The Cascade Identity: 2SLS as a Policy Parameter in Capacity-Constrained Settings
级联恒等式:容量约束情境下作为政策参数的 2SLS
Governments routinely adjust capacity in rationed programs such as university fields, medical training and public housing, where admitting one individual displaces others and triggers chains of reallocation. We show that in such settings, the standard multi-treatment two-stage least squares (2SLS) coefficient identifies exactly the total societal effect of a marginal expansion, including all downstream reallocations. The result is an algebraic identity: under instrument…