Nonlinear Impulse Response Functions and Local Projections

Abstract

The goal of this paper is to extend the nonparametric estimation of Impulse Response Functions (IRF) by means of local projections in the nonlinear dynamic framework. We discuss the existence of a nonlinear autoregressive representation for Markov processes and explain how their IRFs are directly linked to the Nonlinear Local Projection (NLP), as in the case for the linear setting. We present a fully nonparametric LP estimator in the one dimensional nonlinear framework, compare its asymptotic properties to that of IRFs implied by the nonlinear autoregressive model and show that the two approaches are asymptotically equivalent. This extends the well-known result in the linear autoregressive model by Plagborg-Moller and Wolf (2017). We also consider extensions to the multivariate framework through the lens of semiparametric models, and demonstrate that the indirect approach by the NLP is less accurate than the direct estimation approach of the IRF.