Simultaneous Clustered Orthogonalization

2026-09-10

AI Summary

研究提出了同时聚类正交化方法，解决了在向量自回归中如何在保持经济意义的集群内相关性的同时跨集群施加正交性的问题。

Abstract

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.

Problem

• Simultaneous Clustered Orthogonalization
• vector autoregressions
• orthogonality
• clusters
• correlation

Innovation

• Simultaneous Clustered Orthogonalization
• contemporaneous dependence
• cluster ordering independence
• quadratic matrix equation
• closed-form solution