Nonlinear Impulse Response Functions and Local Projections

TL;DR

This paper extends nonparametric estimation of impulse response functions to nonlinear dynamic models using local projections, establishing their asymptotic equivalence and exploring multivariate extensions.

Contribution

It introduces a fully nonparametric local projection estimator for nonlinear IRFs and compares its properties to nonlinear autoregressive models, extending linear results.

Findings

Nonlinear IRFs can be estimated nonparametrically using local projections.

The proposed estimator is asymptotically equivalent to nonlinear autoregressive IRFs.

Direct estimation of IRFs is more accurate than indirect NLP approaches in multivariate settings.

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.