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Efficient Estimation of Factor Models

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  • In Choi

    ()
    (Department of Economics, Sogang University, Seoul)

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Abstract

This paper considers the factor model Xt = Ft + et. Assuming a nor- mal distribution for the idiosyncratic error et conditional on the factors fFtg, conditional maximum likelihood estimators of the factor and factor- loading spaces are derived. These estimators are called generalized prin- cipal component estimators (GPCEs) without the normality assumption. This paper derives the asymptotic distributions of the GPCEs of the fac- tor and factor-loading space. It is shown that variances of the GPCEs of the common components are smaller than those of the principal com- ponent estimators studied in Bai (2003). The approximate variance of the forecasting error using the GPCE-based factor estimates is derived and shown to be smaller than that based on the principal component es- timators. The feasible GPCE (FGPCE) of factor space is shown to be asymptotically equivalent to the GPCE. The GPCEs and FGPCEs are shown to be more efficient than the principal component estimators in finite samples.

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Bibliographic Info

Paper provided by Research Institute for Market Economy, Sogang University in its series Working Papers with number 0701.

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Length: 43 pages
Date of creation: Mar 2007
Date of revision: Dec 2010
Handle: RePEc:sgo:wpaper:0701

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Related research

Keywords: factor model; maximum likelihood estimation; generalized principal component estimation; feasible generalized principal component estimation;

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References

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  1. 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.
  2. 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.
  3. Bai, Jushan & Ng, Serena, 2010. "Instrumental Variable Estimation In A Data Rich Environment," Econometric Theory, Cambridge University Press, vol. 26(06), pages 1577-1606, December.
  4. 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.
  5. 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, 06.
  6. Chamberlain, Gary & Rothschild, Michael, 1982. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Scholarly Articles 3230355, Harvard University Department of Economics.
  7. 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.
  8. Jean Boivin & Serena Ng, 2003. "Are More Data Always Better for Factor Analysis?," NBER Working Papers 9829, National Bureau of Economic Research, Inc.
  9. Jushan Bai & Serena Ng, 2000. "Determining the Number of Factors in Approximate Factor Models," Econometric Society World Congress 2000 Contributed Papers 1504, Econometric Society.
  10. MOON, Hyungsik Roger & PERRON, Benoit., 2002. "Testing for a Unit Root in Panels with Dynamic Factors," Cahiers de recherche 2002-18, Universite de Montreal, Departement de sciences economiques.
  11. Jushan Bai & Serena Ng, 2001. "A Panic Attack on Unit Roots and Cointegration," Economics Working Paper Archive 469, The Johns Hopkins University,Department of Economics.
  12. James H. Stock & Mark W. Watson, 2005. "Implications of Dynamic Factor Models for VAR Analysis," NBER Working Papers 11467, National Bureau of Economic Research, Inc.
  13. 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.
  14. Kapetanios, George & Marcellino, Massimiliano, 2006. "A Parametric Estimation Method for Dynamic Factor Models of Large Dimensions," CEPR Discussion Papers 5620, C.E.P.R. Discussion Papers.
  15. Sydney Ludvigson & Serena Ng, 2006. "The Empirical Risk-Return Relation: a factor analysis approach," 2006 Meeting Papers 236, Society for Economic Dynamics.
  16. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
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Citations

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Cited by:
  1. Bai, Jushan & Wang, Peng, 2012. "Identification and estimation of dynamic factor models," MPRA Paper 38434, University Library of Munich, Germany.
  2. Bai, Jushan & Liao, Yuan, 2012. "Efficient Estimation of Approximate Factor Models," MPRA Paper 41558, University Library of Munich, Germany.
  3. In Choi & Seong Jin Hwang, 2012. "Forecasting Korean inflation," Working Papers 1202, Research Institute for Market Economy, Sogang University.
  4. Trapani, Lorenzo, 2013. "On bootstrapping panel factor series," Journal of Econometrics, Elsevier, vol. 172(1), pages 127-141.
  5. In Choi, 2013. "Model Selection for Factor Analysis: Some New Criteria and Performance Comparisons," Working Papers 1209, Research Institute for Market Economy, Sogang University.

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