Malnutrition Gap as a New Measure of Child Malnutrition: A Global Application

"Leaving no one behind" is an overarching principle of the Sustainable Development Goals. Many countries are prioritizing resources for those who are furthest behind. Existing malnutrition indicators?underweight, stunting, wasting, overweight, and severe wasting?are headcount ratios. They do not capture how far behind malnourished children are relative to the World Health Organization growth standards. To understand the severity of malnutrition, this study develops a new malnutrition measurement, using the method originally developed for estimating poverty. This study estimates the prevalence, gap, and gap squared for stunting, wasting, overweight, and underweight, using data from 94 developing countries over 20 years. The results show that although in most cases the headcount measures and gap measures are moving in the same direction, in many other cases, they are moving in opposite directions. Moreover, employing the new measures, the study can identify countries that have low levels of headcount for a malnutrition measure but comparatively high severity of malnutrition according to the gap measures, and vice versa. This suggests that these new malnutrition measures provide additional information on the severity of malnutrition that is not possible to be known from headcount measures. These new measures of the severity of malnutrition can therefore improve the monitoring of child malnutrition across countries, and consequently help countries to achieve their Sustainable Development Goals.


Introduction
A renewed aspiration from the Millennium Development Goals (MDGs), the second Sustainable Development Goal (SDG) calls for achieving, by 2025, the internationally agreed targets for reduction of stunting and wasting in children under 5 years of age. 1 "Leaving no one behind" is an overarching principle of the newly adopted SDGs. The UN 2016 SDGs Report states, "In committing to the realization of the 2030 Agenda for Sustainable Development, Member States recognized that the dignity of the individual is fundamental and that the Agenda's Goals and targets should be met for all nations and people and for all segments of society. Furthermore, they endeavored to reach first those who are furthest behind." (UNSD 2016, p. 48) The World Health Organization (WHO) defines child malnutrition as growth measures more than 2 standard deviations (SD) below the median WHO growth standards. In addition, the WHO defines severe acute child malnutrition as weight for height below -3SD from the median WHO growth standards (WHO and UNICEF 2009). Existing child malnutrition indicators include prevalence of underweight (weight for age below -2SD), stunting (height for age below -2SD), wasting (weight for height below -2SD), overweight (weight for height above 2SD), and severe wasting (weight for height below -3SD).
These prevalence indicators are headcount measures and do not vary with the distance between individual Z-scores (number of SD) and the WHO reference lines. And thus, such headcount measures fail to identify malnourished children furthest away from the reference line, i.e. the inequality in malnutrition present among the malnourished population. As the SDGs require 3 more granular data to monitor progress, it has motivated us to develop new indictors to provide supplemental, yet critical, evidence to the conventional indicators.
There have only been a limited number of studies that attempt to develop a measure of severity of child malnutrition. McDonald et al. (2014) proposes a measure of malnutrition based on the notion of multiple anthropometric deficits. For example, a child is considered to be severely malnourished if she/he is both stunted and underweight. However, this measure is still a headcount measure, and it compounds the information when people want to know how stunted and how underweight a child is separately.
In contrast, studies by Shekar et al. (2015) and Jolliffe (2004Jolliffe ( & 2004 adopt the techniques used for measuring poverty to measure nutrition outcomes. Specifically, they put the Foster, Greer and Thorbecke (1984, hereafter referred to as FGT) class of poverty indicators in the context of malnutrition. Shekar et al. (2015) estimated FGT(0) as the stunting prevalence (similar to the poverty headcount measure) and FGT(1) as the stunting gap (similar to the poverty gap) in Mali from 2001 to 2013. Similarly, Jolliffe (2004Jolliffe ( & 2004 uses FGT to calculate the overweight gap and gap-squared to understand the overweight problem in the U.S. They demonstrated that the stunting gap and overweight gap, analogous to the poverty gap, can provide further information in addition to the stunting prevalence in nutrition diagnostics and policy recommendations. This paper aims to provide supplementary, but critical, information to the conventional headcount measures of malnutrition. Specifically, following Shekar et al. (2015), this paper will adopt the techniques used for measuring the depth and severity of poverty to measure the severity of malnutrition. More specifically, we develop the following eight measures of malnutrition in this study: (i) stunting gap, (ii) stunting gap squared, (iii) wasting gap, (iv) wasting gap squared, (v) 4 overweight gap, (vi) overweight gap squared, (vii) underweight gap, and (viii) underweight gap squared.
This study makes two important contributions to the research literature. First, while the stunting gap measure has been developed by Shekar et al. (2015), the other seven measures of malnutrition are developed for the first time in this study. Hence, in addition to the conventional headcount indicators, these proposed indicators can provide useful information about a country's malnutrition status, especially on the depth and severity of malnutrition, which can consequently improve evidence-based decision-making. Second, we employ over 20 years of malnutrition data from 94 developing countries to calculate the new measures. Employing the new measures, we are able to identify countries that have low levels of headcount for a malnutrition measure, but comparatively high severity of malnutrition according to the gap and gap-squared measures, and vice versa. This allows us to identify cases where headcount measures may be providing an incomplete description of a certain country's malnutrition status.
From a policy perspective, it is important to distinguish between malnutrition measures based on the headcount and measures of depth and severity in malnutrition. As countries are in particular committed to reach first those who are furthest behind in order to realize the SDGs 2030 agenda, high-quality data are needed for monitoring the progress of these individuals and providing evidence for effective policy making.
We proceed as follows. Section 2 discusses the methodology for the new measures. Section 3 describes the data used in the empirical application. Section 4 presents the results. Section 5 concludes.

5
While we adopt the method of Shekar et al. (2015), it is not the only application of the FGT poverty indicators in non-monetary indicators. Nguyen andWodon (2012, 2015) applied the same approach to the estimation of child marriage. Apart from estimating the incidence of child marriage (the share of girls marrying before age 18), they also estimated the "child marriage gap," which accounts for how early a girl marries.
We intend to generalize the method for all of the aforementioned existing malnutrition indicators and produce the gap estimate for every country with data, using a standardized data set of growth Z-scores calculated from Demographic and Health Surveys (DHS) and Multiple Indicator Cluster Surveys (MICS). We will also extend the calculation to the squared malnutrition gap, i.e., FGT(2). Foster, Greer, and Thorbecke (1984) showed that the FGT class of poverty indicators have a number of attractive axiomatic properties such as additive decomposability and subgroup consistency.
Analog to the poverty gap, the malnutrition gap is defined as the average shortfall of children's Z-scores of an anthropometric measure from the reference line (counting zero shortfall for non-malnourished children) as a proportion of the reference line. It measures how far off a child is from the WHO growth standards. Taking stunting as an example, the national average stunting gap (Gap) can be expressed as where N denotes the total number of children under 5 years of age in a given population, M denotes the number of stunted children, and denotes individual Z-scores of stunting and 2 in this equation. Implicitly in this equation, the shortfall for non-stunted children is zero when 2.
Subsequently, the national average squared stunting gap (SqGap) can be expressed as 6 ∑ . (2) The squared malnutrition gap takes into account not only the distance between the malnourished children and the reference line (the malnutrition gap), but also the inequality among the malnourished children. That is, a higher weight is placed on those who are further away from the reference line.

Data
We reanalyzed all DHS and MICS, phases 3 onwards, and calculated individual Z-scores for all children with available anthropometric data according to the WHO standard approach. As of today, we obtained estimates for 168 DHS from 1993 to 2014 and 70 MICS from 2005 to 2014.
These surveys combined cover 94 countries. Annex 1 lists all the surveys included in this data set.
The recalculation of Z-scores was based on the WHO child growth standards and prevalence estimates were generated following standard analysis as per available Stata macro (http://www.who.int/childgrowth/software/en/). The recalculated Z-scores may generate slightly different prevalence estimates from those published by DHS and MICS reports, mainly due to the use of the WHO standard approach, which (i) uses all valid Z-scores for each child, and (ii) imputes the missing day of birth as 15.
Each of our surveys is representative for the data collection areas, and most are nationally representative for the country. Therefore, we use survey weights in our analysis to ensure that we have a representative estimation for the country or the areas where data were collected.

Comparison of Changes in Malnutrition Headcount and Malnutrition Gap
We applied the class of FGT measures to each of the malnutrition indicators and produced results for all eight measures mentioned in section 1. Given the space limitation, we limit our discussions on the results to the primary malnutrition indicator -stunting. For interested audiences, the whole data set is available upon request.
One of the motivations to develop these new measures is to obtain insight that is not offered by the headcount measures. For example, if the malnutrition gap of a country increases significantly over time, but the malnutrition headcount does not, it would indicate that malnutrition severity in a country is increasing over time, a fact that is not captured by the headcount measure.
This is why we examine whether the headcount measure and gap measure change in a similar manner over time for each country.
To understand these changes, we measure the change in malnutrition headcount and the change in malnutrition gap over each consecutive survey rounds for each country. We identify whether the headcount measure and gap measure increase significantly, decrease significantly, or face no significant change over time. If there is a significant change in one measure (headcount or gap), but no significant change or a significant change in the opposite direction for the other measure, then we categorize those two differing changes as "headcount and gap moving in different directions." In contrast, if both the headcount and gap remain statistically unchanged, or increase or decrease statistically significantly, then we categorize them as "headcount and gap moving in the same direction."    Source: Authors' calculations using DHS and MICS.

4.2: Comparison of Severity for Countries with Similar Headcounts
In addition to understanding changes in malnutrition over time, it would also be useful to examine how the malnutrition gap and gap-squared vary for countries with similar headcount rates.  1993-2000, 2001-2005, 2006-2010, and 2011-2014. Both Figure 2 and Table 2 illustrate how diverse the stunting gaps can be for countries with similar stunting prevalence. In In  Source: Authors' calculations using DHS and MICS.

4.3: Regional Analysis
Until now we have focused on headcount and gap measures only at the country level.
Extending this analysis to the regional level may provide further insight on malnutrition across the world. Therefore, we examine the regional averages of malnutrition. As survey data are not available every year for most countries, only a few countries in a particular region have a survey in a given year, with some regions having no survey conducted in certain years.
There are two common practices for calculating regional averages in such cases: (1) modeling methods and (2) aggregating over a range of years. An example of modeling methods closely related to this study is the UNICEF-WHO-World Bank joint child malnutrition estimates (JME) (UNICEF, WHO, and the World Bank 2018). The JME adopts linear mixed-effect models allowing for random effects at the country level and for heterogeneous covariance structures. One model is fitted for each region or country group for calculating its aggregated number. Such modeling methods are beyond the scope of this study. For simplicity, we chose to calculate regional averages for a range of years following the exercise in Nguyen and Wodon (2015). Thus, we create regional averages for five-year periods : 1993-1997, 1998-2002, 2003-2007, and 2008-2012. We use these five-year periods so that the middle years of these ranges,1995, 2000, 2005, 18 and 2010, coincide with the years in which under-five population data are compiled for each country in the sample. We create regional averages of stunting measures weighted by the under-five population of each country of the middle of each reference period. Following the World Bank regional classification, we divide the countries in our sample into six regions: East Asia and Pacific (  around 7 percent. This shows the importance of the gap measure, providing us further insight in addition to the headcount measures.

Income-group Analysis
Next we conduct our analysis by different income groups as defined by the World Bank: low income, lower-middle income, and upper-middle income. The results are presented in Figure 4.
Similar to our regional analysis, we find that the trend of the stunting gap can reveal a different story than the trend of the stunting headcount. Specifically, the stunting headcount of lowermiddle-income countries as a whole was slightly lower than that of low-income countries until sometime between 2000 and 2005. However, the trend of the stunting gap of lower-middle-income countries during this period of time was higher than that of low-income countries. In the reference year of 2000, the difference amounted to 2 percentage points.

Population Coverage
Next, we examine the population coverage in our analysis, i.e. the percentage of population in low-and middle-income countries that we cover through the nationally representative surveys in our analysis in each of the time ranges. We use data from WHO on the number of children below the age of 5 for all low-and middle-income countries in five-year intervals: 1995, 2000, 2005, and 2010 Table 3 presents the population coverage for each five-year time period. We find that for the initial surveys from 1993 to 1997, the population coverage of low-and middle-income countries in our analysis was 18%. However, we see population coverage increase over the years to 47%, 57%, and 38% for the periods 1998-2002, 2003-2007, and 2008-2012, respectively. This shows that population coverage improved, likely because the number of surveys across countries increased over the years. While we may not have sufficient data for precise aggregation at this point, as more surveys are conducted in the future, we will have greater population coverage and greater precision in future analysis. Similarly, in Table 4 we present the population coverage for the regional aggregations in Figure 3. As we can see, while South Asia and Africa are well-represented in several of the timewindows, the coverage for the other regions are generally well below 50%. This demonstrates that the regional coverage estimates need to be interpreted with caution. However, it is important to note that the purpose of this exercise is not to create regional aggregates with sufficient coverage.
It is instead to show how these new indicators and new estimates can be used for analysis. 23

Conclusions
This paper develops a new method of measuring malnutrition across the world. The current key measures of malnutrition, such as stunting and wasting, are based on headcount measures, i.e.
the proportion of children who are suffering from malnutrition. However, a potential drawback of these headcount measures is that they do not inform us about the depth and severity of malnutrition.
It is possible that a country with a low headcount rate for a particular malnutrition measure also has a high severity of malnutrition compared to countries with a similar headcount rate, and vice versa. Therefore, it is important to develop a measure of the severity of malnutrition.
To develop a measure of the severity of malnutrition, this study adopts a particular technique used in the development literature, specifically the Foster, Greer and Thorbecke (1984)  Due to space limitations, this paper presents the results on stunting only, although all results have been calculated. It is of our interest to explore all our results in our future studies to understand if the additional information provided by the gap and gap squared measures is more useful for one malnutrition indicator than for another.
The malnutrition gap as a new measure enables us to monitor the development progress of those furthest away from the reference line, serving the principle of SDGs. Employing the new measures, we are also able to identify countries that have low levels of headcount for a malnutrition 24 measure, but have comparatively high severity of malnutrition according to the gap measures, and vice versa. This allows us to identify numerous cases where headcount measures may be providing a misleading description of a certain country's malnutrition status. Additionally, through regional and income-group analysis, we identify differences in the headcount and gap measurements. This study is extremely important from a policy perspective because comparing countries with similar headcount measures could hide important differences in the depth of malnutrition as reflected by differences in the malnutrition gap.