Analysis of Food Stamp Program Participation and Food...

Analysis of Food Stamp ProgramParticipation and Food

Expenditures

David M. Smallwood and James R. Blaylock

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

A fundamental objective of the FoodStamp Program (FSP) is to increase thediet quality of low income households viaincreasing their food expenditures to thatof a reference standard. To achieve thisgoal, eligible households choosing to par-ticipate in the program are provided withan income subsidy in the form of foodstamps which can only be spent on foodfor home consumption.l The effectivenessof the program in achieving this goal can,in. part, be evaluated by analyzing partic-ipation rates of the target population andthe subsequent effect of this in-kind trans-fer on food expenditures.

David M. Smallwood and James R. Blaylock are ag-ricultural economists with the United States Depart-ment of Agriculture, Economic Research Service,National Economics Division. The views expressedin this paper are not necessarily those of ERS orUSDA.

1 Food stamps with several minor exceptions may onlylegally be used to purchase foods at authorized "re-tail food establishments" which are intended for useand/or preparation at home. Food stamps may notbe used to purchase foods traditionally referred toas away-from-home food, such as at fast-food es-tablishments and restaurants. Henceforth, unlessotherwise specified, the word food will be used todenote food which may be purchased with stamps.

Many microeconomic analyses of theFSP have modeled the household's deci-sion to participate in the program sepa-rately from the program's effect on foodexpenditures (Neenan and Davis; Epper-son et al.; Huang et al.; Lane et al.). Ingeneral, a single equation logit or probitmodel has been used to examine the par-ticipation decision as a function of house-hold characteristics and income. Food ex-penditures are usually modeled separatelyfrom the participation decision and spec-ified as a function of household charac-teristics, money income, bonus stamp in-come, and an FSP participation variable.

The purpose of this paper is to developand estimate an economic model of be-havior which considers simultaneously thelikelihood of participation by eligiblehouseholds and the effect of program par-ticipation on food expenditures. The pro-posed model postulates that a household'sdecision to participate in the Food StampProgram is influenced by the potential forenhancing both its food and nonfood ex-penditures. Although food stamps mayonly legally be used to purchase food,households are afforded an opportunity toreallocate some money to nonfood use that

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

Western Journal of Agricultural Economics

was previously allocated to food. Themodel disaggregates net program benefits(bonus food stamps) into these two com-ponents and allows each to have poten-tially different effects on participationrates, and hence, household food expen-ditures. The model also incorporates acost/benefit ratio which measures the rel-ative cost of program entry to the totalmonetary benefits accruing to householdparticipation. Hopefully, disaggregationof net program benefits together with thecost/benefit ratio will allow for improvedestimates of a household's behavioral re-sponses to FSP policy instruments. Also,because the model contains explicit FSPpolicy instruments, it may be used to sim-ulate the effects of proposed programchanges on food expenditures and pro-gram participation.

The following section contains the de-velopment of an economic model of par-ticipant behavior in the FSP. An outlineof the proposed statistical model is pre-sented in the third section. Data and vari-able specification are discussed in thefourth part. The fifth section contains em-pirical results and a discussion of their rel-evance to policy analysis. A section con-taining conclusions and future researchdirections concludes the paper.

Theoretical Framework

Prior to elimination of the purchase re-quirement in 1979, the value of the stampsreceived, termed the allotment, was basedon household size.2 The amount an eligi-ble household was required to pay for the

2 The assumption of a purchase requirement is keptthroughout this discussion because of its importanceas a policy instrument. The program as it existstoday can be expressed in this framework by settingthe purchase requirement equal to zero. It shouldbe noted that when the purchase requirement waseliminated the allotment was decreased by approx-imately the same amount (Stucker and Boehm).

stamps, termed the purchase require-ment, was based on both household sizeand income. The difference between theallotment and the purchase requirement,termed the bonus, is the net subsidy ortransfer of in-kind income to the house-hold.

A conventional economic model ofhousehold behavior as developed bySouthworth and advanced by Mittelham-mer and West; Clarkson; Huang et al.,and others provides the conceptual frame-work for this study.3 Since this model iswell known, only the highlights will bepresented here. Briefly, participant be-havior is modeled within the classicalhousehold utility maximizing frameworkof demand theory and incorporates amodified income constraint to allow forthe in-kind provisions of the FSP. Withinthis framework, the household is assumedto maximize utility subject to a budgetconstraint which is determined, in part,by FSP participation and program rules.

The above model implies that the effectof bonus stamps on food expenditures isidentical to that of money income for thosehouseholds that spend more than their al-lotment of stamps on food at home. Onlyin the case where the allotment exceedsdesired food expenditures is the effect ofthe FSP on food expenditures hypothe-sized to be larger than that of a cash trans-fer. Empirically, the number of house-holds in this latter group appears to belimited. Food expenditure data for partic-ipating and eligible nonparticipatinghouseholds contained in the supplemental

3Household income has traditionally been consid-ered exogenous in FSP models. While the authorsbelieve that the labor supply effects of the FoodStamp Program are important, especially whenconsidered jointly with other means-tested welfareprograms, such as Aid to Families with DependentChildren, they are beyond the scope of this study.For an excellent review of the literature on the la-bor supply effects of means-tested transfer pro-grams, see Danziger et al.

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July 1985

Food Stamp Program Analysis

low-income sample to the 1977-78 USDANationwide Food Consumption Surveyreveals that the average weekly food ex-penditures exceeded the average weeklyallotment by more than $7 per householdand that less than 5% of the householdsparticipate in the program on a partialbasis (i.e., purchase less than the full al-lotment). Thus, few households appear tobe constrained by the allotment.

The hypothesis that bonus food stampsaffect food expenditures the same as mon-ey income is generated from a model thatsimplifies from the complexities of actualbudgeting decisions in low income house-holds. West and Price found the house-hold budgeting process to be quite com-plex with the marginal propensities tospend (MPS) on food differing by sourceof income. In addition, virtually all em-pirical studies of the FSP have found theMPS for food out of bonus income to betwo to three times the size of the MPS forfood out of cash income (West and Price;Benus et al.; Neenan and Davis; Huanget al.; Chen and Johnson; Johnson et al.).

Several possible explanations for morecomplex spending behavior than is im-plied by the conventional model comereadily to mind. First, a household's re-ported income (i.e., last month's) may notaccurately portray the household's finan-cial status relevant to this month's foodpurchases. Transitory income fluctuationsembodied in reported income may causea systematic bias to occur in the estimatedmoney income and bonus income re-sponse parameters (Friedman). Second,food stamp coupons may facilitate finan-cial management and budgeting in lowincome households. For example, foodstamp households cannot be pressured bybill collectors to pay their financial obli-gations with stamps. Third, low-incomehouseholds may be hedonistic in their fi-nancial planning like that which is com-monly observed with enlisted militarypersonnel. That is, they spend their mon-

ey and stamps today and heavily discountthe value of future consumption. Conse-quently, if all stamps are used early in themonth, the household may use periodiccash receipts to supplement food purchas-es at the end of the month. Due to theseand other possibilities, it is important thata true statistical evaluation of the theoret-ical model allow for potential differencesbetween the effects of bonus income andmoney income on food expenditures. It isthen possible to statistically test the valid-ity of the theoretical model.

A household's decision to enter the FSPis based on expected costs and benefits.The major benefit derived from FSP par-ticipation is the in-kind income transferassociated with the bonus food stamps (i.e.,the value of the food stamp allotment lessthe purchase requirement). This increasein income, while in the form of foodstamps, may free-up income previouslyallocated to food and thus enable partici-pating households to increase both foodand nonfood expenditures. To the extentthat stamps are less fungible than cash,households may place differing values onbonus stamps in terms of the participa-tion decision. That is, eligible householdsmay place different values on the poten-tial for increasing food expenditures ver-sus the potential for increasing nonfoodexpenditures depending upon their abilityto allocate the in-kind income as theywould cash.

Another economic factor associated withprogram participation is measured by acost/benefit ratio. This is defined as theratio of the purchase requirement to theallotment. The purchase requirementmeasures the direct financial outlays re-quired for program participation and theallotment represents the gross benefits ofparticipation. While it would also be de-sirable to include indirect costs incurredin program participation, such as time,gasoline, child care, and the psychic costsof program stigma, these are not included

43

Smallwood and Blaylocke


due to data limitations.4 While not mod-eled formally, other studies have pointedto the purchase requirement as a substan-tial deterrent to program participation formany households (Rungeling and Smith;Epperson et al.; Searce et al.; Love). 5

Many economic models of the FSP em-phasize the net benefits of participation(i.e., the bonus) and choose to ignore fi-nancial problems that households mayhave in collecting the required cash need-ed to purchase a month's worth of stamps.The allocation of scarce cash resources topurchase food stamps may reduce sub-stantially the liquidity of an already"poor" household. Thus, by participatingin the program a household could placeitself at considerable risk to unanticipatedfinancial obligations, even if only on atemporary basis. The cost/benefit ratiorepresents a balance between the relativecosts and benefits of program participa-tion. Another similar interpretation is thatit represents the price of participation inthe sense that it measures the direct costper dollar of the food stamp allotment.

Disaggregation of bonus income intofood and nonfood expenditure compo-nents allows one to examine separatelytheir effects on FSP participation. Undera pure income transfer program, onewould expect a household to allocate ad-ditional income between food and non-food so as to obtain equal benefit from themarginal food and nonfood dollar. Oth-erwise, the household could always real-locate expenditures towards the morehighly valued item. Conversely, an "ef-fective" food oriented program from so-

4 To the extent that stigma and other important "cost"

variables are correlated with variables included in

the model, their effects will be confounded with

other effects attributed to these variables. Conse-

quently, our reported parameter estimates may in-clude an effect for stigma.

5Approximately 17 percent of the eligible nonpar-

ticipating households in the sample used in this

study, said they weren't participating because "itcost too much."

ciety's viewpoint may be thought of as onein which a household's consumption op-portunities and/or purchase incentives areenhanced primarily in the direction ofmore food (Thurow). Under a food ori-ented program, a household's consump-tion opportunities are more limited thanthat of a pure income transfer and possi-bly less preferred from the household'sviewpoint. Thus, with a food orientedprogram the implicit value of the margin-al food dollar may be less than that of themarginal nonfood dollar and the subse-quent influence of the stamps on a house-hold's decision to participate in the FSPmay be less than that of a pure incometransfer.

In the following section a simultaneousequations model of FSP participation andfood expenditures is developed which in-corporates the above enhancement andcost-benefit hypotheses.

Statistical Model

Based on the preceeding theoretical dis-cussion, a two equation statistical modelof a household's behavioral response to theFood Stamp Program is proposed. Oneequation is used to model a household'sdecision to participate in the FSP and theother is used to model a household's foodexpenditure response. The model and itsdevelopment follows closely the pioneer-ing work of Schmidt in his analysis of theimpact of unions on wage rates.

The expected dollar value of bonus foodstamps represents the most obvious eco-nomic benefit to participating households.However, as discussed above, the valuehouseholds place on the bonus stamps willdepend on restrictions that the stampsplace on their ability to allocate resources.Consequently, one must estimate the in-fluence of the program on spending be-havior. The food expenditure enhance-ment (FEE) is estimated as the differencebetween food expenditures conditioned on

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July 1985


being in the program versus being out ofthe program. The nonfood expenditureenhancement (NEE) is then calculated asa residual: the expected dollar bonus lessthe food expenditure enhancement. As-suming that the marginal propensity tospend on food out of bonus income liesbetween 0 and 1, both FEE and NEE willbe non-negative.

Mathematically, the food expenditure-FSP participation model can be expressedfor each household i as:

P(D, = 1)log p(D 1) = Qi5 + a,(FEE,) + a2(NEEi)

+ a3(PRj/ALLOTi) (1)

FE,/F = ZiP + (DiX,)y + e,

i = (1 . . .N), e ~ N(O, a2) (2)

where

P: denotes the probability of anevent;

Di: participation in the FSP; Di =1if household participates,zero otherwise;

Qi: row vector of socioeconomicvariables;

6: column vector of parameters;a1 , a2, a3 : scalar parameters;

FE,: food expenditures;FEEi: food expenditure enhance-

ment, FiXiyi;NEEi: nonfood expenditure en-

hancement, EBi - FEEi;Fi: household size;

EBi: expected bonus;PRi: purchase requirement

ALLOTi: allotmentZi: row vector of explanatory

variables;3: column vector of parameters:

(DiXi): row vector of interactionsfound by multiplying a vec-tor of exogenous variables Xiby the scalar participationdummy Di;

y: column vector of parameters;ei: normally distributed error

term with zero mean, con-

stant variance, and assumedindependent of Di and Zi;

and Qi and Xi may be subsets of the vari-ables in Zi.

The household food expenditure en-hancement (i.e., the difference betweenper capita food expenditure conditional onparticipation times household size) can bederived from equation (2) as follows:

FEE, = [(FEi I Di = 1) - (FE I Di = 0)]

= [(ZiP + Xiy + e) - (ZiP + ei)]Fi= FiXiy.

(3)

The value of FiXi, corresponds to the foodexpenditure enhancement (FEE) portionof the bonus in equation (1). The expectedbonus minus FiXiy is the potential in-crease in nonfood expenditure (NEE) as-sociated with program participation inequation (2).

Estimation requires the independenceof ei and Di. This appears to be reasonablein the present context since participationis modeled as a function of the food andnonfood expenditure differentials ratherthan the level of expenditures. The errorterm in the expenditure equation is as-sumed to be the same for a householdwhether or not it participates in the FoodStamp Program; hence, it cancels out whenthe differential is calculated as in equation(3) above. Consequently, ei does not affectthe determination of Di, and the indepen-dence of Di and ei, although Di is endog-enous, is a reasonable assumption(Schmidt).

The food expenditure equation is spec-ified on a per capita basis. This allows oneto interpret the effects of dummy vari-ables on regional location, race, and otherfactors as being an expenditure differen-tial associated with an individual. For ex-ample, the household effect of race on atwo member household is twice as largeas for a one member household. This ap-pears more reasonable than the assump-tion of a constant differential per house-hold independent of its size because it also

45

Smallwood and Blaylocke


allows the effects of the other variables,including the Food Stamp Program, to dif-fer by household size.6 Also, the per per-son expenditure equation may easily beinterpreted as a household equation bymultiplying through by household size.

Two testable hypotheses follow directlyfrom the conventional economic model.First, if the influence of bonus stampincome is equivalent to that of moneyincome, the model predicts that the mar-ginal effect of enhanced nonfood expen-ditures on participation is the same as themarginal effect of enhanced food expen-ditures. Thus, one hypothesis is that a,a2 in the participation equation. Second,the theory implies that the marginal pro-pensity to spend on food out of moneyincome is equal to that out of bonus stampincome. That is, the coefficients on moneyincome and bonus income in the expen-diture equation are equal. Alternatively,under an effective food-oriented programindividuals would be forced to spend moreon food than they otherwise would if giv-en cash resources. Thus, from the margin-al conditions of consumer demand, thisimplies that the marginal food dollarwould be less preferred than the marginalnonfood dollar, and consequently, a, < a 2in the participation equation. Also, an ef-fective food oriented program would im-ply that the marginal propensity to spendon food out of bonus income exceeds that

'out of money income in the food expen-diture equation.

Efficient parameter estimators for themodel can be obtained by the method ofmaximum liklihood and consistent, al-though not generally efficient, estimators,may be obtained by a recursive procedure(Schmidt). The latter procedure consistsfirst of OLS estimation of the expenditure

6 In addition, heteroscedasticity in the error termwhich is commonly observed in household expen-diture models is often mitigated in per capita spec-ifications.

equation. Next, the food and nonfood ex-penditure enhancements associated withprogram participation are calculated fromthe OLS parameters and the relevantcharacteristics of each household. The dif-ferentials are then entered into the partic-ipation equation which is estimated viathe logit procedure. These recursive esti-mators are consistent but not asymptoti-cally efficient unless a, = a2. In the specialcase of a, = a 2, one can combine the twoendogenous components, FEE and NEE,to form the expected bonus. Since the ex-pected bonus is predetermined, the twoequations can be estimated independent-ly.7 In the case where a1 = a2 the consis-tent estimates are useful as starting valuesfor the more complex maximum likeli-hood estimators.

Data

Data for the analysis of FSP participa-tion and food expenditures are obtainedfrom computer tapes of the 1977-78USDA Nationwide Food ConsumptionSurvey, Low Income Supplemental Sam-ple (NFCS-LI). 8 The NFCS-LI data werecollected between November 1977 andMarch 1978 from a representative sampleof approximately 4,500 low incomehouseholds deemed eligible for the FoodStamp Program. Approximately 41 per-cent of the sample households were par-ticipating in the Food Stamp Program.

Information on household characteris-tics and food use was obtained during per-sonal interviews with the household mem-ber(s) most responsible for food planningand preparation. The sample householdswere contacted at least one-week prior to

7 Of course, one cannot be sure that a, = a2 untilsimultaneous estimation of the system is complete.

8 Public use tapes of the 1977-78 NFCS are availablefrom National Technical Information Service, U.S.Department of Commerce.

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July 1985


the interview and asked to keep unstruc-tured notes on household food usage andcosts. During the actual interview a de-tailed food list was used to assist the home-maker to recall the kinds, quantities, andvalues of foods used from home suppliesduring the last 7 days. The recall data onthe total money value of purchased foodused (less alcoholic beverages) provides thebasis for this study. The money value ofalcoholic beverages and nonpurchasedfood are excluded from the analysis sincethey cannot be directly purchased withstamps.

Household food expenditures are pos-tulated to be a function of region and ur-ban location of household residence, race,number of guest meals served, householdmoney income, and whether the house-hold receives reduced or free schoollunches. These variables are typical ofthose used in similar types of expenditureequations and, hence, will not be elabo-rated upon. The effects of household agecomposition are accounted for by includ-ing the proportion of household membersin specified age groups. This approachmay be viewed as a pragmatic alternativeto a theoretically pure adult equivalentscale specification. To allow for slope andintercept changes between participantsand nonparticipants, the above variables,bonus income, and a unit vector (to allowfor a change in the intercept) were inter-acted with the dummy participation vari-able. Only bonus income, the North Cen-tral region, urbanization, and variablesrepresenting the presence of infants andthe elderly were found to be statisticallysignificant.

The decision to participate in the FSPis postulated to be influenced by regionand urban location of household resi-dence, home ownership, race, employ-ment status of male and/or female head,education level of household head, pres-ence of person(s) over 65 years old in thehousehold, presence of only a female

household head, a participation cost/ben-efit ratio, and the potential food and non-food expenditure enhancements. The lo-cation of household residence variables arenot of direct interest but are included inthe model to adjust for environmental andrelated factors which are not directly ob-servable.

Home ownership is expected to have anegative influence on participation.Households which own homes will gen-erally have both higher assets and futureincome streams than similar non home-owning households, hence, the need tosupplement food expenditures via pro-gram entry is diminished.

Sex, age, education, race, and employ-ment status of the household head, as wellas the presence of both a male and femalehead, measure characteristics of individ-uals in the household that are expected tobe related to the household's employmentopportunities, earning potential and per-manent income. Epperson et al. and Laneet al. found that money income was neg-atively related to FSP participation. Con-sequently, the effect of these variables onparticipation is hypothesized to be in-versely related to their effect on income.

The cost/benefit ratio is expected to benegatively related to participation. Highercosts of program entry relative to expect-ed benefits make the program less attrac-tive to eligible households.

Both the food and nonfood differentialsshould be positively related to programentry as both variables essentially relate toprogram benefits. The higher the poten-tial benefits to participation the greater isthe probability a household will enter theFSP.

The actual variables utilized in theanalysis are described in Table 1. Thevariables corresponding to the vectors Qi,Xi, and Zi are detailed in the same table.The actual sample size used in the analysisis 3,852. The loss in observations from theoriginal sample is due largely to missing

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Smallwood and Blaylock


TABLE 1. Definitions of Model Variables.

Included in Vector

Label Qj Zj Xj Definition

v NC = 1 if household resides in North Central; zero otherwiseS = 1 if household resides in South; zero otherwiseW = 1 if household resides in West; zero otherwiseU = 1 if household resides in an SMSA suburban area; zero other-

wiseHO = 1 if household owns a home; zero otherwiseR = 1 if household head is black; zero otherwiseD = 1 if household received food stamps last month and this month;

zero otherwiseNumber of guest mealsSLR = 1 if household had school lunches at reduced prices; zero oth-

erwiseFood expenditure enhancementNonfood expenditure enhancementDollar value per person of purchased food used from home supplies

in a weekEM = 1 if household has an employed male head; zero otherwiseEF = 1 if household has an employed female head; zero otherwiseFH = 1 if household has a female head and no male head; zero other-

wiseE = 1 if household head is at least a high school graduate; zero oth-

erwisev Proportion of household composed of members under age 3

Proportion of household composed of members of age 3 to 12Proportion of household composed of members of age 13 to 19Proportion of household composed of members of age 20 to 39

v Proportion of household composed of members of age 65 or olderLast month's household income in dollars on a weekly per person ba-

sisv Expected weekly bonus value of food stamps to eligible households

regardless of whether they participateELD = 1 if male or female household head is 65 years or older; zero

otherwiseExpected weekly purchase requirement divided by expected weekly

allotment

data on income and reporting errors infood stamp information.

Empirical Results

Due to cost considerations, the statisti-cally consistent recursive estimator men-tioned above was used during preliminarymodel selection. Parameter estimates forthe selected model were found to be ro-bust to the entry and exit of other socio-economic variables considered. Subse-quently, these parameter estimates wereused as starting values in obtaining the

maximum liklihood estimates reported inTable 2. Estimates obtained from the twoprocedures were found to be virtuallyidentical.

Results from the estimated expenditureequation reveal that urbanization andgeographic region of household residence,size and age composition of the house-hold, number of guest meals served, race,number of reduced price and free schoollunches, money income, and participationin the Food Stamp Program were signifi-cant determinants of the level of food ex-penditures. For example, per person

48

NCSWU

HORD

GMSLR

V

V

VV

V

FEENEEFE/F

EMEFFH

E

V

V

,/

P1/FP2/FP3/FP4/FP5/FY/F

V

V

V

V

V

V

EB

ELD

PR/ALLOT

V

V

July 1985


weekly food expenditures were found tobe highest in the Northeast region andlowest in the South. Blacks were found tospend more per person on food from homesupplies than nonblacks. Whether this lat-ter result is due to underlying racial influ-ences on the types and quantities of foodpurchased is unknown. As would be ex-pected, food expenditures increased withthe number of guest meals served.

Households with children receiving re-duced or free school lunches spent less thantheir counterparts not receiving thelunches. This is consistent with the hy-pothesis that government subsidized mealssubstitute, at least partially, for meals thatwould otherwise have been purchased bythe household.

The estimated marginal propensity tospend (MPS) on food out of bonus incomewas over twice as large as that for moneyincome and the two coefficients werefound to be statistically different at the0.05 level. The MPS on food out of moneyincome was about 9.9 cents per dollar andthe corresponding MPS out of bonus in-come was approximately 23 cents per dol-lar. The above indicates that one can re-ject the hypothesis generated from thetraditional economic model that bonus in-come is allocated the same as money in-come.

In addition to the estimated effect ofbonus income on food expenditures, anadditional program participation effectwas found which varies with region andurban locations of household residence andage of household members. The partici-pation effect on food expenditures wasfound to be significantly larger for house-hold members under three and those 65and older than for those of other ages. Forexample, holding bonus income and otherfactors constant, the participation effectincreased food expenditures $3.14($2.9435 + $0.1981) weekly for each childunder 3 years and $1.72 ($1.5218 +$0.1981) weekly for each adult 65 yearsor older compared with the participation

TABLE 2. Asymptotically Efficient Estimatesof FSP Participation and Food Ex-penditure Model.

Participation Equation

Variable Coefficient Variable Coefficient

Constant 1.2639 FH 0.5774(0.2491) (0.0880)

NC -0.8101 E -0.3996(0.1777) (0.0933)

S -1.2395 ELD -0.3417(0.1443) (0.198)

W -1.1639 R 0.3201(0.1841) (0.0816)

U -0.4246 PR/ -1.4477(0.1245) ALLOT (0.3564)

HO -0.6589 FEE 0.0265(0.0832) (0.0161)

EM -1.5216 NEE 0.0256(0.1314) (0.0078)

EF -1.055(0.1168)

Variable Food Expenditure Equation

Coefficient Variable Coefficient

Constant 11.4846 P3/F 2.3751(0.5574) (0.6594)

NC -0.9760 P4/F -0.6411(0.5025) (0.5117)

S -1.4548 P5/F -2.3494(0.3625) (0.3701)

W -0.5524 Y/F 0.0991(0.4760) (0.0082)

U -0.1346 D 0.1981(0.3250) (0.7782)

SLR -0.9754 (EB/F)*D 0.2328(0.3250) (0.1098)

R 1.0271 NC*D 0.9501(0.2070) (0.6021)

GM/F 1.2453 U*D -0.9600(0.1015) (0.5689)

P1/F -7.8727 (P1/F)*D 2.9435(1.2201) (1.6894)

P2/F -3.4046 (P5/F)*D 1.5218(0.6600) (0.5393)

Note: Asymptotic standard errors in parentheses.

effect for the base group (all other ages)of approximately $0.20 per person perweek. Consequently, the program appearsto increase food expenditures most forthose population subsets often identified

49



TABLE 3. Effects of a 1-Unit Change in theIndependent Variables on theProbability of FSP Participation byEligible Households. a

Change inIndependent Variable Probability

RegionNorth Central -0.1713South -0.2955West -0.2265

SMSA, non central city -0.0953Home ownership -0.1509Race 0.0750Female head only 0.1344Female head works -0.2167Male head works -0.2974Elderly head -0.0788Education of meal planner -0.0909Cost-benefit ratiob -0.0032Expected bonus stamps 0.0060

a The effects of changes in the independent variablesare computed from the estimated participation equa-tion evaluated at the mean values of the independentvariables.

b A unit change in the cost-benefit ratio is assumed tobe a 1-percentage point change.

as most in need of public assistance (i.e.,the elderly and infants). 9

Most coefficients estimated in the par-ticipation equation were statistically sig-nificant at the usual confidence levels withthe signs as expected a priori. The modelcorrectly classifies 72.6 percent of the ob-servations using the (0.5, 0.5) criteria. Forthis criterion, a correct classification meansthat the predicted probability equals orexceeds 0.5 for participating households

9 An expenditure equation similar to the one above,except that interactions between household agecomposition, region, urbanization, and FSP partic-ipation were excluded, was estimated. The resultwas to increase the effect attributed to bonus in-come to about 3 times the effect of money income(i.e., an MPS for money income of 0.10 and an MPSfor bonus income of 0.32). This latter result is con-sistent with some earlier studies (Neenan and Davis;West and Price) which also omitted the interactioneffects but is misleading as the model omits statis-tically relevant variables which are correlated withthe included variables. The net effect is to attributeeffects to bonus income which should be attributedto other variables.

TABLE 4. Effect on the Probability of FSPParticipation Given Changes in thePurchase Requirement.a

Pur- Proba-chase Bonus Value bility of

Require- Allot- Partici-ment ment Total FEE NEE pation

0 32 32 9.93 22.07 0.615 32 27 8.74 18.26 0.53

13b 32 b 19 6.83 12.17 0.3918 32 14 5.63 8.37 0.3125 32 7 3.96 3.04 0.21

................................................................................................................................

0 19 19 6.83 12.17 0.53

aAll variables except the weekly purchase require-ment, allotment, and expected bonus are evaluatedat the sample means.

b Sample means of allotment and purchase require-ment rounded up.

or is below 0.5 for nonparticipating house-holds.

The estimated effects of the indepen-dent variables on the probability of FSPparticipation are reported in Table 3.Variables, other than the one being ex-amined, are held constant at their respec-tive sample means. For example, theprobability of FSP participation in theNortheast (omitted base) region rangesfrom 17 to 30 percentage points higher atthe sample means than in the other threeregions. The probability of participationwas lowest in the South followed by theWest and North Central regions.

Households residing in the suburbanportion of an SMSA were found less likelyto participate in the program. Thesehouseholds had a probability of partici-pation approximately 10 percentage pointsless than other households. Eligible house-holds which don't own a home had aprobability of participation that was 15percentage points higher than for home-owners. Black households were about 7 to8 percentage points more likely to partic-ipate than similar nonblack households.Households with only a female head were13 percentage points more likely to par-ticipate than other similar households. Aworking male or female head of house-

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hold was associated with a reduction inthe probability of FSP participation rang-ing from 22 to 30 percentage points overhouseholds with unemployed heads.Households with an elderly head wereabout 8 percent less likely to participatethan similar nonelderly households. Also,households in which the primary mealplanner had completed high school were10 percent less likely to participate in theFSP than similar households where themeal planner has less education.

The cost/benefit ratio was negativelyrelated to participation, as expected. 10 A10 percent increase in the cost/benefit ra-tio was asociated with a 3.2 percentagepoint decline in the likelihood of partici-pation at the sample means. This indicatesthat as the purchase requirement is de-creased (with the allotment held constant)participation would be expected to in-crease. Consequently, the purchase re-quirement may be viewed as a significantdeterrent to participation.

The effects of the potential food andnonfood expenditure enhancements onFSP participation were found to be vir-tually identical and a statistical test for theequality of a, and a2 was not rejected atthe .05 level. This implies that households,in deciding whether or not to participatein the FSP, place equal value on the po-tentials for increasing food and nonfoodspending. However, as shown above, thosehouseholds that actually decide to partic-ipate appear to allocate bonus incomemore towards food expenditures thanwould be predicted via an equivalent

10 A purchase requirement to income ratio variablewas tried as an alternative to the purchase require-ment to allotment ratio in a preliminary modelspecification. However, all specifications that in-cluded an income term gave problems due to theclose functional relationship between the FSP vari-ables and income. Because we thought that pro-gram benefits were more important to participa-tion than the potential effect of declining marginalutility of income, we chose not to include incometerms.

amount of money income. Consequently,the fact that potential benefits are in theform of food stamps rather than cash doesnot appear to be a deterrent to partici-pation although the bonus stamp benefitsare allocated differently than the moneyincome. Furthermore, this result (a, = a,)is of particular importance because it im-plies that the two-equation system neednot be estimated simultaneously and thata simpler model which combines the foodand nonfood expenditure enhancementsinto the expected bonus provides efficientparameter estimates. Also, as shown in Ta-ble 3, a $10 increase in the expectedweekly bonus stamps was associated witha 6 percentage point increase in the like-lihood of program participation.

The model can be used to simulate theeffects of policy instruments on the prob-ability of participation and the subse-quent effect on the food and nonfood en-hancements. The major policy instrumentsby which administrators can influenceparticipation and food expenditures arethe allowable deductions from income, thepurchase requirement, asset limits, and theallotment amount. Changes in asset limitsand allowable income deductions havebeen the primary policy instruments used.Since the purchase requirement is deter-mined by household size, income, and al-lowable income deductions, changes in in-come and allowable income deductionscan be viewed within our model as directchanges in the purchase requirement. This,in turn, will influence bonus stamp in-come and the cost-benefit ratio.

Presented in Table 4 are the results ofalternate scenarios involving hypotheticalchanges in the purchase requirement. Forexample, if the purchase requirement iseliminated and all other exogenous vari-ables including the allotment are evalu-ated at their sample means, the probabil-ity of participation increases from 0.39 to0.61. In addition, the household's weeklyfood and nonfood expenditure enhance-ments increase from $6.83 and $12.17 to

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$9.93 and $22.07, respectively, under thisscenario. Conversely, increasing the pur-chase requirement or decreasing the al-lowable income deductions decreases bo-nus income, the food and nonfoodexpenditure enhancements, and the prob-ability of participation. Also presented inTable 4 are the results of simultaneouslyeliminating the purchase requirement andreducing the allotment by the same dollaramount. This scenario is similar to the leg-islated removal of the purchase require-ment in January 1979. Our simulations in-dicate that eliminating the purchaserequirement would increase the probabil-ity of participation by 14 percentage pointsfrom the base probability calculated at thesample means of all variables. Assumingno change in the eligible population, thisimplies a 36-percent increase in programenrollment. Actual FSP enrollment in-creased 17.9 percent and 15.9 percent, re-spectively, in the two calendar years fol-lowing the elimination of the purchaserequirement (EPR). Of course, actual en-rollment growth during this time was par-tially due to an increase in eligible house-holds caused by poor economic conditions.In summary, while regulations governingnet transfers per household changed onlymodestly with elimination of the purchaserequirement, total program cost increasedsubstantially due to increased enrollment.

Conclusions

An economic model of household be-havior was developed to analyze the ef-fects of FSP policy control variables onfood expenditures and program partici-pation rates. The model postulated thatFSP participation by eligible householdsis determined, in part, by the opportu-nities households have and choices house-holds make with regard to the allocationof their in-kind income transfer. The op-portunities to enhance food and nonfoodspending via program participation andreceipt of bonus stamp income were found

to have the same effects on program par-ticipation. In the context of our model,this finding implies that the participationdecision can be considered independentlyof the allocation of both money incomeand food stamps to food and nonfooditems. Thus, there was no indication thathouseholds with a greater preference forfood (larger food expenditure enhance-ment) were more likely to participate thanother households.

Statistical tests revealed that the levelof expected bonus stamp income has a sig-nificant positive influence on the proba-bility of program participation. For ex-ample, a $10 increase in expected weeklybonus stamp income was found to in-crease the probability of participation byapproximately 6 percentage points. Also,additional bonus stamp income was foundto have more than twice the effect on foodspending as additional money income.This suggests that replacing stamps withcash would be substantially less effectiveas a food enhancing program.

Food expenditure differentials associ-ated with FSP participation were foundto be larger for households with elderlypersons or infants present. Whether thiseffect is due to pure program effects or tothe type of household self-selecting intothe program is not clear. Some simple testsfor sample selection bias using Heckman'sprocedure did not indicate its presence forthis sample. In any case, these householdtypes appear to benefit more from FSPparticipation in terms of increased foodexpenditures than others.

The cost-benefit ratio associated withparticipation, defined as the ratio of theexpected purchase requirement to the al-lotment, was found to be a significant fac-tor influencing participation. Programparticipation was found to decline mark-edly as the cost-benefit ratio was in-creased. Since the most needy householdstend to have lower cost-benefit ratios, thisresult suggests that policy instrumentswhich influence this ratio can be used as

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effective tools to control program costwhile minimizing the deleterious effectsof program budget reductions. That is, thepurchase requirement, if re-enacted, couldbe used as a policy instrument to limitparticipation of "marginal" householdswithout further restricting the eligibilityrequirements or reducing the net transferof benefits per household. In this sense,the purchase requirement may be a polit-ically acceptable means of controlling theFSP budget.

These empirical findings together withthose of Clarkson, Huang et al., Mittel-hammer and West, and many others sug-gest that the traditional indifference curvemodel of consumer behavior used to ana-lyze the FSP does not adequately explainthe effects of FSP on food spending. Tobetter understand the determinants ofprogram participation and the program ef-fects on food spending and nutritional ad-equacy, improved economic models willhave to be developed. Future research ef-forts on theoretical modeling will proba-bly be most fruitful in the area of mod-eling the income constraint and thosefactors related to financial managementand resource allocation in low incomehouseholds. Lastly, we offer our results inhope that this research may stimulate de-bate on the appropriateness of the tradi-tional food stamp model and will generatehypotheses which can be tested with morerecent data (after elimination of the pur-chase requirement) such as the 1979-80supplemental low income sample to theUSDA Nationwide Food ConsumptionSurvey.

References

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Simultaneous Equations Analysis with Qualitativeand Continuous Dependent Variables." Paper pre-sented at the Regional Research Committee Meet-ing, S-165, Atlanta, Georgia, October 19, 1982.

Clarkson, Kenneth. Food Stamps and Nutrition.American Enterprise Institute, Washington, D.C.,1975.

Danziger, Sheldon, Robert Haveman, and RobertPlotnick. "How Income Transfer Programs AffectWork, Savings, and the Income Distribution: ACritical Review." Journal of Economic Litera-ture, (1981): 975-1028.

Epperson, J. E., C. L. Huang, S. M. Fletcher, and W.K. Searce. "The Determinants of Food Stamp Pro-gram Participation." Southern Journal of Agri-cultural Economics, 12(1980): 93-7.

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Heckman, Jes. "Sample Selection Bias as a Specifi-cation Error." Econometrica, 47(1979): 153-61.

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Rao, C. R. Linear Statistical Inference and Its Ap-plications. John Wiley and Sons, Inc., New York,1965.

Rungeling, B. and L. H. Smith. Factors AffectingFood Stamp Program Nonparticipation in theRural South. University of Mississippi: Center forManpower Studies, January 1975.

Schmidt, Peter. "Estimation of a Simultaneous Equa-tions Model with Jointly Dependent Continuousand Qualitative Variables: The Union-EarningsQuestion Revisited." International Economic Re-view, (1978): 453-65.

Searce, W. K., P. J. Marshall, and R. B. Jensen. "FoodStamps: A Study in Two Virginia Localities." De-partment of Agricultural Economics, VirginiaPolytechnic Institute and State University, Blacks-burg, Virginia, March 1975.

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