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Causal state-dependent local projections

Author

Listed:
  • Joel M. David
  • Raffaella Giacomini
  • Xiya Jiao
  • Weining Wang

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.

Suggested Citation

  • Joel M. David & Raffaella Giacomini & Xiya Jiao & Weining Wang, 2026. "Causal state-dependent local projections," CeMMAP working papers 16/26, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:16/26
    DOI: 10.47004/wp.cem.2026.1626
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    References listed on IDEAS

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    1. Emmanuel Rio, 2009. "Moment Inequalities for Sums of Dependent Random Variables under Projective Conditions," Journal of Theoretical Probability, Springer, vol. 22(1), pages 146-163, March.
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