Permanent-Transitory decomposition of cointegrated time series via Dynamic Factor Models, with an application to commodity prices

We propose a cointegration-based Permanent-Transitory decomposition for non-stationary Dynamic Factor Models. Our methodology exploits the cointegration relations among the observable variables and assumes they are driven by a common and an idiosyncratic component. The common component is further split into a long-term non-stationary and a short-term stationary part. A Monte Carlo experiment shows that incorporating the cointegration structure into the DFM leads to a better reconstruction of the space spanned by the factors, compared to the most standard technique of applying a factor model in differenced systems. We apply our procedure to a set of commodity prices to analyse the comovement among different markets and find that commodity prices move together mostly due to long-term common forces; while the trend for the prices of most primary goods is declining, metals and energy exhibit an upward or at least stable pattern since the 2000s.

VALIDATING DSGE MODELS WITH SVARS AND HIGH-DIMENSIONAL DYNAMIC FACTOR MODELS

A popular validation procedure for Dynamic Stochastic General Equilibrium (DSGE) models consists in comparing the structural shocks and impulse-response functions obtained by estimation-calibration of the DSGE with those obtained in an Structural Vector Autoregressions (SVAR) identified by means of some of the DSGE restrictions. I show that this practice can be seriously misleading when the variables used in the SVAR contain measurement errors. If this is the case, for generic values of the parameters of the DSGE, the shocks estimated in the SVAR are not “made of” the corresponding structural shocks plus measurement error. Rather, each of the SVAR shocks is contaminated by noncorresponding structural shocks. We argue that High-Dimensional Dynamic Factor Models are free from this drawback and are the natural model to use in validation procedures for DSGEs.

Dynamic factor models: Does the specification matter?

Dynamic factor models (DFMs), which assume the existence of a small number of unobserved underlying factors common to a large number of variables, are very popular among empirical macroeconomists. Factors can be extracted using either nonparametric principal components or parametric Kalman filter and smoothing procedures, with the former being computationally simpler and robust against misspecification and the latter coping in a natural way with missing and mixed-frequency data, time-varying parameters, nonlinearities and non-stationarity, among many other stylized facts often observed in real systems of economic variables. This paper analyses the empirical consequences on factor estimation, in-sample predictions and out-of-sample forecasting of using alternative estimators of the DFM under various sources of potential misspecification. In particular, we consider factor extraction when assuming different number of factors and different factor dynamics. The factors are extracted from a popular data base of US macroeconomic variables, widely analyzed in the literature without consensus about the most appropriate model specification. We show that this lack of consensus is only marginally crucial when it comes to factor extraction, but it matters when the objective is out-of-sample forecasting.

Determining Number of Factors in Dynamic Factor Models Contributing to GDP Nowcasting

Real-time nowcasting is a process to assess current-quarter GDP from timely released economic and financial series before the figure is disseminated in order to catch the overall macroeconomic conditions in real time. In economic data nowcasting, dynamic factor models (DFMs) are widely used due to their abilities to bridge information with different frequencies and to achieve dimension reduction. However, most of the research using DFMs assumes a fixed known number of factors contributing to GDP nowcasting. In this paper, we propose a Bayesian approach with the horseshoe shrinkage prior to determine the number of factors that have nowcasting power in GDP and to accurately estimate model parameters and latent factors simultaneously. The horseshoe prior is a powerful shrinkage prior in that it can shrink unimportant signals to 0 while keeping important ones remaining large and practically unshrunk. The validity of the method is demonstrated through simulation studies and an empirical study of nowcasting U.S. quarterly GDP growth rates using monthly data series in the U.S. market.