Causal State-Dependent Local Projections

2026-05-06

AI Summary

This study addresses the lack of a clear causal interpretation in existing state-dependent local projection (LP) methods when estimating heterogeneous responses of microeconomic agents to macroeconomic shocks. We demonstrate that, under linearity of the conditional mean in the macro shock, state-dependent LP identifies causal impulse responses, thereby providing the first rigorous causal foundation for this approach. To operationalize this insight, we develop a sieve-based nonparametric LP estimator that enables both consistent estimation and valid pointwise inference. Empirical application reveals that incorporating nonparametric state dependence substantially alters the estimated heterogeneous responses of firm investment to monetary policy shocks and reshapes the implied macroeconomic transmission mechanism.

Abstract

State-dependent local projections (LPs) are widely used to estimate how responses to exogenous aggregate shocks vary as a function of observable state variables, yet their causal interpretation remains unclear. We show that this interpretation obtains under the sufficient condition that the conditional mean is linear in the aggregate shock at each horizon, and that this condition holds in a broad class of canonical micro-macro environments, including first-order perturbation solutions of heterogeneous-agent models and macro-finance models. Under this condition, LPs recover causal impulse responses without requiring specification of the full data-generating process. We further show that the causal interpretation of state-dependent LPs is robust to the choice of state variable. By contrast, commonly used linear interaction LPs generally fail to recover causal objects. We therefore develop a sieve-based nonparametric LP estimator that restores causal interpretation and delivers valid pointwise and uniform inference in micro-macro panels. Empirically, allowing for nonparametric state dependence materially changes both the pattern of heterogeneous firm investment responses and their aggregate implications for the transmission of monetary policy shocks.

Problem

• causal interpretation
• state-dependent local projections
• aggregate shocks
• heterogeneous responses
• nonparametric estimation

Innovation

• causal inference
• state-dependent local projections
• nonparametric estimation
• heterogeneous-agent models
• impulse response