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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
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Handle: RePEc:ecb:ecbwps:20060674
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  1. Jean Boivin & Marc Giannoni, 2006. "DSGE Models in a Data-Rich Environment," NBER Technical Working Papers 0332, National Bureau of Economic Research, Inc.
  2. Mario Forni & Domenico Giannone & Marco Lippi & Lucrezia Reichlin, 2008. "Opening the Black Box: Structural Factor Models with Large Cross-Sections," Working Papers ECARES 2008_036, ULB -- Universite Libre de Bruxelles.
  3. Giannone, Domenico & Reichlin, Lucrezia & Small, David, 2005. "Nowcasting GDP and Inflation: The Real Time Informational Content of Macroeconomic Data Releases," CEPR Discussion Papers 5178, C.E.P.R. Discussion Papers.
  4. 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.
  5. repec:adr:anecst:y:1999:i:54:p:05 is not listed on IDEAS
  6. Bai, Jushan & Ng, Serena, 2008. "Large Dimensional Factor Analysis," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(2), pages 89-163, June.
  7. Bańbura, Marta & Modugno, Michele, 2010. "Maximum likelihood estimation of factor models on data sets with arbitrary pattern of missing data," Working Paper Series 1189, European Central Bank.
  8. 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.
  9. Jushan Bai & Serena Ng, 2000. "Determining the Number of Factors in Approximate Factor Models," Boston College Working Papers in Economics 440, Boston College Department of Economics.
  10. Sentana, E. & Shah, M., 1994. "An Index of Co-Movements in Financial Time Series," Papers 9415, Centro de Estudios Monetarios Y Financieros-.
  11. Gary Chamberlain & Michael Rothschild, 1982. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," NBER Working Papers 0996, National Bureau of Economic Research, Inc.
  12. 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.
  13. Stock, J.H. & Watson, M.W., 1989. "New Indexes Of Coincident And Leading Economic Indicators," Papers 178d, Harvard - J.F. Kennedy School of Government.
  14. Lucrezia Reichlin & Domenico Giannone & Luca Sala, . "Monetary policy in real time," ULB Institutional Repository 2013/10177, ULB -- Universite Libre de Bruxelles.
    • 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.
  15. 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.
  16. Doz, Catherine & Giannone, Domenico & Reichlin, Lucrezia, 2007. "A Two-Step Estimator for Large Approximate Dynamic Factor Models Based on Kalman Filtering," CEPR Discussion Papers 6043, C.E.P.R. Discussion Papers.
  17. Danny Quah & Thomas J. Sargent, 1992. "A dynamic index model for large cross sections," Discussion Paper / Institute for Empirical Macroeconomics 77, Federal Reserve Bank of Minneapolis.
  18. 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.
  19. Reis, Ricardo & Watson, Mark W, 2007. "Relative Goods’ Prices and Pure Inflation," CEPR Discussion Papers 6593, C.E.P.R. Discussion Papers.
  20. 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.
  21. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 1999. "The Generalized Dynamic Factor Model: Identification and Estimation," CEPR Discussion Papers 2338, C.E.P.R. Discussion Papers.
  22. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  23. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
  24. 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.
  25. Watson, Mark W. & Engle, Robert F., 1983. "Alternative algorithms for the estimation of dynamic factor, mimic and varying coefficient regression models," Journal of Econometrics, Elsevier, vol. 23(3), pages 385-400, December.
  26. Ben S. Bernanke & Ilian Mihov, 1998. "Measuring Monetary Policy," The Quarterly Journal of Economics, Oxford University Press, vol. 113(3), pages 869-902.
  27. 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.
  28. repec:hal:journl:peer-00844811 is not listed on IDEAS
  29. 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.
  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.
  31. 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.
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