Abstract

This study examines how earnings variability affects Food Stamp Program participation and how the effects differ 

depending on a household’s income position relative to the eligibility threshold. The study uses survey data from the 

Three-City Study, which is a longitudinal survey of low-income families with children living in Boston, Chicago, 

and San Antonio. The data in the Three-City Study have been linked to administrative case records on program 

participation. The study estimates longitudinal fixed-effect regression models of the times that households spend on 

food stamps and distinguishes between households that appear to be eligible or ineligible for food stamps based on 

longer run income data. Temporary earnings increases and higher annual earnings variability reduce participation for 

households with low levels of permanent income. Higher annual earnings variability also reduces program participation for higher income households, but the effect is smaller in magnitude.

By Robert Moffitt, Johns Hopkins University, and David C. Ribar, 

University of North Carolina at Greensboro

Variable Effects of Earnings Volatility 

on Food Stamp Participation

Technical Report

Contractor and Cooperator Report No. 52

May 2009

This study was conducted by Johns Hopkins University and the University 

of North Carolina at Greensboro under a cooperative research contract with 

USDA’s Economic Research Service (ERS) Food and Nutrition Assistance 

Research Program (FANRP): contract number 43-3AEM-4-80116 (ERS project 

representative: Constance Newman). The views expressed are those of the 

authors and not necessarily those of ERS or USDA.
Acknowledgments 

Much of the material in this report was originally prepared for the National Poverty Center and 

Economic Research Service conference on “Income Volatility and Implications for Food 

Assistance Programs II,” November 16-17, 2006 in Washington, DC and published as a chapter 

in Income Volatility and Food Assistance in the United States, edited by Dean Jolliffe and James 

Ziliak. The authors gratefully acknowledge financial assistance from the National Institute of 

Child Health and Human Development under grant numbers R01 HD36093 and R01 HD050370 

and from the Economic Research Service of the U.S. Department of Agriculture under 

cooperative agreement number 43-3AEM-4-80116. They thank Paula Fomby and Bianca 

Frogner for their help preparing the survey data; Robert Goerge, Daniel Shroeder, and Jesse 

Valente for their help preparing the administrative data, and Rich Depolt and Irene Navarrete for 

valuable research assistance. They also thank Doug Besharov, Thomas DeLeire, Dean Jolliffe, 

John Kirlin, Constance Newman, and Jim Ziliak for helpful comments. The views expressed in 

this report are those of the authors and are not necessarily shared by the supporting agencies. 

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Contents 

Introduction......................................................................................................................................1 

Conceptual analysis of earnings volatility .......................................................................................3 

Data sources and measures ..............................................................................................................6 

Descriptive analysis .......................................................................................................................12 

Multivariate analyses .....................................................................................................................14 

Conclusions....................................................................................................................................18 

References......................................................................................................................................21 

Notes ..............................................................................................................................................23 

Tables.............................................................................................................................................25 

Appendix........................................................................................................................................32
Variable Effects of Earnings Volatility on Food Stamp Participation: 

Technical Report 

Introduction 

There are several sound reasons to suppose that earnings volatility plays a role in Food 

Stamp Program participation and other types of assistance program behavior.1 However, the 

results from previous empirical studies have been equivocal. To the extent that they have 

considered volatility, researchers have mostly focused on different types and definitions of this 

concept, such as short-term versus long-term shocks in earnings or the overall variability of 

earnings histories. Researchers have not considered how associations might appear for some 

groups but not for others. In this report, we examine how the effects of earnings variability on 

program participation differ depending on a family’s position in the income distribution. 

Specifically, we investigate whether there are asymmetries in these effects depending on whether 

the family is initially above or below an eligibility threshold. 

There are many reasons why asymmetric effects might appear, including a simple 

“mechanical” explanation. Consider a family whose long-term, trend earnings places it within 

the eligibility guidelines of the Food Stamp Program or some other assistance program. If 

earnings and other characteristics are completely stable so that there is no short-term variability, 

the family will remain eligible for the program over time and may participate, depending on how 

it values the program’s benefits relative to its costs of enrollment and compliance (Moffitt 1983, 

2003). If we instead allow for some earnings variability, there is a chance that the family will 

lose eligibility from time to time, leading to a decrease in the opportunities and incentives to 

participate. Thus, among initially eligible households, we expect a mechanical association in 

which greater variability reduces participation. These expected associations are reversed, 

1
however, when we consider households that are initially above the eligibility threshold. For 

these households, stable incomes lead to continuous periods of ineligibility and nonparticipation, 

while unstable incomes lead to temporary periods of eligibility and perhaps participation. We 

subsequently discuss additional conceptual reasons for the association between earnings 

volatility and program participation, but as this simple explanation shows, asymmetries in effects 

should be considered. 

We examine the relationship between earnings volatility and food stamp participation 

using survey data from the Three-City Study that have been linked to administrative case records 

on program participation. The Three-City Study is a longitudinal survey of low-income families 

with children who were living in Boston, Chicago, and San Antonio. A distinct advantage of the 

Three-City Study is that while it is a low-income sample and includes many food stamp 

recipients, it was not initially limited to program participants. Thus, the survey includes 

participating and non-participating households as well as eligible and near-eligible households. 

At each wave, the survey also gathered information about people’s work and earnings histories. 

These features facilitate our analyses of program participation, earnings volatility, and 

asymmetric effects. 

Another advantage of the Three-City Study is that its survey responses have recently 

been linked to administrative data. Previous household-level research on participation in food 

assistance programs has usually relied on one or the other of these two types of data. Our 

approach of using combined survey and administrative data addresses some of the weaknesses of 

the individual sources. From the administrative data, we obtain more accurate and lengthy 

descriptions of participation histories than we could through surveys, overcoming the recall 

problems inherent in retrospective questionnaires. At the same time, the survey data help us to 

2
surmount some of the shortcomings of administrative data. Program records only describe 

behavior after people have applied to or joined a program and can only be used in limited ways 

to examine people’s participation decisions, especially their program entry decisions. 

Administrative data also typically lack important explanatory variables and covariates, such as 

measures of disability and health status. 

We use these data to compare times spent on the Food Stamp Program for households 

with different circumstances, including different levels and histories of earnings. Our analyses 

further distinguish between households that appear to be eligible or ineligible for food stamps 

based on longer-run income data. We estimate longitudinal fixed-effect regression models of the 

times that households spend on food stamps; these models account for additional permanent, 

unmeasured characteristics of households that might be conflated with their earnings histories 

and program outcomes. Our multivariate results indicate that short-term earnings changes and 

earnings variability are each negatively associated with program participation for households 

with low levels of permanent income. There is also evidence that these sources of volatility are 

negatively associated with participation for households with higher levels of permanent income, 

but these effects are smaller in magnitude and lower in statistical significance 

Conceptual analysis of earnings volatility 

A gap in program research, which this report addresses, concerns the role of previous 

earnings and program experiences. While numerous studies have examined the associations 

between people’s short-term characteristics, such as their immediate monthly incomes, and their 

program behavior, only a few have considered the impacts of income histories, the variability of 

their incomes or other longer-term characteristics, on participation (see, e.g., Farrell et al. 2003). 

3
There are reasons to believe that earnings histories and variability might be relevant in a number 

of ways. 

First, as mentioned in the introduction, increased earnings variability can lead to more 

frequent changes in eligibility.2

 For households that are initially eligible, these changes would 

take the form of brief periods of ineligibility; for households that are initially ineligible, they 

would take the form of brief periods of eligibility. The changes in eligibility could in turn lead to 

changes in participation. 

A second, related consideration is that, other things held constant, higher rates of 

volatility will lead to shorter continuous spells of eligibility and potential participation. Because 

there are fixed costs associated with entering or re-entering the Food Stamp Program (e.g., 

completing the initial application; supplying earnings records, birth certificates, social security 

cards, and other documentation; and attending an interview), the reduction in potential spell 

lengths could deter participation in the first place. This effect should exist for both low-income 

and high-income households, and therefore could increase the negative effects of volatility on 

program participation among long-run eligibles and decrease the positive effects among long-run 

ineligibles. 

Third, the program itself may place higher compliance demands on households with 

variable earnings. As Ribar and Edelhoch (2008) document, some states require more frequent 

recertification intervals for households with earnings or with unstable incomes than for other 

households. At the start of our study period, Massachusetts and Texas had shorter recertification 

intervals for non-elderly households with earnings than those without earnings. Near the end of 

the study, all three states had semi-annual recertification intervals for households with earnings, 

and two of the states, Illinois and Massachusetts had longer intervals for households without 

4
earnings. States also differ in terms of their income reporting requirements within certification 

intervals. Within our sample, one state, Texas, required households to immediately report any 

change in work status—change in job, change in pay rate, or loss of job—while the other two 

states only required households to report changes in monthly earnings of $100 or more.3

 Higher 

compliance costs associated with earnings or income changes would again reduce the incentives 

to enter the program or to continue participating. Further, as in the last case discussed, this effect 

should occur for low- and high-income households and should therefore tend to reduce 

participation for both. 

Fourth, while increased earnings volatility likely affects eligibility and compliance costs, 

it may also increase the value of food stamp participation to recipients. As a mean-tested 

program, food stamps provide a form of social insurance, issuing more generous benefits when 

incomes are low and less generous benefits when incomes are high. Thus, the Food Stamp 

Program helps to smooth consumption for families who lack assets or opportunities to borrow. 

Households with variable earnings would benefit more from this consumption-smoothing feature 

than would households with stable earnings, possibly contributing to a positive association 

between volatility and participation. This effect should occur equally for low-income and highincome households, although decreasing marginal utility of income would imply that it should be 

stronger for low-income households. This would therefore tend to dampen the negative effect of 

volatility on program participation for these households. 

Fifth, we need to remember that households’ observed earnings may not be entirely 

exogenous but may instead reflect behavioral elements, which may themselves be influenced by 

program behavior. Consider a household that receives an earnings shock in the form of a higher 

hourly wage rate, perhaps from an unexpected raise or a minimum wage increase. If the 

5
household’s work hours remain fixed, this wage increase would translate into an earnings 

increase. However, if the household places a premium on its non-market time or just on 

maintaining its food stamp eligibility, it might cut back its work hours, leading to little change in 

earnings. In this case, we would observe that stable earnings were associated with continued 

participation, but earnings would not be the causal factor. In our analyses, we address possible 

confounding influences between earnings and program participation by estimating longitudinal 

fixed-effect regression models that account for permanent unobserved characteristics of 

households. Additionally, our analyses will examine the association between current and past 

earnings outcomes, on the one hand, and future program outcomes, on the other, to remove any 

concurrent reverse effects of participation on earnings. 

As the preceding discussion indicates, there are several reasons why earnings volatility 

might be associated with program participation as well as reasons why the associations might 

vary with a household’s level of income. Most of the factors we have discussed lead us to 

expect a negative relationship between volatility and program participation for low-income 

households, while the factors provide a more mixed reading of what we should expect for highincome households. It remains an empirical matter, however, to determine whether and for 

whom there are relationships. 

 

Data sources and measures 

The data for our analyses consist of interview data from the Three-City Study matched 

with administrative case records for food stamp and TANF receipt. The Three-City Study is a 

longitudinal survey of 2,458 children and their caregivers who were initially living in lowincome neighborhoods in Boston, Chicago, and San Antonio. At the time of the first interview 

6
in 1999, the families all had incomes below 200 percent of the poverty line. Although the survey 

includes many public assistance recipients, it was not specifically restricted to this group. Also, 

by design it includes both poor and near-poor families. 

After the initial interviews, follow-up interviews were conducted in 2000-1 and 2005. 

Retention rates were high with 88 percent of the original sample participating in the second 

round and 80 percent of the original sample participating in the third round. In each wave, 

interviews were conducted with both a selected child (the study researchers refer to this child as 

the “focal child”) and that child’s caregiver. In cases where the child and caregiver separated, 

both were subsequently followed and interviewed. For this report, we rely on the information 

provided by the current and former caregivers as they were in the best position to describe the 

households’ economic circumstances, demographic composition and other characteristics. 

In the most recent (third) wave of the survey, the caregivers who participated in face-toface interviews were asked to give permission for the research team to gather administrative 

information about them.4

 Caregivers who agreed to this provided names and social security 

numbers, which were then used to search for food stamp and TANF records. Of the 1,980 

caregivers who completed in-person interviews, 1,448 gave permission to be included in the 

administrative part of the study, and of this smaller number, 1,286 were successfully matched to 

case files in Illinois, Massachusetts, or Texas.5

The administrative records from the state agencies cover the period from January 1997 to 

June 2006 and indicate the specific months in which the caregiver was a member of an assistance 

unit that received food stamps, TANF or both. As outcome measures in our analyses, we use the 

administrative data to form counts of the months that the caregiver received food stamp 

assistance in the quarter and half-year following each of the three interviews. Measuring food 

7
stamp receipt over several months allows us to observe more variation in participation than 

measuring usage for just a single month. However, we must also consider that our earnings 

measures and other explanatory variables become less relevant to participation decisions farther 

from the interview date. We use measures of different lengths to see whether our results are 

sensitive to these issues. 

Besides the food stamp outcome measures, we also use the administrative data to 

construct measures of the number of months out of the prior 12 that a caregiver received food 

stamp assistance or TANF. We use the measures of prior receipt as conditioning variables in our 

analyses. 

The use of administrative case records is an essential feature of this analysis. As 

mentioned, the administrative data are likely to be more accurate than the retrospective reports of 

program participation. Also, the data allow us to measure program participation prospectively 

from the time of the interview while controlling for other self-reported characteristics 

contemporaneously or retrospectively from the time of the interview. The use of these records 

also has drawbacks. Most notably, we are only able to match survey responses for caregivers 

who ever participated in the Food Stamp Program or TANF program sometime between 1997 

and 2006 in the three states. This results in an analysis sample is more disadvantaged along 

some dimensions than the Three-City sample as a whole (see Appendix A for a comparison of 

characteristics between the matched and unmatched samples). It also means that the analysis 

sample is choice-based with more food stamp participants and less participation variability than 

the larger Three-City sample. 

The interview data from the Three-City Study provide us with most of our other 

explanatory variables. We are especially interested in the earnings of the caregivers. To 

8
measure current earnings, we use a constructed variable, supplied with the public-use version of 

the survey, of the caregiver’s labor earnings in her primary job during the month leading up to 

the interview; the measure includes her wages and salary along with possible commissions and 

tips. 

The survey also includes retrospective questions regarding the caregiver’s primary jobs 

for up to two years prior to each interview. From these questions, we form several summary 

measures of the caregiver’s earnings over the preceding 12-month interval, including an 

indicator for whether there were any earnings during the period, the average monthly level of 

earnings, the maximum amount of earnings reported in any of the months, and the coefficient of 

variation for earnings. Because a non-trivial portion of the histories are incomplete (about eight 

percent), we also include a dummy variable for whether summary measures could be formed. 

All of the earnings variables are adjusted for inflation using the Consumer Price Index for Urban 

Wage Earners (CPI-U) and expressed in 2005 values. We interpret the 12-month average of 

earnings as an indicator of the long-term or persistent level of earnings, and we interpret the 

maximum monthly amount over this period as an indicator of earnings capacity. The coefficient 

of variation is used as a measure of earnings variability. When we condition on the earnings 

history, the current earnings variable can be interpreted as an indicator for short-term changes in 

earnings. 

While the retrospective earnings data are useful, there are some notable weaknesses in the 

measures. First, they only describe the earnings of the caregiver and omit other household 

members. Second, the data are limited to primary jobs and exclude other sources of income. 

Third, the measures are limited to usual monthly earnings for a given job; they do not vary 

within job spells and only change when there is a switch in jobs or employment status. Finally, 

9
the reports are subject to recall error. We believe that several of these properties, especially the 

limitations to usual monthly figures for primary jobs, may contribute to the earnings histories 

understating earnings variability. 

A unique element of our analyses is that they distinguish between households that appear 

to be eligible for food stamps based on their long-term incomes and households that appear to be 

either ineligible or marginally eligible. As mentioned, there are three primary tests for food 

stamp eligibility: a household’s income must be below 130 percent of the poverty threshold 

(gross income test), a household’s income after adjusting for program deductions and 

exemptions must be below 100 percent of the poverty threshold (net income test), and a 

household’s assets must be below a certain value (asset test). Because we lack detailed 

information on likely deductions and exemptions and on the level of assets, we focus on the 

gross income test. In each wave of the Three-City study, caregivers were asked about all of the 

sources of income from all household members. The public-use version of the survey contains a 

measure of the income-to-needs ratio that incorporates the available information on total incomes 

and household composition. We fit household-specific trend lines through the 1999, 2000-1, and 

2005 income-to-needs measures and use the values along these trend lines as our indicators of 

long-term income-to-needs. Households whose trend values in a given wave are below 1.3 are 

classified as gross-income eligible on the basis of their long-term circumstances, while 

households whose trend values are above 1.3 are classified as gross-income ineligible. About 

three quarters of the wave-specific observations in our analysis sample are classified as being 

eligible under this definition, and 90 percent of the caregivers are categorized as eligible in at 

least one wave. 

The Three-City Study also asked caregivers about other economic circumstances of their 

10
households. We use responses to several different questions to measure access to capital and 

possible financial difficulties. One direct measure of access to capital is a binary indicator for 

whether anyone in the caregiver’s household had a bank account, savings account or other 

investment account. Another direct measure is an indicator of whether the household had any 

outstanding loans, including loans from family and friends. Our analyses also include separate 

indicators for whether the household owned a car or a home. Car and home ownership would 

not only reveal some previous financial wherewithal but would also represent collateral against 

which the household might borrow. Finally, we include an index of recent financial strains, 

supplied with the public-use file, that is constructed from five questions on topics such as how 

frequently the household needed to borrow money to pay bills and whether it usually ended up 

with any money at the end of the month. 

The interview data from the survey also provide us with demographic information about 

the caregiver and her household, including the caregiver’s age, race/ethnicity, education, marital 

status and health status and the numbers of children and adults in the household. These variables 

are routinely included in studies of benefit receipt. In all of our multivariate analyses, we also 

include controls for the year and month in which the interview took place to account for 

unmeasured changes in policies and economic conditions. 

We limit our analysis to caregivers who participated in all three waves of the survey and 

who could be linked to administrative records. After omitting observations with item nonresponse and dropping a small number of separated caregivers who no longer had any children in 

their households, we are left with an analysis sample of 931 caregivers and 2,793 wave-specific 

observations. Geographically, the observations are split nearly equally across the three cities. 

Means and standard deviations for the analysis variables calculated separately for each city are 

11
reported in Table 1. 

The analysis sample is clearly disadvantaged, having not only been initially selected on 

the basis of low incomes but also subsequently being restricted to households appearing in the 

assistance program records for the three states. The statistics are consistent with this selection. 

On average, the households spent more than half of each quarter or half-year following their 

interviews on food stamps. Average inflation-adjusted monthly earnings just before the 

interviews were $648 in Boston, $556 in Chicago, and $502 in San Antonio. Average earnings 

for the prior year were somewhat lower in Boston and San Antonio, but somewhat higher in 

Chicago. More than half the caregivers reported no earnings at all in the preceding year. Just 

over a third of the households had some kind of financial account, with the average incidence 

varying substantially across cities. Roughly half of the households reported outstanding loans. 

While this latter statistic might appear to be favorable, it likely reflects a lack of access to credit 

for many of the families. Only about one out of eight of the households owned the homes they 

lived in, and just over half of the caregivers were without a car. Few of the caregivers were 

married, and less than two-thirds had completed or gone beyond high school. Most of the 

caregivers were black or Hispanic (98 percent in San Antonio). About one-sixth reported 

disabilities severe enough to interfere with work. Lastly, the average number of children was 

high at just under three per household. 

Descriptive analysis 

Food stamp and TANF receipt in the two cities were strongly associated with several 

economic characteristics of the caregivers. Table 2 shows the average months of each type of 

program receipt in the year following the interview calculated separately for some of these 

12
characteristics. From top to bottom, the table is divided into three sections: the first section 

reports estimates for the general sample of households; the second section reports estimates for 

households with trend incomes below the gross-eligibility threshold, and the third section reports 

estimates for households with trend incomes above the gross-eligibility cut-off. Near the top of 

the table, the estimates show the anticipated result that the months of subsequent food stamp 

participation generally fall with the level of current earnings and with average annual earnings. 

Participation rates for caregivers without earnings two and a half times higher than the 

participation rates for caregivers with $1,000 or more in monthly earnings. Moffitt and Winder 

(2003) and Frogner et al. (2007) similarly found that earnings and program receipt were 

negatively related when they examined self-reports of program participation in these data. 

The next rows report participation levels for households with positive earnings whose 

coefficient of variation was positive but below one-half and participation levels for households 

with more variable earnings. In the sample, more variable incomes were associated with higher 

levels of participation. 

Households with trend incomes below the food stamp gross eligibility threshold have 

participation rates that are more than twice as high as households with larger trend incomes. 

Though the participation rates for the “high trend income” households are much smaller in 

relative terms, they are still appreciable. Differences in actual versus trend incomes account for 

much of the residual participation; differences in the timing of the income and participation 

reports also account for some of the residual. 

The results from Table 2 provide some evidence of asymmetric associations between 

earnings volatility and food stamp participation. Among caregivers with trend incomes above 

the gross-income eligibility thresholds, we see that more variable earnings are strongly positively 

13
associated with program participation. Also, differences in earnings are especially strongly 

associated with participation. Among caregivers with lower trend incomes, we see the same 

patterns, though the strength of the associations is muted. The positive association between 

earnings variability and participation for higher income households is consistent with the 

“mechanical” explanation that we offered earlier, but the positive association for lower income 

households is not. 

Multivariate analyses

The simple conditional means reported in Table 2 show gross associations and do not 

account for confounding influences from other variables. For example, the bivariate crossprogram associations between caregivers’ earnings variability and their subsequent food stamp 

participation may be an artifact of mutual correlations between these measures and the level of 

earnings. Alternatively, the association may reflect correlations with some other variable. To 

address these possible sources of mutual correlation, we estimate longitudinal fixed-effect 

regression models of the characteristics associated with the caregivers’ food stamp receipt. The 

estimates from these models represent partial associations that hold the other observed 

characteristics constant. 

Coefficient estimates and standard errors for the models of program receipt are reported 

in Table 3. The first two columns of Table 3 list results from models of food stamp participation 

in the quarter and the half-year following the caregivers’ interviews. In these models we 

constrain the effects of the earnings history variables to be the same for households with trend 

incomes above and below the gross eligibility threshold. The next two columns list results from 

models that allow the coefficients for the earnings history variables to differ depending on trend 

14
income. Explanatory variables are listed in the rows of the table. In addition to the variables 

found in the table, each of the models also includes an intercept and controls for age, education, 

missing earnings effects, and piecewise-linear trends for the year and month of the interview. 

Each of the models in Table 3 pools data across the three cities. 

As with the descriptive analyses, the regression results from the first two columns 

indicate that earnings in the month prior to the interview are negatively related to subsequent 

food stamp participation. The sizes of these associations, however, are modest. A $1,000 

increase in current earnings, holding all else constant, is estimated to reduce food stamp 

participation in the subsequent three months by just over a week. Recall that the fixed effects 

regression controls for permanent characteristics of the households, such as their permanent 

incomes. So, the coefficient on current earnings must be interpreted as a change in this variable 

holding permanent income and the other observed characteristics constant. In other words, the 

coefficient represents the association between food stamp receipt and a temporary (and 

permanent-income compensated) change in earnings. 

In contrast to the descriptive results, the estimates from the first two models indicate that 

more variable earnings are negatively, albeit modestly, associated with subsequent food stamp 

participation. Again, these are estimates that hold permanent characteristics constant, including 

permanent incomes and permanent income variability. Thus, temporary positive earnings shocks 

and increased medium-term earnings variability both appear to modestly reduce food stamp 

receipt. 

The estimates from the first two columns indicate that the association between prior and 

subsequent food stamp receipt is statistically and substantively large. For example, being on 

food stamps for the entire year before the interview increases the expected participation in the 

15
following quarter by 2.1 months and increases the expected participation in the following halfyear by 3.6 months. 

Increases in the number of adults are estimated to be negatively associated with food 

stamp receipt. None of the other estimated coefficients in the first two columns is statistically 

significant. 

The next two columns in Table 3 report results from fixed effect models that include 

interactions of the indicator for having a trend income above 130 percent of the poverty 

threshold and each of the earnings history measures. Except for these interactions, all of the 

other explanatory variables are identical to those in the previous two specifications. 

The added interactions are jointly marginally insignificant (the p-values for joint 

significance for the 3- and 6-month outcome models are 0.17 and 0.12, respectively).6

 Including 

the interactions does alter several of the uninteracted coefficients. In particular, the coefficient 

on the uninteracted current earnings variable becomes approximately one-third larger in 

magnitude compared to the previous specifications. The absolute value of the uninteracted 

earnings variability measure, which now measures the effect of variability for low-income 

households, becomes 10 percent larger in the 3-month model and one third larger in the 6-month 

model. Also, the uninteracted coefficient on having any earnings during the past year becomes 

significantly positive. The changes suggest that the program behavior of households with trend 

incomes below the gross income threshold is more sensitive to changes in earnings histories than 

that of higher income households. 

The positive coefficients on the interaction term between the high-income variable and 

earnings variability in the 3- and 6-month outcome models imply that the effects of earnings 

variability on program participation are smaller for high-income households than for low-income 

16
households. However, the estimated effects for high-income households are still negative, 

though statistically insignificant (the p-values in the 3- and 6-month models are .28 and .54, 

respectively). As we noted previously, the sign of the effect for high-income households could 

be negative if the factors leading to declines in participation in response to higher variability 

dominated those leading to increases. 

We re-estimated each of the interacted models separately for each of the three cities. 

Recall from the discussion of conceptual issues that some states have policies that effectively 

increase the compliance costs for households with volatile incomes. By estimating separate 

models we can see whether our results come from a particular state or particular policy 

environment. Results from the state-specific fixed effects models are listed in Table 4. 

From the table, current earnings are consistently negatively related with food stamp 

participation among low-income households. In the 3-month models, the point estimates 

indicate that a $1,000 increase in earnings is associated with one to two fewer weeks of food 

stamp participation. In the 6-month models, the effect size is on the order of two to three fewer 

weeks. The modest associations in each of the states are again consistent with the coefficients 

capturing temporary changes in earnings. 

Earnings variability among low-income households is also consistently negatively 

associated with food stamp participation; however, only three of the six coefficients are 

statistically significant. The significant negative associations between earnings variability and 

participation appear for Massachusetts and Illinois, but not for Texas. One difference in policies 

that could lead to greater sensitivity to income changes in these states is that they both have 

program waivers that allow them to change benefits within certification periods based on 

changes reported to other programs such as Medicaid; Texas does not coordinate in the same 

17
way. Texas, however, has more stringent income reporting requirements for its Food Stamp 

Program than do the other two states; so, we might have expected stronger associations there. 

Among low-income households, food stamp participation is higher if the caregiver had 

any earnings at all during the preceding year, although only one of these associations is 

statistically significant. The positive associations could reflect the different treatment of work 

income in the benefit and eligibility formulas; specifically, low levels of earnings are not counted 

against the benefit formula, while earnings above the exemption amount are “taxed” at a lower 

rate than other income. 

Among the other coefficients, prior food stamp receipt is consistently positively 

associated with subsequent food stamp receipt. Increases in financial assets are negatively 

associated with food stamp receipt in Illinois but not in the other two states. Disability is 

positively associated with food stamp receipt in Texas. Adding an adult or a child to the 

household is significantly negatively associated with food stamp receipt in Massachusetts; 

adding a child to a household in Texas is positively associated with food stamp receipt. 

 

Conclusions 

This report examines the relationship between earnings histories and program 

participation in a sample that matches administrative data on program outcomes with 

longitudinal survey information from the Three-City Study about earnings and other household 

characteristics. We conduct multivariate analyses, employing fixed effect regression models that 

account for time-invariant characteristics of households, such as their permanent incomes. A 

unique aspect of our analyses is that we separately consider households with long-term trend 

incomes that make them more or less likely to be eligible for food stamps. 

18
The report finds strong evidence that increases in current monthly earnings reduce 

program participation. This result is expected, as higher earnings reduce the needs for assistance 

and also impact the eligibility and benefits associated food stamps. What may be more 

surprising is that the magnitudes of the estimated associations are all relatively modest. The 

small sizes of the associations are likely due to our use of longitudinal fixed effect controls and 

numerous other economic controls. With these controls, the identifying variation in current 

earnings comes from temporary changes. 

We also find evidence that medium-term earnings variability, measured by the coefficient 

of variation for the preceding year’s earnings, is negatively associated with food stamp 

participation, at least among low-income households. There are several potential explanations 

for these results. For households that are initially below the eligibility threshold, variable 

earnings could lead to occasional periods of ineligibility and shorter eligibility spells. Program 

compliance costs may also increase with earnings variability. Other possible explanations for the 

negative association are that participation affects earnings, reducing variability, or that some 

other characteristic affects both earnings and variability. While we cannot rule out these other 

explanations, our empirical methodology, which controls for permanent unobserved 

characteristics and which relates past earnings variability to subsequent program participation, 

makes them less likely. 

We also find a negative relationship between program participation and earnings 

variability for high-income households, but the effect is smaller in magnitude and weaker in 

statistical significance than for low-income households. We interpret this finding as indicating 

that the factors which discourage program participation among such households, such as the 

shorter expected program durations that come from higher volatility, dominate those which 

19
encourage program participation, such as a greater number of periods of income eligibility. 

Additionally, the estimation results provide modest evidence that program behavior in 

households with low long-term incomes is more sensitive to changes in their earnings and 

earnings variability than behavior in households with higher long-term incomes. When 

interactions of the earnings history variables and the long-term income indicator are included in 

our models, the estimated coefficients for the earnings and earnings variability measures for the 

low-income segment of our sample each increase. The changes in the coefficients are consistent 

with earnings volatility reducing eligibility among low-income households but not among 

higher-income households. 

20
References

Farrell, Mary, Michael Fishman, Matthew Langley and David Stapleton. 2003. “The 

Relationship of Earnings and Income to Food Stamp Participation.” E-FAN Report no. 

03-011. Washington, DC: U.S. Department of Agriculture. 

Finegold, Kenneth, William Margrabe and Caroline Ratcliffe. 2007. “Food Stamp Program 

Rules Database Documentation.” Washington, DC: Urban Institute. 

Frogner, Bianca, Robert Moffitt and David Ribar. 2007. “How Families Are Doing Nine Years 

after Welfare Reform: 2005 Evidence from the Three-City Study.” Unpublished 

manuscript. Baltimore, MD: Johns Hopkins University. 

Moffitt, Robert. 1983. “An Economic Model of Welfare Stigma.” American Economic Review

73(5): 1023-1035. 

____________________. 2003. “The Role of Nonfinancial Factors in Exit and Entry in the Food 

Stamp Program.” Journal of Human Resources 38(Supplement): 1221-1254. 

Moffitt, Robert and Katie Winder. 2003. “The Correlates and Consequences of Welfare Exit and 

Entry.” Unpublished manuscript. Baltimore, MD: Johns Hopkins University. 

Ribar, David and Marilyn Edelhoch. 2008. “Earnings Volatility and the Reasons for Leaving the 

Food Stamp Program.” In Dean Jolliffe and James Ziliak (eds.), Income Volatility and 

Food Assistance in the United States. Kalamazoo, MI: W. E. Upjohn Institute for 

Employment Research, pp. 63-102. 

Rosenbaum, Dorothy. 2000. “Improving Access to Food Stamps: New Reporting Options Can 

Reduce Administrative Burdens and Error Rates.” Unpublished report. Washington, DC: 

Center on Budget and Policy Priorities. 

21
U.S. Department of Agriculture. 2005. Food Stamp Program State Options Report, 5th edition. 

Washington, DC: U.S. Department of Agriculture. 

22
23

 

Notes

1 The Food Stamp Program was renamed the Supplemental Nutrition Assistance Program on 

October 1, 2008. Throughout this report, we refer to the Food Stamp Program, the name of the 

program during the period of the study.

2

 The Food Stamp Program is a means-tested program, with eligibility depending on a 

household’s monthly income and level of assets or on its participation in another means-tested 

program, such as Temporary Assistance for Needy Families or Supplemental Security Income. 

Non-elderly, non-disabled households that are not otherwise “categorically eligible” have to 

satisfy three criteria for food stamp eligibility: have monthly gross incomes below 130 percent of 

the poverty threshold, have net/adjusted incomes below 100 percent of the poverty threshold, and 

have assets below $2,000. Once a food stamp application is approved, a household is certified to 

receive benefits for at least one month but usually more. Eligibility is checked rigorously at the 

initial certification and at subsequent recertifications. Within a certification period, households 

are required to report some changes in income, depending on the state’s rules. All households 

are required to report changes in gross income that would put them above the 130 percent 

threshold. 

3

 Recertification intervals were obtained from the Food Stamp Program Rules Database

(Finegold et al. 2007), while the reporting requirements were obtained from the Food Stamp 

Program State Options Report (USDA 2005). 

4

 Of the 2,056 current and former caregivers who participated in the third wave, 1,980 were 

interviewed in person and asked permission to obtain administrative records. 

5

 Robert Goerge at the Chapin Hall Center at the University of Chicago supplied the records for 

Illinois; Daniel Shroeder from the Ray Marshall Center at the University of Texas supplied the 
 

records for Texas, and Jesse Valente from the Massachusetts Department of Transitional 

Assistance provided the records for that state. 

6

 Evidence of differences in behavior is considerably stronger in alternative specifications that 

omit the maximum earnings variable and in random effect specifications. 

24
25

Table 1. Characteristics of analysis sample 

Boston Chicago San Antonio 

Mean (Std. dev.) Mean (Std. dev.) Mean (Std. dev.)

Months on food stamps in next 3 1.57 (1.47) 1.64 (1.45) 1.92 (1.38)

Months on food stamps in next 6 3.13 (2.85) 3.24 (2.82) 3.81 (2.64)

Earnings in interview month 648.47 (878.46) 555.83 (747.09) 502.03 (677.20)

Any earnings in last year 0.56 (0.50) 0.61 (0.49) 0.59 (0.49)

Average earnings in last year 614.39 (792.75) 579.44 (718.72) 494.35 (643.47)

Coefficient of variation for 

earnings in last year 

0.39 (0.78) 0.42 (0.77) 0.46 (0.81)

Maximum earnings in last year 840.99 (936.03) 793.53 (849.55) 693.20 (761.58)

Prior year’s earnings 

information missing 

0.09 (0.29) 0.07 (0.25) 0.09 (0.28)

Household income-to-needs 1.09 (0.70) 1.02 (0.63) 0.91 (0.57)

Bank, savings or financial 

account 

0.52 (0.50) 0.29 (0.46) 0.35 (0.48)

Outstanding loans 0.47 (0.50) 0.44 (0.50) 0.52 (0.50)

Owns home 0.04 (0.19) 0.15 (0.36) 0.19 (0.39)

Owns vehicle 0.38 (0.49) 0.37 (0.48) 0.57 (0.50)

Financial strain index 0.05 (0.73) 0.03 (0.73) -0.01 (0.72)

Months on food stamps in last 

year 

6.61 (5.43) 6.69 (5.31) 8.09 (4.87)

Months on TANF in last year 4.49 (5.35) 3.78 (5.16) 2.78 (4.42)

Non-hispanic black 0.32 (0.47) 0.55 (0.50) 0.39 (0.49)

Hispanic 0.50 (0.50) 0.35 (0.48) 0.59 (0.49)

Age 35.07 (9.11) 33.76 (9.68) 31.80 (8.99)

Completed high school or GED 0.47 (0.50) 0.33 (0.47) 0.35 (0.48)

Completed college 0.22 (0.41) 0.22 (0.41) 0.22 (0.42)

Disability that prevents work 0.23 (0.42) 0.16 (0.37) 0.17 (0.38)

Number of minors in household 2.50 (1.26) 2.88 (1.42) 2.72 (1.37)

Married, spouse present 0.08 (0.28) 0.16 (0.37) 0.18 (0.38)

Number of adults in household 1.56 (0.80) 1.85 (0.96) 1.71 (0.82)

Number of caregivers 308 300 323 

Number of observations 924 900 969 

Note: Statistics calculated using interview data from the Three-City Study matched to 

administrative records.
Table 2. Months of food stamp assistance following the interview for households with 

different income and earnings characteristics 

Average months on 

food stamps in next 

Characteristic N 3 months 6 months 

All caregiver observations 2,793 1.7 3.4 

Earnings in interview month a 

 None 1,347 2.1 4.2 

 $0 to $1000 537 1.9 3.7 

 $1000 or more 680 0.8 1.7 

Average monthly earnings in last year a 

 None 925 2.1 4.2 

 $0 to $1000 957 2.0 3.9 

 $1000 or more 682 0.8 1.5 

C.V. of earnings in last year a,b 

 Less than .5 975 1.2 2.3 

 .5 or higher 664 1.9 3.8 

Observations with trend income below 

gross eligibility threshold 2,168 2.0 3.9 

Earnings in interview month a 

 None 1,189 2.2 4.3 

 $0 to $1000 468 2.0 3.9 

 $1000 or more 327 1.2 2.4 

Average monthly earnings in last year a 

 None 827 2.2 4.3 

 $0 to $1000 807 2.1 4.2 

 $1000 or more 350 1.1 2.2 

C.V. of earnings in last year a,b 

 Less than .5 606 1.6 3.1 

 .5 or higher 551 2.1 4.1 

Observations with trend income above 

gross eligibility threshold 625 0.8 1.7 

Earnings in interview month a 

26
27

 None 158 1.5 2.9 

 $0 to $1000 69 1.0 2.0 

 $1000 or more 353 0.5 1.0 

Average monthly earnings in last year a 

 None 98 1.5 3.0 

 $0 to $1000 150 1.3 2.4 

 $1000 or more 332 0.4 0.9 

C.V. of earnings in last year a,b 

 Less than .5 369 0.5 1.1 

 .5 or higher 113 1.2 2.3 

Note: Statistics calculated using interview data from the Three-City Study matched to 

administrative records. 

a

 Excludes observations with missing earnings information. 

b

 Excludes observations with zero earnings.
Table 3. Fixed effects regression models of food stamp receipt following the interview 

Models with uniform effects 

of earnings history – 

Models with variable effects 

of earnings history – 

Months receiving food 

stamps out of next 

months receiving food 

stamps out of next 

3 months 6 months 3 months 6 months 

Earnings ($000) in interview -0.282** -0.516** -0.361** -0.675** 

 month (0.048) (0.092) (0.060) (0.115) 

Any earnings in last year 0.100 0.133 0.217** 0.388* 

(0.091) (0.175) (0.106) (0.204) 

Average earnings ($000) in -0.019 -0.116 -0.025 -0.276 

 last year (0.102) (0.196) (0.136) (0.261) 

Coefficient of variation for -0.098** -0.194** -0.115** -0.263** 

 earnings in last year (0.044) (0.084) (0.051) (0.097) 

Maximum earnings ($000) last 0.051 0.132 -0.003 0.141 

 year (0.085) (0.163) (0.106) (0.204) 

Trend HH inc. > gross elig. X 0.119 0.258 

 earnings in interview month (0.092) (0.176) 

Trend HH inc. > gross elig. X -0.274 -0.671* 

 any earnings in last year (0.179) (0.343) 

Trend HH inc. > gross elig. X -0.035 0.305 

 average earnings in last year (0.208) (0.399) 

Trend HH inc. > gross elig. X 0.009 0.147 

 c.v. earnings in last year (0.111) (0.213) 

Trend HH inc. > gross elig. X 0.166 0.025 

 maximum earnings last year (0.181) (0.348) 

Trend HH income-to-needs 0.035 -0.032 0.006 -0.071 

(0.079) (0.152) (0.084) (0.162) 

Household income-to-needs 0.043 0.088 0.047 0.093 

(0.063) (0.122) (0.063) (0.122) 

Months on food stamps in last 0.172** 0.299** 0.172** 0.300** 

 year (0.006) (0.011) (0.006) (0.011) 

Months on TANF in last year 0.004 0.013 0.003 0.011 

(0.006) (0.011) (0.006) (0.011) 

Bank, savings or financial -0.057 -0.116 -0.062 -0.129 

 account (0.053) (0.103) (0.053) (0.103) 

Outstanding loans 0.034 0.054 0.035 0.054 

(0.050) (0.097) (0.050) (0.097) 

Own home 0.010 -0.004 0.008 -0.011 

(0.084) (0.162) (0.085) (0.163) 

Own vehicle 0.008 0.096 0.014 0.110 

(0.056) (0.107) (0.056) (0.108) 

Financial strain index 0.031 0.108 0.031 0.107 

(0.036) (0.070) (0.036) (0.070) 

Disability that limits work 0.098 0.119 0.092 0.104 

28
(0.080) (0.154) (0.080) (0.154) 

Number of minors in 0.025 0.018 0.027 0.023 

 household (0.025) (0.048) (0.025) (0.048) 

Married, spouse present 0.040 -0.023 0.049 -0.006 

(0.080) (0.155) (0.081) (0.155) 

Number of adults in household -0.065** -0.104* -0.063** -0.102* 

(0.029) (0.056) (0.029) (0.056) 

R2 0.60 0.66 0.61 0.66 

Note: Longitudinal fixed-effect regression models estimated using interview data from the 

Three-City Study matched to administrative records. Models also include intercepts, controls for 

age, education, missing earnings histories, and calendar time. Standard errors appear in 

parentheses. 

* Significant at .10 level. ** Significant at .05 level. 

29
Table 4. Fixed effects regression models of food stamp receipt following interview by city 

Boston Chicago San Antonio 

Months receiving 

food stamps out of 

next 

Months receiving 

food stamps out of 

next 

Months receiving 

food stamps out of 

next 

3 months 6 months 3 months 6 months 3 months 6 months

Earnings ($000) in interview -0.440** -0.765** -0.298** -0.561** -0.260** -0.500**

 month (0.096) (0.189) (0.108) (0.207) (0.110) (0.204) 

Any earnings in last year 0.226 0.601 0.336* 0.575 0.111 0.080 

(0.205) (0.403) (0.190) (0.363) (0.172) (0.321) 

Average earnings ($000) in 0.185 0.294 -0.351 -0.851* 0.083 -0.268 

 last year (0.232) (0.455) (0.232) (0.443) (0.256) (0.478) 

Coefficient of variation for -0.151 -0.360** -0.155* -0.314* -0.036 -0.088 

 earnings in last year (0.092) (0.181) (0.089) (0.170) (0.085) (0.159) 

Maximum earnings ($000) last 0.023 -0.118 0.127 0.449 -0.197 -0.053 

 year (0.189) (0.371) (0.188) (0.359) (0.181) (0.338) 

Trend HH inc. > gross elig. X 0.074 0.120 0.042 0.086 0.253 0.555 

 earnings in interview month (0.141) (0.276) (0.167) (0.320) (0.191) (0.357) 

Trend HH inc. > gross elig. X -0.213 -0.789 -0.226 -0.243 -0.650** -1.372**

 any earnings in last year (0.332) (0.653) (0.308) (0.587) (0.315) (0.587) 

Trend HH inc. > gross elig. X -0.146 -0.017 0.322 0.740 -0.157 0.295 

 average earnings in last year (0.341) (0.671) (0.369) (0.704) (0.394) (0.735) 

Trend HH inc. > gross elig. X 0.089 0.409 -0.096 -0.218 0.124 0.341 

 c.v. earnings in last year (0.188) (0.370) (0.208) (0.397) (0.188) (0.350) 

Trend HH inc. > gross elig. X 0.251 0.466 -0.051 -0.352 0.279 0.002 

 maximum earnings last year (0.293) (0.576) (0.333) (0.636) (0.335) (0.625) 

Trend HH income-to-needs -0.119 -0.272 0.163 0.257 -0.033 -0.286 

(0.133) (0.260) (0.159) (0.304) (0.156) (0.290) 

Household income-to-needs 0.037 0.049 0.069 0.143 0.093 0.216 

(0.105) (0.206) (0.111) (0.212) (0.116) (0.217) 

Months on food stamps in last 0.167** 0.280** 0.182** 0.327** 0.169** 0.293**

 year (0.011) (0.021) (0.010) (0.020) (0.010) (0.019) 

Months on TANF in last year 0.004 0.020 -0.013 -0.021 -0.0001 -0.004 

(0.011) (0.022) (0.011) (0.021) (0.011) (0.020) 

Bank, savings or financial 0.005 0.189 -0.333** -0.639** 0.071 -0.013 

 account (0.088) (0.172) (0.116) (0.221) (0.084) (0.157) 

Outstanding loans -0.130 -0.219 0.083 0.074 0.116 0.189 

(0.091) (0.179) (0.090) (0.171) (0.085) (0.159) 

Own home -0.120 -0.134 0.037 0.024 0.045 0.017 

(0.229) (0.450) (0.141) (0.268) (0.122) (0.228) 

Own vehicle 0.143 0.293 -0.061 0.078 -0.089 -0.128 

(0.093) (0.183) (0.110) (0.209) (0.095) (0.177) 

Financial strain index 0.095 0.233* 0.058 0.125 -0.013 0.043 

(0.065) (0.128) (0.072) (0.137) (0.057) (0.107) 

Disability that limits work -0.023 -0.247 0.020 0.044 0.254** 0.444* 

30
(0.141) (0.276) (0.158) (0.301) (0.126) (0.236) 

Number of minors in -0.119** -0.319** 0.057 0.118 0.090** 0.158**

 household (0.048) (0.094) (0.044) (0.084) (0.041) (0.076) 

Married, spouse present -0.019 -0.026 0.041 -0.005 0.115 0.046 

(0.156) (0.306) (0.144) (0.275) (0.130) (0.242) 

Number of adults in household -0.124** -0.202* -0.036 -0.086 -0.035 -0.034 

(0.053) (0.105) (0.047) (0.090) (0.052) (0.096) 

R2 0.15 0.11 0.51 0.61 0.11 0.20 

Note: Longitudinal fixed-effect regression models estimated using interview data from the 

Three-City Study matched to administrative records. Models also include intercepts, controls for 

age, education, missing earnings histories, and calendar time. Standard errors appear in 

parentheses. 

* Significant at .10 level. ** Significant at .05 level. 

31
32

Appendix A. Characteristics of analysis and excluded samples 

Analysis sample Excluded sample 

Mean (Std. dev.) Mean (Std. dev.) 

p-value for 

equality of means

Earnings in interview month 567.81 (773.00) 580.48 (789.18) 0.63 

Any earnings in last year 0.59 (0.49) 0.56 (0.50) 0.11 

Average earnings in last year 561.48 (721.27) 563.56 (755.76) 0.93 

Coefficient of variation for 

earnings in last year 

0.42 (0.79) 0.37 (0.75) 0.06* 

Maximum earnings in last year 774.42 (852.64) 760.47 (876.21) 0.64 

Prior year’s earnings 

information missing 

0.08 (0.27) 0.10 (0.30) 0.06* 

Household income-to-needs 1.00 (0.64) 0.99 (0.65) 0.47 

Bank, savings or financial 

account 

0.39 (0.49) 0.40 (0.49) 0.48 

Outstanding loans 0.48 (0.50) 0.47 (0.50) 0.48 

Owns home 0.13 (0.33) 0.16 (0.37) <0.01** 

Owns vehicle 0.44 (0.50) 0.51 (0.50) <0.01** 

Financial strain index 0.02 (0.73) -0.06 (0.72) <0.01** 

Non-hispanic black 0.42 (0.49) 0.39 (0.49) 0.13 

Hispanic 0.48 (0.50) 0.53 (0.50) 0.01* 

Age 33.51 (9.35) 34.03 (9.55) 0.11 

Completed high school or GED 0.38 (0.49) 0.36 (0.48) 0.11 

Completed college 0.22 (0.41) 0.25 (0.43) 0.03* 

Disability that prevents work 0.19 (0.39) 0.13 (0.33) <0.01** 

Number of minors in household 2.70 (1.36) 2.59 (1.38) 0.02* 

Married, spouse present 0.14 (0.35) 0.22 (0.41) <0.01** 

Number of adults in household 1.71 (0.87) 1.74 (0.91) 0.20 

Boston 0.33 (0.47) 0.46 (0.50) <0.01** 

Chicago 0.32 (0.47) 0.30 (0.46) 0.21 

Reported receiving food stamps 

in interview month 

0.62 (0.48) 0.47 (0.50) <0.01** 

Number of observations 2,793 1,254 

Note: Statistics calculated using interview data from the Three-City Study. “Analysis sample” 

contains longitudinal survey observations matched to administrative records; “excluded 

sample” contains longitudinal survey observations that could not be matched to 

administrative records.