This article examines how data on INS border apprehensions are related to the flow of undocumented migrants crossing the southern U.S. border. Its centerpiece is a demographic model of the process of unauthorized migration across the Mexico-U.S. frontier. This model is both a conceptual framework that allows us to see theoretical linkages between apprehensions and illegal migrant flows, and a methodological device that yields estimates of the gross number of undocumented migrants. One implication of the model is that, for the first time, the relation between apprehensions and illegal flows can be examined empirically. We show that the ratio in each period between apprehensions and the undocumented flow is simply the odds of being located and arrested on any given attempt to enter the United States clandestinely. In addition, data for 1977–1988 suggest that the simple linear correlation between the number of apprehensions and the volume of illegal immigration is approximately 0.90 and that the size of the illegal migrant flow is roughly 2.2 times the number of Border Patrol arrests. The article concludes with a discussion of the conditions under which it is appropriate to use INS apprehensions data as an indicator for the flow of undocumented U.S. migrants.
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