Causal state-dependent local projections

Joel M. David, Raffaella Giacomini, Xiya Jiao and Weining Wang

No 16/26, CeMMAP working papers from Institute for Fiscal Studies

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.

Date: 2026-09-09
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Persistent link: https://EconPapers.repec.org/RePEc:azt:cemmap:16/26

DOI: 10.47004/wp.cem.2026.1626

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