当心大冲击！一种非参数结构性通货膨胀模型

Elena Bobeica,Sarah Holton,Florian Huber,Catalina Martínez Hernández AbstractWepropose a novel empirical structural inflation model that captures non-linear shocktransmissionusing a Bayesian machine learning framework that combines VARs withnon-linear structural factor models. Unlike traditional linear models, our approach allows fornon-linear effects at all impulse response horizons.Identification is achieved via sign, zero,and magnitude restrictions within the factor model. Applying our method to euro area energyshocks, we find that inflation reacts disproportionately to large shocks, while small shockstrigger no significant response.These non-linearities are present along the pricing chain,more pronounced upstream for commodity and producer prices and gradually attenuatingdownstream for consumer prices.For policy makers, the finding that large shocks transmitdifferently implies that they may require a differentiated response.KEYWORDS: Inflation, non-linear model, machine learning, energy, euro area. JEL: E31, C32, C38, Q43ECB Working Paper Series No 3052 Non-technical summaryEconomists widely acknowledge that economic shocks can impact inflation in a non-linear way.Despite this consensus, traditional inflation models are often linear, and when non-linearities areconsidered, they are typically imposed in a rigid and predetermined way.The unprecedentedinflation surge following the pandemic further exposed important missing elements in traditionalmodels. Even when large models incorporated new inflationary sources, such as disruptions inglobal supply chains or gas price shocks, they struggled to fully account for the post-pandemicspike. This paper argues that non-linearities related to the size of shocks can help to understandinflation developments during this unprecedented episode, as we find large shocks amplify theirtransmission to inflation, while small shocks do not trigger a significant reaction.This paper develops a novel econometric framework for modelling euro area inflation, withminimal assumptions regarding the form of non-linearities. We leverage traditional time seriesmodels and machine learning techniques by blending a Bayesian Vector Regression (BVAR) withBayesian Additive Regression Trees (BART). While machine learning models are promising forforecasting, their use in structural analysis has been limited. Our model addresses this gap inthe literature by allowing the reduced-form errors to be non-linearly driven by structural shocks,which are identified through sign, zero, and magnitude restrictions.We identify four structural shocks - energy, global supply chains, demand and domesticsupply - and examine how inflation reacts to differently-sized shocks. We find evidence of non-linearities being relevant mostly for energy price shocks. Energy shocks have been a significantsource of inflation volatility, especially post-COVID. The analysis reveals that inflation respondsnon-linearly to energy shock sizes. Small shocks induce negligible price reactions, while largershocks have disproportionately stronger effects.These non-linearities increase smoothly withshock sizes, suggesting that models with few regime shifts may oversimplify actual inflationdynamics.The non-linear pricing behaviour is evident across the pricing chain, being morepronounced upstream with energy and producer prices, and attenuating downstream towardsconsumer prices. The model also demonstrates improved forecasting performance, offering moreaccurate predictions compared to linear models, especially for higher-order forecasts.The key policy implication of this paper is that exceptionally large cost-push shocks mayrequire a differentiated monetary policy response as they transmit more forcefully. While centralbanks can afford to “look through” small supply shocks when designing monetary policy, theycannot ignore larger ones.ECB Working Paper Series No 3052 2 1IntroductionEconomists tend to agree that economic shocks have a non-linear impact on inflation and theeffects might be subject to time variation. Starting with the seminal idea of Phillips (1958), wageinflation is linked to unemployment in a non-linear way. In a tight labour market, wages are moreflexible, as firms bid up wages rapidly, while in a downturn, wages would fall more slowly. Yet,mainstream inflation models tend to be linear. When non-linearities are investigated, modellersfrequently impose ex-ante a certain type of non-linearity in a rigid way. This increases the riskof model mis-specification, eventually translating into larger forecast errors of inflation such asthe ones observed during the post-pandemic recovery.The extent to which inflation surprised economists during the post-pandemic recoverymade it clear that some elements were missing from traditional models. There was an interestto employ larger models that are able to account for more (and new) sources of inflation-ary pressures (such as global supply side bottlenecks or more types of energy price