Income and food insecurity among SNAP recipients: a consideration of the SNAP benefit formula

Abstract

The Supplemental Nutrition Assistance Program (SNAP) has substantially reduced food insecurity in the USA, but almost half of the participants remain food insecure. We use the 2018 Survey of Income and Program Participation to examine the relationship between food insecurity and two components of benefit determination—gross income and deductions. For all SNAP recipients, in most specifications, gross income is inversely related to food insecurity, and deductions are positively correlated with food insecurity. When examining policy-relevant sub-categories, households with a senior or someone with a disability have positive associations between food insecurity and deductions, suggesting possible changes in benefit construction.

1. Introduction

The Supplemental Nutrition Assistance Program (SNAP, formerly known as the Food Stamp Program) is the central component of efforts to alleviate food insecurity in the USA. The program is by far the largest in the U.S. Department of Agriculture (USDA)—in 2022, total expenditures were $114 billion, serving 41.2 million persons (U.S. Department of Agriculture, 2023). To direct benefits to those most in need, households are eligible for the program if they meet three criteria—income below a gross income threshold, gross income minus various deductions below a net income threshold and an asset test. For these deemed eligible, benefit levels are set inversely related to net income.

The extensive literature has examined the impact of SNAP on various outcomes, with particular attention paid to its impact on food insecurity (Smith and Gregory, 2023). These studies have concentrated on comparisons between SNAP participants and eligible non-participants. What is less understood, however, is, among SNAP recipients, the association of gross income with food insecurity and the association of deductions with food insecurity.

The SNAP benefit formula is constructed such that the benefits equal the maximum allotments based on the household size minus 30 per cent of net income (i.e. adjusted gross income accounting for allowable deductions). This paper contributes to a parallel frame of work that has examined the adequacy of the SNAP maximum benefit as a means to address the relatively high food insecurity among SNAP recipients (Chojnacki et al., 2021; Gundersen, 2021; Gundersen et al., 2018; Gundersen, Waxman and Crumbaugh, 2019; Ziliak, 2016) by exploring two primary issues. First, the SNAP benefit formula implicitly assumes that, all else equal, those with higher gross incomes are in less need, so benefit levels are lower. Thus, our first question examines the relationship between gross income and food insecurity. When setting SNAP benefit levels, the USDA also incorporates deductions to reflect things beyond gross income. This, therefore, motivates our second question—the relationship between deductions and food insecurity.

The relationship between gross income and food insecurity and deductions and food insecurity may differ depending on which segment of the SNAP population is being examined. In response, we consider four groups of SNAP recipients who, over at least some dimension, face different eligibility criteria and/or different benefit formulation. Two of the groups—households with a senior and households with someone with a disability—face different eligibility thresholds than households without a senior or someone with a disability. The next two groups—households with children and single parents with children—have avenues to SNAP eligibility that are not available to other households.

We consider these topics with data from wave 1 of the 2018 Survey of Income and Program Participation (SIPP) panel. Unlike other nationally representative data sets, SIPP has the information needed to calculate gross and net income and assets, along with questions about food insecurity status. Our primary findings are three-fold. First, we find that, in most specifications, food insecurity and very low food security (VLFS) rates are lower among those with higher gross incomes, even after controlling for relevant covariates. This relationship is more pronounced for VLFS than for food insecurity. Second, the deductions used to construct net income are positively related to food insecurity/VLFS in some of our specifications. These deductions are designed to be higher for those in greater need. This positive relationship reflects that, on the one hand, the deductions reach those in need and, on the other hand, are not sufficient enough to raise households out of food insecurity, which is of concern. Third, we find substantial heterogeneity by sub-groups in terms of the association between gross income and food insecurity and deductions and food insecurity. While there is no statistically significant relationship between gross income and food insecurity and deductions and food insecurity for households with children, there are statistically significant relationships for households with a senior or someone with a disability. A reconsideration of the SNAP benefit formula for households with a senior or someone with a disability may be worth considering.

2. Background

To be eligible for SNAP, applicants need to meet three criteria. First, the household’s gross income before any deductions must be less than 130 per cent of the federal poverty line, although most states have set a higher threshold of up to 200 per cent of the poverty line. The gross income threshold is not binding for households with seniors or persons with disabilities. Second, net income must be less than the poverty threshold (this is covered in greater detail below.) Third, asset values cannot exceed $2,250; for a household with a senior or disabled member, the threshold is up to $3,500. This asset requirement is waived completely or set higher than the federal threshold in most states.

We also consider the state-level broad-based categorical eligibility (BBCE) rule as an alternate pathway to SNAP eligibility. BBCE allows households receiving other means-tested programs like Supplemental Social Security Income (SSI), Temporary Assistance for Needy Families (TANF) program, or General Assistance to be eligible for SNAP. Programs like these are often only open to segments of the population. For example, households with children and, in particular, single-parent families receiving TANF automatically qualify for SNAP in the majority of states where BBCE is implemented.

For those who are eligible, the SNAP benefit level is calculated based on a formula that has changed little since its establishment. The benefit formula comprises three components—the maximum benefit allotments based on the household size, the benefit reduction rate and net income. It is constructed such that the benefits equal the maximum allotments minus 30 per cent of net income. USDA has structured SNAP benefits such that all SNAP recipients should have the resources to purchase an adequate amount of food based on the household composition and size, irrespective of the amount of SNAP benefits received. Namely, ‘the SNAP program assumes that each household with income can contribute 30 per cent of that income to the purchase of food’ (IOM (Institute of Medicine) and NRC (National Research Council), 2013, p.28). Furthermore, ‘the Federal Government chooses a benefit level such that benefits plus a proportion of cash resources suffice to purchase a certain bundle of foods, defined in the Government’s Thrifty Food Plan’ (Wilde, 2001: 1).

As noted above, after controlling for non-random selection into SNAP, recipients have lower rates of food insecurity than eligible non-recipients. This does not imply, however, that SNAP benefit levels combined with a household’s income are sufficient to make all recipients food secure. In fact, SNAP benefit levels are, on average, inadequate to ensure sufficient levels of food consumption (Davis, You and Yang, 2020; Hoynes, McGranahan and Schanzenbach, 2015). Consistent with this, 39.9 per cent of SNAP recipients were food insecure in 2021 (Coleman-Jensen et al., 2022).

Along the same lines, there have been arguments supporting increasing the SNAP maximum amount to reduce food insecurity. Ziliak (2016), for instance, suggested an increase in benefits incorporating the time cost of food preparation and differences in food prices by geography. Schanzenbach (2019) proposed an increase in benefits to selected household types, such as those with teenagers or those facing temporary surges in food costs in the family. Chojnacki et al. (2021) introduced two new deductions with respect to transportation costs and additional earning deductions. Similarly, Gundersen, Waxman and Crumbaugh (2019), Gundersen, Kreider and Pepper (2018) and Gundersen (2021) identified various approaches to increasing the maximum benefits and associated predicted declines in food insecurity.

In response to concerns about the adequacy of SNAP benefit levels and the research demonstrating these problems, the USDA recently re-evaluated the Thrifty Food Plan (TFP), which serves as the basis of the maximum SNAP allotments, for the first time since its initiation. The latest TFP updates the food costs of the dietary compositions aligned with the Dietary Guidelines for Americans, 2020–2025, resulting in around a 21 per cent increase in the maximum SNAP benefits (roughly a $1.20 increase per person per day) (U.S. Department of Agriculture, 2021).

A broader literature has examined the influence of income and poverty on food insecurity. For example, in 2021, 32.1 per cent of households under the poverty line were food insecure, compared with 5.0 per cent of those with an income-to-poverty ratio of more than 1.85 (Coleman-Jensen et al., 2022). Existing work has also presented that food insecurity is inversely associated with income (e.g. Anderson et al., 2016; Gundersen and Ziliak, 2018; Wight et al., 2014). In fact, virtually all papers that examine the determinants of food insecurity include a household income variable. Our work adds to current knowledge on income and food insecurity by concentrating on SNAP recipients.

In addition, this work builds on existing research on the deductions used to set SNAP benefit levels. Prell, Newman and Scherpf (2015), for example, used SIPP to account for excess shelter expenses, medical expenses, dependent care expenditures and child support payments when measuring SNAP eligibility and participation rates at the annual and monthly levels. Looking at similar issues pertaining to eligibility and participation rates over a seven-year period, Vigil (2019) considered the earned income deductions and excess shelter expense deductions as part of a set of household characteristics to estimate net income using SIPP. In addition to this work with SIPP, Ismail et al. (2023) examined the role of the excess shelter deduction when calculating SNAP benefits with data from the National Household Food Acquisition and Purchase Survey (FoodAPS) and the SNAP Quality Control system. Our paper extends this research by considering the relationship between deductions and food insecurity.

3. Data and Methodology

3.1. Sample construction

The data used in this paper are from the 2018 wave 1 of the SIPP panel. SIPP is a multistage stratified sample of more than 53,000 households surveyed annually for four years. Conducted by the U.S. Census Bureau, SIPP is the only nationally representative data set with the information needed to calculate the deductions used to derive net income.¹ In addition, it has the relevant food hardship measures used to calculate food insecurity.² We restrict the samples to SNAP households residing in the 48 contiguous USA and the District of Columbia because they are regulated by the standard SNAP eligibility and benefit level criteria.³

Our sample is defined as follows. First, we limit the sample to those with an annual average non-negative gross income below 200 per cent of the poverty line, the upper limit states can set as the gross income cut-off for households without a senior or disabled member.⁴ Second, we limit the sample to households reporting that they received positive SNAP benefits in the previous month.⁵ Third, there are a few cases where the deductions are perhaps inaccurately reported in SIPP. We find this to be the case for medical expenses, child support payments and excess shelter expenses of SNAP recipients.⁶ In response, we drop observations where the values are more than ten times the average for these variables. This results in observations being dropped where households report monthly spending of more than $2,837 of medical expenses, $1,723 of child support payments and $3,235 of excess shelter expenses.⁷ This leaves 2,362 observations in this study.

3.2. Food insecurity measure

The standard measure of food insecurity in the U.S. is the 18-item U.S. Household Food Security Survey Module (Coleman-Jensen et al., 2022). The SIPP has a modified, oft-used six-item scale that has been verified as consistent with the results from the 18-item measure (Bickel et al., 2000).⁸ The full set of questions concerning household food insecurity status during the reference year (i.e. 2018) is in Table A1. A household’s food insecurity score is the sum of affirmative responses. We then define a binary measure of food insecurity if the household responded affirmatively to two or more. Households that are categorised as food insecure are further identified as having LFS with a raw score from 2 to 4 or VLFS for those with five or six affirmative responses.⁹ (Information about the module is available at https://www.ers.usda.gov/media/8282/short2012.pdf).

3.3. Deduction calculation

A description of how the administrative procedures are used to calculate SNAP benefits and their corresponding measures in the 2018 SIPP panel is found in Table A2. The components of the deductions are: a 20 per cent earned income deduction, a standard deduction (based on household size), a dependent care deduction, out-of-pocket medical expenditures that exceed $35 for senior or disabled members, child support payment deduction and an excess shelter expense deduction. With respect to the excess shelter deduction, this is calculated in three steps based on the USDA’s procedures. First, we subtract the non-shelter deductions from the household gross income. Second, we subtract 50 per cent of the value calculated in the first step from the household-level shelter expenses, namely, the rent, mortgage and utility payments. And third, the value is capped at $535 unless an elderly or disabled member is in the household. We calculate the deductions by summing up these items noted above.

3.4. Household characteristics

One of the central goals of this paper is to look at whether the impacts of gross income and deductions differ for groups with different SNAP eligibility policies and/or different benefit formulations. The first two groups are households with at least one member over the age of 60 and households with at least one member with a disability.¹⁰ Households with at least one member falling into these two groups are waived from a standard gross income test, face a higher asset limit (in states that do not alter the federal asset limit) and whose excess out-of-pocket medical expenses, shelter costs at higher thresholds and dependent care costs are accounted for in the calculation of deductions. The third group is households with children. These households can claim deductions for dependent care and child support payments. Among this category, we construct the fourth category headed by a single parent. This group is potentially eligible for TANF, which makes them automatically eligible for SNAP.¹¹

In the same vein, we include other characteristics that influence both food insecurity and are potentially tied to the determinants of SNAP benefit levels. These covariates are receipt of SSI, homeownership status, receipt of housing assistance (monetary assistance to help pay for housing, public housing, or housing vouchers) and whether the household is headed by someone who is non-Hispanic Black or Hispanic.

3.5. Robustness checks

To check the robustness of our results, we perform analyses on four other samples. First, as noted above, we limit our main sample to households with incomes below 200 per cent of the poverty line. We also consider our results when we use the entire 2,930 households reporting SNAP receipt in SIPP. Our second subsample removes those who report receiving SNAP but have net incomes above the poverty line and thus are seemingly ineligible under the standard SNAP criteria. This results in 1,971 observations. Third, in our main sample, we only consider those currently receiving SNAP. We expand this sample to include households who have received SNAP in at least one month over the previous year,¹² resulting in 2,509 observations. Fourth, our main results use annual income converted to an average monthly income. For this robustness check, we use income from the most recent month and limit the sample to households below 200 per cent of the poverty line based on this same time frame.

3.6. Empirical approach

The central goal of this paper is to examine the extent of food insecurity among SNAP recipients by gross income and deductions. We begin with figures depicting the relationship between food insecurity/VLFS and gross income. Next, we portray the relationship between food insecurity/VLFS and income deductions. We normalise the results by considering the ratio of the gross income-to-poverty line and income deductions-to-poverty line.¹³

We then turn to the multivariate regression analysis to examine the association between food insecurity and gross income and income deductions. We implement a nonparametric regression model because it does not require functional form assumptions of the relationship between the outcome and the covariates (Deaton, 1989). In other words, the nonparametric model is preferred for its more flexible and intuitive portrayal of parametric frameworks when such parametric modelling assumptions might be invalid (Ichimura and Todd, 2007).¹⁴

We use the nonparametric local–linear (LL) kernel regression to examine the primary outcomes of interest, household food insecurity and VLFS. Let |$F{I_i}$| represent the probability of a household being food insecure (⁠|$F{I_i}$|⁠)¹⁵ and |${X_i}$| represent a multi-dimensional vector of covariates. Of particular note are the variables of interest, gross income-to-poverty ratio (|$G{I_i}$|⁠) and deductions-to-poverty ratio (|$Dedu{c_i}$|⁠), and other covariates noted above, while i denotes a household. Consider |${X_i}$| in a neighbourhood of x, the local regression equation can be written as

where |${e_i}$| is the error term and |${\rm{E}}\left( {{e_i}{\rm{|}}{X_i}} \right) = 0$|⁠. The estimate of interest in equation (1) is m(⁠|${X_i}$|⁠), namely, the relationship between the probability of a household being food insecure and its gross income level and the income deductions, conditional on a set of covariates. Using all data points x to estimate |${\rm{E}}\left( {F{I_i}{\rm{|}}{X_i} = x} \right)$| allows us to solve for the estimate of |${\rm{E}}\left( {F{I_i}{\rm{|}}{X_i}} \right)$|⁠, which is equal to m(⁠|${X_i}$|⁠). The function m(·) is smooth yet unknown which will be determined by the data. The LL regression can be solved from

where |$\beta = {\left( {{\beta _0},\beta _1^{^{\prime}}} \right)^{^{\prime}}}$| and |$K\left( {{X_i},x,h} \right)$| is the product of each covariate’s kernel

where |${K_j}\left( {{X_{ij}},{X_j},{h_j}} \right) = 1$| if |${X_{ij}} = {X_j}$| and |${K_j}\left( {{X_{ij}},{X_j},{h_j}} \right) = {h_j}$|⁠, otherwise.

The solution to equation (2) comprises the derivative of the mean function for each data point x. The kernel function assigns weights to each observation |${X_i}$| depending on the bandwidth h and its distance to a local neighbourhood x—the smaller the h is, and the closer the observation is to x, the larger the weight is assigned (Fan and Gijbels, 1996).

Suppose |$Z$| is an|$\,n \times \left( {k + 1} \right)$| matrix. The ith row is |${\left( {1,{{\left( {{X_i} - x} \right)}^{^{\prime}}}} \right)^{^{\prime}}}$|⁠, and R is an |$n \times n$| diagonal matrix with |$K\left( {{X_i},x,h} \right)$| as the ith diagonal. We obtain the LL estimator

The bandwidth h captures the size of the neighbourhood around |${X_i}$|—the wider h leads to a smoother curve yet a higher bias. To minimise the trade-off between bias and variance, we use the cross-validation approach to select this smoothing parameter (Li and Racine, 2004). To do this, let the leave-one-out prediction |$\widetilde {F{I_i}} = {\tilde m_{ - i}}\left( {{X_i}} \right)$| denote the nonparametric estimator without including one observation |${X_i}$|⁠. Using the remaining data points to predict the one left out, we derive the leave-one-out prediction error as

We then seek an h such that minimising the weighted average mean squared prediction errors, |${\rm{CV}}\left( {\rm{h}} \right) = \mathop \sum \limits_{i = 1}^n {\left( {F{I_i} - \widetilde {F{I_i}}} \right)^2}$|⁠. Finally, the model estimates the averages of the predicted derivatives, including our two variables of primary interest:

For this study, |$\widehat {{\beta _1}}$| and |$\widehat {{\beta _2}}$| are the average marginal effect of an additional unit of gross income to the poverty threshold and an additional unit of income deductions to the poverty threshold, respectively, on the probability of a household being food insecure or VLFS after controlling for other covariates. We also apply the same model to conduct the analyses discussed in Section 3.5.

4. Results

4.1. Descriptive results

Figure 1 shows the relationship between gross income and food insecurity/VLFS outcomes. Food insecurity declines from 38.7 per cent to 33.7 per cent as gross income increases from the lowest grouping to the highest. The same inverse relationship holds when looking at the VLFS outcomes, yet there is a much sharper proportional decline in VLFS as gross income increases. Households with the lowest gross incomes have the highest VLFS (21.2 per cent), while those with the highest gross incomes have VLFS rates of 13.6 per cent.

The relationship between food insecurity and income deductions is presented in Figure 2. In the main, food insecurity increases as the deductions rise. The highest food insecurity rate lies in households with a ratio of deductions to the poverty line between 0.8 and 1 (44.8 per cent), and those below 0.2 have the lowest rate (33.3 per cent). A similar increasing trend between deductions and VLFS exists, where VLFS ranges from 15.8 per cent (from 0 to 0.2 of the poverty line) to 22.8 per cent (above 1.0 of the poverty line) as deductions rise.

In Table 1, we present descriptive statistics for the full set of variables in our models.¹⁶ In column (1), all households are portrayed. We then break down the samples by food secure (column (2)) and food insecure (column (3)) households and VLFS (column (4)) and not-VLFS (column (5)) households. Consistent with the results in Figures 1 and 2, gross income is higher and deductions are lower for food-secure households. For example, in column (2), the mean gross income-to-poverty ratio and income deductions-to-poverty ratio are 0.88 and 0.48, respectively, while they are 0.84 and 0.52, respectively, in column (3). The differences in gross income and deductions in columns (2) and (3), though, are not statistically significant. In addition, VLFS households have a relatively lower gross income, 0.80, and higher deductions, 0.53, than non-VLFS households. The gap in gross income between columns (4) and (5) is more prominent than that between columns (2) and (3). With respect to the three household types we are examining, fewer households with children, households with seniors or households headed by a non-Hispanic Black or Hispanic are categorised as food insecure than food secure and VLFS than not-VLFS. Conversely, a higher proportion of households with someone with a disability are in the food insecure and VLFS subgroups. Also, households receiving SSI and/or housing assistance are more likely to be food insecure. The homeownership status, however, does not differ by food insecurity status.

We now turn to the relationship between food insecurity/VLFS and gross income and deductions with respect to the policy-relevant subsamples noted above: households (a) with seniors, (b) with someone with a disability, (c) with children and (d) headed by a single-parent. We present a series of figures based on each subsample akin to Figures 1 and 2.¹⁷

Consistent with our findings for all SNAP households, the inverse relationship between gross income and food insecurity/VLFS holds for all subgroups (Figure 3). The characteristics of these inverse relationships differ by category. However, as seen in panel (a), while households with seniors have lower food insecurity rates than non-seniors except for at the lowest income level, the proportional declines of food insecurity/VLFS are slightly sharper than those without seniors. As gross income increases, food insecurity (VLFS) of those without seniors declines by 5.0 (5.6) percentage points, and for those with seniors, the decline is 10.1 (9.9) percentage points. In panel (b), the absolute differences in food insecurity/VLFS are more stark between those with a member with a disability and those without one. Although food insecurity /VLFS is higher for those with someone with a disability across all income levels, the proportional declines as gross income increases are similar.

Panel (c) shows that households with children generally have lower food insecurity /VLFS than those without children, regardless of income category. Although the proportional declines of food insecurity as gross income rises are similar between both subgroups, the VLFS of households with children changes little (decreases by 3.4 per cent) as income rises. This decline is less than households without children, where the decrease is 11.4 per cent. Panel (d) further explores the compositions of households with children. In the main, the negative correlation between gross income and food insecurity outcomes holds. While single-parent households have higher food insecurity/VLFS than married-couple households in the lowest income level, their food insecurity outcomes are similar to married-coupled households at higher incomes.

The positive correlation between food insecurity and deductions also holds for various subgroups, albeit with some variations (Figure 4). Panel (a) shows that households with seniors have lower food insecurity rates than those without across all deduction levels. The highest food insecurity rate lies in a ratio of deductions to the poverty line above 0.75 (38.8 per cent), and those below 0.25 have the lowest rate (28.1 per cent). The increase in food insecurity is especially pronounced at the highest deductions-to-poverty ratio. Second, for households with someone with a disability, food insecurity (VLFS) is constantly higher than those without across deduction levels, and it increases steadily from 37.5 per cent to 50.1 per cent (20.9 per cent to 25.6 per cent) as the deductions rise (panel (b)).

Third, like with gross incomes, households with children have lower food insecurity than those without, except at the lowest deduction level (panel (c)). The positive correlation is, however, less pronounced for those with children than those without. Specifically, as deductions increase, food insecurity (VLFS) of those with children increases by 3.1 per cent (1.2 per cent), lower magnitudes than those without (an increase of 13.6 per cent and 7.2 per cent, respectively). Changes in food insecurity as the deductions rise are also not pronounced for both single-parent and married-couple households with children (panel (d)). In some cases, nonetheless, there is a negative correlation between food insecurity /VLFS and deductions, which contrasts our findings of other subgroups.

4.2. Nonparametric regression results

The nonlinearities in Figures 1 and 2 motivate us to examine the nonparametric regression results in Table 2.^18,19 In the upper panel, we concentrate on the relationship between the probability of a household being food insecure and two variables of interest—gross income and income deductions. In column (1), we examine the impact of gross income without controlling for other covariates. We find an inverse relationship between food insecurity and gross income, where a 0.1 increase in the gross income-to-poverty ratio (e.g. a $209.8 increase in gross income for a family of four) is associated with a 0.39 percentage point decrease in the probability of food insecurity. In column (2), we find a positive association between income deductions and food insecurity. When the ratio of income deductions to the poverty line increases by 0.1 (e.g. a $209.8 increase in income deductions for a family of four), the probability of food insecurity rises by 1.31 percentage points.

The signs are consistent once we include both gross income and income deductions in column (3). While the impact of gross income changes little compared to that in column (1), there is a 61.8 per cent drop in magnitude for the income deductions from that in column (2). In column (4), after controlling for a set of covariates, although the positive association of food insecurity with income deductions remains, gross income is no longer statistically significant.

The inverse relationship is more pronounced for gross income and VLFS than for food insecurity. The lower panel of Table 2 shows that, whether examining the impact of gross income alone (column (1)), along with the income deductions (column (3)), or controlling for other factors (column 4), the inverse relationship between gross income and VLFS is statistically significant. Column (4) shows a decline of 0.40 percentage points in the probability of VLFS as the gross income-to-poverty ratio rises by 0.1. With respect to deductions, a 0.1 increase in the deductions-to-poverty ratio is associated with a 0.44 percentage points increase in VLFS, a smaller magnitude than that for food insecurity.²⁰

4.3. Heterogeneity analysis

We now turn to the regression results by the policy-relevant subgroups²¹ in Tables 3–5. For households with seniors (Table 3), the signs of gross incomes and deductions are consistent with that in Table 2, yet with greater magnitudes. For example, as the ratio of income deductions to the poverty line increases by 0.1, the probability of food insecurity (VLFS) rises by 1.12 (0.63) percentage points. We also show that gross income correlates more closely with VLFS but not food insecurity. For households with disabled members (Table 4), the negative correlation between gross income and food insecurity and the positive correlation between deductions and food insecurity also hold. However, when examining VLFS, the coefficients are much lower than in Table 2, and none are statistically significant. For households with children (Table 5), the coefficients of neither food insecurity nor VLFS are statistically significant after controlling for other covariates. The statistical insignificances remain when an additional indicator of whether the household is headed by a single parent is included.

4.4. Robustness checks

We now turn to our robustness checks. Tables A10–A13 portray the food insecurity outcome in the first panel and VLFS in the second panel. Within each panel, like in the tables above, we start by presenting the results with the two variables of interest, the gross income and the income deductions, followed by controlling for other factors. This is in columns (1) and (2) for food insecurity and (3) and (4) for VLFS. In what follows, we compare these robustness checks with the results from columns (3) and (4) in Table 2 from the top panel (food insecurity) and the bottom panel (VLFS).

First, we consider the results with a different sample of SNAP participants. In our previous specifications, we limit the samples to SNAP recipients with gross incomes under 200 per cent of the poverty line. Here, we consider all SNAP recipients in SIPP regardless of gross income levels (Table A10).²² For food insecurity, after controlling for other factors, the magnitude of the coefficients is similar for deductions but slightly larger and now statistically significant for gross income. For VLFS, after controlling for other factors, the magnitudes are similar for gross income and deductions, albeit now statistically insignificant for the latter.

Second, we examine the set of SNAP participants whose net incomes are below the poverty line (Table A11). The magnitudes and statistical significance are similar to those in Table 2.

Third, we use a broader time frame to determine SNAP enrolment status. In the previous tables, we define SNAP recipients as those receiving SNAP in the most current month. Table A12 expands this to include those who received SNAP in at least one month over the previous year. The coefficients are similar to those found in Table 2. There is one change in statistical significance—gross income in the food insecurity specification.

Fourth, we substitute the income measure with the income from the latest month rather than the annual average income (Table A13). The results in terms of statistical significance and magnitudes are very similar to those in Table 2.

5. Conclusions

A high proportion of SNAP recipients are food insecure. This has often been ascribed to inadequate SNAP benefit levels, but what has received less attention is the contribution of the structure of the SNAP benefit formula to food insecurity. Our work extends the existing studies on the impacts of increases to the maximum SNAP benefit level on food insecurity by examining the relationship between food insecurity and the central components of benefit determination, gross income and the deductions used to calculate net income. We consider this for the full population of SNAP recipients and then turn to a consideration of whether there are differential impacts among policy-relevant sub-groups. We find, first, that gross income among SNAP recipients is inversely related to food insecurity, and the relationship is more pronounced for VLFS. Second, the deductions are positively related to food insecurity/VLFS, even after controlling for relevant factors. The results pertaining to both factors are, in the main, consistent in the robustness checks. For example, there are no cases where, say, the sign or the magnitudes of our focal variables change dramatically, although statistical significance varies in some specifications. Third, heterogeneity exists across policy-relevant subgroups. While there are statistically significant relationships between gross income and food insecurity and deductions and food insecurity for households with a senior or someone with a disability, no statistically significant relationship is found for households with children.

Our results have two central policy implications. First, there are food assistance programs with benefit levels independent of income whereby all recipients receive the same amount.²³ In contrast, SNAP benefit levels are inversely related to the incomes of households. Our findings (in some but not all specifications) that gross income is inversely related to the probability of food insecurity demonstrates that there may be advantages to allowing SNAP benefit levels to vary by income levels.²⁴

Second, our findings about the differential relationship of deductions to food insecurity among the policy-relevant sub-groups may provide policy insights regarding the optimal setting of benefits. For example, there is no statistically significant increase in food insecurity for households with children as deductions increase. In contrast, for households with seniors and/or someone with a disability, as deductions increase, so does food insecurity. If a goal is to ensure that there are similar rates of food insecurity for all deduction levels—as one may desire from effective directing of benefits—changes to the benefit formula by directing more benefits to seniors and persons with a disability may be considered. Currently, the greater potential need of these subgroups is reflected in the eligibility criteria—this would be extended to the benefit levels, as well.

This paper leads to an array of future research topics, some examples of which are listed here. First, our findings provide evidence of the advantages of setting benefit levels being inversely related to income, like SNAP. There are advantages to having everyone receive the same benefit (e.g. less administrative burdens, easier application processes). Future research may consider whether varying benefit levels by income is worth pursuing in other programs. Second, as noted above, there may be scope to increase benefits to seniors and/or those with disabilities to ensure equal probabilities of food insecurity across deductions. One possible way to approach this may be by examining households with children, whereby food insecurity rates are relatively similar across deduction levels. For example, is there something about how the equivalency scales in SNAP benefits are set such that larger household sizes receive proportionally the correct benefit amounts (viz. food insecurity)? Or, for example, do particular types of deductions only available to households with children contribute to this? Third, SNAP benefits were recently increased across the board due to an increase in the TFP. Along with increasing benefit levels (and, hence, likely lower food insecurity rates among SNAP recipients), this will also change the composition of recipients insofar as more eligible households may enter the program due to higher benefits. Once data are available from SIPP for the post-2021 period, researchers may examine if the relationships between gross income and food insecurity and deductions and food insecurity have changed. Finally, in addition to considerations of the U.S. context, the approach used here applies to evaluations of assistance programs in other countries. More specifically, it would be applicable when benefits are phased out as incomes increase with modifications of this phasing out due to other factors.

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