A Distributed Lag Approach to the Generalised Dynamic Factor Model

TL;DR

This paper introduces a new estimation method for the Generalised Dynamic Factor Model that simplifies computation, handles weak factors, and demonstrates strong empirical performance on macroeconomic data.

Contribution

The authors develop a static principal components-based estimator for GDFM that avoids frequency-domain methods and accommodates weak factors, with proven consistency and asymptotic normality.

Findings

The new estimator performs well on large macroeconomic datasets.

It uncovers a significant weak common component in sentiment indicators.

Standard methods overlook the dynamics captured by the proposed approach.

Abstract

We propose a new estimator for the Generalised Dynamic Factor Model (GDFM) that simplifies estimation by avoiding frequency-domain methods. Our key theoretical insight shows that under reasonable conditions the dynamic common component can be represented in terms of a finite number of lags of contemporaneously pervasive factors. In this case the dynamic factor decomposition of the GDFM reduces to the OLS regression of observed variables on estimated factors and their lags, with factors obtained via static principal components. The approach naturally accommodates weak (non-pervasive) factors within the dynamic common space addressing an important limitation of existing methods. We establish consistency and asymptotic normality for both the dynamic and weak common components. An application to a large European macroeconomic dataset demonstrates strong empirical performance and uncovers a sizeable weak common component - particularly in sentiment indicators and several other variables - revealing dynamics that standard methods overlook.