Abstract
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.
Highlights
In recent decades, dynamic factor models (DFMs) have been widely used to represent comovements within large systems of macroeconomic and financial variables, in which the cross-sectional dimension is often relatively large compared with the time dimension; see Stock and Watson (2017) for the importance of Dynamic factor models (DFMs) in time series econometrics
The maximum correlation, 1.00, is obtained when it is assumed that r = 1 and p = 3 and the parameters are estimated by Maximum Likelihood (ML) either maximizing numerically the likelihood or using the expectation maximization (EM) algorithm; see Lewis et al (2020), who conclude that the factors are robust to whether principal components (PC) or Kalman filter and smoothing (KFS) is implemented for factor extraction when constructing a weekly index of real activity (EWI) based on N = 10 variables for USA and Breitung and Tenhofen (2011b), who conclude that, in the context of PC factor extraction, the specification of the underlying factors is not important when N is large
The factors are highly correlated among them regardless of the procedure or estimator used for their extraction and the number of lags specified for their autoregressions
Summary
Dynamic factor models (DFMs) have been widely used to represent comovements within large systems of macroeconomic and financial variables, in which the cross-sectional dimension is often relatively large compared with the time dimension; see Stock and Watson (2017) for the importance of DFMs in time series econometrics. This paper contributes to the literature by analyzing the empirical consequences on factor estimation and in-sample predictability and outof-sample forecasting of extracting factors using PC and KFS under various sources of potential misspecification. In the particular US macroeconomic data set analyzed in this paper, we show that specifications with more factors and more lags are favored in-sample when looking both at log-likelihood ratio tests and at measures of fit of factor-augmented predictive regressions. We analyze the differences in terms of point and interval estimation of factors, in sample prediction and out-of-sample forecasting, when factors are extracted using PC and the KFS under different assumptions on the number of factors and their dynamic dependence.
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