Survey misreporting is known to be pervasive and bias common statistical analyses. In this paper, I first use administrative data on SNAP receipt and amounts linked to American Community Survey data from New York State to show that survey data can misrepresent the program in important ways. For example, more than 1.4 billion dollars received are not reported in New York State alone. 46 percent of dollars received by house- holds with annual income above the poverty line are not reported in the survey data, while only 19 percent are missing below the poverty line. Standard corrections for measurement error cannot remove these biases. I then develop a method to obtain consistent estimates by combining parameter estimates from the linked data with publicly available data. This conditional density method recovers the correct estimates using public use data only, which solves the problem that access to linked administrative data is usually restricted. I examine the degree to which this approach can be used to extrapolate across time and geography, in order to solve the problem that validation data is often based on a convenience sample. I present evidence from within New York State that the extent of heterogeneity is small enough to make extrapolation work well across both time and geography. Extrapolation to the entire U.S. yields substantive differences to survey data and reduces deviations from official aggregates by a factor of 4 to 9 compared to survey aggregates.