The Impact of Food Stamps on Food Expenditures: Rejection - of the Traditional Model


 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
  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

 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 Association
38 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

Senauer and Young
                                                                                Impact of Food Stamps on Food Expenditures
  Table 1. The Marginal Propensities to Consume for Food
                                                         at Home from Money Income and
  Food Stamp Bonus from Various 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
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
                                        (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.

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.]

The empirical evidence rejects the traditional
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