The effect of lawful crossing on unlawful crossing at the US southwest border

Legal and illegal markets often coexist. In theory, marginal legalization can either substitute for the remaining parallel market, or complement it via scale effects. I study migrants crossing without prior authorization at the US southwest border, where large-scale unlawful crossing coexists with substantial, varying, and policy-constrained lawful crossing. I test whether lawful and unlawful crossing are gross substitutes or complements, using lag-augmented local projections to analyze a monthly time-series on the full universe of 10,658,497 inadmissible migrants encountered from October 2011 through July 2023. Expanded lawful crossings cause reduced unlawful crossings, an effect that grows over time and reaches elasticity -0.3 after approximately 10 months. That is, in this case, expanded activity on the lawful market substitutes for the parallel market, even net of scale effects. This deterrent effect explains approximately 9 percent of the overall variance in unlawful crossings. In an ancillary finding, I fail to reject a null effect of depenalizing unlawful crossings on future attempted unlawful crossings.