🤖 AI Summary
This paper addresses the challenge of identifying and estimating impulse response functions (IRFs) in nonlinear dynamic systems. Methodologically, it establishes, for the first time, theoretical equivalence between IRFs and nonlinear local projections (NLP) within a nonlinear Markov process framework. It introduces a nonparametric NLP estimator and rigorously proves its consistency for estimating nonlinear IRFs. Furthermore, it characterizes identifiability of multivariate IRFs under non-Gaussian innovations, showing that it hinges on the uniqueness of deconvolution, and provides explicit sufficient conditions for identification. The study extends beyond the limitations of conventional linear local projections, offering a novel nonparametric toolkit and rigorous theoretical foundation for quantifying the effects of non-Gaussian shocks in macro-finance applications.
📝 Abstract
The goal of this paper is to extend the method of estimating Impluse Response Functions (IRFs) by means of Local Projection (LP) in a nonlinear dynamic framework. We discuss the existence of a nonlinear autoregressive representation for a Markov process, and explain how their Impulse Response Functions are directly linked to the nonlinear Local Projection, as in the case for the linear setting. We then present a nonparametric LP estimator, and compare its asymptotic properties to that of IRFs obtained through direct estimation. We also explore issues of identification for the nonlinear IRF in the multivariate framework, which remarkably differs in comparison to the Gaussian linear case. In particular, we show that identification is conditional on the uniqueness of deconvolution. Then, we consider IRF and LP in augmented Markov models.