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A multilevel factor model: Identification, asymptotic theory and applications

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  • In Choi
  • Dukpa Kim
  • Yun Jung Kim
  • Noh‐Sun Kwark
Abstract
This paper studies a multilevel factor model with global and country factors. The global factors affect all individuals, whereas the country factors affect only those within each specific country. A sequential procedure to identify the global and country factors separately is proposed. In the initial step, the global factors are estimated by canonical correlation analysis. Using this initial estimator, the principal component estimators (PCEs) of the global and country factors are constructed. It is shown that the PCEs estimate the spaces of the global and country factors consistently and are normally distributed in the limit. Several information criteria that can estimate the number of country factors are proposed. The number of global factors is assumed to be known. Extensive simulation results demonstrate that the sequential procedure and information criteria work well in finite samples. The method of this paper is applied to 25 OECD countries to identify an international business cycle. It is reported that the method extracts a global factor reasonably well.

Suggested Citation

  • In Choi & Dukpa Kim & Yun Jung Kim & Noh‐Sun Kwark, 2018. "A multilevel factor model: Identification, asymptotic theory and applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(3), pages 355-377, April.
    • Handle: RePEc:wly:japmet:v:33:y:2018:i:3:p:355-377
    DOI: 10.1002/jae.2611
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    1. Choi, In, 2012. "Efficient Estimation Of Factor Models," Econometric Theory, Cambridge University Press, vol. 28(2), pages 274-308, April.
    2. S. Borağan Aruoba & Francis X. Diebold & M. Ayhan Kose & Marco E. Terrones, 2011. "Globalization, the Business Cycle, and Macroeconomic Monitoring," NBER International Seminar on Macroeconomics, University of Chicago Press, vol. 7(1), pages 245-286.
    3. Filippo Altissimo & Antonio Bassanetti & Riccardo Cristadoro & Lucrezia Reichlin & Giovanni Veronese, 2001. "The construction of coincident and leading indicators for the euro area business cycler of the euro area business cycle," Temi di discussione (Economic working papers) 434, Bank of Italy, Economic Research and International Relations Area.
    4. Domenico Giannone & Lucrezia Reichlin & Luca Sala, 2005. "Monetary Policy in Real Time," NBER Chapters, in: NBER Macroeconomics Annual 2004, Volume 19, pages 161-224, National Bureau of Economic Research, Inc.
    5. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2003. "Do financial variables help forecasting inflation and real activity in the euro area?," Journal of Monetary Economics, Elsevier, vol. 50(6), pages 1243-1255, September.
    6. Breitung, Jörg & Tenhofen, Jörn, 2011. "GLS Estimation of Dynamic Factor Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1150-1166.
    7. Bai, Jushan & Ng, Serena, 2010. "Instrumental Variable Estimation In A Data Rich Environment," Econometric Theory, Cambridge University Press, vol. 26(6), pages 1577-1606, December.
    8. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    9. Greenaway-McGrevy, Ryan & Han, Chirok & Sul, Donggyu, 2012. "Asymptotic distribution of factor augmented estimators for panel regression," Journal of Econometrics, Elsevier, vol. 169(1), pages 48-53.
    10. Christian Schumacher, 2007. "Forecasting German GDP using alternative factor models based on large datasets," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(4), pages 271-302.
    11. M. Ayhan Kose & Christopher Otrok & Eswar Prasad, 2012. "Global Business Cycles: Convergence Or Decoupling?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(2), pages 511-538, May.
    12. Moon, H.R.Hyungsik Roger & Perron, Benoit, 2004. "Testing for a unit root in panels with dynamic factors," Journal of Econometrics, Elsevier, vol. 122(1), pages 81-126, September.
    13. Reichlin, Lucrezia & Sala, Luca & Giannone, Domenico, 2002. "Tracking Greenspan: Systematic and Unsystematic Monetary Policy Revisited," CEPR Discussion Papers 3550, C.E.P.R. Discussion Papers.
    14. Dreger, Christian & Schumacher, Christian, 2002. "Estimating Large-Scale Factor Models for Economic Activity in Germany: Do They Outperform Simpler Models?," Discussion Paper Series 26321, Hamburg Institute of International Economics.
    15. Nigar Hashimzade & Michael A. Thornton (ed.), 2013. "Handbook of Research Methods and Applications in Empirical Macroeconomics," Books, Edward Elgar Publishing, number 14327.
    16. Lippi, Marco & Reichlin, Lucrezia & Hallin, Marc & Forni, Mario & Altissimo, Filippo & Cristadoro, Riccardo & Veronese, Giovanni & Bassanetti, Antonio, 2001. "EuroCOIN: A Real Time Coincident Indicator of the Euro Area Business Cycle," CEPR Discussion Papers 3108, C.E.P.R. Discussion Papers.
    17. Seung C. Ahn & Alex R. Horenstein, 2013. "Eigenvalue Ratio Test for the Number of Factors," Econometrica, Econometric Society, vol. 81(3), pages 1203-1227, May.
    18. Alexei Onatski, 2009. "Testing Hypotheses About the Number of Factors in Large Factor Models," Econometrica, Econometric Society, vol. 77(5), pages 1447-1479, September.
    19. Banerjee, Anindya & Marcellino, Massimiliano, 2006. "Are there any reliable leading indicators for US inflation and GDP growth?," International Journal of Forecasting, Elsevier, vol. 22(1), pages 137-151.
    20. Ludvigson, Sydney C. & Ng, Serena, 2007. "The empirical risk-return relation: A factor analysis approach," Journal of Financial Economics, Elsevier, vol. 83(1), pages 171-222, January.
    21. Michael Artis & Anindya Banerjee & Massimiliano Marcellino, "undated". "Factor forecasts for the UK," Working Papers 203, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    22. Forni, Mario & Giannone, Domenico & Lippi, Marco & Reichlin, Lucrezia, 2009. "Opening The Black Box: Structural Factor Models With Large Cross Sections," Econometric Theory, Cambridge University Press, vol. 25(5), pages 1319-1347, October.
    23. Marcellino, Massimiliano & Stock, James H. & Watson, Mark W., 2003. "Macroeconomic forecasting in the Euro area: Country specific versus area-wide information," European Economic Review, Elsevier, vol. 47(1), pages 1-18, February.
    24. Amengual, Dante & Watson, Mark W., 2007. "Consistent Estimation of the Number of Dynamic Factors in a Large N and T Panel," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 91-96, January.
    25. Ayhan Kose, M. & Otrok, Christopher & Whiteman, Charles H., 2008. "Understanding the evolution of world business cycles," Journal of International Economics, Elsevier, vol. 75(1), pages 110-130, May.
    26. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    27. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    28. M. Hashem Pesaran, 2006. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," Econometrica, Econometric Society, vol. 74(4), pages 967-1012, July.
    29. Kapetanios, George, 2004. "A note on modelling core inflation for the UK using a new dynamic factor estimation method and a large disaggregated price index dataset," Economics Letters, Elsevier, vol. 85(1), pages 63-69, October.
    30. George Kapetanios & Gonzalo Camba-Mendez, 2005. "Forecasting euro area inflation using dynamic factor measures of underlying inflation," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 24(7), pages 491-503.
    31. Filippo Altissimo & Antonio Bassanetti & Riccardo Cristadoro & Mario Forni & Marco Lippi & Lucrezia Reichlin & Giovanni Veronese, 2001. "A real time coincident indicator of the euro area business cycle," Temi di discussione (Economic working papers) 436, Bank of Italy, Economic Research and International Relations Area.
    32. Bai, Jushan & Ng, Serena, 2007. "Determining the Number of Primitive Shocks in Factor Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 52-60, January.
    33. Peter C. B. Phillips & Donggyu Sul, 2003. "Dynamic panel estimation and homogeneity testing under cross section dependence *," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 217-259, June.
    34. Alexei Onatski, 2010. "Determining the Number of Factors from Empirical Distribution of Eigenvalues," The Review of Economics and Statistics, MIT Press, vol. 92(4), pages 1004-1016, November.
    35. Ard H.J. den Reijer, 2005. "Forecasting Dutch GDP using Large Scale Factor Models," DNB Working Papers 028, Netherlands Central Bank, Research Department.
    36. Dias Francisco & Pinheiro Maximiano & Rua António, 2013. "Determining the number of global and country-specific factors in the euro area," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(5), pages 573-617, December.
    37. Massimiliano Marcellino & Carlo A. Favero & Francesca Neglia, 2005. "Principal components at work: the empirical analysis of monetary policy with large data sets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(5), pages 603-620.
    38. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, July.
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    7. Yufeng Mao & Bin Peng & Mervyn J Silvapulle & Param Silvapulle & Yanrong Yang, 2021. "Decomposition of Bilateral Trade Flows Using a Three-Dimensional Panel Data Model," Monash Econometrics and Business Statistics Working Papers 7/21, Monash University, Department of Econometrics and Business Statistics.
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    9. Ergemen, Yunus Emre & Rodríguez-Caballero, C. Vladimir, 2023. "Estimation of a dynamic multi-level factor model with possible long-range dependence," International Journal of Forecasting, Elsevier, vol. 39(1), pages 405-430.
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    18. Carlos Vladimir Rodríguez-Caballero, 2016. "Panel Data with Cross-Sectional Dependence Characterized by a Multi-Level Factor Structure," CREATES Research Papers 2016-31, Department of Economics and Business Economics, Aarhus University.
    19. Camacho, Maximo & Lopez-Buenache, German, 2023. "Factor models for large and incomplete data sets with unknown group structure," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1205-1220.
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    22. Shiwen Liu & Zhen Zhang & Junhua Yang & Wei Hu, 2022. "Exploring Increasing Urban Resident Electricity Consumption: The Spatial Spillover Effect of Resident Income," Energies, MDPI, vol. 15(12), pages 1-17, June.

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