We prove that local projections (LPs) and Vector Autoregressions (VARs) estimate the same impulse responses. This nonparametric result only requires unrestricted lag structures. We discuss several implications: (i) LP and VAR estimators are not conceptually separate procedures; instead, they are simply two dimension reduction techniques with common estimand but different finite‐sample properties. (ii) VAR‐based structural identification—including short‐run, long‐run, or sign restrictions—can equivalently be performed using LPs, and vice versa. (iii) Structural estimation with an instrument (proxy) can be carried out by ordering the instrument first in a recursive VAR, even under noninvertibility. (iv) Linear VARs are as robust to nonlinearities as linear LPs.

中文翻译：

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局部投影和VAR估计相同的脉冲响应

我们证明局部投影（LP）和矢量自回归（VAR）估计相同的脉冲响应。这种非参数结果仅需要不受限制的滞后结构。我们讨论了几个含义：（i）LP和VAR估计量在概念上不是分开的程序；相反，它们只是具有共同估计值但具有不同有限样本属性的二维降维技术。（ii）基于VAR的结构识别（包括短期，长期或符号限制）可以等效地使用LP进行，反之亦然。（iii）即使在不可逆的情况下，也可以通过在递归VAR中首先订购仪器来进行仪器（代理）的结构估算。（iv）线性VAR对非线性的鲁棒性与线性LP一样。