We generalise the spectral EM algorithm for dynamic factor models in Fiorentini, Galesi, and Sentana (2014) to bifactor models with pervasive global factors complemented by regional ones. We exploit the sparsity of the loading matrices so that researchers can estimate those models by maximum likelihood with many series from multiple regions. We also derive convenient expressions for the spectral scores and information matrix, which allows us to switch to the scoring algorithm near the optimum. We explore the ability of a model with a global factor and three regional ones to capture inflation dynamics across 25 European countries over 1999–2014.
We are grateful to Ángel Estrada and Albert Satorra, as well as to audiences at the Advances in Econometrics Conference on Dynamic Factor Models (Aarhus 2014), the EC2 Advances in Forecasting Conference (UPF 2014), the Italian Congress of Econometrics and Empirical Economics (Salerno 2015), the V Workshop in Time Series Econometrics (Zaragoza 2015) and the XVIII Meeting of Applied Economics (Alicante 2015) for helpful comments and suggestions. Detailed comments from two anonymous referees have also substantially improved the paper. Of course, the usual caveat applies. Financial support from MIUR through the project ‘Multivariate statistical models for risk assessment’ (Fiorentini) and the Spanish Ministry of Science and Innovation through grant 2014-59262 (Sentana) is gratefully acknowledged.
Fiorentini, G., Galesi, A. and Sentana, E. (2016), "Fast ML Estimation of Dynamic Bifactor Models: An Application to European Inflation", Dynamic Factor Models (Advances in Econometrics, Vol. 35), Emerald Group Publishing Limited, Bingley, pp. 215-282. https://doi.org/10.1108/S0731-905320150000035006
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