Identification and Estimation in Non-Fundamental Structural VARMA Models

• 成果类型: Article
• 署名作者: Gourieroux, Christian; Monfort, Alain; Renne, Jean-Paul
• 署名单位: University of Toronto; Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Institut Polytechnique de Paris; ENSAE Paris; European Central Bank; Bank of France; University of Lausanne
• 刊物名称: REVIEW OF ECONOMIC STUDIES
• ISSN/ISSBN: 0034-6527
• DOI: 10.1093/restud/rdz028
• 发表日期: 2020
• 页码: 1915-1953
• 关键词: moving average representations; Independent Component Analysis; maximum-likelihood-estimation; impulse-response analysis; vector autoregressions; aggregate fluctuations; time-reversibility; fiscal-policy; INFORMATION; restrictions

摘要

The basic assumption of a structural vector autoregressive moving average (SVARMA) model is that it is driven by a white noise whose components are uncorrelated or independent and can be interpreted as economic shocks, called structural shocks. When the errors are Gaussian, independence is equivalent to non-correlation and these models face two identification issues. The first identification problem is static and is due to the fact that there is an infinite number of linear transformations of a given random vector making its components uncorrelated. The second identification problem is dynamic and is a consequence of the fact that, even if a SVARMA admits a non-invertible moving average (MA) matrix polynomial, it may feature the same second-order dynamic properties as a VARMA process in which the MA matrix polynomials are invertible (the fundamental representation). The aim of this article is to explain that these difficulties are mainly due to the Gaussian assumption, and that both identification challenges are solved in a non-Gaussian framework if the structural shocks are assumed to be instantaneously and serially independent. We develop newparametric and semi-parametric estimation methods that accommodate non-fundamentalness in the MA dynamics. The functioning and performances of these methods are illustrated by applications conducted on both simulated and real data.