2.1. SNAP’s effects on food expenditures

Cuffey, Beatty, and Harnack (Reference Cuffey, Beatty and Harnack2016) identify 51 studies conducted between 1974 and 2014 examining the effect of SNAP benefits (using MPS) on food-at-home spending or the difference in effects between SNAP benefits and other income (MPS − MPC). Average MPS and MPC values from previous studies were 0.327 and 0.105, respectively. The reported average difference between MPS and MPC was 0.245. A limitation of most of the studies identified in the authors’ review is that they do not correct for systematic biases that might be present because of unobservable factors. Most of the literature that the authors’ review also did not consider potential separate effects of SNAP participation on quantity purchased and prices paid for food items.

A more recent study by Hastings and Shapiro (Reference Hastings and Shapiro2017) uses retail panel and administrative data to motivate three methods for causal inference on the effect of SNAP participation on food expenditures. Estimated MPS ranges from 0.5 to 0.6. These authors also explore the effect of SNAP participation on shopping effort (which is related to prices paid) by analyzing store brand share changes and coupon redemption behavior after households start receiving SNAP benefits. Both store brand share and coupon redemption drop after households enter the program.

2.2. Food prices and SNAP

Hastings and Washington (Reference Hastings and Washington2010) use 26 months of scanner data (2006–2008) from three Nevada stores to explore these retailer price changes in response to consumer demand shifts generated by regular SNAP benefits distribution. First, they construct a price index for a SNAP recipient’s typical food basket. They subsequently estimate a linear regression model with the price index as the dependent variable and as explanatory variables dummies for the week of the month. They find that the price of the basket was comparatively more expensive during the weeks after SNAP benefit distribution. They also find that SNAP participants did comparatively more food shopping when they received their benefits. Both findings suggest that SNAP recipients might pay higher aggregate food prices than do nonrecipients, although they do not directly compare prices paid by participants and nonparticipants. Using a similar empirical approach and weekly scanner price data (2006–2012) from the 48 contiguous states and Washington, D.C., Goldin, Homonoff, and Meckel (Reference Goldin, Homonoff and Meckel2016) find similar monthly cycles in the food expenditures of SNAP-eligible households. However, the authors find no evidence that retailers’ food prices are associated with the SNAP issuance timing.

With respect to the relation between SNAP-Ed efforts and prices participants pay, Kaiser et al. (Reference Kaiser, Chaidez, Algert, Horowitz, Martin, Mendoza, Neelon and Ginsburg2015) find SNAP-Ed participation is associated with the use of behaviors related to cost minimization including using coupons and comparing prices of goods. However, SNAP-Ed currently constitutes approximately 1% of SNAP’s total budget and number of participants, making its impact relatively minimal.Footnote ¹ These factors suggest that SNAP-Ed is unlikely to have a major influence on SNAP participants’ food costs.

Although a separate food assistance program, previous literature examining the impact of the Women, Infants, and Children (WIC) program’s impact on prices charged by manufacturers and retailers for WIC-eligible products provides similarly mixed results. Examining California retailers, Saitone, Sexton, and Volpe (Reference Saitone, Sexton and Volpe2015) find that WIC food prices vary widely by retailer size but that only smaller vendors excessively mark up these products. Using data on manufacturers of infant formula WIC rebate bids (1986–2007) from several states, Davis (Reference Davis2012) finds WIC has no impact on wholesale price.

2.3. Other determinants of food prices

Previous literature finds a consistent positive relationship between higher household income and prices paid for food items. One explanation for this relationship is that better-quality food is more affordable at higher income levels (Aguiar and Hurst, Reference Aguiar and Hurst2007; Kyureghian, Nayga, and Bhattacharya, Reference Kyureghian, Nayga and Bhattacharya2013). Consistent with this hypothesis, some health literature finds that lower-income households purchase comparatively more food items with greater energy density and higher fat content, but these are typically less expensive (Drewnowski and Specter, Reference Drewnowski and Specter2004; Morland, Wing, and Roux, Reference Morland, Wing and Roux2002). Even when food items are of the same quality, higher-income households may be willing to pay higher prices because they face comparatively higher trade-offs to search for lower prices (Becker, Reference Becker1965). Cronovich, Daneshvary, and Schwer (Reference Cronovich, Daneshvary and Schwer1997) find that households earning more than $75,000 annually were less likely to use coupons compared with those that thought their income was “inadequate” (p. 1639).Footnote ²

A household’s level of education, similar to household income, may also affect purchasing decisions. In theory, individuals with more education are more likely to understand and implement cost-saving strategies, such as using coupons, to pay lower prices for food (Narashman, Reference Narashman1984). However, Cronovich, Daneshvary, and Schwer (Reference Cronovich, Daneshvary and Schwer1997) find no statistically significant relationship between coupon use and college education. Conversely, the authors found a statistically significant relation between coupon use and households with at least one full-time college student.

Household composition and age of household members also affect food decisions and food prices. Households with comparatively more children are less likely to form specific buying habits (Békési, Loy, and Weiss, Reference Békési, Loy and Wiess2013) or use coupons (Cronovich, Daneshvary, and Schwer, Reference Cronovich, Daneshvary and Schwer1997). Households with comparatively older shoppers are more likely to develop buying patterns based on past purchases (Békési, Loy, and Weiss, Reference Békési, Loy and Wiess2013), purchase food products believed to have higher nutritional quality (Blanciforti, Green, and Lane, Reference Blanciforti, Green and Lane1981), and be more willing to search for lower food prices (Aguiar and Hurst, Reference Aguiar and Hurst2007).

Racial composition also may help explain disparities in prices paid for food. African American and Hispanic households are significantly less likely to use coupons than are other racial groups (Cronovich, Daneshvary, and Schwer, Reference Cronovich, Daneshvary and Schwer1997). Geographic proximity to food providers (in many cases related to neighborhoods’ racial composition) also affects a household’s local food environment. Cummings and Mcintyre (Reference Cummings and Macintyre2006), as well as Zenk et al. (Reference Zenk, Shultz, Israel, James, Bao and Wilson2005), find that predominantly African American neighborhoods are more likely to be located farther from food retailers than are neighborhoods with other racial compositions. When combined with limited transportation options, this affects where a household can shop, which influences food prices (Chung and Myers, Reference Chung and Myers1999; Morland, Wing, and Roux, Reference Morland, Wing and Roux2002). According to Kunreuther (Reference Kunreuther1973), households in similar situations are “more likely to patronize the neighborhood store than to travel some distance to [a] chain store” (pp. 373–74). Hoch et al. (Reference Hoch, Kim, Montgomery and Rossi1995) find that “isolated stores display less price sensitivity than stores close to their competitors” (p. 28). Rose et al. (Reference Rose, Bordor, Swalm, Rice, Farley and Hutchinson2009) find that citizens of New Orleans who did not own a means of transportation paid approximately $11 per month more in travel costs than did those with their own vehicles.Footnote ³

Although many of these factors are beyond the household’s control, behaviors that reduce or improve their ability to pay comparatively lower food prices are not. For example, with budgeting and financial education, food purchasers may be able to use cost-saving strategies better, such as using coupons (Cronovich, Daneshvary, and Schwer, Reference Cronovich, Daneshvary and Schwer1997; Narashman, Reference Narashman1984). Similarly, lower-income households may fail to recognize that certain food items exhibit “size effects,” in which lower unit prices are available if larger quantities are purchased (Beatty, Reference Beatty2010; Kunreuther, Reference Kunreuther1973; Mendoza, Reference Mendoza2011; Rao, Reference Rao2000). Educational programs could improve consumer knowledge and result in increased use of these and other money-saving buying strategies.

Our analyses extend the literature by examining the effect of SNAP participation on prices paid. The FoodAPS data set provides a more direct means to examine prices SNAP participants paid and includes more explanatory variables than were available in the previous literature.

4.1. The expensiveness index

Following Aguiar and Hurst’s (Reference Aguiar and Hurst2007) method, we construct a food price index that we refer to as an expensiveness index to address the variety of food products each household purchased. This expensiveness index reflects the cost of a household’s food basket at the average prices all households in the sample paid relative to the actual cost of the basket at the prices which the household paid (Aguiar and Hurst, Reference Aguiar and Hurst2007; Beatty, Reference Beatty2010).Footnote ¹⁰ We calculated total expenditures for household j in period m ( $\bi{X}_{\bi{m}}^{\bi{j}})$ as follows:

(3) $${\bi{X}}_{\bi{m}}^{\bi{j}} = \sum\nolimits_{i \in I,{\rm{}}t \in m} {p_{i,t}^jq_{i,t}^j} = \sum\nolimits_{i \in I,{\rm{}}t \in m} {X_{i,t}^j} ,$$

where $p_{i,t}^j$ denotes the price paid per ounce, $q_{i,t}^j$ denotes the number of ounces purchased, and $X_{i,t}^j$ denotes expenditures for good i and shopping trip t. We calculated the average price paid for product i across all households in period m ( ${\bar p_{{\rm{i}},m}}$ ) as

(4) $${\bar p_{{\rm{i}},m}} = \sum\nolimits_{j \in J,t \in m} {({{X_{i,t}^j{W_j}} \over {{{\bar q}_{i,m}}}})} ,$$

where $${\bar q_{i,m}} = \sum\nolimits_{j \in J,t \in m}\hskip -3pt.\hskip 1pt {q_{i,t}^j} $$ is the total quantity of food item i all households purchased during period m, and W_j is the survey households’ weights.Footnote ¹¹ The cost of household j’s food basket at average prices is

(5) $${\tilde X_j} = \sum\nolimits_{i \in I} {{{\bar p}_{i,m}}\,q_{i,t}^j} .$$

Finally, the expensiveness index for the set of all goods I for household j is (P^j ):

(6) $${P^{\boldsymbol{j}}} = {{{X_j}} \over {{{\tilde X}_j}}}.$$

We normalized the price index around 1 by dividing the index for each household by the mean expensiveness index overall. An expensiveness index greater than 1 indicated that a household spent more than average on its food basket, and a value less than 1indicated that the household spent less than average. In our final analysis, equations (1) and (2) considered the entire period of observation for all households (10 months) as a single period (m = 1).

4.2. Regression model

We used the following linear model:

(7) $${P^j} = \alpha {\rm{}} + {\rm{}}{\beta _{SNAP}}SNAP + \beta _{{X^H}}^{\rm{’}}{\bi{Z}}_{\bi{j}}^{\bi{H}} + {\rm{}}\beta _{{X^C}}^{\rm{’}}{\bi{Z}}_{\bi{j}}^{\bi{C}}{\rm{}} + {\rm{}}\beta _{{X^M}}^{\rm{’}}{\bi{Z}}_{\bi{j}}^{\bi{M}}{\rm{}} + {\rm{}}{e_j}.$$

As previously noted, P^j represents our expensiveness index and was regressed against our Z ^H , Z ^C , and Z ^M vectors that consisted of our household, food consumer competency-related, and food market environment variables, respectively. Term e_j is random error, and the $\beta^\prime _{\rm{s}}$ are coefficients. SNAP, our primary variable of interest is a binary variable that indicates the household participated in the SNAP program. Households were identified as SNAP recipients if they indicated they received benefits and their participation was confirmed by administrative match (to avoid misreporting participation that could bias our results).Footnote ¹² Non-SNAP households included both low-income SNAP-eligible households and noneligible households. High-income noneligible households were also included in the comparison group to better capture price differences stemming from supply related explanations including strategic retailer behavior targeting stores with low-income consumers (including SNAP participants and nonparticipants).

Our household control vector included the logarithm of the annual household income, its squared value, and the logarithm of the household size.Footnote ¹³ We used the same age distinctions as those of Beatty (Reference Beatty2010) to determine the effects of household composition on prices paid for food items, in which we included the percentage of household members over 60 years old, between 5 and 17 years old, and less than 5 years old. Table 2 provides a complete list of all variables used and how they were measured. Table 3 provides variable summary statistics.

Table 2. Variable categories and explanations

Note: SNAP, Supplemental Nutrition Assistance Program.

Table 3. Summary statistics

^a These are the 5th and 95th percentiles, except for StateIncomePerCapita and StateUnemployment, which correspond to the 20th and 80th percentiles. We do not report minimum and maximums because of data disclosure concerns. The 20th and 80th percentiles for StateIncomePerCapita and StateUnemployment are percentiles of the empirical distribution containing only state-level data, not household-level data.

Note: SNAP, Supplemental Nutrition Assistance Program.

4.3. OLS regression estimation methods

We first used the OLS approach with different groups of control variables in our analysis. OLS allowed us to explore the association between the expensiveness index and all explanatory variables. In model 1, we included only our SNAP variable. Model 2 included the SNAP variable and our household control vector. Model 3 included the SNAP variable along with our household and food consumer competency-related control vectors. Model 4 included the SNAP variable and all of our control vectors. Adding explanatory variables to the model allowed us to explore how the relationship between our expensiveness index and the SNAP variable changed as different control categories were introduced.

4.4. Instrumental variable methods

The SNAP variable might still be correlated with some unobservable food price determinants even after including a large set of control variables. For example, previous SNAP recipients may be impatient, which is an unobserved trait (Hastings and Washington, Reference Hastings and Washington2010). Similarly, the ability to search and process information to compare prices effectively might also be correlated with the ability to find assistance programs and correctly apply for them (e.g., filling out relevant paperwork).

We used an IV approach to account for the endogeneity of selection into the SNAP program (Ratcliff, McKernan, and Zhang, Reference Ratcliff, McKernan and Zhang2011). We used three state policy variables as outside instruments to identify the causal SNAP participation variable: a dummy variable representing whether the state allows households to use a streamlined application process for recipients of Supplemental Security Income, a binary variable representing whether the state allows households to apply for SNAP benefits online, and the proportion of SNAP units with earnings that have recertification periods longer than a year.Footnote ¹⁴ All of these instruments reduce the cost to participate in SNAP.

We obtained these variables for 2012 and 2013 from the USDA’s SNAP Policy Database (https://www.ers.usda.gov/data-products/snap-policy-data-sets/). Following the method used by Ng and Bai (Reference Ng and Bai2009), we only included instruments with a t-statistic greater than 2.50 using a first stage regression approach. We also only included instruments that had the expected sign in the first stage regression to ensure their theoretical validity.Footnote ¹⁵

It is important to note that these variables are determined at the state level and are not controlled by sample members. However, it is possible that changes in state-level SNAP policies are correlated with state-level macroeconomic conditions that could affect aggregate food demand and prices. We controlled for this by including state-level unemployment and income per capita controls in the IV models.Footnote ¹⁶ We also tested the instruments’ validity using a Hansen test for overidentification (Wooldridge, Reference Wooldridge2010).

We also used the IV method developed by Lewbel (Reference Lewbel2012) both as a robustness check and to obtain potential efficiency gains (Almada, McCarthy, and Tchernis, Reference Almada, McCarthy and Tchernis2015; Baum, Reference Baum2011; Lewbel, Reference Lewbel2007, Reference Lewbel2012). Lewbel’s (Reference Lewbel2012) procedure works as follows. For simplicity, the main model for price P in equation (7) can be rewritten as

(8) $$P = {\rm{}}{\bi{Z{\rm{’}}{\gamma _1}}} + {\beta _{SNAP}}SNAP + e,$$

where index j has been omitted, Z is the vector of all explanatory variables excluding the SNAP variable, γ ₁ is the corresponding vector of parameters, and e represents the error term. A reduced form model for participation in the SNAP program can be written as

(9) $$SNAP = {\bi{{Z_S}{\gamma _2}}} + \varepsilon ,$$

where Zs is the vector of variables affecting participation including both Z and a vector of outside instruments H (i.e., Z_s = [ Z H ]). γ ₂ is the vector of coefficients in the participation equation, and ε is the error term. Identification and estimation of equations (8) and (9) are based on the following moment conditions and heteroscedasticity of the errors (Lewbel, Reference Lewbel2012):

(10) $${\bi E}\left( {{\bi Z}e} \right) = 0,{\rm{}}{\bi E}\left( {{\bi Z_S}\varepsilon } \right) = 0,\,\,\,Cov\left( {{\bi Z_L},e\varepsilon } \right) = 0,$$

where Z_L can be equal to Z_S or a subset of it. The first two sets of moment conditions correspond to the standard moment conditions used when instruments and explanatory variables are exogenous. The third set of moment conditions requires Z_L to be uncorrelated with the product of errors. Although the last moment conditions are not very intuitive, the validity can be assessed using a Hansen’s overidentification test. More importantly, the third moment conditions make it possible to identify and estimate parameters in equations (8) and (9) without outside instruments or to use this additional information to improve efficiency. In our application, Z_S = Z_L ; thus, the additional moment conditions were used to gain efficiency and to test the sensitivity of our results to additional model assumptions. Implementation of the procedure was carried out using STATA (Baum, Reference Baum2011).

5.1. Sensitivity analysis

We also conducted a series of sensitivity analyses to evaluate the robustness of our results to various model assumptions with a special emphasis on the robustness of the SNAP coefficient (Table 7). The first groups of robustness checks consider alternative subsample groups. Although our regression models controlled for income level, the sample includes both high- and low-income participants. Thus, observed differences in the expensiveness index might be because of differences in the income level. To test the sensitivity of our analysis to difference effects stemming from varying income levels, we also estimated our models using a subsample of households that receive SNAP benefits and SNAP-eligible nonparticipants (Table 7, S2). A household is SNAP eligible if its annual income is less than 130% of the poverty threshold. These thresholds are determined by the U.S. Department of Health and Human Services (HHS) annual poverty guidelines. We followed the 2012 and 2013 guidelines for the 48 contiguous states and Washington, D.C., to determine SNAP eligibilityFootnote ²² and found no statistically significant effect of SNAP participation on our expensiveness index for SNAP-eligible, but nonparticipating households.

Table 7. Summary of Sensitivity Analysis: SNAP Coefficient

Notes: Model 1 regresses our expensiveness index on our Supplemental Nutrition Assistance Program (SNAP) variable. Model 2 includes SNAP and household variables. Model 3 includes SNAP, household, and food consumer competency-related variables. Model 4 includes our SNAP, household, food consumer competency-related, and market variables. *P ≤ 0.1, **P ≤ 0.05, and ***P ≤ 0.01. Regressions are reported with robust standard errors. IV-2SLS, instrumental variable two-stage least squares.

The other results were very similar to our previous findings. For example, the OLS regressions indicated that SNAP participants’ mean expensiveness index was approximately 0.08 points lower (i.e., 8%) than that of SNAP-eligible nonparticipants (relative to the previous 10% difference). The SNAP coefficient that estimates this difference remained statistically significant but decreased to 5% when we added household control variables. When we controlled for food competency variables and market environments, the difference was approximately 3.5% and became statistically insignificant (Table 7, S2).

We also tested the robustness of our findings by removing outlying observations (Table 7, S3). We defined outliers as values exceeding 150% of the difference between the interquartile below and above the first and third quartile values, respectively. We removed outlier values above and below these thresholds in the expensiveness index, the logarithm of annual household income, the density of supermarkets in a county, the logarithm of household size, the distance to the nearest SNAP-authorized retailer, the density of nonsupermarkets in a county, and the county population variables. Removing these observations increased our R ² values from 0.08 to 0.12 for our OLS and IV regressions for our models with all control vectors. However, there was little change in the statistically significant relationships.

To test whether changes in statistical significance or coefficient values of the SNAP variable are caused by a decrease in the number of observations from models 1 to 4, we estimated each model using all the available observations (2,920) to estimate model 4 (Table 7, S2). The results were again largely similar to those in the baseline specification.Footnote ²³

We also considered additional and alternative sets of controls for our model. To see whether seasonal food price fluctuations affected the expensiveness index, we included summer, autumn, and winter binary variables (with spring as our base variable; Table 7, S5). Although these variables were statistically significant, our other results remained largely the same. To account for the previous literature showing that SNAP households spend much of their food dollars at the beginning of the month, we included a dummy variable indicating whether the survey took place in the first week of the month (Table 7, S6) literature. This variable was not statistically significant and did not affect our regression results. We then included state dummy variables instead of regional dummies and implemented the three econometric procedures for model 4 (Table 7, S7). The results using OLS were very similar to those in the baseline specification. However, the SNAP coefficient, and corresponding standard error, changed considerably when using the IV-2SLS (instrumental variable two-stage least squares) method and Lewbel IV procedure. However, all other results remained largely similar, and the SNAP variable was still not statistically significant. However, because our instruments are state-level policy variables, adding state dummies when using the standard IV procedure generated a weak instrument problem.

We also used sample weights to estimate our empirical model, as well as the log of the expensiveness index rather than the expensiveness index (Table 7, S8 and S9). Both procedures added little explanatory power.Footnote ²⁴ Finally, we used clustered standard errors (S10, Table 7). Following Abadie et al. (Reference Abadie, Athey, Imbens and Wooldridge2017), we used the survey sample clusters (50 in total) for standard error calculations. The clusters corresponded to the PSUs described in Section 3. Our results were robust to the use of these types of standard errors.