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.
