Analysis of Food Stamp Program Participation and Food Expenditures.pdf by zhaonedx


									              Analysis of Food Stamp Program
                   Participation and Food
                         David M. Smallwood and James R. Blaylock

             A two equation model is developed to examine jointly the determinants of household food
         stamp program participation and program effects on food expenditures. The model is unique
         in that it postulates that the participation decision is based on a cost-benefit ratio, selected
         socioeconomic characteristics, and the potential for increasing both food and nonfood expen-
         ditures. Data from the 1977-78 USDA Nationwide Food Consumption Survey Supplemental
         Low Income Sample is used to estimate the model. Findings suggest that households, in making
         the participation decision, place equal value on the potential for increasing their food and
         nonfood expenditures. However, at the margin, bonus stamp income is found to have more
         than twice the impact of money income on food expenditures. The model's potential for policy
         analysis is also examined.

   A fundamental objective of the Food                        Many microeconomic analyses of the
Stamp Program (FSP) is to increase the                     FSP have modeled the household's deci-
diet quality of low income households via                  sion to participate in the program sepa-
increasing their food expenditures to that                 rately from the program's effect on food
of a reference standard. To achieve this                   expenditures (Neenan and Davis; Epper-
goal, eligible households choosing to par-                 son et al.; Huang et al.; Lane et al.). In
ticipate in the program are provided with                  general, a single equation logit or probit
an income subsidy in the form of food                      model has been used to examine the par-
stamps which can only be spent on food                     ticipation decision as a function of house-
for home consumption.l The effectiveness                   hold characteristics and income. Food ex-
of the program in achieving this goal can,                 penditures are usually modeled separately
in. part, be evaluated by analyzing partic-                from the participation decision and spec-
ipation rates of the target population and                 ified as a function of household charac-
the subsequent effect of this in-kind trans-               teristics, money income, bonus stamp in-
fer on food expenditures.                                  come, and an FSP participation variable.
                                                              The purpose of this paper is to develop
David M. Smallwood and James R. Blaylock are ag-           and estimate an economic model of be-
ricultural economists with the United States Depart-       havior which considers simultaneously the
ment of Agriculture, Economic Research Service,
                                                           likelihood of participation by eligible
National Economics Division. The views expressed
in this paper are not necessarily those of ERS or          households and the effect of program par-
USDA.                                                      ticipation on food expenditures. The pro-
1 Food  stamps with several minor exceptions may only      posed model postulates that a household's
 legally be used to purchase foods at authorized "re-      decision to participate in the Food Stamp
 tail food establishments" which are intended for use      Program is influenced by the potential for
 and/or preparation at home. Food stamps may not           enhancing both its food and nonfood ex-
 be used to purchase foods traditionally referred to       penditures. Although food stamps may
 as away-from-home food, such as at fast-food es-
 tablishments and restaurants. Henceforth, unless
                                                           only legally be used to purchase food,
 otherwise specified, the word food will be used to        households are afforded an opportunity to
 denote food which may be purchased with stamps.           reallocate some money to nonfood use that

Western Journalof Agricultural Economics, 10(1): 41-54
© 1985 by the Western Agricultural Economics Association
July 1985                                                      Western Journal of Agricultural Economics

was previously allocated to food. The                   stamps, termed the purchase require-
model disaggregates net program benefits                ment, was based on both household size
(bonus food stamps) into these two com-                 and income. The difference between the
ponents and allows each to have poten-                  allotment and the purchase requirement,
tially different effects on participation               termed the bonus, is the net subsidy or
rates, and hence, household food expen-                 transfer of in-kind income to the house-
ditures. The model also incorporates a                  hold.
cost/benefit ratio which measures the rel-                 A conventional economic model of
ative cost of program entry to the total                household behavior as developed by
monetary benefits accruing to household                 Southworth and advanced by Mittelham-
participation. Hopefully, disaggregation                mer and West; Clarkson; Huang et al.,
of net program benefits together with the               and others provides the conceptual frame-
cost/benefit ratio will allow for improved              work for this study.3 Since this model is
estimates of a household's behavioral re-               well known, only the highlights will be
sponses to FSP policy instruments. Also,                presented here. Briefly, participant be-
because the model contains explicit FSP                 havior is modeled within the classical
policy instruments, it may be used to sim-              household utility maximizing framework
ulate the effects of proposed program                   of demand theory and incorporates a
changes on food expenditures and pro-                   modified income constraint to allow for
gram participation.                                     the in-kind provisions of the FSP. Within
   The following section contains the de-               this framework, the household is assumed
velopment of an economic model of par-                  to maximize utility subject to a budget
ticipant behavior in the FSP. An outline                constraint which is determined, in part,
of the proposed statistical model is pre-               by FSP participation and program rules.
sented in the third section. Data and vari-                The above model implies that the effect
able specification are discussed in the                 of bonus stamps on food expenditures is
fourth part. The fifth section contains em-             identical to that of money income for those
pirical results and a discussion of their rel-          households that spend more than their al-
evance to policy analysis. A section con-               lotment of stamps on food at home. Only
taining conclusions and future research                 in the case where the allotment exceeds
directions concludes the paper.                         desired food expenditures is the effect of
                                                        the FSP on food expenditures hypothe-
                                                        sized to be larger than that of a cash trans-
Theoretical Framework                                   fer. Empirically, the number of house-
                                                        holds in this latter group appears to be
   Prior to elimination of the purchase re-             limited. Food expenditure data for partic-
quirement in 1979, the value of the stamps              ipating and eligible nonparticipating
received, termed the allotment, was based               households contained in the supplemental
on household size. 2 The amount an eligi-
ble household was required to pay for the
                                                        3Household income has traditionally been consid-
                                                         ered exogenous in FSP models. While the authors
2 The assumption of a purchase requirement is kept       believe that the labor supply effects of the Food
 throughout this discussion because of its importance    Stamp Program are important, especially when
 as a policy instrument. The program as it exists        considered jointly with other means-tested welfare
 today can be expressed in this framework by setting     programs, such as Aid to Families with Dependent
 the purchase requirement equal to zero. It should       Children, they are beyond the scope of this study.
 be noted that when the purchase requirement was         For an excellent review of the literature on the la-
 eliminated the allotment was decreased by approx-       bor supply effects of means-tested transfer pro-
 imately the same amount (Stucker and Boehm).            grams, see Danziger et al.

Smallwood and Blaylocke                                          Food Stamp Program Analysis

 low-income sample to the 1977-78 USDA         ey and stamps today and heavily discount
 Nationwide Food Consumption Survey            the value of future consumption. Conse-
 reveals that the average weekly food ex-      quently, if all stamps are used early in the
 penditures exceeded the average weekly         month, the household may use periodic
allotment by more than $7 per household        cash receipts to supplement food purchas-
and that less than 5% of the households        es at the end of the month. Due to these
participate in the program on a partial        and other possibilities, it is important that
basis (i.e., purchase less than the full al-   a true statistical evaluation of the theoret-
lotment). Thus, few households appear to       ical model allow for potential differences
be constrained by the allotment.               between the effects of bonus income and
   The hypothesis that bonus food stamps       money income on food expenditures. It is
affect food expenditures the same as mon-      then possible to statistically test the valid-
ey income is generated from a model that       ity of the theoretical model.
simplifies from the complexities of actual        A household's decision to enter the FSP
budgeting decisions in low income house-       is based on expected costs and benefits.
holds. West and Price found the house-         The major benefit derived from FSP par-
hold budgeting process to be quite com-        ticipation is the in-kind income transfer
plex with the marginal propensities to         associated with the bonus food stamps (i.e.,
spend (MPS) on food differing by source        the value of the food stamp allotment less
of income. In addition, virtually all em-      the purchase requirement). This increase
pirical studies of the FSP have found the      in income, while in the form of food
MPS for food out of bonus income to be         stamps, may free-up income previously
two to three times the size of the MPS for     allocated to food and thus enable partici-
food out of cash income (West and Price;       pating households to increase both food
Benus et al.; Neenan and Davis; Huang          and nonfood expenditures. To the extent
et al.; Chen and Johnson; Johnson et al.).     that stamps are less fungible than cash,
   Several possible explanations for more      households may place differing values on
complex spending behavior than is im-          bonus stamps in terms of the participa-
plied by the conventional model come           tion decision. That is, eligible households
readily to mind. First, a household's re-      may place different values on the poten-
ported income (i.e., last month's) may not     tial for increasing food expenditures ver-
accurately portray the household's finan-      sus the potential for increasing nonfood
cial status relevant to this month's food      expenditures depending upon their ability
purchases. Transitory income fluctuations      to allocate the in-kind income as they
embodied in reported income may cause          would cash.
a systematic bias to occur in the estimated       Another economic factor associated with
money income and bonus income re-              program participation is measured by a
sponse parameters (Friedman). Second,          cost/benefit ratio. This is defined as the
food stamp coupons may facilitate finan-       ratio of the purchase requirement to the
cial management and budgeting in low           allotment. The purchase requirement
income households. For example, food           measures the direct financial outlays re-
stamp households cannot be pressured by        quired for program participation and the
bill collectors to pay their financial obli-   allotment represents the gross benefits of
gations with stamps. Third, low-income         participation. While it would also be de-
households may be hedonistic in their fi-      sirable to include indirect costs incurred
nancial planning like that which is com-       in program participation, such as time,
monly observed with enlisted military          gasoline, child care, and the psychic costs
personnel. That is, they spend their mon-      of program stigma, these are not included

July 1985                                                Western Journal of Agricultural Economics

due to data limitations. 4 While not mod-         ciety's viewpoint may be thought of as one
eled formally, other studies have pointed         in which a household's consumption op-
to the purchase requirement as a substan-         portunities and/or purchase incentives are
tial deterrent to program participation for       enhanced primarily in the direction of
many households (Rungeling and Smith;             more food (Thurow). Under a food ori-
Epperson et al.; Searce et al.; Love). 5          ented program, a household's consump-
Many economic models of the FSP em-               tion opportunities are more limited than
phasize the net benefits of participation         that of a pure income transfer and possi-
(i.e., the bonus) and choose to ignore fi-        bly less preferred from the household's
nancial problems that households may              viewpoint. Thus, with a food oriented
have in collecting the required cash need-        program the implicit value of the margin-
ed to purchase a month's worth of stamps.         al food dollar may be less than that of the
The allocation of scarce cash resources to        marginal nonfood dollar and the subse-
purchase food stamps may reduce sub-              quent influence of the stamps on a house-
stantially the liquidity of an already            hold's decision to participate in the FSP
"poor" household. Thus, by participating          may be less than that of a pure income
in the program a household could place            transfer.
itself at considerable risk to unanticipated         In the following section a simultaneous
financial obligations, even if only on a          equations model of FSP participation and
temporary basis. The cost/benefit ratio           food expenditures is developed which in-
 represents a balance between the relative        corporates the above enhancement and
 costs and benefits of program participa-          cost-benefit hypotheses.
 tion. Another similar interpretation is that
 it represents the price of participation in
 the sense that it measures the direct cost       Statistical Model
 per dollar of the food stamp allotment.
    Disaggregation of bonus income into                  Based on the preceeding theoretical dis-
 food and nonfood expenditure compo-                  cussion, a two equation statistical model
 nents allows one to examine separately               of a household's behavioral response to the
 their effects on FSP participation. Under            Food Stamp Program is proposed. One
 a pure income transfer program, one                  equation is used to model a household's
 would expect a household to allocate ad-             decision to participate in the FSP and the
 ditional income between food and non-                other is used to model a household's food
 food so as to obtain equal benefit from the          expenditure response. The model and its
 marginal food and nonfood dollar. Oth-               development follows closely the pioneer-
 erwise, the household could always real-             ing work of Schmidt in his analysis of the
 locate expenditures towards the more                 impact of unions on wage rates.
 highly valued item. Conversely, an "ef-                 The expected dollar value of bonus food
 fective" food oriented program from so-              stamps represents the most obvious eco-
                                                      nomic benefit to participating households.
4To the extent that stigma and other important "cost" However, as discussed above, the value
 variables are correlated with variables included in  households place on the bonus stamps will
 the model, their effects will be confounded with     depend on restrictions that the stamps
 other effects attributed to these variables. Conse-  place on their ability to allocate resources.
 quently, our reported parameter estimates may in-
 clude an effect for stigma.                          Consequently, one must estimate the in-
                                                      fluence of the program on spending be-
5Approximately 17 percent of the eligible nonpar-
                                                      havior. The food expenditure enhance-
 ticipating households in the sample used in this
 study, said they weren't participating because "it   ment (FEE) is estimated as the difference
 cost too much."                                      between food expenditures conditioned on

Smallwood and Blaylocke                                                         Food Stamp Program Analysis

being in the program versus being out of                                   stant variance, and assumed
the program. The nonfood expenditure                                       independent of Di and Zi;
enhancement (NEE) is then calculatedas
a residual: the expected dollar bonus less                 and Qi and Xi may be subsets of the vari-
the food expenditure enhancement. As-                      ables in Zi.
suming that the marginal propensity to                       The household food expenditure en-
spend on food out of bonus income lies                     hancement (i.e., the difference between
between 0 and 1, both FEE and NEE will                     per capita food expenditure conditional on
be non-negative.                                           participation times household size) can be
   Mathematically, the food expenditure-                   derived from equation (2) as follows:
FSP participation model can be expressed
for each household i as:                                        FEE, = [(FEi IDi = 1) - (FE I Di = 0)]    (3)
                                                                     = [(ZiP + Xiy + e) - (ZiP + ei)]Fi
      P(D,= 1)                                                       = FiXiy.
  log p(D           1) = Qi5 + a,(FEE,) + a2(NEEi)
                                                            The value of FiXi, corresponds to the food
                        + a3(PRj/ALLOTi)             (1)    expenditure enhancement (FEE) portion
 FE,/F = ZiP + (DiX,)y + e,                                 of the bonus in equation (1). The expected
             i = (1 . . .N),      e ~ N(O, a2)       (2)    bonus minus FiXiy is the potential in-
where                                                       crease in nonfood expenditure (NEE) as-
                                                            sociated with program participation in
             P: denotes the probability of an               equation (2).
                  event;                                       Estimation requires the independence
             Di: participation in the FSP; Di =1            of ei and Di. This appears to be reasonable
                  if household participates,                in the present context since participation
                  zero otherwise;                          is modeled as a function of the food and
             Qi: row vector of socioeconomic               nonfood expenditure differentials rather
                  variables;                               than the level of expenditures. The error
              6: column vector of parameters;              term in the expenditure equation is as-
 a1 , a 2,   a3 :    scalar parameters;                    sumed to be the same for a household
      FE,: food expenditures;                              whether or not it participates in the Food
    FEEi: food expenditure enhance-                        Stamp Program; hence, it cancels out when
              ment, FiXiyi;                                the differential is calculated as in equation
    NEEi: nonfood expenditure en-                          (3) above. Consequently, ei does not affect
             hancement, EBi - FEEi;                        the determination of Di, and the indepen-
       F i: household size;                                dence of Di and ei, although Di is endog-
      EBi: expected bonus;                                 enous, is a reasonable assumption
      PRi: purchase requirement                            (Schmidt).
 ALLOTi: allotment                                             The food expenditure equation is spec-
       Zi: row vector of explanatory                       ified on a per capita basis. This allows one
             variables;                                    to interpret the effects of dummy vari-
        3: column vector of parameters:                    ables on regional location, race, and other
   (DiXi): row vector of interactions                      factors as being an expenditure differen-
             found by multiplying a vec-                   tial associated with an individual. For ex-
             tor of exogenous variables Xi                 ample, the household effect of race on a
             by the scalar participation                   two member household is twice as large
             dummy Di;                                     as for a one member household. This ap-
        y: column vector of parameters;                    pears more reasonable than the assump-
       ei: normally distributed error                      tion of a constant differential per house-
             term with zero mean, con-                     hold independent of its size because it also

    July 1985                                                         Western Journal of Agricultural Economics

    allows the effects of the other variables,                  equation. Next, the food and nonfood ex-
    including the Food Stamp Program, to dif-                   penditure enhancements associated with
    fer by household size. 6 Also, the per per-                program participation are calculated from
    son expenditure equation may easily be                     the OLS parameters and the relevant
    interpreted as a household equation by                     characteristics of each household. The dif-
    multiplying through by household size.                     ferentials are then entered into the partic-
       Two testable hypotheses follow directly                 ipation equation which is estimated via
    from the conventional economic model.                      the logit procedure. These recursive esti-
    First, if the influence of bonus stamp                     mators are consistent but not asymptoti-
    income is equivalent to that of money                      cally efficient unless a, = a2. In the special
    income, the model predicts that the mar-                   case of a, = a , one can combine the two

    ginal effect of enhanced nonfood expen-                    endogenous components, FEE and NEE,
    ditures on participation is the same as the                to form the expected bonus. Since the ex-
    marginal effect of enhanced food expen-                    pected bonus is predetermined, the two
    ditures. Thus, one hypothesis is that a,                   equations can be estimated independent-
    a 2 in the participation equation. Second,                 ly.7 In the case where a 1 =a 2 the consis-
  the theory implies that the marginal pro-                    tent estimates are useful as starting values
  pensity to spend on food out of money                        for the more complex maximum likeli-
 income is equal to that out of bonus stamp                    hood estimators.
 income. That is, the coefficients on money
 income and bonus income in the expen-
 diture equation are equal. Alternatively,
 under an effective food-oriented program                      Data
 individuals would be forced to spend more                      Data for the analysis of FSP participa-
 on food than they otherwise would if giv-                  tion and food expenditures are obtained
 en cash resources. Thus, from the margin-                 from computer tapes of the 1977-78
 al conditions of consumer demand, this                     USDA Nationwide Food Consumption
 implies that the marginal food dollar                     Survey, Low Income Supplemental Sam-
 would be less preferred than the marginal                 ple (NFCS-LI). 8 The NFCS-LI data were
 nonfood dollar, and consequently, a, < a 2                collected between November 1977 and
 in the participation equation. Also, an ef-               March 1978 from a representative sample
 fective food oriented program would im-                   of approximately 4,500 low income
 ply that the marginal propensity to spend                 households deemed eligible for the Food
 on food out of bonus income exceeds that                  Stamp Program. Approximately 41 per-
'out of money income in the food expen-                    cent of the sample households were par-
 diture equation.                                          ticipating in the Food Stamp Program.
    Efficient parameter estimators for the                     Information on household characteris-
 model can be obtained by the method of                    tics and food use was obtained during per-
 maximum liklihood and consistent, al-                     sonal interviews with the household mem-
 though not generally efficient, estimators,               ber(s) most responsible for food planning
 may be obtained by a recursive procedure                  and preparation. The sample households
 (Schmidt). The latter procedure consists                  were contacted at least one-week prior to
 first of OLS estimation of the expenditure
                                                               Of course, one cannot be sure that a, = a2 until
                                                               simultaneous estimation of the system is complete.
6   In addition, heteroscedasticity in the error term
    which is commonly observed in household expen-         8
                                                               Public use tapes of the 1977-78 NFCS are available
    diture models is often mitigated in per capita spec-       from National Technical Information Service, U.S.
    ifications.                                                Department of Commerce.

Smallwood and Blaylock                                            Food Stamp Program Analysis

the interview and asked to keep unstruc-        household head, a participation cost/ben-
tured notes on household food usage and         efit ratio, and the potential food and non-
costs. During the actual interview a de-        food expenditure enhancements. The lo-
tailed food list was used to assist the home-   cation of household residence variables are
maker to recall the kinds, quantities, and      not of direct interest but are included in
values of foods used from home supplies         the model to adjust for environmental and
during the last 7 days. The recall data on      related factors which are not directly ob-
the total money value of purchased food         servable.
used (less alcoholic beverages) provides the       Home ownership is expected to have a
basis for this study. The money value of        negative influence on participation.
alcoholic beverages and nonpurchased            Households which own homes will gen-
food are excluded from the analysis since       erally have both higher assets and future
they cannot be directly purchased with          income streams than similar non home-
stamps.                                         owning households, hence, the need to
   Household food expenditures are pos-         supplement food expenditures via pro-
tulated to be a function of region and ur-      gram entry is diminished.
ban location of household residence, race,         Sex, age, education, race, and employ-
number of guest meals served, household         ment status of the household head, as well
money income, and whether the house-            as the presence of both a male and female
hold receives reduced or free school            head, measure characteristics of individ-
lunches. These variables are typical of         uals in the household that are expected to
those used in similar types of expenditure      be related to the household's employment
equations and, hence, will not be elabo-        opportunities, earning potential and per-
rated upon. The effects of household age        manent income. Epperson et al. and Lane
composition are accounted for by includ-        et al. found that money income was neg-
ing the proportion of household members         atively related to FSP participation. Con-
in specified age groups. This approach          sequently, the effect of these variables on
may be viewed as a pragmaticalternative         participation is hypothesized to be in-
to a theoretically pure adult equivalent        versely related to their effect on income.
scale specification. To allow for slope and        The cost/benefit ratio is expected to be
intercept changes between participants          negatively related to participation. Higher
and nonparticipants, the above variables,       costs of program entry relative to expect-
bonus income, and a unit vector (to allow       ed benefits make the program less attrac-
for a change in the intercept) were inter-      tive to eligible households.
acted with the dummy participation vari-           Both the food and nonfood differentials
able. Only bonus income, the North Cen-         should be positively related to program
tral region, urbanization, and variables        entry as both variables essentially relate to
representing the presence of infants and        program benefits. The higher the poten-
the elderly were found to be statistically      tial benefits to participation the greater is
significant.                                    the probability a household will enter the
   The decision to participate in the FSP       FSP.
is postulated to be influenced by region           The actual variables utilized in the
and urban location of household resi-           analysis are described in Table 1. The
dence, home ownership, race, employ-            variables corresponding to the vectors Qi,
ment status of male and/or female head,         Xi, and Zi are detailed in the same table.
education level of household head, pres-        The actual sample size used in the analysis
ence of person(s) over 65 years old in the      is 3,852. The loss in observations from the
household, presence of only a female            original sample is due largely to missing

July 1985                                                   Western Journal of Agricultural Economics

TABLE 1. Definitions of Model Variables.
               Included in Vector
       Label    Qj     Zj     Xj                               Definition
NC                            v     NC = 1 if household resides in North Central; zero otherwise
S                                   S = 1 if household resides in South; zero otherwise
W                                   W = 1 if household resides in West; zero otherwise
U                                   U = 1 if household resides in an SMSA suburban area; zero other-
HO              V
                                    HO = 1 if household owns a home; zero otherwise
R               V                   R = 1 if household head is black; zero otherwise
D                                   D = 1 if household received food stamps last month and this month;
                       V              zero otherwise
GM                                  Number of guest meals
SLR                                 SLR = 1 if household had school lunches at reduced prices; zero oth-
FEE                                 Food expenditure enhancement
NEE                                 Nonfood expenditure enhancement
FE/F                                Dollar value per person of purchased food used from home supplies
                                      in a week
EM              V                   EM = 1 if household has an employed male head; zero otherwise
EF              V                   EF = 1 if household has an employed female head; zero otherwise
FH                                  FH = 1 if household has a female head and no male head; zero other-
E               ,/                  E = 1 if household head is at least a high school graduate; zero oth-
P1/F                   V      v     Proportion of household composed of members under age 3
P2/F                   V            Proportion of household composed of members of age 3 to 12
P3/F                   V            Proportion of household composed of members of age 13 to 19
P4/F                   V            Proportion of household composed of members of age 20 to 39
P5/F                   V      v     Proportion of household composed of members of age 65 or older
Y/F                    V            Last month's household income in dollars on a weekly per person ba-
EB                            v     Expected weekly bonus value of food stamps to eligible households
                                      regardless of whether they participate
ELD             V                   ELD = 1 if male or female household head is 65 years or older; zero
PR/ALLOT        V                   Expected weekly purchase requirement divided by expected weekly

data on income and reporting errors in              maximum liklihood estimates reported in
food stamp information.                             Table 2. Estimates obtained from the two
                                                    procedures were found to be virtually
Empirical Results                                   identical.
                                                       Results from the estimated expenditure
   Due to cost considerations, the statisti-        equation reveal that urbanization and
cally consistent recursive estimator men-           geographic region of household residence,
tioned above was used during preliminary            size and age composition of the house-
model selection. Parameter estimates for            hold, number of guest meals served, race,
the selected model were found to be ro-             number of reduced price and free school
bust to the entry and exit of other socio-          lunches, money income, and participation
economic variables considered. Subse-               in the Food Stamp Program were signifi-
quently, these parameter estimates were             cant determinants of the level of food ex-
used as starting values in obtaining the            penditures. For example, per person
Smallwood and Blaylock                                               Food Stamp Program Analysis

weekly food expenditures were found to           TABLE 2. Asymptotically Efficient Estimates
be highest in the Northeast region and                    of FSP Participation and Food Ex-
                                                          penditure Model.
lowest in the South. Blacks were found to
spend more per person on food from home                       Participation Equation
supplies than nonblacks. Whether this lat-       Variable    Coefficient    Variable       Coefficient
ter result is due to underlying racial influ-    Constant       1.2639     FH                 0.5774
ences on the types and quantities of food                      (0.2491)                      (0.0880)
purchased is unknown. As would be ex-            NC           -0.8101      E                -0.3996
pected, food expenditures increased with                       (0.1777)                      (0.0933)
the number of guest meals served.                S            -1.2395      ELD              -0.3417
   Households with children receiving re-                      (0.1443)                      (0.198)
duced or free school lunches spent less than     W            -1.1639      R                  0.3201
their counterparts not receiving the                           (0.1841)                      (0.0816)
lunches. This is consistent with the hy-         U            -0.4246      PR/              -1.4477
                                                               (0.1245)      ALLOT           (0.3564)
pothesis that government subsidized meals
                                                 HO           -0.6589      FEE                0.0265
substitute, at least partially, for meals that                 (0.0832)                      (0.0161)
would otherwise have been purchased by           EM           -1.5216      NEE                0.0256
the household.                                                 (0.1314)                      (0.0078)
   The estimated marginal propensity to          EF           -1.055
spend (MPS) on food out of bonus income                        (0.1168)
was over twice as large as that for money        Variable   Food Expenditure Equation
income and the two coefficients were
                                                             Coefficient        Variable   Coefficient
found to be statistically different at the
0.05 level. The MPS on food out of money         Constant      11.4846     P3/F               2.3751
                                                               (0.5574)                      (0.6594)
income was about 9.9 cents per dollar and
                                                 NC           -0.9760      P4/F             -0.6411
the corresponding MPS out of bonus in-
                                                               (0.5025)                      (0.5117)
come was approximately 23 cents per dol-
                                                 S            -1.4548      P5/F             -2.3494
lar. The above indicates that one can re-                      (0.3625)                      (0.3701)
ject the hypothesis generated from the           W            -0.5524      Y/F                0.0991
traditional economic model that bonus in-                      (0.4760)                      (0.0082)
come is allocated the same as money in-          U            -0.1346      D                  0.1981
come.                                                          (0.3250)                      (0.7782)
   In addition to the estimated effect of        SLR          -0.9754      (EB/F)*D           0.2328
bonus income on food expenditures, an                          (0.3250)                      (0.1098)
additional program participation effect          R              1.0271     NC*D               0.9501
was found which varies with region and                         (0.2070)                      (0.6021)
urban locations of household residence and       GM/F           1.2453     U*D              -0.9600
                                                               (0.1015)                      (0.5689)
age of household members. The partici-
                                                 P1/F         -7.8727      (P1/F)*D           2.9435
pation effect on food expenditures was                         (1.2201)                      (1.6894)
found to be significantly larger for house-      P2/F         -3.4046      (P5/F)*D           1.5218
hold members under three and those 65                          (0.6600)                      (0.5393)
and older than for those of other ages. For      Note: Asymptotic standard errors in parentheses.
example, holding bonus income and other
factors constant, the participation effect
increased food expenditures $3.14                effect for the base group (all other ages)
($2.9435 + $0.1981) weekly for each child        of approximately $0.20 per person per
under 3 years and $1.72 ($1.5218 +               week. Consequently, the program appears
$0.1981) weekly for each adult 65 years          to increase food expenditures most for
or older compared with the participation         those population subsets often identified

 July 1985                                                                    Western Journal of Agricultural Economics

TABLE 3. Effects of a 1-Unit Change in the                 TABLE 4. Effect on the Probability of FSP
         Independent Variables on the                               Participation Given Changes inthe
         Probability of FSP Participation by                        Purchase Requirement.a
         Eligible Households. a
                                                                Pur-                                                                                                              Proba-
                                          Change in            chase                                                           Bonus Value                                        bility of
      Independent Variable                Probability       Require-                          Allot-                                                                              Partici-
                                                                ment                          ment                 Total                  FEE                  NEE                 pation
       North Central                      -0.1713                        0                       32                    32                9.93                22.07                   0.61
       South                              -0.2955                        5                       32                    27                8.74                18.26                   0.53
       West                               -0.2265                     13b                        32 b                  19                6.83                12.17                   0.39
                                                                        18                           32                      14                  5.63                    8.37               0.31
SMSA, non central city                    -0.0953                      25                            32                         7                3.96                    3.04               0.21
Home ownership                            -0.1509          ................................................................................................................................

Race                                        0.0750                       0                       19                    19                6.83                12.17                   0.53
Female head only                            0.1344
Female head works                                          aAll  variables except the weekly purchase require-
                                                             ment, allotment, and expected bonus are evaluated
Male head works                           -0.2974            at the sample means.
Elderly head                              -0.0788          b Sample means of allotment and purchase require-
Education of meal planner                 -0.0909            ment rounded up.
Cost-benefit ratiob                       -0.0032
Expected bonus stamps                       0.0060
a The effects of changes in the independent variables       or is below 0.5 for nonparticipating house-
  are computed from the estimated participation equa-      holds.
  tion evaluated at the mean values of the independent         The estimated effects of the indepen-
b A unit change in the cost-benefit ratio is assumed to    dent variables on the probability of FSP
  be a 1-percentage point change.                          participation are reported in Table 3.
                                                            Variables, other than the one being ex-
as most in need of public assistance (i.e.,                amined, are held constant at their respec-
the elderly and infants). 9                                tive sample means. For example, the
   Most coefficients estimated in the par-                 probability of FSP participation in the
ticipation equation were statistically sig-                Northeast (omitted base) region ranges
nificant at the usual confidence levels with               from 17 to 30 percentage points higher at
the signs as expected a priori. The model                  the sample means than in the other three
correctly classifies 72.6 percent of the ob-               regions. The probability of participation
servations using the (0.5, 0.5) criteria. For              was lowest in the South followed by the
this criterion, a correct classification means             West and North Central regions.
that the predicted probability equals or                       Households residing in the suburban
exceeds 0.5 for participating households                   portion of an SMSA were found less likely
                                                           to participate in the program. These
9 An expenditure equation similar to the one above,        households had a probability of partici-
  except that interactions between household age           pation approximately 10 percentage points
  composition, region, urbanization, and FSP partic-       less than other households. Eligible house-
  ipation were excluded, was estimated. The result         holds which don't own a home had a
  was to increase the effect attributed to bonus in-
  come to about 3 times the effect of money income
                                                           probability of participation that was 15
  (i.e., an MPS for money income of 0.10 and an MPS        percentage points higher than for home-
  for bonus income of 0.32). This latter result is con-    owners. Black households were about 7 to
  sistent with some earlier studies (Neenan and Davis;     8 percentage points more likely to partic-
  West and Price) which also omitted the interaction       ipate than similar nonblack households.
  effects but is misleading as the model omits statis-
                                                           Households with only a female head were
  tically relevant variables which are correlated with
  the included variables. The net effect is to attribute   13 percentage points more likely to par-
  effects to bonus income which should be attributed       ticipate than other similar households. A
  to other variables.                                      working male or female head of house-
Smallwood and Blaylock                                                    Food Stamp Program Analysis

hold was associated with a reduction in                  amount of money income. Consequently,
the probability of FSP participation rang-               the fact that potential benefits are in the
ing from 22 to 30 percentage points over                 form of food stamps rather than cash does
households with unemployed heads.                        not appear to be a deterrent to partici-
Households with an elderly head were                     pation although the bonus stamp benefits
about 8 percent less likely to participate               are allocated differently than the money
than similar nonelderly households. Also,                income. Furthermore, this result (a, = a,)
households in which the primary meal                     is of particular importance because it im-
planner had completed high school were                   plies that the two-equation system need
10 percent less likely to participate in the             not be estimated simultaneously and that
FSP than similar households where the                    a simpler model which combines the food
meal planner has less education.                         and nonfood expenditure enhancements
   The cost/benefit ratio was negatively                 into the expected bonus provides efficient
related to participation, as expected. 1 A 0             parameter estimates. Also, as shown in Ta-
10 percent increase in the cost/benefit ra-              ble 3, a $10 increase in the expected
tio was asociated with a 3.2 percentage                  weekly bonus stamps was associated with
point decline in the likelihood of partici-              a 6 percentage point increase in the like-
pation at the sample means. This indicates               lihood of program participation.
that as the purchase requirement is de-                      The model can be used to simulate the
creased (with the allotment held constant)               effects of policy instruments on the prob-
participation would be expected to in-                   ability of participation and the subse-
crease. Consequently, the purchase re-                   quent effect on the food and nonfood en-
quirement may be viewed as a significant                 hancements. The major policy instruments
deterrent to participation.                              by which administrators can influence
   The effects of the potential food and                 participation and food expenditures are
nonfood expenditure enhancements on                      the allowable deductions from income, the
FSP participation were found to be vir-                  purchase requirement, asset limits, and the
tually identical and a statistical test for the          allotment amount. Changes in asset limits
equality of a, and a2 was not rejected at                and allowable income deductions have
the .05 level. This implies that households,             been the primary policy instruments used.
in deciding whether or not to participate                Since the purchase requirement is deter-
in the FSP, place equal value on the po-                 mined by household size, income, and al-
tentials for increasing food and nonfood                 lowable income deductions, changes in in-
spending. However, as shown above, those                 come and allowable income deductions
households that actually decide to partic-               can be viewed within our model as direct
ipate appear to allocate bonus income                    changes in the purchase requirement. This,
more towards food expenditures than                      in turn, will influence bonus stamp in-
would be predicted via an equivalent                     come and the cost-benefit ratio.
                                                             Presented in Table 4 are the results of
                                                          alternate scenarios involving hypothetical
10A purchase requirement to income ratio variable
                                                          changes in the purchase requirement. For
  was tried as an alternative to the purchase require-
  ment to allotment ratio in a preliminary model
                                                          example, if the purchase requirement is
  specification. However, all specifications that in-     eliminated and all other exogenous vari-
  cluded an income term gave problems due to the          ables including the allotment are evalu-
  close functional relationship between the FSP vari-     ated at their sample means, the probabil-
  ables and income. Because we thought that pro-          ity of participation increases from 0.39 to
  gram benefits were more important to participa-
  tion than the potential effect of declining marginal    0.61. In addition, the household's weekly
  utility of income, we chose not to include income       food and nonfood expenditure enhance-
  terms.                                                  ments increase from $6.83 and $12.17 to
July 1985                                            Western Journalof Agricultural Economics

$9.93 and $22.07, respectively, under this     to have the same effects on program par-
scenario. Conversely, increasing the pur-      ticipation. In the context of our model,
chase requirement or decreasing the al-        this finding implies that the participation
lowable income deductions decreases bo-        decision can be considered independently
nus income, the food and nonfood               of the allocation of both money income
expenditure enhancements, and the prob-        and food stamps to food and nonfood
ability of participation. Also presented in    items. Thus, there was no indication that
Table 4 are the results of simultaneously      households with a greater preference for
eliminating the purchase requirement and       food (larger food expenditure enhance-
reducing the allotment by the same dollar      ment) were more likely to participate than
amount. This scenario is similar to the leg-   other households.
islated removal of the purchase require-          Statistical tests revealed that the level
ment in January 1979. Our simulations in-      of expected bonus stamp income has a sig-
dicate that eliminating the purchase           nificant positive influence on the proba-
requirement would increase the probabil-       bility of program participation. For ex-
ity of participation by 14 percentage points   ample, a $10 increase in expected weekly
from the base probability calculated at the    bonus stamp income was found to in-
sample means of all variables. Assuming        crease the probability of participation by
no change in the eligible population, this     approximately 6 percentage points. Also,
implies a 36-percent increase in program       additional bonus stamp income was found
enrollment. Actual FSP enrollment in-          to have more than twice the effect on food
creased 17.9 percent and 15.9 percent, re-     spending as additional money income.
spectively, in the two calendar years fol-     This suggests that replacing stamps with
lowing the elimination of the purchase         cash would be substantially less effective
requirement (EPR). Of course, actual en-       as a food enhancing program.
rollment growth during this time was par-         Food expenditure differentials associ-
tially due to an increase in eligible house-   ated with FSP participation were found
holds caused by poor economic conditions.      to be larger for households with elderly
In summary, while regulations governing        persons or infants present. Whether this
net transfers per household changed only       effect is due to pure program effects or to
modestly with elimination of the purchase      the type of household self-selecting into
requirement, total program cost increased      the program is not clear. Some simple tests
substantially due to increased enrollment.     for sample selection bias using Heckman's
                                               procedure did not indicate its presence for
Conclusions                                    this sample. In any case, these household
                                               types appear to benefit more from FSP
   An economic model of household be-          participation in terms of increased food
havior was developed to analyze the ef-        expenditures than others.
fects of FSP policy control variables on          The cost-benefit ratio associated with
food expenditures and program partici-         participation, defined as the ratio of the
pation rates. The model postulated that        expected purchase requirement to the al-
FSP participation by eligible households       lotment, was found to be a significant fac-
is determined, in part, by the opportu-        tor influencing participation. Program
nities households have and choices house-      participation was found to decline mark-
holds make with regard to the allocation       edly as the cost-benefit ratio was in-
of their in-kind income transfer. The op-      creased. Since the most needy households
portunities to enhance food and nonfood        tend to have lower cost-benefit ratios, this
spending via program participation and         result suggests that policy instruments
receipt of bonus stamp income were found       which influence this ratio can be used as
Smallwood and Blaylock                                                   Food Stamp Program Analysis

effective tools to control program cost               Simultaneous Equations Analysis with Qualitative
                                                      and Continuous Dependent Variables." Paper pre-
while minimizing the deleterious effects
                                                      sented at the Regional Research Committee Meet-
of program budget reductions. That is, the            ing, S-165, Atlanta, Georgia, October 19, 1982.
purchase requirement, if re-enacted, could
be used as a policy instrument to limit              Clarkson, Kenneth. Food Stamps and Nutrition.
                                                       American Enterprise Institute, Washington, D.C.,
participation of "marginal" households
without further restricting the eligibility
requirements or reducing the net transfer            Danziger, Sheldon, Robert Haveman, and Robert
of benefits per household. In this sense,             Plotnick. "How Income Transfer Programs Affect
the purchase requirement may be a polit-              Work, Savings, and the Income Distribution: A
                                                      Critical Review." Journal of Economic Litera-
ically acceptable means of controlling the
                                                      ture, (1981): 975-1028.
FSP budget.
   These empirical findings together with            Epperson, J. E., C. L. Huang, S. M. Fletcher, and W.
those of Clarkson, Huang et al., Mittel-               K. Searce. "The Determinants of Food Stamp Pro-
hammer and West, and many others sug-                  gram Participation." Southern Journal of Agri-
                                                       cultural Economics, 12(1980): 93-7.
gest that the traditional indifference curve
model of consumer behavior used to ana-              Friedman, Milton. A Theory of the Consumption
lyze the FSP does not adequately explain               Function. Princeton University Press, Princeton,
the effects of FSP on food spending. To                N.J., 1957.
better understand the determinants of
                                                     Heckman, Jes. "Sample Selection Bias as a Specifi-
program participation and the program ef-
                                                      cation Error." Econometrica, 47(1979): 153-61.
fects on food spending and nutritional ad-
equacy, improved economic models will                Huang, Chung L., Stanley M. Fletcher, and Robert
have to be developed. Future research ef-             Rauniker. "Modeling the Effects of the Food Stamp
forts on theoretical modeling will proba-             Program on Participating Households' Purchases:
                                                      An Empirical Application." Southern Journal of
bly be most fruitful in the area of mod-
                                                      Agricultural Economics, 13(1981): 21-8.
eling the income constraint and those
factors related to financial management              Johnson, Stanley, James Burt, and Karen Morgan.
and resource allocation in low income                  "The Food Stamp Program: Participation, Food
households. Lastly, we offer our results in            Costs, and Diet Quality for Low Income House-
                                                       holds." Food Technology, 35(1981): 58-70.
hope that this research may stimulate de-
bate on the appropriateness of the tradi-            Lane, Sylvia, John Kushman, and Christine Ranney.
tional food stamp model and will generate              "Food Stamp Program Participation: An Explor-
hypotheses which can be tested with more              atory Analysis." Western Journal of Agricultural
recent data (after elimination of the pur-             Economics, 8/1(1983): 13-26.
chase requirement) such as the 1979-80               Love, H. G. "The Reasons Participants Drop Out of
supplemental low income sample to the                 the Food Stamp Program: A Case Study of Its Im-
 USDA Nationwide Food Consumption                      plications." American Journal of Agricultural
 Survey.                                               Economics, 52(1970): 387-94.

                                                     Mittelhammer, Ron and Donald A. West. "Food
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 July 1985                                                      Western Journal of Agricultural Economics

Rao, C. R. Linear Statistical Inference and Its Ap-      Southworth, Herman M. "The Economics of Public
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Rungeling, B. and L. H. Smith. Factors Affecting         Stucker, Thomas A. and William T. Boehm. "A Guide
  Food Stamp Program Nonparticipation in the               to Understanding the 1977 Food and Agricultural
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  and Qualitative Variables: The Union-Earnings          Thurow, Lester C. "Cash Versus In-Kind Transfers."
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                                                         West, Donald A. and David W. Price. "The Effects
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  burg, Virginia, March 1975.


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