Food Stamps and Food Insecurity : What Can Be Learned in the Presence of Nonclassical Measurement Error ?

Policymakers have been puzzled to observe that food stamp households appear more likely to be food insecure than observationally similar eligible nonparticipating households. We reexamine this issue allowing for nonclassical reporting errors in food stamp participation and food insecurity. Extending the literature on partially identified parameters, we introduce a nonparametric framework that makes transparent what can be known about conditional probabilities when a binary outcome and conditioning variable are both subject to nonclassical measurement error. We find that some prevailing conclusions in the food assistance literature hinge critically on implicit assumptions about the nature and degree of classification errors in the data.