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UseofInformalSafetyNetsduringtheSupplementalNutritionAssistanceProgramBenefitCycle.pdf

Use of Informal Safety Nets during the Supplemental Nutrition Assistance Program Benefit Cycle: How Poor Families Cope with Within-Month Economic Instability

anika schenck-fontaine Duke University

anna gassman-pines Duke University

zoelene hill New York University

abstract Poor families often combine public benefits with social network and

community resources to cope with economic instability. This study shows that de-

cisions to combine formal and informal resources are as dynamic as the economic

instability they are intended to buffer. Using survey data of poor families receiving

Supplemental Nutrition Assistance Program (SNAP) benefits in Durham, North Car-

olina, this study takes advantage of the within-month economic instability created

by the SNAP benefit cycle to show how families intentionally combine their formal

and informal resources throughout a benefit month. Results show that families re-

ceiving SNAP benefits are more likely to borrow money for food 3 weeks after re-

ceiving SNAP benefits. Household food insecurity remains stable throughout the

SNAP month, suggesting that this use of families’ informal social safety nets may

effectively buffer against economic instability.

introduction

An increasing number of US families struggle to cope with economic insta- bility, particularly families with household incomes below the federal pov- erty line (Ziliak, Hardy, and Bollinger 2011; Hannagan and Morduch 2015). Emerging evidence suggests that economic instability can compound the

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detrimental consequences of low income on children’s health, well-being, and development (Sandstrom and Huerta 2013; Poonawalla et al. 2014; Gen- netian et al. 2015). Economic instability is associated with increased levels of material hardship and may even perpetuate poverty by demanding con- stant focus and attention on balancing and buffering the instability (Gen- netian and Shafir 2015; Heflin 2016). Moreover, by making it difficult to es- tablish routines, economic instability may also uniquely affect parents and children over and above the influence of household income (Hill et al. 2013).

Social safety net programs, such as the Supplemental Nutrition Assis- tance Program (SNAP; formerly known as food stamps), are intended to buffer instability for families by providing additional economic supports. However, although SNAP provides crucial buffering of instability for fam- ilies, there is also evidence that SNAP benefits are insufficient to meet many families’ food needs for a full month, and families frequently run out of SNAP benefits before the end of the month (Wilde and Ranney 2000; Sha- piro 2005; Hastings and Washington 2010).This insufficiency in SNAP ben- efits thereby creates a within-month instability in resources for SNAP- recipient families. Although the research reporting this insufficiency of SNAP and resulting within-month instability is robust, research on how SNAP families mitigate the instability is limited. Existing research does not focus on how families strategically use other informal social safety net resources within the SNAP benefit cycle to buffer the economic insta- bility that results from the early depletion of SNAP benefits. Extant knowl- edge about how families use informal resources to complement formal re- sources from SNAP is limited to point-in-time estimates and, therefore, likely does not reflect the dynamic nature of benefit use and families’ use of informal coping strategies. This article will begin to fill this gap in the literature by exploring the dynamic patterns of informal coping strategies throughout the SNAP benefit cycle.

background

Economic instability refers to repeated, unpredictable changes in employ- ment, income, or financial well-being over time. Economic instability is in- creasingly common among low-income families in the United States, who are more likely than their higher-income counterparts to experience job losses and income fluctuations (Ziliak et al. 2011; Hannagan and Morduch

Informal Safety Nets during the SNAP Benefit Cycle | 457

2015). Although most of the research on economic instability has focused on variation between months or years, we note that an emerging body of research suggests that low-income families also experience variability in work hours and schedules from day to day within a month (Presser and Cox 1997; Presser 2005; Hsueh and Yoshikawa 2007; Gassman-Pines 2011). Since such instability can compound the detrimental consequences of low income on children’s health, well-being, and development (Sandstrom and Huerta 2013; Poonawalla et al. 2014; Gennetian et al. 2015), it is important to identify effective policy responses.

One key way of addressing such economic instability among low- income families is through social policies meant to provide additional fi- nancial supports. An important social policy that does so is SNAP. In fiscal year 2015, 45.8 million individuals received SNAP in an average month and a total of $69.7 billion was spent on benefits for the year (Gray, Fisher, and Lauffer 2016). Of those individuals receiving SNAP in fiscal year 2015, an estimated 19.9 million (44 percent) were children (Gray et al. 2016). SNAP provides benefits to low-income individuals and families solely in order for them to purchase food. These benefits are transferred to recipients once a month and constitute a large percentage of many families’ budgets.

SNAP is designed to buffer economic instability. SNAP benefits are not designed to cover food expenditures for the full month but rather are meant to supplement individuals’ income in order to provide additional resources with which to purchase food. The benefits are calculated on the basis of the Thrifty Food Plan, which estimates the amount of combined income and SNAP benefits that it would take to purchase sufficient food to provide adequate nutrition for a family. Thus, the goal of SNAP is to mitigate eco- nomic instability by supporting families’ food needs through benefits that can be combined with income from earnings,which vary depending on hours worked each week.

However, there is a growing body of evidence suggesting that those de- sign elements—monthly delivery and benefits that are meant to supple- ment individual income—may contribute to intramonth instability in SNAP-recipient families, as they are only sufficient for part of each month (e.g., Wilde and Ranney 2000; Todd 2015). Indeed, several studies find that SNAP recipients’ food spending, consumption, and choices vary within the benefit month (Wilde and Ranney 2000; Shapiro 2005; Hastings and Wash- ington 2010; Castner and Henke 2011; Castellari et al. 2015; Todd 2015; Goldin, Homonoff, and Meckel 2016; Smith et al. 2016).The food spending

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patterns of SNAP recipients vary throughout the month, with food expen- ditures being highest within the first 3 days after the SNAP benefit transfer and dropping sharply thereafter (Wilde and Ranney 2000; Shapiro 2005; Hastings and Washington 2010; Castellari et al. 2015; Todd 2015; Goldin et al. 2016; Smith et al. 2016). In addition, many families with children tend to use most of their benefits in the first 2 weeks (Castner and Henke 2011). The consequence of this lumpy spending pattern is that SNAP families eat fewer calories toward the end of the SNAP benefit month (Shapiro 2005; Mastrobuoni and Weinberg 2009; Seefeldt and Castelli 2009; Darko, Eggett, and Richards 2013; Todd 2015; Hamrick and Andrews 2016). Additionally, the foods that families eat toward the end of a SNAP month tend to be less nutritious, comprising fewer vegetables and less milk and meat products and larger amounts of prepackaged foods and cheap carbohydrates (Tarasuk, McIntyre, and Li 2007; Seefeldt and Castelli 2009; Darko et al. 2013; Khar- mats et al. 2014; Todd 2015).

Emerging research is more equivocal but provides suggestive evidence that this within-month variability may not be limited to food spending and consumption but can also be observed in other domains of health and well- being. For example, hospital admissions of low-income patients with hypo- glycemia may increase at the end of SNAP benefit months (Seligman et al. 2014). However, in that analysis, the SNAP benefit month was confounded with the calendar month, and results could be driven by the monthly pay cycle or other public benefits transferred at the beginning of the month. Research that was able to disentangle calendar month and SNAP month ef- fects did not find a relationship between SNAP month and hospital admis- sions for hypoglycemia (Heflin, Hodges, and Mueser 2016).

The within-month instability associated with the depletion of SNAP benefits early in a benefit month may shape the development and academic performance of low-income children. A study that was able to disentangle calendar month from SNAP month links SNAP administrative data to end- of-grade test scores and finds a curvilinear relationship between test per- formance and benefit transfer timing, with students performing best ap- proximately 2–3 weeks after the SNAP distribution date (Gassman-Pines and Bellows 2015). Another study links SNAP administrative data to school disciplinary records and finds that school disciplinary events increase sig- nificantly at the end of a SNAP month (Gennetian et al. 2016). However, in that analysis, calendar month and SNAP month were confounded. In sum, the evidence on the effects of the SNAP cycle on outcomes in other do-

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mains of health and well-being is mixed, and further research—especially research that is able to disentangle calendar month and SNAP month effects—is needed.

Perhaps because SNAP may be insufficient to buffer economic instabil- ity for a full month, there is growing evidence that families combine em- ployment income and SNAP benefits with other informal methods to buffer economic instability and address their food needs. Many families coping with instability have to package employment income and resources from so- cial safety net programs with social and community supports (Kalil and Ryan 2010; Edin et al. 2013). SNAP-recipient parents report relying on family net- works, as well as food banks, for food or money for food (Edin et al. 2013).

Access to family networks that are able to provide food or money for food appears to be an important factor in mitigating food insecurity (Edin et al. 2013). Informal loans, made by borrowing and lending money within social networks, are a very common financial tool used by low-income fam- ilies (Morduch, Ogden, and Schneider 2014). Not surprisingly, therefore, low-income families frequently draw on family, friends, and neighbors to provide material support through meal sharing, borrowing money for food, or directly borrowing food items to cope with food insecurity and instabil- ity (Stack 1983; Ahluwalia, Dodds, and Baligh 1998; Morton et al. 2007; Swanson et al. 2008; Seefeldt and Castelli 2009). In addition to borrowing money or food, families also regularly use food banks,which are community- based organizations that collect and distribute donated food free of charge (Bhattarai, Duffy, and Raymond 2005; Lombe, Yu, and Nebbitt 2009; See- feldt and Castelli 2009; Yu, Lombe, and Nebbitt 2010).

Although it is clear that many families rely on a combination of formal and informal supports to buffer economic instability and meet their food needs, there is little existing research on the dynamics of how families draw on informal resources throughout the SNAP benefit cycle. One de- scriptive study of a racially diverse sample of low-income individuals finds that food security was especially unstable at the end of the month before individuals received paychecks or benefits (Ahluwalia et al. 1998). In addi- tion, a qualitative study of SNAP recipients finds that those who have ac- cess to family networks often rely on those networks for access to food or resources for food at the end of the SNAP benefit month (Edin et al. 2013). Individuals also reported that they turn to their family and social network as a first line of assistance before using food banks (Edin et al. 2013). Among food insecure households, individuals report food bank

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use as a last resort (Loopstra and Tarasuk 2015).This tendency to first turn to social networks can perhaps be attributed to the emotional stress and stigma of using of food banks (Ahluwalia et al. 1998; Tarasuk and Beaton 1999; Edin et al. 2013).

Combining earnings and public benefits, such as SNAP, with informal resources, such as social networks and community resources, is a common strategy that families use to mitigate poverty and economic instability. However, the dynamics of how SNAP-recipient families access informal resources at different points in the SNAP benefit cycle are not yet well un- derstood. Most research on such economic coping strategies focuses on point-in-time estimates, which can mask significant day-to-day variability and, thus, does not adequately reflect families’ lived experiences. Research that identifies the variable patterns of informal coping within a month is a necessary complement to the broader study of economic instability.

current study

This article is an initial effort to address that gap in the literature by ex- ploring the dynamic patterns of coping strategies throughout the SNAP benefit cycle. Using data from a survey of families receiving SNAP in Dur- ham, North Carolina, this article explores the dynamics of families’ use of informal resources to buffer the intramonth instability of the SNAP benefit cycle. Although this local sample may not generalize to SNAP-recipient families across the United States, this analysis is a preliminary effort to un- derstand how families combine formal and informal resources to mitigate economic instability throughout the SNAP benefit cycle. Specifically, this article will provide exploratory insight into when, during a SNAP benefit month, a sample of SNAP-recipient parents typically borrows money from friends or family or uses food banks to supplement their SNAP benefits. This study, therefore, brings together two typically disparate strands of lit- erature: one strand that focuses on the within-month instability associated with the SNAP benefit cycle and one strand that focuses on informal coping strategies.

As described briefly above, one potential issue raised in prior research on within-month variation in SNAP recipients’ well-being is that effects could also be due to the monthly pay cycle. Indeed, prior research has shown that families’ consumption patterns vary with the monthly pay cy- cle,with people spending more in cash immediately after having received a

Informal Safety Nets during the SNAP Benefit Cycle | 461

pay check than right before receiving the next pay check (Huffman and Barenstein 2004; Stephens 2006). Although benefit issuance schedules vary from state to state, in states where all SNAP recipients receive their benefits on the first of the month, research on the SNAP cycle might be confounded with the monthly pay cycle. The current study addresses this issue by using data from North Carolina, in which SNAP distribution days are staggered throughout the month (between the third and twenty-first) and the date on which any given household receives SNAP is determined by the last digit of the head of household’s social security number (SSN). Thus, the SNAP cycle is unlikely to be confounded with the monthly pay cycle in this study, and this analysis is able to take advantage of this quasi- random SNAP distribution to identify common patterns in economic coping strategies using a cross-sectional sample.

methodology sample and procedure

Data for this analysis come from a survey of a convenience sample of SNAP households with children in Durham, North Carolina. Surveys were con- ducted between February and July 2015. Respondents had the choice of completing the survey independently using pencil and paper or having the survey administered to them by research staff. During the development phase, survey experts and community partners reviewed the survey tool and determined that the questions were able to be answered independently without difficulty by the participants.The vast majority of participants chose to complete the survey independently.

Households were eligible for participation if they received SNAP at the time of the survey and had at least one child under age 18 in the household. Study respondents were recruited at Durham Housing Authority resident council meetings, outside of Durham County Social Services offices, at community events and markets, and in other urban public spaces, such as in parks, in shopping center parking lots, and on residential streets.This recruitment approach likely captured SNAP households who are more connected to their communities generally and, in particular, to the formal social safety net. We are less likely to have captured those who are more disadvantaged, disconnected, or isolated, such as recipients with disabili- ties. Moreover, because recruitment was done in primarily urban spaces,

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this sample likely does not include many SNAP recipients living in rural en- vironments.

Of the recruited 351 households, 87.4 percent of respondents were Af- rican American, 5.4 percent were non-Hispanic white, 5.7 percent were Hispanic, and 1.5 percent identified as being of another racial or ethnic background. Table 1 shows further sample characteristics. Approximately 71.1 percent of respondents were female and the average age of respon- dents was 36.7 years old. Only 21.4 percent of respondents were married or living with a partner, and 69.1 percent of respondents had an educational level of high school diploma or less. Approximately 30.8 percent attended religious service once a week or more. On average, households in the sam- ple consisted of 1.6 adults and 2.3 children. Approximately half (49.6 per-

table 1. Summary Statistics

Full Sample Analysis Sample

Demographics: Male respondents (%) 28.9 30.1 Age 36.7 (12.2) 37.1 (11.8) Race/ethnicity (%): Black 87.4 87.5 White 5.4 5.7 Hispanic 5.7 6.1 Other race 1.5 .7

Married or cohabiting (%) 21.4 20.1 Level of education (%): Less than high school diploma 24.0 24.5 High school diploma/GED only 45.1 42.0 Some college 25.7 28.2 College degree or more 5.2 5.5

Attend religious services at least once a week 30.8 32.4 Household composition: No. of adults 1.6 (1.4) 1.7 (1.6) No. of children 2.3 (1.4) 2.4 (1.5) WIC-eligible households (%) 49.6 49.2

Food shopping and coping habits: No. of food shopping trips per month 3.4 (1.6) 3.4 (1.6) Food expenditures on day before survey ($) 67.07 (96.31) 61.13 (94.94) Use more than half of SNAP in first week (%) 69.0 67.1 Borrowed money in last 7 days (%) 51.1 53.6 Used food bank in last 7 days (%) 39.1 37.9

Days since SNAP* 13.4 (8.8) 17.8 (6.6) Food hardship 2.9 (.8) 2.9 (.7) N (households) 351 238

Note.—Standard deviation in parentheses. Full sample includes all families who received SNAP less than 29 days before the survey. Analysis sample is restricted to families who received SNAP less than 7 days or more than 29 days before the survey. SNAP 5 Supplemental Nutrition Assistance Program; WIC 5 Special Supplemental Nutrition Program for Women, Infants, and Children.

* Range for full sample is 0–29 days. Range for analysis sample is 7–29 days.

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cent) of the households in the sample had children under age 5 and were, therefore, also eligible for benefits from the Special Supplemental Nutri- tion Program for Women, Infants and Children (WIC).On average, respon- dents completed the survey approximately 13 days after they had received their most recent SNAP benefit transfer.

We compared the characteristics of the sample of survey respondents with data on SNAP-recipient families in Durham County, North Carolina, using the American Community Survey (ACS) to assess whether the sam- ple differs from the population of interest. The study sample is slightly younger on average than the Durham County population of SNAP-recipient families and is slightly less likely to be married. African American families are overrepresented in the study sample, while non-Hispanic whites and Hispanics are underrepresented. The study sample also includes a slightly larger share of respondents with a high school diploma or less. The house- hold composition in the study sample is similar to the average household composition of SNAP-recipient families in Durham County, including sim- ilar numbers of adults and children and a similar share of WIC-eligible households.

Because of concerns related to the underreporting of SNAP benefit re- ceipt, which can lead to biased estimates of household characteristics (Meyer and Goerge 2011), we also compared the sample of survey respon- dents to ACS data on Durham County families with incomes below the fed- eral poverty line.Compared to poor families in Durham County, the sample of survey respondents includes a greater overrepresentation of African American families and of respondents with a high school diploma or less than the comparison to Durham County SNAP families suggests. Table A1 (appendix tables A1 and A2 and fig. A1 available online only) shows a full comparison of the sample of survey respondents against the two Durham ACS samples, as well as comparisons to SNAP-recipient and poor families across the United States.

measures

Time since SNAP Transfer The primary predictor of families’ use of informal resources to buffer the intramonth instability of the SNAP benefit cycle, the amount of time passed since a household’s most recent SNAP benefit transfer,was measured using the self-reported SNAP benefit transfer day. In North Carolina, the day of

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SNAP benefit receipt is determined by the last digit of the head of house- hold’s SSN. According to the Benefit Issuance Schedule, families should re- ceive SNAP benefits on the 3rd, 5th, 7th, 9th, 11th, 13th, 15th, 17th, 19th, and 21st of each month, depending on the SSN of the household head. Those whose SSN ends in 1 receive their SNAP benefit on the 3rd of the month, those whose SSN ends in 2 receive their benefit on the 5th of the month, and so on. Therefore, when completing the survey, some participants are in families that just received their SNAP benefits, while other participants are in families that received their SNAP benefits several weeks earlier. For example, if the survey is administered on the 16th of a calendar month, a participant who is in a family that receives its benefits on the 11th (i.e., the household head’s SSN is 5) takes the survey 5 days after receiving SNAP benefits, whereas a participant in a family that receives SNAP benefits on the 19th (i.e., the household head’s SSN is 9) takes the survey 27 days after receiving SNAP benefits, assuming a 30 day month. Figure A1 visually dem- onstrates how the number of days passed since SNAP benefit receipt can differ for four hypothetical respondents who are each surveyed on the same calendar day but have different SNAP transfer days. Comparing the survey responses for these survey participants yields information about the association between time passed since SNAP benefit receipt and use of formal and informal coping strategies. Because the date of receipt is quasi- randomly assigned, this serves to control for any unobservable differences between respondents in the number of days that have elapsed between SNAP receipt and the date of the survey that might also be related to respon- dents’ economic coping strategies (analyses that examined this assumption are described below).

In addition to the self-reported SNAP benefit transfer day, respondents were asked to provide the last digit of the SSN of the head of household. However, 21.9 percent of households did not provide this information. Where information for both measures was available, the agreement be- tween the SSN-derived date and the self-report date was high (78 percent) and results were substantively the same for both measures (these are avail- able from the authors on request). Therefore, the self-reported measure was used for all analyses.

We conducted a number of checks to examine the randomization of SNAP transfer days within our sample (all results are available from the au- thors on request). First, we examined the distribution of the sample by SNAP distribution days. Figure 1 shows that the families in the sample

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are relatively uniformly distributed across SNAP distribution days.There is a slightly larger share of households that receive their benefits on the 3rd of the month.This is explained by the fact that both families with a household head’s SSN that ends in 1 and families with no SSN receive their SNAP ben- efits on the 3rd. Second, we tested the relationship between recency of SNAP transfer and various demographic and household characteristics, in- cluding WIC eligibility, number of children in the household, and how long a household has been receiving SNAP benefits.We find no significant rela-

FIGURE 1. Distribution of respondents by SNAP benefit transfer day. A, Full sample; B, analysis sample.

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tionships between recency of SNAP transfer and any of the demographic or household characteristics examined.Third,we examined whether the date of SNAP transfer was related to any of the outcomes of interest.The SNAP transfer dates in and of themselves were unrelated to any of the outcomes of interest. Finally, the recruitment location for the surveys was unrelated to the number of days passed since the most recent SNAP transfer and to outcomes of interest. Taken together, and consistent with the notion that variation in SNAP transfer is essentially randomly assigned, these checks suggest that the amount of time that passed between the day of SNAP trans- fer and the survey administration was not systematically related to any of the family or household characteristics or outcomes.

Formal and Informal Coping Strategies Although no one has quantified what the most common strategies for cop- ing with within-month economic stability and the SNAP benefit cycle are, two strategies, borrowing money and using a food bank, come up most frequently in qualitative interviews (Ahluwalia et al. 1998; Seefeldt and Castelli 2009).To measure these coping strategies, respondents were asked whether their household “borrowed money from friends and family to buy food” or “got food from a food bank or food kitchen” on any day during the 7 days before the survey. Initial pilot results suggested that families are unlikely to borrow money or use the food bank many times during any given month; asking about these coping strategies during the week before the survey better captures this behavior.

Food Hardship A developing body of research suggests that families experience substantial volatility in income (Wolf et al. 2014), which is masked in typical point-in- time and average measures of income. Similarly, it is possible that the com- monly used point-in-time and average measures of food hardship also mask high levels of variability.Therefore, to assess whether families’ level of food hardship varies during the course of a SNAP month, we developed a daily measure of food hardship building on the Six-Item Short Form of the Household Food Security Scale (Blumberg et al. 1999; USDA ERS 2012). In addition to the five items asking about adult food hardship on the orig- inal short form, we included three items that are specific to families with children from the original 18-item Household Food Insecurity Scale (Ham- ilton et al. 1997). Items were rephrased to reflect food hardship at the time

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when the survey was completed, and the original short-form item asking about the frequency of the food hardship experiences was excluded. The response options were also changed to a balanced-response five-item scale to reduce acquiescence bias (Groves et al. 2009). A household’s level of food hardship is determined by calculating the scale mean. Four of the eight items were reverse coded, such that a higher value reflects a greater level of food hardship. The full adapted scale and the response values can be seen in table A2.

Covariates Respondents were asked to provide basic demographic information and in- formation about household composition and experience with SNAP bene- fits. Demographic information included the respondent’s age, whether the respondent was married or lived together with a partner, and the frequency with which the respondent attended religious services. Respondents pro- vided the number of children and adults living in the household, as well as whether the household included any children age 5 or younger to account for WIC eligibility. Respondents were also asked how frequently they shopped for food each month and how much money, from SNAP benefits or other income sources, they spent on food the day before the survey. Fi- nally, respondents were asked how much of their SNAP benefits they typi- cally spent in the first week after the transfer, with answer choices ranging from none to most or all, because the use of a greater share of SNAP bene- fits in the first week likely reflects a greater reliance on SNAP (Wilde and Ranney 2000; Shapiro 2005).

missing data

Although not especially high, item nonresponse was a concern given the small sample size. Of 351 survey responses, 17.2 percent of surveys were missing data for some items. Most surveys were missing responses to only one question (78.2 percent), although this question varied across partici- pants. At most, a survey was missing responses to four items. Because we could not assume the data were missing at random, and in order to use the complete sample of 351 households for analyses,we employed multiple imputation to address the missing data. Multiple imputation replaces miss- ing data with a probable value based on other available information from the data set. Analyses then produce estimates and confidence intervals that

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take into account missing-data uncertainty. For these analyses, multivari- ate imputation was conducted using Stataversion 13.1.The imputation model included all available information for all covariates and was chosen to be compatible with the analyses to be performed on the imputed data sets, such that all variables in the analytical models were present in the imputa- tion model. All subsequent analyses take the multiple imputation into ac- count in the calculation of standard errors. Although this method cannot completely account for bias due to missing data, it improves consistency and efficiency compared to other methods, such as list-wise deletion (John- son and Young 2011).

data analyses

Multivariate linear and logistic regression models were used to estimate the association between the number of days passed since a SNAP benefit transfer and the use of economic coping strategies, as well as a household’s level of food hardship. Because the regression models predict borrowing and food bank use during the 7 days before the survey as the outcomes, the analyses are restricted to families who had received their SNAP bene- fits at least 7 days earlier. That is, the models exclude households who re- ceived their SNAP benefits between 0 and 6 days before the survey. This constraint ensures that the outcomes do not capture borrowing or food bank use that occurred before the most recent benefit transfer,which could bias the results. These models also exclude the small number of house- holds who received their SNAP benefits 30 days before the survey, which was uncommon because of the variation in the length of different months. The final sample size for the regression models is 238 households. Table 1 shows the descriptive statistics for the analysis sample, which is highly similar to the full sample across demographic and household character- istics.

For each outcome of interest, we present two sets of models. The first set of models includes days passed since SNAP as a continuous predictor, while the second set of models uses indicators for 4-day groupings and week groupings of days, as well as indicators for first and second half of the month as the predictors, to allow for nonlinearity. All models control for demographics, household composition, and food shopping and SNAP use habits.Coefficient estimates of logistic regressions were exponentiated and are provided as odds ratios for ease of interpretation.

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results

As shown in table 1, on average, families in the analysis sample experi- enced a relatively high level of food hardship (2.9 on a scale of 1–5). Con- sistent with prior literature, the majority of families (67.1 percent) reported that they typically used up most or all of their SNAP benefits in the first week after receiving them. Approximately one-half (53.6 percent) of families re- ported borrowing money for food, and 37.9 percent reported using a food bank in the week before the survey. Together, these results suggest that SNAP benefits alone may not be sufficient for most families and that many families needed to draw on social networks to get through the month. How- ever, of families who reported either borrowing money or using a food bank, only one-third reported using both strategies (38.2 percent). Families who reported using food banks have different characteristics than families who reported borrowing money. Compared to respondents who reported bor- rowing money, respondents who reported using a food bank were more likely to be male (p < :05) and more likely to be single ( p < :10), and they were younger, on average ( p < :01).

descriptive results

Figure 2 shows the share of respondents who reported that their family borrowed money or used a food bank in the 7 days before completing the survey over the course of a SNAP benefit month, with each bubble scaled based on the sample size for each day. These bubble graphs include the full sample. The analysis sample, indicated in the figure, includes only families who received their most recent SNAP benefit 7–29 days before the survey. Figure 2A shows that the share of families who borrowed money appears to increase later in the SNAP month. The figure also sug- gests that this increase in the share of families who borrowed money is not linear throughout the SNAP month. Figure 2B suggests that the share of families who used a food bank does not change over the course of the SNAP month.

regression results

Table 2 presents results from logistic multivariate regression models test- ing the association between days passed since the most recent SNAP trans-

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fer and the outcomes of interest, where days since SNAP is a continuous variable. As shown in column 1, a family’s odds of having borrowed money to supplement SNAP benefits increased by 6.2 percent ( p < :01) with every day that passed after receiving SNAP benefits starting on day 7 of the SNAP

FIGURE 2. Share of respondents using food coping strategies by number of days since SNAP benefit transfer. A, Share of respondents who borrowed money in past week; B, share of respondents who used food bank in past week. Analysis sample dates are underlined.

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month.Thus, holding all other factors constant, a family’s odds of borrow- ing were 1.37 times higher at the end of a SNAP month (29 days after trans- fer) compared to on day 7 of the SNAP month. Since, on average, 28.3 per- cent reported on day 7 of the SNAP month that they had borrowed money in the last week, this suggests that an additional 38.8 percent of families are likely to report having borrowed money for food in the last week at the end of the SNAP month, compared to day 7. As shown in column 2, families’ odds of having used a food bank did not change significantly over the course of the SNAP month.

While the regressions results presented in table 2 show that there is a significant relationship between borrowing money and days passed since the most recent SNAP transfer, these models do not capture the possible nonlinear relationship between the likelihood of borrowing and the num- ber of days since the SNAP benefit transfer shown in figure 2A.To capture nonlinearity, the models presented in table 3 used indicators for 4-day groupings of days since the SNAP transfer,week indicators, as well as indi- cators for first and second half of the month as the predictors. Model 1 uses 4-day grouped predictors (e.g., 10–13 days since SNAP transfer, 14–17 days since SNAP transfer), and all coefficients are compared to families who

table 2. Logistic Regressions of the Effect of Days since SNAP Benefit Transfer on Food Coping Strategies

Borrowed Money Used Food Bank (1) (2)

Days since SNAP 1.062**(.024) 1.012 (.022) No. of children .945 (.090) .956 (.092) No. of adults 1.143 (.150) 1.195 (.169) WIC eligible 1.124 (.386) 1.132 (.348) No. of food shopping trips per month 1.429**(.136) 1.070 (.097) Amount of SNAP benefits used in first week 1.432* (.207) 1.304y (.184) Food expenditures on day before survey 1.000 (.002) 1.003 (.002) Male 1.697 (.555) 1.732y (.541) Age .984 (.014) 1.008 (.014) Married or cohabiting .760 (.264) .662 (.235) Frequency of religious services attendance 1.050 (.150) .984 (.141) Base rate (day 7; %) 28.27 21.99

Note.—Coefficients presented as odds ratios. Standard errors in parentheses. Models exclude households who received SNAP less than 7 days or more than 29 days before the survey. SNAP 5 Sup- plemental Nutrition Assistance Program; WIC 5 Special Supplemental Nutrition Program for Women, Infants, and Children. N (households) 5 238.

y p < .1. * p < .05. ** p < .01.

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were 7–9 days post-SNAP transfer because families who received SNAP fewer than 7 days before the survey were excluded from the sample. Model 2 uses week indicators (e.g., week 2 of SNAP month), and all coefficients are compared to families who were 7–13 days post-SNAP transfer. Model 3 uses indicators for the first half of the month (i.e., 7–14 days since SNAP transfer) and second half of the month (i.e., 15–29 days since SNAP transfer), and the coefficient is relative to families who were 7–14 days post-SNAP transfer.

The model 1 results presented in column 1 of table 3 show that, relative to a base rate of 31.2 percent on days 7–9 after the SNAP transfer date, the odds of borrowing were higher for families for whom more than 18 days had passed since the SNAP transfer. Specifically, families for whom 18– 21 days had passed since SNAP transfer had 6.28 (p < :01) greater odds of having borrowed money than families for whom only 7–9 days had passed. Families for whom 22–25 days had passed since transfer had 2.92 ( p < :05) times higher odds of having borrowed money than families

table 3. Logistic Regressions Predicting Food Coping Strategies Using Grouped Indicator Predictors

Borrowed Money Used Food Bank (1) (2)

Model 1—4-day predictors: 7–9 days since SNAP . . . . . . 10–13 days since SNAP 2.081 (1.087) 1.509 (.774) 14–17 days since SNAP 1.381 (.822) .466 (.303) 18–21 days since SNAP 6.279** (3.586) 1.591 (.831) 22–25 days since SNAP 2.921* (1.499) .799 (.407) 26–29 days since SNAP 3.557* (2.138) 1.929 (1.106) Base rate (days 7–9) 31.16 32.17

Model 2—week predictors: Week 2 of SNAP month (7–13 days since SNAP) . . . . . . Week 3 of SNAP month (14–21 days since SNAP) 1.861y (.636) .853 (.282) Week 4 of SNAP month (22–29 days since SNAP) 1.938* (.624) .949 (.292) Base rate (days 7–13) 41.12 39.69

Model 3—half-month predictors: First half of SNAP month (days 7–14) . . . . . . Second half of the SNAP month (days 15–29) 2.294** (.693) .926 (.271) Base rate (days 7–14) 39.52 38.28

Note.—Coefficients are presented as odds ratios. Standard errors are in parentheses. Models ex- clude households who received SNAP less than 7 days or more than 29 days before the survey. All mod- els control for demographics, household composition, and food shopping and SNAP use habits. SNAP 5 Supplemental Nutrition Assistance Program. N (households) 5 238.

y p < .1. * p < .05. ** p < .01.

Informal Safety Nets during the SNAP Benefit Cycle | 473

for whom only 7–9 days had passed. Finally, families for whom 26–29 days had passed had 3.56 ( p < :05) greater odds of having borrowed money. Consistent with figure 2A, the odds of borrowing money (compared to 7–9 days after the SNAP transfer) peaked between days 18 and 21, ebbed somewhat between days 22 and 25, and increased again at the very end of the SNAP month.

Model 2 results presented in column 1 of table 3 suggest that, relative to a base rate of 41.1 percent on days 7–13 after the SNAP transfer date, the odds of borrowing were higher for families for whom more than 2 weeks had passed since the SNAP transfer date. Specifically, families in the third week of the SNAP month (i.e., 14–21 days since the SNAP transfer) have 1.86 ( p < :01) greater odds of borrowing money than families in the second week of the SNAP month (i.e., 7–13 days since SNAP transfer). Families in the fourth week of the SNAP month (i.e., 22–29 days since the SNAP trans- fer) have 1.94 ( p < :05) greater odds of borrowing money than families in the second week of the SNAP month.

Model 3 results presented in column 1 of table 3 show, relative to a base rate of 39.5 percent in the first half of the month (i.e., 7–14 days since the SNAP transfer), families in the second half of the month (i.e., 15–29 days since the SNAP transfer) had significantly higher odds of borrowing. Spe- cifically, families in the second half of the SNAP month have 2.29 ( p < :01) greater odds of borrowing money than families in the first half of the SNAP month.Together, the result from models 1, 2, and 3 suggest that SNAP fam- ilies are more likely to borrow money from friends or family to purchase food at the end of the SNAP month than at the beginning of the month. The relationship between the number of days since the SNAP transfer and using a food bank is not statistically significant in any of the nonlinear specifications (see col. 2 of table 3).

snap timing and food hardship

To gain insight into whether borrowing money for food or using a food bank to supplement SNAP benefits helps to stabilize households, we also tested the association between household food hardship and the number of days passed since the SNAP transfer. As table 4 shows, households’ levels of food hardship remained stable throughout the SNAP month.That is, de- spite the within-month instability introduced by the SNAP benefit cycle,

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households did not report more food hardship at the end of the SNAP month than at the time when the SNAP benefits were transferred.

specification checks

We conducted a number of specification checks (all results are available from the authors on request). First, to check that the results were not bi- ased by the multiple imputation, we repeated all analyses using the non- imputed sample, and the results using the nonimputed data were substan- tially similar to the results of analyses using the imputed data. Second, we repeated all analyses using the full sample, including families who received their SNAP benefits less than 7 days before the survey. Again, the results were substantially similar to the results presented here using the restricted analysis sample.Thus, the sample restrictions and the multiple imputation do not appear to be biasing the results.

Finally, to ensure that the effect of the number of days passed since the last SNAP transfer does not reflect an underlying effect driven by the monthly pay cycle, we examined whether the likelihood of borrowing and using a food bank increased over the course of a calendar month. Fig- ure 3 shows that the share of families who borrowed money remained rel- atively stable during the calendar month, with small fluctuations through-

table 4. Ordinary Least Squares Regressions Predicting Household Food Insecurity

Food Hardship

Model 1—continuous: Days since SNAP 2.002 (.007)

Model 2—4-day predictors: 7–9 days since SNAP . . . 10–13 days since SNAP .065 (.171) 14–17 days since SNAP 2.067 (.197) 18–21 days since SNAP .216 (.180) 22–25 days since SNAP 2.072 (.166) 26–29 days since SNAP .019 (.195)

Model 3—week predictors: Week 2 of SNAP month (7–13 days since SNAP) . . . Week 3 of SNAP month (14–21 days since SNAP) .093 (.114) Week 4 of SNAP month (22–29 days since SNAP) 2.034 (.106)

Model 4—half-month predictors: First half of the SNAP month . . . Second half of the SNAP month 2.067 (.099)

Note.—Standard errors in parentheses. Models exclude households who received

SNAP less than 7 days or more than 29 days before the survey. All models control for demographics, household composition, and food shopping and SNAP use habits. SNAP 5 Supplemental Nutrition Assistance Program. N (households) 5 239.

Informal Safety Nets during the SNAP Benefit Cycle | 475

out the month. The share of families who used a food bank also remained relatively stable during the calendar month.We also repeated the continu- ous and nonlinear regression analyses using the number of days passed since the first day of the calendar month as the predictor instead of the

FIGURE 3. Share of respondents using food coping strategies by calendar day. A, Share of respondents who borrowed money in past week; B, share of respondents who used food bank in past week. Analysis sample dates are underlined.

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number of days passed since a SNAP transfer (table 5).We find that families have 2.92 ( p < :10) higher odds of borrowing money between the 22nd and 25th of a calendar month compared to the 7th to the 9th. However, this result is not robust to the continuous or any of the other nonlinear speci- fications. Similarly, families have 3.15 ( p < :05) higher odds of using a food bank between the 22nd and 25th of a calendar month compared to the 7th to the 9th. That result is also not robust to the continuous or other non- linear specifications. Together, these results suggest that there may be a calendar month pattern to borrowing money and using a food bank inde- pendent of the SNAP benefit cycle pattern.

discussion

Building on research on the within-month instability associated with the SNAP benefit cycle and research on resource packaging among low- income families, this study is the first to provide insight into the dynamic patterns of how poor families combine SNAP with informal resources to buffer the effects of economic instability. We take advantage of the quasi- random assignment of SNAP benefit distribution days in North Carolina

table 5. Logistic Regressions of the Effect of Calendar Day on Food Coping Strategies

Borrowed Money Used Food Bank (1) (2)

Model 1—continuous: Calendar day .981 (.018) .999 (.019)

Model 2—4-day predictors: 7th–9th . . . . . . 10th–13th 1.156 (.552) .708 (.345) 14th–17th .808 (.365) .992 (.455) 18th–21st .581 (.299) .805 (.419) 22nd–25th 2.916y (1.745) 3.152* (1.771) 26th–30th .736 (.349) .736 (.354)

Model 3—week predictors: Week 2 (7th–13th) . . . . . . Week 3 (14th–22nd) .691 (.206) 1.271 (.391) Week 4 (23rd–30th) .997 (.322) 1.462 (.475)

Model 4—half-month predictors: 7th–14th . . . . . . 15th–30th .742 (.198) 1.294 (.354)

Note.—Coefficient presented as odds ratios. Standard errors in parentheses. Models exclude households who were surveyed between the 1st and the 6th of the calendar month. All models control for demographics, household composition, and food shopping and SNAP use habits. SNAP 5 Supple- mental Nutrition Assistance Program. N (households) 5 239.

y p < .1. * p < .05.

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to identify when poor families draw on economic coping strategies to buffer the within-month instability of resources associated with the SNAP bene- fit cycle. We find that the odds of borrowing money for food increase over the course of the SNAP month, while the odds of using a food bank do not change significantly. Although families are more likely to borrow money for food toward the end of the SNAP month, levels of household food hard- ship remain relatively high and stable throughout the SNAP month.

Consistent with findings from earlier studies (Wilde and Ranney 2000; Castner and Henke 2011), we find that a majority of SNAP households spend more than half of their benefits in the first week. Our findings sug- gest that SNAP families combine their earned income and SNAP benefits with money borrowed from their social networks to sustain their food pur- chases through the end of the month. That families become significantly more likely to borrow money specifically for the purchase of food as the SNAP month progresses suggests that SNAP benefits alone may not be suf- ficient to mitigate economic instability for the full month.

The odds of borrowing money do not increase in a linear fashion begin- ning when families receive their SNAP benefits. Instead, the increase in the odds of borrowing money are concentrated in the second half of the SNAP month. Specifically, 3 weeks after receiving their SNAP benefits, families have more than six times higher odds of borrowing than 1 week after re- ceiving their benefits. That the odds of borrowing money ebb again after peaking between days 18 and 21 may reflect that the amount borrowed is intended to suffice for the remainder of the SNAP month and that families typically borrow money only once during a SNAP month, as was suggested by pilot study results.

That families’ odds of using food banks do not increase toward the end of the SNAP benefit month is surprising. However, since families tend to first turn to social networks because using food banks can be emotionally stress- ful and can make people feel stigmatized (Ahluwalia et al. 1998; Tarasuk and Beaton 1999; Edin et al. 2013), it is possible that families’ economic strain as- sociated with the SNAP benefit cycle is not so severe that families need to consistently turn to food banks. It is also possible that the question about borrowing money does not precisely measure money borrowed only for food and may, instead, capture borrowing money to address economic instability more broadly,while food bank use is strictly related to accessing food.Thus, the divergent findings may reflect that a families’ overall need for informal supports increases toward the end of the SNAP month but that food-related

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hardship alone does not increase significantly. Finally, respondents who re- ported using a food bank are on average more likely to be younger, single, and male than respondents who reported borrowing money. Future research should disentangle whether the differential characteristics associated with food bank use and borrowing money explain why only borrowing money in- creases during the SNAP benefit cycle.

Because SNAP distribution in North Carolina is quasi-random and stag- gered throughout the month, the pattern in borrowing behavior through- out the SNAP cycle is unlikely to be driven by an underlying calendar month pattern. The within-month variation in borrowing is also unlikely to be explained by the receipt of other welfare benefits, such as WIC, Tempo- rary Assistance for Needy Families, and Supplemental Security Income because, in North Carolina, those are all disbursed at different intervals and on different days than SNAP and one another. However, the specifi- cation checks find that the odds of both borrowing money for food and using a food bank may also vary systematically over the calendar month, suggesting that there may be a calendar month pattern to using these two coping strategies independent of any association between SNAP benefit timing.Those findings warrant additional research to further explore the pat- terns and predictors of borrowing money and food bank use throughout the calendar month.

The finding that household food hardship levels are stable throughout the SNAP month is also somewhat surprising. Research on the SNAP cycle consistently reports decreases in food expenditures and food consumption throughout the SNAP month (Shapiro 2005; Mastrobuoni and Weinberg 2009; Seefeldt and Castelli 2009; Hastings and Washington 2010; Darko et al. 2013; Castellari et al. 2015; Todd 2015; Goldin et al. 2016; Hamrick and Andrews 2016). Because our measure of food hardship encompasses worry about food expenditures, as well as reduced food consumption, we expected that food hardship would increase as a function of time passed since the most recent SNAPdistribution. However, it is possible that house- hold food hardship remains stable because families are able to continue to buffer food hardship by combining their SNAP benefits with money bor- rowed from friends and family.Our finding that food hardship remains sta- ble may indicate that combining formal and informal resources is an effec- tive strategy to buffer against economic instability.

While householdfoodhardshipremainsstablefor mostfamilies through- out the SNAP month, the level of food hardship is relatively high. Although

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such high levels of food hardship are consistent with the literature (Daponte et al. 1998; Daponte 2000; Swanson et al. 2008; Lombe et al. 2009), it is con- cerning that families continue to experience food hardship despite the use of formal as well as informal supports.This stable, but moderately high, level of food hardship underscores the point that SNAP benefit amounts may not be sufficient to lift families out of food hardship even in combination with earned income and the use of informal supports.

It is important to consider the generalizability of this study’s findings, as the study was conducted in a single county in North Carolina and may not generalize to other regions in the United States. As table A1 shows, a larger share of poor and SNAP-recipient families in Durham, North Carolina, are African American than in the US population, and fewer poor and SNAP- recipient families in Durham are eligible for WIC benefits than is the case nationally. However, Durham is a midsized city with a demographically diverse population and substantial numbers of poor families living in both concentrated-poverty and mixed-income areas, and it faces many of the sociodemographic challenges relevant to the nation as a whole.Therefore, although Durham County is not nationally representative, it is neverthe- less an instructive region within which to conduct such research.

Additionally, although the survey sample does not differ drastically on observable characteristics from the population of SNAP-recipient families in Durham County, it is, nevertheless, not representative of Durham.On av- erage, the study sample is younger, less educated, and less likely to be mar- ried than the population of SNAP-recipient families in Durham. It is pos- sible that these characteristics may influence the probability of borrowing money for food. Moreover, additional research should give particular atten- tion to populations that may have very different access to social and commu- nity resources, such as families living in rural areas and SNAP recipients with disabilities, since this sample likely also includes an overrepresentation of urban families and families who are comparatively more advantaged and connected to their communities. Attention should be given to whether fam- ilies with more extensive experience using SNAP are less affected by the SNAP cycle than families who are new to receiving SNAP benefits. It would also be useful to replicate this research in other geographic areas.

African American families are overrepresented in the study sample.Cop- ing with economic instability is a significant challenge for all low-income families in the United States, but African American families are especially vulnerable to economic instability since they have the highest rate of poverty

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of any US racial or ethnic group (DeNavas-Walt and Proctor 2014) and are more affected by income and employment instability than other racial or ethnic groups (Ma, Gee, and Kushel 2008; Shapiro, Meschede, and Osoro 2013). Moreover, African American families are more likely to live in com- munities with limited access to supermarkets with low-cost, healthy food options (Moore and Diez Roux 2006; Powell et al. 2007; Larson, Story, and Nelson 2009; Walker, Keane, and Burke 2010). This lack of community food resources may place particular strain on African American families’ food budgets and may compromise their food security. It is possible that poor African American families may have a greater need to draw on their informal safety nets to supplement their SNAP benefits.Thus, it is also im- portant to assess whether these patterns of resource packaging hold for SNAP recipient families who are non-Hispanic white and Hispanic.

In order to ensure that the outcomes do not capture borrowing or food bank use that occurred before the most recent benefit transfer,which could bias the results, it was necessary to constrain the analyses to families who had received their SNAP benefits at least 7 days before the survey date be- cause of the recall period of the questions. However, because of this sample restriction, the regression results do not provide any insight about families’ choices to borrow money or use a food bank during the first week of the SNAP benefit month. Additional research is needed to examine how fam- ilies draw on these two coping mechanisms during the first week of the benefit month and how that differs from the second half of the month.

Finally, the relatively small sample size of this study limits our ability to examine moderating factors or to identify whether different types of fam- ilies have different patterns of resource packaging. Despite these limita- tions, this study’s findings represent an important expansion on the extant literature on how poor families combine formal and informal resources to buffer economic instability.

Because this study is the first to examine the dynamic relationship be- tween resource packaging and economic instability during the SNAP ben- efit month, it raises additional questions. Additional research is needed to better understand the role of social networks in buffering and, possibly, perpetuating economic instability. As mentioned above, these results do not speak to the role of the quality and strength of families’ social networks. The survey also did not collect information about families lending money to their social networks. Therefore, whether the borrowing and lending of resources within social networks could perpetuate economic instability

Informal Safety Nets during the SNAP Benefit Cycle | 481

in the long run while buffering families from the immediate influence of instability, especially in segregated and resource-poor communities, is of particular interest.

Despite these limitations, this study provides important policy-relevant insight into how SNAP-recipient families cope with the within-month in- stability associated with the SNAP benefit cycle. To address the concern that SNAP families experience relatively high levels of food hardship and recurring within-month economic instability, much of the prior literature on SNAP benefit cycles suggests that SNAP benefits should be disbursed at more frequent intervals, as this may help recipients to smooth their con- sumption.We agree that it is likely that more frequent distributions within a benefit month may help to reduce the within-month economic instability introduced by SNAP design and administration. Yet, this argument assumes that SNAP benefits on the whole are enough for families and that the within- month instability is a result of suboptimal budgeting. Our results indicate otherwise and, in fact, suggest that families intentionally budget their use of formal and informal supports throughout a given benefit month. There- fore, in addition to more frequent SNAP distributions, an increase in SNAP benefits could help address within-month economic instability for SNAP families. Indeed, a recent study finds that families who received increased SNAP benefit amounts due to the American Recovery and Reinvestment Act were able to more effectively smooth their food consumption through- out the month (Todd 2015).

That money borrowed from social networks makes up a core compo- nent of poor families’ monthly budget also highlights the reality that poor families’ well-being and ability to cope with economic instability may well hinge on the economic well-being of their social networks. For that reason, families with particularly resource-poor networks are at a higher risk of the adverse consequences associated with economic instability. While our results indicate that the majority of families rely on their social networks, this study cannot provide insight on how the level of connectedness to net- works and the quality of these social networks may shape individual fam- ilies’ abilities to buffer economic instability. This is a question for future research on economic instability with important implications for policy. While an increase in SNAP benefit amounts may reduce families’ reliance on their social networks, the importance of more connected, higher-income social networks highlights the need for policy that effectively addresses economic segregation.

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Understanding the patterns of economic coping in response to within- month economic instability is a necessary complement to understanding the role that economic instability plays in the lives of poor families. Anal- yses that focus only on static estimates of resource packaging may mask significant variability in economic coping decisions over time. Since this var- iability could have an influence on families’ short- and long-term well-being, research that treats such economic coping decisions as dynamic and vari- able factors, much like income and employment, can give much better in- sight into how economic instability affects families’ daily lives. By taking advantage of the quasi-random distribution of SNAP benefits in North Car- olina, this initial exploratory study sheds light on how families dynamically buffer economic instability by intentionally combining their formal and in- formal resources.

note

Anika Schenck-Fontaine is a PhD candidate in the Sanford School of Public Policy at Duke University. She studies how macroeconomic phenomena influence family life and the devel-

opment of children, with a focus on how antipoverty policies buffer families from these in-

fluences.

Anna Gassman-Pines is an associate professor of public policy and psychology and neuro- science in the Sanford School of Public Policy and Duke University. She studies low-wage

work, family life, and the effects of welfare and employment policy on child and family

well-being in low-income families.

Zoelene Hill is a postdoctoral research scientist at the New York University Institute for Hu-

man Development and Social Change. Zoelene researches early education policies and the

experiences of low-income and minority children and families.

The authors thank Laura Bellows, Danton Noriega, and Scott Lynch for helpful comments on

an earlier version of this article. This work was supported by the National Science Founda-

tion (award DRL-1418333).

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