The Impact of Food Stamps on Food Expenditures: Rejection - of the Traditional Model
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II The Impact of Food Stamps on Food Expenditures: Rejection of the Traditional Model Ben Senauer Nathan Young Reprinted from the American Journal of Agricultural Economics Vol. 68, No. 1, February 1986 Reprint No. 86
The IniDact of Food Stamps on Food
Expetditures: Rejection of the Traditional
Model
Ben Senauer and Nathan Young
For food stam recipients whose ;..rmal food purchases
exceed their coupon
allotment, the traditional economic model predicts that the
impact of food stamps on
food spending will be the same as for an equal cash transfer.
The Tobit analysis in
this study indicates that, for these recipients, food stamps
have a substantially greater
impact on at-home food ,;xpenditures than an equal amount
of cash income. These
results reject the traditional model. Several possible explanations of this behavior are
discussed.
Key words: food exp2nditures, food stamps, Tobit analysis.
The effectiveness of the Food Stamp Program spend no additional cash beyond their food
(FSP) at expanding recipients' food expendi- stamp allotment on food.
tures is an issue of significant policy interest The primary purpose of this study was spe
and has received considerable research atten- cifically to implement a test of the Southworth
tion. A model first presented in a 1945 article model. The empirical analysis utilized data
by' Herman South worth, and refined and mod- from the University of Michigan's Panel Study
ified by others since then, has become uni- of Income Dynamics (PSID). By using data for
versally accepted as the conceptual basis for 1978 and 1979, the impact of food stamps on
explaining the relation between food stamps food spending prior to and following the elimi
and food spending (Huang, Fletcher, and nation of the purchase requirement (EPR)
Raunikar; Mittelhammer and West; Neenan could be assessed. The empirical results dem
and Davis; Olsen; and Phillips and Price). The onstrate that the Southworth model is incom
Southworth model distinguishes between two plete. Several possible factors are suggested
types of households receiving food stamps. to explain the observed difference between
For participating households whose food ex- the impact of cash income and food stanps on
penditures exceed their coupon allotment, the household food expenditures, even for in
program is inframarginal and functions as an framarginal recipients.
unrestricted transfer. For those recipients the
marginal effect of food stamps on food pur
chases should be no different than for an The Traditional Model and Previous Research
equivalent cash income subsidy. The other
cate:gory of participants includes those house- The traditional Southworth model may be
holds for which the program is extramarginal summarized as:
and acts as a restricted transfer. For these Maximize U = U(FX)
households the coupon allotment exceeds subj e +-F
their pre-participation level of food spending; subject to: PMX + PfF M + FSBON
and, while participating in the program, they and PA,'togethe.
which M imply: PfF >-FSBON
Ben Senauer is a professor and Nathan Young is a graduate re + FSPA Y
search issistant in the Department of Agricultural and Applied
Economics, University of Minnesota. This paper was completed where the utility function contains F (food
while Senauer was a visiting research used at home) and X (food away from home
fellow at the
Food Policy Research Institute. Washington DC. international and nonfood), and P,and Pf are the respective
Review was coordinated by Bruce Gardner, associate editor,
prices with M (money income), FSBON (food
Copyright 1986 Americar Agricultural Economics Association38 February 1986 Amer. J. Agr. Econ.
stamp bonus value), and FSPA Y (food stamp because a sufficient number of hou';eholds
payment) in the budget constraints. The final were assumed to be in the extramarginal, re
constraint simply indicates that all food stricted recipient category to explain the
stamps received are used to purchase food. higher MPC from food stamps (Chavas, p.
After elimination of the purchase requirement, 226), However, given the various reforms of
FSPA Y is zero and FSBON equals FS (food the FSP over the last twenty years which have
stamp allotment); otherwise FS equals continually reduced the number of extramar
+SBON plus FSPAY. One common hy- ginal recipients, this rationalization has be
pothesis generated by this model is that for come increasingly dubious. This paper conclu
inframarginal households with PfF > FS.then sively demonstrates that this explanation does
MPC = MPCFsBON; the marginal propen- not adequately account for the higher MPC
sities to consume for food at home from cash from food stamps than cash.
income (M) and the food stamp bonus
(FSBON) should be equal, if at-home food
spending exceeds the allotment. The Data and Statistical Model
However, in regressions that are nonlinear
in variables, this hypothesis could be difficult The PSID surveys covered approximately
to test since the marginal impact of a factor is 5,000 families, who were interviewed in the
not constant but depends on the level at which spring of each year, oversampling the lower
it is evaluated. An alternative, testable hy- income portion of the population (Institute for
pothesis used in this analysis is that for in- Social Research). The sample used in our
framarginal households the proportion of total econometric analysis was limited to inc!ude
hoisehold income received in the form of only households currently receiving food
bonus food stamps :;hould have no impact on stamps for two reasons. First, the questions
food spending. If PROPis defined as ESBON eliciting food expenditure information in the
(M 4-FSBON), then based on the Southworth PSID surveys were different for food stamp
model the expected impact of PROP on at- recipient and nonrecipient households. Sec
home food expenditures (PIF)is zero, if PIF ond, the impact of possible functional form
FS. misspecification can be partially offset if local
Table I summarizes the results of the previ- approxination properties are improved by
ous major empirical studies on the impact of making the sample more homogenous. The
food stamps on food expenditures. The data samples used contained 573 households for
bases, specific methodological approaches, 1978 and 574 for 1979. Separate regressions
and statistical techniques differed among were run for each year: 1978, which was prior
these studies. Nevertheless, each of these to EPR, and 1979, which was after EPR. The
studies provides a separate estimate of the purchase requirement was eliminated on a
marginal propensity to consume (MPC) for nationwide :asis in January 1979. In 1978, 164
food used at home from money income and households spent no additional cash on food
the food stamp bonus. 1In every study an addi- beyond their food stamp allotment. In 1979, 82
tional dollar of bonus food stamps has a sub- families were in this category. Therefore, the
stantially greater impact on food used at home program was an inframarginal, unrestricted
than a dollar increment in money income. The transfer for 71.4% of the recipients in 1978 and
marginal propensity related to the food stamp for 85.7% in 1979. The larger number of in
bonus is at least twice as large as that for cash framarginal recipients in 1979 reflected zhe im
income in every case. pact of EPR.
A shortcoming of these studies, though, is The design of the empirical analysis was ad
that they have not distinguished between in- justed for the fact that the food expenditure
fra- and extramarginal food stamp recipients and income data were not collected for a con
and have thus averaged together two possibly current period of tinme in the PSID. In the
quite different types of behavior. Further- PSID interview, the food expenditure ques
more, the traditional Southworth model has tion related to the previous month, whereas
not been rejected on the basis of these results the income questions related to the preceding
calendar year. For example, the income data
Sumc. of these studies relate to household ifood expenditures collected in the spring 1979 PSID survey are
and others to (he valueofactual food consumed. rhe term MPC is for 1978, arid the 1980 survey contains 1979
applie 4 ,oboth cases, calendar year income data. To overcome this
nVSenauer and Young
Impact of Food Stamps on Food Expenditures
39
Table 1. The Marginal Propensities to Consume for Food
at Home from Money Income and
Food Stamp Bonus from Various Studies
Studies'
MPC (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Money income .14 .05 .03 .03 .05 .13 .06 .06 .10
Bonus .35 .86 .08
.56 .31 .30 .37 .45 .17 .23 .30
Sources: Study (1) Hyman and Shapiro. p 267 (fie, res given are
for urban. os-income household,): (21Benus. Kmenta. mnd Shapiro.
p. 137; (3)West, p.49 (Model I). (4) West. Price. and Pnce. p.
(5) West and Pnce. pp. 728-29; (6)Chavas and Iroung. p. 136 137 (evaluatd at the mean, MP( for income denrd from the elasticily:
(estimae, are for metrop.ilitan households %.ithnon-black. non-college.
educated heads; (7)Neenn and Davis. p. 95 (for fond stamp
participant, e,,aluated i! group sample means). (HoJohnson.
Morgan, pp. 62-63 [equation (3)1:(9) Smallwood and IPlay)ock. Burt. and
p. 20; (1) Allen an I Gadson. p. 42.
problem, the regression analysis included as PROPL, the proportion of total income re
explanatory variables both the current calen- ceived as bonus food stamps in [he year pre
dar year's income and that for the previous ceding the food expenditure data; LnAGEH,,
year. This approach also had the beneficial ef- the log of the age of the household head in
feet of reducing the bias introduced by transi- years; LntAE,, the log of an adult equivalent
tcry income. To e.plain household food cx- scale, which accounts for family size and com
penditures in the spring 1979 month, for position; SEXH, the sex of the household
example, both the income data for calendar head, 0 if male and I if female; RACE,. race of
year 1979 and 1978 were included. Some the household head, 0 if white and I if non
thought was given to combining current and white: LnFSj, the log of the food stamp allot
lagged income in some arbitrary weighted av- ment received: and ui is the error term.
erage. However, it seemed preferable to in- The logarithmic functional form utilized dis
clude both terms and to allow the data to dic- played a more homogenous error structure
tate the proper weighting. For the same reason than a linear form. Since the simple double
as for income, current and lagged variables for log formulation imposes a constant income
the proportion of total household incime re- elasticity, the income squared terms were
ceived in the form of bonus food stamps included. Inclusion of four income terms in
(PROP) were introduced, equation (la) undoubtedly introduced some
The full empirical model specified for infra- "i"%icollinearity.
However, as the point of the
marginal households was statistical analysis was a specific hypothesis
Y)2 2 test,
(1a) LnFEH =a + bLnli + b(LnYL) some alossconservative approach wa s to accept
in efficiency and in the power of the
+ b3jLnY~ +!,-b4(LiiYL1) test, in order to avoid invalidating the test due
+ cPROP + C2PROPL to omitting relevant variables. The dependent
+ dLnAGEH, + eLnAEi variable was specified on a household basis, as
+ fSEXH + gRACE + u, was done by Basiotis, Brown, Johnson, and
and the model for extramarginal households Morgan and Chen and Johnson, rather than on
was a per capita or per adult equivalent basis.- The
(Ib) LnFEH, = LnFSi 2 Our basic specification is also nmathematically equivalent
to
where LnFE1i is the log of the annual value of' the per adult equivalent model used by several previous
ers. In that model household food expenditure and income research
divided by the number of adult are
the ith household's food expenditures equivalent persons and adult
for use equivalent units are also included as a separate variable (Hyman
at home, including food purchased with food and Shapiro, and West and Price). Our basic model in exponential
stamps; LnY, the log of total household in- form is
come, including the value of bonus food
stamps, in the same year as the food expendi- FEa = ae ( AE) ,
If bot sides of this equation are divided by AE, one obtains
ture data; Ln YL,, the log of total household -
income, including the value of bonus food FEH/AE - a(Y) 5 (AE~d .
Then. if the terms on the right-hand side are rearranged by multi.
stamps received, in the year preceding the plying b)(AU'IAP.):
food expenditure data; PROPi, the proportion "
)
of total income received as bonus food stamps FEHIAE = a(YIAE) (AE *d - 1.
Only the interpretation of the coefficients for adult equivalent
in the same year as the food expenditure data; units is different between the above model and the specification
which we estimate.40 February 1986 Amer. J. Agr. Econ. sociodemographic vanables included as ex- To apply Tobit analysis, equations (la) and planatory factors are typical of those utilized (Ib) were respecified as in previous cross-sectional analyses of house hold food expenditures (Huang, Fletcher, and (2a) LnFEH1 = 3Xi + el, if 13X 1 + e1 > LnFSi Raunikar, pp. 23-24). An adult equivalent (2b) LnFEH = LnFSi, if P3Xi + ej
Senaver and Young Impact of Food Stamps on Food Expenditures 41
Table 2. Tobit Regression Results for Food Southworth model provides the null hypothe
Expenditures for Use at Home sis that the proportion of income received as
bonus food stamps should have no impact on
Independent Variables 1978 1979 food expenditures for nonlimit households.
CONSTANT .424 -2.765 Specifically, the variables PROP and PROPL
(.15)" (.93) are not expected to affect LnFEH. In additiou
LnY -. 136 1.850 to the regressions repoiled in table 2, re
2
(1.04) (2.90) stricted regressions which omitted PROP and
(LnY) .011 . PROPL were also estimated. A likelihood
(1.26) 6273
L.YL 1.436 -. 078 ratio test was then utilized !o test the joint
(2.27) (.32) significance of the curreat and lagged propor
(LnYI.)2 -. 172 .015 tion variables. Under the null hypothesis
(198) (0 0 which conforms to the Southworth model,
PROP. .077 .350
(.38) (I.66) twice the difference in value of the two log
PROPL .678 .274 likelihoods calculated will be distributed as a
(3.58; (1.30) chi-square variable with two degrees of free
LnAGEII -. 195 .014 dom. The chi-square statistics, plus the level
LnA E (3.54) (.25) of statistical significance, are given at the bot
.8017 .707
(00.6b) (8.44) tom of table 2. The traditional Southworth
SEXII -. 050 -. 043 model is rejected in both years at least at a 5%
(I.II) (.97) significance level.
RACE - .056 - .017
1.20) (.34)
Chi-square statistic 16.92 6.64
Significance level .01 .05 Possible Explanations
'The asymptotic t-ratiom are given in parentheses. The proptkrtion
of ob.ervations at the limit 1%.714 for 1978 and .857 for 1979. the Several possibilities exist which could explain
estimated varance of the error in the Tobit equations is .420 for the greater impact of food stamps than cash on
1978 and .455 for 1979. food spending, even when the transfer is unre
stricted. The first is that food stamps may gen
Interestingly, in 1979 the current income erate a sense of gratitude or responsibility
variables as well as the current proportion among recipients. Recipients could feei that
(PROP) are significant, and the lagged vari- since society intends for food stamps to be
ables are not. In 1978 the pa;iern is reversed, used to expand their food consumption, they
This reversal of pattern for these variables can should in fact use their allotment for that pur
perhaps be explained by the impact of the sub- pose. Second, intrahousehold differences in
stantial changes in FSP rules that coincided tastes may exist. Food stamps could give a
with eliminating the purchase requirement. In household member(s) with a greater prefer
the 1979 regressions the current income and ence for food or nutrition more control over
proportion variables reflect the impact of the the household budget, since they must be le
1979 rule change which included EPR, gaily allocated to food. A preliminary indirect
whereas the lagged variables do not. There test of this model, based upon interacting
was also a considerable turnover in the popu- SEXH with PROP and PROPL, failed to re
lation of food stamp recipients at that ime, as veal a significant intrahousehold preference
some recipient households with higher income difference effect. 4 However, further work
levels lost their eligibility. A test foi structural must be done to conclusively demonstrate this
difference between the 1978 and 1979 regres- result.
sions suggests the 1979 rule changes caused a A third possible explanation is provided by
shift in structure and that multicollinearity is the permanent income hypothesis. Food
unlikely to be a complete explanation for the stamps could be viewed as a more permanent
observed differences, source of income than that earned through em
Our statistical test of the Southworth model ployment, given the high unemployment rate
is based on its central implication, that for in- and temporary nature of employment experi-
framarginal recipients cash and food stamps
are equivalent in their effect on at-home food Amore extensive discussion of this test may be obtained from
expenditures. For our specification, the the authors.
(L..42 February 1986 Amer. J. Agr. Econ.
enced by many low-income households. ent household food expenditures, then the
Fourth, the dynamics of the household Food Stamp Program should not be cashed
budgetary process may be altered by the re- out.
ceipt of food stamps. When a household re- Finally, rejection of the traditional model
ceives a monthly food stamp allotment, larger poses significant new research questions. Pos
and/or more expensive food purchases are sible explanations of the observed behavior of
typically made early in the month. As the food food stamp recipients need to be refined and
purchased with food stamps runs out later in empirically tested. This investigation will
the month, the family may begin to eat less likely require a close examination of the actual
well, but also will spend cash to buy additional process households utilize to determine
food (West, Price, and Price). budget allocations.
[Received January 1984: final revision
received September 1984.]
Conclusions
The empirical evidence rejects the traditional
model, which predicts that for inframarginal References
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