979 and 2018, at a native resolution of 0.25° and three-hour intervals (as an input to the process). While CHIRPS data could not be used in place of ERA5 at the modeling stage, they were used to augment a climatological adjustment to reflect “real” rainfall readings and climatology compared to ERA5.

41
The result is 250 independent stochastic realizations of what a 40-year precipitation time series might be. The pseudo-precipitation values generated based on ERA5 (prior to the adjustment for CHIRPS) were subsequently used to generate SWI and NDVI catalogs using empirical correlations known to exist between precipitation and these two variables to develop statistical relationships. Each stochastic realization of NDVI and SWI was thus obtained from (and consistent with) the stochastic realizations of precipitation.

# **Validation**

Stochastic catalogs are designed to provide a view of hazard that goes beyond the data available in the historical record. In developing such catalogs, care must be exercised to avoid compromising the ability to realistically represent the physical processes governing the natural phenomena being modeled.

Several diagnostic figures were generated using the rainfall catalog to show that the catalog created statistically robust stochastic realizations. Specifically, these realizations (i) preserved the intrinsic properties in terms of spatial and temporal correlations; (ii) were consistent with the empirical distributions of precipitation at each individual location; and (iii) produced a realistic view of hazard, consistent with historical observations while allowing for the creation of new extremes.

Validation diagnostics included several comparisons:

- The synthetic rainfall time series was compared with historical data (CHIRPS satellite rainfall data and gauge rainfall data), across different spatial aggregations; this included comparing the distribution of monthly rainfall averages for each month in the stochastic catalog (figure C.1) with the CHIRPS data set. The result shows that the stochastic catalog captures well both historical trends and an extension of the tails of the monthly distributions, suggesting the presence of previously unseen extremes and consistent with physical processes at play.

- The cumulative distribution functions (CDFs) for historical and simulated hazards were compared to assess the relationship between frequency of an event’s occurrence and its severity.

- The spatial distributions of rainfall averaged over various time scales were compared.

42
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