Causal State-Dependent Local Projections

Joel David, Raffaella Giacomini, Xiyu Jiao () and Weining Wang

No WP 2026-18, Working Paper Series from Federal Reserve Bank of Chicago

Abstract: State-dependent local projections (LPs) are widely used to study how causal effects vary as a function of economic states, but shock exogeneity alone does not identify this response function. We show that identification follows when the underlying conditional mean is linear in the shock with a state-dependent coefficient, a condition satisfied in canonical micro-macro environments, including first-order perturbation solutions of heterogeneous-agent and macro-finance models. Even then, standard linear-interaction LPs generally recover only a projection of the response function, motivating LPs with nonparametric state dependence. We develop a sieve estimator and establish pointwise and uniform inference for micro-macro panels, where a distinctive challenge is that the estimator can converge at different rates across the state space. Applied to firm investment, the method uncovers a hump-shaped response to monetary policy shocks and shows that standard linear-interaction LPs substantially understate the aggregate role of financial heterogeneity.

Keywords: Impulse response functions; Identification; uniform inference; heterogeneous agent (search for similar items in EconPapers)
JEL-codes: C12 C14 C23 E32 (search for similar items in EconPapers)
Pages: 88
Date: 2026-09
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DOI: 10.21033/wp-2026-18

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