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.

翻译：政府常对定量配给项目（如大学专业名额、医学培训及公共住房）进行容量调整，此时接纳个体会挤占他人名额并引发一连串重新分配。我们证明在此类情境下，标准多处理两阶段最小二乘法（2SLS）系数精确识别边际扩张的总社会效应，包括所有下游重新分配。该结果呈现代数恒等式：在工具变量相关性及单一对齐条件（集中招生系统可满足此条件）下，2SLS系数等于放松容量约束的一般均衡影子价值，而单一工具Wald比率仅反映直接效应。两者差值无需额外结构即可还原完整的均衡调整过程，单调性条件亦非必需。该恒等式适用范围超越队列分配机制，可延伸至任何固定供给环境，包括含价格工具的竞争性市场。我们将此框架应用于瑞典大学招生中的两项政策问题——通过集中抽签机制将边际学生分配至不同专业。首先，重新审视经济学与商科教育是否侵蚀亲社会价值观的争论，发现扩大商科规模对慈善捐赠的直接效应精确为零，但扩大商科生被挤出的低竞争专业领域则产生显著亲社会效应。其次，分析性别导向的STEM政策发现，每接纳四名女性进入高竞争STEM专业，将通过下游空缺额外产生一名男性STEM学位获得者。两者均为单一工具方法无法捕捉的一般均衡效应。