Participation in the Food Stamp Program a multivariate analysis

              United States
Department ot
Agriculture
Food and
Nutrition
Service
Office of
Analysis and
Evaluation
£)AW.2: ^73/5
Current Perspectives on Food Stamp Program Participation
Participation in the
Food Stamp Program:
A Multivariate Analysis
^j[r\?^h \opX-COMPIETtD
I
Current Perspectives on Food Stamp Program Participation
Titles in this series:
Food Stamp Program Participation Rates
(November 1988) Pat Doyle and Harold Beebout
Food Stamp Program Participation Rates Among the Poverty
Population, 1980-1987
(November 1988) Carole Trippe and Harold Beebout
Determinants of Participation in the Food Stamp Program:
A Review of the Literature
(November 1989) Susan Allin and Harold Beebout
Estimating Rates of Participation in the Food Stamp Program:
A Review of the Literature
(November 1989) Carole Trippe
Food Stamp Program Participation Rates:
August 1985
(April 1990) Pat Doyle
The Effects of Food Stamps on Food Consumption:
A Review of the Literature
(October 1990) Thomas M. Fraker
Food Stamp Program Participation Rates:
January 1988
( February 1992) Carole Trippe and Pat Doyle
Participation in the Food Stamp Program:
A Multivariate Analysis
(March 1992) Alberto Martini
United States Food and 3101 Park Center Drive
Department of Nutrition Second Floor
Agriculture Service Alexandria, VA 22302
Participation in the
Food Stamp Program:
A Multivariate Analysis
Alberto Martini
A product of
Mathematica Policy Research, Inc.
600 Maryland Avenue, S.W.
Suite 550
Washington, DC 20024
March 1992
ACKNOWLEDGMENTS
The author would like to thank several people who contributed to this report Gary Bickel,
Steven Carlson, Bob Darlymple, Christine Kissmer, and Christy Schmidt of the Food and Nutrition
Service provided comments on the draft version of the report Susan Allin, Thomas Fraker, Harold
Beebout, and Pat Doyle of Mathematics Policy Research, Inc., provided technical consultation and
review. Thomas Good edited the final document
MPR Project Number: 7890-002
FNS Contract Number: 53-3198-9-31
FNS Project Officer: Christine Kissmer
w
CONTENTS
Chapter Page
EXECUTIVE SUMMARY ix
I INTRODUCTION 1
n DATA AND METHODOLOGY 5
A. SIMULATING FSP-ELIGEBUJTY WITH SIPP DATA 6
B. SPECIFYING THE PARTICIPATION EQUATION 9
C. THE PROBLEM OF THE UNDERREPORTING OF
PARTICIPATION 11
D. THE EXPLANATORY VARIABLES IN THE
PARTICIPATION EQUATION 15
E PRESENTING THE ESTIMATION RESULTS 18
ffl FSP PARTICIPATION AND THE DEMOGRAPHIC
CHARACTERISTICS OF HOUSEHOLDS 21
A COMPARISON OF THE AVERAGE PARTICIPATION RATES .... 22
B. AGE OF THE REFERENCE PERSON 24
C EDUCATION OF THE REFERENCE PERSON 29
D. THE RACE AND ETHNICITY OF THE
REFERENCE PERSON 32
E. THE PRESET ICE OF CHILDREN AND HOUSEHOLD SIZE 35
IV FSP PARTICIPATION AND THE ECONOMIC
CHARACTERISTICS OF HOUSEHOLDS 41
A. HOUSEHOLD INCOME AS A PERCENTAGE OF
THE POVERTY THRESHOLD 41
B. H1Z RECEIPT OF PUBLIC ASSISTANCE 47
C. THE RECEIPT OF EARNINGS 48
D. THE PRESENCE OF ASSETS 51
V THE RELATIONSHIP BETWEEN FSP PARTICIPATION
AND THE FOOD STAMP BENEFIT AMOUNT 53
A PREVIOUS ESTIMATES OF THE BENEFIT-PARTICIPATION
RELATIONSHIP 54
B. SIPP-BASED ESTIMATES OF THE BENEFIT-PARTICIPATION
RELATIONSHIP 57
•••V
CONTENTS (continued)
Chapter Page
VI SUMMARY AND CONCLUSIONS 71
A. THE DEMOGRAPHIC CHARACTERISTICS OF HOUSEHOLDS .. 71
B. THE ECONOMIC CHARACTERISTICS OF HOUSEHOLDS 72
C THE FSP BENEFIT AMOUNT 73
REFERENCES 75
APPENDDC A: 77
APPENDDC B: 81
APPENDDC C: 85
APPENDK D: 93
APPENDDC E: 99
IV
VI
TABLES
Table Page
HI FACTORS THAT AFFECT THE SIMULATION OF FOOD
STAMP ELIGIBILITY BASED ON SEPP DATA, AND THE
DIRECTION OF THE BIAS &
H.2 COMPARISON OF SELECTED CHARACTERISTICS OF
FSP PARTICIPANTS IN THE SIPP AND IOCS DATA BASES 14
E.3 OVERLAP AMONG FOUR DEMOGRAPHIC SUBGROUPS
OF THE FSP-ELIGIBLE POPULATION 17
ELI AVERAGE PARTICIPATION RATES AMONG ALL FSP-EIJGIBLE
HOUSEHOLDS AND AMONG SUBGROUPS
OF THE FSP-ELIGIBLE POPULATION 22
IH2A PARTICIPATION RATES AMONG ALL FSP-ELIGIBLE
HOUSEHOLDS, BY THE AGE OF THE REFERENCE
PERSON 25
m.2B PARTICIPATION RATES AMONG SUBGROUPS OF THE
FSP-ELIGIBLE POPULATION, BY THE AGE OF THE
REFERENCE PERSON 27
DI.3A PARTICIPATION RATES AMONG ALL FSP-ELIGIBLE
HOUSEHOLDS, BY THE EDUCATION OF THE
REFERENCE PERSON 30
IIL3B PARTICIPATION RATES AMONG SUBGROUPS OF THE
FSP-ELIGB3LE POPULATION, BY THE EDUCATION
OF THE REFERENCE PERSON 31
m.4A PARTICIPATION RATES AMONG ALL FSP-ELIGIBLE
HOUSEHOLDS, BY THE RACE AND ETHNICITY OF
THE REFERENCE PERSON 32
HUB PARTICIPATION RATES AMONG SUBGROUPS OF THE
FSP-ELIGIBLE POPULATION, BY THE RACE AND
ETHNICnY OF THE REFERENCE PERSON 34
HL5A PARTICIPATION RATES AMONG ALL FSP-ELIGIBLE
HOUSEHOLDS, BY THE SIZE OF THE HOUSEHOLD
AND THE PRESENCE OF CHILDREN 35
IBL5B PARTICIPATION RATES AMONG SUBGROUPS OF THE
FSP-ELIGIBLE POPULATION, BY THE SIZE OF THE
HOUSEHOLD 37
I///
TABLES (continued)
Table Va&
ffl.6 PARTICIPATION RATES AMONG ALL FSP-ELIGIBLE
HOUSEHOLDS, BY THE SIZE OF THE HOUSEHOLD
AND THE PRESENCE OF AN ELDERLY MEMBER 39
IV1A PARTICIPATION RATES AMONG ALL FSP-ELIGIBLE
HOUSEHOLDS, BY HOUSEHOLD INCOME RELATIVE
TO THE POVERTY THRESHOLD 43
IV IB PARTICIPATION RATES AMONG SUBGROUPS OF THE
FSP-ELIGIBLE POPULATION, BY HOUSEHOLD INCOME
RELATIVE TO THE POVERTY THRESHOLD 46
IV.2A PARTICIPATION RATES AMONG ALL FSP-ELIGIBLE
HOUSEHOLDS, BY THE RECEIPT OF PUBLIC
ASSISTANCE AND THE PRESENCE OF EARNINGS
AND ASSETS 47
IV.2B PARTICIPATION RATES AMONG SUBGROUPS OF THE
FSP-ELIGIBLE POPULATION, BY THE RECEIPT OF
PUBLIC ASSISTANCE AND THE PRESENCE OF
EARNINGS AND ASSETS 49
V.l ESTIMATES OF THE EFFECT OF THE BENEFIT AMOUNT
ON THE PROBABILITY OF FSP PARTICIPATION 55
V.2A PARTICIPATION RATES AMONG ALL FSP-ELIGIBLE
HOUSEHOLDS, BY THE FSP BENEFIT AMOUNT 60
V.2B PARTICIPATION RATES AMONG SUBGROUPS OF THE
FSP-ELIGIBLE POPULATION, BY THE FSP BENEFIT
AMOUNT 62
V.3 THE BENEFIT-PARTICIPATION RELATIONSHIP
ESTIMATED WITH ALTERNATIVE SPECIFICATIONS
OF THE BENEFIT VARIABLE 66
VI
VlU
FIGURES
Figure Pa8e
V.l ALTERNATIVE SPECIFICATIONS FOR THE BENEFIT-PARTICIPATION
RELATIONSHIP 68
vu
IX
■UP?
EXECUTIVE SUMMARY
The most recent estimates of participation in the Food Stamp Program (FSP) indicate that
approximately 60 percent of FSP-eligible households participate in the program. Policymakers and
program administrators have expressed concern about this less than universal participation, and are
interested in the factors that are associated with nonparticipation and how program reforms affect
the participation rate.
This report uses data from the Survey of Income and Program Participation (SIPP) to conduct
an analysis of the determinants of FSP participation among eligible households. This analysis relies
extensively on multivariate statistical techniques, which reveal how the participation rate varies with
a given household characteristic, when the influence of other household characteristics is removed.
In other words, a multivariate analysis indicates whether a given household characteristic per se has
an effect on the probability of participation. This analysis is applied to the universe of households
eligible for the FSP, and to four subgroups of this universe-households with an elderly member,
households with a disabled member, female-headed households with children, and two-parent
households with children.
Previous studies have used econometric analysis to examine the relationship between
participation and household characteristics; however, most of these studies have relied on survey data
collected prior to the elimination of the food stamp purchase requirement in 1979. This report uses
SIPP data collected in 1985.
DEMOGRAPHIC CHARACTERISTICS AND FSP PARTICIPATION
The report examines the relationship between FSP participation and five demographic
characteristics of eligible households: the age, education, race and ethnicity of the household head,
the presence of children, and household size. The following are the major findings of this component
of the analysis.
The age ofthe household head seems to affect the probability of participation, but
not in systematic manner. Participation is substantially higher than average when
the household head is 30 to 39 years old, and substantially lower when he or she
is older than age 70, while all remaining age groups participate at approximately
the same rate.
Participation is significantly higher among households headed by a
persons who is 60 to 69 years old than among households headed by
a person older than 70.
As found by previous research, participation tends to decline as the education ofthe
household head increases; participation is highest among households in which the
household head has less than 12 years of education.
The net effect of the race ofthe household head on participation seems to be much
smaller than indicated by previous research. A small difference between black and
white households is found in the overall population, with black households
participating at a higher rate. However, among female-headed households with
children and households with an elderly member, essentially no difference in
participation exists according to the race of the household head.
Hispanic households participate at the same rate as white non-
Hispanic households, with the exception of two-parent households
with children, in which Hispanic households participate at a much
lower rate.
Another finding that diverges from the results of previous studies is that the
presence of children by itself does not have a sizeable effect on the probability of
participation.
Participation increases with the size of the household up to household size three,
after which it levels off. The fact of being a one-person household has a strong
negative effect on the probability of participation, and this effect is found to be
independent of whether the household contains an elderly person.
ECONOMIC CHARACTERISTICS AND FSP PARTICIPATION
The report examines the relationship between FSP participation and four economic
characteristics of households: whether the household receives public assistance, whether it has assets,
whether it has earnings, and the household's gross income (divided by the poverty threshold). The
following are the major findings of this component of the analysis.
• The receipt ofpublic assistance (AFDC and SSI) is the strongest predictor of FSP
participation-FSP-eligible households that receive public assistance participate at
dramatically higher r?tes than those that do not
• Eligible households with countable assets participate in the FSP at rates that are
significantly lower than those of households without countable assets.
• Unlike previous research, this study does not find that the presence of earnings is
negatively associated with participation among FSP-eligible households. The only
exception pertains to female-headed households with children, which participate
at a lower rate when they have earnings.
• Households with less income, as measured by the ratio of gross household income
and thepoverty threshold, are substantially more likely to participate in the program.
This finding implies that more needy households are more likely to be served by
the FSP. The only exception to this negative relationship between income and
participation pertains to households that report zero gross income. These
households participate at a much lower rate than would be expected given their
reported lack of resources. This odd result is likely due to the underreporting of
income in SIPP.
Xtl
THE BENEFIT AMOUNT AND FSP PARTICIPATION
This report devotes special attention to estimating the relationship between FSP participation
and the food stamp benefit amount to which a household is entitled. In addition to providing
descriptive information on this relationship, the analysis generates an estimate of the participation
response that can be used to simulate the effects of program reforms-that is, to predict how FSP
participation would change under a reform that altered the size and distribution of the benefit across
households. The following are the major findings.
The relationship between the FSP benefit amount and participation in the program
is positive overall. However, the estimated net effect of a change in the benefit
amount on participation is rather small.
An intuitive way to express the relationship between benefits and participation is
the percentage point increase in participation associated with a $10 increase in
benefits (the benefit amounts are expressed in 1985 dollars). The analysis suggests
that this increase elicits a different response according to the current level of
benefits: at $30, the participation response to a $10 increase is 1.5 percentage
points; however, the response drops to 0.35 percentage points at $150 of current
benefits.
XI
Xtt
I. INTRODUCTION
Although estimates of the rate o.? participation in the Food Stamp Program (FSP) vary across
stjdies, the consensus among analysts is that substantially less than 100 percent of the households that
are eligible to participate in the program actually do so. The most recent estimates have indicated
that approximately 60 percent of FSP-eligible households participate in the program (Doyle and
Beebout, 1988; Ross, 1988; and Doyle, 1990). Policymakers and program administrators have
expressed concern about this less than universal participation, and are interested in the factors
underlying nonparticipation and how program reforms might affect the participation rate.
Some researchers have used data from household surveys, such as the Panel Study on Income
Dynamics (PSED), to investigate the reasons reported by FSP-eligibles for not participating (Blaylock
and Smallwood, 1984; and U.S. General Accounting Office, 1988). Although extremely valuable, this
type of research is based exclusively on subjective, perceptual data and thus cannot address the
quantitative effects of the factors associated with nonparticipation, nor help predict the impact of FSP
reforms on the participation rate.
Another strand of research on FSP participation has attempted to identify the demographic and
economic characteristics associated with participation among FSP-eligible households. Applying
multivariate analysis to household survey data, researchers have estimated the net effect of a given
characteristic on the probability of participation-that is, the effect of a given characteristic
independent of the effects of other characteristics. Estimates of these net effects can be useful for
targeting outreach efforts toward specific demographic groups, for forecasting changes in participation
associated with changes in the economy, and for simulating the changes in caseloads and expenditures
stemming from changes in program regulations.
However, several methodological and survey data problems limit the reliability of the findings
from this type of research: (1) income and program participation are typically underreported in
household surveys; (2) some surveys provide only a small part of the information necessary for
simulating the food stamp eligibility determination process and the amount of benefits to which the
eligible household is entitled; and (3) most surveys provide no information on the time and out-of-pocket
costs that households incur to participate in the program.
Despite these limitations, studies of the factors associated with participation in the FSP have
generated a consistent set of findings. In particular, households headed by an employed person,
an elderly person, or a relatively more educated person are less likely to participate in the FSP, while
households that participate in other assistance programs and households that are female-headed or
nonwhite are more likely to participate in the program. However, most of these studies are based
on data collected before the Food Stamp Act of 1977 was fully implemented. If participation
behavior changed after the elimination of the purchase requirement-the major provision of the 1977
Act-the findings of the existing literature cannot be applied to the FSP in its present form.
In this report, we use 1985 data from the Survey of Income and Program Participation (SIPP)
to update previous multivariate analyses of the relationship between household characteristics and
FSP participation. Although we cannot overcome most of the limitations imposed by survey data, we
attempt to improve upon the existing research in four ways. First, we used a sophisticated computer
simulation based on SIPP data (Doyle, 1990) to obtain our sample of FSP-eligible households and
the amount of benefits to which they are entitled. Because SIPP provides sub-annual information
on a household's income, assets, expenses, composition, and program participation, it is the best
available data source for estimating FSP eligibility and potential benefits.
Appendix A provides a synopsis of these findings.
As discussed in Chapter V, less consensus has been reached about the relatior ship between the
FSP benefit amount for which the household is eligible and the probability of its participation.
Before the purchase requirement was eliminated, households were required to spend a portion
of their income to obtain a given dollar value of food stamps. When this requirement was eliminated,
the program became more accessible to eligible, low-income households, since they no longer needed
to trade in cash in order to receive the food stamps.
Second, we devote special analytical attention to the relationship between participation and the
amount of the FSP benefit A knowledge of the response of the participation rate to changes in
benefit levels is essential for forecasting the impact of reforms on program caseload and expenditures.
We examine the methodological and practical problems involved in estimating this response.
Third, our analysis applies not only to all eligible households, but also to four subgroups of the
eligible population: households with an elderly member, households with a disabled member, female-headed
households with children, and two-parent households with children. Thus, we can examine
whether the relationship between participation and household characteristics varies across
demographic subgroups.
Finally, we present our estimation results in a way that facilitates their interpretation. Rather
than presenting estimates of the coefficients of the participation equation, we use these estimates to
calculate predicted participation rates for a household with average characteristics. Then we show the
net effect on participation of a specific characteristic by computing the predicted participation rate
at different levels of that characteristic, while we keep all the other characteristics fixed at their
average values.
The remainder of this report is organized as follows. Chapter II contains a detailed discussion
of the data and methodology used in the analysis. The findings of the analysis are presented in
Chapters III through V. Chapter III examines the relationship between the demographic
characteristics of households and their participation in the FSP, while Chapter IV extends the analysis
to the economic characteristics of households. Findings on the relationship between the FSP benefit
amount and participation in the program are presented in Chapter V. Chapter VI provides a
summary of the findings and offers some concluding remarks.
4
H. DATA AND METHODOLOGY
This chapter discusses the methodological issues involved in our multivariate analysis of
participation in the FSP.
An analysis of FSP participation consists of several steps. The first step is to define a sample
of households that are representative of the population of households eligible to receive food stamps
at a given point in time. This task is particularly challenging, since neither existing household surveys
nor existing administrative data contain direct information on eligibility status. Second, once a sample
of eligible households is constructed, the researcher must consider how participation is associated with
the household's characteristics. This step entails specifying a "participation equation"--that is,
postulating the link between the outcome (participation or nonparticipation) and the observed
characteristics that may "explain" why certain eligible households will participate and others will not.
The final step entails estimating the magnitude of these relationships from the data. These estimates
allow the researcher to calculate the probability of participation for any particular type of household,
depending upon its particular combination of characteristics.
In the first section in this chapter, we describe how we used data from the Survey of Income and
Program Participation to obtain a sample of households simulated to be eligible for the FSP. Section
B discusses how the participation equation can be specified, while Section C discusses how the
underreporting of participation in households surveys can be addressed. Section D presents the types
of variables included in the participation equation. Finally, Section E illustrates how we present the
estimation results in this report
A. SIMULATING FSP-EUGEBELITY WITH SIPP DATA1
The Survey of Income and Program Participation (SIPP) is a nationally representative
longitudinal survey of adults in the United States, providing detailed monthly information on income,
labor force activity, and program participation. It is a multipanel longitudinal survey to which a new
sample ("panel") is added each year. At the time this study was initiated, only data from the first two
panels (1984 and 1985) were available. Each panel contains information on persons in a longitudinal
sample who are followed for a period of over two and one-half years. The adults in the sample, age
15 or older, are interviewed every four months. In each round of interviewing (or "wave"), a core
questionnaire collects information on each of the four months preceding the interview date. In most
waves, the monthly core questions are supplemented with questions on a variety of topical issues that
vary from wave to wave. Because the interviewing process is staggered whereby one-fourth of all
sampled households are interviewed in a month, the reference period covered in any given wave is
not the same for all sample members.2
One feature of the SIPP design that is particularly relevant to this study is that the SIPP panels
overlap for part of their duration. Thus, cross-sectional samples can be constructed with observations
from more than one panel, thereby generating larger sample sizes. The data set used in our analysis
combines data from the 1984 and 1985 panels of SIPP for the month of August 1985.3
1This section draws heavily on Doyle (1990). The reader familiar with SIPP and with the issues
involved in eligibility simulation can skip to Section B.
For further information on the design and scope of SIPP, see U.S. Department of Commerce
(1987).
More specifically, we derived our sample by combining observations from Wave 7 of the 1984
panel and Wave 3 of the 1985 panel. We merged each of the two waves with information collected
in other selected waves of the respective panels. Although Wave 7 of the 1984 panel and Wave 3
of the 1985 panel were independent samples of the U.S. population, they were administered
simultaneously. Furthermore, a straightforward adjustment to the sample weights allows estimates
to be based on combined panels. We chose these two waves for the following reasons: (!) they
contain topical information on assets; (2) together, they provide a relatively large sample size (27,660
households); and (3) they sampled the population in the month of August, making the reference
period comparable to available administrative data, which is useful for purposes of quality control.
The sample that is used to estimate a food stamp participation equation must be restricted to
households that are eligible for the Food Stamp Program. Since eligibility cannot be observed
directly, it must be simulated on the basis of the household information provided in the survey. The
procedure for simulating the eligibility for each household in the SIPP dataset is designed to replicate
the actual FSP eligibility determination process as closely as possible. In other words, program
eligibility and benefit criteria are applied to each household as if it had actually applied for food
stamps. Details on the eligibility simulation and on the file development process are provided in
Mathematica Policy Research (1990) and in Doyle (1990).
Although SIPP contains more information on the variables necessary for determining FSP
eligibility and benefits than does any other available household survey, some limitations still remain.
Despite the adjustments and enhancements made to the SIPP data, the simulation procedures cannot
perfectly replicate the eligibility and benefit determination process mandated in the legislation. The
specific discrepancies are as follows:
Unit definition. Because SIPP does not measure the complete set of characteristics
that the program uses to determine a food stamp unit-especially information on
which dwelling-unit members customarily purchase and prepare food together—the
simulated food stamp household may not be the same as the unit determined by
the food stamp case worker. For this study, the program unit composition reported
in SIPP by households receiving FSP benefits was used to simulate the food stamp
unit In other dwelling units that receive only cash assistance, the food stamp unit
was equal to the cash assistance unit, plus any spouse or related children under age
18 in the dwelling. In all other dwelling units, the simulated food stamp unit was
the same as the Census household-the group of individuals who live in the
dwelling unit
Countable assets. We used the financial, nonfinancial, and vehicular assets reported
in SIPP to estimate countable assets, according to program rules. However, SIPP
does not explicitly measure all of the information necessary for this purpose, such
as cash on hand.
Gross income. The measure of gross income used in this study is close to, but not
precisely the same as, gross income reported to the food stamp case worker. First
survey data on income and program participation, including the data collected in
SIPP, tend to be underreported. Second, the definition of income measured in
SIPP is not precisely the same as the definition of income used to determine food
stamp eligibility. Third, as noted above, the household composition simulated with
SIPP data differs from the case worker's determination of the food stamp unit, thus
leading to different aggregate income amounts for food stamp households.
Net income. The measure of net income used to simulate eligibility in this study is
not precisely the same as net income determined by the food stamp case worker:
(1) we use approximated medical expenses for elderly and disabled individuals; (2)
we use approximated shelter expenses for individuals in the 1985 panel; and (3)
there is measurement error in the collection of shelter and child care expenses in
SIPP. The SIPP definitions of shelter and dependent-care expenses also differ
slightly from the FSP definitions.
Disability status. We determined disability status on the basis of reported disability
and reported income receipt, as specified under the program. Reporting and
measurement errors in SIPP may somewhat distort the number of disabled
individuals identified in this manner.
Table ELI shows the possible bias due to each of these measurement and reporting errors.
TABLE II.l
FACTORS TBAT AFFECT THE SIMULATION OF FOOD STAMP ELIGIBILITY
BASED ON SD?P DATA, AND THE DIRECTION OF THE BIAS
Effect on Estimates of
Source of Error the Number of Elieibles
Unit Definition Underestimate
Countable Assets Overestimate
Gross Income:
Underreporting Overestimate
Definition Underestimate
Net Income Unknown
Disability Status Underestimate
SOURCE: Figure A-l in Doyle (1990).
The underreporting of gross income will bias estimates of the number of eligible households
upward, since more households will appear to have met the income limits than actually did. On the
other hand, the omission of some types of expenses may bias the measurement of net income upward,
8
thus leading to underestimates of the number of eligible households. Moreover, the inability to
perfectly replicate program regulations for calculating deductions from expenses may generate the
reverse effect, or may reinforce the bias from omitting valid deductions. SIPP also omits selected
assets, thus leading to overestimates of the size of the eligible population.
B. SPECIFYING THE PARTICIPATION EQUATION
We follow the existing literature on the determinants of participation in the FSP (Allin and
Beebout, 1989) by spscifying the econometric model of participation as a one-equation model, in
which the dependent variable is the reported4 participation status of the household (participant or
nonparticipant), the explanatory variables are household characteristics (such as income, the presence
of children, or the age of the household head), and the estimation sample consists of households
simulated to be eligible for the FSP on the basis of current characteristics. The participation equation
can be written as:
(1) P = XB + e,
where P is reported participation, a discrete outcome, coded as one if the household participates, and
zero otherwise; X is the vector of observed household characteristics; and B is the vector of
parameters which represent the "net effect" of each variable on participation. XB denotes that each
variable in the X vector is multiplied by the corresponding element in the B vector. Finally, e is the
error term that represents all unobserved factors that affect participation.
Once equation (1) is estimated, the coefficients can be used to predict the probability of
participation for any particular type of household-that is, for a household wfth a particular set of
values for the variables contained in the vector X. This probability of participation can also be
Issues associated with the underreporting ofFSP participation are discussed later in this chapter.
9
interpreted as the predicted participation rate for that type of household. Each coefficient in the
vector B can be interpreted as the net effect of a given characteristic on the participation rate.
One important complication arises in the estimation of equation (1). The fact that the
dependent variable P is a discrete variable that assumes only two values makes the application of
standard regression techniques (ordinary least squares, or OLS) very problematic (Amemyia, 1985).
Among other things, if equation (1) is estimated with OLS, the predicted value of P for some
households might lie outside of the interval between zero and one, which is equivalent to saying that
the associated predicted participation rate can be less than zero or greater than 100 percent. The
standard approach to this problem is to use a nonlinear model, such as a probit or a logit model
(Maddala, 1983). These models constrain the predicted probability of participation to be positive and
less than one.
From a conceptual standpoint, probit and logit models are typically rationalized in terms of the
so-called latent variable'1 models. In this framework, observed participation or nonparticipation status
is seen as the dichotomous realization of an underlying latent continuous variable, that in our case
can be thought as the "propensity to participate" in the FSP. Let us represent this continuous
variable as P . The model then becomes:
(2) P* ■ XB + e
(3) P = 1 (the household participates) if P* > 0
(4) P = 0 (the household does not participate) if P < 0
Equation (2) implies that the latent propensity to participate depends both on observable and
on unobservable household characteristics. If the latent variable were observed (i.e., if we knew the
value of the propensity of each household to participate), then equation (2) could be estimated with
standard regression techniques. However, all we observe is the discrete outcome, participation or
10
nonparticipation. This does not prevent us from estimating the effect of the observable
characteristics X on the probability of participation, provided that we are willing to make an
assumption about the probability distribution of the error term e.
One assumption used widely in the literature is that e has a standard normal distribution. This
assumption generates the probit model. The probability of participation for household i with
characteristics Xj can be written as:
(5) Prob(participation) = Prob (P* > 0) = Prob (-e, < XjB) = $(X,B)
and the probability of nonparticipation as:
(6) Prob(nonparticipation) = Prob (P* < 0) = Prob (-ej > XjB) = 1 - <D(X,B)
where <D( ) is the cumulative distribution function of the standard normal distribution. With this
assumption of a normally distributed error term, the vector of marginal effects B can be estimated
with econometric techniques referred to as maximum likelihood estimation.
C. THE PROBLEM OF THE UNDERREPORTING OF PARTICIPATION
An implicit assumption in the previous discussion is that the dependent variable of the
participation equation is correctly observed for all eligible households. Unfortunately, there is solid
evidence that household survey respondents underreport participation in the FSP (as well as in other
welfare programs). Thus, some of the households that are simulated to be eligible and that actually
are participating in the program are classified as not participating due to erroneous reporting.
5The choice of the probability distribution for the error term determines the particular estimation
model Normality leads to a probit model, while a logistic distribution yields a logit model. The
estimation results typically do not differ substantially between the two models. We arbitrarily chose
the probit model, but we verified that the logit model yields the same results.
"The opposite phenomenon take*- place as well-that is, some households that report participating
in the program are simulated to be ineligible according to the income and assets information they
(continued...)
11
However, whether such underreporting biases estimates of the determinants of participation must still
be determined. The existence of such bias crucially depends on whether underreporting is
nonrandom-that is, correlated with the variables that determine participation.
Let us hypothesize that underreporting is negatively correlated with, say, the education of the
household head, in the sense that more educated household heads are more likely to report
participation, given that they participate. Let us also assume that education has a true negative effect
on participation, in the sense that more educated household heads are less likely to participate in the
program. In this case, the estimated effect of education on participation (measured by the coefficient
on education in the participation equation) might actually be zero, because the true negative effect
is offset by the positive effect of education on reporting. More generally, in the oresence of
nonrandom underreporting, the estimated coefficients in the participation equation would reflect both
the true impact of the characteristic on the probability of participation and its effect on the
probability of underreporting.
Unfortunately, the underreporting problem in the context of a study that relies on micro-level
data-that is, data on the individual households-cannot be resolved easily. In the context of an
aggregate approach for estimating participation rates, Doyle and Beebout (1988) and Doyle (1990)
have confronted underreporting by using counts of participants derived from administrative data,
rather than survey data, as the numerator of the participation rate.7 This solution is clearly not
(...continued)
provide during the interview {seemingly ineligible participants). We exclude these households from
the analysis in order to provide symmetry with households for which the same "error" is made in the
eligibility simulation process (Le., they are eligible but are simulated as ineligible), but that do not
report participating. These households are necessarily excluded from the analysis, since the error
cannot be detected in these cases. Thus, we avoid an asymmetry that could lead to biased estimates
of the determinants of participation.
7In these studies, the denominator of the participation rate is taken to be the weighted count of
eligible households based on SIPP data.
12
applicable here, since this study requires information on eligibility and participation for each
individual household, and not aggregate counts.
Since no direct solution to the underreporting of participation seems to be available, ascertaining
the relationship between underreporting and household characteristics would be useful The ideal
way to obtain a measure of this relationship would require a dataset in which both the participation
status reported in the survey and the true participation status obtained from administrative data are
available for each household. This information would support estimating ? multivariate model of
"participation reporting", in which the universe is defined as the households t'uat are truly participating
at a given point in time, and the dependent variable is whether those households report in the survey
that they participate.
Unfortunately, datasets that contain this type of information are not available. A more indirect
way to acquire a "sense" the relationship between underreporting and household characteristics is to
compare the distribution of these characteristics among FSP participants in two different datasets,
one affected by underreporting (such as SIPP) and one not affected by it (such as FSP program data).
Following this approach, we have calculated the average values of the characteristics of households
that report food stamp receipt in SIPP, and of FSP participants observed in the program's Integrated
Quality Control System (IQCS) dataset The results of this comparison are shown in Table n.2.
Let us use the age of the household head as an example of how the figures in Table 11.2 could
be interpreted. The fact that SIPP contains on average older FSP participants than IQCS does could
be attributed to the fact that younger participants are more likely to underreport participation.
However, other factors could affect the comparison of these characteristics between SIPP and IQCS,
besides systematic underreporting in SIPP: small sample size, errors in the eligibility simulation,
errors in measuring the characteristic itself in one or both data sources.
With this caveat in mind, the figures in Table n.2 could be interpreted as suggesting that
households headed by a younger person or a black person, smaller households, households with less
13
income or more FSP benefits, and households that do not receive Public Assistance or do not report
any earnings are more likely to underreport participation. However, most of the SIPP-IQCS
differences in Table H2 are rather small; the largest difference between SIPP and the IQCS is only
8.4 percent. While these small differences do not exclude the possibility that some of the estimates
presented in the following chapters are biased due to underreporting, it suggests that this bias might
not be large enough to affect the major findings of that analysis.
TABLE II.2
COMPARISON OF SELECTED CHARACTERISTICS OF FSP PARTICIPANTS
IN THE SIPP AND IQCS DATA BASES
SIPP
Mean or
Percentage
IOCS
Mean or
Percentage
Percentage
Difference
Age of Reference Person 43.9 42.2 + 4.0
Race of Reference Person (% Black) 35.6% 36.4% - 12
Number of Persons 2.80 2.67 + 4.8
Presence of Children 61.8% 59.2% + 4.4
Gross Income $417 $397 + 5.0
FSP Benefit Amount $119 $116 + 2.6
Receiving Public Assistance 69.7% 64.3% + 8.4
Reporting Earnings 21.1% 19.6% + 7.6
SOURCE: SIPP estimates are obtained from the August 1985 Food Stamp Eligibility File. IQCS estimates
are obtained from the August 1985 analysis file of the Integrated Quality Control System.
f OTE: The food stamp unit is the unit of analysis for all estimates presented in the table.
14
D. THE EXPLANATORY VARIABLES IN THE PARTICIPATION EQUATION
This section addresses several issues associated with the explanatory variables that we chose for
the participation equation. It also describes the demographic subgroups that we nalyzed.
The explanatory variables of the participation equation are essentially the demographic and
economic characteristics of households. In measuring these characteristics, we adopted the Census
definition of the household-the group of individuals who live in the dwelling unit. This definition
deviates from the unit definition that we used in the eligibility and benefit simulation process,
described in the first section of this chapter. In simulating eligibility, we used the information in SIPP
to construct a unit that resembles the food stamp unit However, replicating the food stamp unit in
this way is not possible for households that currently do not participate in the FSP or do not receive
cash assistance. For these households, the food stamp unit used in the eligibility simulation coincides
with the Census household.
The choice to be made in the context of a multivariate analysis of FSP participation is whether
one should use the characteristics of the simulated food stamp unit, with the limitations described
above, or use in every case the characteristics of the Census household. We believe that the latter
choice, although far from ideal, is less problematic. The main problem with using the characteristics
of the simulated food stamp unit to analyze participation is the asymmetric treatment of participants
and nonparticipants: the explanatory variables would be defined on the basis of a criterion that is
correlated with the dependent variable (that is, participation status). Some characteristics might
appear to affect participation only because they have been defined differently for participants and
for nonparticipants. Therefore, we define all explanatory variables in the participation equation with
reference to the Census household.
The first group of explanatory variables consists of the demographic characteristics of the
household head (age, race and Hispanic origin, and level of education) and of the household itself
(the number of persons and the presence of children). The relationship between these variables and
15
participation in the FSP is analyzed in Chapter III. The second group of explanatory variables
consists of economic characteristics: total household income (expressed as a percentage f the poverty
threshold), the presence of any earnings, asset ownership, and public assistance receipt The
relationship between these variables and FSP participation is discussed in Chapter IV. Finally, the
relationship between participation and the amount of food stamp benefits for which the household
is eligible is explored in Chapter V.
All of the explanatory variables enter into the participation equation as categorical variables,
including variables that are continuous (e.g., age and income). Thus, we broke the continuous
variables down into discrete intervals. The choice of transforming continuous variables into categorical
ones has two motivations. First, this provides a convenient way to detect whether the sign and
magnitude of the net effect of a characteristic on participation changes at different levels of the
characteristic. For example, we find that participation is highest for the 30-39 age group and lowest
for the 70 and older age group, while it is virtually the same for the other age groups. Specifying age
solely as a continuous variable (even in nonlinear form) would not capture this irregular pattern.
Second, the availability of estimated coefficients that correspond to different levels of an explanatory
variable facilitates the task of computing predicted participation rates. For example, we show the
effect of the age of the reference person on participation by computing the participation rate for each
of the five age groups, holding all other variables constant at their sample means. Section E contains
a more detailed discussion on how the results are presented in the report.
Our subgroup analysis encompasses four demographic groups within the food stamp population:
(1) households that contain an elderly member, (2) households that contain a disabled member, (3)
female-headed households with children, and (4) two-parent households with children. The four
subgroups are not defined to be mutually exclusive. For example, a household can be counted not
only as an elderly household but also as a female-headed household. Table 11.3 shows the extent to
which the four groups overlap.
16
It is interesting to note that households that contain a disabled member overlap with other
subgroups to the greatest extent: approximately 50 percent of them are also classified in another
subgroup. This implies that the results for this subgroup will often tend to be similar to those
obtained for the overall FSP-eligible population. Households that contain an elderly member overlap
much less; only about 10 percent of them are classified elsewhere.
TABLE EL3
OVERLAP AMONG FOUR DEMOGRAPHIC SUBGROUPS
OF THE FSP-ELIGIBLE POPULATION
(unweighted counts)
Households Counted as:
Containing
an Elderly
Member
Containing
a Disabled
Member
Female-Headed
with Children
Two-Parent
with Children
Also Counted as:
Containing an
Elderly Member
- 57
(17.2%)
53
(5.6%)
67
(10.0%)
Containing a
Disabled Member
57
(4.2%)
- 64
(6.8)
53
(7.9)
Female-Headed Household*
with Children
53
(3.9)
64
(19.3)
- 0
(0-0)
Two-Parent Households
with Children
67
(5.0)
53
(16.0)
0
(0.0)
-
Total 1346 331 940 668
SOURCE: August 1985 Food Stamp Eligibility File.
NOTE: The numbers in parentheses are percentages of the column total.
Table B.l in Appendix B presents the frequency distributions for all the explanatory variables
used in the analysis, both for the overall FSP-eligible population and for the four demographic
subgroups.
17
E. PRESENTING THE ESTIMATION RESULTS
We use two different formats to present the estimation results. We present the estimated
coefficients of the participation equation (and their associated t-statistics) only in an appendix,
because these coefficients are not the most intuitive way to illustrate the net relationships between
participation and household characteristics. In the main body of the report, we use a more intuitive,
illustrative approach by displaying the participation rate at the different levels of the characteristic
under consideration, while fixing all the other characteristics at their sample means. In addition to
these "predicted," or "regression-adjusted," participation rates, the tables in the main body of the
report contain the corresponding "observed," or "unadjusted," participation rates-that is, the rates
computed simply by dividing the number of (reported) participating households by the number of
(simulated) eligible households.
We use the estimated coefficients to compute the predicted participation rates in the following
way. Let us consider a variable-for example, the education of the household head-that has three
different values: in this case, less than high school, high school, and more than high school. Of the
three values, two (say, the two highest values) enter into the participation equation as 0-1 dummy
variables. Thus, we obtain two estimated coefficients for education: Bj, the marginal impact on
participation of having a high school education versus having less than high school, and B2, the
marginal impact of having more than high school versus less than high school In computing the
predicted participation rates for the three levels of education, we must fix all the other characteristics
at some common value in order to eliminate the effect of the other characteristics on the
participation rates. Thus, we fix these characteristics at their sample means. Given this setup, the
predicted, or regression-adjusted, participation rates for the three levels of education are computed
as follows:
Tliese observed participation rates differ from the participation rates presented in Doyle (1990),
where the count of participants (the numerator) is derived from administrative data, and only the
count of eligibles (the denominator) is derived from SEPP.
18
PRless than high school = 1<W*(XB)
(7) PRhigh school = lOO'^XB + Bi)
PRmore than high school = «»*•(* B + *2>
where X is the vector of the sample means of all the explanatory variables with the exclusion the
education dunrnies, B is a vector of coefficients, and the BjS are the coefficients on the education
dummies. <X>() represents the cumulative distribution function of the standard normal distribution,
so that 4>(X B) represents the probability of program participation by a household headed by a person
without a high school diploma and whose other characteristics have values equal to their sample
means.
The only drawback to presenting predicted participation rates rather than presenting the probit
coefficients directly is that the standard errors cannot similarly be displayed, so that the difference
between the rates predicted at different levels of a given explanatory variable cannot be tested
directly for statistical significance. To remedy this lack of information, we also present the probit
coefficients and their associated t-statistics (Appendix C). These coefficients are presented as the
marginal effects on the probability of participation, rather than as "raw" probit coefficients (that is,
the coefficients in the B vector in the participation equation).9 Each of these marginal effects
represents the percentage point difference in the participation rate relative to the excluded category
of a given variable, while all the other explanatory variables are evaluated at their sample means.
One point should be noted about how we present the results in Appendix C, since our
presentation deviates from how these results are traditionaUy reported. We present the marginal
effects from several algebraically equivalent specifications of the probit equation. However, each
Deriving marginal effects entails multiplying the "raw" probit coefficients by the standard normal
density evaluated at the sample means. More formally, the coefficients presented in Appendix C are
equal to 0(XB) * Bj * 100, where <p( ) is the density of the standard normal. The value of #(XB)
is also displayed, so that the raw coefficients Bj can be recovered. Details on how marginal impacts
are derived from discrete-choice models are presented in Maddala (1983).
19
specification uses a different excluded category for each variable. This apparently confusing approach
has an important motivation. It is intended to overcome a drawback to using variables in discrete
rather than continuous form--the fact that the pattern of statistical significance of the coefficients of
a discrete variable depends on the excluded category for that variable.
This point is better illustrated with an example. Returning to the three education categories
referred to above, let us conjecture that the only statistically significant difference in participation is
between the two extremes: less than high school and more than high school If the participation
equation is specified whereby the excluded category is the intermediate one (high school), the t-statistics
will suggest that the difference in participation between each of these two extreme categories
and the intermediate category is not significant. This result cannot be interpreted as evidence that
education does not have any statistically significant impact on participation among the eligible
population. In fact, if less than high school were the excluded category, the t-statistic on the more-than-
high-school dummy would reveal a statistically significant difference.
The solution presented in Appendix C obviates the arbitrariness in choosing the excluded
categories. This solution entails estimating a number of algebraically equivalent alternative
specifications, all of which generate the same predicted participation rates. However, each
specification generates a different pattern of statistical significance of the coefficients. When the
analysis presented in the next three chapters requires a test of the difference between the
participation rates computed at any two discrete levels of the same variable, we will refer to the
results from the relevant specification presented in Appendix C.
20
El. FSP PARTICIPATION AND THE DEMOGRAPHIC
CHARACTERISTICS OF HOUSEHOLDS
In this chapter, we examine how participation varies according to the demographic characteristics
of FSP-eligible households. We present the analysis for all eligible households and separately for
households with an elderly person, households with a disabled member, female-headed households
with children, and two-parent households with children. Most of the tables in this chapter are
arranged in groups of two: Table A presents participation rates among the entire FSP-eligible
population, and Table B presents rates among the four subgroups.
The presentation follows the methodology outlined in Chapter II: we examine the relationship
between participation and each household characteristic by comparing the "predicted" participation
rates calculated at different levels, or categories, of that characteristic. For example, we analyze the
relationship between FSP participation and the age of the household head by examining how much
the predicted participation rate varies across age levels while all other characteristics are held
constant at their average values. When appropriate, we also compare the pattern of the predicted
rates with the corresponding pattern of the "observed" rates, which are the ratio of participants to
eligibles within each level or category.
Before we begin the type of analysis described here, it is useful to compare the simple "average"
participation rates among the four demographic subgroups and in the overall FSP-eligible population.
The average predicted rate for a group is the rate computed for an "average household"-that is, one
that has average values for all the characteristics for that group. Analogously, the average observed
rate for a group is simply the the ratio of participants to eligibles in that group. The next section is
devoted to a discussion of these average participation rates.
21
A. COMPARISON OF THE AVERAGE PARTICIPATION RATES
The predicted participation rate for an average FSP-eligible household is 43.7 percent (Table
mi). The corresponding average observed participation rate is only slightly higher, 44.2 percent.
At first glance, these rates seem quite low; however, it is important to keep in mind that the rates
reported in this paper are based entirely on survey data, and are thus substantially lower than those
based on administrative data for the numerator and survey data for the denominator, as was discussed
in Chapter IL As reported by Doyle (1990), the household participation rate for all eligible
households in August 1985 is 59.4 percent-15 percentage points higher than the observed rate based
solely on survey data.
TABLE m.1
AVERAGE PARTICIPATION RATES
AMONG ALL FSP-ELIGIBLE HOUSEHOLDS AND
AMONG SUBGROUPS OF THE FSP-ELIGD3LE POPULATION
Participation Rates Sample
Predicted Observed Size
All FSP Eligible Households 43.7% 44.2% 3,559
Households with an Elderly Person 30.2 3X2 1346
Households with a Disabled Person 55.8 55.7 331
Female-Headed Households
with Children 78.9 69.6 940
Two-Parent Households
with Children 423 41.0 668
SOURCE: August 1985 SIPP Food Stamp Eligibility File.
The predicted participation rates for an average household within the four demographic
subgroups vary substantially around the rate for all FSP-eligible households. In particular, the
22
predicted participation rate among households that contain an elderly person is substantially lower
(30 percent), while the rate among female-headed households with children is much higher (79
percent). This pattern is consistent with previous findings, including the participation rates presented
in Doyle (1985), once we allow for the "downward shift" due to underreporting. Among households
with a disabled member, the predicted rate is about 12 percentage points higher than the overall rate
(56 versus 44 percent),1 while the rate among two-parent households with children is very similar
to the overall rate.
With one exception, the predicted rate for an average household within each subgroup is very
close to its observed counterpart, which merely says that the participation rate predicted for a
household with "average" characteristics is similar to the average participation rate across all
households in the group. However, a nonlinear model (such as probit) does not always generate
average predicted rates that coincide with the observed ones. The participation rate of female-headed
households is a case in point Among this group, the predicted rate for an average household
is significantly higher than the observed rate (79 percent, compared with 70 percent). The
discrepancy between the predicted and observed rate tends to increase as the predicted rate moves
away from 50 percent A more formal explanation for this phenomenon is presented in Appendix
D. However, it should be emphasized that this discrepancy does not affect the validity of the
subsequent analysis. Our primary objective is to examine how predicted rates vary across different
levels of a characteristic while all the other characteristics are held constant In some instances, we
compare the variation in predicted rates with the variation in the observed rates, in order to highlight
how a rnultivariate analysis can lead to conclusions that differ from those based on a simpler
This finding differs from the finding presented in Doyle (1990), in which the overall rate among
households with a disabled person is nearly 13 percentage points lower than the rate among all
households (46.7 percent compared with 59.4 percent). This difference is due to the fact that the
administrative data used in the numerator of Doyle's participation rates capture only those disabled
persons who receive SSL In contrast, SIPP captures disabled individuals who also receive Social
Security or Veteran's benefits due to their disability.
23
descriptive analysis. The fact that the average predicted rates are "shifted away" from the observed
rates does not hinder our ability to conduct either type of investigation.
We now examine how participation varies by the demographic characteristics of the household.
B. AGE OF THE REFERENCE PERSON
This and the next two sections examine differences in participation rates by the age, education,
race, and ethnicity of the household reference person, respectively. The reference person in SIPP
is defined as the first household member mentioned to the interviewer as the owner or renter of the
dwelling unit If no cash payments are made for rent, then the reference person is the first household
member mentioned who is 18 years or older.
It is conceivable that the characteristics of the other household members may not be the same
as those of the reference person, so that the reference person would not be "representative" of the
demographic characteristics of the other members. However, when exarmning the relationship
between FSP participation and person-level demographic characteristics (such as race or education),
one is forced either to choose the characteristics of one household member or to construct some
average measure for the household. We have chosen to follow the approach of exarnining the
characteristics of the household reference person as defined in SIPP.
Table IH2A presents the predicted and observed participation rates disaggregated by the age
of the reference person. The pattern of the predicted rates shows that the relationship between age
and participation is not systematic, in the sense that it is not always increasing or always decreasing.
Two age groups participate at rates that differ substantially from the overall rate. Households in
which the reference person is 30 to 39 years old participate at a higher rate (53 percent), and
households in which the reference person is 70 years or older participate at a much lower rate (31
percent). The participation rates of the other three age groups are much closer to the overall
24
average rate.2 Moreover, the t-statistics reported in Table C.1 suggest that the differences in
participation among these three groups are not statistically significant.
TABLE HL2A
PARTICIPATION RATES AMONG ALL FSP-EIJGIBLE HOUSEHOLDS,
BY THE AGE OF THE REFERENCE PERSON
Participatior Rates Sample
Predicted Observed Size
All FSP-Eligible Households 43.7% 44.2% 3,559
Age of Reference Person:
15 to 29 years 47.0 51.9 805
30 to 39 years 53.3 52.6 713
40 to 59 years 45.2 47.8 769
60 to 69 years 43.1 37.9 502
70 years or older 30.9 26.9 770
SOURCE: August 1985 SEPP Food Stamp Eligibility File.
NOTE: The predicted participation rates are computed from the probit coefficients presented in Appendix
C. Hie observed participation rates are computed as the weighted number of households reporting
FSP participation divided by the weighted number of households simulated to be eligible.
The age pattern of the predicted rates differs from the age pattern of the observed rates. Hie
latter exhibit an almost steadily decreasing pattern across the age distribution, from 52 percent among
the youngest group to 27 percent among older one. The largest difference between the pattern of
predicted and observed rates occurs among households headed by a 60- to 69-year-old. For this
group, the observed rate is 10 percentage points lower than the rate for households headed by a 40-
to 59-year-old, while this difference almost disappears with the predicted rates, leaving only
households headed by a person 70 years of age or older with a participation rate below 40 percent.
This pattern represents an example in which a multivariate analysis of participation can unravel
^The break at age 60, instead of the more usual 65, was chosen because the FSP elderly
provisions apply to persons age 60 and older.
25
phenomena that go unnoticed with a simple univariate analysis. The multivariate results suggest that
some of the differences in participation implied by the observed rates are due to other factors that
are correlated with age, rather than to age per se.
Table HL2B presents our analysis of the relationship between age of the reference person and
participation for the four demographic subgroups. We discuss these results separately for each
subgroup.
1. Households with an Elderly Member
In approximately 95 percent of households that contain an elderly member, one of the elderly
persons in the household is also reported as the household reference person. Thus, very few
households that contain an elderly person are headed by a person younger than 60 years of age. To
analyse the pattern of participation by the age of the reference person among households that
contain an elderly person, we collapsed the younger age categories hiio one category-the reference
person is younger than age 60.
Table IIL2B shows that the predicted and observed participation rates of households with an
elderly member exhibit different patterns by the age of the reference person. Households in which
the reference person is younger than age 60 have a substantially higher observed participation rate
than those in which the reference person is 60 to 69 years or 70 years or older. When characteristics
other than age are held constant in the predicted rates, the difference between the younger than 60
and 60 to 69 years of age categories is no longer statistically significant (Table C.2). By contrast,
households whose reference person is 70 years or older participate at a statistically significant lower
rate.3
^epredicted rates for the two elderly subgroups in Table ffl.2A and Table IH.2B differ because
the mean values of the characteristics other than age differ (education, race, household size, and
income and assets.) The rates in Table IE.2B are computed for an average elderly household, and
those in Table IK2A for an average household.
26
TABLE HI.2B
PARTICIPATION RATES AMONG SUBGROUPS OF THE FSP-ELIGIBLE POPULATION,
BY THE AGE OF THE REFERENCE PERSON
Participation Rates
Predicted Observed
Sample
Size
Households with an Elderly Person 30.2%
Less than 60 years
60 to 69 years
70 years or older
32.2%
31.1 47.2
35.6 37.9
26.8 26.9
1,346
74
502
770
Households with a Disabled Person 55.8 55.7 331
15 to 29 years
30 to 39 years
40 to 59 years
60 years or older
65.7 63.2
69.0 63.2
52.1 53.1
42.9 47.8
36
62
193
40
Female-Headed Households
with Children
15 to 29 years
30 to 39 years
40 to 59 years
60 years or older
78.9
82.2
81.9
69.2
68.5
69.6
77.3
68.5
58.0
65.3
940
349
335
212
44
Two-Parent Households
with Children
15 to 29 years
30 to 39 years
40 to 59 years
60 years or older
42.3
36.8
48.8
38.0
50.7
41.0
36.7
40.7
42.8
57.6
668
207
242
176
43
SOURCE: August 1985 SIPP Food Stamp Eligibility File.
NOTES: The predicted participation rates are computed from the probit coefficients presented in
Appendix C. The observed participation rates are computed as the weighted number of
households reporting FSP participation divided by the weighted number of households
simulated to be eligible.
27
The major implication of these findings is that the elderly FSP-eligible population should not be
seen as a homogeneous group as far as participation is concerned: the older group among the elderly
population has a particularly low rate of participation.
2. Households with a Disabled Member
Due to the small number of households with a disabled member in which the reference person
is older than 60 years of age, we collapsed the two highest age categories into one category, 60 years
and older. Both the observed and the predicted rates indicate that participation among households
with a disabled member declines with the age of the reference person. Participation among the two
youngest age groups is well above 60 percent, declines to about 50 percent for the 40- to 59-year-old
group (which comprises the majority of households with a disabled member), and declines further to
nearly 40 percent for the elderly. However, the difference between the latter two groups is not
statistically significant
3. Female-Headed Households with Children
The participation rates among female-headed households with children, disaggregated by the age
of the reference person, exhibit an interesting pattern. The predicted rates clearly cluster around two
levels: above 80 percent among households whose reference person is younger than age 40, and less
than 70 percent for households whose reference person is older than age 40. The differences within
the two broad groups are not statistically significant (Table C.4).
It appears that female-headed households with children exhibit different participation behavior
when the reference person is younger than age 40 than when she is older than age 40. The situations
of these two types of female-headed households may be very different: those in which the reference
person is younger than age 40 are more likely to comprise mothers who live alone with very young
children, while those in which the reference person is older may comprise three-generation families
We made the same aggregation for female-headed and two-parent households with children.
28
(e.g., an unmarried mother who lives with her mother) or families in which an older mother has
school-age children.
4. Two-Parent Households with Children
If one were to consider only the observed participation rates, one would conclude that
participation among two-parent households with children increases steadily with the age of the
reference person, ranging from 37 percent for households headed by a 15- to 29-year-old, to 58
percent for households headed by a person 60 years of age or older. The predicted rates offer a
different picture, which is more in line with the results obtained for other demographic groups. As
was true among all eligible households, the participation rate among two-parent households in which
the reference person is 30 to 39 years old is significantly higher than for the two adjacent age groups.
An unexpected result is the higher participation rate among households whose reference person is
older than age 60. This result could be due to the fact that elderly couples who live with their
grandchildren participate at higher rates than younger couples who live with their own children.
However, due to the small sample size of this group, this rate does not differ statistically from the
rate for any other age group (Table G5).
C EDUCATION OF THE REFERENCE PERSON
Consistent with the findings of previous research, the better educated the household reference
person, the less likely the household is to participate in the FSP. Among all eligible households
(Table m.3A), predicted and observed participation rates decline systematically with the education
of the reference person.
The largest difference in predicted rates between adjacent education categories occurs between
households in which the reference person has more than 12 years of education and those in which
he or she has exactly 12 year of education (11 percentage points). A smaller, although still
statistically significant, difference exists between the latter group and the group with less than 12 years
29
of education (5 percentage points). One interesting point to note is ttiat the observed rates are very
similar to the predicted rates, which implies that none of the other explanatory variables in the
participation equation is highly correlated with the education of the reference person.
TABLE m.3A
PARTICIPATION RATES AMONG ALL FSP-ELIGIBLE HOUSEHOLDS,
BY THE EDUCATION OF THE REFERENCE PERSON
Participation Rates
Predicted Observed
Sample
Size
All FSP-Eligible Households 43.7% 44.2%
Education of the Reference Person:
Less than 12 years 47.2 47.9
Exactly 12 years 42.4 43.6
More than 12 years 31.6 293
3,559
2,081
1,018
460
SOURCE: August 1985 SIPP Food Stamp Eligibility File.
NOTE: The predicted participation rates are computed from the probit coefficients presented in Appendix
C The observed participation rates are computed as the weighted number of households reporting
FSP participation divided by the weighted number of households simulated to be eligible.
The patterns of predicted rates by the education of the reference person among households with
an elderly or a disabled member (Table EQ.3B) are similar to the pattern among all households
(participation declines monotonically with an increase in education), but the dispersion in the
subgroup rates is much smaller, and the differences arc never statistically significant The range
between the highest and lowest predicted rates is about 4 percentage points for households with an
elderly member and 8 percentage points for households with a disabled member. It should be noted
that the sample sizes for the more-than-high-school category are very small, making it difficult to
detect any significant effect.
Among female-headed and two-parent households, the irregular pattern of participation by level
of education might at first seem to contradict the decreasing pattern found for the other groups and
for the overall population. However, the only statistically significant differences-between less than
30
TABLE IH.3B
PARTICIPATION RATES AMONG SUBGROUPS OF THE FSP-EUGIBLE POPULATION,
BY THE EDUCATION OF THE REFERENCE PERSON
Participation Rates Sample
Predicted Observed Size
Households with an Elderly Person 30.2% 32.2% 1346
Less than 12 years 31.1 34.5 1,048
Exactly 12 years 26.9 25.5 209
More than 12 years 26.8 22.4 89
Households with a Disabled Person 55.8 55.7 331
210
87
34
940
484
345
111
Two-Parent Households with Children 42.3 41.0 668
Less than 12 years 41.9 44.8 327
Exactly 12 years 47.6 39.9 241
More than 12 years 31.4 31.1 100
SOURCE: August 1985 SIPP Food Stamp Eligibility File.
NOTES: The predicted participation rates are computed from the probit coefficients presented in
Appendix C. The observed participation rates are computed as the weighted number of
households reporting FSP participation divided by the weighted number of households
simulated to be eligible.
Less than 12 years
Exactly 12 years
More than 12 years
58.1
52.6
49.7
60.1
50.4
43.7
Female-Headed Households
with Children 78.9 69.6
Less than 12 years
Exactly 12 years
More than 12 years
82.4
73.9
77.7
76.4
63.8
59.3
31
12 years and exactly 12 years for female-headed households (Table C.4) and between exactly 12 years
and more than 12 years for two-parent households (Table C.5)--are consistent with the overall
decreasing pattern observed before.
D. THE RACE AND ETHNICITY OF THE REFERENCE PERSON
A comparison of the predicted participation patterns by the race and Hispanic origin of the
household reference person (Table III.4A) yields some interesting results. Among all households,
those whose reference person is black and non-Hispanic (hereafter referred to as black households)
are more likely to participate than households whose reference person is white and non-Hispanic
(hereafter referred to as white households) or Hispanic, while the latter two groups participate at
nearly the same rate.
TABLE m.4A
PARTICIPATION RATES AMONG ALL FSP-ELIGIBLE HOUSEHOLDS,
BY THE RACE AND ETHNICITY OF THE REFERENCE PERSON
Participation Rates Sample
Predicted Observed Size
All FSP-Eligible Households 43.7% 44.2% 3,559
Race/Ethnicity of the Reference Person:
White non-Hispanic 42.7 37.5
Black non-Hispanic 47.7 56.3
Hispanic 39.8 50.4
2,195
963
401
SOURCE: August 1985 SIPP Food Stamp Eligibility File.
NOTE: The predicted participation rates are computed from the probit coefficients presented in Appendix
C The observed participation rates are computed as the weighted number of households reporting
FSP participation divided by the weighted number of households simulated to be eligible.
The latter finding is particularly relevant, in light of the observed rates, which indicate that
Hispanic households participate at a rate that is 13 percentage points higher than among white
32
households.5 Further, the gap in the predicted participation rates of black and white households
is much smaller than the gap in the observed rates, falling from a 19 percentage point difference to
a much lower, although still statistically significant, 5 percentage point difference. This pattern
suggests that most of the difference in participation shown by the observed rates is due to factors that
are correlated with race, rather than to race per se.
We observe a similarly declining gap in racial and ethnic differences in predicted participation
rates among households with an elderly member and among female-headed households (Table III.4B).
While differences are substantial among observed rates, the predicted rates vary only slightly. A net
effect of race and ethnicity on participation does seem to exist for the other two subgroups. Race
seems to be strongly associated with FSP participation among households with a disabled member,
for which a substantial difference (over IS percentage points) exists in the predicted participation
rates of black and white households. Finally, among two-parent households with children, the
distinctive findings are the near equality in the predicted participation rates of black and white
households versus the substantially lower participation rate of households headed by an Hispanic
person (14 percentage points lower than among white households).
To summarize, net differences in the predicted participation rates of black and white households
seem to exist only among households that contain a disabled member, and a small but still significant
difference between the two racial groups is found in the overall population. The participation rates
of Hispanic households and white households tend to be similar, after the influence of all other
factors is controlled for; the only exception is a much lower participation among Hispanic two-parent
households.
Doyle (1990) also found that Hispanic households participate at a higher rate than do white non-
Hispanic households. It is important to remember that Doyle's participation rates are more akin to
the observed rates presented in this paper than to the predicted rates.
33
TABLE III.4B
PARTICIPATION RATES AMONG SUBGROUPS OF THE FSP-ELIGIBLE POPULATION,
BY THE RACE AND ETHNICITY OF THE REFERENCE PERSON
Participation Rates
Predicted Observed
Sample
Size
Households with an Elderly Person 30.2% 32.2% 1,346
White non-Hispanic
Black non-Hispanic
Hispanic
28.8 27.0
33.9 45.3
30.6 38.2
913
338
95
Households with a Disabled Person 55.8 55.7 331
White non-Hispanic
Black non-Hispanic
Hispanic
50.1
65.6
57.4
49.7
66.2
57.7
Female-Headed Households
with Children 78.9 69.6
White non-Hispanic
Black non-Hispanic
Hispanic
78.8
79.3
77.9
64.2
72.7
767
Two-Parent Households
with Children 42.3 41.0
White non-Hispanic
Black non-Hispanic
Hispanic
44.7
45.0
31.7
41.7
44.9
34.3
194
104
33
940
418
383
139
668
434
113
121
SOURCE: August 1985 SD?P Food Stamp Eligibility File.
NOTES: The predicted participation rates are computed from the probit coefficients presented in
Appendix C. The observed participation rates are computed as the weighted number of
households reporting FSP participation divided by the weighted number of households
simulated to be eligible.
34
E. THE PRESENCE OF CHILDREN AND HOUSEHOLD SIZE
We examine the variation in the participation rate by the presence of children only among the
total eligible population (Table IH.5A), and not among the four subgroups, because two of the
groups-female-headed households and two-parent households-are defined on the basis of the
presence of children, and the other two groups contain only a small number of households with
children.
TABLE HL5A
PARTICIPATION RATES AMONG ALL FSP-KIJGIBLE HOUSEHOLDS,
BY THE SIZE OF THE HOUSEHOLD AND THE PRESENCE OF CHILDREN
Participation Rates Sample
Predicted Observed Size
All FSP-Eligible Households 43.7% 44.2% 3,559
Presence of Children Under 18:
Not present 40.6 31.6 1,850
Present 47.1 57.6 1,709
Size of the Household:
1 person 34.5 28.2 1,222
2 persons 45.4 45.6 747
3 persons 53.0 57.4 559
4 persons 48.4 553 464
5 or more persons 48.8 56.0 567
SOURCE: August 1985 SIPP Food Stamp Eligibility File.
NOTE: The predicted participation rates are computed from the probit coefficients presented in Appendix
C. The observed participation rates are computed as the weighted number of households reporting
FSP participation divided by the weighted number of households simulated to be eligible.
The presence of children younger than age 18, independent of other household characteristics
(such as household size), does not have a substantial effect on the predicted participation rate. The
observed rates show a very large difference (26 percentage points) between households with and
without children; the predicted rates show only a small difference (6 percentage points) after the
influence of other factors is controlled for. The large difference in the observed rates is only showing
35
the high correlation between the presence of children younger than age 18 and the receipt of public
assistance.6 The result shown in Table ITJ.5A suggests that, between the presence of children and
receipt of public assistance, it is the latter that has most of the effect on participation among FSP-eligibles.
We now analyze the effect of household size on participation. The overall pattern is that
predicted participation rates increase with the size of the household. Among the overall eligible
population (Table m.5A), we observe a 20 percentage point difference in the predicted participation
rates of one-person and three-person households. The rates for larger households decline slightly
relative to the ratio for three-person households, but the differences are not statistically significant
(Table C.1).
FSP participation also increases with household size among households with a disabled member,
ranging from 46 percent for one-person households to over 69 percent for larger (four-person and
larger) households (Table IH.5B). Although the predicted participation rate is low among three-person
households with a disabled member relative to two- and four-person households, these
differences are not statistically significant (as shown in Table C.3). Among female-headed households
with children, participation increases monotonically with size, but a much smaller gap exists between
the rates for small and large households. Two-parent households show a reverse pattern (that is,
participation declines with household size), but none of the differences is statistically significant
The preceding discussion shows that one-person households participate at lower rates than do
larger households. We also know that the majority of households with an elderly member contain
only one person, while only 20 percent of all nonelderly eligible households are one-person house-
According to SIPP, 77 percent of the FSP-eligible households that were receiving public
assistance in August 1985 were receiving Aid to Families with Dependent Children (Doyle, 1990).
By definition, there are no one-person female-headed households with children, and no two-parent
households with fewer than three persons.
^The converse is also true: 66 percent of eligible persons who live alone are elderly.
36
TABLE HL5B
PARTICIPATION RATES AMONG SUBGROUPS OF THE FSP-ELIGIBLE POPULATION,
BY THE SIZE OF THE HOUSEHOLD
Participation Rates
Predicted Observed
Sample
Size
Households with an Elderly Person 30.2%
1 person
2 persons
3 persons
4 persons
5 or more persons
32.2%
25.7 26.8
31.6 32.5
43.1 47.3
4&5 61.6
51.6 63.4
1,346
812
320
94
48
72
Households with a Disabled Person 55.8 55.7 331
1 person
2 persons
3 persons
4 persons
5 or more persons
Female-Headed Households
with Children
46.2 46.3
57.4 56.6
49.0 56.1
69.9 68.4
69.1 68.8
78.9 69.6
105
94
49
35
48
940
2 persons
3 persons
4 persons
5 or more persons
Two-Parent Households
with Children
71.6 63.9
78.2 67.5
82.2 77.0
83.2 72.3
42.3 41.0
227
293
205
215
668
3 persons
4 persons
5 or more persons
49.1 41.4
40.6 35.1
40.5 44.8
139
213
316
SOURCE: August 1985 SIPP Food Stamp Eligibility File.
NOTES: The predicted participation rates are computed from the probit coefficients presented in
Appendix C. The observed participation rates are computed as the weighted number of
households reporting FSP participation divided by the weighted number of households
simulated to be eligible.
37
holds. This predominance of one-person households among the elderly raises several questions. Is
the low participation rate among households with an elderly member due primarily to an unusually
low tendency by persons who live alone to participate in the FSP? Alternatively, is the low
participation rate among persons who live alone due primarily to a low tendency by the elderly to
participate in the FSP? Which of the two effects prevails as an explanation for the very low
participation rate among older persons who live alone? We conclude this section with a more in-depth
discussion of the interaction of household size and elderly status in determining participation in
the FSP.
In order to auswer these questions, we estimated a variant of the participation equation on which
the results presented in this chapter are based. We estimated a participation equation for the overall
eligible population, including two dummy variables among the regressors~one indicating whether the
household contains an elderly member, and another indicating whether the household contains one
person or more than one person. We also included an interaction term (that is, the product of the
two dummy variables). The other regressors were the same as those used thus far. The estimated
coefficients of this equation allow us to compute separate predicted participation rates for (1)
nonelderly, multi-person households; (2) elderly, multi-person households; (3) noneiderly, one-person
households; and (4) elderly, one-person households. These rates are presented in Table m.6. Before
we discuss these rates, it is important to mention that, while the two separate characteristics (the
presence of an elderly person and the presence of just one person in the household) have large and
statistically significant negative coefficients, the interaction term has a very small and insignificant
positive coefficient, indicating that being a one-person household and being an elderly person does
not reduce participation any further than the sum of the separate effects of these characteristics.
A comparison among the predicted rates in Table m.6 provides some insights into the relative
importance of the "elderly effect" versus the living alone effect" at explaining the lower probability
of FSP participation. Table m.6 shows two complementary measures of the elderly effect-one for
38
multi-person households (the difference between lines (1) and (2), 13.6 percentage points) and one
for one-person households (the difference between lines (3) and (4), 9.3 percentage points). The
measures of the living-alone effect are derived similarly-one for nonelderly households (the
difference between lines (1) and (3), 20.8 percentage points) and one for elderly households (the
difference between lines (2) and (4), 16.5 percentage points). Overall, the living-alone effect is larger
than the elderly effect, although the latter is also substantial.
These simple calculations suggest a resolution of the two questions. Something idiosyncratic
about households headed by an elderly person seems to lead to their low FSP participation rate.
Ponza and Wray (1990) found that elderly persons decide not to participate in the available USDA
TABLE m.6 .
PARTICIPATION RATES AMONG ALL FSP-ELIGIBLE HOUSEHOLDS,
BY THE SIZE OF THE HOUSEHOLD AND THE
PRESENCE OF AN ELDERLY MEMBER
Participation Rates Sample
Predicted Observed Size
All FSP-Eligible Households 43.7% 44.2% 3,559
Presence of Elderly Member and
Size of the Household:
(1) Nonelderly, multiperson
(2) Elderly, multiperson
(3) Nonelderly, one-person
(4) Elderly, one-person
55.2
41.6
34.4
25.1
55.6
40.1
30.6
26.8
1,877
460
410
812
SOURCE: August 1985 SIPP Food Stamp Eligibility File.
NOTE: The predicted participation rates are computed from the probit coefficients presented in Appendix
C The observed participation rates are computed as the weighted number of households reporting
FSP participation divided by the weighted number of households simulated to be eligible.
programs, including the FSP, for several reasons: they feel that they do not need the assistance or
would rather rely on other sources; they dislike certain features of the programs (e.g., the application
39
process, the location of the program office, or the form of the program benefit); they believe that
they are ineligible; or their decision is based on some combination of all these reasons. In particular,
they found that many elderly persons do not participate in the FSP because they are entitled only to
a small benefit amount
Independent of the elderly effect, persons who live alone also seem to have an even lower
propensity to participate in the FSP. These persons might be more likely to rely on other households
for their food consumption and meal preparation, so that the in-kind benefits provided by the FSP
would be relatively less valuable to them. The attempt in SIPP to include "money received from
relatives and friends" among the sources of income might not be sufficient to capture the complexity
of the inter-household transfer of resources, most ofwhich might be in-kind (such as health insurance
coverage, the provision of clothing and transportation, and food sharing). Therefore, on average,
one-person households might have more resources available to them than is revealed by their income
Q
and assets, which could partially explain their very low rate of FSP participation.
An alternative explanation, which can easily be extended to small households, is associated with
the importance of the costs of participation. More specifically, both monetary and nonmonetary costs
are involved in applying for benefits and in obtaining the coupons every month. At the same time,
the size of the benefit increases with the size of the household, everything else held constant.
Small households are thus more likely to feel that the size of the benefit is insufficient to compensate
for the costs of participation. Whether the latter is a "size effect" or a "benefit effect" is an important
question, and one difficult to answer, since the size of the benefit depends strictly on the size of the
household.11 Chapter V discusses this issue more extensively.
9Over 25 percent of all FSP-eligible nonelderry, nondisabled individuals who live alone reported
zero income in August 1985.
10More precisely, the size of the benefit increases with the size of the food stamp unit, but the
distinction is immaterial for this discussion.
^More precisely, it is the guarantee amount (Le., the benefit for a household with zero net
income) that depends strictly on the size of the food stamp unit
40
IV. FSP PARTICIPATION AND THE ECONOMIC
CHARACTERISTICS OF HOUSEHOLDS
This chapter examines differences in participation in the FSP by the economic characteristics of
households. In particular, we examine differences in household participation rates by (1) the ratio
of the household's income to the OMB poverty threshold, (2) whether the household receives public
assistance, (3) whether the household has earnings, and (4) whether the household has positive assets.
As in Chapter m, this analysis applies to all FSP-eligible households (Table A in each set of
tables) and then to the four demographic subgroups of the eligible population: households with an
elderly or a disabled member, female-headed, and two-parent households with children (Table B in
each set).
A. HOUSEHOLD INCOME AS A PERCENTAGE OF THE POVERTY THRESHOLD
Before we discuss the relationship between participation and household gross income, it is useful
to recall that we are using as explanatory variables the characteristics of the Census household-that
is, the group of individuals who live in the dwelling unit In Chapter II we decided to use the
characteristics of the Census household on the grounds that the food stamp unit as defined by
program regulations is not known for those who do not report FSP participation because SIPP asks
about the composition of the food stamp unit only for those households that report participation.
Using a "double standard" (the characteristics of the food stamp unit for participants and the
characteristics of the Census household for nonparticipants) might bias the estimates of the effects
of the explanatory variables on participation. Some characteristics might appear to affect
participation only because they have been defined differently for participants and for nonparticipants.
From this standpoint, the explanatory variables that are a major concern are those constructed
from "summing over" all household members, such as income or household size, while variables that
represent the characteristics of the reference person are not a concern because the reference person
41
is not likely to change according to different definitions of the household unit For example, let us
hypothesize that household members with earnings are less likely than individuals with no earnings
to be reported to the food stamp office as part of the food stamp unit-that is, as part of the group
of individuals customarily purchasing and preparing food together. The survey would capture the
exclusion of such members from the food stamp unit only among participating households. Thus,
households with larger earnings would be overrepresented among nonparticipating households, and
the estimated relationship between participation and earnings (and possibly income) would be
distorted toward a negative value.
To avoid this potential distortion, we used the characteristics of the Census household as
explanatory variables for both participants and nonparticipants. However, the definition of the
income variable somewhat complicates the analysis. The income variable used as an explanatory
variable in the participation equation no longer coincides with the gross income used for determining
FSP eligibility (Chapter n, Section A). For example, while only elderly and disabled households are
exempt from the gross income screen (130 percent of the OMB poverty threshold), our sample
contains a substantial number of nonelderly and nondisabled households who are simulated to be
eligible but whose household income exceeds 130 percent of the OMB poverty threshold. More
generally, the distribution of household income among FSP participants in our sample no longer
coincides with the distribution of gross income among participants observed in administrative data.
This discrepancy between household income and gross income used in the eligibility determination
led us to adopt a different breakdown of the income/poverty variable than typically used in FSP
participation studies (for example, by Doyle, 1990). In particular, we do not show a separate "above
130 percent of poverty" category.
With these caveats in mind, we now examine the estimated relationship between participation
and household income. In Tables IV.lA, we see that this relationship has an overall negative pattern,
which is in accordance with expectations: households that have greater need (a lower income to
42
poverty ratio) are more likely to be served by the FSP than less needy households. The only
exception to this negative pattern pertains to households that report DO income at all; among these
households, the participation rate is lower than among households that have income between 1 and
50 percent of the poverty threshold. Before discussing households that have positive income, we
explore this odd result for zero-income households in more detail.
TABLE IV.1A
PARTICIPATION RATES AMONG ALL FSP-ELIGBBLE HOUSEHOLDS,
BY HOUSEHOLD INCOME RELATIVE TO THE POVERTY THRESHOLD
Participation Rates Sample
Predicted Observed Size
All FSP-Eligible Households 43.7% 44.2% 3,559
Household Income as a Percent
of the Poverty Threshold:
Zero 41.7 24.9 160
1 to 50 percent 58.6 68.0 650
51 to 75 percent 55.7 59.8 654
76 to 100 percent 44.2 41.1 910
101 percent or more 30.2 26.4 1,185
SOURCE: August 1985 SIPP Food Stamp Eligibility Fde.
NOTE: The predicted participation rates are computed from the probit coefficients presented in Appendix
C The observed pai ticipation rates are computed as the weighted number of households reporting
FSP participation divided by the weighted number of households simulated to be eligible.
1. Zero-Income Households
A priori, one would expect that households that do not receive income would participate in the
FSP at relatively high rates, since they apparently have no other resources. However, previous
research based on survey data has found that estimated participation rates among households that
report no income are surprisingly low. For example, using data from the 1979 Income Survey
Development Program (ISDP), Czajka (1981) found that the observed participation rate among
43
households with zero gross monthly income was almost 38 percentage points lower than the rate
among households whose income was 1 to 50 percent of the poverty threshold (5 percent, compared
with 43 percent).
Our findings on zero-income households are somewhat less dramatic. First, we find that a lower
proportion of all eligible households report zero income: only 4.5 percent of the eligible population
report zero income, compared with about 10 percent of the sample of eligible households examined
by Czajka. The frequency of zero reported income varies considerably by demographic subgroup.
It is very low among households with an elderly member, and (by definition) none of the households
with a disabled member has zero income.2 Zero income is also rarely reported by female-headed
households (2.1 percent), while the proportion of zero-income two-parent households is close to the
overall average (4.6 percent). This finding implies that the bulk of zero-income households comprise
households that are excluded from the four demographic subgroups examined here. In fact, almost
halfoi all zero-income households constitute individuals who live alone, are younger than age 60, and
are not disabled, while these individuals represent less than 10 percent of all FSP-eligible households.
Both the predicted and observed participation rates among zero-income households in SIPP are
below those for households at higher income levels. However, while Czajka found that only 4.6
percent of zero-income households participate in the FSP, we obtain a 25 percent observed rate and
a 42 percent predicted rate (Table IV.1A). The large difference between observed and predicted
rates reinforces the notion that the characteristics of zero-income households tend to differ from
those of the rest of the FSP-eligible population: in the predicted participation rate, the multivariate
adjustment has removed the effect of nonincome variables; in the observed rates, this effect remains.
Although higher than their observed rate, the predicted rate of zero-income households' is still 17
1These figures are weighted averages of the participation rates calculated for the three months
of the ISDP examined by Czajka.
2Disabled persons are defined as those individuals who collect SSI, Social Security, or Veteran's
benefits due to their disability.
44
percentage points below that of households in the next higher income category, 1 to SO percent of
the poverty threshold. As indicated in Table C.1, the latter difference is statistically significant
Although less dramatic than in Czajka's study, this pattern of participation among zero-income
households in SIPP is still at variance with our expectations. It seems counterintuitive that
households in (apparently) dire need would be less likely to seek FSP benefits than less needy
households. A plausible explanation for the low participation of zero-income households is the
underreporting of income. Let us hypothesize that the number of households that truly do not have
income of any type is very small. At the same time, the number of households whose income is high
enough to make them ineligible for the FSP is very large. If even a very small proportion of these
ineligible households erroneously report no income and are thus misclassified as eligible, the absolute
number of these households would easily be large enough to outweigh the number of households that
truly do not have income, thereby creating the perverse pattern of low participation that we observe
for the entire group of seemingly zero-income households.
2. Households with Positive Incomes
In general, and in line with expectations, participation in the FSP declines as household income
increases relative to the poverty threshold. The predicted participation rate is almost 60 percent
among households in the lowest income bracket (1 to SO percent of poverty), and only 30 percent
among households whose income is above the poverty line. As shown in Table C.1, the differences
in the predicted participation rate between any two contiguous income brackets are statistically
significant, with the exception of the difference between the 1 to 50 percent and 51 to 75 percent
of poverty categories, which is small and not significant
The participation pattern by household income of all FSP-eligible households observed in Table
IV.1A does not exactly replicate the participation pattern of the four demographic subgroups in Table
IV.IB. For all subgroups except female-headed households, the predicted participation at 1 to 50
percent of poverty is marginally lower than the rate at 51 to 75 percent of poverty. However, these
45
TABLE IV.1B
PARTICIPATION RATES AMONG SUBGROUPS OF THE FSP-ELIGIBLE POPULATION,
BY HOUSEHOLD INCOME RELATIVE TO THE POVERTY THRESHOLD
Participation Rates
Predicted Observed
Sample
Size
Households with an Elderly Person 30.2%
Zero
1 to 50 percent
51 to 75 percent
76 to 100 percent
101 percent or more
32.2%
20.8 14.8
29.8 31.4
40.9 40.9
38.0 38.9
21.6 24.1
1,346
7
79
192
579
Households with a Disabled Person 55.8 55.7 331
1 to 50 percent 61.9 66.8
51 to 75 percent 67.1 71.7
76 to 100 percent 57.9 59.1
101 percent or more 46.8 41.9
Female-Headed Households
with Children 78.9 69.6
Zero 58.0 29.6
1 to 50 percent 86.8 87.4
51 to 75 percent 84.0 80.1
76 to 100 percent 70.3 59.6
101 percent or more 64.4 36.7
16
87
87
141
940
20
320
244
157
199
Two-Parent Households
with Children 42.3 41.0 668
Zero
1 to 50 percent
51 to 75 percent
76 to 100 percent
101 percent or more
47.0 28.6
58.9 57.2
60.2 60.5
35.6 33.6
29.3 29.9
31
134
107
160
236
SOURCE: August 1985 SIPP Food Stamp Eligibility File.
vIOTES: The predicted participation rates are computed from the probit coefficients presented in
Appendix C. The observed participation rates are computed as the weighted number of
households reporting FSP participation divided by the weighted number of households
simulated to be eligible.
46
differences are not statistically significant (Table C.2 through C.5). For all demographic groups
except elderly households, the largest drop in participation takes place between 51 to 75 percent and
76 to 100 percent of the poverty threshold.
B. THE RECEIPT OF PUBLIC ASSISTANCE
Not surprisingly, the receipt of public assistance (PA) is a strong predictor of a household's
participation in the FSP, as shown in Tables IV.2A. (In this report, public assistance refers to SSI,
AFDC, general assistance, foster child care payments, and other welfare.) Households that receive
TABLE IV.2A
PARTICIPATION RATES AMONG ALL FSP-ELIGIBLE HOUSEHOLDS,
BY THE RECEIPT OF PUBLIC ASSISTANCE AND
THE PRESENCE OF EARNINGS AND ASSETS
Participation Rates Sample
Predicted Observed Size
All FSP-Eligible Households 43.7% 44.2% 3,559
Do not receive public assistance 25.5 22.0 2,094
Receive public assistance 71.0 76.9 1,465
Do not have earnings 46.9 48.7 2300
Have earnings 37.9 35.6 1,259
Do not have countable assets 50.0 572 1,996
Have countable assets 35.9 27.1 1,563
SOURCE: August 1985 SIPP Food Stamp Eligibility File.
NOTE: The predicted participation rates are computed from the probit coefficients presented in Appendix
C The observed participation rates are computed as the weighted number of' useholds reporting
FSP participation divided by the weighted number of households simulated to be eligible.
^Previous research has consistently found a strong positive relationship between participation in
the FSP and participation in public assistance programs, as shown in Table A.1.
47
public assistance are between two and three times more likely to participate in the FSP than are
households that do not Among all eligible households, the difference in the predicted participation
rates between households that do not receive public assistance and those that do is a dramatic 45
percentage points, from a 26 percent rate to a 71 percent rate. The difference is even larger among
two-parent households, from 28 percent to 83 percent (Table IV.2B).
It is noteworthy that the differentials in the predicted rates of PA recipients and PA
nonrecipients are only marginally smaller than in the observed rates. For example, among all
households, the observed rates are 77 and 22 percent, respectively, while the predicted rates are 71
and 26 percent. In other words, the wide differential in the observed rates is not due to the fact that
other observable factors are correlated with the receipt of public assistance: FSP-eligible households
seem to have a true propensity to apply for food stamps according to whether they receive or do not
receive public assistance, even when their income and other characteristics differ.
This large difference in FSP participation by PA receipt and PA non-receipt is subject to several
interpretations. The difference could, at least in part, reflect a true effect; for example, households
that enroll in the AFDC program might be sent automatically to the FSP caseworker by the AFDC
caseworkers, while similar households that do not apply for AFDC have less chance to come in
contact with the FSP caseworker. On the other hand, the apparent PA effect on food stamp
participation could be due to the fact that the decision to apply for food stamps is part of a more
general decision to apply for the available "welfare package." In this case, AFDC and FSP
participation are the joint outcomes of some underlying decision process that cannot be observed, and
which might involve decisions about living arrangements or labor force participation.
C. THE RECEIPT OF EARNINGS
For the most part, previous research has found that households that receive earnings, or those
in which the head of household is employed, are significantly less likely to participate in the FSP than
are households that do not receive earnings, even when total income is held constant. We find some
48
TABLE IV.2B
PARTICIPATION RATES AMONG SUBGROUPS OF THE FSP-ELIGIBLE POPULATION,
BY THE RECEIPT OF PUBLIC ASSISTANCE AND
THE PRESENCE OF EARNINGS AND ASSETS
Participation Rates Sample
Predicted Observed Size
Households with an Elderly Person 30.2% 32.2% 1,346
814
532
1,147
199
669
677
Households with a Disabled Person SS.8 SS.7 331
76
255
262
69
203
128
Do Not Receive Public Assistance
Receive Public Assistance
18.9
51.4
16.7
57.9
Do Not Have Earnings
Have Earnings
30.2
30.0
30.8
41.5
Do Not Have Countable Assets
Have Countable Assets
37.2
23.9
43.7
20.9
Do Not Receive Public Assistance
Receive Public Assistance
33.4
62.5
32.0
63.1
Do Not Have Earnings
Have Earnings
59.2
43.0
58.5
43.4
Do Not Have Countable Assets
Have Countable Assets
58.1
52.1
61.8
46.2
Female-Headed Households
with Children 78.9 69.6
Do Not Receive Public Assistance
Receive Public Assistance
45.7
90.7
30.4
92.4
Do Not Have Earnings
Have Earnings
84.4
68.6
86.1
43.5
Do Not Have Countable Assets
Have Countable Assets
81.1
713
77.0
46.5
940
341
599
566
374
708
232
49
TABLE IV.2B (continued)
Participation
Predicted
Rates
Observed
Sample
Size
Two-Parent Households
with Children 423 41.0 668
Do Not Receive Public Assistance
Receive Public Assistance
273
83.2
26.9
84.7
495
173
Do Not Have Earnings
Have Earnings
38.0
443
52.0
353
226
442
Do Not Have Countable Assets
Have Countable Assets
51.1
36.0
56.6
29.7
284
384
SOURCE: August 1985 SIPP Food Stamp Eligibility File.
NOTES: The predicted participation rates are computed from the probit coefficients presented in
Appendix C. The observed participation rates are computed as the weighted number of
households reporting FSP participation divided by the weighted number of households
simulated to be eligible.
50
support for this finding, but not for all demographic groups, and the effect of earnings is small,
particularly when compared with the effect of public assistance. Among the overall eligible
population (Table IV.2A), the difference by receipt of earnings is statistically significant but not very
large, about 9 percentage points. About one-third of all FSP-eligible households in SIPP report
earnings.
Among female-headed households with children (Table IV.2B) the effect of earnings is
relatively large (and statistically significant); the predicted participation rates among female-headed
households with and without earnings are 69 and 84 percent, respectively. It is important to
remember that this differential in predicted participation does not merely reflect the differential
between those that receive and do not receive public assistance, because PA receipt is included in
the participation equation.
Among households with a disabled person, the participation differential by the presence of
earnings is large (16 percentage points), but, due to the small proportion of households that report
any earnings, the difference is not statistically significant (Table C.3). Among households with an
elderly member, the presence of earnings has no impact on participation, and the proportion that
report earnings is very small. Among two-parent households with children the pattern of participation
by presence of earnings seems to be reversed. The predicted participation rate of two-parent
households is higher (44 percent), rather than lower, than the rate for those without earnings (38
percent). However, this difference is not statistically significant (Table C.5). Surprisingly, the
observed rates exhibit the opposite, and more usual, pattem-35 percent and 52 percent for
households with and without earnings, respectively.
D. THE PRESENCE OF ASSETS
Among all eligible households and among three of the subgroups (households with an elderly
member, female-headed households, and two-parent households with children), households with
51
positive assets participate at significantly lower rates than do households without assets. In most
cases, this predicted differential is about IS percentage points. The only apparent exception to this
pattern pertains to households with a disabled member, for which the differential is smaller (6
percentage points) and not statistically significant
4In this report, we consider only assets that are countable under the FSP.
52
V. THE RELATIONSHIP BETWEEN FSP PARTICIPATION
AND THE FOOD STAMP BENEFIT AMOUNT
This chapter investigates the relationship between the size of the food stamp benefit and the
probability of FSP participation. From a public policy perspective, this relationship is more important
than the relationship between participation and the demographic and economic characteristics of
households. Policymakers have only a limited ability to affect the demographic and economic
characteristics of households, particularly in the short run, but are able to change the level of food
stamp benefits by adjusting the parameters of the program, such as the maximum allotment, the
benefit reduction rate, and shelter, medical, and child care deductions.
In fact, most of the FSP reform proposals considered periodically by Congress imply changes in
the amount of benefits for at least some eligible households. Thus, forecasting the impact of program
reforms on participation requires an understanding of how participation varies across households that
qualify for different levels of benefits, and, in particular, how a change in the benefit amount for a
given household affects that household's probability of participation. In recognition of the
importance of the benefit-participation relationship, and in light of the methodological problems
involved in estimating such a behavioral relationship, we devote a separate chapter and a more in-depth
analysis to this topic.
The remainder of this chapter is organized as follows. Section A evaluates the estimates of the
benefit-participation relationship found in previous studies and discusses the methodological problems
associated with these estimates. Section B contains our estimates of the benefit-participation
relationship based on the 1985 SIPP data.
Congress and program administrators also have partial control over aspects of the program that
might affect the costs of participation, such as work-registration requirements for able-bodied adult
recipients, the geographical distribution of food stamp offices, the amount of documentation required
for verifying income and expenses, and the type of benefit issuance. However, typical household
surveys, such as SIPP and CPS, do not contain any information on the costs that households incur
when they participate in the FSP.
53
A. PREVIOUS ESTIMATES OF THE BENEFIT-PARTICIPATION RELATIONSHIP
The empirical evidence on the relationship between the benefit amount and FSP participation
is mixed. On an a priori basis, one would expect that the data would show a positive relationship
between participation and potential benefit amounts. In other words, one would expect that a
household entitled to a large food stamp benefit would be more likely to participate in the FSP than
would a household entitled to a smaller benefit, everything else held constant. The primary reason for
this expectation lies in the existence of costs of participation-that is, the monetary and nonmonetary
costs that participants incur in applying for benefits and obtaining the coupons each month. Most
of these costs are fixed-that is, they do not vary with the amount of the benefit. Thus, it seems
plausible that as the amount of the benefit rises without a contemporaneous change in the costs of
participation, the probability of participation increases. However, existing studies have yielded
divergent findings about both the sign and the magnitude of this effect.
Some studies, such as Smallwood and Blaylock (1985), Johnson et al. (1982), and Devaney and
Fraker (1987), have found a positive sign for the effect of potential benefits on participation. All
three of these studies used a linear specification for the benefit variable (explained later in this
section), and were based on the 1977-78 Nationwide Food Consumption Survey, Low-Income sample
(NFCS-LI). Despite these similarities, the magnitude of the estimated benefit effect varied
substantially across the three studies (and even within each study), depending on how the
participation equation was specified and how the benefit variable was constructed for nonparticipating
households.
Johnson et al. used two methods to construct the potential benefit amount. The first method
entailed using rather crude proxies for the benefit amount-namely household's maximum allotment
and the size of the household. The second method entailed imputing the potential benefit for
nonparticipating households using the self-reported benefit amount and other characteristics of
54
participating households. The estimates of the benefit effect varied widely across the different
specifications, in part because not all the measures of potential benefits were expressed in the same
units. But even if one restricts the comparison to the estimates obtained with the imputation
procedures, the differences are stiil substantial, as shown in the first two columns of Table V.l. The
effect estimated with one imputation procedure is more than twice that estimated with the other
procedure.
TABLE V.l
ESTIMATES OF THE EFFECT OF THE BENEFIT AMOUNT
ON THE PROBABILITY OF FSP PARTICIPATION
Data Set/Yeai NFCS 1977-78 PSID 1979
Author(s)
Johnson et al.
(1982)
Smallwood
& Blaylock
(1985)
Devaney
& Fraker
(1987)
Coe
(1983)
Method Benefits imputed by
OLS Tobit
No. of children
excluded included
Percentage point difference
in the probability of
participation related to a
$10 difference in the
monthly benefit amount
2.3 4.8 1.5 1.7 0.6 -0.10
NOTE: The estimates presented by the authors were transformed to increase comparability. However, the
comparability is far from perfect, due to differences in sample definitions, model specifications, and
reference years. These studies are based on the Nationwide Food Consumption Survey, Low-Income
sample (NFCS-LI) and on the Panel Study of Income Dynamics (PSID).
Although the primary objective of the studies by Devaney and Fraker and Smallwood and
Blaylock was not to analyze FSP participation, each study included a participation equation in its
model of food expenditures to control for differences between FSP participants and nonparticipants
in factors that could affect expenditures on food. The two studies obtained very similar estimates of
^Two alternative statistical techniques were used to perform the imputation: one technique was
ordinary least squares (OLS) regression corrected for selection bias using the Heckman correction
procedure; the second method was a Tobit estimation procedure.
55
the benefit effect on participation, but they are much smaller than those obtained by Johnson et al.
(Table V.l).3
None of these studies included household size or the number of children among the explanatory
variables in the participation equation. Coe (1983) found that the estimates of the benefit effect
were very sensitive to the inclusion of the number of children. When this variable was excluded from
the equation, the estimated effect was positive and significant (although three times smaller than that
estimated by Devaney and Fraker). When the number of children was included, the effect became
negative and significant, indicating that the positive effect obtained in the first specification should
be interpreted as an effect of household size and composition, rather than as a net benefit effect
(Table V.l).
All of the studies discussed thus far in this chapter used a linear specification for the benefit
variable. A linear specification does not allow the benefit-participation relationship to change in
magnitude (nonlinearity) or in sign (nonmonotonicity) over different ranges of the benefit variable.
The study by Czajka (1981), based on 1979 Income Survey Development Program (ISDP) data,
relaxed the linearity assumption by treating the benefit amount as a discrete variable of benefit ranges
and including in the participation equation a dummy variable for each discrete interval. Czajka found
that the benefit-participation relationship was positive overall but nonmonotonic-that is, it increased
over certain ranges of benefits but decreased over others.
These contradictory findings in the literature are symptomatic of the methodological problems
involved in analyzing the benefit-participation relationship. Based on the literature review, as well
as on our own experience, we have identified the following three broad methodological issues:
3Devaney and Fraker used a Tobit regression to impute the benefit amount for nonparticipants.
Smallwood and Blaylock did not report the method they used to derive the benefit amount for
nonparticipants.
Johnson et al. included household size only as a proxy for the benefit amount, and not
simultaneously with it.
56
1. The benefit amount cannot be observedfor nonparticipants. The benefit amount must
be imputed or simulated on the basis of the household's demographic and
economic characteristics as reported in the survey, ihus, the simulated or imputed
benefit variable is sensitive to a wide range of reporting errors and missing
information. For example, households that underreport income during the
interview are simulated to be eligible for a benefit amount larger than the amount
for which they are actually eligible.
2. The benefit amount does not vary independently from household characteristics.
Differences in the FSP benefit amount across households at a given point in time
depend exclusively on differences in the characteristics of these households, notably
differences in income, household size, and allowable deductions. If all the
household characteristics were to enter the participation equation in exactly the
same form as they enter the benefit determination formula, they would be perfectly
collinear with the benefit amount, and the benefit effect on participation could not
be identified. In order to identify this effect with cross-sectional data, one must
impose: (a) exclusion restrictions, which means that some of the determinants of the
benefit amount (e.g. the shelter deduction) are assumed a priori not to affect the
participation decision, so that they are excluded from the participation equation;
or (b) functional form assumptions, which is to say that the determinants of the
benefit amount enter the participation equation in a different form than they enter
the benefit determination formula. In the next section we discuss in more detail
which restrictions and functional form assumptions we imposed in order to identify
the benefit effect on participation.
3. The complexity of the participation decision may go beyond our modelling ability and
the availability ofdata. The decision process undertaken by households in choosing
whether to participate in the program is likely based on factors and circumstances
that are not adequately reflected in survey data nor captured by a simple one-equation
econometric model. The omission of some of these circumstances might
distort the estimates of the benefit-participation relationship. One example is a
lack of knowledge about program eligibility rules by nonparticipating households.
Households eligible for small benefit amounts may be less likely to be aware of
their eligibility, but a simple model attributes their lower participation rate to the
smaller benefit amounts, rather than to their lack of knowledge.
B. SIPP-BASED ESTIMATES OF THE BENEFIT-PARTICIPATION RELATIONSHIP
Our approach to the analysis of the benefit-participation relationship is more elaborate than that
found in the literature, and is designed to address some of the methodological concerns discussed in
the previous section. Moreover, our approach is more complex than that followed in Chapters III
and IV to analyze the relationship between participation and the other household characteristics.
Therefore, a brief overview of the methodology is in order.
57
To remedy the fact that the benefit amount for nonparticipants cannot be observed, we simulated
the benefit amount on the basis of the current characteristics of food stamp households in SIPP.
Measurement error and the lack of some information in SIPP (for example, on medical expenses)
make this simulation imperfect. However, we believe that this solution represents a substantial
advance over regression-based imputation methods or the use of crude proxies, such as household
size. It is important to note that we simulated the benefit amount for all households, regardless of
whether they were in fact receiving and reporting a benefit amount. Using reported benefits for
participants but simulated benefits for nonparticipants would create a "double standard" that could
bias the estimates of the benefit effect.
We imposed several assumptions on the participation equation that help identifying the benefit
effect. Most of these are ad hoc assumptions-that is, they are not suggested by any formal behavioral
model of program participation.
Our participation equation excludes the amounts of the allowable deductions.
However, the presence of some deductions is captured by the explanatory variables
included in the equation: (a) the receipt of earnings variable captures the earnings
deduction; (b) the presence of elderly captures the possibility that a medical
deduction is claimed; and (c) the presence of children captures the possibility that
the dependent care deduction is claimed. However, none of these explanatory
variables enters the participation equation in exactly the same form as they enter
the benefit determination formula. For example, the amount of earnings
determines the earnings deduction, while we control only for the receipt of
earnings. Our participation equation totally excludes the excess shelter deduction,
since it is not captured by any of the explanatory variables.
Household size enters the benefit determination formula through the maximum
allotment, which increases gradually with household size, in order to reflect
economies in food consumption that can be realized by larger households. Our
participation equation includes household size as a categorical variable—that is, as
a series of dummy variables for each household size, which allows also for a
nonlinear pattern. Thus, in this case, we do not impose any restriction that helps
identify the benefits effect. In other words, the benefit effect that we estimate is
a true effect, net of any household-size effect.
Table II.2 (page 15) shows that the average simulated benefit for participants is 2.6 percent
higher than the average benefit observed in the FSP administrative data for the same period.
58
Income enters the benefit determination formula as income net of allowable
deductions, while our participation equation controls for gross income divided by
the poverty threshold and expressed as a categorical variable.
Finally, all explanatory variables in the participation equation are defined for the
Census households, while the benefit amount is computed for the (simulated) food
stamp unit For about 13 percent of the observations, the Census household and
the simulated food stamp unit do not coincide. These cases reduce the overall
correlation between the simulated benefit amount and the variables that enter into
the benefit determination formula.
The last issue pertains to the specification of the benefit variable itself. We estimate two
different versions of the participation equation. In the first model, the benefit variable is specified
in discrete intervals, in the same manner that we treated the other continuous variables-age,
education, income, and household size-in the previous two chapters. This specification allows us to
compute and compare observed and predicted participation rates for each discrete benefit interval.
In the second model, we treat the benefit amount as a continuous variable, which is necessary in
order to simulate the effect of program reforms on participation. In a simulation context, one must
be able to simulate the effect of any change in the benefit amount, including a change that may be
too small to move a given household from one benefit interval to the next.
1. FSP Participation and the Benefit Amount The Discrete Case
The results for all FSP-eligible households are shown in Table V.2A. The predicted participation
rates by level of benefits show an overall increasing pattern. Predicted participation rates range from
35 percent for households entitled to $10 wor