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GMM Estimation of the Number of Latent Factors

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  • Perez, Marcos
  • Ahn, Seung Chan

Abstract

We propose a generalized method of moment (GMM) estimator of the number of latent factors in linear factor models. The method is appropriate for panels a large (small) number of cross-section observations and a small (large) number of time-series observations. It is robust to heteroskedasticity and time series autocorrelation of the idiosyncratic components. All necessary procedures are similar to three stage least squares, so they are computationally easy to use. In addition, the method can be used to determine what observable variables are correlated with the latent factors without estimating them. Our Monte Carlo experiments show that the proposed estimator has good finite-sample properties. As an application of the method, we estimate the number of factors in the US stock market. Our results indicate that the US stock returns are explained by three factors. One of the three latent factors is not captured by the factors proposed by Chen Roll and Ross 1986 and Fama and French 1996.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 4862.

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Date of creation: 09 Sep 2007
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Handle: RePEc:pra:mprapa:4862

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Keywords: Factor models; GMM; number of factors; asset pricing;

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References

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  1. K. J├Âreskog, 1967. "Some contributions to maximum likelihood factor analysis," Psychometrika, Springer, vol. 32(4), pages 443-482, December.
  2. Connor, Gregory & Korajczyk, Robert A., 1988. "Risk and return in an equilibrium APT : Application of a new test methodology," Journal of Financial Economics, Elsevier, vol. 21(2), pages 255-289, September.
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  4. Seung C. Ahn & Young H. Lee & Peter Schmidt, 2006. "Panel Data Models with Multiple Time-Varying Individual Effects," Working Papers 0702, University of Crete, Department of Economics.
  5. 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.
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  7. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
  8. Seung Ahn & Young Lee & Peter Schmidt, 2007. "Stochastic frontier models with multiple time-varying individual effects," Journal of Productivity Analysis, Springer, vol. 27(1), pages 1-12, February.
  9. 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.
  10. Allan W. Gregory & Allen C. Head, 1996. "Common and Country-specific Fluctuations in Productivity, Investment, and the Current Account," Working Papers 931, Queen's University, Department of Economics.
  11. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May.
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  13. Grinblatt, Mark & Titman, Sheridan, 1985. " Approximate Factor Structures: Interpretations and Implications for Empirical Tests," Journal of Finance, American Finance Association, vol. 40(5), pages 1367-73, December.
  14. Chen, Nai-Fu & Roll, Richard & Ross, Stephen A, 1986. "Economic Forces and the Stock Market," The Journal of Business, University of Chicago Press, vol. 59(3), pages 383-403, July.
  15. Hannan, E. J., 1981. "Estimating the dimension of a linear system," Journal of Multivariate Analysis, Elsevier, vol. 11(4), pages 459-473, December.
  16. Brown, Stephen J & Weinstein, Mark I, 1983. " A New Approach to Testing Asset Pricing Models: The Bilinear Paradigm," Journal of Finance, American Finance Association, vol. 38(3), pages 711-43, June.
  17. Raymond Kan & Chu Zhang, 1999. "Two-Pass Tests of Asset Pricing Models with Useless Factors," Journal of Finance, American Finance Association, vol. 54(1), pages 203-235, 02.
  18. Ferson, Wayne E. & Foerster, Stephen R., 1994. "Finite sample properties of the generalized method of moments in tests of conditional asset pricing models," Journal of Financial Economics, Elsevier, vol. 36(1), pages 29-55, August.
  19. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  20. Brown, Stephen J, 1989. " The Number of Factors in Security Returns," Journal of Finance, American Finance Association, vol. 44(5), pages 1247-62, December.
  21. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
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Cited by:
  1. Barry Eichengreen & Ashoka Mody & Milan Nedeljkovic & Lucio Sarno, 2009. "How the Subprime Crisis Went Global: Evidence from Bank Credit Default Swap Spreads," NBER Working Papers 14904, National Bureau of Economic Research, Inc.
  2. Castagnetti, Carolina & Rossi, Eduardo, 2008. "Estimation methods in panel data models with observed and unobserved components: a Monte Carlo study," MPRA Paper 26196, University Library of Munich, Germany.

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