On Time-Varying VAR Models: Estimation, Testing and Impulse Response Analysis

TL;DR

This paper proposes a new class of time-varying VAR models with smoothly changing coefficients and covariance matrices, along with methods for estimation, testing, and impulse response analysis, validated through simulations and an application to U.S. monetary policy.

Contribution

Introduces a novel time-varying VAR framework with theoretical properties, model selection criteria, and hypothesis testing tools, enhancing dynamic economic analysis.

Findings

The models effectively capture evolving economic relationships.

Simulation results support the theoretical properties.

Application demonstrates practical usefulness in monetary policy analysis.

Abstract

Vector autoregressive (VAR) models are widely used in practical studies, e.g., forecasting, modelling policy transmission mechanism, and measuring connection of economic agents. To better capture the dynamics, this paper introduces a new class of time-varying VAR models in which the coefficients and covariance matrix of the error innovations are allowed to change smoothly over time. Accordingly, we establish a set of theories, including the impulse responses analyses subject to both of the short-run timing and the long-run restrictions, an information criterion to select the optimal lag, and a Wald-type test to determine the constant coefficients. Simulation studies are conducted to evaluate the theoretical findings. Finally, we demonstrate the empirical relevance and usefulness of the proposed methods through an application to the transmission mechanism of U.S. monetary policy.