Local Projections and VARs Estimate the Same Impulse Responses
证明局部投影和向量自回归在无限制滞后结构下估计相同的脉冲响应，说明两者并非概念上分离的方法，而是同一估计量的不同降维技术，并讨论了结构识别、工具变量和非线性稳健性等含义。
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.