Food Stamps and Food Insecurity Among Families With Children: What Can be Learned in the Presence of Nonclassical Measurement Error?
Research Center: Institute for Research on Poverty, University of Wisconsin-Madison
Investigator: Gundersen, Craig, and Brent Kreider
Institution: Iowa State University
Department of Human Development and Family Studies
Iowa State University
74 LeBaron Hall
Ames, IA 50011
The central goal of the Food Stamp Program is to alleviate food insecurity in the United States. Given this goal, policymakers have been puzzled to observe that food stamp households with children are more likely to be food insecure than similar nonparticipating eligible households. In 2003, food stamp participants had food insecurity rates of 52.3 percent while eligible nonparticipants had food insecurity rates of 34.4 percent, a gap of 17.8 percentage points. For a more severe measure of food insecurity, food insecurity with hunger, the gap between participants and eligible nonparticipants was 6.4 percentage points. This positive association between food stamp participation and food insecurity has been ascribed to several factors, including self-selection, the timing of food insecurity versus food stamp receipt, misreporting of food insecurity status, and misreporting of food stamp receipt.
This study focuses on misreporting issues with data from the Core Food Security Module (CFSM), a component of the Current Population Survey (CPS). More specifically, the study investigates what can be inferred when food stamp participation and food insecurity status are subject to nonclassical measurement error. This work contrasts with the previous literature on the connection between food stamps and food insecurity that has implicitly assumed that both indicators are measured without error.
The assumption of no errors in reports of food stamp participation status and food insecurity status is questionable.
In terms of food stamp participation status, previous studies have demonstrated that the weighted number of food stamp participants in nationally representative surveys is substantially fewer than that found in administrative records. The underreporting is about 15 percentage points in the CPS. In terms of food insecurity status, while not as straightforward, there are reasons to expect inaccurate reports of food insecurity. For example, some food stamp recipients might misreport being food insecure if they believe that to report otherwise could jeopardize their eligibility. Alternatively, some parents may misreport being food secure if they feel ashamed about heading a household in which their children are not getting enough food to eat.
In light of the problems of misreporting in food stamps and food insecurity, the study introduces a nonparametric framework for assessing what can be inferred about conditional probabilities when a binary outcome (food insecurity) and a binary conditioning variable (food stamp participation) are both subject to nonclassical measurement error. The study first posits that food stamp participation is not accurately reported but food insecurity is accurately reported. Under this assumption, the study considers three cases:
- Corrupt sampling bounds, where no assumptions are made about reporting errors.
- Orthogonal errors, where classification errors arise independently of true participation status
- Corrupt sampling bounds with no false positives, where reported food stamp nonparticipants are allowed to be participants but not vice versa.
Misreporting rates of under 13 percent may be sufficient to prevent identification of the positive relationship between food insecurity and food stamp participation.
Under corrupt sampling bounds, if as few as 7.1 percent of eligible households misreport food stamp participation status, the positive association between food insecurity and food stamp participation is no longer identified. For orthogonal errors and “no false positives,” the figures are 8.2 percent and 10.1 percent. When considering the case of food insecurity with hunger, under corrupt sampling bounds and orthogonal errors, if as few as 1.8 percent and 2.9 percent of the eligible sample misreport their food stamp participation status, the positive association between food insecurity and food stamp participation is no longer identified. For “no false positives,” the number of misreports is higher—12.4 percent. Given that previous work has found that food stamp participation rates are underreported in the CPS by about 15 percent, findings in this study may be of importance. Specifically, if misreporting rates of less than 13 percent are sufficient to prevent identification of the positive relationship between food insecurity and food stamp participation, policymakers may wish to be cautious about drawing conclusions about the relationship between food insecurity and food stamps.
Policymakers should be even more cautious once errors are allowed in reports of both food stamp participation and food insecurity. For example, under the assumption of orthogonal errors in food insecurity reports with no false positive reports of food stamp participation, if as few as 4.1 percent of households misreport their food insecurity status, the positive relationship between food insecurity and food stamp participation is no longer identified.