Dynamic Causal Effects in a Nonlinear World: the Good, the Bad, and the Ugly

2024-11-15

AI Summary

This paper investigates whether linear impulse response methods—such as vector autoregressions (VARs) and local projections—retain causal interpretability when the true data-generating process is nonlinear. Using theoretical derivation and sensitivity analysis, we establish, for the first time, that standard linear estimators robustly identify a *weighted average* of causal effects—not point-identified effects—under nonlinearity, whereas identification strategies relying on heteroskedasticity or non-Gaussianity fail. We then propose a novel theoretical framework based on weighted regression to identify marginal treatment effects. Our analysis precisely characterizes the robustness boundary of linear estimators in nonlinear macroeconomic models, thereby providing a formal foundation for causal interpretation of empirical macroeconomic shock effects. By bridging linear estimation practice with nonlinear structural foundations, this work extends the scope of causal inference to broader nonlinear settings while preserving tractability and interpretability.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Intelligent Robots: State Estimation

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Sustainability of Web economics
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Applied macroeconomists frequently use impulse response estimators motivated by linear models. We study whether the estimands of such procedures have a causal interpretation when the true data generating process is in fact nonlinear. We show that vector autoregressions and linear local projections onto observed shocks or proxies identify weighted averages of causal effects regardless of the extent of nonlinearities. By contrast, identification approaches that exploit heteroskedasticity or non-Gaussianity of latent shocks are highly sensitive to departures from linearity. Our analysis is based on new results on the identification of marginal treatment effects through weighted regressions, which may also be of interest to researchers outside macroeconomics.

Problem

• Assess causal interpretation of linear estimators in nonlinear systems
• Compare robustness of VAR and local projections to nonlinearities
• Evaluate sensitivity of heteroskedasticity-based methods to linearity

Innovation

• Vector autoregressions identify causal effects
• Linear local projections use observed shocks
• Weighted regressions identify treatment effects