Philippe Goulet Coulombe
- 27 August 2025
- WORKING PAPER SERIES - No. 3105Details
- Abstract
- Local projections (LPs) are widely used in empirical macroeconomics to estimate impulse responses to policy interventions. Yet, in many ways, they are black boxes. It is often unclear what mechanism or historical episodes drive a particular estimate. We introduce a new decomposition of LP estimates into the sum of contributions of historical events, which is the product, for each time stamp, of a weight and the realization of the response variable. In the least squares case, we show that these weights admit two interpretations. First, they represent purified and standardized shocks. Second, they serve as proximity scores between the projected policy intervention and past interventions in the sample. Notably, this second interpretation extends naturally to machine learning methods, many of which yield impulse responses that, while nonlinear in predictors, still aggregate past outcomes linearly via proximity-based weights. Applying this framework to shocks in monetary and fiscal policy, global temperature, and the excess bond premium, we find that easily identifiable events—such as Nixon’s interference with the Fed, stagflation, World War II, and the Mount Agung volcanic eruption—emerge as dominant drivers of oftenheavily concentrated impulse response estimates.
- JEL Code
- C32 : Mathematical and Quantitative Methods→Multiple or Simultaneous Equation Models, Multiple Variables→Time-Series Models, Dynamic Quantile Regressions, Dynamic Treatment Effect Models, Diffusion Processes
C53 : Mathematical and Quantitative Methods→Econometric Modeling→Forecasting and Prediction Methods, Simulation Methods
E31 : Macroeconomics and Monetary Economics→Prices, Business Fluctuations, and Cycles→Price Level, Inflation, Deflation
E52 : Macroeconomics and Monetary Economics→Monetary Policy, Central Banking, and the Supply of Money and Credit→Monetary Policy
E62 : Macroeconomics and Monetary Economics→Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook→Fiscal Policy