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A quasi maximum likelihood approach for large approximate dynamic factor models

  • Doz, Catherine
  • Giannone, Domenico
  • Reichlin, Lucrezia

This paper considers quasi-maximum likelihood estimations of a dynamic approximate factor model when the panel of time series is large. Maximum likelihood is analyzed under different sources of misspecification: omitted serial correlation of the observations and cross-sectional correlation of the idiosyncratic components. It is shown that the effects of misspecification on the estimation of the common factors is negligible for large sample size (T) and the cross sectional dimension (n). The estimator is feasible when n is large and easily implementable using the Kalman smoother and the EM algorithm as in traditional factor analysis. Simulation results illustrate what are the empirical conditions in which we can expect improvement with respect to simple principle components considered by Bai (2003), Bai and Ng (2002), Forni, Hallin, Lippi, and Reichlin (2000, 2005b), Stock and Watson (2002a,b). JEL Classification: C51, C32, C33

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Paper provided by European Central Bank in its series Working Paper Series with number 0674.

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Date of creation: Sep 2006
Date of revision:
Handle: RePEc:ecb:ecbwps:20060674
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  1. James H. Stock & Mark W. Watson, 1988. "A Probability Model of The Coincident Economic Indicators," NBER Working Papers 2772, National Bureau of Economic Research, Inc.
  2. Catherine Doz & Lucrezia Reichlin, 2011. "A two-step estimator for large approximate dynamic factor models based on Kalman filtering," Post-Print peer-00844811, HAL.
  3. Domenico Giannone & Lucrezia Reichlin & David H Small, 2007. "Nowcasting GDP and Inflation: The Real-Time Informational Content of Macroeconomic Data Releases," Money Macro and Finance (MMF) Research Group Conference 2006 164, Money Macro and Finance Research Group.
  4. Connor, Gregory & Korajczyk, Robert A, 1993. " A Test for the Number of Factors in an Approximate Factor Model," Journal of Finance, American Finance Association, vol. 48(4), pages 1263-91, September.
  5. 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.
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  7. James H. Stock & Mark W. Watson, 1989. "New Indexes of Coincident and Leading Economic Indicators," NBER Chapters, in: NBER Macroeconomics Annual 1989, Volume 4, pages 351-409 National Bureau of Economic Research, Inc.
  8. Chamberlain, Gary & Rothschild, Michael, 1982. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Scholarly Articles 3230355, Harvard University Department of Economics.
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  10. Ricardo Reis & Mark W. Watson, 2007. "Relative Goods' Prices, Pure Inflation, and the Phillips Correlation," NBER Working Papers 13615, National Bureau of Economic Research, Inc.
  11. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  12. Boivin, J. & Giannoni, M., 2007. "DSGE Models in a Data-Rich Environment," Working papers 162, Banque de France.
  13. Marta Bańbura & Michele Modugno, 2014. "Maximum Likelihood Estimation Of Factor Models On Datasets With Arbitrary Pattern Of Missing Data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(1), pages 133-160, 01.
  14. Catherine DOZ & Fabrice LENGLART, 1999. "Analyse factorielle dynamique : test du nombre de facteurs, estimation et application à l'enquête de conjoncture dans l'industrie," Annals of Economics and Statistics, GENES, issue 54, pages 91-127.
  15. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2002. "The Generalized Dynamic Factor Model: One-Sided Estimation and Forecasting," CEPR Discussion Papers 3432, C.E.P.R. Discussion Papers.
  16. 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(05), pages 1319-1347, October.
  17. 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.
  18. Jushan Bai & Serena Ng, 2006. "Confidence Intervals for Diffusion Index Forecasts and Inference for Factor-Augmented Regressions," Econometrica, Econometric Society, vol. 74(4), pages 1133-1150, 07.
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  21. Connor, Gregory & Korajczyk, Robert A., 1986. "Performance measurement with the arbitrage pricing theory : A new framework for analysis," Journal of Financial Economics, Elsevier, vol. 15(3), pages 373-394, March.
  22. Mario Forni & Lucrezia Reichlin, 2001. "Federal policies and local economies: Europe and the U.S," ULB Institutional Repository 2013/10141, ULB -- Universite Libre de Bruxelles.
  23. Gregory Connor and Robert Korajczyk., 1987. "Risk and Return in an Equilibrium APT," Research Program in Finance Working Papers 174, University of California at Berkeley.
  24. Thomas J. Sargent & Christopher A. Sims, 1977. "Business cycle modeling without pretending to have too much a priori economic theory," Working Papers 55, Federal Reserve Bank of Minneapolis.
  25. Danny Quah & Thomas J. Sargent, 1993. "A Dynamic Index Model for Large Cross Sections," NBER Chapters, in: Business Cycles, Indicators and Forecasting, pages 285-310 National Bureau of Economic Research, Inc.
  26. Bai, Jushan & Ng, Serena, 2008. "Large Dimensional Factor Analysis," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(2), pages 89-163, June.
  27. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
  28. Reis, Ricardo & Watson, Mark W, 2007. "Relative Goods’ Prices and Pure Inflation," CEPR Discussion Papers 6593, C.E.P.R. Discussion Papers.
  29. M. Ayhan Kose & Christopher Otrok & Charles H. Whiteman, 2003. "International Business Cycles: World, Region, and Country-Specific Factors," American Economic Review, American Economic Association, vol. 93(4), pages 1216-1239, September.
  30. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-62, April.
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