Validation study of reported program participation by Marquis and Moore (1990) reveals a bias due to net under-reporting of Food Stamp Program participation of 13% (Wave 1-2 data from the 1984 Survey of Income and Program Participation). We extend that analysis conditioning on demographic and economic covariates. The resulting model of over- and under-reporting is included in MLE of the probability of Food Stamp Program participation (David and MacDonald 1992). Survey response and administrative data are aggregated to families in this analysis. Under-reporting is modeled by probit analysis on demographic and economic variables using conceptual insights from cognitive research and economic theory. Aggregation of reports to families eliminates apparent errors associated with discrepancies in identifying the individual certified to receive Food Stamps and multiple reporting of recipiency for a family group. The probability of under-reporting Food Stamp recipiency increases with family income normalized by family size. Other results from the response error analysis are less stable across interviews, and have greater sampling errors. Women are better reporters than men, and married couples are more reliable than single householders. Estimating the model of Food Stamp participation using the models of over- and under-reporting results in substantial shifts of the probit coefficients. Estimates of several coefficients of particular conceptual interest in modeling Food Stamp participation are more than fifty percent larger in the model conditioned on probabilities of response errors.