HNCC Presentation 8 May 2014

SNAP and Diet Quality: A New Approach
Christian A. Gregory Shelly Ver Ploeg Margaret Andrews
Alisha Coleman-Jensen
Economic Research Service, USDA
Human Nutrition Coordinating Committee
Washington, DC
May 8, 2014
The views expressed are those of the authors and should
not be attributed to ERS or USDA.

Background & Motivation
Background: Intent of Program
• SNAP authorizing legislation: ”To alleviate such hunger and
malnutrition, a supplemental nutrition assistance program is
herein authorized which will permit low-income households to
obtain a more nutritious diet through normal channels of trade
by increasing purchasing power ...”
• food security and nutrition declared goals of SNAP
Gregory, Ver Ploeg, et al. SNAP and Diet Quality February 13, 2014

Background: Public Perceptions
• ”As I look at what this card is paying for in the orders being
scanned at the register, I see T-bone steaks, thick-cut sirloins,
thick-cut pork chops (all expensive cuts of meat). I see crab
legs, bags of shrimp, and box after box of pastries, cakes and
doughnuts from the bakery department, and bagged candy,
chips and cookies from the snack aisles. Then come the sodas,
energy drinks and Starbucks coﬀee drinks... The people using
this card are eating better than most families that have two
incomes.” -Letter to Frederick News Post

Background: SNAP & Food Security
• recent research: SNAP ⇓ food insecurity
• Yen et al. (2008); DePolt et al. (2009); Shaefer and Gutierrez
(2012); Nord and Golla (2009); Nord and Prell (2011);
Ratcliﬀe et al. (2011); Mabli et al. (2013)
• estimates suggest SNAP participation ⇓ food insecurity 33 -
40 percent

Background: SNAP & Diet Quality
• recently–a good deal of concern
• many expensive chronic illnesses associated with low-income
populations
• public bears sizable fraction of cost
• policy suggestions:
– restrict foods eligible for SNAP (as in WIC)
– Wholesome Wave Double Coupon
– Healthy Incentives Pilot
• interim report 1/5 c ⇑ in TFV for HIP/SNAP participants

Motivation
• large extant literature (detail below)
• some–improved intakes (Devaney and Moffitt, 1991; Wilde
et al., 1999)
• some–poorer intakes (Butler and Raymond, 1996; Yen, 2010)
• difficult to identify treatment effects
selection on unobservables
• selection: adverse or beneficial?

Our Contribution
• use individual data (NHANES) matched to state-level data
identify SNAP selection
• estimate treatment effects by isolating unobservables in SNAP
and diet
• show that marginal effect of SNAP is positive and significant
for some HEI components; adverse selection accounts for
worse diet outcomes

Preview of Results
• as measured by HEI total and component scores
– SNAP participants comparable diets
– total effect of SNAP (including selection): slightly lower HEI
scores
– economically significant?
– effect of SNAP on marginal participant is positive for whole
fruit, negative for darkgreen veg
• robust to specification choice?
• suggest policy caution: tradeoff improving nutritional quality,
changing selection into the program

Previous Research
Previous Research
• comprehensive review of literature (Fox et al., 2004)
• wrt intakes, few find significant impact ↑, ↓
• highlight Gleason et al. (2000)–array of outcomes including
HEI–rule out large effects in either direction
• studies that find positive effects: Wilde et al. (1999);
Kramer-LeBlanc et al. (1997); Basiotis et al. (1998)
• more recent studies: Cole and Fox (2008); Yen (2010)
• Waehrer and Deb (2012) used latent factor model/IV–SNAP
participants ↑ caloric sweetened beverages ↓ fruits/vegetables

Data
Data: NHANES 2001-08
• individual: NHANES 2001-02, 2003-04, 2005-06, 2007-08
• dependent variable: Healthy Eating Index Score (HEI) (day 1), total and
component
– total = sum of 12 elements
– total fruit, whole fruit, total veg, dark green and orange veg, total
grains, whole grains, milk, meat and beans, oils, sat fat, sodium,
SoFAAS
– for food groups and oils: zero intake = score of zero; meet/exceed
dietary recommendation = perfect score; linear interpellation b/w

Data
Data: NHANES 2003-08 (cont)
• dependent variable: Healthy Eating Index Score (HEI) (day 1), total and
component (continued)
• how to score “moderation” components? (i.e. things you should eat less
of)
– 85th pctile of consumption = score of zero; meet Dietary Guidelines
recommendation = score of 8; meet somewhat higher standard, below
dietary rec = score of 10; linear interpellation b/w amounts at 0 and 8,
8 and 10.
– example: sat fat. – fraction of total energy (2001-2002 NHANES data)
• 85th pctile: 15 % : score of 0
• DG: less than 10 %: score of 8
• below 7% : score of 10
– weights: milk, meat/beans, oils, sat fat, sodium = 10; total fruit, whole
fruit, total veg, dark green and orange veg, total grains, whole grains
=5 ; SoFAAS = 20

Data
Data: NHANES 2003-08
• independent variable of interest: HH SNAP participation
– 2001, 2003, 2005 waves: 2 questions HH SNAP participation: number
of persons authorized to receive SNAP, whether HH authorized to
receive SNAP now.
– 2007 wave: time since HH receive SNAP (less than 31 days)
– robustness check: sample person currently receiving SNAP
• other rhs variables: race/ethnicity, income, education, SR weight 1 year
ago, age, marital status, employment status, vigorous ex./week, nutrition
ed per poor person, hh size, state ﬁxed-eﬀects
• 200% FPL

Data
Data: SNAP Policy Database
• in model (following) we need exogenous variables to identify
participation in SNAP
– state-month level variation in two policies:
– expanded categorical eligibility–relaxed asset and/or
income requirements
– vehicle exemption whether state exempts 1 vehicle from
calculation of total assets to determine eligibility
• valid: the policies aﬀect SNAP participation but not diet
quality/HEI (except through SNAP)

Methods
Treatment Eﬀects Model
• one might begin with
HEIi = Xi β + SNAPi δOLS + ǫi (1)
• problem: SNAP is endogenous to HEI
• another way to proceed
HEIi = Xi β + SNAPi δZ + ǫi (2)
SNAP∗
i = Zi γ + Xi θ + υi (3)
• Z exogenous variables for SNAP
• SNAP∗
latent index of SNAP participation
• X other variables correlated w/ SNAP, HEI
• ǫ and υ bivariate normal w/covariance matrix
V =
σ2 ρσ
ρσ 1

Methods
Identification & Marginal Effects
• model is theoretically identified by functional form imposed by
distribution of ǫ and υ.
• we use exogenous policy variables to identify SNAP
participation
• total effects of SNAP :
µi = δZ + ρσ
φ(Zi γ + Xi θ)
Φ(Zi γ + Xi θ) ∗ [1 − Φ(Zi γ + Xi θ)]
(4)
this is what δOLS will estimate

Methods
Identification & Marginal Effects
• without selection: µi = δOLS ; with selection δZ + difference in
expected value of errors conditional on participation (See
Greene, 2011)
• unconditional on selection, δZ measures marginal affects of
SNAP on participants
• standard errors (of total effects) (ν) by delta method: let
α = [γ, θ]
νµ =
∂µ
∂α
M
∂µ
∂α
′
, (5)
where M is the covariance matrix of the selection equation

Results
Descriptive
51.8
47.8
4950515253
HEIScore
No SNAP SNAP Participants
Data: NHANES, 2003−08
SNAP Participation Status
HEI Score and SNAP Participation
Figure: Diﬀerences in HEI over SNAP Participation

Results
Descriptive
2094
2124.3
2044207421042134
TotalEnergyIntake
No SNAP SNAP Participants
Data: NHANES, 2003−08
SNAP Participation Status
Total Food Energy and SNAP Participation
Figure: Diﬀerences in Energy over SNAP Participation

Results
Descriptive
Table: Means of HEI Components by SNAP Participation
HEI Component No SNAP SNAP Diﬀerence
TotalFruit 2.11 1.73 -0.38***
(0.07) (0.07) (0.12)
WholeFruit 1.93 1.39 -0.54***
(0.06) (0.06) (0.10)
TotalVeg 3.00 2.63 -0.37***
(0.04) (0.07) (0.08)
DkGOrVeg 1.17 0.83 -0.34***
(0.05) (0.05) (0.08)
TotGrain 4.27 4.07 -0.20***
(0.03) (0.04) (0.06)
WholeGrain 0.93 0.66 -0.27***
(0.04) (0.03) (0.05)
N 6,668

Results
Descriptive
Table: Means of HEI Components by SNAP Participation, cont’d
HEI Component No SNAP SNAP Diﬀerence
Milk 4.77 4.39 -0.38**
(0.09) (0.11) (0.15)
Sodium 4.12 4.52 0.40***
(0.07) (0.09) (0.11)
SoFAAS 9.47 7.96 -1.51***
(0.20) (0.25) (0.41)
N 6,668

Results
Marginal Eﬀects of SNAP
Table: Marginal Eﬀects of SNAP=δ
HEI TotalFruit WholeFruit TotalVeg DkGOrVeg
δ -1.441 0.270 2.795*** -0.660 -0.735***
νδ (4.503) (0.710) (0.209) (0.592) (0.187)
TotGrain WholeGrain Milk MeatBeans Oils
δ -0.039 -0.383 -0.054 -0.248 0.372
νδ (0.147) (0.233) (0.590) (0.310) (0.741)
SatFat Sodium SoFAAS
δ -0.193 -0.046 -0.820
νδ (0.987) (0.740) (1.423)
N 6,668

Results
Questions
• δs seem too large to be believed
• δwf = 2.795, ¯x = 1.39

Results
Distribution of Components
0.1.2.3.4.5
Density
0 1 2 3 4 5
Score
Data: NHANES 2003−08, 200% FPL
Kernel Density WholeFruit Component Score
Figure: Distribution of Whole Fruit Component
• modewf = 0, modewg = 0

Results
Distributional Concerns
• need to address the violation of distributional assumptions
• GMM, 2SLS, larger std errs, size of δZ still a concern
• ﬁnite mixture model (latent class model) – probabilities as
function of SNAP participation

Results
Solution: Bivariate Probit
Table: Bivariate Probit: Effect of SNAP on Score >0
Whole Fruit
Parameter Marginal Effect
SNAP 0.548** 0.238
(0.32)
N 6,668
• effect on SNAP is to increase by 24 percentage points points
prob of eating any whole fruit
• too large? less than 30% of sample eat any whole fruit or
whole grain
• SNAP increases likelihood that those eating no whole fruit will
eat some.

Results
Correlation, IV Strength
Table: Selection Paramter: ρ
ρ 0.007 -0.112 -0.979*** 0.199 0.216***
νρ (0.195) (0.201) (0.084) (0.203) (0.052)
ρ -0.049 0.125 -0.054 -0.033 0.372
νρ (0.051) (0.092) (0.096) (0.067) (0.115)
ρ 0.073 0.057 0.050
νρ (0.145) (0.136) (0.121)
• All F-tests of instruments < 10. (Reasons and caveats.)

Results
Expected Diﬀerences
Table: Total Eﬀects of SNAP (Current) on HEI/Component Scores
µ -1.249*** -0.186*** -0.678*** 0.023 0.030
νµ (0.006) (0.013) (0.105) (0.021) (0.023)
µ -0.157*** -0.031*** -0.376*** -0.431*** -0.123***
νµ (0.003) (0.011) (0.010) (0.005) (0.015)
µ 0.344*** 0.325*** -0.163***
νµ (0.016) (0.011) (0.020)
N 6,668

Results
How Big Are These Diﬀerences?
• Saturated Fat: SNAP participants 5.5 (12) calories less in
saturated fat per day than low-income non-participants (high
income persons).
• Sodium: SNAP participants 75 (160) mg less in sodium than
low-income non-participants (high income persons).
• statistically signiﬁcant, economically so?
• 1-ounce bag of potato chips – about 80 mg sodium

Discussion
Discussion
• SNAP has positive effect on whole fruit and negative effect on dark
green and orange vegetables of SNAP participants ⇑ in
P(Score) > 0 (whole fruit)
• expected differences (after taking SNAP into account) statistically
significant, though uncertain in health/economic significance
• adverse selection into SNAP whole fruit models, beneficial selection
in dark green orange vegetable models
• participants in general have slightly less healthy diets compared to
similar non-participants–SNAP participation alone does not close gap
in diet quality.
• suggests caution when thinking about restricting SNAP benefits
– most households consume more in food than they get in SNAP
benefits–changing what can be included not likely to change
behavior
– however, changing foods that can be purchased could change mix
of participants–change ameliorative affect on food insecurity

Discussion
Discussion
• Further Questions
– controlled for endogeneity fully?
– distribution of error terms–alternative distributions
– how might SNAP improve DQ w/o adversely aﬀecting
selection/eﬀectiveness?
– subsidies instead of restrictions? (Wholesome Wave, Healthy
Incentives)

Discussion
Further Discussion?
Thank You
cgregory@ers.usda.gov

HNCC Presentation 8 May 2014

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