同时聚类正交化

中文摘要 AI 辅助

向量自回归中的识别涉及两个不同的选择：冲击正交化的程度，以及正交化是顺序施加还是同时施加。广义识别不施加正交化；Sims (1980) 顺序施加完全正交化；Francis et al. (2026) 同时施加完全正交化；而Buchwalter et al. (2026a) 提供了顺序的聚类部分正交化。我们通过发展同时聚类正交化（SCO）填补了剩余的情形。SCO 在经济上有意义的聚类内保留同期依赖关系，同时联合地在聚类间施加正交化，从而消除了对聚类顺序的依赖。我们构建了相关的相关性最大化识别问题，并证明在相关性空间中，该问题简化为一个二次矩阵方程。这产生了一个闭式解，并且我们证明了相关的识别矩阵是唯一的全局最大化者。SCO 具有顺序不变性和尺度不变性，并将广义识别和完全同时正交化作为特例包含在内，从而产生了一个由聚类数量和组成索引的灵活的结构分解族。

英文摘要

Identification in vector autoregressions involves two distinct choices: how extensively to orthogonalize shocks and whether orthogonality is imposed sequentially or simultaneously. Generalized identification imposes no orthogonality; Sims (1980} imposes full orthogonality sequentially; Francis et al. (2026) impose full orthogonality simultaneously; and Buchwalter et al. (2026a) provide clustered partial orthogonalization sequentially. We fill the remaining case by developing simultaneous clustered orthogonalization (SCO). SCO preserves contemporaneous dependence within economically meaningful clusters while imposing orthogonality across clusters jointly, thereby eliminating dependence on cluster ordering. We formulate the associated correlation-maximizing identification problem and show that, in correlation space, it reduces to a quadratic matrix equation. This yields a closed-form solution, and we prove that the associated identification matrix is the unique global maximizer. SCO is order- and scale-invariant and nests generalized identification and full simultaneous orthogonalization as special cases, yielding a flexible family of structural decompositions indexed by the number and composition of clusters.

发表机构

• SKEMA Business School（SKEMA商学院）
• Université Côte d’Azur（蔚蓝海岸大学）
• University of Pennsylvania（宾夕法尼亚大学）
• NBER（美国国家经济研究局）
• Koç University（科奇大学）

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