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 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 nV
Senauer 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 recipients the impact of food stamps is solely Allen Joyce E., and Kenneth E.Gadson. "Nutrient Con- through the income effect. The results indicate Al sumption npe Patterns attens ofof Low-Income Hu eholds." L o n . Households." that food stamps have a significantly greater Washington DC: U.S. Department of Agriculture, impact on food purchases than an equal Economic Research Service, Tech. Bull. No. 1685. amount of cash income, even when they are June 1983. an unrestricted transfer. These findings have Basiotis, Peter, Mark Brown, S. R.Johnson. and Karen J. important implications for both current policy Morgan. "Nutrient Availability, Food Costs and and future research concerning the Food Food Stamp Program Participation for Low-Income Stamp Program. Households." Amer. J. Agr. Econ. 65(1983):685-93. A recent issue of significant policy debate Benus, J., J. Krii,.zta, and H. Shapiro. "The Dynamics of was the effect of elimination of the food stamp Household Budget Allocation to Food Expenditure." purchase requirement (EPR) on tile program's Rev. Econ. and Statist. 58(1976):129-38. ipcasenreuadir ng fChavas. Jean-Paul. "Future Directions for Domestic impact on expanding food demand. Predic- Food Policy." Amer. J.Agr. Econ. 66(1984):225-31. t~ons were made that after EPR the program's Chavas, Jean-Paul, and M. L. Young. "Effects of the impact on food spending would be severely Food Stamp Program on Food Consumption in the reduced and would be only slightly greater Southern United States." S.J.Agr. Econ. 14(1982): than a cash transfer (Salathe, p. 92). Based on 131-39. the traditional theory, the reasoning was that Chen, Jain-Shing A., and Stanley R. Johnson. "Food EPR would shift a substantial number of recip- Stamp Program Participation and Food Cost: A ient households from an extramarginal, re- Simultaneous Equations Analysis with Qualitative stricted transfer situation to an inframarginal, and Continuous Dependent Variables." Paper pre unrestricted one. The results for 1979, follow- sented at the Regional Research Committee Meeting, S-165, Atlanta GA, 19 Oct. 1987. ing EPR, confirm that food stamps still have a Huang, Chung L.. Stanley M. Fetcher, and Robert substantially greater impact on food spending Raunil:ar. "Modeling the Effect; of the Food Stamp than an equivalent amount of cash income. Program or. Participating House;holds' Purchases: An A current policy issue involves the effect Empirical Application." S. J.Agr. Econ. 13(1981): cashing-out the present program, replacing 21-28. food stamps with a cash transfer, would have Hyman, Saul, and Harold Shapiro. "The Allocation of on household food expenditures and aggregate Household Income to Food Consumption." Five food demand. The traditional model, given the Thousand American Families-Patterns of Eco large proportion of inframarginal recipients af- nomic Progress, vol. 2. ed. Greg J. Duncan and ter EPR,, suggests ses a relatively James N. Morgan, toer bPR. small impact. artilysalloimpact for Social Research,pp.I niversity "3-79. Ann Arbor: Institute of Michigan, 1974. However, because inframarginal households Institute for Social Research, Survey Research Center, treat stamps differently than cash, the decline tJr.versity of Michigan. A Panel Study of Income in food expenditures with a cash-out could be Dynamics: Procedures and Tape Codes-1979 Inter substantial. The results of this study suggest viewing Year-Wave XIi, A Supplement. Ann Arbor that if a policy objective is to increase recipi- 1I1, Is0. yo
Senauer and Young Impact oj Food Stamp.%on Food tpenditures 43 Johnson, Stanley R., James A. Burt. and Karen J.Mor- cisions." Ph.D. thesis, University of California, gan. "The Food Stamp Program: Participation, Food Davis, 1983. Costs, and Diet Quality for Low-Income House- Salathe, Larry. "Impact of Elimination of the Food holds." Food Technol. 359!981:58-70. Stamp Program's Purchase Requirement on Parlici Judge, George G., William E. Uriffiths, R. Carter Hill. pants' Food Purchases." S. J. Agr. Econ. 12(1980): and Tsoung-Chao Lee. The Theory and Practice of 87-92. Econometric.. New York: John Wiley & Sons. 1980. Smaliwood, David M., and James Blaylock. "Analysis of McDonald, John F., and Robert A. Moffitt. "The Uses of Food Stamp Program Particiztion and Food Exlpen Tobit Analysis." Rev. Econ. and Stati.t. 62(19910): ditures." Mimeographed. Washington DC: U.S. De 318-21. partment of Agriculture, Economic Research Ser Mittelhammer. Ronald, and Donald A. West. "Food vice, Feb. 1983. Stamp Participation among Low-Income House- Southworth, Herman M. "The Economics of Public Mea holds: Theoretical Considerations of th:- Impact on sures to Subsidize Food Consumption." J. Farm the Demand for Food." S. J. Agr. Econ. 711975):223- Econ. 27(1945):38-66. 31. Tobin, James. "Estimation of Relationships for Limited Neenan, Pameia H., and Carlton G. Davis. "Impact of the Dependent Variables." Eonometrica 26(19581:24 Food Stamp Program on Low-income Household 36. Food Consumption in Rural Florida." S. J. Agr. West. Donald. "Effects of the Food Stamp Program on Econ. 9(1977):89-97. Food Expenditures: An Analysis of the BLS Con Olsen, Edgar 0. "Some Theorems in the Theory of Effi- sumer Expenditure Survey 1973-74 Dairy Data." Re cient Transfers." J. Polit. Econ. 79(1971):166-76. port to the Food and Nutrition Service. U.S Depart Phillips, Kathryn S.. and David W. Price. "A Compara- ment of Agriculture. 1979. tive Theoretical Analysis of the Impact of the Food West. Donald A.. and David W. Price. "The Effects of Stamp Program as Opposed to Cah Transfers on the Income. Assets, Food Programs, and Household Size Demand for Food." Wc.'.t. J. Agr. Econ. 6(1982):53- on Food Consumption." Amer. J. Agr. Econ. 66. 58(19761:725-30. Price, David W. "Unit Equivalent Scales for Specific West, Donald A., David W. Price, and Dorothy A. Price. Food Commodities." Amer. J. Agr. Econ. 52(1970): "Impacts of the Food Stamp Pro',ram on Value of 224-33. Food Consumed and Nutrient Intake among Wash Ranney. Christine. "A Study of the Interdependent Food ington Households with 8-12-Year-Old Children.*" Stamp Program Participation and Food Demand De- West. J.Agr. Econ. 3(1978):131-44.
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