Asymptotically Valid Bootstrap Inference for Proxy SVARs*

Proxy structural vector autoregressions identify structural shocks in vector autoregressions with external variables that are correlated with the structural shocks of interest but uncorrelated with all other structural shocks. We provide asymptotic theory for this identification approach under mild <i>α</i>-mixing conditions that cover a large class of uncorrelated, but possibly dependent innovation processes. We prove consistency of a residual-based moving block bootstrap (MBB) for inference on statistics such as impulse response functions and forecast error variance decompositions. The MBB serves as the basis for constructing confidence intervals when the proxy variables are strongly correlated with the structural shocks of interest. For the case of one proxy variable used to identify one structural shock, we show that the MBB can be used to construct confidence sets for normalized impulse responses that are valid regardless of proxy strength based on the inversion of the Anderson and Rubin statistic suggested by <b>Montiel Olea, Stock, and Watson</b> (<b>forthcoming</b>).

代理结构向量自回归（Proxy Structural Vector Autoregressions）利用与目标结构冲击相关、但与其余所有结构冲击互不相关的外部变量，在向量自回归（Vector Autoregressions）模型中识别结构冲击。本文在温和的α-混合（α-mixing）条件下，为该识别方法提供了渐近理论，这类条件涵盖了一大类互不相关但可能存在相依性的新息过程。本文证明了基于残差的移动块自助法（Moving Block Bootstrap, MBB）在脉冲响应函数、预测误差方差分解等统计量推断中的一致性。当代理变量与目标结构冲击强相关时，移动块自助法可作为构建置信区间的基础。针对使用单个代理变量识别单个结构冲击的场景，本文证明，借助蒙蒂埃尔·奥莱亚（Montiel Olea）、斯托克（Stock）与沃森（Watson）即将发表的研究中提出的安德森-鲁宾统计量（Anderson and Rubin Statistic）的反转方法，可通过移动块自助法构建无论代理变量强度如何均有效的标准化脉冲响应置信集。