# Poor health and food insecurity among food assistance recipients: Evidence from France

Romane Vandroux, François-Charles Wolff

► To cite this version:

Romane Vandroux, François-Charles Wolff. Poor health and food insecurity among food assistance recipients: Evidence from France. Food Policy, 2025, 134, pp.102895. 10.1016/j.foodpol.2025.102895. hal-05251693

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# Poor health and food insecurity among food assistance recipients: Evidence from France☆

Romane Vandroux<sup>a, *,</sup> François-Charles Wolff<sup>b</sup>

<figure><img src="image_2.png" /></figure>

## ARTICLE INFO

JEL classification:

I12

I14

I38

Keywords:

Food insecurity

Poor health

Food assistance

France

## ABSTRACT

This paper examines the relationship between food insecurity and poor health among food assistance recipients in France using a dataset collected in 2021 from nearly 4,000 respondents. For these individuals from disadvantaged socio-economic backgrounds, food assistance may eliminate the association between food insecurity and health reported in surveys of the general population. Regression estimates show a strong positive association between food insecurity and poor health (self-reported health, chronic disease, activity limitation). This correlation is significantly higher for native respondents than for migrants. After accounting for the endogeneity of food insecurity through a free-instrument approach that estimates bounds, we confirm the positive association between food insecurity and poor health. The low frequency of visits to food banks may explain why food insecurity persists among participants and continues to affect health.

## 1. Introduction

According to the Food and Agriculture Organization of the United Nations, food insecurity is defined as the lack of access to adequate food for normal growth and development and for a healthy and active life. It has multiple causes, mainly related to poverty, unemployment, chronic health conditions, large family size, single parenthood, weak social networks, inadequate social safety nets, food waste or climate change (Smith et al., 2000; Gundersen and Ziliak, 2014). Food insecurity is a serious concern not only in developing countries, but also in rich countries (Smith et al., 2017). From a health perspective, food insecurity is consistently associated with a range of adverse outcomes, including increased risk of chronic disease, impaired mental health, obesity, or premature mortality (Gundersen et al., 2015, 2018; Weaver and Fasel, 2018, 2021; Trudell et al., 2021).

Many developed countries have attempted to respond to food insecurity by providing food assistance, either through food assistance programs such as the Supplemental Nutrition Assistance Program in the United States or access to food banks and other charitable food services provided by third sector organizations (Loopstra, 2018). These programs

have positive effects on their recipients (Ratcliffe et al., 2011; Huang and Barnidge, 2016), but food insecurity still remains a public health concern in wealthy countries, presumably because food assistance does not address the root causes of food insecurity (Roncarolo & Potvin, 2016; Pollard and Booth, 2019). Community-based food interventions may even have harmful effects. Seeking food assistance is associated with, and may then reinforce, precariousness and marginalization (Thompson et al., 2018), and people who use food banks very often report stigma and shame (Middleton et al., 2018).

This paper examines the strength of the relationship between food insecurity and poor health among food assistance recipients in France. Unlike high-income countries such as Canada and the United States, which regularly monitor food insecurity in population and national health surveys, there is very little empirical evidence for France due to a lack of adequate household-level data, although there are some exceptions (Roustit et al., 2010; Martin-Fernandez et al., 2014; Bocquier et al., 2015; Pryor et al., 2016).

Differences in social policies and cultural factors can lead to variations in the relationship between poor health and food insecurity across countries. In France, the food assistance system and social safety net

<footnote><sup>a</sup> Anthropo-Lab, ETHICS EA 7446, Lille Catholic University, France</footnote>

<footnote><sup>b</sup> LEMNA, Nantes Université and TEPP, BP 52231 Chemin de la Censive du Tertre, 44322 Nantes Cedex, France</footnote>

<footnote>* We are indebted to the co-editor-in-chief, Christopher Barrett, and three anonymous reviewers for their numerous constructive comments and very helpful suggestions. We would also like to thank Moustapha Sarr, Philippe Tessier, Nicolas Vaillant and the participants of the ETEPP Winter School (Aussois) and the Journées de Microéconomie Appliquée (Lille). Access to the survey data "lil-1582: Enquête aide alimentaire – 2021" was obtained through a signed agreement with the Archives des Données Issues de la Statistique Publique (ADISP). Any remaining errors are ours.</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail addresses: romane.vandroux@univ-catholille.fr (R. Vandroux), francois.wolff@univ-nantes.fr (F.-C. Wolff).</footnote>
differ from those in North America. In particular, the French context may moderate the relationship through universal health coverage. We examine the association between food insecurity on poor health using a survey on food assistance that was conducted in 2021 on a sample of nearly 4,000 respondents interviewed at food assistance distribution sites. The focus on people from disadvantaged socioeconomic backgrounds is interesting because food assistance is expected to reduce food insecurity and therefore weaken or even eliminate the association between food insecurity and poor health.

In our empirical analysis, we highlight the precarious situation of respondents interviewed at food distribution centers who are twice as likely as the general population to report being in fair or poor health. We find a very strong positive correlation between poor health and food insecurity, regardless of the measure of health used (self-reported health, chronic disease, activity limitation). Interestingly, we contrast the situation of the native-born with that of the foreign-born. We find a weaker correlation between poor health and food insecurity among immigrants. Since food insecurity may be endogenous in the health equations (Gundersen and Ziliak, 2015), we further assess the robustness of our results by estimating bounds for the association between poor health and food insecurity using a free-instrument approach.

The remainder of our paper is organized as follows. In Section 2, we briefly review the literature and discuss our research hypothesis in the context of food assistance recipients. Section 3 presents some information on food assistance in France and describes the data. Section 4 includes descriptive statistics on both food insecurity and health for the selected sample. The econometric results are discussed in Section 5. Section 6 examines the robustness of our results with respect to endogeneity issues. Finally, Section 7 provides a discussion along with some limitations of our analysis.

## 2. Background on food insecurity and health

*Mechanisms and evidence.* Food insecurity is expected to affect health in a number of ways, both directly and indirectly. In terms of direct effects, food insecurity is likely to lead to nutrient deficiencies, which can have adverse consequences such as impaired growth and development or increased susceptibility to infection (World Bank, 2006; WHO, 2021). It can also increase the risk of developing chronic diseases such as heart disease and type 2 diabetes (Venci and Lee, 2018; Weaver and Fasel, 2018; Thomas et al., 2021). The risk of malnutrition can damage the brain and impair cognitive function, which can affect learning, memory or attention (Scrimshaw, 1998; Kar et al., 2008; de Souza et al., 2011). Food insecurity can also increase the likelihood and severity of stress and anxiety, leading to an increased risk of depression or other mental health problems (Huang et al., 2013; Thomas et al., 2021; Elgar et al., 2021).

There may also be some indirect effects when food insecurity reduces access to health care, which can prevent people from getting the treatment they need for their health problems. Food insecurity is also often associated with adverse social and economic conditions, such as poverty, unemployment, and low educational attainment. Several reviews have been conducted on the association between food insecurity and health, in both developed and developing countries (Lee et al., 2012; Gundersen and Ziliak, 2015; Darmon and Caillavet, 2017; Weaver et al., 2018; Pourmotabbed et al., 2020; Trudell et al., 2021; Beyene, 2023). All studies show that the correlation between food insecurity and good health is negative, whether measured by self-reported or clinical indicators.

While the prevalence of food insecurity is regularly assessed in North American countries through national surveys, very few studies have focused on the relationship between health and food insecurity in France. In this country, the first studies on food insecurity were initially limited in geographical scope (Martin-Fernandez et al., 2013; Martin-Fernandez et al., 2014) or focused on disadvantaged socioeconomic groups (Roustit et al., 2010). The first national survey to explicitly

introduce a measure of food insecurity was conducted in 2006 and 2007 (Dubuisson et al., 2010). Bocquier et al. (2015) find that individuals who are food insecure spend more time watching television and are more likely to be occasional or daily smokers. Using a cohort of employees of a national gas and electric company, Pryor et al. (2016) show that food insecurity among young adults is associated with an increased risk of depression, suicidal ideation, and substance abuse problems.

Issue of causality and endogeneity are important when focusing on the relationship between food insecurity and health (Gundersen and Ziliak, 2015, p. 1836). In a few cases, the causal direction is obvious, such as when limited nutrient intake leads to health problems. In many situations, however, it is less clear whether food insecurity is the cause of health problems or vice versa. For example, people with depression may gradually lose their jobs and experience a worsening economic situation, which would have a negative impact on their food insecurity. Controlling for observables when studying the relationship between food insecurity and health can be misleading, as there may be unobserved factors that make people both more likely to be food insecure and more likely to suffer from health problems. Section A of the external Appendix briefly summarizes papers that have reported causal evidence.

*Research hypothesis in the context of food assistance.* We examine the impact of food insecurity on the health of individuals who receive food assistance. Such programs may help to mitigate or even eliminate the association between food insecurity and health, by providing access to nutritious foods and enabling families to meet their dietary needs. First, food assistance programs provide access to a variety of nutritious foods and improved diet quality should contribute to a reduction in obesity, heart disease, or diabetes. Second, food assistance will alleviate the severity of food insecurity by providing a safety net for people who face challenges in accessing sufficient and nutritious food. Third, food assistance can facilitate access to healthcare services by freeing up financial resources that would otherwise be spent on food. Fourth, access to nutritious food can support children's growth and cognitive development and have long-lasting effects on health and well-being.

A few papers have examined whether participation in food assistance programs ameliorates some or all of the effects of food insecurity and adverse health outcomes (Frongillo, 2003; Jones et al., 2003). Looking at older adults in the United States, Kim and Frongillo (2007) show that food-insecure elders who participate in food assistance programs are less likely to be overweight and depressed. Focusing on the Covid pandemic, Lee et al. (2023) find that participation in food pantries and food programs moderates the association between food insecurity and lower food consumption. Using a randomized trial, Ferrer et al. (2019) show that patients with type 2 diabetes improved after receiving fresh products from the food bank, along with discussions with a registered dietitian.

Gundersen and Ziliak (2015, p. 1838) suggest that food assistance programs can be useful “to alleviate food insecurity and, in turn, its associated poor health consequences”. In their systematic review, Bazerghi et al. (2016) conclude that food banks play an important role in providing solutions to severe food deprivation, but point to some limitations in the ability of food banks to fundamentally improve food insecurity. Food banks may provide insufficient amounts of nutritious foods and may not meet the needs of recipients due to cultural or religious requirements. Local agencies have limited capacity to provide food to a growing number of people in need. Finally, accessing food assistance can be stigmatized, leading to feelings of shame or embarrassment that may discourage people from seeking help.

Thus, we hypothesize that food bank use may moderate or even eliminate the negative association between poor health and food insecurity. However, the correlation may still persist if food assistance programs do not provide recipients with sufficient resources to escape food insecurity.
### 3. Context and data

**Context.** In France, food assistance is provided primarily through a network of organizations and associations, such as food banks (Banques Alimentaires), Les Restos du Cœur, Secours Populaire and the Croix-Rouge. Food banks correspond to non-profit organizations that collect, store, and distribute food to individuals and families in need, often through partnerships with charities, community organizations, and social service agencies. They aim to reduce food insecurity by providing access to essential food supplies, either directly or through local distribution networks.

These organizations collect food donations from a variety of sources, including supermarkets, the food industry, and private donors, and redistribute them to people facing economic hardship. According to Accardo et al. (2022), most beneficiaries in France receive food assistance in the form of food parcels (71 %), followed by social food shops (29 %) and meal distribution services (12 %). Food parcels consist of pre-selected food items that are delivered directly to beneficiaries. Social grocery stores operate like regular shops, but offer products at significantly reduced prices (10–30 % of market prices). Meal distribution services provide ready-to-eat meals, often without strict eligibility requirements.

Food assistance does not include direct financial support. However, some beneficiaries may receive additional social benefits such as the Revenu de Solidarité Active (RSA) or the Allocation de Solidarité Spécifique (ASS), which are granted on the basis of income, employment status and household composition. Eligibility for food assistance requires individuals to demonstrate financial hardship through an application process assessed by social workers or partner organizations. These criteria ensure that food assistance is targeted to those most in need.

Access to food assistance is determined by socioeconomic conditions rather than nationality. Immigrants with legal status are eligible for these programs, as well as social assistance under certain conditions. Asylum seekers may also be eligible for specific assistance programs, such as emergency assistance or targeted assistance for vulnerable persons. However, undocumented migrants may face administrative barriers to accessing public assistance, although they are often supported by humanitarian organizations to ensure that those without official documentation can receive assistance in times of need.

In terms of access to health care, immigrants with regular status have access to the Universal Health Coverage (PUMa), which guarantees access to health care while contributing to cost sharing, particularly through co-payments and medical deductibles. Immigrants with irregular status can benefit from the State Medical Assistance (AME), which provides basic health coverage under certain conditions. However, administrative and financial barriers may limit access to care for some populations, thereby exacerbating health inequalities.

In terms of eligibility, individuals applying for food assistance are generally required to provide evidence of financial hardship. This may include documentation such as proof of income, employment status, and family situation. Social workers or partner agencies evaluate these documents to determine the applicant's eligibility. In addition, some agencies may have specific requirements, such as residency status or temporary housing situations, to further ensure that assistance reaches those most in need.

A recent survey by Byrne and Just (2022) provides a comparative view of food bank systems in high-income countries. Compared to other countries, France is a distinctive hybrid case shaped by binding regulatory instruments that secure the supply chain for charities, while raising challenges in terms of food diversity and territorial equity. The French model stands out for its strong national coordination, integration into public policy, and unique regulatory framework. The Garot Law (2016) requires large supermarkets to donate unsold food items to charitable organizations. This obligation ensures a more regular and predictable supply chain, which is often dominated by non-perishable

goods. However, this comes at the cost of reduced nutritional diversity, particularly for fresh or high-value items.

In contrast, other high-income countries tend to rely on indirect incentives. For example, the United States, Australia and Canada provide legal protections for food donors in case of food safety issues. Australia also implements federal subsidy programs. Fiscal incentives are common in Canada, the United Kingdom, Germany, Spain, and South Korea. While these approaches often result in a greater diversity of food donations, including fresh products, they also lead to significant regional disparities and dependency on corporate donors' logistics and strategies. Priorities diverge as well. Germany emphasizes reducing food waste, while the United States focuses more on addressing food insecurity. France attempts to reconcile both goals, but the comparatively low density of its food bank network, particularly in rural and overseas areas, raises concerns about local accessibility.

**Data.** The data come from the Food Assistance survey conducted by the National Institute for Statistics and Economic Studies (INSEE). The aim of this survey was to better understand the population using food assistance in distribution centers located in metropolitan France, particularly those made vulnerable by the COVID-19 health crisis (Accardo et al., 2022). The survey was primarily designed to collect sociodemographic characteristics of food aid recipients, with a focus on those who were visiting the centers for the first time due to the pandemic. However, the survey was not designed to measure food hardship, which could have affected responses due to social desirability bias. This would occur if respondents underreported their food insecurity for fear of losing access to food assistance. This is unlikely to be the case, as the survey focused on the living conditions of the respondents.

This survey, conducted between November 15 and December 10, 2021, targeted recipients of food assistance. They were interviewed face-to-face at food assistance distribution sites. Data were collected from 235 food distribution centers in metropolitan France. The sample is representative of food assistance activities provided by the nonprofit sector, including large food assistance networks and independent associations. Face-to-face interviews were conducted with a random sample of individuals visiting each center. Participants were required to be at least 16 years old. For those who did not speak French, questionnaires were administered in English. As all respondents are dependent on food assistance, they are characterized by a situation of considerable vulnerability: those seeking food assistance are generally the poorest of the poor in monetary terms. According to Accardo et al. (2022), between 3.2 and 3.5 million people in France received food aid in 2021.

The following selections were applied to the sample of the Food Assistance survey. First, we consider only respondents between the ages of 18 and 75 (101 observations dropped). We then delete 51 observations for which the nationality at birth was not reported, and we drop observations for which information on our variables of interest is missing (104 observations for health, 193 observations for food insecurity). For education, we construct a special category for missing diplomas (8.6 %). Monthly income was obtained using a method of simulated residuals (Gouriéroux et al., 1987), since almost one-third of the households reported their income within an interval rather than an exact amount. In total, the sample consists of 4,066 observations.

We compare the characteristics of the participants in the Food Assistance survey with those of the participants in the Employment survey conducted by INSEE in 2021. Table 1 shows the large difference between the sample of food aid recipients (Food Assistance survey, column 1) and the sample representative of the general population (Employment survey, column 4). The proportion of women is much higher among food aid recipients (65.4 %) than in the general population (51.6 %). They are on average younger (43.8 years compared to 46.6) and more likely to be single. Conversely, there is a much higher proportion of people with foreign citizenship at birth in the Food Assistance survey (44.1 % against 12.2 %). Food assistance recipients are less educated, less likely to be in employment, and more than five times as likely to be unemployed. The average income of food aid
<table><caption>**Table 1**

Descriptive statistics of the sample, by origin.</caption><thead><tr><th rowspan="2">Variables</th><th colspan="3">Food assistance survey</th><th colspan="3">Employment survey</th></tr><tr><th>(1) All</th><th>(2) Native</th><th>(3) Foreign</th><th>(4) All</th><th>(5) Native</th><th>(6) Foreign</th></tr></thead><tbody><tr><td>Female</td><td>0.654</td><td>0.676</td><td>0.627</td><td>0.516</td><td>0.514</td><td>0.530</td></tr><tr><td>Age</td><td>43.8</td><td>47.8</td><td>38.6</td><td>46.6</td><td>46.6</td><td>46.7</td></tr><tr><td>In couple</td><td>0.290</td><td>0.231</td><td>0.364</td><td>0.621</td><td>0.613</td><td>0.674</td></tr><tr><td>With children</td><td>0.480</td><td>0.451</td><td>0.516</td><td>0.500</td><td>0.487</td><td>0.599</td></tr><tr><td>Foreign-born</td><td>0.441</td><td>0.000</td><td>1.000</td><td>0.122</td><td>0.000</td><td>1.000</td></tr><tr><td>EducationNo diploma</td><td>0.266</td><td>0.241</td><td>0.300</td><td>0.150</td><td>0.124</td><td>0.334</td></tr><tr><td>At most high school</td><td>0.518</td><td>0.633</td><td>0.365</td><td>0.410</td><td>0.429</td><td>0.269</td></tr><tr><td>More than high school</td><td>0.216</td><td>0.126</td><td>0.336</td><td>0.361</td><td>0.368</td><td>0.315</td></tr><tr><td>Employed</td><td>0.145</td><td>0.159</td><td>0.126</td><td>0.601</td><td>0.608</td><td>0.551</td></tr><tr><td>Unemployed</td><td>0.283</td><td>0.343</td><td>0.207</td><td>0.049</td><td>0.045</td><td>0.079</td></tr><tr><td>Inactive</td><td>0.578</td><td>0.506</td><td>0.669</td><td>0.350</td><td>0.347</td><td>0.370</td></tr><tr><td>Income in euros Average</td><td>932.4</td><td>1039.0</td><td>797.4</td><td></td><td></td><td></td></tr><tr><td>Median</td><td>897.2</td><td>986.1</td><td>780.8</td><td>1930.0*</td><td></td><td></td></tr><tr><td>Number of observations</td><td>4,066</td><td>2,311</td><td>1,755</td><td>254,663</td><td>226,380</td><td>28,283</td></tr></tbody></table>

Source: authors' calculations, data from INSEE Food assistance survey 2021 and INSEE Employment survey 2021.

Note: # the median income is an estimation based on the INSEE Fiscal and Social Income survey 2021 (Albouy et al., 2023). Significance levels for the mean-comparison tests are 1% (***), 5% (**) and 10% (*).

recipients is 932 euros (the median income is 890 euros). These figures illustrate the precarious situation of food aid recipients.

Table 1 also shows notable differences between native and foreign-born respondents according to the Food Assistance survey (columns 2 and 3). The proportion of female respondents is slightly higher (67.6%

against 62.7%), native-born persons are on average much older (47.8 years against 38.6 years), and fewer native-born individuals live in a couple (23.1% against 36.4%). Foreign-born individuals are more likely to have more than a high school education (33.6% against 12.6%), but their unemployment rate is 1.66 times higher than that of

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Pattern of food insecurity, by origin.</figcaption></figure>

Source: authors' calculations, data from INSEE Food assistance survey 2021.
natives (34.3 % against 20.7 %). Finally, native individuals have a higher average income (+30 %, 1039 euros against 797.4 euros). These differences highlight the disadvantaged position of foreign-born individuals in relation to food assistance.

## 4. Descriptive statistics on food insecurity and health

The Food Assistance survey includes a specific module on food insecurity. Respondents are asked to answer the following seven questions about their experiences in the past month: 1) “Did you worry that your household would not have enough food?”; 2) “Did you go to bed hungry?”; 3) “Did you eat food that you liked less because it was cheaper?”; 4) “Did you reduce the variety or diversity of food you eat?”; 5) “Have you borrowed food or relied on help from friends or relatives?”; 6) “Have you reduced the quantities of food eaten by adults for the benefit of children?”; 7) “Have you reduced the quantity of food at mealtimes or the number of meals you take?”. Possible answers are “often”, “sometimes” and “never”. We exclude the sixth question on intergenerational trade-offs because of the large proportion of childless respondents.

The Food Assistance survey includes several indicators that assess the prevalence of coping strategies in the face of food insecurity. Fig. 1 shows the different forms of food insecurity reported by food aid recipients in the past month, both for the whole sample and by origin. Households were more concerned about eating cheaper food (37.9 % often, 31.2 % sometimes) or reducing the variety of food consumed (36.2 % often, 33.2 % sometimes). About one in two respondents said they had worried about running out of food and had reduced the frequency of meals or the amount eaten. Foreign-born people are more likely than natives to worry about eating cheaper food and to reduce the quantity of food or the number of meals. We construct a single synthetic index of food insecurity from these six questions using a polychoric principal component analysis (Kolenikov and Angeles, 2009) (see Section A of the external appendix).

The Food Assistance survey includes three questions that provide information about the health status of respondents. The first question concerns self-assessed health: “What is your health status in general?”, with five responses: “very good”, “good”, “fair”, “poor” and “very poor”. The three categories “fair”, “poor” and “very poor” are combined into a single indicator of poor health (as opposed to “good” and “very good”). The second question asks about the presence or absence of chronic diseases: “Do you have any chronic or long-term illness or health problem?”, with two answers: “yes” or “no”. The third question asks about any limitations in daily activities due to the participant’s health status: “Have you been limited, for at least six months in the activities that people usually do because of a health problem?”, with three answers: “yes”, “yes, but not much”, “no, not at all” (the first two modalities are grouped together). These are the questions usually asked in the various surveys carried out by INSEE in France, and these three measures are available in the 2021 Employment survey.

Table 2 shows marked differences between food aid recipients (column 1) and the general population (column 4) for the three health indicators. Food aid recipients are almost twice as likely to be in poor health. Almost one in two respondents (49.6 %) receiving food aid reported fair or poor health (23.3 % of the general population), 47.0 %

reported a chronic illness (against 29.9 %), and 39.4 % reported being limited in their activities due to health problems (against 17.6 %). Data from the Food Aid survey 2021 also indicates that native-born individuals tend to have worse health outcomes than foreign-born individuals (columns 2 and 3). This pattern may be related to the healthy immigrant effect, with self-selection of healthier individuals who are more likely to leave their country of origin (Newbold, 2005, 2006; Kennedy et al., 2015; Elshahat et al., 2022). Foreign-born individuals tend to be in better health than natives upon arrival in a new country, but the health advantage of immigrants may diminish over time due to acculturation and the adoption of less healthy behaviors.

We then look at the correlation between poor health and food insecurity. Fig. 2 shows a positive association for each health indicator (poor health, chronic disease, activity limitation). For instance, the food insecurity index is -0.22 for respondents who report good or very good self-assessed health, but 0.20 for those in poor or fair health. The coefficients of correlation for the three health indicators range from 0.10 to 0.15.

Since there are differences in health between the native and foreign-born people, we study whether this affects the correlation between poor health and food insecurity. On the one hand, the association between these two outcomes is always positive. On the other hand, the correlation is about twice lower for the foreign-born than for the native-born: 0.09 against 0.19 for fair-poor health, 0.08 against 0.12 for chronic disease, and 0.08 against 0.16 for activity limitation. In the next Section, we turn to an econometric analysis to assess the role of respondent characteristics on the relationship between health and food insecurity.

## 5. Estimates of health under exogenous food insecurity

We now study the relationship between food insecurity and the three health variables, controlling for the influence of respondent characteristics. Let $H^k$ be a health indicator with $k \in \{1, 2, 3\}$ such that $H^k = 1$ denotes poor health status (self-assessed poor health for $k = 1$, chronic disease for $k = 2$, and activity limitation for $k = 3$), and $H^k = 0$ otherwise. We use the following linear probability models:

$$H_{ci}^k = \delta^{k*} FII_{ci} + X_{ci} \rho^k + \theta_c^k + \varepsilon_{ci}^k \quad (1)$$

where $FII_{ci}$ is the food insecurity index for individual $i$ interviewed in center $c$, $X_{ci}$ is a vector of demographic and socioeconomic characteristics, $\delta^k$ and $\rho^k$ are parameters to be estimated, $\theta_c^k$ is a distribution center fixed effect, and $\varepsilon_{ci}^k$ is a residual. Because respondents were interviewed at a number of distribution centers during their food assistance visits, we are able to account for the center characteristics through the fixed effect $\theta_c^k$. It captures time-invariant characteristics specific to each distribution center and is helpful in controlling for supply-side factors. The association between $FII$ and $H$ is measured by the coefficient $\delta^k$. We assume that $E[\varepsilon_{ci}^k | FII_{ci}, X_{ci}] = 0$. The food insecurity index is supposed to be exogenous in equation (1). Since we have multiple respondents per food assistance distribution center, standard errors are clustered at the level of these distribution centers.

The results for the full sample are shown in panel A of Table 3. For the three health indicators, we find a positive correlation between food insecurity and poor health status that is statistically significant at the 1

<table><caption>**Table 2**
Pattern of poor health, by origin.</caption><thead><tr><th rowspan="2">Variables</th><th colspan="3">Food Aid survey 2021</th><th colspan="3">Employment survey 2021</th></tr><tr><th>(1) All</th><th>(2) Native</th><th>(3) Foreign</th><th>(4) All</th><th>(5) Native</th><th>(6) Foreign</th></tr></thead><tbody><tr><td>Poor self-assessed health</td><td>0.496</td><td>0.565</td><td>0.408</td><td>0.233</td><td>0.226</td><td>0.279</td></tr><tr><td>Chronic disease</td><td>0.470</td><td>0.573</td><td>0.340</td><td>0.299</td><td>0.297</td><td>0.312</td></tr><tr><td>Activity limitation</td><td>0.394</td><td>0.477</td><td>0.289</td><td>0.176</td><td>0.173</td><td>0.195</td></tr><tr><td>Observations</td><td>4,066</td><td>2,311</td><td>1,755</td><td>41,498</td><td>36,854</td><td>4,644</td></tr></tbody></table>

Source: authors' calculations, data from INSEE Food assistance survey 2021 and INSEE Employment survey 2021.
<figure><img src="image_4.png" /><figcaption>Fig. 2. Correlation between poor health and food insecurity.</figcaption></figure>

Source: authors' calculations, data from INSEE Food assistance survey 2021.

percent level. The probability of reporting poor health is 8.3 percentage points higher when the food insecurity index increases by one standard deviation (1.426*0.058 = 0.083). The increase is 6.3 points for chronic disease and 7.1 points for activity limitation. Each regression controls for the following individual characteristics: gender, age (11 five-year groups), marital status, parental status, foreign origin, educational attainment, having a job, unemployment and income quartiles. The detailed estimates are presented in Table B1 of Section B of the external Appendix. Panel A shows large differences between native-born and foreign-born respondents, with the latter being much less likely to report poor health (around -8 percentage points).

We further examine the role of origin by estimating separate regressions for natives (panel B) and foreign-born (panel C) (see also Tables B2 and B3 in the external appendix). The estimates are consistent with the descriptive results presented in Fig. 2. In each column, the positive coefficient found for the food insecurity index is higher for the native-born than for the foreign-born. For instance, when the food insecurity index increases by one standard deviation, the probability of reporting poor self-assessed health is 11.5 points higher (1.455*0.079 = 0.115) for natives, but only 4.0 points higher (1.388*0.029 = 0.040) for the foreign-born. We estimate seemingly unrelated regressions to test the null assumption of equal parameters $\delta^k$ for natives and foreign-born. The Chi² statistic associated with this test is 19.32 (p = 0.000) for poor health, 5.01 (p = 0.025) for chronic disease, and 6.79 (p = 0.009) for activity limitation. Thus, the null hypotheses are all rejected, meaning that the association between food insecurity and poor health is lower for the foreign-born than for the native-born.

We conduct three robustness checks. First, we relax the linear

probability specification and instead consider fixed effect Logit regressions, since the three dependent variables are binary (Chamberlain, 1980). We report the estimates in Tables C1, C2 and C3 in Section C of the external Appendix. Unsurprisingly, we obtain very similar results. For instance, the coefficient of food insecurity in the poor self-assessed health equation with the conditional Logit estimator is 0.050 (p = 0.000), which is very close to the coefficient of 0.058 obtained from the linear probability model for this outcome.

Second, we treat the self-assessed health variable as categorical and examine the relationship between the food insecurity index and the five health categories, ranging from “very good” to “very poor”. In Fig. 3, we plot the predictive margins (average predicted probability) obtained from an ordered Logit regression for each level of self-assessed health for the full sample, with food insecurity levels ranging from -2 to 2. Consider first the case of “very good” health. The probability is halved as the food insecurity index moves from -2 to +2. The trend also shows a decrease for “good” health, although the coefficient of food insecurity is less pronounced. Conversely, the trend increases for “fair” health, but the influence of food insecurity is also limited. The situation is different for “poor” health and “very poor” health. Respondents with a high food insecurity index are much more likely to report these poor health outcomes. We also plot the profiles for natives and foreign-born. Regardless of the level of health, we observe that the curves are flatter for the foreign-born than for the natives, confirming the weaker association.

Third, we explore other potential sources of heterogeneity in the association between poor health status and food insecurity using three different criteria: gender, age (with three groups, 35 and under, 36 to 55, and over 55), and income quartiles. We estimate specific regressions for
<table><caption>**Table 3**
Estimates of health outcomes.</caption><thead><tr><th>Variables</th><th>(1) Fair/poor self-assessed health</th><th>(2) Chronic disease</th><th>(3) Activity limitation</th></tr></thead><tbody><tr><td>Panel A. All</td><td></td><td></td><td></td></tr><tr><td>Food insecurity index</td><td>0.058***<br>(0.006)</td><td>0.044***<br>(0.006)</td><td>0.050***<br>(0.005)</td></tr><tr><td>Foreign origin</td><td>-0.090***<br>(0.019)</td><td>-0.082***<br>(0.019)</td><td>-0.082***<br>(0.019)</td></tr><tr><td>Control variables</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Centre fixed effects</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Number of observations</td><td>4,066</td><td>4,066</td><td>4,066</td></tr><tr><td>R<sup>2</sup></td><td>0.177</td><td>0.227</td><td>0.203</td></tr><tr><td>Panel B. Native</td><td></td><td></td><td></td></tr><tr><td>Food insecurity index</td><td>0.079***<br>(0.007)</td><td>0.051***<br>(0.007)</td><td>0.059***<br>(0.007)</td></tr><tr><td>Control variables</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Centre fixed effects</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Number of observations</td><td>2,311</td><td>2,311</td><td>2,311</td></tr><tr><td>R<sup>2</sup></td><td>0.208</td><td>0.230</td><td>0.217</td></tr><tr><td>Panel C. Foreign</td><td></td><td></td><td></td></tr><tr><td>Food insecurity index</td><td>0.029***<br>(0.010)</td><td>0.027***<br>(0.009)</td><td>0.032***<br>(0.009)</td></tr><tr><td>Control variables</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Centre fixed effects</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Number of observations</td><td>1,755</td><td>1,755</td><td>1,755</td></tr><tr><td>R<sup>2</sup></td><td>0.247</td><td>0.298</td><td>0.291</td></tr></tbody></table>

Source: authors' calculations, data from INSEE Food assistance survey 2021.

Note: estimates from linear probability models with standard errors clustered at the distribution center level in parentheses. Significance levels are 1% (***), 5% (**) and 10% (*).

<figure><img src="image_5.png" /><figcaption>**Fig. 3. Predictive margins of food insecurity index on self-assessed health.**</figcaption></figure>

Source: authors' calculations, data from INSEE Food assistance survey 2021. Note: predictive margins from an ordered Logit model with standard errors clustered at the distribution center level. Confidence intervals are at the 95% level.
<figure><img src="image_6.png" /><figcaption>Fig. 4. Heterogeneity in the correlation between poor health and food insecurity.</figcaption></figure>

Source: authors' calculations, data from INSEE Food assistance survey 2021. Note: estimates from fixed effect linear models with standard errors clustered at the distribution center level. Confidence intervals are at the 95% level.

each subsample. We report the marginal effects of the food insecurity index obtained from fixed effect linear regressions in Fig. 4. The main result is that there is no difference in the magnitude of the correlation for gender, age, and income quartile, which contrasts with the role of origin emphasized earlier.

We further examine the situation of migrants by first taking into account the years spent in the country of origin. Due to the sample size, we distinguish between migrants who arrived in France in the last five years (between 2018 and 2022, 619 migrants) and those who arrived before 2018 (1001 migrants). For both self-assessed health and activity limitation, we find a positive correlation between poor health and food insecurity for migrants who arrived in France more than 5 years ago, but the association is insignificant for recent migrants. For poor self-assessed health, the coefficient of food insecurity is 0.026 (p = 0.129) for recent migrants compared to 0.035 (p = 0.010) for older migrants.

We also examine the influence of the place of birth by considering three groups: North African immigrants (53.4% of foreign respondents), Sub-Saharan African immigrants (28.1%), and other immigrants (18.6%). The proportion of respondents reporting poor health is 45.4% for North African immigrants, 31.3% for Sub-Saharan African immigrants, and 42.1% for other origins. We estimate a fixed effect linear regression with origin-specific dummies and interaction terms that cross the different nationalities at birth and the food insecurity index. Regarding poor self-assessed health, the correlation is 0.077 (p = 0.000) for respondents with French nationality at birth. For North Africans, it is 0.035 (p = 0.007), and for other origins, it is 0.048 (p = 0.000). Conversely, this correlation is not significant for Sub-Saharan African immigrants (0.014 with p = 0.276). A similar result is observed for chronic disease, with a non-significant correlation of 0.010 (p = 0.443) for Sub-Saharan immigrants, but the correlation is significant for activity limitation (0.026, p = 0.040).

## 6. Endogeneity issues

So far, we have assumed the exogeneity of the food insecurity index in the health equations. However, if the covariate *FII* is correlated with the error term $\varepsilon^k$ in the health equations, the estimation of $\delta^k$ in (1) could be biased. Given our static framework, there are three potential sources of endogeneity: measurement error, omitted variables, and simultaneity.

The first concern relates to the measurement error in the food insecurity index. Suppose that $FII^*$ is the true index of food insecurity, but that we observe only the imperfectly constructed index $FII = FII^* + \omega$, where $\omega$ is the measurement error. The unbiased association between food insecurity and health would be obtained by estimating $H_i^k = \delta^{k*}FII_i^* + X_i\beta^k + \varepsilon_i^k$, from which we deduce $H_i^k = \delta^{k*}FII_i^* + X_i\beta^k + \zeta_i$ with $\zeta_i = -\delta^k\omega + \varepsilon_i^k$. In this case, both $FII_i$ and $\zeta_i$ are correlated because they depend on $\omega$.

If the mean-zero error is uncorrelated with the true variable, then measurement error in an explanatory variable will typically lead to attenuation bias and the true association between food insecurity and health is likely to be underestimated. However, in our context, measurement error may be either non-classical or mean-reverting, with systematic under-reporting among severely food-insecure households or over-reporting due to stigma. Such a pattern can alter the direction or magnitude of bias in ways that differ from classical predictions (Bollinger and David, 1997).

A second concern arises when endogeneity results from a confounding variable Z that is correlated with both the dependent variable and at least one explanatory factor. This is a situation where we estimate $H_i^k = \delta^{k*}FII_i^* + X_i\beta^k + \varepsilon_i^k$, whereas the correct model should be $H_i^k = \delta^{k*}FII_i^* + X_i\beta^k + \theta^k Z_i + \varepsilon_i^k$. The correlation between the omitted variable (s) and the error term is expected to bias the estimate of $\delta^k$. The direction
<figure><img src="image_7.png" /><figcaption>Fig. 5. KLS estimates of the effect of food insecurity.</figcaption></figure>

Source: authors' calculations, data from INSEE Food assistance survey 2021. Note: estimates from KLS with endogeneity correlation ranging between -0.1 and +0.1, with confidence intervals at the 95% level.

of the bias will depend on the sign of the correlation between the omitted variables and the included explanatory variables.

The third and final concern is the simultaneity that may occur when both health status and food insecurity are jointly determined. While we are considering an influence mechanism from food insecurity to poor health, it is plausible that health status may impact food insecurity. Individuals with health problems may be less likely to participate in the labor market, which would reduce their economic resources and may affect their perceptions of food accessibility. Under simultaneity, it follows that $E[FII_{ci}e_{ci}^k] \neq 0$, and the coefficient $\delta^k$ can be either upward or downward biased.

Methods based on instrumental variables (IV) provide a solution for identifying and estimating regression models with endogeneity. The instruments must satisfy two conditions. First, they must be sufficiently correlated with the endogenous regressor (relevance criterion). If this is not the case, endogeneity-corrected coefficients may be severely biased and characterized by unreliable inference (Stock et al., 2002). Second, the instruments should not have a direct effect on the outcome (exclusion restriction). They should only have an indirect effect on the dependent variable, through the instrumented endogenous regressor. In our setting, there is no source of exogenous variation that provides valid instruments. Finding suitable instruments remains a challenge in observational studies where true experiments are not feasible. This lack of valid instruments means that we cannot rely on IV methods to address

endogeneity concerns.

Recently, several studies have discussed identification strategies in the absence of excluded instruments (Lewbel, 2019; Lewbel et al., 2024; Tsyawo, 2023). Here, we rely on the Kinky Least Squares (KLS) approach, as described in Kiviet (2020) and Kripfganz and Kiviet (2021). This approach involves estimating a set of regression coefficients (bounds) under different assumptions about the degree of regressor endogeneity. We choose the KLS estimator because it includes, as a special case, sensitivity analyses that have recently been developed to account for omitted variable bias in linear regression models (see Krauth, 2016; Oster, 2019; Masten et al., 2024).

Since the fixed effect model (1) can be expressed as either $H_{ci}^k = \delta^{k*}FII_{ci} + X_{ci}\beta^k + \theta_c^k + \epsilon_{ci}^k$ or $H_{ci}^k = \delta^{k*}FII_{ci} + X_{ci}\beta^k + \sum_c \theta_c^{k*}I_c + \epsilon_{ci}^k$, we simplify the notation in (1) so that $H_{ci}^k = \delta^{k*}FII_{ci} + Z_{ci}/\sqrt{k} + \epsilon_{ci}^k$, where Z includes both the covariates X and the various distribution center dummies $I_c$. The KLS approach relies on the non-orthogonality condition $E[FII_{ci}e_{ci}^k] = \rho\sigma_{FII}\sigma_{ci}^k$, where $\rho$ is the correlation coefficient between FII$_{ci}$ and $\epsilon_{ci}^k$, and $\sigma_{FII}$ and $\sigma_{ci}^k$ are the standard deviations of FII$_{ci}$ and $\epsilon_{ci}^k$. Note that the correlation $\rho$ is unknown at this point. The KLS estimator $\hat{\delta}_{KLS}^k$ corrects for the bias in the OLS coefficient $\hat{\delta}_{OLS}^k$:

$$ \hat{\delta}_{KLS}^{k}(\rho) = \hat{\delta}_{OLS}^{k} - \rho * \hat{\sigma}_{\epsilon,KLS}^{k}(\rho) * h(\hat{\sigma}_{FII}, \hat{\sigma}_{FII,Z}, \hat{\sigma}_{Z,Z}) \quad (2) $$
<table><caption>**Table 4**

RCR and KLS effect of food insecurity on poor health.</caption><thead><tr><th rowspan="2">Variables</th><th colspan="2">(1) Poor self-assessed health</th><th colspan="2">(2) Chronic disease</th><th colspan="2">(3) Activity limitation</th></tr><tr><th>point. est.</th><th>95 % CI</th><th>point. est.</th><th>95 % CI</th><th>point. est.</th><th>95 % CI</th></tr></thead><tbody><tr><td colspan="7"><strong>Panel A. All</strong></td></tr><tr><td>OLS λ = 0</td><td>0.058</td><td>[0.047;0.068]</td><td>0.044</td><td>[0.033;0.054]</td><td>0.050</td><td>[0.039;0.060]</td></tr><tr><td>RCR Bounds 0 ≤ λ ≤ 1</td><td>0.058—0.074</td><td>[0.046;0.093]</td><td>0.044—0.062</td><td>[0.033;0.079]</td><td>0.050—0.065</td><td>[0.048;0.082]</td></tr><tr><td>KLS: r = -0.1</td><td>0.093</td><td>[0.082;0.104]</td><td>0.078</td><td>[0.068;0.089]</td><td>0.084</td><td>[0.073;0.095]</td></tr><tr><td>KLS: r = -0.05</td><td>0.075</td><td>[0.064;0.086]</td><td>0.061</td><td>[0.051;0.071]</td><td>0.067</td><td>[0.056;0.077]</td></tr><tr><td>KLS: r = 0</td><td>0.058</td><td>[0.047;0.068]</td><td>0.044</td><td>[0.033;0.054]</td><td>0.050</td><td>[0.039;0.060]</td></tr><tr><td>KLS: r = 0.05</td><td>0.040</td><td>[0.029;0.051]</td><td>0.027</td><td>[0.016;0.037]</td><td>0.033</td><td>[0.022;0.043]</td></tr><tr><td>KLS: r = 0.1</td><td>0.022</td><td>[0.011;0.033]</td><td>0.009</td><td>[0.001;0.020]</td><td>0.015</td><td>[0.005;0.026]</td></tr><tr><td colspan="7"><strong>Panel B. Natives</strong></td></tr><tr><td>OLS λ = 0</td><td>0.079</td><td>[0.065;0.093]</td><td>0.051</td><td>[0.037;0.065]</td><td>0.059</td><td>[0.046;0.073]</td></tr><tr><td>RCR Bounds 0 ≤ λ ≤ 1</td><td>0.079—0.101</td><td>[0.065;0.128]</td><td>0.051—0.072</td><td>[0.037;0.099]</td><td>0.059—0.073</td><td>[0.046;0.098]</td></tr><tr><td>KLS: r = -0.1</td><td>0.110</td><td>[0.095;0.124]</td><td>0.085</td><td>[0.071;0.099]</td><td>0.094</td><td>[0.080;0.109]</td></tr><tr><td>KLS: r = -0.05</td><td>0.092</td><td>[0.078;0.106]</td><td>0.068</td><td>[0.054;0.082]</td><td>0.077</td><td>[0.063;0.091]</td></tr><tr><td>KLS: r = 0</td><td>0.075</td><td>[0.061;0.089]</td><td>0.051</td><td>[0.037;0.065]</td><td>0.059</td><td>[0.046;0.073]</td></tr><tr><td>KLS: r = 0.05</td><td>0.058</td><td>[0.044;0.072]</td><td>0.034</td><td>[0.020;0.048]</td><td>0.042</td><td>[0.028;0.056]</td></tr><tr><td>KLS: r = 0.1</td><td>0.040</td><td>[0.026;0.054]</td><td>0.017</td><td>[0.003;0.031]</td><td>0.025</td><td>[0.010;0.039]</td></tr><tr><td colspan="7"><strong>Panel C. Foreign-born</strong></td></tr><tr><td>OLS λ = 0</td><td>0.029</td><td>[0.012;0.047]</td><td>0.027</td><td>[0.010;0.043]</td><td>0.032</td><td>[0.016;0.047]</td></tr><tr><td>RCR Bounds 0 ≤ λ ≤ 1</td><td>0.028—0.029</td><td>[-0.003;0.049]</td><td>0.024—0.027</td><td>[-0.005;0.044]</td><td>0.032—0.033</td><td>[0.015;0.059]</td></tr><tr><td>KLS: r = -0.1</td><td>0.066</td><td>[0.048;0.084]</td><td>0.061</td><td>[0.045;0.078]</td><td>0.065</td><td>[0.049;0.081]</td></tr><tr><td>KLS: r = -0.05</td><td>0.048</td><td>[0.031;0.065]</td><td>0.044</td><td>[0.028;0.060]</td><td>0.048</td><td>[0.033;0.064]</td></tr><tr><td>KLS: r = 0</td><td>0.029</td><td>[0.013;0.046]</td><td>0.267</td><td>[0.011;0.043]</td><td>0.032</td><td>[0.016;0.047]</td></tr><tr><td>KLS: r = 0.05</td><td>0.011</td><td>[-0.006;0.028]</td><td>0.009</td><td>[-0.007;0.025]</td><td>0.015</td><td>[-0.001;0.031]</td></tr><tr><td>KLS: r = 0.1</td><td>-0.007</td><td>[-0.025;0.010]</td><td>-0.008</td><td>[-0.025;0.009]</td><td>-0.002</td><td>[-0.018;0.014]</td></tr></tbody></table>

Source: data from INSEE Food Assistance survey 2021.

Note: estimates from RCR with parameter $\lambda$ ranging between 0 and 1 and estimates from KLS with endogeneity correlation ranging between -0.1 and + 0.1, with confidence intervals at the 95 % level.

where $h(.)$ is a complex function of variance and covariance terms and the residual $\hat{\sigma}_{\varepsilon,KLS}^k(\rho)$ depends on both $\hat{\sigma}_{\varepsilon,OLS}^k(\rho)$ and $\rho$ (Kiviet, 2020; Kripfganz and Kiviet, 2021, pp. 775-776). Three comments are in order. First, the OLS estimator is a special case of the KLS estimator which is obtained under exogeneity (when $\rho = 0$). Second, the OLS estimator is biased when $\rho \neq 0$ and $\hat{\sigma}_{\varepsilon,KLS}^k(\rho)$ is a decreasing function of the correlation $\rho$. Third, the KLS estimator depends on the unknown value of $\rho$. Thus, the empirical strategy when turning to the data is to select a set of possible endogeneity correlations $r \in [r_{min}; r_{max}]$ and to obtain a range of values $\hat{\sigma}_{\varepsilon,KLS}^k(r)$ along with their corresponding confidence intervals. However, knowing the set of plausible values for $r$ from which to choose from remains challenging.

An interesting feature of the KLS estimator is that it extends recent instrument-free approaches based on sensitivity parameters (Krauth, 2016; Oster, 2019; Diegert et al., 2022; Masten and Poirier, 2023). In particular, Krauth (2016) proposes to bound linear causal effects using relative correlation restrictions (RCR), where the sensitivity parameter $\lambda$ is the ratio of the correlation between the endogenous regressor and the residual to the correlation between the endogenous regressor and the other exogenous covariates. For instance, $\lambda = 1$ is the case where the correlation between FII and unobservables is equal to the correlation between FII and observables. As shown in Kripfganz and Kiviet (2021, pp. 804), the sensitivity parameter $\lambda$ is such that $\hat{\lambda} = r/\text{corr}(\text{FII}_{ci}, X_{ci}\hat{\beta}_{\text{KLS}}^k(r))$, where $\hat{\beta}_{\text{KLS}}^k(r)$ are the KLS estimates of the exogenous covariates for a given value of the endogeneity correlation $r$.

We proceed with the data as follows. Considering first the full sample, we select values for $r$ ranging between -0.1 and + 0.1. For the poor self-assessed health outcome, this corresponds to values of $\lambda$ ranging between 1.95 (when $r = -0.1$) and -2.85 (when $r = 0.1$). This means that we allow the correlation with unobservables to be at least twice as large as the correlation with observables, whatever the sign of the correlation. Even in such scenarios, Fig. 5 shows that the association between the food insecurity index and the three indicators of poor health remains positive and statistically significant. When $\lambda$ is allowed to vary

between 0 and 1, Table 4 shows that the lower bound of the 95 % confidence interval is 0.046 for poor self-assessed health, 0.033 for chronic disease and 0.048 for activity limitation.

Fig. 5 and Table 4 also show the KLS estimates by origin. For natives, the correlation between food insecurity and poor health remains positive regardless of the degree of endogeneity correlation. When the parameter $r$ is set to 0.1, the lower bounds of the 95 confidence intervals are 0.026 for poor self-assessed health, 0.003 for chronic disease, and 0.010 for activity limitation. For the foreign-born, the KLS point estimate of food insecurity is always significant when the parameter $r$ is negative, but not when $r$ is positive. However, even the case where $r = 0.05$ corresponds to large values of $\lambda$ (5.4 for self-assessed health or 3.9 for chronic disease).

It is difficult to know a priori whether the endogeneity correlation $r$ is positive or negative. Under classical measurement errors, the parameter $r$ would typically be negative and the OLS estimates would be biased downward. But if measurement errors are correlated with the true level of food insecurity or other unobserved factors, the sign of $r$ and the direction of the bias could be different. Table 4 shows that when the potential influence of endogeneity is controlled for, the association between food insecurity and poor health is about twice as large for natives as for the foreign-born for a fixed value of $r$. Unfortunately, there is no clear reason to assume that the endogeneity correlation $r$ is the same for natives and immigrants.

Denoting these two groups by $nat$ and $mig$, we now focus on the combinations $(r^{nat}, r^{mig})$ and calculate the difference $\Lambda(r^{nat}, r^{mig}) = \hat{\sigma}_{\varepsilon,KLS}^k(r^{nat}) - \hat{\sigma}_{\varepsilon,KLS}^k(r^{mig})$. The endogeneity correlations are such that $-0.1 \le r^{nat} \le 0.1$ and $-0.1 \le r^{mig} \le 0.1$, and we consider an increment of 0.005, so there are 21 different values of $r$ in each group (441 cases in total). Fig. 6 shows the range of values obtained for the differences $\Lambda(r^{nat}, r^{mig})$ associated with poor self-assessed health, with blue areas corresponding to scenarios where the KLS estimate of food insecurity on poor health is larger for immigrants than for natives ($\Lambda < 0$).

The main result is that the most likely outcome is a positive value for $\Lambda(r^{nat}, r^{mig})$, which occurs in 92.7 % of the cases (409 out of 441).
<figure><img src="image_8.png" /><figcaption>Fig. 6. KLS estimated difference $\Lambda(r^{\text{native}}, r^{\text{foreign}})$: poor self-assessed health.</figcaption></figure>

Source: authors' calculations, data from INSEE Food assistance survey 2021. Note: the estimated difference is obtained from KLS estimates for natives and immigrants with endogeneity correlations ranging between -0.1 and +0.1 in each group.

Negative values are found only in the subset of combinations where $r^{\text{native}}$ is negative, which decreases $\hat{\delta}_{\text{KLS}}(r^{\text{native}})$, and $r^{\text{foreign}}$ is positive, which increases $r^{\text{foreign}}$. Section E in the external Appendix leads to similar conclusions for the other two health outcomes.

## 7. Discussion and concluding comments

This paper examines the association between food insecurity and poor health in France. In contrast to North American countries, there is very little empirical evidence on this issue in this country due to the lack of adequate data on food insecurity in national surveys. Our focus is on the specific group of food assistance recipients, for whom we hypothesize that the use of food banks may moderate or even eliminate the commonly reported positive association between poor health and food insecurity.

Estimation of regression models shows that there is a positive correlation between poor health and food insecurity, even after controlling for the influence of demographic and socioeconomic characteristics and heterogeneity at the level of food distribution centers. Following the recommendation of Gundersen and Ziliak (2015), we strengthen the robustness of our analyses by addressing issues of endogeneity. In the absence of an exogenous shock in our data, we cannot consider an IV strategy and instead turn to a free-instrument approach that estimates bounds on the effect of food insecurity. This sensitivity analysis supports the idea that respondents facing increased food insecurity are more likely to be on poor health.

Our estimated effects are fully consistent with findings from studies in other high-income countries. Studies from the United States and Canada have reported that food insecurity is associated with a substantial increase in the odds of being in poor health (Gundersen and

Ziliak, 2015). However, it is much more difficult to know whether the adverse health effects of food insecurity in France are broadly comparable in magnitude to those observed in other high-income settings. The main reason is that we do not consider a survey representative of the entire French population. Instead, we focus on a specific subsample of food bank participants. This limitation does not even allow us to compare the situation of these participants with the general population in France, as there is no specific survey in this country that allows to study the relationship between food insecurity and poor health at the national level.

An important finding of our study is the difference between people of French and foreign nationality. As immigrants are more likely to be in better health than natives, this may affect the association between food insecurity and poor health. Interestingly, we find that the relationship is weaker for the foreign-born than for the native-born. There are several possible interpretations to explain this finding. First, it is consistent with the healthy immigrant effect, where healthier individuals are more likely to immigrate and therefore may be less sensitive to food insecurity issues. Over time, the health advantage of migrants tends to erode, and their health outcomes tend to converge or even become worse than those of the native population. This would be consistent with the lower correlation found for recently arrived immigrants.

Second, because the survey was conducted among food bank participants, there may be some selection of respondents based on the way they prioritize health and seek out health services. This selection is expected to differ not only between natives and immigrants, but also among immigrants depending on their country of origin. For example, foreign-born respondents from countries where French is spoken will face fewer language and cultural barriers to knowing the landscape of available services. While the Food Assistance survey does not allow for
further investigation of such differential selection, this argument is interesting as it may explain differences in the relationship between poor health and food insecurity not only by years spent in France since migration, but also between different migrant-sending countries.

Third, Frongillo et al. (2019) suggest that the relationship between food insecurity and subjective well-being varies depending on the socioeconomic context and individuals’ reference norms. In countries where food insecurity is widespread, it may be socially normalized, reducing its perceived impact on well-being. Conversely, in a country such as France, where food insecurity is less common and more

stigmatized, food insecure individuals tend to compare themselves to those with secure access to food, potentially amplifying its negative impact on mental health. In developing countries, populations face multiple sources of stress, and food insecurity is part of a broader set of structural deprivations. Its specific impact on subjective well-being may therefore be less pronounced than that of other stressors. This perspective offers another explanation for why the effect between food insecurity and health may be weaker for foreigners than for natives.

Overall, our findings suggest that food distribution centers do not succeed in eliminating the association between food insecurity and poor

<figure><img src="image_9.png" /><figcaption>Fig. 7. Food distribution center attendance and food insecurity, by origin.</figcaption></figure>

Source: authors’ calculations, data from INSEE Food assistance survey 2021
health outcomes. Among the various interventions implemented in high-income countries to address food insecurity, previous research has reached mixed conclusions. On the one hand, specific programs based on food subsidies and cash transfers lead to substantial reductions in food insecurity (Nord, 2012; Mabli and Ohls, 2015), but recipients of these means-tested programs still experience food insecurity. On the other hand, results on the impact of community-level interventions appear to have much more limited effects (Loopstra, 2018). This is the case with food banks, where participants typically report very high levels of food insecurity at entry, but continue to experience food insecurity despite access to the food bank. The regularity and intensity of assistance may not be sufficient to ensure that households have adequate levels of food, and the stigma and shame experienced by participants in such assistance may result in infrequent visits to food pantries.

In the questionnaire, each participant indicated how often they had received food assistance in the past four weeks at the center where they were interviewed, with four possible responses: “every day or almost”, “3 to 5 times a week”, “1 to 2 times a week”, “1 to 2 times a month”. In addition, each participant indicated whether they received food assistance from another food bank during the same period (up to nine different food banks were recorded). As shown in Fig. 7, the proportion of participants who visited the distribution site at least 3 to 5 times per week is 6.8 % (3.9 % every day or almost, 2.9 % 3 to 5 times), but 40.3 % of respondents visited the center once or twice per month. Taking into account all the centers that provided food aid, only 8.0 % visited a structure regularly during the week, 57.7 % once or twice a week, and 34.4 % once or twice a month. The comparison between natives and foreign-born also shows that there is almost no difference between the two groups in the frequency of visiting the food distribution sites. The null assumption of independence between origin and frequency of visits cannot be rejected ($p = 0.213$).

This low level of participation in food banks may explain why food insecurity persists among participants and why it continues to have positive effects on poor health. According to Fig. 7, participants who visit the distribution site more often have a lower food insecurity index, with this pattern driven primarily by immigrants. Focusing only on the main site, the average score for almost daily recipients is -0.20, compared to 0.04 for participants who visit the center once or twice per month. This suggests that regular attendance is key to eliminating food insecurity. However, because the proportion of regular recipients is very low, this likely explains why food assistance through distribution sites does not eliminate the association between food insecurity and health. Another difficulty is that the frequency of visits to food distribution sites is itself endogenous. The most food-insecure people are more likely to visit the centers more often in order to access food.

Our empirical analysis has limitations that need to be kept in mind. First, we are working with a selected sample of the general population composed of recipients of food assistance. Currently, food insecurity is hardly measured statistically by public data collection agencies in France. As a result, even if our sample is representative of the population receiving food assistance, we do not cover all people who are in a situation of food insecurity. In particular, there are very few elderly people in the sample, which may be explained by their physical or psychological difficulties in accessing food assistance. It would also be interesting to compare our results with those of the general population.

Second, due to data limitations, our assessment of the health of food assistance recipients remains partial because it is limited to self-reported health, the presence of chronic diseases, and activity limitations. Unfortunately, we are unable to address health issues related to obesity, mental health conditions such as anxiety or depression, or social isolation, in line with the broader definition of health as “a state of complete physical, mental and social well-being and not merely the absence of disease or infirmity” (World Health Organization). It is clear that food assistance can be a lever to address different aspects of food insecurity, covering the physical, mental and social dimensions, and we therefore underestimate the potential positive impact of food assistance on health.

Third, our analysis uses cross-sectional data. Using a variety of econometric tools, we have tried our best to account for potential endogeneity issues that could lead to biased coefficients for food insecurity in explaining poor health. However, observing health and insecurity at only one point in time does not allow us to assess how any reduction in food insecurity expected from participation in food assistance programs improves (or does not improve) both the physical and mental health of individuals. The availability of longitudinal data would be extremely useful in better understanding the relationship between food insecurity and health. It would shed light on the trajectories of individuals in the food assistance system and how food insecurity evolves over time.

As it stands, our results provide new insights into the association between food insecurity and health in France, a country that has been little studied to date due to the lack of relevant information in national surveys. Our focus on the population of food assistance recipients confirms the positive correlation between poor health and food insecurity widely reported in the literature. All of the various health outcomes are worse with higher food insecurity, even after correcting for endogeneity bias, but we are unable to compare the strength of the association for our specific sample with that for the general population. Another interesting finding is the difference between native and foreign-born respondents, with a higher correlation between poor health and food insecurity for the former group. Since natives and foreign-born have similar attendance at the distribution centers, this suggests that differences in health status between the two groups may be at play.

From a public policy perspective, our results show that despite the increasing reliance on food banks and community-based food interventions to address food insecurity, such interventions are not sufficient to eliminate food insecurity. As a result, the negative association between health and food insecurity persists even among people from disadvantaged backgrounds who receive food assistance, although the association is weaker when people are in better health. In terms of future research, it would be interesting to assess the impact of the recent high inflation rates in France, which are likely to have increased the number of food insecure people, as this may have affected the effect of food insecurity on poor health.

### CRediT authorship contribution statement

Romane Vandroux: Writing - review & editing, Writing - original draft, Methodology, Formal analysis, Conceptualization. François-Charles Wolff: Writing - review & editing, Writing - original draft, Validation, Supervision, Methodology, Formal analysis, Conceptualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.foodpol.2025.102895.

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