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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