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Food assistance programs and food insecurity: implications for Canada in light of the mixing problem


In light of concerns about high rates of food insecurity, some have suggested that it might be time for Canada to implement national food assistance programs like those provided in the US, namely the Supplemental Nutrition Assistance Program (SNAP) and the National School Lunch Program (NSLP). In this paper, we assess how adopting these types of assistance programs would change the food insecurity rate in Canada among households with children. Using data from the Current Population Survey (CPS), we first evaluate the causal impact of these programs on food insecurity rates in the US using the Canadian definition of food security. Following other recent evaluations of food assistance programs, we use partial identification methods to address the selection problem that arises because the decision to take up the program is not random. We then combine these estimated impacts for the US with data from the Canadian Community Health Survey (CCHS) to predict how SNAP and NSLP would impact food insecurity rates in Canada. Partial identification methods are used to address the “mixing problem” that arises if some eligible Canadian households would participate in SNAP and others would not. The strength of the conclusions depends on the strength of the identifying assumptions. Under the weakest assumptions, we cannot determine whether food insecurity rates would rise or fall. Under our strongest nonparametric assumptions, we find that food insecurity would fall by at least 16% if SNAP were implemented and 11% if NSLP were implemented.

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  1. Food insecurity has become a leading health and nutrition issue in North America. A vast literature has documented numerous negative health consequences associated with food insecurity. See, e.g., Gundersen et al. (2011), Gundersen and Ziliak (2014, 2015), and Tarasuk et al. (2016).

  2. See, for example, McIntyre et al. (2016), Ionescu-Ittu et al. (2015), and Loopstra et al. (2015).

  3. In the US, 15.4% of the population (48.1 million individuals) lived in food insecure households, meaning they were “...uncertain of having, or unable to acquire, enough food because they had insufficient money or other resources” (Coleman-Jensen et al. 2015). About one-third were classified as “very low food secure,” the more serious level of food insecurity.

  4. The analysis in Sect. 3 provides an important extension to the results reported in Kreider et al. (2012) and Gundersen et al. (2012) which used data from the 2001–2006 National Health and Nutrition Examination Survey (NHANES) and the December Supplement of the 2003 CPS. Our current analysis uses data from the 2011 CPS and applies the Canadian definition of food insecurity. Focusing on recent data, including years ensuing the Great Recession, may be especially important given that SNAP participation rose substantially after 2007 and has remained at those high levels.

  5. In addition to accounting for the selection problem, Kreider et al. (2012) also address the classification problem that arises if some self-reports of food assistance status are erroneous. They do not, however, consider the mixing problem associated with introducing a program to a different population. While there is much evidence of substantial underreporting in national surveys, we follow the norm in the literature by assuming self-reports are accurate. We leave to future work the problem of simultaneously addressing all three identification problems. We do, however, assess the sensitivity of inferences on the Canadian food insecurity rate to our estimates derived using the CPS data (see Sect. 4).

  6. Also, changes in local policies may be endogenously related to observed food insecurity rates.

  7. Analysis of partial identification of treatment effects began with Manski (1990). See Manski (2007) for a textbook exposition and, e.g., Manski and Pepper (2000), Pepper (2000), Molinari (2008), and Kreider et al. (2012) for applications.

  8. In both the CPS and CCHS, income is reported within categories rather than as a continuous measure. We measure a household’s income as the midpoint of a category.

  9. Given our focus on households with children, this criterion should not lead to substantial errors in defining eligibility (Gundersen and Offutt 2005). Due to a lack of information needed to calculate net income in the CPS, we follow most of the previous literature and set the gross income threshold at 130% of the poverty threshold for all households. Virtually, all gross income-eligible households under the 130% of the poverty threshold are also net income eligible. Some states do set a higher gross income threshold (e.g., 200%), but in such cases many households turn out to be ineligible based on net income.

  10. We combine the two categories free (income below the 130% of the poverty line) and reduced price (income between 130 and 185% of the poverty line) since the reduced price cost is quite low at 40 cents per meal.

  11. We observe household income in the CPS and CCHS but not whether a child is an enrolled student. Moreover, these surveys use slightly different age groupings for children in the publicly available data, so we are not able to perfectly align the ages in these restricted subsamples.

  12. This approach is consistent with the scenario that Canada adopts one program but not both. Ideally, we would model interactions between these programs. Such an approach, however, is beyond the scope of this analysis.

  13. For the US, we use the official poverty thresholds found in Canada has not established an official definition of poverty akin to poverty lines set by the US government. Canada does, however, establish Low-Income Cut-Offs (LICOs) analogous to poverty lines. In both countries, the income thresholds are adjusted for family size and composition. Our analysis uses Canadian LICOs for 2009. See for more information. In Canada, unlike the US, poverty thresholds are adjusted by degree of urbanization. Because we do not observe these locations in the CCHS, we use an averaged value of the LICO as provided in the link above. The results in Table 1 use the US poverty thresholds for the analyses using the CPS and the Canadian poverty thresholds for the analyses using the CCHS.

  14. Despite the lower threshold in Canada, food insecurity rates there are substantially below the US. For additional information, see Tarasuk et al. (2014).

  15. This section closely follows discussion in Kreider et al. (2012) as foundation. Section 4 extends this analysis to additionally consider the mixing problem.

  16. We simplify notation by suppressing the conditioning on subpopulations of interest. For this analysis, we focus on income-eligible households with children in the US (or Canada, in Sect. 4).

  17. Kreider et al. (2012) allow for the possibility that some self-reports of food assistance status are erroneous. In that case, the observed participation indicator, Z, may not reveal true receipt. As described above, we eschew this complication and focus instead on the selection and mixing problems.

  18. Eslami and Cunnynhgam (2014) provide information on differences between SNAP recipients and nonrecipients over commonly observed covariates. See, e.g., Gundersen and Oliveira (2001) and Currie (2003) for speculation about differences over unobserved characteristics.

  19. To find the MIV bounds on the rates of food insecurity, one takes the appropriate weighted average of the plug-in estimators of lower and upper bounds. Following Kreider et al. (2012), we use 20 PIR groups observed in the data. As discussed in Manski and Pepper (2000), this MIV estimator is consistent but biased in finite samples. We employ Kreider and Pepper’s (2007) modified MIV estimator that accounts for the finite sample bias using a nonparametric bootstrap correction method. Under the joint MTS-MIV assumption, the MTS assumption is assumed to hold at each value of the instrument, v.

  20. The assumption that \(Z= 0\) for all income ineligible households may not be valid for the observed income threshold if income is misreported or if the eligibility measures reflect different time periods than measures collected in the CPS. A household whose eligibility was established in one period may have income that exceeds the threshold when the survey is conducted. With a “fuzzy” threshold where \(Z = 1\) for some “ineligible” respondents, the methods could be adapted to allow for selection and measurement error within “ineligible” subgroups (see Gundersen et al. 2012). In that case, the data would provide informative bounds on both latent outcome probabilities.

  21. These findings are similar to those reported in other recent analyses applying partial identification methods to evaluate the impact of SNAP on food insecurity in the US. Using data from NHANES, Kreider et al. (2012), for example, find that SNAP reduces food insecurity (using the US definition) by at least 13 percentage points and Gundersen et al. (2012) find that NSLP reduces food insecurity by at least 3 percentage points.

  22. Since Canada has much lower rates of food insecurity than the US, the level effects are likely to differ. In fact, the data reject the possibility that the level effects are identical in Canada and the US. The ATE estimates in Sect. 3 are, in some cases, larger in absolute value than the observed Canadian food insecurity rate.

  23. There is currently no well-developed method for deriving valid intervals in this setting involving multiple interrelated estimated bounds—bounds on the ATE, \(P_C [Y(1)=1]\) for Canada, and the prospective food insecurity rate with mixing.

  24. Given the constraints we use, the intuition leads to sharp bounds in this application. However, for other constraints, the upper bound may exceed \(P_C [Y(1)=1]\). Suppose, for example, that only 5% of eligible households would participate in SNAP. Given the data, we know that at least 5.4% of households would be better off participating. Thus, in this case, the upper bound would be 0.4 points higher than \(P_C [Y(1)=1]\).

  25. This MTR assumption is stronger than the one used in Sect. 2, Eq. (6). In particular, this assumption now applies to each household, whereas the MTR assumption in Sect. 2 only applies on average across households with the same realized treatment.


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This study was funded by a Programmatic Grant in Health and Health Equity from the Canadian Institutes of Health Research (CIHR) (grant no. FRN 115208). The opinions, results and conclusions reported in this paper are those of the authors and are independent from the funding sources. No endorsement by the CIHR is intended or should be inferred. The study sponsors had no role in the design of the study, the collection, analysis or interpretation of data, the writing of the report, or the decision to submit the article for publication.

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Correspondence to Craig Gundersen.

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Gundersen, C., Kreider, B., Pepper, J. et al. Food assistance programs and food insecurity: implications for Canada in light of the mixing problem. Empir Econ 52, 1065–1087 (2017).

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  • Supplemental Nutrition Assistance Program
  • National School Lunch Program
  • Food insecurity
  • Partial identification
  • Mixing problem
  • Selection problem
  • Treatment effects
  • Nonparametric bounds

JEL Classification

  • C18
  • I1
  • H4