Snapshot Models of Undocumented Immigration.

Accurately estimating the size of the undocumented immigrant population is a critical component of assessing the health and security risks of undocumented immigration to the United States. To provide one such estimate, we use data from the Mexican Migration Project (MMP), a study that includes samples of undocumented Mexican immigrants to the United States after their return to Mexico. Of particular interest are the departure and return dates of a sampled migrant's most recent sojourn in the United States, and the total number of such journeys undertaken by that migrant household, for these data enable the construction of data-driven undocumented immigration models. However, such data are subject to an extreme physical bias, for to be included in such a sample, a migrant must have returned to Mexico by the time of the survey, excluding those undocumented immigrants still in the United States. In our analysis, we account for this bias by jointly modeling trip timing and duration to produce the likelihood of observing the data in such a "snapshot" sample. Our analysis characterizes undocumented migration flows including single-visit migrants, repeat visitors, and "retirement" from circular migration. Starting with 1987, we apply our models to 30 annual random snapshot surveys of returned undocumented Mexican migrants accounting for undocumented Mexican migration from 1980 to 2016. Scaling to population quantities and supplementing our analysis of southern border crossings with estimates of visa overstays, we produce lower bounds on the total number of undocumented immigrants that are much larger than conventional estimates based on U.S.-based census-linked surveys, and broadly consistent with the more recent estimates reported by Fazel-Zarandi, Feinstein, and Kaplan.