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 2SLSAI 解读 ↓
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级联恒等式：容量约束情境下作为政策参数的 2SLS
- 研究问题
- 在名额固定、录取会引发他人重新分配的项目中，多处理 2SLS 能否识别扩容的总体社会效应及下游均衡调整？
- 方法与思路
- 作者在工具相关性和一个对齐条件下建立代数恒等式，将多处理 2SLS 对应容量影子价值，并与单工具 Wald 比率比较。
- 材料陈述的贡献
- 摘要称，该恒等式无需单调性，两种系数之差可恢复均衡调整，并通过瑞典大学录取研究展示下游重新分配效应。
- 阅读关注点
- 应核对对齐条件的精确定义、容量边际变化与系数的对应关系，以及录取抽签和多处理结构如何支撑应用中的解释。
- 阅读边界
- 所据为 arXiv 预印本，同行评审或期刊接收未核实；摘要未给出完整工具识别条件，均衡解释不能推广到任意 2SLS。
原文摘要
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 relevance and a single alignment condition, satisfied in centralized admissions systems, the 2SLS coefficient equals the general-equilibrium shadow value of relaxing a capacity constraint, while the single-instrument Wald ratio captures only the direct effect. Their difference recovers the full equilibrium adjustment without additional structure. Monotonicity is not required. The identity extends beyond queue-based allocation to any fixed-supply setting, including competitive markets with price instruments. We apply the framework to two policy questions in Swedish university admissions, where marginal students are allocated across fields through a centralized lottery mechanism. First, revisiting the debate on whether economics and business education erodes prosocial values, we find that the direct effect of expanding business on charitable giving is precisely zero, but expanding the less competitive fields that business students are displaced from has large prosocial effects. Second, analyzing gender-targeted STEM policies, we find that admitting four women to competitive STEM generates one additional male STEM degree through downstream vacancies. Both are general-equilibrium effects invisible to single-instrument methods.