Structural FECM: Cointegration in large‐scale structural FAVAR models

Abstract

Starting from the dynamic factor model for nonstationary data we derive the factor-augmented error correction model (FECM) and its moving-average representation. The latter is used for the identification of structural shocks and their propagation mechanisms. We show how to implement classical identification schemes based on long-run restrictions in the case of large panels. The importance of the error correction mechanism for impulse response analysis is analyzed by means of both empirical examples and simulation experiments. Our results show that the bias in estimated impulse responses in a factor-augmented vector autoregressive (FAVAR) model is positively related to the strength of the error correction mechanism and the cross-section dimension of the panel. We observe empirically in a large panel of US data that these features have a substantial effect on the responses of several variables to the identified permanent real (productivity) and monetary policy shocks. 1 Forni, Giannone, Lippi, and Forni et al. (2009) provide an empirical illustration of the stochastic trends analysis of King, Plosser, Stock and Watson (1991) in the context of large stationary panels. Eickmeier (2009) works with a nonstationary panel and identification of structural shocks with sign restrictions. Forni,

Non-Stationary Dynamic Factor Models for Large Datasets

“…Third, our asymptotic results could be straightforwardly extended to estimation of IRFs in a non-stationary Factor Augmented VAR setting (see Bai and Ng, 2006, for the stationary case) and form the theoretical foundation of the existing empirical studies based non-stationary factor models (see e.g. Eickmeier, 2009;Banerjee et al, 2017). Last, our approach could be generalized to build an unrestricted Non-Stationary DMF, similar to the one proposed by Forni et al (2017Forni et al ( , 2015 for stationary data.…”

“…First, I(0) idiosyncratic components imply that the x's and the factors are cointegrated. This property is exploited in Banerjee et al (2017), who assume I(0) idiosyncratic components and study a Factor Augmented Error Correction Model. However, not only the assumption of I(0) idiosyncratic components is empirically not supported by typical macroeconomic datasets, as the one analyzed in this paper, but also, as we argue in Section 2, I(0) idiosyncratic components imply "too much cointegration" among the variables x it themselves.…”

A note on the predictive power of survey data in nowcasting euro area GDP

“…In the framework of the generalized DFM, Bai () analytically considers the existence of a cointegrating relationship between nonstationary factors. Consequently, Banerjee, Marcellino, and Masten (, ) extend the DFM by modeling an error correction mechanism. They show that the error correction mechanism generally contributes to higher forecasting precision.…”

An Overview of the Factor-augmented Error-Correction Model

“…Another connected though different paper is Barigozzi, Lippi and Luciani (2014). They work with a non-parametric static version of the factor model with common I(1) factors only, while in our context we have a parametric representation of a fully dynamic model where the factors can be both I(1) and I(0), which complicates the analysis, in particular for structural applications related to permanent shocks (see Banerjee et al (2014b)). They also assume that the factors follow a VAR model, and show that their first differences admit a finite order ECM representation, which is an interesting result.…”

“…The lag lengths are determined by the BIC information criterion. 7 As for the cointegration test for determining the cointegration ranks of the ECM and the FECM, we have considered two approaches: the Johansen trace test (Johansen, 1995) The levels of all variables are treated as I(1) with a deterministic trend, which means that the dynamic forecasts of the differences of (the logarithm of) the variables h steps ahead produced by each of the competing models are cumulated in order to obtain the forecasts of the level h steps ahead. We consider four different forecast horizons, h = 1, 2, 4, 8.…”