SNAP solves food insecurity – defense doesn’t assume endogeneity.

Results Food Insecure: The naïve probit model results, which do not control for the endogeneity of SNAP receipt, show that SNAP receipt is associated with higher food insecurity. The estimated coefficient on SNAP participation suggests that participating in SNAP is associated with an 8.6 percentage point increase in the probability of being food insecure (Table 2, model 1). This result is consistent with the self-selection of more needy and food-insecure households into SNAP. Results from the bivariate probit model, which controls for the endogeneity of SNAP receipt, suggest a different relationship. The receipt of SNAP benefits is found to reduce the likelihood of food insecurity by 16.2 percentage points (Table 2, model 2).18 Nearly one-quarter of our low-income sample is food insecure, so these results suggest that SNAP has a substantial effect on households’ food insecurity and is achieving exactly what the program was designed to do—reduce food-related hardship. To further put this number in context, we use the marginal effect along with the SNAP recipients’ level of food insecurity to estimate the percent (versus percentage point) decline in food insecurity implied by our model. Our summary statistics show that 35.6 percent of SNAP recipients are food insecure. The bivariate probit model estimates suggest that SNAP recipients’ food insecurity would be 16.2 percentage points higher (51.8 percent), if SNAP benefits were not available. The decrease in the likelihood of food insecurity from 0.518 without the SNAP program to 0.356 with the program suggests that SNAP receipt reduces food insecurity by 31.2 percent. The magnitude of this decline is consistent with Nord and Golla (2009), who find that the likelihood of being very food insecure falls by roughly onethird when households begin receiving SNAP benefits.

A comparison of the SNAP receipt coefficients from the probit and bivariate probit models suggests that controlling for selection into SNAP is important for disentangling the effect of SNAP receipt on food insecurity. The model that does not control for the endogeneity of 18 The marginal effects are calculated as the average difference in the predicted probability of being food insecure for those with and without SNAP receipt. The calculations are based on the estimated parameters from the bivariate probit food insecurity equation (equation 1), which have been corrected for the endogeneity of SNAP receipt. Estimation of the univariate probablities is appropriate because our goal is to understand how SNAP receipt affects food insecurity, not the joint probabilities. We estimate the marginal effects using the Stata marginal effects command, mfx, with the option predict(pmarg1). 15 SNAP receipt shows that SNAP participation is associated with increased food insecurity, while the model that does control for the endogeneity shows that SNAP participation reduces food insecurity. Further, the correlation coefficient from the bivariate probit model indicates a positive and statistically significant correlation between unobservables that affect SNAP receipt and food insecurity (ρ=0.509 with a standard error of 0.054). Households that are more likely to be food insecure are also more likely to participate in SNAP. As discussed above, the validity of our IV model depends on the quality of the instruments. Because our model is overidentified, we are able to test the exogeneity of the instruments. Using Hansen’s J-test, we conclude that the instruments are indeed exogenous (we do not reject the null hypothesis that all of the instruments are exogenous, p=0.89). Using the Kleibergen-Papp statistic, we test whether the instrumental variables identify the model and reject the null hypothesis that the model is underidentified (p=0.0002). Each of the four instruments has the anticipated sign and statistically significantly (p<0.1) affects SNAP receipt (Table 3), and a joint test for significance of the four instruments indicates that they are jointly statistically significant at the one percent level (χ2 (4)=15.8, p=0.003). The coefficients and standard errors of the instruments from the reduced-form SNAP participation equation are presented in Table 3 (column 1).

Many household demographic characteristics are important determinants of food insecurity (Table 3, column 2). Households headed by younger persons are more likely to be food insecure, as are households headed by minorities and persons with limited education. Households with more children are also more likely to be food insecure. Female-headed and male-headed households are more likely than two-adults-headed households to be food insecure. Finally, having a disabled person in the household is associated with a higher likelihood of food insecurity. The state unemployment rate and employment-population ratio do not affect food insecurity, although a stronger economy as measured by quarterly GDP is found to reduce food insecurity. Very Food Insecure: Findings from our analysis of the relationship between SNAP participation and the likelihood of being very food insecure show a similar pattern. The model that does not control for selection into SNAP finds a positive, statistically significant relationship between SNAP receipt and being very food insecure, while the model that does control for selection finds that SNAP receipt statistically significantly reduces the likelihood of being very 16 food insecure (Table 2, models 3 and 4). Fewer households are very food insecure than food insecure (10.3 percent versus 24.4 percent, respectively), and the magnitudes of the estimated coefficients are consistent with this lower prevalence. The bivariate probit model results suggest that SNAP benefit receipt reduces the likelihood of being very food secure by 3.9 percentage points. Translating this percentage point decline into a percent decline (as done above for food insecurity), we find that SNAP reduces the likelihood of being very food insecure by 20.2 percent. This is lower than the roughly 30 percent decline found for food insecurity, although is still substantial. Like our analysis of food insecurity, the correlation coefficient indicates a positive and statistically significant relationship between unobservables that affect SNAP receipt and being very food insecure (ρ=0.284 with a standard error of 0.035). Also, we again find that Hansen’s Jtest suggests that all of the instruments are exogenous (p=0.53) and the Kleibergen-Papp statistic leads us to reject the null hypothesis that the model is underidentified (p=0.0002). Each of the four instruments has the anticipated sign and statistically significantly (p<0.1) affects SNAP receipt, and a joint test for significance of the four instruments indicates that they are jointly statistically significant at the 1 percent level (χ2 (4)=14.9, p=0.005). Appendix Table A-2 presents the full set of coefficients from this model.

Additional Specifications: As discussed above, we estimate our model on somewhat different samples to test the sensitivity of our results. First, we examine households with incomes below 130 percent of the poverty threshold, which more closely mimics the SNAP eligibility criteria. Analyses based on this more disadvantaged population show very similar results. The naïve models that do not control for selection into SNAP find a positive relationship between SNAP receipt and food insecurity, while models that control for selection find that SNAP receipt reduces food insecurity (Table 4). The bivariate probit results suggest that SNAP receipt reduces the likelihood of being food insecure by 12.8 percentage points and reduces the likelihood of being very food insecure by 3.4 percentage points. These percentage point declines translate into declines of 27.8 percent and 18.2 percent, respectively. These declines are very similar to what was found for the broader population of households with incomes below 150 percent of the poverty threshold. We also examine whether our findings are sensitive to having each household in the study sample for up to four months, by estimating the model on a sample that includes each 17 household only once. Results from the bivariate probit model (estimated with this smaller sample) suggest that SNAP receipt statistically significantly (at the 1 percent level) reduces the likelihood of being food insecure by 16.0 percentage points and the likelihood of being very food insecure by 3.9 percentage points (not shown). These estimated effects are nearly identical to those presented in Table 3 (16.2 and 3.9 percentage points, respectively). We also estimate models on a sample that includes households that have imputed food-insecurity or SNAP-receipt data, and again find very similar results. In this case, the bivariate probit model results suggest that SNAP receipt statistically significantly (at the 1 percent level) reduces the likelihood of being food insecure by 16.0 percentage points and being very food insecure by 4.1 percentage points (not shown). In addition to testing sensitivity to different study populations, we examine another measure of food-related hardship—food insufficiency—which has also been examined in the literature. Food insufficiency captures a relatively severe level of food hardship and is more similar to our very-food-insecure than to our food-insecure measure. Food-insufficient households are those that report sometimes or often not having enough to eat. Food insufficiency is not our primary outcome, because USDA official statistics report on food insecurity, not food insufficiency. Among our sample of households with incomes below 150 percent of the poverty threshold, 6.9 percent are food insufficient (compared with 10.3 percent that are very food insecure). Results from the bivariate probit model suggest that SNAP participation statistically significantly (at the 1 percent level) reduces food insufficiency by 2.7 percentage points, or by 19.4 percent. This is nearly identical to our finding that SNAP reduces the likelihood of being very food insecure by 20.2 percent. Discussion and Conclusion Using nationally representative data from the late 1990s and early- to mid-2000s and instrumental variables models, this study provides evidence that SNAP reduces households’ food-related hardships. We find that SNAP participation reduces the likelihood of being food insecure, very food insecure, and food insufficient. How much does SNAP reduce food-related hardship? The results suggest that the effect of the program is sizable. Results from our primary specification suggest that participation in SNAP reduces the likelihood of being food insecure by 16.2 percentage points (31.2 percent) and reduces the likelihood of being very food insecure by 3.9 percentage points (20.2 percent). Results from our specification tests show similar declines. 18 Further, we find that SNAP receipt reduces food insufficiency by about 20 percent. These estimated effects are substantial and provide evidence that SNAP is meeting its key goal of reducing food-related hardship. Given inherent difficulties in identifying causal effects where individuals self-select into programs (such as SNAP), the conclusions of any single analysis cannot be taken as definitive. This study contributes recent, nationally representative findings from models designed to control for self-selection to a growing body of literature that finds SNAP reduces food insecurity. For example, this study provides results consistent with Nord and Golla’s recent study (2009) using CPS data, which finds that food insecurity falls by roughly one-third after entry into SNAP. Our results are also consistent with analyses by DePolt et al. (2008) and Yen et al. (2008) that find SNAP reduces food hardship using data from the National Food Stamp Program Survey and the Three-City Study, respectively. In the current economic downturn, it is important for policymakers and program administrators to understand the effectiveness of their programs so they can better serve lowincome households and those experiencing food-related hardship. The results of this study suggest that program administrators can improve the well-being of households by increasing their enrollment in SNAP. Prior research suggests that this can be accomplished by making SNAP program rules more lenient, for example, and by expanding outreach (e.g., Bartlett, Burstein, and Hamilton 2004; Ratcliffe, McKernan, and Finegold 2008; Yen et al. 2008; Ziliak, Gundersen, and Figlio 2003). In addition, easing SNAP rules is a cost-efficient way for states to increase SNAP participation and improve the well-being of residents, as the federal government pays roughly half of the programs’ administrative costs and the full cost of benefits. States, however, should weigh concerns about program fraud and abuse and federal resources in deciding whether and which SNAP policies to ease.