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Determining the Number of Factors in Approximate Factor Models

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Author Info
Jushan Bai () (Dept. of Economics, Boston College, U.S.A.)
Serena Ng () (Dept. of Economics, Johns Hopkins University, Baltimore, U.S.A.)

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Abstract

In this paper we develop some econometric theory for factor models of large dimensions. The focus is the determination of the number of factors ("r"), which is an unresolved issue in the rapidly growing literature on multifactor models. We first establish the convergence rate for the factor estimates that will allow for consistent estimation of "r". We then propose some panel criteria and show that the number of factors can be consistently estimated using the criteria. The theory is developed under the framework of large cross-sections ("N") and large time dimensions ("T"). No restriction is imposed on the relation between "N" and "T". Simulations show that the proposed criteria have good finite sample properties in many configurations of the panel data encountered in practice. Copyright The Econometric Society 2001.

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Publisher Info
Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 70 (2002)
Issue (Month): 1 (January)
Pages: 191-221
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Handle: RePEc:ecm:emetrp:v:70:y:2002:i:1:p:191-221

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References listed on IDEAS
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  1. Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250. [Downloadable!] (restricted)
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  3. Forni, Mario & Reichlin, Lucrezia, 1998. "Let's Get Real: A Factor Analytical Approach to Disaggregated Business Cycle Dynamics," Review of Economic Studies, Blackwell Publishing, vol. 65(3), pages 453-73, July. [Downloadable!] (restricted)
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  5. David Backus & Silverio Foresi & Abon Mozumdar & Liuren Wu, 1998. "Predictable Changes in Yields and Forward Rates," NBER Working Papers 6379, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  6. Gregory, Allan W. & Head, Allen C., 1999. "Common and country-specific fluctuations in productivity, investment, and the current account," Journal of Monetary Economics, Elsevier, vol. 44(3), pages 423-451, December. [Downloadable!] (restricted)
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  7. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May. [Downloadable!] (restricted)
  8. Ghysels, E. & Ng, S., 1996. "A Semi-Parametric Factor Model for Interest Rates," Cahiers de recherche 9612, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  9. Schwert, G William, 1989. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(2), pages 147-59, April.
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  10. Stock, James H. & Watson, Mark W., 1999. "Forecasting inflation," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 293-335, October. [Downloadable!] (restricted)
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  11. Dhrymes, Phoebus J & Friend, Irwin & Gultekin, N Bulent, 1984. " A Critical Reexamination of the Empirical Evidence on the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 39(2), pages 323-46, June. [Downloadable!] (restricted)
  12. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2000. "Reference Cycles: The NBER Methodology Revisited," CEPR Discussion Papers 2400, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
  13. James H. Stock & Mark W. Watson, 1990. "New Indexes of Coincident and Leading Economic Indicators," NBER Reprints 1380, National Bureau of Economic Research, Inc.
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  14. Lehmann, Bruce N. & Modest, David M., 1988. "The empirical foundations of the arbitrage pricing theory," Journal of Financial Economics, Elsevier, vol. 21(2), pages 213-254, September. [Downloadable!] (restricted)
  15. Gregory, Allan W & Head, Allen C & Raynauld, Jacques, 1997. "Measuring World Business Cycles," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(3), pages 677-701, August.
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  16. 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. [Downloadable!]
  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. [Downloadable!] (restricted)
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  18. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December. [Downloadable!] (restricted)
  19. Geweke, John F & Meese, Richard, 1981. "Estimating Regression Models of Finite but Unknown Order," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(1), pages 55-70, February. [Downloadable!] (restricted)
  20. 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. [Downloadable!] (restricted)
  21. 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. [Downloadable!] (restricted)
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