欧洲央行-打开局部投影的黑匣子（英）

Working Paper Series Opening the black box of local projections Philippe Goulet Coulombe, Karin Klieber Disclaimer: This paper should not be reported as representing the views of the European Central Bank (ECB). The views expressed are those of the authors and do not necessarily reflect those of the ECB. No 3105 AbstractLocal projections (LPs) are widely used in empirical macroeconomics to estimate im-pulse responses to policy interventions. Yet, in many ways, they are black boxes. Itis often unclear what mechanism or historical episodes drive a particular estimate.We introduce a new decomposition of LP estimates into the sum of contributionsof historical events, which is the product, for each time stamp, of a weight and therealization of the response variable. In the least squares case, we show that theseweights admit two interpretations. First, they represent purified and standardizedshocks. Second, they serve as proximity scores between the projected policy inter-vention and past interventions in the sample. Notably, this second interpretationextends naturally to machine learning methods, many of which yield impulse re-sponses that, while nonlinear in predictors, still aggregate past outcomes linearly viaproximity-based weights. Applying this framework to shocks in monetary and fiscalpolicy, global temperature, and the excess bond premium, we find that easily iden-tifiable events—such as Nixon’s interference with the Fed, stagflation, World WarII, and the Mount Agung volcanic eruption—emerge as dominant drivers of oftenheavily concentrated impulse response estimates.JEL Classification: C32, C53, E31, E52, E62Keywords: Local projections, Monetary policy, Fiscal multipliers, Climate, Financial shocksECB Working Paper Series No 31051Nontechnical SummaryLocal projections (LPs) are a widely used statistical tool in economics to estimate how theeconomy responds to policy interventions, such as unexpected shifts in government spend-ing or monetary policy. However, LP estimates often function as a black box. It is unclearwhat underlying mechanisms drive the results, or whether they genuinely reflect the histor-ical events they appear to explain. This paper introduces tools to break down LP estimatesand reveal which past events contribute most to the impulse response function.We propose a decomposition technique that expresses LP estimates as a sum of contribu-tions from historical events. These contributions are determined by proximity weights, whichreflect how similar past policy changes are to the one being studied. In simple terms, thismethod allows researchers to see whether the estimated response is based on a broad rangeof historical experiences or just a few key episodes. This weighting approach applies notonly to traditional, linear LP methods but also to more complex machine learning (ML) mod-els. By using the same weighting framework, ML-based impulse responses can be directlycompared to their linear counterparts, uncovering nonlinearities in the