New methods for timely estimates GEORGE KAPETANIOS, MASSIMILIANO MARCELLINO, FOTIS PAPAILIAS, GIAN LUIGI MAZZI 2020 edition Euro area and EU employment flash estimates flash employment EU and area Euro 2 020 edition edition 020 STATISTICAL WORKING PAPERSBOOKS New methods for timely estimates GEORGE KAPETANIOS, MASSIMILIANO MARCELLINO, FOTIS PAPAILIAS, GIAN LUIGI MAZZI 2020 edition Manuscript completed in February 2020. Printed by the Publications Office in Luxembourg. The Commission is not liable for any consequence stemming from the reuse of this publication. Luxembourg: Publications Office of the European Union, 2020 © European Union, 2020 Reuse is authorized provided the source is acknowledged. The reuse policy of European Commission documents is regulated by Decision 2011/833/EU (OJ L 330, 14.12.2011, p. 39). Copyright for the photographs: Cover lisheng2121/Shutterstock For any use or reproduction of photos or other material that is not under copyright of the European Union, permission must be sought directly from the copyright holders. For more information, please consult: https://ec.europa.eu/eurostat/about/policies/copyright The information and views set out in this publication are those of the authors and do not necessarily reflect the official opinion of the European Union. Neither the European Union institutions and bodies nor any person acting on their behalf may be held responsible for the use which may be made of the information contained therein. Collection: Statistical working papers Theme: Economy and finance ISBN 978-92-76-16891-1 ISSN 2315-0807 doi: 10.2785/600130 KS-TC-20-005-EN-N Abstract Abstract We provide a survey of the literature on panel vector autoregression (pVAR) models and of their main characteristics. We also assess the possible gains pVAR models might yield for flash estimation, now-casting and economic short-term (point and density) forecasting, and discuss some yet unexploited applications where pVAR models could be effectively used in official statistics. Next, we examine empirically the out-of-sample forecasting performance of mixed-frequency pVAR models for four key macroeconomic variables using data for four European economies. We evaluate point, directional and also interval and density forecasts. Overall, the empirical results provide mixed evidence in favour of pVAR models but suggest that at least for point forecasts they can be more accurate than VAR models. Keywords: Panel data, Vector Autoregressions, Timely Estimates, Forecasting, Official statistics. Authors: George Kapetanios (1), Massimiliano Marcellino (2), Fotis Papailias (3), Gian Luigi Mazzi (4), Acknowledgement: We would like to thank Matyas Meszaros for useful comments on a previous version. (1) [email protected] (2) [email protected] (3) [email protected], [email protected] (4) [email protected] New methods for timely estimates 3 Table of contents Table of contents 1. Introduction ............................................................................................................. 7 2 Description of pVAR models ................................................................................. 10 2.1 Standard VAR models .......................................................................................................... 10 2.2 Standard pVAR models ........................................................................................................ 11 2.3 Dynamic Interdependencies and a generalised framework .............................................. 12 2.4 Time varying coefficients ..................................................................................................... 13 2.5 A Simple example ................................................................................................................. 14 2.5.1 pVAR(1) without Dynamic Interdependencies ................................................................ 14 2.5.2 pVAR(1) with Dynamic Interdependencies and Time Variation ...................................... 15 2.6 A Comparison with alternative methodologies.................................................................. 16 2.6.1 Large Scale VARs .......................................................................................................... 16 2.6.2 Spatial VARs .................................................................................................................. 16 2.6.3 Global VARs ................................................................................................................... 17 2.6.4 Two main types of pVAR models ................................................................................... 18 3. Estimation ............................................................................................................. 19 3.1 pVAR without dynamic interdependencies ........................................................................ 19 3.1.1 GMM Estimation ............................................................................................................. 19 3.1.2 Partial Pooling ................................................................................................................ 20 3.2 pVAR with dynamic interdependencies.............................................................................. 22 3.2.1 OLS Estimation ............................................................................................................... 23 3.2.2 Bayesian Approach ........................................................................................................ 24 3.3 pVAR with dynamic interdependencies and time variation .............................................. 24 3.3.1 A Panel-Type Hierarchical Prior ..................................................................................... 24 3.3.2 Factorisation ................................................................................................................... 25 3.4 Seven panel and large-scale VAR priors ............................................................................ 25 4 Forecasting with pVAR models ............................................................................ 27 5 Use of pVAR models in the literature ................................................................... 29 5.1 Business cycles and average effects ................................................................................. 29 5.2 Shocks transmission, heterogeneities & macroeconomic applications ......................... 30 5.3 Nowcasting and Forecasting: A Growing Topic ................................................................ 32 5.4 The potential usefulness of PVAR models for official statistics ...................................... 32 6 Should we use pVAR models? .............................................................................. 34 7 Methodology used in our empirical study............................................................ 35 7.1 pVAR ...................................................................................................................................... 35 7.2 Exogenous variables and factors........................................................................................ 35 7.3 Mixed-Frequency ................................................................................................................. 36 New methods for timely estimates 4 Table of contents 8 Data description ..................................................................................................... 38 8.1 Targets ................................................................................................................................... 38 8.2 Predictors .............................................................................................................................. 38 8.3 Transformations.................................................................................................................... 38 8.4 Time span .............................................................................................................................. 39 8.5 Data summary ....................................................................................................................... 39 9 Forecasting setup .................................................................................................. 40 9.1 Direct forecasts ..................................................................................................................... 40 9.2 Forecasting exercise ............................................................................................................ 40 9.3 Forecast evaluation .............................................................................................................. 41 9.4 Settings .................................................................................................................................. 42 9.4.1 Models ............................................................................................................................ 42 9.4.2 pVAR Specifications ....................................................................................................... 42 9.4.3 Forecasting Horizons ...................................................................................................... 43 10 Summary of results ............................................................................................. 44 10.1 Reading a table ..................................................................................................................