  The Mexican Migration Project (MMP) is 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 US. 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 1980-2016. Contrary
to published estimates based on these same data, our results imply migrants
remain in the US much longer than previously estimated based on analysis that
ignored the physical snapshot bias. Scaling to population quantities, we
produce lower bounds on the total number of undocumented immigrants that are
much larger than conventional estimates based on US-based census-linked
surveys, and broadly consistent with the estimates reported by Fazel-Zarandi,
Feinstein and Kaplan (2018).
