Large-Dimensional Dynamic Factor Models: Estimation of Impulse-Response Functions with $I(1)$ Cointegrated Factors

TL;DR

This paper develops consistent estimation methods for large-dimensional dynamic factor models with $I(1)$ cointegrated factors, enabling accurate impulse-response analysis and revisiting empirical applications with new insights.

Contribution

It introduces novel estimators for cointegrated factors and their IRFs in large-dimensional models, accounting for deterministic trends and unrestricted VARs, with proven consistency as data dimensions grow.

Findings

Oil price shocks have only temporary effects on US real activity.

Positive news shocks lead to an initial boom followed by a mild recession.

Proposed estimators perform well in finite samples, as shown by Monte Carlo simulations.

Abstract

We study a large-dimensional Dynamic Factor Model where: (i)~the vector of factors $\mathbf F_t$ is $I(1)$ and driven by a number of shocks that is smaller than the dimension of $\mathbf F_t$; and, (ii)~the idiosyncratic components are either $I(1)$ or $I(0)$. Under~(i), the factors $\mathbf F_t$ are cointegrated and can be modeled as a Vector Error Correction Model (VECM). Under (i) and (ii), we provide consistent estimators, as both the cross-sectional size $n$ and the time dimension $T$ go to infinity, for the factors, the loadings, the shocks, the coefficients of the VECM and therefore the Impulse-Response Functions (IRF) of the observed variables to the shocks.~Furthermore: possible deterministic linear trends are fully accounted for, and the case of an unrestricted VAR in the levels $\mathbf F_t$, instead of a VECM, is also studied. The finite-sample properties the proposed estimators are explored by means of a MonteCarlo exercise. Finally, we revisit two distinct and widely studied empirical applications. By correctly modeling the long-run dynamics of the factors, our results partly overturn those obtained by recent literature. Specifically, we find that: (i) oil price shocks have just a temporary effect on US real activity; and, (ii) in response to a positive news shock, the economy first experiences a significant boom, and then a milder recession.