Immigration, integration pipelines, and local innovation intensity

This note derives a local ranking result for immigration and innovation within a two-stage integration pipeline. Immigrants first enter an unintegrated state, then transition to a partially integrated stage, and finally reach full integration. Each transition is governed by a stage-specific hazard rate that declines with congestion, reflecting capacity constraints in language training, credential recognition, licensing, and innovation-network access. At the no-immigration baseline, a proportional expansion of later-stage capacity raises the local slope of innovation intensity more than the same proportional expansion of earlier-stage capacity, if and only if fully integrated workers carry a sufficiently large innovation weight relative to their partially integrated counterparts. This ranking has no analogue in a one-stage benchmark, where proportional easing merely rescales a single transition margin. An auxiliary result shows that, under a common-congestion schedule, the model can generate a hump-shaped pattern for innovation intensity when the local-gain condition holds. An illustrative parameterization demonstrates that the late-minus-early gap widens when selection into full integration is stronger or the later bottleneck is tighter. These findings suggest that, for innovation intensity, where capacity is expanded within the integration pipeline matters as much as how much capacity is added overall.