metadata: authors: 0: author: Baez,Javier E.
1: author: Kshirsagar,Varun
2: author: Skoufias,Emmanuel
count: Malawi,Tanzania,Mozambique,Zambia,Zimbabwe
docna: 0: docna: Adaptive Safety Nets for Rural Africa :
            Drought-Sensitive Targeting with Sparse Data
docty: Policy Research Working Paper
abstracts: cdata!: This paper combines remote-sensed data
            and individual child-, mother-, and household-level data
            from the Demographic and Health Surveys for five countries
            in Sub-Saharan Africa (Malawi, Tanzania, Mozambique, Zambia,
            and Zimbabwe) to design a prototype drought-contingent
            targeting framework that may be used in scarce-data
            contexts. To accomplish this, the paper: (i) develops simple
            and easy-to-communicate measures of drought shocks; (ii)
            shows that droughts have a large impact on child stunting in
            these five countries -- comparable, in size, to the effects
            of mother's illiteracy and a fall to a lower wealth
            quintile; and (iii) shows that, in this context, decision
            trees and logistic regressions predict stunting as
            accurately (out-of-sample) as machine learning methods that
            are not interpretable. Taken together, the analysis lends
            support to the idea that a data-driven approach may
            contribute to the design of policies that mitigate the
            impact of climate change on the world's most vulnerable populations.
geo_reg_key: 517195,517191
repnme: repnme: Adaptive Safety Nets for Rural Africa :
            Drought-Sensitive Targeting with Sparse Data
display_title: Adaptive Safety Nets for Rural
            Africa : Drought-Sensitive Targeting with Sparse Data
listing_relative_url: /research/2019/12/31602154/adaptive-safety-nets-rural-africa-drought-sensitive-targeting-sparse-data
publishtoextweb_dt: 2019-12-02T00:00:00Z
origu: EFI-AFR1-POV-Poverty and Equity (EAEPV)
no_of_pages: 59
author_keys: 0: author_key: 810339
1: author_key: 177660
model_extractions: Policy Research Working Paper 9071 Adaptive Safety Nets for Rural Africa Drought-Sensitive Targeting with Sparse Data _Javier E. Baez Varun Kshirsagar Emmanuel Skoufias_ Poverty and Equity Global Practice December 2019
Policy Research Working Paper 9071

# **Abstract**

This paper combines remote-sensed data and individual child-, mother-, and household-level data from the Demographic and Health Surveys for five countries in Sub-Saharan Africa (Malawi, Tanzania, Mozambique, Zambia, and Zimbabwe) to design a prototype drought-contingent targeting framework that may be used in scarce-data contexts. To accomplish this, the paper: (i) develops simple and easy-to-communicate measures of drought shocks; (ii) shows that droughts have a large impact on child stunting in these five countries—comparable, in size, to the effects of mother’s illiteracy and a fall to a lower wealth quintile; and (iii) shows that, in this context, decision trees and logistic regressions predict stunting as accurately (out-of-sample) as machine learning methods that are not interpretable. Taken together, the analysis lends support to the idea that a datadriven approach may contribute to the design of policies that mitigate the impact of climate change on the world’s most vulnerable populations.

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 eskoufias@worldbank.org.

_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
Adaptive Safety Nets for Rural Africa: Drought-Sensitive Targeting with Sparse Data<sup>_∗_</sup>

**Javier E. Baez**<sup>_†_</sup> **Varun Kshirsagar**<sup>_‡_</sup> **Emmanuel Skoufias**<sup>§</sup>

# **JEL CLASSIFICATION** : I32, Q54, N57

**KEY WORDS** : Poverty, Child Welfare, Climate Change, Poverty Targeting, Social Protection, Child Malnourishment, Stunting

> _∗_ This paper was funded by the World Bank’s Poverty and Equity Global Practice under its global knowledge program "Welfare Implications of Climate Change, Fragility and Conflict Risks". We would like to thank John Baffes, Molly Brown, Frank Davenport, Gary Eilerts, Chris Funk, Madhur Gautam, Sharada Ramanathan, and especially David M. Johnson for invaluable conversations. In addition, we benefited from comments from participants at presentations at the World Bank and the 2019 American Agricultural Economics Association Meetings.

> _†_ Senior Economist at the World Bank. Email: jbaez@worldbank.org

> _‡_ Independent. Email: varun.kshirsagar@gmail.com

> §Lead Economist at the World Bank. Email: eskoufias@worldbank.org
# **1 Introduction**

Rural Sub-Saharan Africa has the largest concentration of poor and deprived households in the world (World Bank (2018), Skoufias et al. (2019)). These households are particularly vulnerable to anomalous weather events.<sup>1</sup> These events are projected to increase in frequency and become more severe in a warmer world. However, policy responses to these events are often slow and large funding gaps are the norm. A transparent and data-driven early warning and monitoring framework may engender the requisite budget flexibility and responsiveness.<sup>2</sup> Yet, survey data that would inform such a framework are collected infrequently and at a considerable cost (Beegle et al. (2016), Castañeda et al. (2018)). Consequently, existing surveys need to be complemented with current data and additional analysis. Our objective is to contribute to the design of a transparent and comparable early warning framework that identifies deprived children in areas that are both data-constrained and vulnerable to the impacts of climate change.

In what follows, we develop a drought-contingent framework, for five countries in Southern Africa, that identifies children at risk of being stunted. This paper makes four contributions that may inform policies designed to mitigate the impacts that climate change has on the world’s most vulnerable populations. First, we provide a prototype of a drought-contingent targeting system for data-scarce contexts.<sup>3</sup> While several countries (c.f. Devereux and Nzabamwita (2018)) and economists (e.g. Alderman (2009), Barrett (2010), Clarke and Dercon (2016), and Hill et al. (2019)) have advocated for a standard and data-driven approach, there are few studies that provide a detailed empirical analysis of a drought-contingent targeting strategy. In this paper we build prototype droughtframeworks that are across countries because em- contingent targeting comparable they ploy standard, objective and verifiable measures of child and maternal anthropometrics, in addition to standard measures of household deprivation such as those related to housing, sanitation and education.

Second, our design is intended to assist programs in reaching beneficiaries based on

> 1See, for example, Kudamatsu et al. (2012), Alfani et al. (2019), Damania et al. (2017, Ch. 3), Wineman et al. (2017), Lentz et al. (2019), Hill and Mejia-Mantilla (2017), Baez et al. (Forthcoming), and Cooper et al. (2019). For context, see the thoughtful analysis aimed at practitioners by Hallegatte et al. (2016), and the evocative reportage by Sengupta (2018).

> 2While a consensus exists on the need for a timely, transparent and objective framework — see, for example, Alderman (2009), Barrett (2010), Clarke and Dercon (2016), Hill et al. (2019), Maxwell and Gelsdorf (2019), and especially Lentz et al. (2019) — there is little agreement on its design or implementation. de Waal (2018) argues that famines are rare and caused by conflict, which is tenuously related to weather events. We examine episodes of food insecurity, rather than famines.

> 3Our focus here is on the empirical analysis, rather than the implementation details. The latter includes a host of critical issues, including the nature of the support provided, and is outside of the scope of this paper, but is arguably more important. Interested readers may choose to begin with Del Ninno and Mills (2015) or Devereux et al. (2017).

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non-monetary measures of child well-being. This is in contrast to the large poverty targeting literature (e.g. Grosh and Baker (1995), Coady et al. (2004) and Brown et al. (2018)) that has traditionally focused on proxy-means tests that use _poverty scores_ — proxies for household income, consumption or wealth — or community-based assessments that use _ranks_ .<sup>4</sup> measures of while are in _subjective_ Monetary poverty, objective, especially noisy agrarian economies characterized by subsistence agriculture and volatile incomes (Deaton and Zaidi (2002)).<sup>5</sup> In addition, adverse impacts on children are likely to have the most serious long run consequences early in life. These impacts on children’s human capital have been found to have long-run consequences on growth at both macro and micro levels (Alderman et al. (2006), Victora et al. (2008), and Maccini and Yang (2009)). Consequently, we focus on internationally comparable measures of child malnourishment. However, as we discuss below, non-monetary measures are also associated with significant measurement errors. Therefore, we view our analysis as complementary to studies that focus on monetary measures of poverty.

Third, we use remote-sensed data to automate our categorization of both harvest cycles and drought shocks. Our measure of drought shocks — two to four successive belowaverage 10-day rainfall spells during the growing season — while not typically used by economists, is standard in the agronomy literature (e.g. Sivakumar (1992), Barron et al. (2003)). Lentz et al. (2019) use a related measure — the length of the longest dry spell — which is also commonly used in the agronomy literature, but is harder to interpret and standardize across regions and countries with differing lengths of their respective growseasons. We show that our measure is consistent with adverse on ing simple impacts stunting in all five countries that we examine. Especially given the concerns around comparability and timeliness, and the endogeneity of growing season lengths to short-term shocks (Sivakumar (1988)) and climate change (e.g. Linderholm (2006)), it is critical to use measures of growing season disturbances that are robust and standard across different countries in a region.

Fourth, we show that interpretable (white box) methods such as logistic regressions and decision trees are comparable to, in terms of out-of-sample predictive accuracy, black box machine learning methods such as random forests and gradient boosting. Further, we

> 4Community-Based Assessments are subjective and therefore susceptible to elite capture (Del Ninno and Mills (2015)). However, they may be a useful source of local knowledge that is not observable or quantifiable (Alatas et al. (2012), Karlan and Thuysbaert (2016)). Therefore, there is the potential to usefully triangulate this local knowledge with other assessments, as well as more objective information (Premand and Schnitzer (2018)). This perspective is also gaining currency in the humanitarian sector (Maxwell and Gelsdorf (2019)).

> 5In addition, because food prices are particularly volatile in remote rural regions that are likely to be the most affected by weather shocks (e.g. Brown and Kshirsagar (2015), Baffes et al. (2017), Hill and Fuje (2017), and Baez et al. (Forthcoming)), spatial and temporal price adjustments may not be sufficiently granular to adequately capture changes in the real values of household income and expenditure.

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show that conditional inference decision trees (Hothorn et al. (2006)) are almost as robust (to the introduction of additional noise in the stunting measure) as logistic regressions and random forests. In other contexts, decision trees are widely considered to be both less robust to small perturbations of the data and more prone to over-fitting, with the attendant poor out-of-sample performance (Friedman et al. (2001), Murphy (2012)).<sup>6</sup> While we show that the relative disadvantages of using decision trees are less pronounced in our context, their advantages are clear — traditional proxy-means tests based on regressions are harder to interpret and more difficult to implement in the field.

Further, regression-based proxy-means tests that are augmented to include variables that capture droughts, typically assume that droughts influence welfare in a (log) linear manner (e.g. Del Ninno and Mills (2015), Hill et al. (2019)) or with one-level of interactions (e.g. Dercon et al. (2005)). Regression-based approaches can, of course, involve complicated sets of interactions (e.g. Hill and Porter (2016) and Pape and Wollburg (2019)). However, the interpretation gets considerably more involved. We show that decision trees, which involve 4-6 levels of interactions, but with much fewer variables, predict child stunting with comparable out-of-sample accuracy.

A data-driven framework has the potential to complement expert panels, such as those that set _Integrated Food Security Phase Classification_ levels — the current global standard (Maxwell and Gelsdorf (2019)). While USAID’s FEWS NET and the UN’s FAO and WFP have achieved remarkable progress in making sophisticated remote-sensed detection and analyses of weather anomalies publicly accessible, standard approaches to estimating the _human impacts_ of these anomalies are less mature (e.g. Lentz et al. (2019)). Further, expert panels are not always immune to political influence and other sources of local and national bias. This problem is particularly acute in those contexts in which the incentives of local, national and international actors are misaligned (e.g. Alderman (2009), Clarke and Dercon (2016)).

We conduct this analysis for five southern African countries — Malawi, Mozambique, Tanzania, Zambia and Zimbabwe (Figure 1). We have six reasons for selecting these countries. First, all five countries have some segments of their rural populations engaged in subsistence agriculture. Second, stunting rates, particularly for the rural populations, are in all countries. More these countries have low scores on high five broadly, relatively the Human Development Index (see Appendix Figure 2). Third, rural economies and livelihoods in these countries may be characterized as primarily agrarian or agro-pastoral, rather than pastoral. Consequently, harvest cycles determine seasonal patterns. Fourth, in contrast to the countries closer to the equator, there is typically just one harvest cycle every

> 6These weaknesses are particularly relevant to decision trees that have small terminal nodes. The trees we estimate typically have terminal nodes that contain more than a 30 children, and often more than a 100 children.

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year in all sub-national areas of all five countries (Northern Tanzania is an exception). This simplifies the analysis. Fifth, the countries border each other and are sufficiently similar so that some pooled analysis — i.e. analysis that combines data from all five countries — is reasonable. Sixth, unlike, for example Kenya and Ethiopia, drought-contingent targeting and adaptive safety nets had not been systematically implemented during the period in which the surveys were administered.

The rest of the as follows. In addition to the main vari- paper proceeds describing ables, the next section describes the methodology we use to estimate harvest cycles and droughts. Section 3 provides estimates of the average impacts of droughts across the five countries we study, and then shows that these impacts are more pronounced for the poorest households. Section 4 describes our targeting framework and provides estimates for inclusion and exclusion errors for logistic regressions, decision trees, and decision tree ensembles (random forests and gradient boosted trees). We conclude by summarizing our results and discussing future directions.

# **2 Measuring Shocks and Outcomes in Agrarian Contexts**

## **2.1 Child Anthropometrics as a Proxy for Child Well-Being**

The first two Sustainable Development Goals (SDGs) focus on ending poverty and eliminating hunger across the world.<sup>7</sup> Cognizant of the limitations of defining poverty exclusively in monetary terms (Sen (1999), Deaton (2016)), the first goal also targets poverty in a broader sense — including non-monetary and dynamic measures. While goal 1.5 specifically emphasizes the need to " _build the resilience of the poor and those in vulnerable situations and reduce their exposure and vulnerability to climate-related extreme events_ ", precisely how this target may be measured in practice remains unclear.

Closely related, the second goal concerns ending hunger and malnutrition. Objective measures of hunger rely on caloric intake which may not be strongly correlated with nutrition. Therefore, Deaton (2010, pg. 41) recommends measuring anthropometrics, but highlights a key data limitation.

The obvious alternative is to use the anthropometric measures directly. Here there has been enormous progress, through the spread of the Demographic and Health Surveys...These surveys are as close to a gold standard as we are going to get in this area, although the irregularity of the DHS surveys makes it difficult to use them for monitoring, for example for assessing the effects of the food price crisis on the heights and weights of children.

Our study may be viewed as an attempt to address this limitation by combining existing Demographic and Health Survey (DHS) data with remote-sensed information. The

> 7https://www.un.org/sustainabledevelopment/sustainable-development-goals/

5
DHS data are used to estimate the World Health Organization (WHO) measures of malnourishment (WHO Multicentre Growth Reference Study Group and others (2006)).<sup>8</sup> Male and female growth curves and distributions of height/length -for-age, weight-for-age, and weight-for-height, are estimated by the WHO using samples of 882 children (longitudinal survey) and 6669 children (cross-section survey) from six countries (Brazil, Ghana, India, Norway, Oman and the United States). The medians and standard deviations from these distributions are used by the DHS to calculate z-scores for every child.<sup>9</sup> Children under 5, with a z-score below -2 standard deviations (with respect to their age) for a given metric are considered to be malnourished with respect to that metric.

The measurement of child anthropometrics is challenging and several caveats are worth noting.<sup>10</sup> First, it is assumed that children with similar rearing, health care, and exposure to environmental hazards will grow in exactly the same manner. This, in turn, assumes that ethnicity is not related to anthropometrics. For obvious reasons, this is complicated to delve into, but remains an assumption, rather than an established empirical fact.<sup>11</sup> However, there is some reassuring evidence that differences (between African and Indian populations) in anthropometrics that cannot be explained by income, may be explained by the disease environment (Coffey et al. (2013)) and culture (Jayachandran and Pande (2017)). Second, the measurement of a child’s age is challenging (Larsen et al. (2019)). Third, the surveys are implemented by national statistical offices with differing degrees of expertise. Taken together, these facts suggest that we should expect that any empirical analysis using these measures will involve a relatively low signal-to-noise ratio.

Our focus here is on designing a prototype drought-contingent targeting system, rather than providing a systematic analysis of the causes of stunting.<sup>12</sup> However, it is worth noting that other studies have found that stunting is not responsive to single-sector interventions.<sup>13</sup> Multi-sectoral approaches that address food availability, health and sanitation _are_ associated with reductions in stunting rates (Skoufias et al. (2019)).

In this paper, we view the prevalence of stunting as a time-varying, but lagged, sig-

- 8We use a harmonized version of the DHS Surveys constructed by Boyle et al. (2019).

> 9In the case of stunting, this entails subtracting the WHO median height from the child’s height and then dividing by the WHO standard deviation — all with reference to a particular age.

- 10See Assaf et al. (2015) for an analysis of measurement challenges and data quality concerns.

- 11If ethnicity _does_ have a role to play in influencing anthropometrics, policies that target stunted children will have hidden biases that favor some ethnicities over others.

- 12Our results speak to concerns raised by Deaton and Cartwright (2018) regarding the causal attribution of outcomes associated with interventions that are randomly implemented at different locations. We show that weather shocks are frequent and impact stunting. Therefore, shocks that occur _after_ randomization may result in the misattribution of the impacts of interventions that aim to reduce child malnourishment.

- 13For example, using sub-national data from 59 countries, Headey and Palloni (2019) found no impact of water, sanitation and hygiene variables on stunting.

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nal of child deprivation — that may usefully, when combined with remote-sensed data, inform the design of social protection and other government assistance. We do not, however, take a position regarding the precise nature of the support required to alleviate the underlying deprivation(s). Further, a weather disturbance in an agrarian context may be thought of as an additional deprivation (in the sense used by Sen (1999)), because it constrains choices and livelihood opportunities. Support triggered via an adaptive safety net should therefore not be limited to maternal and child health, but instead involve sectors most relevant to that location and country.

# **2.2 Measuring Shocks to Crop Production**

There is no consensus on the best approach to monitoring crop production in Sub-Saharan Africa. At the same time, there is broad agreement on both the challenges and the relevant sources of information. There are two related challenges to measuring crop production in these data-constrained contexts (e.g. Burke and Lobell (2017), Jin et al. (2017)). First, there is a dearth of information on actual crop yields, particularly for small-holder farmers — farmers that constitute the majority of poor households. Second, without adequate ground-truthing, analyses of high-resolution satellite data provide noisy predictions. This is exacerbated by the fact that areas under crop production are constantly changing and the mix of crops produced together is hard to classify across contexts. Consequently, it is also challenging to transfer knowledge gained in a particular context to other locations.

Therefore, organizations charged with monitoring crop production in Sub-Saharan Africa rely on remote-sensed information averaged at broader spatial scales (e.g. Funk et al. (2019)) — traditionally focusing on vegetation (e.g. Becker-Reshef et al. (2010), Brown (2014)) and rainfall (Funk et al. (2015)), both of which have longer time series than the newer measures. Unlike rainfall, the Normalized Difference Vegetation Index (Tucker (1979)) is a cumulative measure. With available ground data, as is the case in the United States, remote-sensed vegetation anomalies can be calibrated to historic crop yields to build models that provide accurate out-of-sample estimates (Johnson (2014)). However, when ground data are scarce, vegetation indices cannot be properly calibrated and less is known about the relationship with crop-productivity in particular contexts (Burke and Lobell (2017)). Rainfall, during the growing season, is unambiguously correlated with crop productivity. However, the influence of rainfall on yields depends on its timing and distribution. Therefore, aggregating rainfall estimates over a growing season can be misleading (Sivakumar (1992), Barron et al. (2003)).

Given these challenges, we employ the following strategy. First, we focus on shocks at a particular spatial scale: a country’s first administrative level (Hijmans et al. (2019)) — 7
which we refer to as a province for the rest of this paper.<sup>14</sup> Adverse weather events are typically spatially correlated, and even expected long-run changes in weather patterns, in Southern Africa and elsewhere, are expected to occur at broad spatial scales (e.g. Shongwe et al. (2009)). This choice is consistent with interpreting our shocks as being those that affect the entire local economy. Second we use Normalized Difference Vegetation Indices (NDVI) — averaged at the province x month level — to determine harvest cycles for each province. Third, we use rainfall estimates, averaged for each province, to estimate sequences of dry spells. In the rest of this section we describe our methodology and results in more detail.

# A. _Estimation of Harvest Cycles_

The NDVI data were collected by the Moderate Resolution Imaging Spectroradiometer (MODIS) sensor aboard the NASA polar orbiting satellite Terra from February 2000 to April 2019. MODIS provided an NDVI estimate every eight days at an approximately 250 meter ground sample (pixel) resolution across the entire study area. To isolate the NDVI to those areas where are the time series was ‘masked’ signal only crops expected by the Croplands and Cropland/Natural Vegetation Mosaic categories found within the IGBP land cover classification (Loveland et al. (2000)). Next, to reduce potential pixel-level noise (both in time and space) and simplify the modeling efforts, the measurements were aggregated to monthly values at a 5 kilometer grid cell size. And finally, the values were spatially and temporally averaged further to each province x month.

We identify harvest cycles — more specifically growing months, the month that a harvest starts, and the lean season — in the following algorithmic manner.<sup>15</sup> First, we calculate the percentage change in monthly NDVI. A month is labeled as a growing month if the percent increase is greater than 20 percent. Second, the start of the harvest season is defined as the first month in which the NDVI falls by at least 5 percent. Third, the lean season is defined as the three months preceding the start of the harvest season.

For a graphical illustration of the use of monthly NDVI averages to estimate harvest cycles, please refer to Figures A-1a to A-1e in the appendix. There are subtle differences in harvest cycle patterns even within a country. For example, in Mozambique (Figure A-1b), the South-Western province of Manica has a slightly earlier harvest cycle than the NorthEastern province of Nampula. In Manica, the average November NDVI is greater than

> 14These are districts in Malawi, regions in Tanzania, and provinces in Mozambique, Zambia and Zimbabwe.

> 15Our purpose is to standardize these definitions so that they can be used to build an automated (i.e. rulesbased) definition of a drought shock. This is a prototype; in practice we could use NDVI data at more disaggregate temporal frequencies, allow for differences in harvest cycles at more refined spatial scales, and incorporate other data (e.g. soil moisture) into this algorithm.

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its average for October, while for Nampula the two months are similar. Consistent with this, NDVI peaks in March in Manica, while it peaks a month later in Nampula. Unlike in temperate countries, tropical Africa has a green harvest and some local food insecurity is alleviated just after the NDVI has reached its peak.<sup>16</sup> More pronounced within-country differences are evident closer to the equator. In Tanzania (Figure A 1-c), Kilimanjaro, in the Northern Highlands, exhibits a bimodal pattern. In contrast, Iringa and Mbeya, in the Southern Highlands, have unimodal harvest cycles.<sup>17</sup> We have chosen not to use deviations from NDVI as a measure of weather averages disturbances. This is because NDVI deviations may reflect deviations in vegetation unrelated to food. However, it is essential to have a broad understanding of what harvest cycles typically look like for each province, to more accurately estimate the impacts of weather disturbances during a child’s birth season. In what follows, we use this understanding, along with rainfall data, to develop measures of drought shocks.

# B. _Identification of Dry Spells_

A consensus is yet to emerge on best-practice approaches to measuring droughts (Trenberth et al. (2014)). Soil moisture, evapotranspiration and water levels are all important. However, there are significant challenges to developing comprehensive measures for tropical Sub-Saharan Africa and other data-scarce contexts. At the same time, there is little that anomalous rainfall the season affects disagreement during growing adversely crop productivity (Funk et al. (2019)). Consistent with our overall objective, here we develop a simple and transparent approach to measuring droughts. Other than the use of the NDVI to estimate harvest cycles, the only data we use are the CHIRPS Rainfall dataset (Funk et al. (2015)).

Our algorithm involves the following steps. First, we calculate the average and standard deviations of total rainfall (in mm) for every 10-day period or decad in a given month in any given province (i.e. decad x month x province).<sup>18</sup> Second, we calculate the standardized anomalies for every decad x month x province x year. Third, we exclude all decads that are not in the growing season. Fourth, we define a dry spell of length _n_ for a given decad, as having below average rainfall in that decad, as well as the _n −_ 1 preceding decads. In addition, at least half the decads in a dry spell are required to receive less than

> 16Expert, on the ground opinion (e.g. http://fews.net/southern-africa/mozambique) is broadly consistent with these observations (scroll down to look at the seasonal calendars for South-Central and Northern Mozambique).

> 17See, for example, http://fews.net/east-africa/tanzania.

> 18The length of the last decad in a month adjusts so that it just covers the month. Consequently, decads may be compared across years.

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-0.5 standard deviations rainfall. Fifth, we define a harvest as being affected by drought if the preceding growing season contains at least one dry spell.

Our measure is designed to capture the idea that large, but infrequent, amounts of rainfall during a growing season may be consistent with close to average total rainfall during a growing season, but will still cause stress and consequently engender belowaverage harvests. In addition, this approach ensures that a dry spell is not characterized by a sequence of decads with below-average rainfall, each of which is close to the average.

Sivakumar (1992) has previously employed a very similar approach. Instead of assuming that, at least, half of the decads in a dry spell have a -0.5 standard deviation rainfall, he sets a threshold in mm (and defines a shock for different definitions of the threshold). Our approach is better suited to be used across regions in a country and across countries because we employ standardized measures.

Table 1 describes the incidence of dry spells for the five countries we study. There are differences across countries. Mozambique and Tanzania had the lowest incidences of 1-decad and 2-decad dry spells. In Mozambique a 1-decad dry spell occurred only 55 percent of the time between 2001 and 2018, while a 2-decad dry spell occurred 43 percent of the time. In contrast, Malawi exhibited the greatest occurrence of dry spells, with a 1-decad dry spell occurring 89 percent of the time and a 2-decad dry spell occurring 71 percent of the time. A 4-decad dry spell occurs rarely — less than 10 percent of the time — in 3 of the countries. Therefore, we choose a 3-decad dry spell as our main measure of drought.<sup>19</sup> When a drought is defined as occurring during a growing season with a 3-decad dry spell, 3 of the countries (Tanzania, Mozambique and Zimbabwe) experienced droughts 22 percent of the time between 2001 and 2018, while Zambia experienced droughts 32 percent of the time, and once again Malawi is the outlier with droughts occurring 45 percent of the time. Further, Mozambique and Malawi experienced greater incidences of droughts in the last decade in comparison to the previous one.

In this section, we have explained our approach to, and rationale behind, measuring child well-being and drought shocks in contexts in which data are scarce. In the next section, we establish a causal relationship between droughts and child stunting, quantify the average magnitudes of the drought impacts, and show that these impacts vary across countries and households.

> 19In the appendix (Tables A3 and A4) we show that other lengths are also consistent with significant impacts of droughts on stunting.

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# **3 Quantifying the Impact of a Drought on Stunting**

## **3.1 Relationship between Droughts and Stunting**

In what follows, we document two important characteristics of the relationship between drought shocks and child stunting. First, we show that our measures of drought shocks are causally related to stunting and other child malnourishment outcomes. Second, we show that the average magnitudes of these impacts are comparable to the impacts associated with differences in wealth status, as well as with differences in a mother’s literacy level.<sup>20</sup> It is possible that droughts occur more frequently in areas that are less developed and that are characterized by a greater prevalence of child malnourishment. The most disaggregate spatial unit in the Demographic and Health Surveys (DHS) is the cluster. This is a village or a small collection of villages. By employing cluster x month fixed effects, we control for time-invariant influences at the cluster level (such as variation in remoteness, local governance and social structures, and in agro-ecological factors such as altitude and soil quality) interacted with the factors related to the month (harvest cycles, festivals, and school calendars). The drought coefficients are identified by variation in the incidence of shocks across years.

When we discuss controlling for month effects, we refer to the month that a child was born. This is measured with error (Larsen et al. (2019)). In the appendix (see Tables A1 and A2), we show that our results are robust to removing children born at the start of the year (January and February), the end of the year (November and December), children with birth months corresponding to whole years, and including _age_ and _age_<sup>2</sup> as explanatory variables.

Table 2 describes results when child outcomes are anthropometric regressed against droughts, with cluster x month fixed effects. The sample includes rural populations of five Southern African countries (Mozambique, Malawi, Tanzania, Zimbabwe and Zambia). For the stunting regression, we control for 2,934 cluster x month fixed effects. As a first-pass estimate of the magnitude of the impact of drought shocks on the likelihood of stunting, it is useful to start with this basic set of regressions that uses wealth quintiles as the only household-level controls (Equation 1). _Sict_ measures whether a child _i_ born in cluster _c_ in year _t_ is stunted at the time of measurement. _Dct_ is a dummy variable that

> 20These are likely to be under-estimates. Responses to droughts — both systematic and ad-hoc — from national governments, international organizations, and even large non-profits, may have mitigated the impacts of previous shocks in all of the countries that we examine. In addition, there are other confounding factors that we have not adjusted for — including those related to migration, and infant and child mortality. As a robustness check, we exclude children whose families moved in the preceding 5 years before they were surveyed and show that our results are robust to this exclusion (Table A5). Further, wealth is measured at the time of the survey and not at the time of the occurrence of a drought.

11
captures whether a drought occurred in cluster _c_ during the growing months leading up to the harvest season ( _t_ ) that coincided with the child’s birth.<sup>21</sup> _Dc_ ( _t_ +1) is similar except it refers to the year after the birth year. _Wi_ is a vector of four dummy variables indicating whether the child was born in a household in one of the top four wealth quintiles (the lowest wealth quintile is the contrast variable). The month of birth x cluster fixed effect is captured by _θcm_ . _α_ is the constant. The error is clustered at the cluster level.

Wealth quintiles are relative measures and cannot be compared across countries. However, after controlling for cluster fixed effects, they may be used to estimate the relationbetween wealth status and the likelihood of for households in the same ship stunting cluster. Two points are worth noting. First, as expected, after controlling for geographic and spatial factors, differences in wealth are associated with differences in child anthropometric measures. When compared with the poorest quintile, every other quintile is significantly less likely to be stunted. Second, drought impacts are comparable to a household falling from the second wealthiest quintile to the poorest quintile. On average (for the five countries taken together), for stunting outcomes, the impact of a drought during a child’s birth season (10 percentage points) is similar to the difference between being born to a household in the poorest quintile instead of the second wealthiest quintile (8 percentage points).

While these numbers are large, three important caveats need to be kept in mind. First, there is limited variation in wealth status within a cluster. Second, the wealth quintiles are constructed (c.f. Rutstein (2015)) in a manner that suggests that this DHS wealth index is probably a very rough approximation of our idea of household wealth — in particular, no attempt is made to account for differences in the quality and price of the underlying assets, especially the two most important rural assets (land and livestock). Third, these impacts are averages across countries. However, what we would like to stress is that the magnitude of the impact of a drought on stunting is substantial, especially given that droughts (based on our definition) occur more than a fifth of the time in all five countries.

Table 3, which reports results from Equation 2 below, uses a more complete set of controls, including maternal biological factors _Mi_ — which include the mother’s height, weight and age and the birth order and the birth interval —- as well as all the assets ( _Ai_ ) that are used to construct wealth indices, instead of the quintiles of the wealth index.

> 21As discussed above, this varies by province, we use the cluster here to make the notation simpler.

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A harvest season at the time of a child’s birth here as at least one 3-decad poor (defined dry spell during the preceding growing season) is associated with a 7 percentage point increase in stunting. Forty-one percent of children under five, in this rural population, are stunted. Therefore, on average, stunting rates are approximately 16 percent higher for children born a harvest If the harvest occurs in the after a during poor year. poor year child’s birth, it is associated with a 4 percentage point increase in stunting. The effects of a drought on a child being underweight are also large. On average, 15.1 percent of children in this population are underweight. A drought causes a 3 percentage point, or 20 percent increase in the likelihood of a child being underweight.<sup>22</sup> We also report results for wasting in Table 3, however, just 5.1 percent of the children in this population are wasted, and we find no impact. A child could be stunted _and_ underweight and not wasted. 12.6 percent of the children are stunted and underweight. A drought is associated with a 3 percentage point increase in children that are both stunted and underweight. 45.2 percent of the children are malnourished based on any of the three metrics. Droughts are associated with a 6 percentage point increase for this category.<sup>23</sup> While employing cluster x month fixed effects provides evidence in favor of a causal relationship between droughts and malnourishment outcomes, the method requires a child to have at least one counter-part, meaning another child under 5 born in the same cluster and month. For the stunting regressions, this approach forces us to eliminate almost a third of our sample ( 31 percent) — 12,800 children out of 40,817 — leaving us with 28,017 observations. To increase our sample size, as well as connect our results to droughtcontingent targeting (discussed in the next section), we use province ( _θp_ ) and year ( _θy_ ) fixed effects for our main regressions.

Table 4 describes results from estimating equation 3. Coefficients are estimated using variation within provinces rather than within clusters. The magnitudes of the drought impacts are comparable to those obtained from the more stringent specifications that use cluster x month fixed effects. Similarly, they are quantitatively similar to the effects of wealth on stunting. The adverse impact of a drought during the birth season ( 6 percentage points) is comparable to a child being born to a household in the poorest wealth quintile instead of the middle wealth quintile (5 percentage points). These impacts are

> 22While it may appear that variables that have the greatest influence are the biological ones involving a mother’s height and age, the mother’s height is correlated with wealth, even within a cluster. Therefore it is difficult to separate biological and economic causes.

> 23A child is stunted (underweight) if her/his height-for-age (weight-for-age) is two standard deviations below the WHO median. A child is wasted if her/his weight-for-height is two standard deviations below the WHO median.

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even larger for droughts that occur the year after a child’s birth. The impact of a drought during the birth season is more muted for a child’s weight (measured at the time of the survey), but it is still statistically significant. Being underweight is likely to be influenced by more contemporaneous factors, while impacts on stunting are more lasting.

This method also allows us to estimate the impacts on a child being born during the lean season. The impact, on stunting, of a child born during the lean season (3 percentage points) is as consequential as the difference in a child being born into a household in the poorest quintile instead of the second poorest quintile. Once again, the likelihood of being underweight, if a child is born during the lean season, is muted (but still statistically significant).

Table 5, comparable to Table 3, uses a full set of controls, but employs province and survey year fixed effects (equation 4 below).

Once again, it is clear that the height of a child’s mother is a major influence on the likelihood of a child being stunted, even after controlling for factors correlated with household wealth and income. The magnitudes of the drought impacts are substantial, when compared to the other factors. A child has a 4 percentage point greater likelihood of being stunted if born a harvest than a normal harvest. This is double the during poor magnitude of the impact associated with having a mother that is not literate. A child born to a partially literate or illiterate mother has a 2 percentage point greater likelihood of being stunted (controlling for other wealth correlates). Similarly, other important deprivations — such as not owning livestock and not treating drinking water — are comparable to drought impacts.

Having established that average drought impacts are causal and significant, both in terms of magnitudes and p-values, it is worth examining how these impacts may vary across countries. This is possible because we can use variation in birth years. If we were trying to understand drought impacts on the diversity of a child’s diet, for example, the available data would limit us to exploiting cross-section variation.<sup>24</sup> Given that weather anomalies are spatially correlated, at different spatial scales, this would necessitate combining data from several countries and regions.

# **3.2 Impacts across Countries**

Droughts may exert differing stunting impacts in different countries, even in the case in which all the countries are in the same region. First, countries have very different so-

> 24The DHS reports nutrition intake for children between 6 and 24 months at the time of the survey.

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cial protection, nutrition and food policies. Second, countries have different historical relationships with international organizations that provide drought-contingent support. Third, countries have different social structures, which result in differences in how societies help the most vulnerable diversify risks associated with shocks. In what follows, we restrict our analysis to stunting outcomes, but it is worth keeping in mind that droughts also impact a child’s weight.

Table 6a describes stunting impacts across the five countries, in a manner that is analogous to Table 3. Specifically, we begin with the first regression in Table 3 and repeat the exercise for each of the five countries separately. With the exception of Malawi, the other four countries exhibit drought impacts that are between 5 and 12 percentage points, all of which are statistically significant. Zambia (12 percentage points) and Zimbabwe (11 percentage points) have the largest impacts. Mozambique is close to the average of the five countries (7 percentage points), and Tanzania is the smallest (5 percent points), but still large.<sup>25</sup> In contrast, a drought during the birth season in Malawi is not associated with a greater likelihood of stunting. We conjecture that there are three possible reasons for this. First, our algorithm may not capture harvest cycles as accurately for Malawi. Second, Malawi may have policies that protect children during the birth year, especially in drought years. Third, Malawi also has recurring floods. Therefore, it is possible that the drought dummy is being compared to both flood years and normal years. However, even in Malawi, droughts do exert a large and significant impact on stunting (9 percentage points) if they occur the season after a child is born.

Table 6b shows results for the same exercise in which a child’s Height for Age Z-Score (HAZ, multiplied by 100) is the dependent variable. The results are very similar. On a the birth season is associated with a 0.19 standard deviation average drought during decrease in the height for age z score. Mozambique, Zambia and Zimbabwe have impacts that are larger than the average and Tanzania and Malawi have impacts that are more muted. But once again, even for height for age, the drought impacts (for either or both the birth season or the season following the birth) are statistically significant for all five countries, even after controlling for cluster x month fixed effects.

Taken together, the results in Tables 6a and 6b support the arguments we made above regarding the causal attribution of the impact that drought shocks have on child stunting. This is encouraging from the perspective of the design of an internationally comparable drought-contingent system, because Tables 6a and 6b provide evidence in support of a causal relationship for each of the five countries. Future work will need to repeat this

> 25All five countries show similar relationships between a mother’s height and stunting, as well as a child’s age and stunting. This speaks to reasonable data quality standards across the surveys.

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exercise for other parts of the world. The Sahel region and the Horn of Africa are important regions, that are different than the countries we have examined here, in terms of both agro-ecology and governance.

# **3.3 Heterogeneous Impacts across Household Types**

Given that budgets are limited, it would be very useful for interventions that aim to mitigate the impacts of droughts to be able to identify ex-ante (at a low-cost) children in households that are most likely to be affected. While this may seem straightforward, there are both conceptual as well as measurement challenges involved. From a conceptual perspective, should interventions target children that are in the poorest households, or children close to the stunting threshold, or children with profiles that have historically exhibited the largest drought impacts?<sup>26</sup> If children that are close to the stunting threshold are also more vulnerable to drought shocks, and in the poorest households, then supporting this group of children would address all three concerns. However, as we show below, these categories may not fully overlap.

From a measurement perspective, the set of surveys that capture child anthropometrics, as well as monetary poverty measures, both of acceptable quality, is very small. The DHS data on child anthropometrics are of reasonable quality, but the surveys do not have measures. any economic We are left with using the wealth indices, which are imperfect, for reasons discussed earlier.

Brown et al. (2017) show that around half of all undernourished children and underweight females, in their sample of 30 countries in Sub-Saharan Africa, are found in the top three DHS wealth quintiles. They use this fact to infer that a large fraction of poor individuals do not live in poor households, as defined by the wealth index. While this is certainly plausible, in our view, at least part of what they attribute to intra-household inequality or local health effects could merely reflect the error associated with measuring a household’s wealth status.<sup>27</sup> In any event, the facts they document, rather than their inferences regarding those facts, are important for our purposes. Figure 2 (which excludes outliers) shows that there is significant overlap in height for age z-scores across the five wealth quintiles for all the five countries in our study. Consequently, the DHS wealth quintiles may not be a good proxy for stunting.

Wealth quintiles are, however, the best available proxy for household wealth in the

> 26The incentives of policy makers and other organizations may be consistent with approaches that meet particular targets, for example, a given reduction in stunting rates. However, the threshold of a negative 2 standard deviation difference from the median is not based on biology or economics.

> 27The data that are needed to address these issues are not available. In the future, there may be surveys that provide good quality measures of anthropometrics and economic variables.

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DHS data. Further, while they may not predict stunting accurately, the impact of a drought may vary across wealth quintiles. Figure 3-a shows the distribution of HAZ scores for the lowest quintile, contingent on a drought. Compare this with Figure 3-b, which shows the drought-contingent HAZ distributions for the top four wealth quintiles. First, the density close to the stunting threshold is higher for the lowest wealth quintile. Second, the shift leftward appears to be more pronounced for the lowest wealth quintile. Tables 7 and 8 Table 7 starts with the regression reported in Table 5 (specification 1) and estimates this regression for different sub-samples of wealth quintiles and countries. Since sample sizes are limited, we group the second and third lowest quintiles and the wealthiest two quintiles. For all the five countries taken together, the impacts are muted for the top two wealth quintiles. The top two quintiles exhibit a 1 percentage point increase in stunting, considerably smaller than the 6 percentage points impact for the bottom quintile. In Mozambique, Malawi (for the season after birth) and Tanzania, the differences in impacts across wealth quintiles are large. The magnitudes of the drought impact for the lowest quintile is more than double the impact for the wealthiest two quintiles. However, in Zimbabwe and Zambia, the drought impacts are comparable across wealth quintiles.

It may be that in Tanzania, Malawi and Mozambique, children in the wealthier quintiles have z-scores significantly above the stunting threshold, and are still vulnerable to drought shocks, even though they do not fall below the threshold. Figure 2 shows that the z-scores for children in the wealthiest quintile in these three countries are, in fact, lower than the z-scores for the comparable children in Zambia and Zimbabwe. There are smaller proportions of children in the wealthiest quintiles in Zambia and Zimbabwe below the -2 standard deviation cut-off.

Table 8, repeats the exercise reported in Table 7, except using height for age z-scores, rather than stunting outcomes as the dependent variable. The results are very similar. In Mozambique, Malawi (once again for the season after birth) and Tanzania, drought shocks are associated with larger impacts for the poorest wealth quintile compared to the wealthiest. The results are most pronounced for Mozambique — a country with large differences in agro-ecological conditions, wealth and connectivity. For the poorest quintile, a drought shock in the birth season is associated with almost half a standard deviation lower z-score (-0.465 standard deviations). In contrast, the wealthiest quintiles have no decline in z- scores (a 0.041 standard deviation increase that is not significantly different from zero). At the opposite extreme, in Zimbabwe, impacts are close to the national average (-0.29 standard deviations) regardless of wealth status.

We draw three conclusions from this exercise. First, although the data are noisy, we show that poor harvests (either during the birth season or the following season) exert a strong adverse impact on children born to households in the lowest wealth quintile in all 17
five countries. This holds true for both stunting as well as for height-for-age outcomes. Second, in four of the countries (Tanzania, a food surplus country, is the exception), children in households in the second and third lowest wealth quintile are also significantly affected by droughts. Third, we show that for the top two quintiles, the impacts vary by country. Mozambique, Tanzania and Malawi show considerably muted impacts, while Zambia and Zimbabwe have impacts that are comparable across the DHS wealth quintiles.<sup>28</sup> Taken together, this suggests that while the impacts of droughts are most pronounced for the lowest wealth quintile (which corresponds to what practitioners refer to as the ultra-poor population), broader segments of the rural populations of all five countries are affected by droughts.

# **4 Pragmatic Drought-Contingent Targeting Strategy**

While machine learning applications to early warning frameworks, and poverty targeting more generally, hold considerable promise — particularly when timeliness and accuracy are critical — the majority of these approaches are not interpretable. Our contribution here is to emphasize the value of simple approaches in contexts that are both controversial and uncertain. Baumol and Quandt (1964) provide a useful characterization of four necessary attributes for _optimally imperfect decisions_ : i) objectively measurable inputs and outputs; ii) objectively communicable decision criteria and an absence of human judgment; iii) a unique and deterministic mapping of inputs to decisions; and iv) decision algorithms that involve inexpensive and verifiable calculations.

It is worth examining a poverty targeting framework from this perspective. McBride and Nichols (2016) seminal application of machine learning to poverty targeting is the first to use an approach that is explicitly designed to improve out-of-sample prediction. However, along with Sohnesen and Stender (2017), they employ a black-box random forest methodology.<sup>29</sup> Mark Schreiner’s insightful and widely-used approach to designing proxy-means tests (e.g. Schreiner (2007), Schreiner (2008)) emphasizes interpretability and ease-of-use, in addition to out-of-sample performance. However, as Diamond et al. (2016) argue, his approach is not based on well-understood statistical methods and, while it does well on

> 28These results may be complemented by surveys that contain more information on wealth, income and consumption to better understand the reasons for these differences. For example, we are unable to separate the mechanisms through which drought shocks impact stunting. Possible channels involve crop income, farm labor and market prices. Further, there are social and economic channels through which shocks could be mitigated. In Zambia, different from the other countries, the mining industry provides a critical source of income and employment for several local economies.

> 29These exercises are done in the context of monetary poverty targeting, which involves a larger number of explanatory variables and a higher signal-to-noise ratio than our context.

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average, its out-of-sample performance is less satisfactory for different parts of a country. Kshirsagar et al. (2017) combine penalized (regularized) regressions with sub-sampling (stability selection) to develop monetary poverty measurement tools that are both interpretable and relevant across a diverse country. This is more useful for constructing monetary poverty PMTs because there are a larger number of candidate explanatory variables.

In what follows, we train commonly used black box machine learning methods (Random Forests and Gradient Boosting) and compare these with logistic regressions and decision trees. The black box methods we use are among the most successful prediction methods for tabular data (Friedman et al. (2001)). We train the models by optimizing hyper-parameters based on the out-of-sample log-loss (cross-entropy) metric using 10fold cross-validation.<sup>30</sup> We test these models using a validation data set that was not used to train the model.

Table 9 summarizes results for the four predictions models. The results are similar for all five countries. Logistic Regressions, Random Forests and Gradient Boosting have almost identical out-of-sample performance. In the context of monetary poverty, Caire and Schreiner (2013) and Brown et al. (2018) argue that objective functions are flat for a range of parameters around the optimum, and therefore more sophisticated prediction methods may not improve the out-of-sample performance of a proxy-means test. With respect to our particular context, the results summarized in Table 9 (and Table 10, discussed below) provide unambiguous support for this hypothesis.<sup>31</sup> Table 9 shows that classification trees are only slightly less accurate than the other methods.<sup>32</sup> Interpreting differences in log-loss measures is less useful than directly estimating out-of-sample targeting errors. However, these errors cannot be summarized by one number, and depend on a government’s (or an organization’s) budget. At one extreme, a government may be able to afford to reach every child. In which case, the proportion of poor children that are excluded from the intervention (i.e. the exclusion error) will be zero. However, the proportion of non-poor children that are included in the intervention (i.e. the inclusion error) will be 1. At the other extreme, if the government does not reach a single child, the exclusion error will be 1 and the inclusion error will be zero. Typically governments and organizations do not have the requisite budgets to reach every single child.

The out-of sample targeting errors are estimated using these four steps. First, data on children in the training set are used to build the model and children in the test set are then

> 30 <u>1</u> For our binary classification problem this is _− N_<sup>∑[</sup><sup>_Silog_(</sup><sup>_pi_) + (1</sup><sup>_−Si_)</sup><sup>_log_(1</sup><sup>_−pi_)]. Where</sup><sup>_Si_is the dummy</sup> capturing whether child _i_ is stunted and _pi_ is the predicted probability that the child is stunted.

> 31In the appendix we show that this is also true for predictions of height for age z-scores (see Table A7).

> 32In the appendix (Table A6) we show that this remains true even after introducing a zero mean and one standard deviation noise term into the height-age z-scores for children in the training set.

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ranked based on the predicted (out-of-sample) probability of not being stunted. Second, for a budget of b, a child is included if the percentile is less than b. Third, this inclusion status is compared with the actual stunting dummy. Fourth, we calculate inclusion and exclusion errors. This exercise is repeated for different budgets.

Table 10 reports out-of-sample inclusion and exclusion errors for different budgets - in which 20, 30, 40, 50 and 60 percent of the children are reached. We draw three conclusions. First, the results are almost identical for logistic regressions, boosting and random forests. This is consistent with the almost identical log-loss measures. At the same time, the predictions from the three models are not perfectly correlated, with correlations typically ranging from 0.85 to 0.95. This suggests the possibility of combining these into an ensemble model that may improve out-of-sample predictive accuracy (Friedman et al. (2001)). We do not pursue this direction in this paper, because our focus is on interpretability.

Second, the methods have explanatory power, although there are errors in exclusion and inclusion. A PMT constructed using a logistic regression, with a budget consistent with reaching 60 percent of the children, will exclude between 24 and 29 percent of stunted children, while also including between 50 and 53 percent of non-stunted children. Therefore, when combined with geographic targeting or a community-based assessment, a quantitative framework designed using these methods will add substantial value to the targeting of an intervention.

Third, and perhaps most usefully for a practitioner, decision trees have comparable out-of-sample performance. Decision trees are easy to interpret and typically involve fewer variables. As such, these trees provide data-driven rules of thumb that are free from the cognitive biases typically associated with heuristics (Tversky and Kahneman (1974)). Further, even compared to logistic regressions, they are much easier to implement in the field. However, practitioners would be limited to a certain number of budget choices, because the predictions depend on the number of terminal nodes, and are therefore discontinuous.

For example, in Mozambique, a budget consistent with reaching 62 percent of the children is consistent with excluding 26 percent of stunted children and including 52 percent of non-stunted children (Table 10). This is comparable to a logistic regression used to reach 60 percent of the children. However, if the government has a smaller budget, it would need to reach just 28 percent of the households. The exclusion errors (63 vs 59) and inclusion errors (21 vs 22) are comparable to a method informed by a logistic regression that reaches 30 percent of the children.

Continuing with Mozambique, Figure 4 illustrates an example decision tree. Zones (i.e. Provinces) 1-6 are in Central and Northern Mozambique.<sup>33</sup> The tree in Figure 4

> 33These are Cabdo Delgado, Niassa, Nampula, Zambezia, Tete and Manica.

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shows that droughts most affect rural children who live in provinces in Northern and Central Mozambique, are above 6 months old and have mothers under 5 ft. These are the provinces that have a greater proportion of households engaged in subsistence agriculture.

Figure 5, for rural Zambia, shows that geography is less important in predicting stunting. Once again, the most vulnerable children are above 6 months old. For children with mothers who are of intermediate height ( between 5 ft and 5ft 3 inches), the drought impacts depend on household assets. In the case of children born to tall mothers (i.e. above 5ft 3 inches in height), the likelihood of stunting is, in fact, high if the mother is underweight and lives in a house with a primitive roof.

Our objective here is to demonstrate that decision trees provide several advantages over less interpretable and harder to implement targeting tools — at least in the context that we have examined. In practice, considerably more work needs to go into incorporating local information, program contexts, and geographic data into the design of a targeting tool. We believe that incorporating objective and feasible targeting tools into program design will allow resources to more efficiently reach their intended beneficiaries.

The shock-sensitive in both and do to use programs Kenya Ethiopia attempt designs informed by regressions — although successful in serving the poor, these programs have experienced challenges expanding and contracting in a state-contingent manner.<sup>34</sup>

# **5 Conclusions**

We have constructed a prototype drought-contingent targeting framework that may be used to inform the design of social safety nets in contexts in which data are scarce. To do this we address three concerns. First, we have developed measures of drought shocks that are simple, transparent and easy-to-communicate. Second, we have shown that droughts have a large impact on stunting in Southern Africa — comparable, in size, to the effects of mother’s illiteracy and in a fall to a lower wealth quintile. Third, we show that interpretable methods such as decision trees and logistic regressions predict stunting as accurately as black-box machine learning methods. Taken together, our analysis lends support to the idea that a data-driven approach may contribute to the design of policies that mitigate the impact that climate change has on the world’s most vulnerable populations.

We have focused on one particular spatial scale — a first administrative level (or province or region). Weather disturbances occur at different spatial scales. At one extreme,

> 34While several studies have documented the positive impacts of Ethiopia’s Productive Safety Net Programme (e.g. Gilligan et al. (2009)), we are not aware of a study documenting its impacts on shock mitigation. Further, Berhane et al. (2017) find that the program did not improve child nutrition outcomes — although there are no controls for weather events or other shocks.

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shocks may occur at the household or village level. At another, shocks may occur at a national or region level. A better understanding of the impacts of shocks at different spatial scales requires knowledge of how food markets operate. Weather disturbances in areas that are connected to national and international markets have a much more muted may impact compared to disturbances that occur in remote rural areas.<sup>35</sup> Further, weather disturbances in food-surplus areas may engender food scarcity in other parts of a country.<sup>36</sup> A drought-contingent targeting framework needs to incorporate this information.

While the data we have used in this study are freely available, collecting these data requires substantial public investment and capacity. Our overarching objective is to leverage nationally representative, comparable and publicly available data to construct frameworks that are transparent and straight-forward to communicate. We believe that these are essential prerequisites to designing shock-sensitive government systems that are both credible and sustainable.

> 35See, for example, Baffes et al. (2017), Hill and Fuje (2017), and Baez et al. (Forthcoming).

> 36Baffes and Kshirsagar (forthcoming) develop a quantitative approach to understanding _market systems_ in Tanzania — in particular, they identify markets that are the main suppliers of maize and rice, and markets from which demand shocks originate.

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**Table 1: The Frequency of Droughts by Country and Decade**

|||**Average I**|**ncidence of**|**Dry Spells**||
|---|---|---|---|---|---|
|**Period**|**1 Decad**|**2 Decads**|**3 Decads**|**4 Decads**|**5 Decads**|
|||**Mozambi**<br>|**que**<br>|||
|2001-2009|0.52|0.39|0.16|0.07|0.04|
|2010-2018|0.61|0.50|0.32|0.13|0.00|
|2001-2018|0.55|0.43|0.22|0.09|0.03|
|||**Malaw**<br>|**i**<br>|||
|2001-2009|0.85|0.64|0.39|0.20|0.15|
|2010-2018|0.95|0.82|0.54|0.23|0.10|
|2001-2018|0.89|0.71|0.45|0.21|0.13|
|||**Tanzan**<br>|**ia**<br>|||
|2001-2009|0.60|0.49|0.26|0.09|0.05|
|2010-2018|0.52|0.35|0.16|0.06|0.01|
|2001-2018|0.57|0.43|0.22|0.07|0.04|
|||**Zambi**<br>|**a**<br>|||
|2001-2009|0.71|0.58|0.32|0.11|0.03|
|2010-2018|0.78|0.61|0.31|0.20|0.09|
|2001-2018|0.74|0.59|0.32|0.14|0.06|
|||**Zimbab**|**we**|||
|2001-2009|0.61|0.41|0.20|0.03|0.01|
|2010-2018|0.79|0.61|0.25|0.11|0.01|
|2001-2018|0.68|0.49|0.22|0.06|0.01|

Notes: A dry spell is defined as below average rainfall (for that province x decad) for every decad in the sequence, with at least half the decads having less than -0.5 standard deviations of rainfall.

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**Table 2: Drought Impacts on Child Anthropometrics OLS with Cluster x Month Fixed Effects and Wealth Quintile Controls**

|**VARIABLES**|(1)<br>**Stunted**|(2)<br>**Underweight**|(3)<br>**Wasted**|(4)<br>**Stunted & Underwt**|(5)<br>**Any**|
|---|---|---|---|---|---|
|Drought: Birth Season|0.10***|0.04***|0.00|0.04***|0.09***|
||[8.16]|[4.01]|[0.01]|[5.11]|[7.20]|
|Drought: Season after Birth|0.10***|0.01|-0.03***|0.03***|0.07***|
||[7.41]|[1.26]|[-4.39]|[3.14]|[5.00]|
|Second Poorest|-0.03**|-0.03**|-0.01|-0.02**|-0.04***|
||[-2.31]|[-2.55]|[-0.90]|[-2.12]|[-2.99]|
|Middle|-0.03**|-0.05***|-0.01|-0.04***|-0.04***|
||[-2.20]|[-4.16]|[-0.81]|[-3.72]|[-2.63]|
|Second Richest|-0.08***|-0.07***|-0.01*|-0.07***|-0.09***|
||[-4.46]|[-5.22]|[-1.69]|[-5.25]|[-4.97]|
|Richest Quintile|-0.14***|-0.08***|-0.01|-0.07***|-0.14***|
||[-4.16]|[-4.04]|[-0.54]|[-4.11]|[-4.03]|
|Constant|0.39***|0.17***|0.06***|0.14***|0.45***|
||[41.12]|[24.47]|[15.17]|[21.39]|[46.53]|
|Observations|28,162|28,144|28,062|28,162|28,162|
|R-squared|0.43|0.40|0.40|0.40|0.42|

Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors are clustered at the DHS cluster level. All regresssions employ cluster x month fixed effects. The weights used are person weights adjusted for the national populations. All regressions use all available data on rural households from 5 Southern African countries (Mozambique, Malawi, Tanzania, Zambia and Zimbabwe). All metrics are based on children being measured below -2 standard deviation thresholds. 41.0 percent of the children are stunted, 15.1 percent are underweight, 5.1 percent are wasted, 12.6 percent are stunted and underweight, and 45.2 percent are malnourished based on any of the three metrics.

24
**Table 3: Drought Impacts on Child Anthropometrics (OLS with Cluster x Month Fixed Effects)**

|**VARIABLES**|(1)<br>**Stunted**|(2)<br>**Underweight**|(3)<br>**Wasted**|(4)<br>**Stunted &**<br>**Underwt**|(5)<br>**Any**|
|---|---|---|---|---|---|
|Drought: Birth Season|0.07***|0.03***|0.00|0.03***|0.06***|
||[5.43]|[2.95]|[0.40]|[3.96]|[4.52]|
|Drought: Season after Birth|0.04***|0.01|-0.01|0.02*|0.03**|
||[3.07]|[0.57]|[-1.28]|[1.77]|[2.43]|
|Mother ht between 152 and 160 cm|0.13***|0.06***|0.01**|0.06***|0.13***|
||[10.75]|[7.79]|[2.39]|[7.97]|[10.83]|
|Mother ht below 152 cm|0.25***|0.13***|0.01*|0.12***|0.24***|
||[17.56]|[11.00]|[1.86]|[11.53]|[16.94]|
|Mother under 19 yrs|0.05***|0.03*|-0.01|0.02*|0.05**|
||[2.72]|[1.87]|[-0.76]|[1.83]|[2.46]|
|Age:7-24 months|0.19***|0.06***|-0.01|0.07***|0.17***|
||[11.98]|[5.32]|[-1.01]|[6.44]|[10.62]|
|Age:25-59 months|0.23***|0.05***|-0.05***|0.07***|0.18***|
||[15.38]|[4.67]|[-5.86]|[6.82]|[12.27]|
|No Livestock|0.03***|0.00|0.00|0.01|0.02*|
||[2.77]|[0.33]|[0.26]|[1.19]|[1.85]|
|Does not treat water|0.03**|0.01|-0.01|0.01|0.02*|
||[2.18]|[0.88]|[-1.62]|[1.55]|[1.78]|
|Mother underweight|0.04**|0.10***|0.03***|0.08***|0.07***|
||[2.19]|[5.97]|[3.00]|[5.73]|[3.79]|
|Mother able to read part of sentence|0.01|-0.01|-0.01|-0.01|0.00|
||[0.70]|[-0.91]|[-1.30]|[-0.96]|[0.23]|
|Mother cannot read at all/Unknown|0.01|0.01|0.01**|0.00|0.02|
||[0.69]|[1.00]|[2.14]|[0.10]|[1.51]|
|Constant|-0.09**|-0.14***|0.06***|-0.16***|-0.02|
||[-2.25]|[-5.26]|[3.34]|[-6.65]|[-0.59]|
|Observations|28,017|28,152|27,987|30,057|30,057|
|R-squared|0.46|0.42|0.41|0.42|0.45|

Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors are clustered at the DHS cluster level. All regresssions employ cluster x month fixed effects. The weights used are person weights adjusted for the national populations. All regressions use all available data on rural households from 5 Southern African countries (Mozambique, Malawi, Tanzania, Zambia and Zimbabwe). Additional controls are for roof, floor and wall quality, cooking fuel, employment in agriculture, source of water, type of toilet, ownership of radio, tv, bicyles, refridgerators, cars, trucks, birth order, birth interval, gender of child and the gender of the household head. All metrics are based on children being measured below -2 standard deviation thresholds. 41.0 percent of the children are stunted, 15.1 percent are underweight, 5.1 percent are wasted, 12.6 percent are stunted and underweight, and 45.2 percent are malnourished based on any of the three metrics.

25
**Table 4: Drought Impacts on Child Anthropometrics**

**OLS with Province  and Year of Survey Fixed Effects and Wealth Quintile Controls**

|**VARIABLES**|(1)<br>**Stunted**|(2)<br>**Underweight**|(3)<br>**Wasted**|(4)<br>**Stunted &**<br>**Underwt**|(5)<br>**Any**|
|---|---|---|---|---|---|
|Drought: Birth Season|0.06***|0.02***|-0.00|0.02***|0.06***|
||[7.64]|[3.40]|[-0.39]|[4.16]|[7.19]|
|Drought: Season after Birth|0.10***|0.01**|-0.02***|0.02***|0.08***|
||[10.66]|[2.07]|[-4.50]|[3.67]|[8.77]|
|Lean Season|0.03***|0.01***|-0.00|0.02***|0.03***|
||[5.05]|[2.80]|[-1.27]|[3.21]|[4.44]|
|Second Poorest|-0.03***|-0.03***|-0.01***|-0.03***|-0.04***|
||[-3.73]|[-4.21]|[-3.33]|[-3.90]|[-4.61]|
|Middle|-0.05***|-0.05***|-0.01**|-0.05***|-0.06***|
||[-5.02]|[-7.02]|[-2.44]|[-6.71]|[-5.84]|
|Second Richest|-0.10***|-0.08***|-0.02***|-0.07***|-0.11***|
||[-8.79]|[-9.61]|[-4.01]|[-9.76]|[-9.72]|
|Richest Quintile|-0.16***|-0.10***|-0.03***|-0.09***|-0.18***|
||[-8.81]|[-8.89]|[-4.30]|[-8.36]|[-9.67]|
|Constant|0.38***|0.12***|0.05***|0.10***|0.41***|
||[9.98]|[6.34]|[3.52]|[5.48]|[11.15]|
|Observations|40,977|40,961|40,870|40,977|40,977|
|R-squared|0.04|0.02|0.01|0.02|0.04|

Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors are clustered at the DHS cluster level. All regresssions employ province and year of survey fixed effects. The weights used are person weights adjusted for the national populations. All regressions use data on rural households from 5 Southern African countries (Mozambique, Malawi, Tanzania, Zambia and Zimbabwe). All metrics are based on children being measured below -2 standard deviation thresholds. 41.0 percent of the children are stunted, 15.1 percent are underweight, 5.1 percent are wasted, 12.6 percent are stunted and underweight, and 45.2 percent are malnourished based on any of the three metrics.

26
**Table 5: Drought Impacts on Child Anthropometrics**

**OLS with Province  and Year of Survey Fixed Effects and Full Set of Controls**

|**VARIABLES**|(1)<br>**Stunted**|(2)<br>**Underweight**|(3)<br>**Wasted**|(4)<br>**Stunted &**<br>**Underwt**|(5)<br>**Any**|
|---|---|---|---|---|---|
|3 Decad Dry Spell: Birth Season|0.04***|0.01*|-0.00|0.01***|0.04***|
||[4.53]|[1.95]|[-0.20]|[2.64]|[4.43]|
|3 Decad Dry Spell: Season after Birth|0.04***|0.00|-0.00|0.01|0.04***|
||[4.33]|[0.29]|[-0.23]|[0.86]|[4.00]|
|Mother ht between 152 and 160 cm|0.12***|0.05***|0.01***|0.05***|0.12***|
||[16.21]|[10.26]|[2.63]|[10.98]|[15.99]|
|Mother ht below 152 cm|0.25***|0.11***|0.01***|0.11***|0.25***|
||[25.99]|[14.26]|[2.84]|[15.32]|[25.46]|
|Mother under 19 yrs|0.05***|0.01|-0.00|0.02*|0.05***|
||[4.28]|[1.57]|[-0.84]|[1.77]|[3.76]|
|Age:7-24 months|0.21***|0.07***|-0.01|0.07***|0.18***|
||[21.23]|[9.54]|[-1.39]|[10.44]|[17.40]|
|Age:25-59 months|0.25***|0.06***|-0.05***|0.08***|0.19***|
||[26.35]|[8.65]|[-8.91]|[11.91]|[19.52]|
|Lean Season|0.03***|0.01**|-0.00|0.01**|0.02***|
||[3.94]|[2.24]|[-0.87]|[2.55]|[3.60]|
|No Livestock|0.02**|0.00|0.00|0.00|0.02**|
||[2.53]|[0.53]|[0.83]|[0.69]|[2.35]|
|Does not treat water|0.02**|0.01*|0.00|0.01*|0.02***|
||[2.51]|[1.93]|[1.05]|[1.87]|[2.78]|
|Mother Underweight|0.07***|0.11***|0.03***|0.09***|0.09***|
||[5.80]|[9.76]|[4.39]|[8.85]|[7.39]|
|No Car, Motor, Fridge|0.04***|0.03***|0.01**|0.02***|0.05***|
||[3.56]|[3.96]|[2.43]|[3.17]|[4.47]|
|Mother able to read only part of sentence|0.02|0.01|0.00|0.01|0.02|
||[1.46]|[0.82]|[0.19]|[0.87]|[1.56]|
|Mother cannot read at all/Unknown|0.02***|0.02***|0.01**|0.01***|0.03***|
||[2.90]|[2.74]|[1.99]|[2.64]|[3.46]|
|Constant|-0.03|-0.07**|0.05***|-0.08***|0.04|
||[-0.74]|[-2.16]|[2.93]|[-2.66]|[1.00]|
|Observations|40,817|40,802|40,714|40,817|40,817|
|R-squared|0.10|0.05|0.03|0.05|0.09|

Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors are clustered at the DHS cluster level. All regresssions employ province and survey year fixed effects. Refer to the Table 3 notes for all other details.

27
**Table 6a: Drought Impacts on Child Stunting (OLS with Cluster x Month Fixed Effects)**

|**VARIABLES**|(1)<br>**All**|(2)<br>**Mozambique**|(3)<br>**Malawi**|(4)<br>**Zimbabwe**|(5)<br>**Tanzania**|(6)<br>**Zambia**|
|---|---|---|---|---|---|---|
|Drought: Birth Season|0.07***|0.07***|-0.03|0.11***|0.05***|0.12***|
||[5.43]|[2.64]|[-0.87]|[4.08]|[2.59]|[4.96]|
|Drought: Season after Birth|0.04***|0.02|0.09***|0.04|0.04*|0.05**|
||[3.07]|[0.47]|[2.62]|[1.21]|[1.84]|[2.01]|
|Mother ht between 152 and 160 cm|0.13***|0.13***|0.13***|0.11***|0.14***|0.09***|
||[10.75]|[4.66]|[3.81]|[5.40]|[7.57]|[4.12]|
|Mother ht below 152 cm|0.25***|0.24***|0.29***|0.25***|0.27***|0.21***|
||[17.56]|[7.45]|[7.49]|[7.19]|[12.08]|[7.44]|
|Mother under 19 yrs|0.05***|-0.00|-0.02|0.05|0.08**|0.02|
||[2.72]|[-0.12]|[-0.45]|[1.30]|[2.45]|[0.68]|
|Age:7-24 months|0.19***|0.15***|0.14***|0.18***|0.18***|0.25***|
||[11.98]|[3.95]|[2.63]|[5.82]|[7.33]|[8.35]|
|Age:25-59 months|0.23***|0.19***|0.18***|0.23***|0.24***|0.22***|
||[15.38]|[5.34]|[4.13]|[8.39]|[10.51]|[7.06]|
|No Livestock|0.03***|-0.01|0.02|-0.04*|0.06***|0.07***|
||[2.77]|[-0.37]|[0.58]|[-1.74]|[2.67]|[2.90]|
|Does not treat water|0.03**|0.02|0.00|0.06*|0.03**|0.00|
||[2.18]|[0.44]|[0.00]|[1.77]|[1.98]|[0.14]|
|Mother underweight|0.04**|0.11**|0.06|0.07*|0.01|0.06*|
||[2.19]|[2.43]|[1.11]|[1.71]|[0.36]|[1.78]|
|Mother able to read part of sentence|0.01|0.04|0.01|-0.00|-0.01|0.05|
||[0.70]|[0.78]|[0.20]|[-0.08]|[-0.23]|[1.43]|
|Mother cannot read at all/Unknown|0.01|0.03|0.05|0.04|-0.00|0.01|
||[0.69]|[1.04]|[1.43]|[1.16]|[-0.03]|[0.57]|
|Constant|-0.09**|-0.00|-0.22*|-0.16*|-0.12*|0.02|
||[-2.25]|[-0.01]|[-1.65]|[-1.86]|[-1.95]|[0.26]|
|Observations|28,017|5,002|3,618|4,400|9,358|5,639|
|R-squared|0.46|0.44|0.52|0.47|0.47|0.46|

Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors are clustered at the DHS cluster level. All regresssions employ cluster x month fixed effects. The weights used are person weights adjusted for the national populations. The first regression is the same as the first regression in table 3. Additional controls are for roof, floor and wall quality, cooking fuel, employment in agriculture, source of water, type of toilet, ownership of radio, tv, bicyles, refridgerators, cars, trucks, birth order, birth interval, gender of child and the gender of the household head. All metrics are based on children being measured below -2 standard deviation thresholds.

28
**Table 6b: Drought Impacts on Child HAZ*100 (OLS with Cluster x Month Fixed Effects)**

||(1)|(2)|(3)|(4)|(5)|(6)|
|---|---|---|---|---|---|---|
||All|Mozambique|Malawi|Zimbabwe|Tanzania|Zambia|
|Drought: Birth Season|-19.83***|-33.31***|8.89|-24.82***|-13.59**|-28.70***|
||[-5.13]|[-3.81]|[0.96]|[-2.80]|[-2.18]|[-3.80]|
|Drought: Season after Birth|-10.63**|5.88|-21.51**|-13.75|-11.29*|-21.15***|
||[-2.57]|[0.48]|[-2.15]|[-1.55]|[-1.79]|[-2.59]|
|Mother ht between 152 and 160 cm|-39.77***|-39.95***|-37.50***|-40.78***|-42.84***|-30.06***|
||[-11.33]|[-3.95]|[-3.69]|[-7.35]|[-8.13]|[-4.33]|
|Mother ht below 152 cm|-75.07***|-64.73***|-79.33***|-82.95***|-81.98***|-69.08***|
||[-17.79]|[-5.69]|[-7.08]|[-8.28]|[-13.29]|[-7.65]|
|Mother under 19 yrs|-21.58***|-10.72|-14.01|-8.80|-30.48***|-6.58|
||[-3.85]|[-0.84]|[-1.00]|[-0.81]|[-3.33]|[-0.59]|
|Age:7-24 months|-80.25***|-60.92***|-47.24***|-95.11***|-80.60***|-106.15***|
||[-15.05]|[-4.41]|[-3.13]|[-8.95]|[-10.32]|[-9.73]|
|Age:25-59 months|-104.15***|-88.39***|-77.60***|-119.63***|-106.90***|-112.55***|
||[-20.02]|[-6.72]|[-5.78]|[-12.35]|[-13.87]|[-10.68]|
|No Livestock|-5.55|0.21|-8.17|10.40|-1.99|-20.15***|
||[-1.43]|[0.03]|[-0.87]|[1.40]|[-0.25]|[-2.76]|
|Does not treat water|-4.07|-1.38|1.87|-22.23**|-4.64|2.66|
||[-1.16]|[-0.08]|[0.22]|[-2.46]|[-1.02]|[0.32]|
|Mother underweight|-14.36***|-35.45**|-15.26|-12.08|-8.95|-13.31|
||[-2.72]|[-2.47]|[-1.10]|[-0.86]|[-1.13]|[-1.53]|
|Mother able to read part of sentence|1.04|-7.36|-1.27|-4.08|10.68|-13.25|
||[0.20]|[-0.54]|[-0.08]|[-0.42]|[1.31]|[-1.18]|
|Mother cannot read at all/Unknown|-0.15|-6.33|-18.93*|3.45|4.48|-6.06|
||[-0.04]|[-0.64]|[-1.84]|[0.27]|[0.90]|[-0.96]|
|Constant|29.17**|22.04|9.21|29.49|48.16***|-8.48|
||[2.52]|[0.69]|[0.27]|[1.17]|[2.64]|[-0.33]|
|Observations|28,017|5,002|3,618|4,400|9,358|5,639|
|R-squared|0.49|0.47|0.56|0.51|0.49|0.48|

Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors are clustered at the DHS cluster level. All regresssions employ cluster x month fixed effects. The weights used are person weights adjusted for the national populations. The first regression is the same as the first regression in table 3. Additional controls are for roof, floor and wall quality, cooking fuel, employment in agriculture, source of water, type of toilet, ownership of radio, tv, bicyles, refridgerators, cars, trucks, birth order, birth interval, gender of child and the gender of the household head. All metrics are based on children being measured below -2 standard deviation thresholds.

29
**Table 7: Drought Impacts on Child Stunting by Country and Wealth Status OLS with Province  and Year of Survey Fixed Effects and Full Set of Controls**

||**Prob**|**ability of Stunti**|**ng (OLS with**|**Province and Su**|**rvey Year F**|**E)**|
|---|---|---|---|---|---|---|
||**All**|**Mozambique**|**Malawi**|**Zimbabwe**|**Tanzania**|**Zambia**|
|||**_Lowe_**|**_st(Poorest) W_**|**_ealthQuintile_**|||
|Drought: Birth Season|0.06***|0.11**|-0.00|0.12***|0.06**|0.09***|
||[4.79]|[2.46]|[-0.07]|[3.58]|[2.34]|[3.65]|
|Drought: Season after Birth|0.04***|0.07|0.07**|0.04|0.07**|0.00|
||[2.97]|[1.32]|[2.34]|[1.20]|[2.58]|[0.13]|
|Observations|11,605|1,517|1,941|2,179|3,302|2,666|
|||**_Second_**|**_and Third W_**|**_ealthQuintiles_**|||
|Drought: Birth Season|0.04***|0.08***|-0.00|0.09***|-0.02|0.11***|
||[3.70]|[2.84]|[-0.25]|[3.50]|[-1.16]|[5.13]|
|Drought: Season after Birth|0.04***|0.04|0.06***|0.03|0.02|0.09***|
||[4.04]|[1.09]|[3.07]|[1.27]|[0.80]|[3.55]|
|Observations|20895|3238|4097|3282|6328|3950|
||,|, <br>**_Fourth_**|, <br>**_and Richest W_**|, <br>**_ealthQuintile_**|,|,|
|Drought: Birth Season|0.01|-0.01|-0.02|0.10**|-0.00|-0.00|
||[0.31]|[-0.17]|[-0.93]|[2.05]|[-0.03]|[-0.08]|
|Drought: Season after Birth|0.03|0.04|0.03|-0.02|-0.01|0.14**|
||[1.51]|[0.70]|[1.24]|[-0.39]|[-0.29]|[2.24]|
|Observations|8,317|1,601|2,338|877|2,859|642|
|||**_Full S_**|**_ample: All We_**|**_althQuintiles_**|||
|Drought: Birth Season|0.04***|0.08***|-0.01|0.10***|0.01|0.10***|
||[4.53]|[3.32]|[-0.80]|[5.33]|[0.57]|[6.56]|
|Drought: Season after Birth|0.04***|0.05*|0.06***|0.03|0.03*|0.07***|
||[4.33]|[1.74]|[3.97]|[1.38]|[1.89]|[3.95]|
|Observations|40,817|6,356|8,376|6,338|12,489|7,258|

Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors are clustered at the DHS cluster level. This table uses the first specification in Table 5 and applies it different countries and wealth quintiles. Refer to the notes in Table 3 for all the other details.

30
**Table 8: Drought Impacts on Child Height-Age Z-Score* 100 by Country and Wealth Status OLS with Province  and Year of Survey Fixed Effects and Full Set of Controls**

||**Hei**|**ght-Age Z-Score***|**100(OLS with**|**Province and**|**Survey Year**|**FE)**|
|---|---|---|---|---|---|---|
||**All**|**Mozambique**|**Malawi**|**Zimbabwe**|**Tanzania**|**Zambia**|
|||**_Lowe_**|**_st(Poorest) W_**|**_ealthQuintile_**|||
|Drought: Birth Season|-19.62***|-46.55***|-1.27|-28.23***|-11.33|-25.00***|
||[-4.63]|[-3.33]|[-0.13]|[-2.71]|[-1.54]|[-3.18]|
|Drought: Season after Birth|-13.06***|-28.49**|-24.93***|-16.91|-17.60***|-0.81|
||[-3.32]|[-2.03]|[-2.67]|[-1.61]|[-2.64]|[-0.10]|
|Observations|11,605|1,517|1,941|2,179|3,302|2,666|
|||**_Secon_**|**_d and Third W_**|**_ealthQuintile_**|**_s_**||
|Drought: Birth Season|-10.92***|-29.02***|6.07|-28.42***|5.05|-28.70***|
||[-3.46]|[-3.50]|[0.95]|[-3.59]|[0.90]|[-3.97]|
|Drought: Season after Birth|-6.72**|7.66|-18.96***|-3.80|1.40|-23.08***|
||[-1.96]|[0.58]|[-3.06]|[-0.54]|[0.23]|[-3.26]|
|Observations|20895|3238|4097|3282|6328|3950|
||,|, <br>**_Fourt_**|, <br>**_h and Richest_**|, <br>**_WealthQuintil_**|, <br>**_e_**|,|
|Drought: Birth Season|0.42|4.15|12.55*|-35.32**|-2.92|2.72|
||[0.08]|[0.25]|[1.72]|[-2.32]|[-0.32]|[0.15]|
|Drought: Season after Birth|-14.40***|-17.93|-15.38*|-6.48|-11.66|-35.52*|
||[-2.76]|[-1.02]|[-1.91]|[-0.44]|[-1.22]|[-1.80]|
|Observations|8,317|1,601|2,338|877|2,859|642|
|||**_Full_**|**_Sample: All W_**|**_ealthQuintiles_**|||
|Drought: Birth Season|-10.73***|-31.29***|6.62|-29.02***|-0.75|-27.75***|
||[-4.22]|[-4.09]|[1.49]|[-5.28]|[-0.18]|[-5.54]|
|Drought: Season after Birth|-9.08***|-6.59|-19.23***|-7.31|-6.39|-18.34***|
||[-3.50]|[-0.70]|[-4.31]|[-1.33]|[-1.46]|[-3.38]|
|Observations|40,817|6,356|8,376|6,338|12,489|7,258|

Notes: *** p<0.01, ** p<0.05, * p<0.1. Robust standard errors are clustered at the DHS cluster level. This table uses the same specification as Table 7, except the dependent variable is the height-age Z-score.

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**Table 9: A Comparision of Out-of Sample Predictive Accuracy of Different Methods**

|**Method**|**Optimal Hyper-Parameter Values (via cross-validation)**|**Log-Loss**|
|---|---|---|
||**_Mozambique_**||
|Logistic Regression|None|0.640|
|Conditional Inference Decision Trees|Level of Significance = 0.95|0.653|
|Random Forest|Min. Node Size = 200 , Number of Var Tried = 6|0.642|
|Gradient Boosted Trees|eta = 0.05,max depth = 3,num rounds = 150,min child wt = 20|0.643|
||**_Malawi_**||
|Logistic Regression|None|0.635|
|Conditional Inference Decision Trees|Level of Significance = 0.90|0.646|
|Random Forest|Min. Node Size = 200 , Number of Var Tried = 9|0.636|
|Gradient Boosted Trees|eta = 0.05,max depth =2,num rounds = 300,min child wt = 60|0.633|
||**_Zimbabwe_**||
|Logistic Regression|None|0.592|
|Conditional Inference Decision Trees|Level of Significance = 0.95|0.597|
|Random Forest|Min. Node Size = 300 , Number of Var Tried = 10|0.592|
|Gradient Boosted Trees|eta = 0.05,max depth =2,num rounds = 150,min child wt = 10|0.591|
||**_Tanzania_**||
|Logistic Regression|None|0.616|
|Conditional Inference Decision Trees|Level of Significance = 0.95|0.644|
|Random Forest|Min. Node Size = 150 , Number of Var Tried = 8|0.617|
|Gradient Boosted Trees|eta = 0.4,max depth = 1,num rounds = 300,min child wt = 20|0.616|
||**_Zambia_**||
|Logistic Regression|None|0.645|
|Conditional Inference Decision Trees|Level of Significance = 0.90|0.655|
|Random Forest|Min. Node Size = 100 , Number of Var Tried = 5|0.640|
|Gradient Boosted Trees|eta = 0.1,max depth = 2,num rounds = 100,min child wt = 10|0.644|

Notes: The models were trained on 70 percent of each set of surveys and tested on the remaining 30 percent. The hyper-parameters were optimized using 10-fold cross-validation (log-loss metric). The table reports the optimized (i.e. minimum) log-loss for each model. The hyperparameter candidate sets are as follows. Conditional Inference Decision Trees: Bonferroni level of significance ( 0.90, 0.95). Random Forests ( R package Ranger): minimum node size (50, 100, 150, 200, 250, 300, 350), number of variables tried at each node (4, 5, 6, 7, 8, 9,10, 11, 12, 13, 14), and number of trees (1000). Gradient Boosted Trees ( R package Xgboost): shrinkage (0.05, 0.1, 0.2, 0.3, 0.4), max depth (1, 2, 3, 4), number of rounds (50, 100, 150, 200, 250, 300) and min. child weight (10, 20, 30, 40, 50, 60).

32
**Table 10:   Out-of Sample Inclusion and Exclusion Targeting Errors**

|**Clas**|**sificatio**|**n Trees**|**Logi **|**stic Reg**|**ression**|**Ra**|**ndom F**|**orest**|**B**|**oosted**|**Trees**|
|---|---|---|---|---|---|---|---|---|---|---|---|
|Incl.|Excl.|Budget|Incl.|Excl.|Budget|Incl.|Excl.|Budget|Incl.|Excl.|Budget|
||||||**_Moza_**|**_mbique_**||||||
|0.21|0.63|0.28|0.13|0.71|0.20|0.13|0.71|0.20|0.13|0.71|0.20|
|0.21|0.63|0.28|0.22|0.59|0.30|0.22|0.59|0.30|0.21|0.58|0.30|
|0.21|0.63|0.28|0.30|0.47|0.40|0.30|0.47|0.40|0.30|0.46|0.40|
|0.52|0.26|0.62|0.39|0.35|0.50|0.39|0.36|0.50|0.39|0.35|0.50|
|0.52|0.26|0.62|0.50|0.27|0.60|0.50|0.27|0.60|0.51|0.28|0.60|
||||||**_Ma_**|**_lawi_**||||||
|0.13|0.76|0.18|0.13|0.70|0.20|0.13|0.70|0.20|0.13|0.69|0.20|
|0.16|0.68|0.23|0.21|0.57|0.30|0.21|0.57|0.30|0.21|0.57|0.30|
|0.32|0.47|0.41|0.30|0.46|0.40|0.31|0.46|0.40|0.30|0.46|0.40|
|0.39|0.38|0.49|0.40|0.36|0.50|0.41|0.36|0.50|0.40|0.36|0.50|
|0.43|0.34|0.53|0.51|0.27|0.60|0.50|0.26|0.60|0.50|0.26|0.60|
||||||**_Zim_**|**_babwe_**||||||
|0.19|0.67|0.23|0.15|0.69|0.20|0.15|0.70|0.20|0.15|0.68|0.20|
|0.19|0.67|0.23|0.24|0.57|0.30|0.24|0.58|0.30|0.24|0.57|0.30|
|0.35|0.42|0.43|0.33|0.45|0.40|0.34|0.46|0.40|0.33|0.46|0.40|
|0.40|0.38|0.47|0.43|0.34|0.50|0.43|0.34|0.50|0.43|0.34|0.50|
|0.40|0.38|0.47|0.53|0.24|0.60|0.53|0.25|0.60|0.53|0.25|0.60|
||||||**_Tan_**|**_zania_**||||||
|0.07|0.84|0.10|0.06|0.83|0.10|0.06|0.83|0.10|0.06|0.83|0.10|
|0.15|0.71|0.20|0.13|0.69|0.20|0.13|0.69|0.20|0.13|0.69|0.20|
|0.27|0.53|0.35|0.22|0.56|0.30|0.21|0.56|0.30|0.22|0.57|0.30|
|0.36|0.43|0.44|0.30|0.44|0.40|0.31|0.45|0.40|0.30|0.44|0.40|
|0.42|0.35|0.51|0.40|0.34|0.50|0.40|0.34|0.50|0.40|0.34|0.50|
|0.48|0.30|0.56|0.50|0.24|0.60|0.51|0.25|0.60|0.51|0.25|0.60|
||||||**_Za_**|**_mbia_**||||||
|0.15|0.74|0.19|0.14|0.72|0.20|0.14|0.72|0.20|0.15|0.72|0.20|
|0.28|0.57|0.34|0.23|0.59|0.30|0.23|0.60|0.30|0.23|0.60|0.30|
|0.28|0.57|0.34|0.32|0.48|0.40|0.32|0.49|0.40|0.32|0.49|0.40|
|0.28|0.57|0.34|0.42|0.39|0.50|0.42|0.39|0.50|0.43|0.40|0.50|
|0.60|0.23|0.67|0.52|0.29|0.60|0.52|0.28|0.60|0.53|0.29|0.60|

Notes: The table reports inclusion and exclusion out-of-sample errors based on the optimal models from Table 9. Inclusion errors are defined as the proportion of non-stunted children labelled as being stunted. Exclusion errors are defined as the proportion of stunted children labelled as being non-stunted. The budget is the proportion of total children reached. The assumption is that every child is either given some fixed amount of support or is not provided anything.

33
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**Figure 2 Height-Age Z-Score*100 Distributions Across Wealth Quintiles**

<!-- Start of picture text --> Malawi Mozambique Zimbabwe<br>Poorest Fourth Middle Second Wealthiest Poorest Fourth Middle Second Wealthiest Poorest Fourth Middle Second Wealthiest<br>Tanzania Zambia<br>Poorest Fourth Middle Second Wealthiest Poorest Fourth Middle Second Wealthiest<br>200<br>0<br>−200<br>−400<br>−600<br>200<br>0<br>Height for age standard deviations from median (WHO) −200<br>−400<br>−600<br><!-- End of picture text --> 35
**Figure 3-a Drought-Contingent Height-Age Distributions: Lowest Wealth Quintile**

<!-- Start of picture text --> −2.0 (Stunted) 0<br>Height−Age Z−Score<br>No Drought Drought<br>.003<br>.002<br>Density<br>.001<br>0<br><!-- End of picture text -->

**Figure 3-b Drought-Contingent Height-Age Distributions: Top 4 Wealth Quintiles**

<!-- Start of picture text --> −2.0 (Stunted) 0<br>Height−Age Z−Score<br>No Drought Drought<br>.003<br>.002<br>Density<br>.001<br>0<br><!-- End of picture text --> 36
# Figure 4: Probability of Child Stunting in Rural Mozambique

<!-- Start of picture text --> mothers_height<br>p < 0.001<br><5ft. >5ft3in, 5ft-5ft3in<br>age zone<br>p < 0.001 p < 0.001<br><7m >24m, 6-24m 1, 2, 3, 4, 5, 6 10, 7, 8, 9<br>zone age age<br>p = 0.002 p < 0.001 p = 0.002<br>1, 2, 3, 4, 5, 6, 810, 7, 9 <7m >24m, 6-24m <7m>24m, 6-24m<br>drought zone mothers_height mothers_height<br>p = 0.032 p = 0.016 p < 0.001 p = 0.028<br>>5ft3in 5ft-5ft3in<br>m_age<br>No Yes 1, 2, 4, 5, 6 3 >5ft3in5ft-5ft3in<br>p = 0.038<br>0 1<br>n = 252 n = 1069 n = 299 n = 291 n = 271 n = 32 n = 453 n = 42 n = 1830 n = 169 n = 472 n = 964<br>0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8<br>0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6<br>0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4<br>0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2<br>0 0 0 0 0 0 0 0 0 0 0 0<br>. . . . . . . . . . . .<br>.. .. .. .. .. .. .. .. .. .. .. ..<br><!-- End of picture text -->
# Figure 5: Probability of Child Stunting in Rural Zambia

<!-- Start of picture text --> age<br>p < 0.001<br><7m >24m, 6-24m<br>mothers_height<br>p < 0.001<br><5ft., 5ft-5ft3in >5ft3in<br>mothers_height mother_underwt<br>p < 0.001 p = 0.008<br><5ft. 5ft-5ft3in 0 1<br>drought drought female_head roof<br>p = 0.045 p < 0.001 p = 0.024 p = 0.001<br>No Yes 0 1<br>tv drought<br>p = 0.014 p = 0.026<br>No Yes No Yes mod natural<br>car_motor_fridge<br>No Yes<br>p = 0.03<br>No Yes<br>n = 782 n = 784 n = 413 n = 2254 n = 897 n = 114 n = 23 n = 1011 n = 306 n = 287 n = 58 n = 142<br>0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8<br>0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6<br>0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4<br>0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2<br>0 0 0 0 0 0 0 0 0 0 0 0<br>. . . . . . . . . . . .<br>.. .. .. .. .. .. .. .. .. .. .. ..<br><!-- End of picture text -->