arXiv subjects

Bernd Funovits

Publications and source records attributed to Bernd Funovits.

7 recordsLinked to original sources

arXiv2022

Estimation of Impulse-Response Functions with Dynamic Factor Models: A New Parametrization

We propose a new parametrization for the estimation and identification of the impulse-response functions (IRFs) of dynamic factor models (DFMs). The theoretical contribution of this paper concerns the problem of observational equivalence between different IRFs, which implies non-identification of the IRF parameters without further restrictions. We show how the previously proposed minimal identification conditions are nested in the new framework and can be further augmented with overidentifying restrictions leading to efficiency gains. The current standard practice for the IRF estimation of DFMs is based on principal components, compared to which the new parametrization is less restrictive and allows for modelling richer dynamics. As the empirical contribution of the paper, we develop an estimation method based on the EM algorithm, which incorporates the proposed identification restrictions. In the empirical application, we use a standard high-dimensional macroeconomic dataset to estimate the effects of a monetary policy shock. We estimate a strong reaction of the macroeconomic variables, while the benchmark models appear to give qualitatively counterintuitive results. The estimation methods are implemented in the accompanying R package.

econ.EM↗

arXiv2021

Identifiability and Estimation of Possibly Non-Invertible SVARMA Models: A New Parametrisation

This article deals with parameterisation, identifiability, and maximum likelihood (ML) estimation of possibly non-invertible structural vector autoregressive moving average (SVARMA) models driven by independent and non-Gaussian shocks. In contrast to previous literature, the novel representation of the MA polynomial matrix using the Wiener-Hopf factorisation (WHF) focuses on the multivariate nature of the model, generates insights into its structure, and uses this structure for devising optimisation algorithms. In particular, it allows to parameterise the location of determinantal zeros inside and outside the unit circle, and it allows for MA zeros at zero, which can be interpreted as informational delays. This is highly relevant for data-driven evaluation of Dynamic Stochastic General Equilibrium (DSGE) models. Typically imposed identifying restrictions on the shock transmission matrix as well as on the determinantal root location are made testable. Furthermore, we provide low level conditions for asymptotic normality of the ML estimator and analytic expressions for the score and the information matrix. As application, we estimate the Blanchard and Quah model and show that our method provides further insights regarding non-invertibility using a standard macroeconometric model. These and further analyses are implemented in a well documented R-package.

econ.EM↗

arXiv2020

All-Pass Functions for Mirroring Pairs of Complex-Conjugated Roots of Rational Matrix Functions

We construct rational all-pass matrix functions with real-valued coefficients for mirroring pairs of complex-conjugated determinantal roots of a rational matrix. This problem appears, for example, when proving the spectral factorization theorem, or, more recently, in the literature on possibly non-invertible or possibly non-causal vector autoregressive moving average (VARMA) models. In general, it is not obvious whether the all-pass matrix function (and as a consequence the all-pass transformed rational matrix with initally real-valued coefficients) which mirrors complex-conjugated roots at the unit circle has real-valued coefficients. Naive constructions result in all-pass functions with complex-valued coefficients which implies that the real-valued parameter space (usually relevant for estimation) is left.

math.ST↗

arXiv2020

Identifiability of Structural Singular Vector Autoregressive Models

We generalize well-known results on structural identifiability of vector autoregressive models (VAR) to the case where the innovation covariance matrix has reduced rank. Structural singular VAR models appear, for example, as solutions of rational expectation models where the number of shocks is usually smaller than the number of endogenous variables, and as an essential building block in dynamic factor models. We show that order conditions for identifiability are misleading in the singular case and provide a rank condition for identifiability of the noise parameters. Since the Yule-Walker equations may have multiple solutions, we analyze the effect of restrictions on the system parameters on over- and underidentification in detail and provide easily verifiable conditions.

econ.EM↗

arXiv2020

Comment on Gouriéroux, Monfort, Renne (2019): Identification and Estimation in Non-Fundamental Structural VARMA Models

This comment points out a serious flaw in the article "Gouriéroux, Monfort, Renne (2019): Identification and Estimation in Non-Fundamental Structural VARMA Models" with regard to mirroring complex-valued roots with Blaschke polynomial matrices. Moreover, the (non-) feasibility of the proposed method (if the handling of Blaschke transformation were not prohibitive) for cross-sectional dimensions greater than two and vector moving average (VMA) polynomial matrices of degree greater than one is discussed.

econ.EM↗

arXiv2020

The Dimension of the Set of Causal Solutions of Linear Multivariate Rational Expectations Models

This paper analyses the number of free parameters and solutions of the structural difference equation obtained from a linear multivariate rational expectations model. First, it is shown that the number of free parameters depends on the structure of the zeros at zero of a certain matrix polynomial of the structural difference equation and the number of inputs of the rational expectations model. Second, the implications of requiring that some components of the endogenous variables be predetermined are analysed. Third, a condition for existence and uniqueness of a causal stationary solution is given.

econ.EM↗

arXiv2019

Identification and Estimation of SVARMA models with Independent and Non-Gaussian Inputs

This paper analyzes identifiability properties of structural vector autoregressive moving average (SVARMA) models driven by independent and non-Gaussian shocks. It is well known, that SVARMA models driven by Gaussian errors are not identified without imposing further identifying restrictions on the parameters. Even in reduced form and assuming stability and invertibility, vector autoregressive moving average models are in general not identified without requiring certain parameter matrices to be non-singular. Independence and non-Gaussianity of the shocks is used to show that they are identified up to permutations and scalings. In this way, typically imposed identifying restrictions are made testable. Furthermore, we introduce a maximum-likelihood estimator of the non-Gaussian SVARMA model which is consistent and asymptotically normally distributed.

econ.EM↗