United States

Department

of Agriculture

www.ers.usda.gov

Electronic Report from the Economic Research Service

Understanding the Food 

Stamp Benefit Formula 

A Tool for Measuring the Component Effects

Parke Wilde

Abstract

This report develops an accounting tool for measuring how the average

benefit amount in the U.S. Food Stamp Program is affected by each major

component of the rules that determine the benefit level. This tool is used

to compare the benefits received by different subpopulations, distinguished

by poverty level, demographic makeup, household size, and region of the

country. This simple decomposition complements more complex tools,

such as microsimulation methods, which help policy analysts understand

and evaluate the effects of detailed Food Stamp Program regulations. 

Keywords

Food Stamp Program, benefit formula, income, household size, poverty

status, deductions

Acknowledgments

The author thanks Mark Nord, Steve Carlson, Craig Gundersen, and Bob

Dalrymple, who commented on an earlier version of this report, and Lou

King, for editorial assistance.

April 2001

Food 

Assistance

and 

Nutrition

Research

Report

Number 14
Contents

page

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Food Stamp Benefit Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Program Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

A Mathematical Statement of Program Rules . . . . . . . . . . . . . . . . . . . . . . . 3

A New Decomposition of Food Stamp Benefits . . . . . . . . . . . . . . . . . . . . . 4

More Detail on the Deductions Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Empirical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Full Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Income Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Demographic Categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Food Stamp Unit Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Census Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Appendix A: Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Appendix B: SAS Software Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

List of Tables

Table page

1. Monthly food stamp benefits for two-person households in the continental .

United States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2. Components and subcomponents of total food stamp benefits . . . . . . . . . . 4

3. Composition of mean per capita benefits, by gross income category of food

stamp unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4. Composition of mean per capita benefits, by demographic category of food

stamp unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

5. Composition of mean per capita benefits, by food stamp unit size . . . . . . 11

6. Composition of mean per capita benefits, by census region . . . . . . . . . . . 12

ii ✥ Understanding the Food Stamp Benefit Formula /FANRR-14 Economic Research Service/USDA
Summary

This report develops an accounting tool for measuring how the average benefit amount in the

U.S. Food Stamp Program is affected by each major component of the food stamp benefit formula. This formula is the set of rules that the Federal Government uses to determine the

amount of program benefits available to each participating household, based on income and

other characteristics. Using this formula, $16 billion in food stamp benefits were distributed

in 1999, providing food assistance to more than 18 million low-income Americans.

The Federal Government chooses a benefit level such that benefits plus a proportion of cash

resources suffice to purchase a certain bundle of foods, defined in the Government’s Thrifty

Food Plan. In general, each eligible household receives the maximum benefit based on its

household size, minus 30 percent of net income. Net income equals the household’s total

cash income from earnings, welfare, and other sources, minus certain allowable deductions.

If the allowable deductions exceed total cash income, net income is simply zero. There is

also a minimum benefit of $10 for households with one or two members. The effects of the

maximum benefit, the minimum benefit, cash income, and deductions interact in a complex

way, so it is useful to have a tool for quantifying these effects.

Food Stamp Program Quality Control data from USDA’s Food and Nutrition Service are used

in this report to study the national food stamp population in 1998. Using these data, the average monthly food stamp benefit per person ($69.25) may be expressed as the sum of the average maximum benefit per person ($112.70) plus four main component effects, which may be

positive or negative: an income effect (-$89.27), a deductions effect ($50.35), a maximum

benefit effect ($-6.78), and a minimum benefit effect ($2.25). 

Using this accounting tool, this report compares and analyzes the benefits received by food

stamp participants with different poverty levels. Average per person benefits do not decrease

as steeply with income as one might expect from a simple reading of the official benefit formula, which has a benefit reduction rate of 30 percent. Near-poor households, with cash

income between 100 percent and 130 percent of the poverty guideline, receive more deductions than do very poor households, with cash income below 50 percent of the poverty guideline. 

Likewise, near-poor households have their average benefits raised by $17 due to the minimum

benefit rule, while very poor households receive no help from this rule. These effects partially offset the income effect, which produces lower benefits for near-poor households in comparison to very poor households.

The report makes similar comparisons for subpopulations distinguished by demographic

makeup, household size, and region of the country. The simple decomposition developed

here complements more complex tools, such as microsimulation methods, which help policy

analysts understand and evaluate the effects of detailed Food Stamp Program regulations.

Economic Research Service/USDA Understanding the Food Stamp Benefit Formula /FANRR-14 ✥ iii
Introduction

The food stamp benefit formula is the set of rules that

the Federal Government uses to determine the amount

of program benefits available to each household participating in the Food Stamp Program (FSP), based on

income and other characteristics. Choosing this formula is a major policy decision: $16 billion in food

stamp benefits were distributed according to this formula in 1999, providing food assistance to more than

18 million low-income Americans (USDA, Food and

Nutrition Service, 2000). The U.S. Congress signals

the policy importance of the benefit formula by deciding every parameter itself, rather than delegating any

aspect of the formula to the State and Federal agencies

that administer the FSP.1

The benefit formula is complex in its details, but the

main thrust is simple: the Federal Government chooses

a benefit level such that benefits plus a proportion of

cash resources suffice to purchase a certain bundle of

foods, defined in the Government's Thrifty Food Plan

(USDA, Center for Nutrition Policy and Promotion,

2000). In addition to food stamp benefits, the

Government expects participant households to spend

30 percent of their "net" cash income on food, after

making allowances for certain expenses (see USDA,

Food and Nutrition Service, 2000 and the discussion

below for further detail on the benefit regulations). 

The complexity arises in translating this general principle into a concrete formula for implementation. The

benefit formula is stated precisely in the next section,

but some of the difficulties are mentioned here. There

are maximum benefit levels for each household size,

and minimum benefits for some household sizes.

Benefits are based on cash income minus several types

of deductions. The deductions include certain medical

expenses, child support payments, child care expenses,

shelter expenses, work expenses, and a standard

deduction. The shelter deduction is based in part on

the cash income remaining after the other deductions

are taken, so the deductions must be computed in a

particular order. These details of the benefit rules have

complicated the analysis of food stamp policy by

increasing the level of expertise required to understand

precisely why different types of households get particular benefit amounts. 

This report asks several questions about the benefit

formula's main components:

• How much is the average benefit affected by the

reduction that accompanies increased cash income?

• How much is the average benefit raised by each of

the deductions permitted in calculating net cash

income?

• To what extent is the average benefit limited by the

maximum benefit amount?

• To what extent is the average benefit increased by the

minimum benefit amount?

The report also examines how each component of the

benefit formula affects food stamp units2 with different

characteristics along several dimensions:

1 ✥ Understanding the Food Stamp Benefit Formula /FANRR-14 Economic Research Service/USDA

1By contrast, the main Federal cash welfare program

(Temporary Assistance for Needy Families) is structured as a

block grant to the States, which are given much leeway in determining cash welfare policies.

2The food stamp unit is the official household definition for the

Food Stamp Program. Technically, a food stamp unit is one or

more individuals who live in a residential unit and purchase and

prepare food together. This report uses food stamp unit and household synonymously.

Understanding the Food 

Stamp Benefit Formula

A Tool for Measuring the Component Effects 

Parke Wilde
• Poverty status;

• Demographic composition;

• Household size;

• Region of residence.

To answer these research questions, the report develops a new tool for measuring each component of the

benefit formula in the same metric—the effect in dollars on the mean food stamp benefit amount. For

example, two-person food stamp units in the continental United States had a maximum benefit amount of

$224 in 1998 (table 1). However, most of these food

stamp units had some cash income, which usually

reduced their benefit amount. 

The extent of this reduction depended on the extent to

which the units were eligible for deductions from

gross income. In all, the mean food stamp benefit for

two-person households ($145.87) is the sum of the

maximum benefit amount plus four main effects

(labeled E1 through E4 in table 1). These effects,

which may be positive or negative, are defined formally and studied in the remainder of this report. This

analysis shows at a glance how each effect contributes

to the average benefit level. 

This report summarizes complicated quantitative information about income, program rules, and benefit

amounts in a consistent and intuitive format. However,

this approach is limited for some purposes. For example, microsimulation methods are superior to this

report's approach for the purpose of assessing policyrelevant counterfactual scenarios (see Jacobson et al.,

2000). 

Likewise, the annual Characteristics reports from the

Food and Nutrition Service contain many useful tabulations of participant characteristics beyond the impact

of the benefit formula (Castner and Rosso, 2000). The

analytic tool presented here is most useful for transparently describing how much each feature of the benefit

formula contributes to the average benefit amount and

for comparing these contributions across different

types of food stamp participants. 

In the authorizing legislation for the Food Stamp

Program, Congress instructed the Secretary of

Agriculture:

to develop and implement measures for evaluating,

on an annual or more frequent basis, the effectiveness of the food stamp program in achieving its stated objectives, including, but not limited to,... the

program's relative fairness to households of different

income levels, different age composition, different

size, and different regions of residence (Food Stamp

Act of 1977, p. 1-89).

To assess the program's fairness requires, first, an

understanding of how program regulations affect different types of households and, second, some criteria

for determining what distribution of effects would be

fair. This report compares food stamp participants

along the same classifications mentioned by Congress:

poverty status, demographic composition, household

size, and region of residence. These comparisons do

not on their own reflect a judgment about the fairness

of the benefit formula.

This report first describes the food stamp benefit formula and explains how the benefit level may be

decomposed into its respective parts. That description

is followed by an empirical analysis, using Food

Stamp Program Quality Control data for 1998. The

final section discusses limitations and advantages of

this approach.

Economic Research Service/USDA Understanding the Food Stamp Benefit Formula /FANRR-14 ✥ 2

Table 1—Monthly food stamp benefits for two-person households in the continental United States

Symbol Component name Deduction

Percent

M Maximum benefit 224.00

E1 Income effect -157.12

E2 Deductions effect 86.80

E3 Maximum benefit effect -9.86

E4 Minimum benefit effect 2.04

Food stamp benefits 145.87

Note: Column entries are rounded to two significant digits after

the decimal

Source: Author’s calculations from 1998 Quality Control Data.
Food Stamp Benefit Formula

Program Rules

To be eligible for food stamp benefits, a household

must have few countable assets and low monthly cash

income.3 The asset limit is $2,000 for households that

do not contain an elderly member and $3,000 for

households that do. The gross income test, which

applies only to households without an elderly or disabled member, requires that monthly cash income

(including labor market earnings, all cash program

benefits, and any other cash income) may not exceed

130 percent of the official poverty guideline. The net

income test, for all households, requires that monthly

cash income after certain deductions (described below)

may not exceed 100 percent of the official poverty

guideline (hereafter, all income and benefit variables

are reported on a monthly basis, unless otherwise

noted). Other eligibility restrictions apply to immigrants, students, strikers, and able-bodied adults without dependents (see Castner and Rosso, 2000, or

USDA, Food and Nutrition Service, 2000, for more

details).

Six types of deductions from gross cash income are

used in computing monthly net income:

• D1—standard deduction ($134 per food stamp unit,

in the contiguous United States in fiscal year 1998).

• D2—an earned income deduction (20 percent of the

combined monthly labor market earnings of household

members).

• D3—a dependent care deduction (certain expenses

for care of children or other dependents while other

household members work, seek employment, or go to

school).

• D4—a medical deduction (nonreimbursed medical

expenses for elderly or disabled members of the

household, beyond the first $35 per month). 

• D5—a child support payment deduction (legally obligated child support payments to somebody who is not

a member of the household).

• D6—an excess shelter expense deduction (monthly

shelter costs that exceed 50 percent of the monthly

income remaining after all other deductions are subtracted from gross income). This deduction has a cap

equal to $250 in 1998, which only applies to households without an elderly or disabled member. Because

the excess shelter expense deduction depends on the

income left after the preceding five deductions, it must

be computed after the others.

Net income equals gross income minus deductions.

Net income may not be reduced below zero, so in

cases where the value of all deductions exceeds gross

cash income, some potential deductions remain

unused—they have no impact on the computation of

net income.4

Net income plays a central role in determining the

benefit amount. Any household with net income of

zero receives the maximum benefit level, which is

based on the Thrifty Food Plan and which varies

according to household size. Households with positive

net income receive the maximum benefit minus 30

percent of net income. For units with one or two members, a minimum benefit of $10 is provided.5

A Mathematical Statement of Program Rules

To state these rules mathematically for purposes of

computing benefits correctly, it is most intuitive to

begin by computing deductions and net income, and

then to compute benefits. Let B be benefits; let M be

the maximum benefit for a household with a certain

number of members; let G be gross income; let D1-D6

be the six deductions defined above; let H (for housing) be the total shelter expenses; let H* be the cap on

the shelter deduction; let N1 be an intermediate net

income value based on all deductions except the shelter deduction;6 and let N2 be the final net income. 

First, intermediate net income is defined as gross

income minus the first five deductions (unless this dif3Not all assets count toward the asset limit for food stamp eligibility. For example, a primary residence and some assets in the

form of an automobile may be excluded for this purpose.

4For readers who are familiar with deductions mainly in an

income tax context, it may be surprising that gross income minus

deductions may ever be equal to or less than zero. Recall, however, that some deductions (such as the standard deduction) do not

depend on a particular income source. Thus, any food stamp unit

with gross income less than $134 will have net income equal to

zero. 

5For practical purposes, the minimum benefit would not be

binding for larger households in any case. In our 1998 sample,

just 0.14 percent of food stamp units with more than two members

had benefits less than $10. In the empirical computations, we drop

this very small group of observations. 

6Because there is no cap on the shelter deduction for households

with an elderly or disabled member, H* is set to equal H for these

households. This is just a mathematical convenience, indicating

that there is no cap limiting the deduction for these households.

3 ✥ Understanding the Food Stamp Benefit Formula /FANRR-14 Economic Research Service/USDA
ference yields a negative number, in which case intermediate net income is simply zero):

(1) N1 = Max [G - (D1 + D2 + D3 + D4 + D5) , 0].

Second, the shelter deduction equals any shelter

expenses that exceed 50 percent of intermediate net

income (H - 0.5 * N1). The minimum shelter deduction is zero, and the deduction is capped at H*:

(2) D6 = Min [H*, Max (H - 0.5 * N1, 0)].

Third, final net income equals gross income minus all

six deductions (unless this difference yields a negative

number, in which case net income is simply zero):

(3) N2 = Max [G - (D1 + D2 + D3 + D4 + D5 + D6),

0].

Fourth, food stamp benefits equal the maximum benefit minus 30 percent of net income (with a minimum

benefit level of $10): 7

(4) B = Max [M - 0.3 * N2 , 10].

A New Decomposition of Food Stamp Benefits

While the approach above is sensible for benefit computation, it is less useful for measuring and comparing

the contribution of each component of the benefit formula toward the final benefit amount. For this purpose,

it helps to restate the benefit amount as a simple sum

of several component effects (table 2).

Economic Research Service/USDA Understanding the Food Stamp Benefit Formula /FANRR-14 ✥ 4

7Once again, to spare the reader some additional notation, we

ignore the trivial number of units with more than two persons who

receive less than $10.

Table 2—Components and subcomponents of total food stamp benefits

Symbol Component name Description (positive or negative sign) Formula

M Maximum benefit Maximum food stamp benefit, depending on M

household size (+)

E1 Income effect Effect of gross cash income on benefits, -0.3*G

all else equal (-)

E2 Deductions effect Effect of deductions on benefits, all else equal (+) 0.3*D

E3 Maximum benefit effect Effect of receiving the maximum benefit 0.3*Max[0,D-G]

instead of M+E1+E2 (-)

E4 Minimum benefit effect Effect of receiving the minimum benefit Max[0,10-(M-0.3*N2)]

instead of M+E1+E2 (+)

E2.1 Standard deduction effect Effect of standard deduction on benefits, 0.3*D1

all else equal (+)

E2.2 Earned income deduction effect Effect of labor market income on benefits, 0.3*D2

all else equal (+)

E2.3 Dependent care deduction effect Effect of dependent care deduction on 0.3*D3

benefits, all else equal (+)

E2.4 Medical deduction effect Effect of medical deduction on benefits, 0.3*D4

all else equal (+)

E2.5 Child support payment Effect of child support payments deduction, 0.3*D5

deduction effect all else equal (+)

E2.6 Shelter deduction effect Effect of the shelter deduction on benefits, 0.3*D6

all else equal (+)

E2.6.1 Raw shelter expense effect Effect of gross shelter expenses on 0.3*H

benefits, all else equal (+)

E2.6.2 Half-income rule effect Effect of disqualifying half of -0.3*Min[0.5*N1,H]

intermediate net income (-)

E2.6.3 Shelter deduction cap effect Effect of the rule that shelter deduction Min[0.3*H*-(E2.6.1+

may not exceed $250 (-) E2.6.2),0]

Notes: M is the maximum benefit, G is gross cash income, D is total deductions, N1 is intermediate net income, N2 is final net income, D1

is the standard deduction, D2 is the earned income deduction, D3 is the dependent care deduction, D4 is the medical deduction, D5 is the

child support payment deduction, D6 is the shelter deduction, H is gross shelter expenses, and H* is the cap on the shelter deduction. "All

else equal" means holding constant all other components or subcomponents.
In overview, food stamp benefits may be expressed as

the sum of the maximum benefit (M) plus four component effects—the income effect (E1), the deductions

effect (E2), the maximum benefit effect (E3), and the

minimum benefit effect (E4). These main effects are

defined below and reported in the top third of table 2

and subsequent tables. 

For some purposes, it is useful to analyze the deductions effect in greater detail. A further decomposition

of the deductions effect is defined later in this report

and detailed in the middle and bottom thirds of table 2

and subsequent tables. Readers who are interested only

in the main component effects may focus on just the

top third of each table of results.

The income effect (E1) is -0.3 (derived from the official benefit reduction rate of 30 percent) times gross

income. If there were no deductions and no minimum

benefit, food stamp benefits would simply equal the

maximum benefit plus the income effect.

(5) E1 = -0.3 * G.

The deductions effect (E2) is 0.3 times total deductions. Except for unused deductions, as noted below,

every dollar of deductions causes food stamp benefits

to rise by 30 cents.

(6) E2 = 0.3 * (D1 + D2 + D3 + D4 + D5 + D6).

The maximum benefit effect (E3) is the effect of the

fact that food stamp benefits may not exceed a maximum amount. If a household with sufficient deductions were permitted to have a net income value (N2)

below zero—in essence, if it could use its unused

deductions—then, according to equation (4), the

household would have food stamp benefits that exceed

the so-called maximum benefit (M).8 The maximum

benefit effect represents the consequences of being

unable to have benefits greater than the maximum benefit. This effect is negative for those households whose

potential deductions exceed their gross income, and is

zero otherwise.

(7) E3 = -0.3 * Max [0, ( D1 + D2 + D3 + D4 + D5 

+ D6) - G].

While the maximum benefit effect is a nonpositive

number, this mathematical representation does not

mean the effect should be interpreted as a penalty in a

policy sense. Recall that the maximum benefit suffices

to purchase the bundle of foods described in the

Thrifty Food Plan. In this sense, the restriction that

benefits may not exceed the maximum benefit is a purposeful policy choice, not a penalty on units with

unused deductions. 

Finally, the minimum benefit effect (E4) represents the

effect of the minimum benefit rule on the benefit

amount. This effect is positive for those one- and twoperson units that would otherwise have received a benefit amount smaller than $10, and is zero for all others.

(8) E4 = Max [0, 10 - (M - 0.3 * N2)].

The benefit formula in equation (4) may be restated as

a simple sum of the maximum benefit plus the four

component effects.

(9) B = M + E1 + E2 + E3 + E4.

The proof is presented in Appendix A.

More Detail on the Deductions Effect

Deductions are a critical factor in determining the

amount of benefits received. Total deductions (including unused deductions) are the simple sum of the six

possible deductions, D1 through D6. Likewise, the

deductions effect (E2), defined in equation (6) above,

is the simple sum of six effects, E2.1 through E2.6,

where each effect equals 0.3 times the corresponding

deduction. 

The excess shelter expense deduction (D6) is especially complex and important in terms of its effect on benefits. We decompose the shelter deduction effect into

three subcomponent effects. 

The raw shelter expense effect (E2.6.1) represents the

impact that shelter expenses would have on benefits if

all shelter expenses were deductible.9

(10) E2.6.1 = 0.3 * H.

The half-income rule effect (E2.6.2) represents the

effect of the rule that only shelter expenses above 50

percent of intermediate net income count towards the

shelter deduction. If intermediate net income is suffi9This is not a purely hypothetical case because 11 percent of

households have zero intermediate net income (N1), so for them,

all shelter expenses are deductible (up to the cap).

8For this reason, the maximum benefit effect might alternatively

have been called the unused deductions effect.

5 ✥ Understanding the Food Stamp Benefit Formula /FANRR-14 Economic Research Service/USDA
ciently high, then this effect completely offsets the raw

shelter expense effect.

(11) E2.6.2 = -0.3 * Min [0.5 * N1 , H].

Finally, the shelter deduction cap effect (E2.6.3)

reflects the impact on food stamp benefits of the cap to

the shelter deduction. This effect is negative for households that would otherwise be eligible for a deduction

that exceeds the cap, and is zero otherwise.

(12) E2.6.3 = Min [0.3 * H* - (E2.6.1 + E2.6.2), 0].

The shelter deduction effect (E2.6) is the simple sum

of these three subcomponent effects:

(13) E2.6 = 0.3 * D6 = E2.6.1 + E2.6.2 + E2.6.3.

The proof is presented in Appendix A.

Economic Research Service/USDA Understanding the Food Stamp Benefit Formula /FANRR-14 ✥ 6
Empirical Analysis

This section employs the tool from the previous section to measure the various components of the food

stamp benefit formula using 1998 data from USDA's

Food and Nutrition Service (FNS). The study analyzes

the mean monthly food stamp benefit for all participants and for specific subpopulations defined by

poverty status, demographic composition, household

size, and region of residence. 

In contrast with table 1, which reported mean food

stamp benefits for two-person food stamp units, the

subsequent analysis reports all monthly income and

benefit variables on a per person basis. The report

takes this approach because food stamp units of different sizes have very different income and benefit levels. 

The alternative approach of reporting results on a per

household basis makes it more difficult to distinguish

the effect of household size from the effects of other

variables. For the reader who would like to reconstruct

the corresponding results on a per household basis,

each table below reports the appropriate mean unit size

variable that is needed for this calculation.

Data

Food Stamp Program Quality Control (FSPQC) data

are generated from monthly quality control reviews of

FSP cases. State agencies conduct these reviews to

assess the accuracy of eligibility determinations and

benefit calculations. Following a specified protocol,

the State agencies send data files from these reviews to

FNS. A contractor for FNS edits and compiles these

files to produce nationally representative Quality

Control (QC) data. In recent years, FNS has made

these microdata available to the public on the agency's

Web site.

These QC data "... are ideal for tabulations of the

characteristics of food stamp units and for simulating

the impact of various reforms to the FSP on current

FSP units" (Brinkley, 1999). They contain detailed

information about food stamp unit composition,

income from various sources, each type of deduction,

and food stamp benefit amounts. The 1998 QC data

used in this report contain 47,145 food stamp unit

observations, which may be used with sampling

weights to represent approximately 8.2 million food

stamp units nationally. 

Full Sample 

The mean monthly per person food stamp benefit in

1998 in our sample was $69.25. The first column of

table 3 reports the decomposition of this mean benefit

for the full sample, using the analytic tool described in

the preceding section. In this subsection, we discuss

each element of the decomposition in turn:

• First, the mean per person maximum benefit (M) was

$112.70. This value is a weighted average of the per

capita maximum benefit for each family size, where

the weights are the proportion of the population with

that family size. 

• Next, the mean per person gross cash income was

$297.57. If every dollar of income counted against

food stamp benefits, this income would have reduced

per capita benefits by $89.27 (using the 30 percent

benefit reduction rate), so the income effect (E1)

equaled -$89.27. 

• However, not all income counted against benefits. On

average, participant households were entitled to deductions from gross income totaling $167.83 per person.

The deductions effect (E2) equaled 0.3 times this sum,

or $50.35. 

• Some food stamp units with sufficiently low income

are entitled to more deductions than the total value of

their cash income. In this case, some of their deductions are essentially unused, because net income is

constrained to be greater than or equal to zero. This

restriction also means that food stamp benefits may

not ever exceed the maximum benefit for a particular

family size. The impact of this limitation on benefits is

called the maximum benefit effect (E3). In 1998, the

mean per person value of E3 equaled -$6.78.

• Finally, one- and two-person food stamp units that

would otherwise have received very low benefit

amounts benefited from the rule setting the minimum

benefit level at $10 per food stamp unit. The mean per

person value of this minimum benefit effect (E4) was

$2.25.

Note that the mean per person food stamp benefit of

$69.25 equaled the sum of the mean maximum benefit

plus these four main effects. 

This decomposition shows how the deductions effects

are central to determining the food stamp benefit level.

About 56 percent of all income was eligible for one

deduction or another ($50.35/$89.27). In the absence

7 ✥ Understanding the Food Stamp Benefit Formula /FANRR-14 Economic Research Service/USDA
Economic Research Service/USDA Understanding the Food Stamp Benefit Formula /FANRR-14 ✥ 8

of deductions, the mean food stamp benefit would

have been reduced by over half.10 The standard deduction effect (E2.1) and the shelter deduction effect

(E2.6) are by far the largest, accounting for 89 percent

of the total deductions effect. 

The earned income deduction effect (E2.2)—the third

largest—had a mean per person value of only $3.77

for the full sample. The final two deductions effects,

the child support deduction effect (E2.3) and medical

deduction effect (E2.4), do not have a large impact on

mean food stamp benefits, but they may be important

to those food stamp units that receive them. For example, only 4 percent of food stamp units receive any

medical deduction effect (E2.4), but for those who

receive this deduction the mean effect is $28.56 (not

shown in table 3).

The further decomposition of the shelter deduction

effect (E2.6) is similar to the main decomposition of

food stamp benefits. The mean per person value of eligible shelter expenses in the 1998 QC data was

$168.83 per month, leading to a raw shelter expense

effect (E2.6.1) of $50.65. 

However, not all shelter expenses are counted in the

shelter deduction. Only shelter expenses over 50 percent of intermediate net income count toward the shelter deduction. This half-income rule effect (E2.6.2)

equaled -$26.85. Finally, the cap on the shelter deduction further reduced benefits by $3.29 per person on

average.

Income Groups 

It is well understood that food stamp benefits vary

inversely with gross cash income because the benefit

reduction rate of 0.3 is a central component of the benefit formula. It is less widely understood how other

stipulations of the benefit formula have differential

effects on participants with different income levels. 

In table 3, we consider three categories of food stamp

units, according to whether the unit has gross income

below 50 percent of the poverty guideline (very poor),

Table 3—Composition of mean per capita benefits, by gross income category of food stamp unit

“Very poor" "Poor" "Near poor"

Full below 50% 50-100% above 100%

Symbol Component name sample of poverty of poverty of poverty

Dollars

M Maximum benefit 112.70 111.01 113.89 112.70

E1 Income effect -89.27 -31.65 -115.45 -168.70

E2 Deductions effect 50.35 37.71 56.52 65.48

E3 Maximum benefit effect -6.78 -15.80 -1.47 -0.92

E4 Minimum benefit effect 2.25 0.00 1.21 16.56

Total food stamp benefits 69.25 101.28 54.68 25.11

E2.1 Standard deduction effect 24.21 21.44 26.21 24.03

E2.2 Earned income deduction effect 3.77 0.86 4.17 12.77

E2.3 Dependent care deduction effect 0.60 0.16 0.61 2.17

E2.4 Medical deduction effect 1.17 0.03 1.12 5.81

E2.5 Child support payment 0.09 0.02 0.11 0.26

deduction effect

E2.6 Shelter deduction effect 20.51 15.21 24.29 20.44

Total deductions effect (E2) 50.35 37.71 56.52 65.48

E2.6.1 Raw shelter expense effect 50.65 26.88 63.43 72.75

E2.6.2 Half-income rule effect -26.85 -7.18 -36.37 -50.80

E2.6.3 Shelter deduction cap effect -3.29 -4.50 -2.77 -1.50

Shelter deduction effect (E2.6) 20.51 15.21 24.29 20.44

Mean food stamp unit size 2.42 2.69 2.24 2.36

Percent

Proportion of all food stamp units 100.0 37.4 52.8 9.8

Note: Column entries are rounded to two significant digits after the decimal.

Source: Author's calculations from 1998 Quality Control data.

10Calculating the mean benefit under the hypothetical case

where no deductions are permitted is not quite as simple as subtracting the deductions effect (E2) from the mean benefit. Recall

that some deductions are "unused," and therefore are counted

under the maximum benefit effect (E3).
between 50 and 100 percent of the guideline (poor), or

greater than 100 percent of the guideline (near-poor).

The income effect (E1) is naturally largest in absolute

value for the near-poor food stamp units (-$168.70 for

near-poor units in comparison to -$31.65 for very poor

units). This income effect reflects the fact that nearpoor units have 5.3 times the mean per person gross

income of very poor units. 

The total deductions effect (E2), by contrast, is smallest for the poorest households. The earned income

deduction effect (E2.2), for example, is $12.77 for

near-poor units, but less than a dollar for very poor

units (which have the lowest labor market earnings).

The shelter deduction effect is also smaller for very

poor food stamp units than for other units. Very poor

food stamp units have much lower shelter expenses—

only 37 percent of the per person shelter expenses that

near-poor units have. 

With lower shelter expenses, the very poor units cannot claim as much benefit from the shelter deduction.

The shelter deduction cap effect is also largest for the

poorest units. These patterns are only partially offset

by the half-income rule—the rule that only shelter

expenses above half of intermediate net income count

toward the shelter deduction. This rule affects units

with more income to a greater extent than other units. 

The very poor food stamp units not only have a lower

total deduction effect (E2), but they have the most substantial maximum benefit effect (E3) (a negative

effect). This effect is -$15.80 for the very poor units,

but just -$0.92 for the near-poor units. A greater

amount of the deductions that the very poor units

would otherwise have been entitled to goes unused due

to lower gross income levels. As a result, only the very

poor units have a substantial maximum benefit effect

(E3). Likewise, the minimum benefit effect provides

no help in raising the mean per person benefit for very

poor units, and it is just $1.21 for poor units. By contrast, the minimum benefit effect is $16.56 for nearpoor units.

The net consequence of these effects is that the benefit

formula provides higher mean food stamp benefits to

the poorest food stamp units (due to E1), but not as

much higher as one might expect. One might anticipate (from the benefit reduction rate of 30 percent)

that food stamp benefits would fall 30 cents for every

dollar of additional income, but in fact the gradient is

not so steep. The deductions effect (E2), maximum

benefit effect (E3), and minimum benefit effect (E4)

each have the least positive value for the poorest food

stamp units. As a consequence, food stamp benefits

generally fall by less than 30 cents if income increases

by $1.00.

Demographic Categories

Patterns of food stamp benefit receipt differ substantially by demographic category. For example, some

stipulations of the benefit formula apply only to food

stamp units that contain an elderly or disabled person.

Food stamp units that contain a single female parent

with children are most likely to participate in the cash

welfare program Temporary Assistance for Needy

Families (TANF), so they differ from other food stamp

units on a variety of demographic and economic characteristics. Food stamp units without children, elderly,

or disabled members face a combination of time limits

and work requirements that may complicate their participation in the Food Stamp Program. 

In this subsection, we compare the benefit decomposition for five major demographic categories: units that

are composed entirely of elderly or disabled persons

(28.5 percent of the full sample), units that contain an

elderly or disabled person living with other persons

(11.1 percent), units without an elderly or disabled

person that contain a single female parent with children (31.7 percent of the full sample), other food

stamp units with children (16.9 percent), and other

food stamp units without children (11.9 percent).

Fewer than 6 percent of food stamp units simultaneously contain an elderly or disabled person and a single female with children, so this division of the sample

into non-overlapping demographic categories seemed

superior to a yet more disaggregated classification. 

The food stamp units composed entirely of elderly or

disabled persons have more than twice as much gross

cash income per person as units in the categories without an elderly or disabled person (table 4 shows that

the income effect E1 is more than twice as large for

the former group). For many elderly or disabled persons, the main source of cash income is Social

Security or Supplemental Security Income (SS/SSI).

Units with an elderly or disabled member are exempted from the gross income test, so in the presence of

sufficient deductions they could in principle have comparatively high gross income and still be eligible to

participate. For the first demographic category alone,

the absolute value of the income effect (E1) is greater

than the mean maximum benefit (M), so the receipt of

9 ✥ Understanding the Food Stamp Benefit Formula /FANRR-14 Economic Research Service/USDA
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positive amounts of food stamp benefits for this category may be attributed almost entirely to the deductions effect (E2).

The deductions effect is highest for units composed

entirely of elderly or disabled members, for several

reasons. First, the mean per person standard deduction

effect (E2.1) is higher for this category and for other

units with no children, simply because household size

tends to be smaller for these categories (the effect of

household size is discussed at length in the next 

subsection). 

Also, units composed entirely of elderly or disabled

members are the only ones with a medical deduction

effect (E2.4) exceeding $1.00. Most importantly, units

composed entirely of an elderly or disabled member

have the highest shelter deduction effect (E2.6). They

have the highest mean per person shelter expenses,

leading to a higher raw shelter expense effect (E2.6.1).

Also, they are specifically exempted from the shelter

deduction cap, which would otherwise limit the shelter

deduction for many of these units (E2.6.3). Because of

lower labor force participation, units with an elderly or

disabled member benefit less from the earned income

deduction (E2.2), but this pattern only slightly offsets

the higher deductions noted above. The mean per person total deductions effect (E2) is $79.10 for units

composed entirely of elderly or disabled members,

compared with $32.89 for the single female parent category and $35.50 for other food stamp units with 

children.

Food Stamp Unit Size

The decomposition of food stamp benefits works in

distinct ways for food stamp units of different sizes

(table 5). Here, for tractability, we compare and contrast food stamp units with one to five members (only

4 percent of all food stamp units have more than five

members).

Table 4—Composition of mean per capita benefits, by demographic category of food stamp unit

With single

Elderly or Elderly or female parent Other units Other units

Full disabled disabled and no elderly with with no

Symbol Component name sample persons only and others or disabled children children

Dollars

M Maximum benefit 112.70 121.60 105.82 107.08 106.06 122.13

E1 Income effect -89.27 -158.61 -80.99 -58.16 -63.63 -50.39

E2 Deductions effect 50.35 79.10 28.99 32.89 35.50 68.90

E3 Maximum benefit effect -6.78 -3.66 -1.43 -3.12 -5.07 -31.40

E4 Minimum benefit effect 2.25 6.97 0.42 0.23 0.17 1.01

Total food stamp benefits 69.25 45.40 52.80 78.92 73.03 110.25

E2.1 Standard deduction effect 24.21 38.49 13.82 14.51 14.99 38.61

E2.2 Earned income deduction effect 3.77 0.45 1.54 5.61 7.40 3.75

E2.3 Dependent care deduction effect 0.60 0.19 0.29 1.34 0.50 0.02

E2.4 Medical deduction effect 1.17 3.90 0.52 0.00 0.00 0.00

E2.5 Child support payment 0.09 0.09 0.07 0.05 0.16 0.12

deduction effect

E2.6 Shelter deduction effect 20.51 35.99 12.76 11.39 12.45 26.40

Total deductions effect (E2) 50.35 79.10 28.99 32.89 35.50 68.90

E2.6.1 Raw shelter expense effect 50.65 87.57 39.38 30.71 35.35 47.60

E2.6.2 Half-income rule effect -26.85 -51.58 -26.62 -15.52 -17.70 -11.09

E2.6.3 Shelter deduction cap effect -3.29 N/A N/A -3.81 -5.21 -10.11

Shelter deduction effect (E2.6) 20.51 35.99 12.76 11.39 12.45 26.40

Mean food stamp unit size 2.42 1.09 3.39 3.12 3.63 1.11

Percent

Proportion of all food stamp units 100.0 28.5 11.1 31.7 16.9 11.9

NA=Households with an elderly or disabled person do not face a cap on the shelter deduction.

Note: Column entries are rounded to two significant digits after the decimal.

Source: Author's calculations from 1998 Quality Control data.
To some extent, differences among different sizes of

food stamp units result from purposeful program

design decisions. For example, the benefit formula

adjusts the maximum benefit by household size, and

the formula explicitly sets the standard deduction at a

fixed value for the food stamp unit (not per person in

the unit). In part, however, differences by household

size may proxy for other demographic or economic

variables. For example, 67 percent of one-person units

are composed of an elderly or disabled person alone,

and most of the remaining one-person units are in the

category "other adults without children." Thus, phenomena that appear related to unit size could in part be

due to the demographic characteristics addressed in the

previous subsection. However, an analysis that crosstabulates family size and other demographic characteristics simultaneously is beyond the scope of this

report.

Mean per person gross income declines steeply with

unit size. In this sense, larger food stamp units tend to

be poorer than smaller food stamp units. One-person

units have the largest income effect (in absolute value),

at -$126.90. However, several of the other effects are

larger for small food stamp units, with the net consequence that mean per person food stamp benefits

remain quite nearly constant in the neighborhood of

$70 for all food stamp units with one to four members

(declining slightly for five-person units).

The mean per person maximum benefit (M) is higher

for smaller units because the Thrifty Food Plan on

which the maximum benefit is based explicitly allows

for economies of scale in food purchase and preparation. The deductions effect (E2) is also highest for

smaller units. For example, the mean per person standard deduction effect (E2.1) falls with unit size

because the standard deduction ($134 per food stamp

unit in 1998) is constant regardless of the number of

members. Shelter costs exhibit strong economies of

scale because common areas of a house or apartment

may be shared among several unit members. Smaller

food stamp units have a much higher per person raw

shelter expense effect (E2.6.1). Even after the partially

offsetting influence of the half-income rule effect

(E2.6.2), the smaller units have a much larger overall

Table 5—Composition of mean per capita benefits, by food stamp unit size

Food stamp unit size

Full 

Symbol Component name sample 1 2 3 4 5

Dollars

M Maximum benefit 112.70 122.69 112.43 107.50 102.48 97.70

E1 Income effect -89.27 -126.90 -78.73 -62.94 -57.53 -55.33

E2 Deductions effect 50.35 79.53 43.47 31.61 24.59 20.20

E3 Maximum benefit effect -6.78 -13.03 -4.92 -2.52 -1.60 -0.90

E4 Minimum benefit effect 2.25 5.27 1.03 0.00 0.00 0.00

Total food stamp benefits 69.25 67.57 73.29 73.64 67.94 61.68

E2.1 Standard deduction effect 24.21 40.39 20.18 13.46 10.09 8.09

E2.2 Earned income deduction effect 3.77 1.54 4.48 5.54 5.54 5.67

E2.3 Dependent care deduction effect 0.60 0.17 0.87 1.09 0.86 0.55

E2.4 Medical deduction effect 1.17 2.54 0.77 0.11 0.02 0.02

E2.5 Child support payment 0.09 0.08 0.09 0.12 0.08 0.10

deduction effect

E2.6 Shelter deduction effect 20.51 34.80 17.09 11.30 8.00 5.76

Total deductions effect (E2) 50.35 79.53 43.47 31.61 24.59 20.20

E2.6.1 Raw shelter expense effect 50.65 77.78 43.46 33.27 27.06 23.79

E2.6.2 Half-income rule effect -26.85 -39.33 -22.66 -18.27 -16.84 -16.20

E2.6.3 Shelter deduction cap effect -3.29 -3.64 -3.71 -3.71 -2.22 -1.82

Shelter deduction effect (E2.6) 20.51 34.80 17.09 11.30 8.00 5.76

Mean food stamp unit size 2.42 1.00 2.00 3.00 4.00 5.00

Percent

Proportion of all food stamp units 100.0 38.6 21.0 17.9 12.3 6.0

Note: Column entries are rounded to two significant digits after the decimal 

Source: Author's calculations from 1998 Quality Control data.

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shelter deduction effect (E2.6). In all, the mean per

person total deductions effect (E2) is almost four times

as large for one-person food stamp units as for fiveperson units. This effect almost entirely offsets the differences in the income effect by unit size, leading

small food stamp units to receive almost the same

mean food stamp benefit as four-person units despite

the smaller units' much higher income per person.

Census Regions

The two components that most strongly affect differences in food stamp benefits across regions of the

country are the income effect (E1) and the shelter

deduction effect (E2.6). Food stamp participants in the

Northeast have comparatively high per person gross

income, leading to an income effect of -$102.96 (table

6). Income is lowest in the South and West, with a corresponding income effect in each region of approximately -$80 (table 6).

Partly offsetting the income effect, food stamp units in

the Northeast have the highest shelter expenses and

likewise the highest shelter deduction effect (E2.6).

These shelter expenses reflect higher property values

in much of the Northeast, and also higher utility costs.

The mean per person raw shelter expense effect

(E2.6.1) is $77.37 in the Northeast, in contrast with

about $41 in the South and West. 

This difference is only partly compensated by the

higher half-income rule effect (E2.6.2) and shelter

deduction cap effect (E2.6.3) in the Northeast. Overall,

the shelter deduction effect raises mean per person

food stamp benefits by $34.93 in the Northeast, and by

approximately $16 in the South and West.

Table 6—Composition of mean per capita benefits, by census region

Census region

Full 1 2 3 4

Symbol Component name sample Northeast Midwest South West

Dollars

M Maximum benefit 112.70 113.50 112.84 111.67 113.75

E1 Income effect -89.27 -102.96 -94.65 -84.01 -79.60

E2 Deductions effect 50.35 65.16 50.84 45.43 44.04

E3 Maximum benefit effect -6.78 -7.45 -6.72 -6.58 -6.55

E4 Minimum benefit effect 2.25 3.34 3.16 1.38 1.88

Total food stamp benefits 69.25 71.59 65.46 67.90 73.53

E2.1 Standard deduction effect 24.21 26.28 25.31 23.43 22.41

E2.2 Earned income deduction effect 3.77 2.61 3.79 4.21 4.11

E2.3 Dependent care deduction effect 0.60 0.59 0.42 0.74 0.51

E2.4 Medical deduction effect 1.17 0.63 2.04 1.36 0.42

E2.5 Child support payment 0.09 0.12 0.09 0.09 0.06

deduction effect

E2.6 Shelter deduction effect 20.51 34.93 19.19 15.61 16.53

Total deductions effect (E2) 50.35 65.16 50.84 45.43 44.04

E2.6.1 Raw shelter expense effect 50.65 77.37 49.91 41.55 41.48

E2.6.2 Half-income rule effect -26.85 -33.92 -28.47 -24.32 -22.71

E2.6.3 Shelter deduction cap effect -3.29 -8.52 -2.25 -1.61 -2.24

Shelter deduction effect (E2.6) 20.51 34.93 19.19 15.61 16.53

Mean food stamp unit size 2.42 2.21 2.32 2.48 2.64

Percent

Proportion of all food stamp units 100.0 20.6 20.8 39.3 19.4 

Note: Column entries are rounded to two significant digits after the decimal.

Source: Author's calculations from 1998 Quality Control data.
Discussion

While the FSP benefit formula is rather complex, the

computations reported here are straightforward (the

SAS software program used to make these calculations

is provided in Appendix B). For research purposes

beyond the goals of this report, more complex tools

such as microsimulation analysis are more suitable

(Jacobson et al., 2000).11 For example, this report's

tool is not consistently useful for understanding counter-factual scenarios, such as "How would benefits

change if gross income rose by $20?" Similarly, the

tool does not address changes to eligibility rules that

influence participation—the focus here is on the distribution of benefits for a fixed sample of participants. In

contrast, microsimulation analysis is specifically

designed for counterfactual investigations, and it does

seek to measure how policy changes affect both the

participation decision and the benefit level for 

participants. 

The main advantage of this report's analytic tool is that

it summarizes in a simple and consistent format a variety of stipulations and regulations that are usually stated in a manner that makes comparison difficult.

Microsimulation analysis requires estimation of a vector of behavioral parameters with one data source from

one time period, and then simulation of policy changes

in a second data source and time period under the

assumption that the behavioral parameters remain 

constant. 

Conclusions from such analysis depend on both the

accuracy of the estimated parameters and the characteristics of the sample in a fashion that may be difficult

for the casual reader to disentangle. The tool developed for this report permits a transparent comparison

of the various components of the benefit formula for

different types of household, and it is simpler than

alternative approaches for this purpose. 

The tool developed in this report quantifies the relative

importance of the reduction in benefits due to cash

income, the increase in benefits due to deductions, and

the minimum and maximum benefit levels. First, the

income effect (E1)—defined here as -0.3 times gross

cash income—is very large in absolute value. For the

full sample, the income effect equals -$89.27, compared to a mean per person maximum benefit of

$112.70. Second, deductions go a long way toward

offsetting the reduction in benefits that would result if

all cash income counted against benefits. For the full

sample, the deductions effect (E2) equals $50.35.

Average benefits are less strongly affected by the maximum benefit effect (E3) of -$6.78 and the minimum

benefit effect (E4) of $2.25, but these effects are not

trivial. In this analysis, the actual mean per person

food stamp benefit ($69.25) may be expressed as the

maximum benefit plus the effects of E1 through E4.

The income effect (negative) and the deductions effect

(positive) are both so large in absolute value that the

balance between these effects is a major factor in

determining the mean food stamp benefit for any population or subpopulation of participants. Differences in

the income effect and deductions effect across subpopulations are typically a dominant source of differences

in the actual benefit received, while differences across

subpopulations in the maximum benefit are often less

important. To understand the distribution of food

stamp benefits across different types of households

requires a comprehensible account of the whole array

of positive and negative effects on the benefits that

participants actually receive. This report takes a step

toward providing such an account.

11Microsimulation analyses estimate how a particular program

change would influence the participation decision and benefit

amount for each household in a particular sample. Then, the

analyses aggregate the individual level responses to report how the

change would affect overall caseloads and average benefit levels.

13 ✥ Understanding the Food Stamp Benefit Formula /FANRR-14 Economic Research Service/USDA
Economic Research Service/USDA Understanding the Food Stamp Benefit Formula /FANRR-14 ✥ 14

References

Brinkley, Mark. Technical Documentation for the

Fiscal Year 1998 FSP QC Database and QC

Minimodel. Washington DC: Mathematica Policy

Research, Inc. June 28, 1999.

Castner, Laura, and Randy Rosso. Characteristics of

Food Stamp Households, Fiscal Year 1998.

Washington DC: Mathematica Policy Research, Inc.

February 2000.

Food Stamp Act of 1977. As Amended Through P.L.

106-171, Feb. 11, 2000.

<http://www.fns.usda.gov/fsp/LEGISLATION/act.htm>.

Jacobson, Jonathan, Nuria Rodriguez-Planas, Loren

Puffer, Mary Grider, and Emily Pas. The

Consequences of Economic Change for the Food

Stamp Program: Illustrations from Microsimulation.

Report submitted to the U.S. Department of

Agriculture, Economic Research Service. Washington,

DC: Mathematica Policy Research, Inc., 2000 (forthcoming).

U.S. Department of Agriculture, Center for Nutrition

Policy and Promotion. "Official USDA Food Plans:

Cost of Food at Home at Four Levels." 

Accessed (March 14, 2001)

<http://www.usda.gov/cnpp/using3.htm>.

U.S. Department of Agriculture, Food and Nutrition

Service. "Food Stamps." Accessed (March 13, 2001)

<http://www.fns.usda.gov/fsp/> and

<http://www.fns.usda.gov/pd/fssummar.htm>.
Appendix A: Proofs

First, we prove that the decomposition in equation (9)

is equivalent to the more traditional statement of the

benefit formula in equation (4). Define total deductions (including unused deductions) as:

(A1) D = D1 + D2 + D3 + D4 + D5 + D6. 

Substitute equations (A1), (5), (6), and (7) into equation (9) to get:

(A2) B = M - 0.3 * G + 0.3 * D - 0.3 Max (0, D-G) + 

E4

= M - 0.3 [G - D + Max (0, D - G)] + E4

= M - 0.3 [Max (G - D, 0)] + E4.

Use equations (3) and (8) with (A2) to get:

(A3) B = M - 0.3 * N2 + Max [0, 10 - (M - 0.3 * N2)]

= Max [M - 0.3 * N2, 10].

This equals the right-hand side of equation (4) to complete the first proof.

Second, we prove that the shelter expense effect in

equation (13) is equivalent to 0.3 times the shelter

deduction (D5) in equation (2). From equations (10),

(11), (12), and (13), we have:

(A4) E2.6 = E2.6.1 + E2.6.2 + E2.6.3

= E2.6.1 + E2.6.2 + Min [0.3 * H* - 

(E2.6.1 + E2.6.2), 0]

= Min [0.3 * H*, E2.6.1 + E2.6.2]

= Min [0.3 * H *, 0.3 * H - 0.3 * Min 

(0.5 * N1, H)]

= Min [0.3 * H*, -0.3 Min (0.5 * N1 - H,

0)]

= 0.3 Min [H*, Max (H - 0.5 * N1, 0)].

This completes the second proof.

15 ✥ Understanding the Food Stamp Benefit Formula /FANRR-14 Economic Research Service/USDA
Economic Research Service/USDA Understanding the Food Stamp Benefit Formula /FANRR-14 ✥ 16

Appendix B: SAS Software Program

*** DECTOOL.SAS

*** Produces tables used in Wilde, 2000.

*** "Understanding the Food Stamp Benefit Formula"

*** Input data: qcfy1998.sd2

*** Parke Wilde

*** 9/1/2000;

*** Define names of input data sets ***;

libname out 'e:/temp/ces/';

libname in 'e:/data/qc/qc98/';

options linesize=100;

*** Create data file DECOMP ***;

data out.decomp;

set in.qcfy1998

( keep = fsndis fsnelder fsnkid fsngmom fsusize fywgt

fsgrinc fsnetinc fstotded fstotde2

fscsexp fsstdded fsernded fsdepded fsmedded

fssltded shelcap benmax fsben

fsminben netscrn state fssltexp

urbrur tpov region);

*** SHELTER SUB-COMPONENT EFFECTS ***;

neldis=fsndis+fsnelder;

if neldis ge 1 then d_diseld=1;

else d_diseld=0;

if d_diseld=0 then hstar=shelcap;

else hstar=fssltexp;

n1 = max(fsgrinc-(fsstdded+fsernded+fscsexp+fsmedded+fsdepded),0);

e261 = 0.3*fssltexp; ** gross shelter;

e262 = -0.3*min(0.5*n1,fssltexp); ** half-income rule;

e263 = min((0.3*hstar)-(e261+e262),0); ** shelter cap effect;

e26 = e261+e262+e263; ** shelter ded effect;

*** DEDUCTIONS EFFECTS ***;

sumded = fsstdded+fsernded+fscsexp+fsmedded+fsdepded+(e26/0.3);

e21 = 0.3*fsstdded; ** standard;

e22 = 0.3*fsernded; ** earned income;

e23 = 0.3*fsdepded; ** dependent care;

e24 = 0.3*fsmedded; ** medical;

e25 = 0.3*fscsexp; ** child support;

e2 = e21+e22+e23+e24+e25+e26; ** deductions effect;

*** MAIN COMPONENT EFFECTS ***;

e1 = -0.3*fsgrinc; ** income effect;

e3 = -0.3*max(0,(sumded-fsgrinc)); ** max effect;

e4 = max(0,10-(benmax-0.3*fsnetinc)); ** min effect;

*** ALTERNATIVE DEFINITIONS FOR DOUBLE-CHECKING ***;

alte26 = 0.3*fssltded; ** alt shelt ded effect;

alte2 = 0.3*fstotded; ** alt deductions effect;

sumfsben = benmax+e1+e2+e3+e4; ** total fs ben;

** INCOME CATEGORY ***;

If tpov le 50 then inccat='1.below 50% pov';

else if 50 < tpov le 100 then inccat='2.50-100% pov';

else if 100 < tpov then inccat='3.above 100% pov';

*** DEMOGRAPHIC CATEGORY ***;

if d_diseld=1 and neldis ge fsusize then demcat='1.all_dis/eld';

else if d_diseld=1 then demcat='2.some_dis/eld';

else if fsngmom=1 then demcat='3.sngmom';

else if fsnkid>0 then demcat='4.other_kids';

else demcat='5.other_nokids';
*** DUMMY FOR RECEIPT OF MEDICAL ***;

IF E24>0 then yesmed=1; else yesmed=0;

*** Observations with benefits below 10 ***;

if fsben < 10 then lowflag=1; else lowflag=0;

if fsusize>2 then fsubig=1; else fsubig=0;

*** PER/PERSON BASIS ***;

* (put comments around this section for hh level analysis option) *;

hh_max = benmax;

hh_e1 = e1;

hh_e2 = e2;

hh_e3 = e3;

hh_e4 = e4;

hh_fsben = fsben;

array effects benmax e1-e4 e21-e26 e261-e263 alte2 alte26 sumfsben fsben;

do over effects;

effects=effects/fsusize;

end;

*** Net income of zero ***;

if n1 le 0 then netzero=1; else netzero=0;

*** Missing shelter values ***;

if (alte26 ne .) and (e261 ne .) and (alte2 ne .) and (e23 ne .);

*** Non-continental US states and territories ***;

if state=2 or state=15 or state=66 or state=72 or state=78 then outstate=1;

else outstate=0;

label

e1 = '. income effect'

e2 = '. deductions effect'

e3 = '. max effect'

e4 = '. min effect'

e21 = '. standard deduction effect'

e22 = '. earnings deduction effect'

e23 = '. dependent care ded. effect'

e24 = '. medical deduction effect'

e25 = '. child support ded. effect'

e26 = '. shelter deduction effect'

e261 = '. gross shelter exp. effect'

e262 = '. half-income rule effect'

e263 = '. shelter cap effect'

alte2 = 'DEDUCTION EFFECT (ALT.)'

alte26 = 'SHELTER DEDUCTION EFFECT (ALT.)'

sumfsben = 'COMPUTED FOOD STAMP BENEFITS (ALT.)'

d_diseld = 'DISABLED/ELDERLY PRESENT';

*** Missing values to aid in formatting output ***;

array missing miss1-miss6;

do over missing; missing=.; end;

run;

*** COUNT UNITS WITH BENEFITS BELOW $10 ***;

proc freq;

table lowflag*fsubig;

run;

*** REMOVE OBS THAT DON'T OBEY MINIMUM BENEFIT ***;

data out.decomp;

set out.decomp;

if lowflag=1 then delete;

run;

*** DESCRIPTIVE FREQUENCIES ***;

17 ✥ Understanding the Food Stamp Benefit Formula /FANRR-14 Economic Research Service/USDA
Economic Research Service/USDA Understanding the Food Stamp Benefit Formula /FANRR-14 ✥ 18

proc freq data=out.decomp;

weight fywgt;

table fsngmom*d_diseld;

table fsusize*demcat;

table inccat*demcat;

table region*demcat;

table yesmed*demcat;

table netzero;

run;

*** PRODUCE TABLE 1 ***;

proc means n sumwgt mean std data=out.decomp;

where fsusize=2 and outstate=0;

weight fywgt;

var hh_max hh_e1 hh_e2 hh_e3 hh_e4 hh_fsben;

run;

*** ANALYSIS BY INCOME CATEGORY ***;

proc sort data=out.decomp;

by inccat;

run;

proc means n sumwgt mean std data=out.decomp;

weight fywgt;

var benmax e1 e2 e3 e4 miss1 miss2

e21 e22 e23 e24 e25 e26 miss3 miss4

e261 e262 e263 miss5 miss6

fsusize d_diseld alte2 alte26 sumfsben fsben;

run;

proc means n sumwgt mean std data=out.decomp;

by inccat;

weight fywgt;

var benmax e1 e2 e3 e4 miss1 miss2

e21 e22 e23 e24 e25 e26 miss3 miss4

e261 e262 e263 miss5 miss6

fsusize d_diseld alte2 alte26 sumfsben fsben;

run;

*** ANALYSIS BY DEMOGRAPHIC CATEGORY ***;

proc sort data=out.decomp;

by demcat;

run;

proc means n sumwgt mean std data=out.decomp;

weight fywgt;

var fsusize fsnkid fsnelder fsndis;

run;

proc means n sumwgt mean std data=out.decomp;

weight fywgt;

by demcat;

var fsusize fsnkid fsnelder fsndis;

run;

proc means n sumwgt mean std data=out.decomp;

by demcat;

weight fywgt;

var benmax e1 e2 e3 e4 miss1 miss2

e21 e22 e23 e24 e25 e26 miss3 miss4

e261 e262 e263 miss5 miss6

fsusize d_diseld alte2 alte26 sumfsben fsben;

run;

*** ANALYSIS BY HOUSEHOLD SIZE ***;

proc sort data=out.decomp;

by fsusize;

run;

proc means n sumwgt mean std data=out.decomp;

where fsusize le 6;

by fsusize;

weight fywgt;

var benmax e1 e2 e3 e4 miss1 miss2
e21 e22 e23 e24 e25 e26 miss3 miss4

e261 e262 e263 miss5 miss6

fsusize d_diseld alte2 alte26 sumfsben fsben;

run;

*** ANALYSIS BY CENSUS REGION ***;

proc sort data=out.decomp;

by region;

run;

proc means n sumwgt mean std data=out.decomp;

by region;

weight fywgt;

var benmax e1 e2 e3 e4 miss1 miss2

e21 e22 e23 e24 e25 e26 miss3 miss4

e261 e262 e263 miss5 miss6

fsusize d_diseld alte2 alte26 sumfsben fsben;

run;

*** ANALYSIS BY RECEIPT OF MEDICAL DEDUCTION ***;

proc sort data=out.decomp;

by yesmed;

run;

proc means n sumwgt mean std data=out.decomp;

by yesmed;

weight fywgt;

var benmax e1 e2 e3 e4 miss1 miss2

e21 e22 e23 e24 e25 e26 miss3 miss4

e261 e262 e263 miss5 miss6

fsusize d_diseld alte2 alte26 sumfsben fsben;

run;

19 ✥ Understanding the Food Stamp Benefit Formula /FANRR-14 Economic Research Service/USDA