美联储-关于“非线性世界中的动态因果效应：好的、坏的与丑陋的”的讨论（英）

Finance and Economics Discussion SeriesFederal Reserve Board, Washington, D.C.ISSN 1936-2854 (Print)ISSN 2767-3898 (Online)Discussion of “Dynamic Causal Effects in a Nonlinear World: theGood, the Bad, and the Ugly”Edward P. Herbst, Benjamin K. Johannsen2025-058Please cite this paper as:Herbst, Edward P., and Benjamin K. Johannsen (2025). “Discussion of “Dynamic CausalEffects in a Nonlinear World: the Good, the Bad, and the Ugly”,” Finance and EconomicsDiscussion Series 2025-058. Washington: Board of Governors of the Federal Reserve System,https://doi.org/10.17016/FEDS.2025.058.NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminarymaterials circulated to stimulate discussion and critical comment. The analysis and conclusions set forthare those of the authors and do not indicate concurrence by other members of the research staff or theBoard of Governors. References in publications to the Finance and Economics Discussion Series (other thanacknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.Discussion of “Dynamic Causal Effects in a NonlinearWorld: the Good, the Bad, and the Ugly”Edward P. Herbst and Benjamin K. Johannsen∗March 2025AbstractThis comment discusses Kolesár and Plagbord-Møller (2025) finding that the stan-dard linear local projection (LP) estimator recovers the average marginal effect (AME)even in nonlinear settings. We apply and discuss a subset their results using a simplenonlinear time series model, emphasizing the role of the weighting function and theimpact of nonlinearities on small-sample properties.1IntroductionKolesár and Plagbord-Møller (2025) (hereafter, KP) is an exciting, important advance inthe literature on the estimation of dynamic causal effects in the context of local projections(LPs) (see Jordà (2005)). The paper establishes that the “standard” linear LP of an outcomeyt+h onto a shock xt (and possibly a vector of controls) estimates an average marginal effect(AME) of the shock on the outcome. This result holds under suitable assumptions even—and perhaps especially—in the case of a nonlinear data generating process for yt. Derivingthe result requires connecting and extending a large literature in microeconometrics.This comment aims to provide an accessible discussion of some of the results reportedin KP that is tailored to macroeconomists. We begin by considering some of the theoreti-cal results in KP under common assumptions in the macroeconomics literature. We devoteparticular attention to the weighting function, ω, that is used to compute the average in theAME. We then analyze the AME and its LP estimation in the context of the quadratic au-toregressive model (QAR(1,1)) model of Aruoba et al. (2017). This is a stationary, nonlinear∗We thank Cristina Scofield for excellent research assistance.The views expressed here are those ofthe authors and do not indicate concurrence by the Board of Governors or anyone else associated witht