A Regularized Factor-augmented Vector Autoregressive Model

TL;DR

This paper introduces a regularized FAVAR model with sparse factor loadings, enabling better economic interpretation and data-driven factor identification, with proven estimator consistency and an empirical application on monetary policy shocks.

Contribution

It develops a novel sparse FAVAR framework that simplifies factor interpretation and provides theoretical consistency results, advancing factor modeling in macroeconometrics.

Findings

Consistent estimators for loadings, factors, and parameters.

Empirical results align with economic intuition on monetary shocks.

Effective identification of structural shocks using combined factor and VAR analysis.

Abstract

We propose a regularized factor-augmented vector autoregressive (FAVAR) model that allows for sparsity in the factor loadings. In this framework, factors may only load on a subset of variables which simplifies the factor identification and their economic interpretation. We identify the factors in a data-driven manner without imposing specific relations between the unobserved factors and the underlying time series. Using our approach, the effects of structural shocks can be investigated on economically meaningful factors and on all observed time series included in the FAVAR model. We prove consistency for the estimators of the factor loadings, the covariance matrix of the idiosyncratic component, the factors, as well as the autoregressive parameters in the dynamic model. In an empirical application, we investigate the effects of a monetary policy shock on a broad range of economically relevant variables. We identify this shock using a joint identification of the factor model and the structural innovations in the VAR model. We find impulse response functions which are in line with economic rationale, both on the factor aggregates and observed time series level.