Data on INS [Immigration and Naturalization Service] 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 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.

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.