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INSTRUMENTAL VARIABLES INFERENCE IN A SMALL-DIMENSIONAL VAR MODEL WITH DYNAMIC LATENT FACTORS

Published online by Cambridge University Press:  10 November 2022

Federico Carlini  and
Patrick Gagliardini
Federico Carlini
Affiliation:
LUISS University Rome
Patrick Gagliardini*
Affiliation:
Università della Svizzera italiana
*
Address correspondence to Patrick Gagliardini, Faculty of Economics, Università della Svizzera italiana, Lugano, Switzerland; e-mail: [email protected].
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Abstract

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We study semiparametric inference in a small-dimensional vector autoregressive (VAR) model of order p augmented by unobservable common factors with a dynamic described by a VAR process of order q. This state-space specification is useful to measure separately the direct causality effects and the responses to dynamic common factors. We show that the state-space parameters are identifiable from the autocovariance function of the observed process. We estimate the model by means of a multistep procedure in closed-form, which combines an eigenvalue–eigenvector matrix decomposition and a linear instrumental variable estimation allowing for Hansen–Sargan specification tests. We study the asymptotic and finite-sample properties of the parameter estimators and of rank tests for selecting the number of unobservable factors and VAR orders. In an empirical illustration, we investigate the dynamic common factors and the spillover effects that explain the co-movements among the log daily realized volatilities of four European stock market indices.

Type
ARTICLES
Information
Econometric Theory , Volume 40 , Issue 4 , August 2024 , pp. 705 - 751
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Footnotes

We are grateful to the Editor, a Co-Editor, three anonymous referees, M. Deistler, C. Gourieroux, S. Johansen, L. Mancini, P. Santucci de Magistris, O. Scaillet, and participants at the 5th Empirical Finance Workshop in Cergy, the ESEM 2018 Conference in Cologne, the SFI 2019 Research Day in Gerzensee, the First Rome Workshop of Time Series and Financial Econometrics, and seminars at LUISS University, Durham University, and Geneva University for useful comments. We thank F. Diebold and K. Yilmaz for kindly providing us with their datasets used in a previous version of the paper circulated under the title of “Vector Autoregressive Model with Dynamic Factors.” The first version of this paper has been written while F. Carlini was a postdoctoral fellow at the Faculty of Economics of the Università della Svizzera italiana, Lugano, Switzerland. We gratefully acknowledge the Swiss National Science Foundation for Grant 105218-162633.

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