Semiparametric Local Projections

2026-06-11

AI Summary

This study addresses the estimation of average impulse response functions in macroeconomic structural dynamic models featuring pervasive nonlinearities—such as nonlinearly transformed regressors, state-dependent coefficients, and nonlinear interactions between shocks and state variables—and proposes the first semiparametric local projection estimator tailored to this class of models. The method relies on doubly robust moment conditions, expressing the target functional as a linear functional of a nonparametric conditional mean, and incorporates a density ratio to characterize the effect of counterfactual shock variations. Cross-fitting is employed to effectively handle serial dependence. The resulting estimator achieves √T-consistency and asymptotic normality, demonstrates robustness across diverse nonlinear data-generating processes, and is validated through two empirical applications.

Abstract

We propose a semiparametric local projection estimator of nonlinear impulse response functions for a broad class of structural dynamic models relevant for applied macroeconomics, including models with nonlinearly transformed regressors, state dependent coefficients, and nonlinear interactions between shocks and state variables. The estimator is based on a doubly robust moment condition that identifies the average response function as a linear functional of a nonparametric conditional mean, augmented by a density ratio that captures the effect of shifting the shock of interest. We combine this moment condition with cross-fitting that handles serial dependence. The resulting estimator is $\sqrt{T}$-consistent and asymptotically normal. We examine the finite-sample performance of the estimator across a range of nonlinear data generating processes and illustrate its use in two empirical examples.

Problem

• nonlinear impulse response
• structural dynamic models
• state-dependent coefficients
• nonlinear interactions
• macroeconomics

Innovation

• semiparametric local projections
• nonlinear impulse response
• doubly robust estimation
• cross-fitting
• density ratio