This note presents a stylized dynamic mechanism through which immigration restrictions may affect output even when their immediate impact appears modest. In the model, economic activity depends not only on the stock of migrants already present but also on the continuation of inflows, because new arrivals become residents, tenants, consumers, and job matches. With constant inflows, output follows a linear trend whose per-period increment is increasing in the inflow rate. A permanent cut in inflows has two effects: an immediate demand loss from forgone arrival expenditure and an accumulating shortfall in resident population relative to the pre-restriction path, which we call demographic debt. In the linear model, the economy moves onto a lower path with a smaller trend increment. If the cumulative resident shortfall exceeds available buffers — vacancies, inventories, labor-market slack, and preserved organizational capacity — additional nonlinear losses can arise, making a delayed downturn possible. Expected reopening and the depreciation of migration-corridor capacity imply that temporary interruptions are less damaging than permanent restrictions and that recovery after a prolonged closure is asymmetric. The paper is a theoretical note. It does not claim causal identification for any historical episode, but it yields testable implications for timing, sectoral incidence, and recovery dynamics.
Roman Petrov (Sat,) studied this question.