Causal State-Dependent Local Projections

TL;DR

This paper clarifies when state-dependent local projections can be interpreted causally, develops a new estimator for causal responses, and demonstrates its importance in macroeconomic analysis.

Contribution

It establishes conditions for causal interpretation of state-dependent LPs, introduces a sieve-based estimator, and applies it to micro-macro data showing significant implications.

Findings

State-dependent LPs recover causal responses under linearity conditions.

The new sieve-based estimator provides valid inference in micro-macro panels.

Flexible state dependence significantly alters macroeconomic impulse response patterns.

Abstract

State-dependent local projections (LPs) are widely used to estimate how impulse responses to exogenous aggregate shocks vary as a function of observable state variables, yet their causal interpretation remains unclear. We show that LPs recover causal impulse responses 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 macro and macro-finance models. We further show that the commonly used linear interaction LPs generally fail to recover causal objects. We therefore develop a sieve-based LP estimator that recovers the causal responses and delivers valid pointwise and uniform inference in micro-macro panels. Empirically, allowing for flexible state dependence materially changes both the pattern of heterogeneous firm investment responses and their aggregate implications for the transmission of monetary policy shocks. Our findings thus place state-dependent LPs on firmer causal footing in micro-macro settings than in purely aggregate ones, provided state dependence is estimated nonparametrically.