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A Food Insecurity Kuznets Curve?

Dennis Wesselbaum*1, Michael D. Smith2, Christopher B. Barrett3, Anaka Aiyar4

August 20, 2021

Abstract Advances in food security proceed unevenly within and across nations. A striking pattern emerges from analysis of >560,000 individual responses to the first globally comparable, nationally representative, repeated food insecurity survey, which is statistically representative of >96% of the world’s population. We find the relationship between the prevalence of food insecurity in a country and intranational, interpersonal inequality in food insecurity follows a strong inverse-U shape, i.e., a Kuznets Curve. The relationship is stable over time and across relevant inequality measures and estimation methods. This finding can help guide the implementation of safety nets and social protection programs to achieve the UN’s Sustainable Development Goal 2 and to satisfy the human right enshrined in Article 25 of the 1948 Universal Declaration of Human Rights.

Keywords: Food Security, Inequality, Kuznets Curve.

JEL Codes: I14, I32, I38, Q18.

1 Corresponding author. Department of Economics, University of Otago, Dunedin, New Zealand. Email: dennis.wesselbaum@otago.ac.nz. 2 National Oceanic and Atmospheric Administration, United States Department of Commerce, 1315 East-West Hwy, Silver Spring, MD 20910, USA. 3 Charles H. Dyson School of Applied Economics and Management, Cornell University, Ithaca, NY, 14853-7801, USA. 4 Department of Economics, University of Nevada, Reno, 1664 N. Virginia Street, Reno, NV, 89557, USA.

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1. Introduction

Reducing food insecurity is a global policy priority of the highest order, enshrined in Article

25 of the Universal Declaration of Human Rights (UDHR) adopted by the United Nations (UN)

in 1948, and in the UN’s 2015 Sustainable Development Goal 2 (SDG2) to “end hunger,

achieve food security and improved nutrition and promote sustainable agriculture” by 2030.

Yet after steadily decreasing for years, the number of undernourished people and the

prevalence of moderate or severe food insecurity in the global population have increased

considerably since 2015 (Figure 1). Recent backsliding, compounded by the COVID-19

pandemic, fuels growing concern about inequality in individuals’ experience of food insecurity.

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Figure 1: Global prevalence (in %) of moderate or severe food insecurity (blue columns) and number of people undernourished (in millions, red line). Note: Prevalence estimates only available since the FIES module launched in 2014. Source: FAO (http://www.fao.org/faostat/en/#data/FS, downloaded 20 August 2021).

Differences among countries in key food systems input, output and outcome indicators,

including food insecurity, are widely recognized (Bell et al., 2021; Downs and Fox, 2021). But

we know far less about what happens to the interpersonal inequality of food insecurity within

a country as the national prevalence of food insecurity and other factors change. Are the

burdens of inadequate diets to maintain an active and healthy life shouldered equitably within,

not just across, nations? Data have previously limited researchers’ ability to generate a rigorous

answer.

Food insecurity, like poverty, is a latent variable reflecting human well-being, and therefore

difficult to measure precisely (Barrett, 2010). Just as scholars and policymakers pay attention

to income inequality and its relationship to mean (per capita) income or the prevalence of

poverty, interpersonal inequality and its relationship to the prevalence is also of intrinsic

interest. Inequality reflects differences in living conditions, risk exposure, and prospects, and

thus affects the political economy of food (e.g., influencing conflict, people's propensity to

cooperate, and investment behaviour). As Nobel Laureate Amartya Sen famously argued,

inequality reflects "the ethics of social arrangements" beyond just the average standard of living

(Sen, 1992). Inequality measures of interpersonal dispersion therefore merit inquiry apart from

our natural interest in the mean level of any given well-being measure, food insecurity

included.

A hypothesized relationship between food insecurity prevalence and interpersonal inequality

in food insecurity mirrors Nobel Laureate Simon Kuznets’ famous conjecture that income

levels and inequality might be related, with inequality first increasing, then decreasing as per

capita incomes grow in the process of economic development (Kuznets, 1955). The resulting

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‘Kuznets Curve’ hypothesis spawned a sizeable literature. One thread directly interrogates

Kuznets’ original conjecture that income inequality follows an inverse-U shape as a nation’s

per capita income changes. Social scientists have found mixed empirical evidence around

Kuznets’ hypothesis. This has itself spawned a large political economy literature attempting to

explain both the phenomenon and the variation in patterns across and within countries

(Acemoglu and Robinson, 2002; Fields, 2002).

Another offshoot of Kuznets’ original hypothesis replaces income inequality with other

socially undesirable outcomes, such as indicators of environmental degradation like air and

water pollution, deforestation, greenhouse gas emissions, or species loss (Cropper and

Griffiths, 1994; Selden and Song, 1994; Grossman and Krueger, 1995). The empirical evidence

on Environmental Kuznets Curves is likewise mixed and interpretation of such evidence

remains hotly contested (Dinda, 2004). Researchers studying other indicators of human

development, from educational attainment (Friedman et al., 2020) to health (Costa-Font et al.,

2018), have similarly looked for Kuznets Curve patterns. But this literature spawned by

Kuznets' classic paper deviates subtly from his original interest in the relationship between

inequality in human well-being and the mean level of human well-being – each proxied by

income in Kuznets' formulation – to study instead the relation between average income and

other indicators. We return to the original spirit of Kuznets' focus: the relationship between the

average and inequality in a measure of human well-being.

Is there a food insecurity Kuznets Curve? The internationally agreed upon and most commonly

used definition holds that “food security exists when all people, at all times, have physical and

economic access to sufficient, safe, and nutritious food to meet their dietary needs and food

preferences for an active and healthy life” (FAO, 1996). Food insecurity exists when this

condition is not met. Measuring food insecurity is complicated, however, by the latent nature

of the concept (Barrett, 2010). As a result, cross-nationally comparable measures of individual

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food insecurity have been scarce-to-non-existent, limiting analysts’ ability to explore

fundamental questions about global food insecurity, such as the possibility of a food insecurity

Kuznets Curve.

Testing the food insecurity Kuznets Curve hypothesis is finally possible. In 2014, the Food and

Agriculture Organization of the United Nations (FAO), working with the Gallup World Poll

(GWP), fielded an eight question Food Insecurity Experience Scale (FIES) module. Using the

2014-17 individual survey responses (N = 562,840) for 142 countries (>95% of world

population) we calculate the country- and year-specific prevalence rates of moderate or severe

food insecurity.

Given that the individual probability and the population-scale prevalence of food insecurity

prevalence are bounded ratio variables that fall in the [0,1] interval, we must be careful in how

we measure inequality. Two problems arise: the consistency problem, our measure should be

invariant to whether we measure attainment toward or shortfall from the desired state, and the

boundary problem, where a measure automatically goes to zero or one at the upper or lower

bounds. We use the measure developed by Permanyer et al. (2018), which most aggressively

corrects for these problems and provide robustness checks using other established measures of

inequality in binary variables typically described by prevalence estimates (Erreygers, 2009;

Erreygers and Van Ourti, 2011).

Several results stand out. We find that the relationship between the prevalence of food

insecurity in a country and intranational, interpersonal inequality in food insecurity follows a

Kuznets Curve. The relationship is stable over time and across relevant inequality measures

and estimation methods. We confirm this in multivariate panel regressions where we identify

the relationship off the inter-year variation within countries that deviates from global changes

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common to all countries in the sample years. Even when we control for income effects (GNI

per capita), we find that our results remain unaffected.

Further, when we move from macro to micro scale and estimate the individual-level

relationship between food insecurity inequality – represented by the variance in the individual-

specific probability of being food insecure conditional on individual characteristics and

country-year fixed effects – the same Kuznets Curve pattern emerges. Finally, by performing

a Shapley decomposition, we find that most of the variation in both the probability of being

food insecure and in the variance of the probability of being food insecure is associated with

country-year fixed effects. This implies that dispersion among otherwise identical individuals

varies more across countries than within countries, consistent with the observation of

considerable cross-country inequality in food system inputs, output, and outcomes (Bell et al.,

2021).

Overall, our findings carry novel and important policy implications. Country-level policies and

programs have the potential to make large impacts on reducing inequality and of food

insecurity, beyond increasing individual-level income. Our results impact the design of safety

nets and social protection programs to honour the UDHR and achieve SDG2. Growing

inequality and prevailing patterns of spatial sorting motivate increased use of carefully targeted

public and private food assistance programs to ensure universal access to sufficient, safe, and

nutritious food (Barrett, 2002; Alderman et al., 2017).

The paper proceeds as follows. Section 2 presents our data set, discusses our measure of

inequality in food insecurity, and provides descriptive statistics. In section 3, we provide our

main results at the macro and micro scales. Section 4 discusses our findings and offers

candidate explanations for the existence of the Kuznets Curve pattern in food insecurity.

Section 5 briefly concludes and discusses future research.

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2. Data and Methods

2.1 Data Set Construction

FAO created the Food Insecurity Experience Scale (FIES) to gather consistent and

comprehensive information on the prevalence and severity of global food insecurity and to

provide countries with a tool to monitor their national food security. This is the first

standardized survey protocol measuring people’s direct experiences of food insecurity at the

global scale with nationally representative samples (FAO, 2016). The severity of food

insecurity varies between uncertainty about the ability to obtain food (mild food insecurity),

via compromising on food quality and variety, reducing quantities, and skipping meals

(moderate food insecurity), to experiencing physiological hunger (severe food insecurity).

FAO contracted with Gallup, Inc. in 2014 to collect data in most countries around the world

through the Gallup World Poll (GWP). The GWP/FAO FIES survey module contains eight

questions designed to assess the adequacy of an individual’s access to food, adapted from the

long-established United States Household Food Security Survey Module (US HFSSM) and the

Latin American and Caribbean Food Security Scale (ELCSA). The precise script and questions

are presented in the appendix (see Appendix A.1). GWP, for most countries, interviews a

nationally representative sample of 1,000 adults. For medium- and high-income countries with

at least 80 percent telephone coverage, telephone interviews are used. For most developing

countries, face-to-face interviews are used. Households are randomly selected using the Kish

grid method (FAO, 2016).

The FIES survey module questions focus on respondents’ behaviors and experiences when they

have encountered difficulties in meeting their basic food needs over the previous 12 months.

Typical of other food insecurity surveys the FIES questions are asked in order of severity. Each

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question in the FIES specifies that the food-insecure condition stems from a lack of money or

other resources to obtain adequate food.

The severity of the respondent’s food insecurity is based on the conditions and behaviors

reported in response to the survey. An individual’s food security status can be determined by

summing the affirmed responses to the eight questions; generating a raw score representing

each respondent’s food security status. Food security classifications based on raw scores are

standard, as in those constructed from the US HFSSM and ELCSA.

FIES raw score classifications are not comparable across countries, however, because the same

number of affirmed responses would not necessarily correspond to the same level of severity

in different countries. Differences across countries in, for example, languages, livelihood

arrangements, and food-related cultural norms and expectations may affect the way in which

the FIES questions are understood by respondents, and, in turn, may affect their responses.

The FAO therefore renders nation-specific scales comparable by creating food insecurity

thresholds that partition the continuum of food insecurity into meaningful and comparable

ranges of food insecurity, a FIES Global Standard Scale (FAO, 2016). To ensure the measured

severity of food insecurity is comparable across countries, FAO uses Item Response Theory

(i.e., the Rasch model) to equate the food insecurity scales for each country to the FIES Global

Standard Scale. The FAO equating procedure maintains cross-country comparability by

creating two standard food insecurity thresholds: moderate food insecurity and severe food

insecurity. The thresholds are adjusted to place each country’s scale on the same metric as the

global standard. The resulting food security prevalence rates and severity measures are then

equivalent and comparable across countries (FAO, 2016; Alderman et al., 2017). These

measures were chosen by FAO and the UN for monitoring progress towards Target 2.1 of

SDG2.

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Individuals whose raw score equals zero are classified as food secure. Individuals with a raw

score of at least one and less than the country specific FIES Global Standard Scale (GSS, for

short) threshold for moderate food insecurity (typically a raw score of either 3 or 4) are

classified as experiencing mild food insecurity. Those who report a raw score at least equal to

the FIES GSS threshold for moderate food insecurity but less than the FIES GSS threshold for

severe food insecurity (typically a raw score of 7) are deemed moderately food insecure. Those

above the country specific FIES GSS threshold for severe food insecurity are classified as such.

Following the SDG Target 2.1 indicator definition, the prevalence of moderate or severe food

insecure individuals represents the sum of those two categories. We use this measure in our

analyses.

FAO estimates individual-specific probabilities of food insecurity to account for measurement

error (i.e., the extent of uncertainty) around the parameter estimate associated with each raw

score (FAO, 2016; Cafiero et al., 2018). The distribution of respondents at each raw score is

assumed to be Gaussian with a mean equal to the parameter for that raw score and standard

deviation equal to the raw score measurement error (Cafiero et al., 2018). Based on these

distributions of severity, each respondent is assigned a probability (a continuous measure in

the [0,1] interval) of being beyond each of the country-specific FIES GSS thresholds of food

insecurity severity. Thus, the probability of experiencing moderate or severe food insecurity

represents the proportion of people in the population represented by the sampled person whose

true food insecurity exceeds the moderate food insecurity threshold. Survey-weighted

summation of these individual probabilities yields a population prevalence estimate.

Importantly, the Rasch transformation is rank preserving even after adjustments are made on

the extreme values. This method of equating responses within and across countries should

reduce variance, not increase it, because it expressly reduces inter-country variance. Hence, the

transformation works against finding inequality and we probably underestimate the inequality.

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2.2 Methods

Considerable care must be taken in representing inequality in food insecurity. Unlike income,

an unbounded positive variable over which the original Kuznets Curve was hypothesized to

exist, both the individual probability and the population-scale prevalence of food insecurity

prevalence are bounded ratio variables that fall in the [0,1] interval. This boundedness raises

two key technical concerns. First, the measure should be invariant to whether one uses the

prevalence either of food security or food insecurity, i.e., a measure of attainment toward or

shortfall from the desired state at any moment in time (Erreygers, 2009; Erreygers and Van

Ourti, 2011; Erreygers et al., 2012; O’Donnell et al., 2016; Permanyer et al., 2018). Inequality

measurement scholars often refer to this as the consistency problem.

Second, many familiar inequality measures suffer from the boundary problem. Indicators like

the standard deviation or coefficient of variation mechanically go to zero at the upper and lower

bounds of a [0,1] variable – because there can be no inter-unit variation at the limiting values

– and rise in between, manufacturing a Kuznets Curve-type inverted-U pattern by construction.

Other measures, like the Gini coefficient, mechanically decrease from value one when only

one person is food secure, and fall to zero as the last person becomes food secure, ruling out a

Kuznets Curve arithmetically. We therefore need an inequality measure that addresses the

boundary and consistency problems, flexibly reflecting individual differences conditional on

prevalence and regardless of how close the population-scale prevalence is to its bounds.

Otherwise, an inverse-U shape can arise or be ruled out purely as an artefact of the inequality

measure's construction.

At least three distinct inequality measures have been widely used in related literatures studying

bounded outcome variables (e.g., the prevalence of health or educational attainment) to address

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the boundary and consistency problems in different ways: the Erreygers, generalized extended

concentration (GEC), and generalized symmetric concentration (GSC) indices. All three

measures are strongly positively correlated in our sample (𝜌𝜌 ∈ [0.96,0.99], Table 1)

(Erreygers, 2009; Erreygers and Van Ourti, 2011; Erreygers et al., 2012; O’Donnell et al.,

2016). But concerns remain about whether these measures fully correct for the mechanical

parabolic relationship between the inequality measure and mean attainment. The new

Permanyer-Seth-Yalonetzky (PSY) inequality measure, however, remedies the boundary and

consistency issues by comparing observed inequality against the maximal inequality that could

possibly be observed in another hypothetical distribution having the same mean, thereby

eliminating the mechanical inverse relation that might otherwise remain in uncorrected

measures (Permanyer et al., 2018). We therefore rely on PSY inequality index measures in our

analyses.

GEC GSC Erreygers GSC 0.957 (0.958) Erreygers 0.970 (0.977) 0.993 (0.993) PSY 0.318 (0.547) 0.388 (0.673) 0.361 (0.624)

Table 1: Bivariate correlation coefficients among different inequality measures. Correlation coefficients within parentheses apply population weights across countries, which necessitates dropping 8 country-year observations for which population data are not available, from Singapore and Taiwan. (N=546).

The PSY index on which we focus our analyses was developed specifically to correct for the

boundary and consistency problems in conventional inequality measures applied to bounded

variables such as prevalence or probability, both of which fall in the [0,1] interval. PSY controls

explicitly for the fact that the maximum attainable inequality depends on the mean value of the

bounded variable. PSY thus corrects most aggressively for the boundary problem, which

accounts for its lower correlation with other inequality indices.

The PSY measure is defined as (Permanyer et al., 2018):

𝑃𝑃𝑃𝑃𝑃𝑃 = 𝑆𝑆𝑆𝑆2

𝑀𝑀(1−𝑀𝑀), (1)

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where M denotes the mean, and SD denotes the standard deviation of the series.

We complement the PSY measures and provide robustness checks by providing estimates of

the more widely used Erreygers, GEC, and GSC inequality measures (See Appendix A.2 for

definitions).

2.3 Descriptive Statistics

We use the individual-level estimates of the probability of being food insecure to estimate the

prevalence of food insecurity for each country in each year. Because we use the complete data

set, there are slight discrepancies in global estimates relative to those FAO publicly reports

(e.g., via FAOStat, as reflected in Figure 1), as those public reports are restricted to a subset of

countries that permit FAO to release their aggregate statistics. The full sample we analyze is

thus more comprehensive, offering a more complete picture of global conditions.

FIES Year

Number of observations

Individuals

Countries

Mean

SD

% world population represented

Population-weighted

Mean SD 2014 143,522 142 0.290 0.229 96.5% 0.230 0.192 2015 132,904 132 0.294 0.242 75.8% 0.235 0.210 2016 141,909 139 0.317 0.265 95.8% 0.259 0.199 2017 144,505 141 0.336 0.274 95.8% 0.279 0.209

Table 2: Descriptive statistics for the FIES sample (N=562,840 individuals, 554 country-years) used in estimation. Mean (and standard deviation) of prevalence of moderate or severe food insecurity adjusted for survey weights. Rightmost columns also adjust for national population weights to represent the global share of population indicated. Note: The share of population represented falls sharply in 2015 because Bangladesh and India are missing that year. Population data comes from World Bank, World Development Indicators. No population data were available for Singapore and Taiwan.

Using the 2014-17 individual survey responses (N = 562,840) for all 142 countries for which

data are available in at least one year, we calculate the country- and year-specific prevalence

rates of moderate or severe food insecurity (see Table 2). By 2017, this survey sample is

statistically representative of 95.8% of the world’s population. The mean population-weighted

food insecurity prevalence for low, lower-middle, upper-middle, and high income countries –

per the 2018 World Bank classifications – were 0.610, 0.334, 0.152, and 0.106, respectively,

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reflecting the strong negative relationship between average income and food insecurity

prevalence. This highlights a widely-unrecognized fact that most food insecure people live in

middle-income countries, not in low-income countries (Figure 2). Prior work has established

that five key household or individual characteristics are most strongly associated with

individuals’ experience of food insecurity: low educational attainment, low household income,

unemployment, modest social capital, and weak social networks (Smith et al., 2017). But

inequality among individuals’ experience of food insecurity remains thus far unexplored.

Figure 2. Estimated number of food insecure individuals (vertical axis in millions) by food insecurity prevalence rate (left panel – horizontal axis) and log Gross National Income per capita (right panel – horizontal axis) for 2017 (similar results are obtained for the other years in the sample). Horizontal lines indicate 25th, 50th, 75th percentiles respectively and vertical lines in the right panel indicate the income cut-offs for the World Bank Development classifications (Lower Income - <$1,006, Lower Middle Income - $1,006-$3,956, Upper-Middle Income - $3,956-$12,235 and High Income - >$12,235).

3. Main Results

3.1 Macro Scale

Figure 3 displays the relationship between country-year-level food insecurity prevalence and

inequality as represented by the PSY index. The inverted-U relationship clearly exists in this

simple scatterplot, as well as in the same scatterplot that uses only severe food insecurity

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(Figure A.1 in the Appendix) and the other measures of inequality in food insecurity (Figure

A.2 in the Appendix).

Figure 3: Scatter plot of country-level prevalence of individual food insecurity (horizontal axis) and inequality measure (PSY index) by year. Colours and symbols represent World Bank development classification. Quadratic bivariate regression line in red in each panel.

We confirm this in multivariate panel regressions with country and year fixed effects, thereby

identifying the relationship off the inter-year variation within countries that deviates from

global changes common to all countries in the sample years. We estimate the relationship

between food insecurity inequality (𝑃𝑃𝑗𝑗𝑗𝑗) and prevalence (𝐹𝐹𝑃𝑃𝑗𝑗𝑗𝑗) for country j in year t, exploiting

the panel structure of the data by controlling for country (𝛾𝛾𝑗𝑗) and year fixed effects (𝛿𝛿𝑗𝑗):

𝑃𝑃𝑗𝑗𝑗𝑗 = 𝛽𝛽0 + 𝛽𝛽1𝐹𝐹𝑃𝑃𝑗𝑗𝑗𝑗 + 𝛽𝛽2𝐹𝐹𝑃𝑃𝑗𝑗𝑗𝑗2 + 𝛾𝛾𝑗𝑗 + 𝛿𝛿𝑗𝑗 + 𝜀𝜀𝑗𝑗𝑗𝑗 . (2)

The country fixed effects control for time-invariant features of countries (e.g., geographic or

historical factors) that explain persistent differences among countries, while the year fixed

effects control for time-varying factors common to all countries (e.g., global macroeconomic

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cycles). We identify the food insecurity Kuznets Curve relationship using within-country

intertemporal variation that deviates from global changes common to all countries in the sample

years. The results in Table 3 strongly indicate an inverted-U shape to the relationship described

by equation 2, with inequality reaching its estimated maximum under the PSY measure when

the food insecurity prevalence reaches 46%, and in the [0.496, 0.550] interval under any of the

other three inequality indices.

Inequality in Food Insecurity PSY GSC Erreygers GEC

Food insecurity prevalence 1.098** 3.824*** 3.786*** 3.404***

(0.475) (0.322) (0.041) (0.160)

Food insecurity prevalence2 -1.188** -3.840*** -3.818*** -3.095***

(0.484) (0.324) (0.037) (0.179)

Observations 546 546 546 546

Adjusted R2 0.712 0.993 0.999 0.998

Table 3: Dependent variable is inequality in food insecurity. Observations corrected for within-country survey weights and country-level population weights. Standard errors (in parentheses) are clustered by country and robust to heteroscedasticity. Includes country and year fixed effects. ***, **, and * indicate statistical significance at the 1, 5, and 10 percent level, respectively. N=546. We undertook robustness checks with and without post-stratification weights and dropping

specific countries for which analysts at FAO privately expressed concern regarding country-

level measurement error that could confound estimation. We also use specifications with linear

time trends, country-specific linear time trends, and country-specific quadratic time trends. Our

results (not shown, available upon request) were essentially unchanged in each of these variants

on our core results.

One might naturally suspect this inverse-U shape reflects a relationship with gross national

income per capita (GNI) rather than with food insecurity. Yet when we replace food insecurity

prevalence with GNI, no statistically significant relationship emerges with the food insecurity

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inequality measure, although the imprecisely estimated relationship suggests that food

insecurity inequality declines at a diminishing rate with GNI (Table 4, Figure A.3).5

Inequality in Food Insecurity PSY GSC Erreygers GEC

Log GNI -1.865 -3.692 -3.228 -2.202

(1.676) (2.680) (2.069) (1.682)

Log GNI2 0.125 0.236 0.204 0.137

(0.101) (0.167) (0.129) (0.104)

Observations 532 532 532 532

Adjusted R2 0.670 0.899 0.902 0.918

Table 4: Dependent variable is inequality in food insecurity. Observations corrected for within-country survey weights and country-level population weights. Standard errors (in parentheses) are clustered by country and robust to heteroscedasticity. Includes country and year fixed effects. ***, **, and * indicate statistical significance at the 1, 5, and 10 percent level, respectively. Relative to prior tables, 14 additional country-year observations were dropped for which GNI is not available (South Sudan in 2017, Macedonia and Somalia in 2014, 2015, 2016, Venezuela in 2015, 2016, 2017, and Taiwan 2014, 2015, 2016, 2017). N=532. Gini measure is only available for 196 country-years in our sample.

One might nonetheless still hypothesize that the Kuznets Curve relationship we find in Table

3 and Figure 3 is confounded by income effects. If we re-estimate, controlling now for both

GNI and food insecurity prevalence, however, the results hardly change. In table 5, we find

that the statistically significant inverse-U shaped relationship between food insecurity

prevalence and inequality in food insecurity remains and becomes more precisely estimated,

as manifested in smaller standard errors and effectively unchanged point estimates on the

coefficients on the linear and quadratic terms in food insecurity prevalence. Each are

statistically significantly different from zero at the one percent level.

5 We use gross national income per capita (GNI) in current international US dollar terms (data drawn from the World Bank, World Development Indicators).

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Inequality in Food Insecurity PSY GSC Erreygers GEC

Food insecurity prevalence 0.944*** 3.748*** 3.788*** 3.449***

(0.300) (0.218) (0.039) (0.111)

Food insecurity prevalence2 -0.924*** -3.717*** -3.821*** -3.186***

(0.259) (0.185) (0.042) (0.125)

Log GNI -1.096 -0.584 -0.009 0.374

(1.174) (0.704) (0.119) (0.335)

Log GNI2 0.077 0.040 0.0002 -0.024

(0.069) (0.042) (0.007) (0.0021)

Observations 532 532 532 532

Adjusted R2 0.732 0.993 0.999 .998

Table 5: Dependent variable is inequality in food insecurity. Observations corrected for within-country survey weights and country-level population weights. Standard errors (in parentheses) are clustered by country and robust to heteroscedasticity. Includes country and year fixed effects. ***, **, and * indicate statistical significance at the 1, 5, and 10 percent level, respectively. N=532. Gini measure is only available for 196 country-years.

3.2 Micro Scale

In order to move beyond using country-year macro-scale aggregates, we also pooled all

individual observations across countries and years to estimate the individual-level conditional

mean and variance of the probability of being food insecure, following the method of Just and

Pope (1978). This involves a two-step estimation. First, we estimated the conventional

conditional mean regression for each individual (i)’s probability of being moderately or

severely food insecure, FSijt, in country j in year t, controlling for a K-dimensional vector of

individual characteristics (taken from Gallup World poll data), X, and country-and-year

specific fixed effects that capture variation common to all survey respondents in that country

and survey year:

𝐹𝐹𝑃𝑃𝑖𝑖𝑗𝑗𝑗𝑗 = 𝛽𝛽0 + ∑ 𝛽𝛽𝑘𝑘𝑋𝑋𝑖𝑖𝑗𝑗𝑗𝑗𝑘𝑘𝐾𝐾𝑘𝑘=1 + 𝛾𝛾𝑗𝑗𝑗𝑗 + 𝜀𝜀𝑖𝑖𝑗𝑗𝑗𝑗 . (3)

Then we exploit the mean zero property of the ordinary least squares regression residuals from

equation 3, which implies that the conditional variance of the probability of an individual being

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food insecure, 𝑉𝑉(𝐹𝐹𝑃𝑃𝑖𝑖𝑗𝑗𝑗𝑗�𝑋𝑋𝑖𝑖𝑗𝑗𝑗𝑗�, equals the conditional expectation function, 𝐸𝐸[∙], of the squared

regression residuals from the conditional mean regression,

𝑉𝑉(𝐹𝐹𝑃𝑃𝑖𝑖𝑗𝑗𝑗𝑗|𝑋𝑋𝑖𝑖𝑗𝑗𝑗𝑗) = 𝐸𝐸 ��𝜀𝜀𝑖𝑖𝑗𝑗𝑗𝑗 − 𝐸𝐸�𝜀𝜀𝑖𝑖𝑗𝑗𝑗𝑗��2� = 𝐸𝐸[𝜀𝜀𝑖𝑖𝑗𝑗𝑗𝑗2 |𝑋𝑋𝑖𝑖𝑗𝑗𝑗𝑗]. (4)

The second step therefore simply regresses the squared residuals from the conditional mean

equation 3 on the same covariates to generate an estimate of the parameters of the conditional

variance function for the probability of food insecurity:

𝜀𝜀𝑖𝑖𝑗𝑗𝑗𝑗2 = 𝛾𝛾0 + ∑ 𝛾𝛾𝑘𝑘𝑋𝑋𝑖𝑖𝑗𝑗𝑗𝑗𝑘𝑘𝐾𝐾𝑘𝑘=1 + 𝜃𝜃𝑗𝑗𝑗𝑗 + 𝜔𝜔𝑖𝑖𝑗𝑗𝑗𝑗 . (5)

The estimated parameters of the food insecurity probability conditional mean function (left

column, Table 6, equation 3) are very similar to previously reported results using the same data

(Smith et al., 2017). For example, the probability that an individual is food insecure declines

at an increasing rate with household income over essentially the full support in the data.

Given our emphasis on inequality in food insecurity, we focus on the results of the conditional

variance equation (right column, Table 6, equation 5). The conditional variance captures how

the interpersonal dispersion of food insecurity within a country and year varies with observable

individual attributes (e.g., educational attainment, gender, income, marital status); reflecting

the dispersion among otherwise identical individuals within the same country and year,

providing a direct measure of inequality. Many of the same individual attributes that are

associated with the probability of a person being food insecure (Smith et al., 2017) also exhibit

a strong, statistically significant relationship with inequality (i.e., the conditional variance) in

food insecurity within a country-year. Interpersonal inequality in food insecurity is greatest at

50 years old, and correlated with being male, unmarried, and having children, low levels of

education and household income, having low levels of social capital and networks, being

located in an urban area, and working less than fulltime (Table 6, column 2). The country-year

fixed effect estimates, 𝜃𝜃�𝑗𝑗𝑗𝑗 , provide one further measure of the country-year-specific inequality,

19

different from the indices generated from the national prevalence estimates. The 𝜃𝜃�𝑗𝑗𝑗𝑗 estimates

represent the average expected country-and-year-specific interpersonal variance in the

probability of food insecurity after controlling for the many individual attributes included in

the 𝑋𝑋𝑖𝑖𝑗𝑗𝑗𝑗𝑘𝑘 vector. Figure 4 plots the 𝜃𝜃�𝑗𝑗𝑗𝑗 estimates against the national level food insecurity

prevalence, providing an analog to the Figure 3 estimates, but now having explicitly controlled

for the considerable within-country variation in food insecurity inequality. When we move

from macro to micro scale and estimate the individual-level relationship between food

insecurity inequality the same Kuznets Curve pattern emerges.

Figure 4: Scatter plot of country-year level prevalence of individual food insecurity (horizontal axis) and within-country-year inequality controlling for individual attributes (Table 6, column 2). Quadratic bivariate regression line in red.

20

Probability of being food insecure (1) - Conditional Mean (2) - Conditional Variance

Age 0.006*** 0.001***

(0.0004) (0.0002)

Age2 -0.0001*** -0.00001***

(0.000004) (0.000002)

Adults 0.003*** 0.001***

(0.001) (0.0003)

Children 0.011*** 0.002***

(0.001) (0.001)

Female 0.002 -0.001*

(0.002) (0.001)

Single -0.002 0.005***

(0.003) (0.001)

Separated, widowed or divorced 0.031*** 0.013***

(0.003) (0.002)

Educational attainment

Secondary -0.070*** -0.009***

(0.004) (0.002)

Post-Secondary -0.106*** -0.030***

(0.006) (0.003)

Log Household Income 0.049*** 0.015***

(0.004) (0.001)

Log Household Income2 -0.007*** -0.002***

(0.0004) (0.0002)

Social Network -0.050*** -0.012***

(0.003) (0.002)

Social Capital -0.106*** -0.010***

(0.005) (0.003)

Rural 0.013 -0.006***

(0.003) (0.001)

Self-employed -0.006** -0.001

(0.003) (0.001)

Part-time Employed 0.040*** 0.007***

(0.003) (0.001)

Unemployed 0.047*** 0.006***

(0.004) (0.002)

R2 0.422 0.123

21

Probability of being food insecure (1) - Conditional Mean (2) - Conditional Variance

Shapley Decomposition Shapley Value (Percent of R2 Explained)

Controls 0.190 (45.06) 0.048 (39.30)

Country-Year Fixed Effects 0.231 (54.65) 0.082 (66.84)

Table 6: Regression results for the conditional mean (left column) and the conditional variance (right column) of the probability of being moderately or severely food insecure. Robust standard errors in parentheses, clustered by country. Of the full sample of 562,840 individuals reported in Table 1, we lose 65,237 observations (11.6%) due to missing observations of one or more of the covariates, for a total of 497,603 observations in these regressions. Survey weights applied to all observations. All regressions include country-year fixed effects. ***, **, and * indicate statistical significance at the 1, 5, and 10 percent level, respectively.

In order to bridge the macro and micro-scale analyses presented above, we perform a Shapley

decomposition, which decomposes the explained variance of individual-level food insecurity

into contributions of each variable or groups of variables (Table 6, bottom panel). Most of the

variation in both the probability of being food insecure and in the variance of the probability

of being food insecure is associated with the country-year fixed effects. Put differently, most

of the variation is not explained by individual-level characteristics but rather by macro-level

phenomena specific to the entire population of a country or to temporal omitted variables

common to all countries. Dispersion among otherwise identical individuals varies more across

countries (and years) than within countries, consistent with previous food system inequity

research (Sheahan and Barrett 2017; Bell et al., 2021). This indicates that country-level policies

and programs (more so than increasing individual income, which is one of the individual-level

controls) have the potential to make large impacts on reducing inequality and of food

insecurity.

4. Discussion

What might give rise to the observed Kuznets Curve-type relationship between the prevalence

of and interpersonal inequality in food insecurity, especially when most of the variation is at

the country level and insignificantly associated with per capita GNI? These observational data

do not permit us to rigorously identify causal mechanisms, but the broader literature suggests

candidate hypotheses that we pose here to seed future research.

22

The populations of low-income agrarian economies are overwhelmingly rural, with high

prevalence rates of food insecurity, limited market access, and low trust in formal institutions

like governments and markets. This leads to greater reliance on informal social networks. These

networks buffer individuals against idiosyncratic shocks such that individuals’ consumption

fluctuations track community-level variation relatively strongly (Townsend, 1994; Ambrus et

al., 2014). This suggests high prevalence rates of food insecurity but relatively low inequality.

As countries urbanize, people come to rely more heavily on food markets, while social ties

weaken, independent of changes in per capita income (Barrett et al., forthcoming). With greater

market integration and access to public food assistance programs, the prevalence of food

insecurity decreases. But if social solidarity networks also weaken, individuals’ idiosyncratic

economic and health shocks might cause increasingly varied interpersonal food insecurity

experiences.

Our estimation results (Table 6) support this hypothesis, showing that inequality in food

insecurity is higher for individuals with smaller social networks. As public and formal private

(e.g., food bank and pantry) food assistance programs increasingly reach an ever-more urban

and higher-income population, filling the void left by the waning of informal social solidarity

networks within close-knit rural communities, both the prevalence and inequality of food

insecurity fall again. We thus hypothesize that the interim stage of urbanization and substitution

of formal social protection programs largely provided by governments and formal private

charitable organizations for informal safety nets – both phenomena only weakly correlated with

per capita GNI (Alderman et al., 2017) – could explain the increase in inequality at intermediate

food insecurity prevalence levels, i.e., the Kuznets Curve shape. These patterns may be

reinforced by organizational changes that occur as agri-food value chains modernize, a process

only weakly related to per capita income growth and urbanization (Barrett et al., forthcoming).

We emphasize, however, that these are conjectures untestable in our data.

23

5. Conclusion

The UN projects that the economic and health damage of the COVID-19 pandemic has

increased the prevalence of food insecurity globally (FAO et al. 2021; UN, 2021). Our

estimates suggest the pandemic will also likely increase within-country inequality in food

insecurity as the global prevalence of food insecurity increases from its pre-pandemic level of

26.4% towards the prevalence level at which food insecurity inequality peaks—roughly 46%

(Tables 3, 5). Our estimates also suggest the targeting of food assistance and other social safety-

net programs toward middle-income households and countries. For example, between 2011

and 2020, most of the countries that experienced a rise in undernourishment and an economic

downturn were middle-income countries (FAO et al., 2021). While the severity of food

insecurity is typically worse among low-income households in low-income countries, there are

simply more food insecure households in middle-income countries, where inequality in food

insecurity is highest. As the current pandemic and associated economic crisis increase the

prevalence of food insecurity globally, they are likely to aggravate existing food insecurity

inequality globally as well.

24

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Appendix

A.1 FIES Questions

“Now I would like to ask you some questions about food. During the last 12 months, was there a time when:

1. You were worried you would not have enough food to eat because of a lack of money or other resources?

2. You were unable to eat healthy and nutritious food because of a lack of money or other resources?

3. You ate only a few kinds of foods because of a lack of money or other resources? 4. You had to skip a meal because there was not enough money or other resources to get

food? 5. You ate less than you thought you should because of a lack of money or other resources? 6. Your household ran out of food because of a lack of money or other resources? 7. You were hungry but did not eat because there was not enough money or other

resources for food? 8. You went without eating for a whole day because of a lack of money or other

resources?”

A.2 Inequality Measures

Erreygers index: 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 = 1

𝑛𝑛∑ [4𝑏𝑏𝑖𝑖(2𝑅𝑅𝑖𝑖 − 1)].𝑛𝑛𝑖𝑖=1 (A1)

Generalized concentration index:

𝐺𝐺𝐸𝐸𝐺𝐺 = 1𝑛𝑛∑ �𝑣𝑣

𝑣𝑣𝑣𝑣−1

𝑣𝑣−1𝑏𝑏𝑖𝑖�𝑛𝑛

𝑖𝑖=1 [1 − 𝑣𝑣(1 − 𝑅𝑅𝑖𝑖)𝑣𝑣−1]. (A2)

Generalized symmetric concentration index:

𝐺𝐺𝑃𝑃𝐺𝐺 = 1𝑛𝑛∑ 4𝑏𝑏𝑖𝑖 �𝛽𝛽2𝛽𝛽−2 ��𝑅𝑅𝑖𝑖 −

12�2�𝛽𝛽−22�𝑅𝑅𝑖𝑖 −

12��𝑛𝑛

𝑖𝑖=1 . (A3)

The variable

𝑏𝑏𝑖𝑖 = 𝑎𝑎𝑖𝑖−𝑎𝑎𝑚𝑚𝑖𝑖𝑚𝑚

𝑎𝑎𝑚𝑚𝑚𝑚𝑚𝑚−𝑎𝑎𝑚𝑚𝑖𝑖𝑚𝑚, (A4)

is a transformation of a bounded variable into an indicator of the proportional deviation from the minimum value which can be obtained. Further, n is the number of observations, 𝑅𝑅𝑖𝑖 is the deviation of the rank from the mean (or median) rank and 𝑎𝑎𝑖𝑖 is the food insecurity indicator for individual i. 𝛽𝛽 is the order of the symmetric concentration index, and the minimum and maximum of the variable of interest are the scalar's lower limit and upper limit, 𝑣𝑣>1. We set 𝛽𝛽=3 and 𝑣𝑣=3 as in the literature (Erreygers, 2009; O’Donnell et al., 2016). Both are distributional sensitivity parameters, which specify the attitude toward inequality within the weights. Put differently, they determine the degree of sensitivity to extremity.

27

Figure A.1. Scatter plot of country-level prevalence of severe food insecurity (horizontal axis) and inequality measure (PSY) by year. Colors represent World Bank development classification. Quadratic bivariate regression line in red in each panel.

28

A.

B.

29

C.

Figure A.2. Scatter plot of country-level prevalence of food insecurity (horizontal axis) and inequality measure—Erreygers (A), GSC (B), and GEC (C) by year. Colors represent World Bank development classification. Quadratic bivariate regression line in red in each panel.

Figure A.3. Scatter plot of log Gross National Income per capita versus the food insecurity prevalence rate for each year. Quadratic bivariate regression line in red in each panel.