Identification of Impulse Response Functions for Nonlinear Dynamic Models

TL;DR

This paper investigates the challenges of identifying impulse response functions in nonlinear dynamic models, proposing methods and conditions under which identification can be achieved, especially considering innovations and transformations.

Contribution

It introduces a nonlinear autoregressive representation with Gaussian innovations and characterizes the identified set, exploring restrictions and conditions for successful identification.

Findings

Identified set arises from nonlinear innovations and transformations that preserve the standard normal density.

Identification depends on the series considered and can be facilitated by non-Gaussianity or learning algorithms.

Conditions for identification in nonlinear dynamic factor models with different latent factor dynamics are discussed.

Abstract

We explore the issues of identification for nonlinear Impulse Response Functions in nonlinear dynamic models and discuss the settings in which the problem can be mitigated. In particular, we introduce the nonlinear autoregressive representation with Gaussian innovations and characterize the identified set. This set arises from the multiplicity of nonlinear innovations and transformations which leave invariant the standard normal density. We then discuss possible identifying restrictions, such as non-Gaussianity of independent sources, or identifiable parameters by means of learning algorithms, and the possibility of identification in nonlinear dynamic factor models when the underlying latent factors have different dynamics. We also explain how these identification results depend ultimately on the set of series under consideration.