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DIRECT SUBSIDIES AND INCOME REDISTRIBUTION: THE FOOD STAMP PROGRAM IN PUERTO RICO

Suphan Andie and Parimal Choudhury

Reprinted from

REVIEW OF SOCIAL ECONOMY Vol. XXXV, No. 1, April 1977

DIRECT SUBSIDIES AND INCOME REDISTRIBUTION: THE FOOD STAMP PROGRAM IN PUERTO RICO By Suphan Andic and Parimal Choudhury* University of Puerto Rico The past several decatles have seen a proliferation of fiscal inci dence studies, drawing inferences as to the redistributive effects of tax and expenditure policies. The more recent contributions have criticized the implicit use in such analyses of average utility functions in allocating the benefits ol public goods. Some have used declining marginal utility functions in allocating pure public goods, leaving the conventional assumptions untouched with respect to specific pub lic goods [Aaron & McGuire; Maital], Others have extended the new locus to specific goods as well. In doing so, some have maintained tlie assumption of marginal utility declining with income [Mann], while others have reversed it and maintained that perceived benefits rise proportionately with income [Neenan].1 In addition, a “consintmption approach" has also been introduced into the analysis in an attempt to reconstruct utility from data on spending behavior [Mann fe Perlis], Most studies, conventional or not, conclude that it would be more fruitful to concentrate attention on analyzing the incidence of limited and specific public expenditure programs. Simultaneously, there is lively discussion in recent literature on the kind of real redistribution society should seek. On the one hand, schemes such as the negative income tax [Friedman] advocate the transfer of general purchasing power to low income families rather than transfers in kind, which many public services and programs in volve, the general argument being that a cash grant would increase the welfare of the recipient more than an equal cost transfer in kind. On the other, it is argued that ordinary citizens are probably unwilling to finance substantial transfers of general purchasing power, but they would be willing to finance specific transfers either as income in kind •The authors would like to express their thanks to Fuat Andic and Ramdn Cao (Univ, of Puerto Rico), George Rohrlich (Temple University) and Dr. S. Hicmstra (U.S. Department of Agriculture) for their valuable comments. They arc grateful Io the Department of Social Services for cooperation in providing the necessary data. 1 'I'he case refers to local government services and the "exploitation" of the cen tral city by the suburbs. The same service is taken to yield a greater benefit for suburbs with median incomes in excess of the median income of the central city. 95

REVIEW OF SOCIAL ECONOMY

or as purchasing power earmarked for specific items of spending, be cause they would like to remove the external effect of poverty on their own well-being. |Buchanan] A change from the traditional welfare economics tenet of confining government interference to transfers of general purchasing power and leaving the allocation of specific goods to the competitive market is also observed in the attempts to show that the government can in general attain the highest level of welfare only by redistributing all goods [Foldes], and that there is a rigorous argument in Paretian welfare economics for subsidies in kind to result in optimal allocation of resources to increase the con sumption of certain goods by subsets of population f Olsen 1969, 1971 ]. 1 This paper represents an attempt to estimate the real redistributive ' impact of one public expenditure program which has the specific purpose of reducing poverty by direct transfers to families at the lower end of the income scale, the Food Stamp Program. The choice of this program is particularly relevant, since, as will be seen subse quently, it implicitly combines a general purchasing power transfer with specific transfers earmarked for the purchase of food. As such it lends itself to the illustration of the utility function approach in attempting to arrive at a subjective valuation by the households of the food that they obtain through the stamps and to count this value, together with the original general purchasing power transfer as the added income of families participating in the Program. The paper , makes no attempt to evaluate the efficiency with which the Program achieves an increase in the consumption of food by needy families. The redistributive impact is gauged with the evidence from Puerto Rico. In this particular case the lar-reaching impact of the program is accentuated by the fact that it is not financed from resources gen erated in the Island, i.e. by taxes levied on Puerto Rican taxpayers, but rather by direct transfers from the Federal budget to a number of families on the Island.2 The complex fiscal relations between Puerto Rico and the Federal Government are beyond the scope of this paper. So are the sociological and other implications, e.g. for

“There is a unique set of politico-economic relationships between Puerto Rico anti the United States which results from the applicability of various U.S. constitu tional provisions and Federal laws to Puerto Rico as well as of the approval of the Commonwealth Constitution of 1952. Among the many features of this relationship are the flow of federal funds for grants-in-aid and transfers, payments to individuals and businesses, partial inapplicability of federal tax legislation on the Island, and freedom to structure the Island’s fiscal system in a manner most appropriate to cope with its needs. For detailed analysis see Andie, Andie and Torruellas.

FOOD STAMP PROGRAM IN PUERTO RICO

work effort, of the Program. The intention is to estimate the direct effects of one particular subsidy on the relative position of families, comparing the pre-transfer with the post-transfer distribution of income.

Section I gives the salient features of the Food Stamp Program within the context of the economic characteristics of Puerto Rico. This is followed in Section II by the methodological foundation of the cal culations. Section III interprets the results. The paper concludes that J the food stamp program has significant redistributive impact in addi: tion to providing for the nutritional needs of economically deprived households. I Food stamps are coupons that can be exchanged only for food items (with some exceptions). Depending upon the level of income and the size of the family, they are either given freely or purchased by the families at a fraction of their face value. In essence, it is an income supplement program. Since the purchase price rises with the level of income, the amount of the supplement declines as incomes rise, for it is equivalent to the difference between the value of the stamps and their purchase price.

The schedule of payments for stamps of different values by families of same size and different levels of income is so constructed that in essence for every additional dollar of net income3 the purchase price rises by 30 cents, up to a maximum level of monthly income. A family of four, for example, with a net income of S300 a month, would pay §83 a month for stamps that are worth §158 and thereby receive addi tional purchasing power of §75 equivalent to 25% of net income. With a monthly income of §'100 the same family would pay §113 a month for the same value of stamps; the additional purchasing power would be reduced to §45 or 11.25% of net monthly income. The maximum allowable income at which this family still qualifies to receive stamps is §540, when payments for the same value of stamps would be §138, leaving a bonus of §20, or of 3.7% of monthly income. Thus, the absolute and the relative significance of the difference be tween the purchase price and the value of stamps (i.e. of the bonus) declines as income rises. 3 Nel income is determined by means of a complicated formula of deductions, which, it is estimated, average out to approximately 18% of gross income.

REVIEW OF SOCIAL ECONOMY

It should be emphasized that the program establishes a floor value for each given family size. In the example of the family of lour, this floor is S158 a month with income ranges between zero and S540 a month. It should be added that the Program allows for a variable purchase option entitling the families to one-fourth, one-half or three-fourths of the basic allotment. It is reported, however, that participant families do not make use of this option and elect to pur chase the basic allotment. The federal program was introduced in Puerto Rico in July 1974, as opposed to its mandatory nationwide application in the mainland in 1973. In the fiscal year 1975 about 43% of the families partici pated in the Program; §387.5 million of stamps were sold; their purchase price was S 106.9 million. The Federal Government was able to inject into the economy a net supplementary income of §280.6 million. This figure represents 4% of the Gross Domestic Product of the year. It is twice the 1975 budget of the Department of Social Services, 3.7 times as high as the fund allocated by the Fed eral Government to that Department, and 60% of federal transfers to individuals in fiscal year 1974 lor medicare, social security benefits and rent subsidies.4 When the Program began to operate, about one-half of the par ticipating families were already recipients of one sort of economic assistance or another. By June 1975 their proportion had declined to 10%. Undoubtedly, as the recession hit the Island’s economy and deepened over the year, and as unemployment reached unprecedented levels,5 the Program has acquired increasing importance in supple menting family incomes. Due to data deficiency, it is impossible to say offhand how many of the participants are unemployed; but un doubtedly most food stamp recipients are poor. Estimates for Novem ber 1975 indicate that 46.7% have reported gross incomes of under §1800 a year, 61.3% of under §3,000 year and 90.5% of under §5,400 a year. Only some 2,000 families (0.6% ol the total registered) ‘ Based on figures provided in P.R. Junta de Planificacidn. Informe EconArnico al Gobcrnador, 1974, Appendix Table 14. and P.R. Prcsupueslo para el aiio fiscal 1915, San Juan. Jan. 1974. - In constant prices the annual growth rate of GDP, which had averaged 7.3% I'Joj and ana 1973, tu/a, fell ten snarpiy between 1965 sharply to 1.7% in 1974; GDP actually declined by rate off-------unemployment "2.4% *“ in * 1975. The ----*-------- * in 1975 was estimated to be 15.4%; a year earlier it was 14.0%, and is expected to average 21% in 1976. By contrast, when the development effort was launched twenty-five y-five yeat sears ago, the island's unemployment rate was 1? ’% and —1 had ■—J declined ->—u.-~t to • - 10.8% 1 na% in 1970. 1 15.3%

FOOD STAMP PROGRAM IN PUERTO RICO

earn more than §9,000 a year. Given this situation, the assessment of the impact of the Program on the distribution of income, and on verifying the degree of its probable effect on the well-being of families with extremely low income levels, acquires a great deal of importance. II The food stamp progr am is one of many that seek to close the in come gap of families whose incomes are below a limit which society deems to be representative of a decent level of living. It is a mixed pro gram of formula-income transfers and in-kind subsidies. It is a for mula-income transfer because the difference between the value of the stamp allotments and their purchase price is determined by a mathematical formula which applies a rate of purchase price against the income deficiency of the family. Eligibility is determined only by an income/asset test for a given size of family; in other words, by income per person. The program requires no justification for not having any income; it pays benefits to all families with an income deficiency. The benefits consist of a subsidy in-kind, since the bonus stamps can be used for the purchase only of food items. These charac teristics make it an effective negative income tax program, but one which restricts the pattern of spending. For it guarantees a level of income for a family of given size, provided that the guaranteed income is all spent on food. The implicit marginal “tax” rate of the program is 30 per cent. The additional benefit that accrues from the program to participat ing families consists of the bonus, the difference between stamp allot ments and purchase price. Two alternatives are used in this paper to assess the distributive impact of this benefit. The first allocates the bonus outright to the appropriate income classes, estimates what private incomes would be with the added bonus of the program, com pares the actual distribution of income with the resulting one, and quantifies the change in the degree of inequality. This method as sumes that the income value of the food subsidy is equal to the cash bonus and that it is the same for each participating family; it ignores the differences in individual preferences. The second method estimates the benefits of participating families by separating the bonus into its two components. The first is the general purchasing power, the difference between food expenditures in the absence of the food stamp program participation and the pur chase price of the stamps. The second is the specific purchasing power,

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the difference between the bonus anti the general purchasing power. Thus, if a given family with a monthly income of S100 were to spend S60 on food in the absence of the program and were required to pay §25 for the purchase of stamps worth S158, the bonus would be $133 ($158 — $25). The general purchasing power would be $35 ($60 — S25) and the specific purchasing power would be §98. The utility benefit corresponding to this latter component will be determined by the recipient’s subjective valuation of this amount which can only be spent on food. The cash value of this subjective evaluation is esti mated by a Cobb-Douglas utility function of the following form [Clark son, p. 711:

U —

(Y — PR)1-'

(FS)' c

’

1-c

— Y

Where: U FS c Y PR

= = = = =

benefit monthly allotment of stamps average propensity to consume food family income purchase requirement

The methodology of computation, the sources of data, and the al location of benefits to the appropriate income groups are given in the Appendix. Suffice it to mention that the utility function used assumes constant elasticity ol income for food and non-food items within a given income bracket and for a given household size, but different elasticity coefficients for different income brackets and house hold sizes, and is assumed to be representative of the individual house holds in each cell of income level and family size. If the subjective value does not differ from the cash value, then general and specific purchasing power will sum up to the bonus. This is the optimal allocation of the subsidized good when the face value of the coupons for each eligible family is just sufficient to per mit the purchase of the optimal quantity at market price, leaving the family with just enough money to purchase the optimal quantities of other goods. [Olsen, 1971] If the subjective value falls short of the cash value, then obviously there is waste in the program. If the sub jective value exceeds the cash value, then the benefits of the program far surpass its cost. Needless to say the optimal levels are determined by the parameters as well as the form of the utility function.

FOOD STAMP PROGRAM IN PUERTO RICO

101

The analysis assumes that food stamps are solely used for purchases of food, i.e. their resale is effectively prevented. This is an assump tion of convenience, for the resale of stamps implies that the bonus would be reduced, and this reduction varies from one family to an other. The size of this reduction being unknown, it is impossible to to carry out a redistributive impact analysis. Furthermore, if one knew the resale value of the stamps for each family or for groups of families by income levels, there would have been no need to esti mate their subjective value by means of the utility function specified above, since the resale value would have been a measure of this sub jective value. The analysis also assumes that the program does not alter market prices; otherwise the utility function of the specified type cannot be applied. In any case the assumption is plausible for two reasons. The first is that the program is financed out of the federal budget and entails no local tax collection; consequently there are no direct ef fects on prices paid by and the disposable money incomes of par ticipating families. The second is that a great portion of consumer goods are imported from the mainland;0 consequently the long-run supply curve can be taken to be perfectly elastic. A further assump tion is the independence of utility functions.

III Basically, the sources of the data are the U.S. 1970 Census [1972, p. 51; 1973, p. 1151], and statistics from the P.R. Department of Social Services. The Census provides the latest information on the distribution of families and unrelated individuals by income levels. This refers to the year 1969. The analysis is, therefore, made in terms of appraising the changes that would occur in the income distribution in 1969 had the food stamp program been in operation in that year. It would have been more difficult and methodologically less desirable to project the income distribution to 1975, since there was no basis for it; the only figure available was the estimate of total families which was put at 726,193. [Choudhury, p. 122] One could have adopted the approach of no change in the relative position of families in 1975 and computed their incomes accordingly. But the resulting figures would have reflected higher incomes in every level of income due only to a greater number of families in each of them, and not take into account price level changes and growth which obviously alter the dis-

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REVIEW OF SOCIAL ECONOMY

tnbutive pattern. Hence the income distribution in 1969 is taken as the base and all data referring to 1975 are deflated. The methodo ogy and the procedure of adjustments are specified in the Appendix. Tables 1 and 2 compare the distribution of income in 1969 in the absence of the food stamp program with those obtained under the two alternatives. The redistributive impact is quite favorable. According to Alter native I, if the program were in existence in 1969 with specifications in effect as of November 1975, half of Puerto Rican families would lave experienced a 50% increase in their income share. The shares ° the top two deciles would have fallen from 70% to 59%, with a decline decline in in the the overall overall coefficient coefficient of of inequality inequality from from .5526 .5526 to .4781. Even more significant is the change in income distribution that re sults from the subjective valuation of the benefits by the individual households as determined by the specific utility function utilized and its coefficients (Alternative II, Table 1). Accordingly the share of the lowest half of the families is evaluated to have increased by 60% with the share of the top two deciles falling to 50.5%, and the coefficient of inequality to 0.4573. Obviously, the subjective valuation of the benefits favors the lower income groups even further. The reasons will be discussed subsequently. 7 able 2 shows the probable increase in average family incomes that would have arisen from the implementation of the Program un der the two alternative methods of benefit allocation. It presents the number of families and unrelated individuals in ascending order of income levels as provided in the 1970 Census, giving their aggregate income before and after the allocation of the net benefits of the Pro gram. For example, 126,270 families had annual incomes of $500 or less in 1969; their average income was calculated to be $196.50.7 °40% of all tradeables and more than 50% of food items consumed on the island are from the U.S.; consequently a very large portion of the bonus leaks out in the form of imports. Moreover, the prices of most of the basic food items are either controlled or frozen, and are permitted to rise only as changes in costs of produc tion allow. Estimates made by the P.R. Department of Social Services did not expect prices to rise appreciably as a result of the implementation of the Program (see Choudhury, p. 155). ’The published volume of the Census does not provide aggregate income figures corresponding to each income bracket. Average income of each bracket was com puted by means of statistical formulae (given in M. Leibenberg and H. Kaitz, “Dis tribution from Income Tax and Survey Data, 1944,” in National Bureau of Eco nomic Research: Studies in Income and Wealth, Vol. 13, New York, 1951, pp. 443445) and then multiplied by the frequencies to obtain the aggregate incomes.

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Allocation of the net bonus of the Program according to the first alternative would have more than tripled their average income moving them tip to the income group of S500-$l,000. Similarly fam ilies with average annual income of $732.00 would have experienced an increase of around 80% which would have located them in the income bracket of $l,000-$2,000. Similar but somewhat more pro nounced results are obtained with the second alternative: for every level of income affected by the food stamp program, increases in average incomes, determined after the valuation attached to food coupons, are greater than those under the mere allocation of the cash bonus. The common characteristic of both estimates is that the significance of the shift towards higher income levels tapers off as actual incomes rise.8

One explanation lies in the fact that the number of families rises with size up to 4-member households, and declines thereafter. Of the 335,779 families registered as participant in November 1975, 61% consisted of households with 1-4 members. Those with 5 members were 15% of the total. The amount of food stamps households are eligible lor depends upon the number of persons in each household. Because of this, the estimated general and specific purchasing power generated by the Program on the whole rises with family size. Never theless the smaller number of large households reduces the relative impact of the bonus and the stamps of the overall distribution of income. Added to this explanation is the concentration of income in the lower income levels for every household size; and although the absolute sum of the estimated specific and general purchasing power remains relatively constant for different levels in every household size, their relative significance is the greater, the lower the household income. These results can be discerned from Table 3 which gives the bonus, the estimates ol the specific and general purchasing powers, and the difference between the two, by income level and family size. The val•The size distribution of income was not restructured by statistical methods so as to reflect this shift. Table 2, therefore, omits the income brackets. Future income and expenditure surveys should incorporate the pertinent questions into their questionnaire so that the net bonuses arising from the Food Stamp Program as well as from other assistance programs can be counted among the various types of incomes received by families. These omissions may be one of the reasons why despite massive efforts to redistribute income to the poor, improvements in the relative position of families at the lower end of the income scale have been insig nificant. [See Browning]

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uation of the food coupons via the Cobb-Douglas utility function is calculated for each cell of family size and level of income relating to the food stamp program, with propensities to consume which vary from one cell to another. In that sense the use by Clarkson [p. 72] of the same average propensity to consume food for different family sizes and levels of income is quite unrealistic. In addition, in Puerto Rico the proportions of food consumed out of income are very much higher than the .33 utilized by Clarkson for the case of the United States. For many families this proportion would imply starvation. The average propensities to consume food utilized in this paper vary from .70 to .90 depending upon family size and levels of income within a given family size. Undoubtedly these are high coefficients, implying the non existence of savings and great reliance on credit for the purchase of other items. But this is not a rare phenomenon in Puerto Rico. Consumer loans are a large proportion of the portfolios of commercial banks; and the use of charge accounts, credit cards, and credits at small grocery stores is widespread. It is also borne out by the results of the income and expenditure surveys of 1963, where food expenditures are indicated to average 56.5% of annual incomes of $1,000 or less and 19.0% of those between SI,000 and S2,000. At all levels of income, except for S7.5OO and above, annual expenditures exceed annual incomes. [P.R. Department of Labor, Table 1-A] One could argue that it is more correct to include spending out of borrowing as part of household income, since it is income plus bor rowing that determines the base from which spending patterns emerge and since the food stamp program may be claimed to be at least a partial substitute for this borrowing, because it injects purchasing power into the families’ pocketbooks. This would no doubt reduce the coefficient of average propensity to consume food. But calcula tions with this lower coefficient do not reflect the household’s "true” desire to consume food and cannot give the “right” valuation to the coupons since usually the household does not look upon borrowing as part of its income. The subjective income-redistributive impact will have to be gauged by coefficients relating to pre-stamp income. In any case the income base of neither the surveys by the Department of Labor and Department of Social Services, nor of the 1970 Census reflect spending out of borrowing as part of income. Moreover, it would have been impossible to estimate its magnitude by family size and income as required for the analysis. The figures of Table 3 are expressed in 1969 dollars to enable the

FOOD STAMP PROGRAM IN PUERTO RICO

109

assessment of the program benefits on income distribution. The esti mated gain of the program for each cell is given in parentheses. This gain is measured as the difference between the bonus (the top left hand figure in the cell) and the sum of the general and specific pur chasing powers (the two bottom figures in each cell). A negative difference indicates a gain, and a positive difference indicates a waste. For example, in the cell of household size 2 and annual income of $250-$500, the bonus per family is $651.34, the general purchasing power it generates is $271.13, the subjective value of the specific pur chasing power is $409.70 and the net gain is $29.49, since the general purchasing power and the specific purchasing power add up to a larger value than the bonus. For the same household size, but with annual income of $0-$250, per family general purchasing power and specific purchasing power sum up to a value lower than the actual bonus; the waste is $40.83 per family. In other words, the value the family attaches to the stamps is lower than their face value. On the whole, for households with up to five members the estimated gain begins at the annual income level of $250-$500, diminishing gradually from $125.67 per family for one-member families to $1.82 per family for 5-member families. For households with 6-8 members the net gain per family appears to begin with annual incomes of $500 or more; the gain is observed at the $700 level for families of larger size. Within a given level of income the gain diminishes with household size, and within a given household size the gain increases with the income level. The latter is attributable to the fact that as incomes rise, estimated food expenditures in the absence of the program are larger than the value of the stamps lor which families be come eligible under the provisions of the program.9 As a result, the general purchasing power transfer of the program acquires a greater significance with income, and the specific purchasing power value of the stamps diminishes with rising income as evidenced by larger nega tive figures in brackets of 'Fable 3. The impact on the household in come (the sum of the two purchasing power transfers) is positive at all levels of income. The reverse phenomenon occurs at the very low levels of income

"If estimated food expenditures per family are compared with the value of stamp allotments, both expressed in 1975 prices, by level of income and household size, the boundary where stamp allotments begin to exceed estimated food expenditures is at annual incomes of $720 or more for one-member households, at $1,803 for two-member households, rises to $3,000 for five-member households and to almost of .$5,000 for households with six members or more.

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where the face value of the stamps far exceeds the expenditures on food households would have made in the absence of the subsidy. 1 he implication here would be that families with very low annual in comes, although appreciating the stamps, wotdd have preferred a somewhat larger general purchasing power than the one that they estimate they receive under the specifications of the program, given their preference function. It is said, therefore, that since such a distortion occurs in consump tion patterns and since the distortion is greater at the low income levels, the net benefit is a smaller percentage of the transfer to the lowest income families than it is to families at higher income levels, and that "tragically, the restriction that the transfer be spent on food consumption is harmful to those who are neediest." [Browning, p. 431 The first part of the statement is borne out by the figures of Table 3. "But the second part neglects the fact that those with low incomes may not have had the amount of food that they should have had to begin with. With food expenditures of the order of S3-8 per family at low income levels, obviously concern with the distortion that the pro gram creates loses much ol its significance. Undoubtedly, nutrition levels at these low income levels could have been raised with lower stamp allotments per family, the rest of the subsidy being given in cash to be spent at the family's discretion. Granted, an optimal food stamp program should result in estimated general and specific pur chasing power values which should add up to the bonus received by each participant. Yet, however mechanized and computerized the available methodological fools may be, it is not possible to formulate (let alone implement) an optimal program of such complexity 'and magnitude, for the mere reason ol the inability to determine utility functions.

This paper has attempted to assess a specific expenditure program in terms of its impact on the overall distribution of incomes, ft has parted ways with the traditional redistribution studies because it allocates the benefts more accurately to their recipients, and from the non-traditional utility-approach studies because it only focuses on one public-expenditure benefit, rather than on a group of expendi tures combined in one general category, such as, e.g., the social ser vices. Its analysis has been specific not only in the selection of the

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public expenditure, but also in its methodology in using mote de tailed assumptions and computations in determining the recipients as well as the size of the benefits, rather than relying on conjectuial criteria. E" The main conclusion of the paper is that the food stamp program I plays a very significant role in redistributing incomes in favor of the relatively poor. This it achieves via income transfers which can only be used to buy food. But the features of the program are such that while providing these transfers it also generates general purchasing power which can be used for the purchase of food and non-food alike. The redistributive impact of the program is assessed first simply as a result of the allocation of the face value of the bonus food stamps to the appropriate income classes, then as the allocation of the value individual households attach to the food coupons. Either way a shaip decline is observed in the Gini coefficient, from 0.5526 to 0.4781 in (_d]e first case, and to 0.4578 in the second. Obviously, the program meets a very urgent need in compensating for the nutrition deficiency of the economically handicapped. One can criticize the program for achieving this aim in a relatively in efficient way, since, as the paper indicates, many families attach a lower value to the stamps than their face value, while some othets attach a greater value. This raises the question of the optimality of the program, the testing of which was not the purpose of the papet. There is no doubt, however, that optimality is of relevance lot the re distribution of incomes, for an optimally designed program means that the sum of the general and specific purchasing powers would have equalled the value of the bonus food stamps. Since the present program seems to lead, at least in this analysis based on Puerto Rico s experience, to a net welfare gain for the majority of the families, op timality would have implied a lesser redistributive impact than the one assessed in the paper. Appendix

Alternative I: The Allocation of the Bonus I he Department of Social Services has information on the net bonus of the food stamp program and the number of participating families by monthly levels of income. The information refers to the month of November, 1975. In converting the monthly data to an annual basis, it was simply assumed that the November estimates would be representative of the entire year and were multiplied by twelve. The figures thus obtained were then deflated by the general consumer price index (CPI) to convert them to the same purchasing power level as the estimates of the

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1970 Census. The use of the CPI is justified because the bonus reflects a transfer of general purchasing power. The deflated data were then retabulated to make them consistent with the Census classification of families and unrelated individuals by income levels. It was thus possible to obtain the average bonus per family and per person in 1969 dollars by income levels corresponding to the Census classifica tion. Since the benefits of the program within a given level of income vary with the size of the family, a larger family with a given level of income receives a larger bonus than a smaller one with identical income. Table 159 of the Census indi cated, however, that in any level of income small families are larger in number than large families and that the average family size did not vary appreciably from one income level to another. A detailed computation of the benefit to be allocated using family size and numbers in a given level of income would not have given a significantly different result than an allocation using overall bonus per family in that level of income. Therefore, the latter procedure was used. Next, the number of eligible families in any given income level, had to be esti mated. For this purpose the program’s limits of maximum allowable monthly net income by number of persons were converted to gross incomes using a factor of .82 (NI = .82 GI) and multiplied by 12. The conversion factor was obtained from a random sample of 500 families, stratified by family size and income level. The annual incomes thus obtained were deflated by the CPI and the results compared with Census data. It was found that all families with annual incomes of S3,000 or less would have been eligible and no family with an annual income of S8.000 or more would have been eligible. All one-member households with annual incomes of S2.000 or more were excluded. Two-member families with annual incomes higher than $3,000, 3 member families with annual incomes of $4,000 or more, 4-member families with annual incomes of $5,000 or more and so on and so forth wete not taken into consideration. Considering that not all eligible households participate in the program their number in each income group was reduced to 79%, the current participation rate. The multiplication of number of households with the corresponding average bonuses gave the estimate of the supplemental income that households with differ ent levels of income would have received if the food stamp program were in effect in 1969. The total bonus allocated in this fashion among different income levels accounted for 95% of the estimate of 1975 expressed in 1969 dollars.

Alternative II: Subjective Valuation of the Benefits of the Food Stamp Program.

These benefits were estimated following the methodology of Clarkson. General purchasing power is defined as the difference between monthly food expenditure in the absence of food stamp participation and the monthly purchase requirement. Monthly food expenditures were estimated with average propensities to consume obtained from household surveys conducted by the Department of Social Services in July and October 1974 in three municipalities of Puerto Rico. These propensities varied according to income level and family size. The highest monthly income recorded in the three areas was S420 a month which corresponds to an annual in come of around of S3,5OO in 1969 dollars. The surveys indicated that food ex penditures per family, on the whole, rise with level of family income up to a level of about S3,000 (S2.300 in 1969 dollars) a year: thereafter they tend to decline somewhat. Up to that level of income it was observed that families spent more on food than the money income they revealed. Moreover, food expenditures per person declined with household size. Finally, income elasticity of demand for food rose with the level of income, which is consistent with findings of other studies, and the marginal propensity to consume tended to decline. The combined implica-

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tion of these latter two coefficients must be a decline in the average propensity to consume. Granted, the results of the survey refer to information given at one particular time of the year and can not necessarily be held to be valid as annual data. But in the absence of any other information and with similar results ob tained by the Puerto Rico Department of Labor in its earlier surveys in 1963, and given that the objective of the program was to eliminate food deficiency of families with very low incomes, who, even with all their money spent on food would not achieve an adequate level of nutrition, it was decided to vary the average propensi ties to consume with family size and level of income and calculate the estimates cell by cell, defined by household size and income level. The analysis, therefore, is based on the assumption that the form of the utility function is the same for all households, but its parameters are different for individual households in individual levels of income. Within each cell it is assumed that the utility function is repre sentative of the individuals composing it. Both the general purchasing power and the specific purchasing power of income levels that would have corresponded to the 1969 distribution were first estimated in 1975 dollars and then converted into 1969 dollars; the first was deflated by the CPI, the second by the food price index. The procedure of allocating the benefits is the same as that described for Alternative I, with the exception that they were allocated according to the distribution of families by income level and family size as given in the 1970 Census. The benefits thus allocated amount to §441 million, which implies that the overall valuation of the program by possibly eligible house holds is about 44% higher than the cash value of the bonus in 1969 prices. References

Aaron, H. and II. McGuire. "Public Goods and Income Distribution," Econometrica, 1970, 38,6: 907-920. Andie, F. M., S. Andie and L. M. Torrucllas. "Economic and Fiscal Implications of the Presidential Vote,” in Six Special Studies Requested for the Ad Hoc Ad- C visory Group on the Presidential Vote for Puerto Rico. Washington: Govern ment Printing Office, 1971, 1-43. Browning, E. Redistribution and the Welfare System. Washington: American Enterprise Institute for Public Policy Research (Evaluative Studies, 22), 1975. Buchanan, J. M. "What Kind of Redistribution Do We Want?” Economica, 1968, 35, 138: 185-190. t/6houdhury, P. el al. The Food Distribution System and Food Stamp Program in Puerto Rico. A Study prepared for U.S. Department of Agriculture and P.R. Department of Social Services, San Juan, 1975. Clarkson, K. W. Food Stamps and Nutrition. Washington: American Enterprise Institute for Public Policy Research (Evaluative Studies, 18), 1975. David, M. and J. Leuthold. “Formulas for Income Maintenance: Their Distribu tional Impact," National Tax Journal, 1968, 21.1: 70-93. Foldes, L. "Income Redistribution in Money and in Kind," Economica, 1967, 34, 133: 30-41. Friedman, M. Capitalism and Freedom. Chicago: University of Chicago Press, 1962, 191-194. Maital, S. "Public Goods and Income Distribution Some Further Results,” Econo metrica, 1973, 41,3: 561-568. Mann, A. and D. Perlis. "Utility Functions, Public Goods and Income Distribution,” Public Finance Quarterly, 1977, 5, 1: 9-22. Neenan, W. B, "Suburban-Central City Exploitation Thesis: One City’s Tale,” National Tax Journal, 1970, 23 (June), 117-139.

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Olsen, E. O. "A Normative Theory of Transfers," Public Choice, 1969, 6, Spring: 39-58. ---------. ‘Some Theorems in the Theory of Efficient Transfers,” Journal of Political Economy, 1971, Jan./Feb.: 166-176. P.R. Department of Labor. Income and Expenditures of the Families, San Juan, 1967. San Juan, 1967. -------- . Report 4-A, Expenditures of All Families. 1963. U.S. Bureau of the Census. Census of Population. Washington, Government Print ing Office, 1970. -------- . General Social and Economic Characteristcis. Final Report PC(1)-C 53, Puerto Rico. Washington: Government Printing Office, 1972. -------- . Detailed Characteristics. Final Report PC (1)-D 53, Puerto Rico. Washing ton: Government Printing Office, 1973. U.S. Department of Agriculture. Food and Nutrition Service. Food Stamp Program. A report prepared for the Committee on Agriculture and Forestry, U.S. Senate. Washington: Government Printing Office. 1975.

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