Opening the Black Box of Local Projections

2025-05-18

AI Summary

Local Projections (LP), widely used for estimating macroeconomic impulse responses to policy shocks, suffer from a “black-box” nature that impedes attribution of responses to specific historical drivers. This paper introduces the first interpretable decomposition framework for LP estimation: it represents impulse responses as weighted sums of historical events, where weights jointly encode standardized shock intensity and temporal proximity. Going beyond linearity, the framework generalizes to nonlinear machine learning models and establishes a cross-model transferable interpretability paradigm. Empirically, applied to monetary policy (Nixon shock), fiscal shocks (WWII), and climate/financial shocks (Mount Agung eruption, bond risk premium fluctuations), the method precisely identifies a small set of pivotal historical events. Results reveal that LP estimates are highly contingent on salient historical nodes, substantially enhancing transparency and verifiability in causal inference.

Technology Category

• Machine Learning: Transparent, Interpretable, Explainable ML
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

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.

Problem

• Decompose LP estimates into historical event contributions
• Interpret weights as purified shocks and proximity scores
• Identify dominant historical drivers of impulse responses

Innovation

• Decompose LP estimates into historical event contributions
• Interpret weights as purified shocks and proximity scores
• Extend framework to nonlinear machine learning methods