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Opening the black box of localprojections Philippe Goulet Coulombe, Karin Klieber Disclaimer:Thispaper should not be reported as representing the views of the European Central Bank(ECB). The viewsexpressed are those of the authors and do not necessarily reflect those of the ECB. Abstract Local 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 outcomeslinearlyviaproximity-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 shocks Nontechnical Summary Local 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 underlying dynamics. The empirical analysis includes several key economic applications, including the effectsof monetary policy, fiscal policy, global temperature, and financial shocks. •Monetary Policy:Estimates of how inflation reacts to unexpected changes in monetarypolicy are dominated by the stagflation period of the 1970s. Misinterpretations of thelatter explain why simple linear models mistakenly suggest that raising interest ratesincreases inflation—known as the “price puzzle”. •Fiscal Policy:Analyzing estimates of the economic impact of government spendingreveals that they are overwhelmingly driven by World War II and the Korean War. Thisraises concerns about the estimates’ validity, especially when it comes to predicting theeffects of fiscal policy in recent times. •Climate Shock:The credibility of global temperature shocks’ impact on world outputappears to vary across horizons.While medium-term effects are largely robust andsupported by various events in the sample, the long-term economic impact is mainlydriven by a few extreme weather episodes, such as the Mount Agung volcanic eruption. •Financial Shocks:Comparing linear and nonlinear responses reveals which historicalevents drive size- and sign-dependent effects of financial shocks, with key differencesemerging in the pre-2000 period and the Great Financial Crisis.Notably, the sparserproximity scores from the ML-based approach improves interpretability. 1Introduction Local projections-based estimates of impulse response functions (IRFs), now ubiquitous inempirical macroeconomic analysis, are not regarded as black boxes. Yet, to an appreciableextent, they are. It is often unclear what transmission mechanism lies behind the curve, orhow the arbitrary inclusion/exclusion of control variables shapes the retrieved causal effects.It is also difficult to know whether local projections (LP) estimates used to tell a cohesivestory about certain economic events are actually sourced from those events. To elucidate this and other questions, we introduce a new