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

TL;DR

This paper examines the validity of impulse response estimators derived from linear models in nonlinear macroeconomic data, highlighting which methods reliably identify causal effects and which are sensitive to nonlinearities.

Contribution

It demonstrates that vector autoregressions and local projections identify causal effects under nonlinearities, while heteroskedasticity-based methods are highly sensitive to such nonlinearities.

Findings

VARs and local projections identify weighted causal effects regardless of nonlinearity.

Heteroskedasticity-based identification methods are sensitive to departures from linearity.

New results on identifying marginal treatment effects through weighted regressions.

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.