Opening the Black Box of Local Projections

TL;DR

This paper introduces a decomposition method for local projections in macroeconomics, clarifying the influence of historical events and enabling interpretation of impulse responses, including those derived from machine learning models.

Contribution

It provides a novel decomposition framework for local projections, linking weights to shocks and proximity scores, applicable to both linear and machine learning-based impulse responses.

Findings

Historical events like Nixon's interference and World War II are key drivers of impulse responses.

The decomposition reveals concentrated impacts of specific episodes on macroeconomic responses.

The approach enhances interpretability of local projections, including nonlinear machine learning models.

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 often heavily concentrated impulse response estimates.