Doubly Robust Nonparametric Local Projections

Nonparametric local projections estimate impulse responses without imposing parametric assumptions on the response function. Existing plug-in implementations identify the response through a nonparametric regression of future outcomes on the structural shock. This paper shows that the same response function can also be identified by reweighting outcomes according to how a structural shock shifts the shock density. Combining the two representations yields a doubly robust estimator: a nonparametric regression estimate augmented with a residual correction based on shock density reweighting. Consistency requires only that either the outcome regression or the density ratio be consistently estimated, making the method less vulnerable to smoothing, approximation, and specification errors. The correction also improves the calibration of confidence intervals, both by reducing centering bias and by producing a score whose variation the standard error fully reflects. In simulations, the residual correction removes persistent regression bias and substantially improves empirical coverage.