Many scholars suggest that visa restrictions push individuals who would have otherwise migrated legally toward illegal channels. This expectation is difficult to test empirically for three reasons. First, unauthorized migration is clandestine and often unobservable. Second, interpersonal ties between migrants and would-be migrants form a self-perpetuating system, which adapts in ways that are difficult to observe or predict. Third, empirical evaluations of immigration policy are vulnerable to endogeneity and other issues of causal inference. In this paper, we pair tailor-made empirical designs with an agent-based computational model (ABM) to capture the dynamics of a migration system that often elude empirical analysis, while grounding agent rules and characteristics with primary data collected in Jamaica, an origin country. We find that some government-imposed restrictions on migrants can deter total migration, but others are ineffective. Relative to a system of free movement, the minimal eligibility conditions required to classify migrants into visa categories alone make migration inaccessible for many. Restrictive policies imposed on student and high-skilled visa categories have little added effect because eligible individuals are likely able to migrate through alternative legal categories. Meanwhile, restrictions on family-based visas result in significant reductions in total migration. However, they also produce the largest reorientation toward unauthorized channels-an unintended consequence that even the highest rates of apprehension do not effectively eliminate.