Perez, Marcos and Ahn, Seung Chan (2007): GMM Estimation of the Number of Latent Factors.
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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.
|Item Type:||MPRA Paper|
|Institution:||Arizona State UNiversity|
|Original Title:||GMM Estimation of the Number of Latent Factors|
|Keywords:||Factor models; GMM; number of factors; asset pricing|
|Subjects:||C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C10 - General
G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing; Trading volume; Bond Interest Rates
C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General
C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models; Multiple Variables > C33 - Models with Panel Data; Longitudinal Data; Spatial Time Series
|Depositing User:||PEREZ MARCOS|
|Date Deposited:||12. Sep 2007|
|Last Modified:||19. Feb 2013 04:52|
Ahn, Seung C., Young H. Lee, and Peter Schmidt, 2007a, Stochastic frontier models with multiple time-varying individual effects, Journal of Productivity Analysis 27 (1), 1-12.
Ahn, Seung C., Young H. Lee, and Peter Schmidt, 2007b, Panel data models with multiple time-varying individual effects, mimeo, Arizona State University.
Ahn, Seung C., Stephan Dieckmann and Marcos F. Perez, 2007, Estimating the Common Factor in Credit Spreads, mimeo, Arizona State University.
Andersen, Torben G., and Bent E. Sørensen, 1996, GMM estimation of a stochastic volatility model: A Monte Carlo study, Journal of Business & Economic Statistics 14, 328-352
Andrews, Donald W.K., 1991, Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59, 817-858.
Atkinson, Anthony .C., 1981 Likelihood ratios, posterior odds and information criteria, Journal of Econometrics 16, 15-20
Bai, Jusan and Serena Ng, 2002, Determining the number of factors in approximate factor models, Econometrica 70, 191-221.
Bai, Jusan, 2003, Inferential theory for factor models of large dimensions, Econometrica 71, 135-171.
Black, Fisher, Michael C. Jensen, and Myron S. Scholes, 1972, The capital asset pricing model: Some empirical tests, in Michael C. Jensen, ed.: Studies in the Theory of Capital Markets, Praeger, New York.
Brown, Stephen J. and Mark I. Weinstein, 1983, A new approach to testing asset pricing models: The bilinear paradigm, Journal of Finance 38, 711-743.
Brown, Stephan J., 1989, The number of factors in security returns, Journal of Finance 44(5), 1247-1262.
Campbell, John Y., Andrew W. Lo, and A. Craig MacKinlay, 1997, The Econometrics of Financial Markets, Princeton University Press, Princeton, New Jersey.
Chamberlain, Gary and Michael Rothschild, 1983, Arbitrage, factor Structure, and mean variance analysis on large asset markets, Econometrica 51, 1281-1304.
Chen, Nai Fu, Richard Roll and Stephen Ross, 1986, Economic forces and the stock market, Journal of Business 59, 368-403.
Connor, Gregory, 1984, A unified beta pricing theory, Journal of Economic Theory 34, 13-31.
Connor, Gregory and Robert A. Korajczyk, 1988, Risk and return in an equilibrium APT: Application of a new test methodology, Journal of Financial Economics 21, 255-289.
Connor, Gregory and Robert A. Korajczyk, 1993, A test for the number of factors in an approximate factor model. Journal of Finance 48, 1263-1291.
Cragg John and Stephen Donald, 1996, On the asymptotic properties of LDU based test of the rank of a matrix, Journal of the American Statistical Association 91, 1301-1309.
Cragg John and Stephen Donald, 1997, Inferring the rank of a matrix, Journal of Econometrics 76, 223-250
Donald Stephen G., Fortuna Natercia, and Vladas Pipiras, 2005, On the rank estimation in symmetric matrices: the case of indefinite estimators, CEMPRE Working Paper
Fama, Eugene F., and James D. MacBeth, 1973, Risk, return, and equilibrium: empirical tests, Journal of Political Economy 71, 607-636.
Fama, Eugene F., and Kenneth R. French, 1993, Common risk factors in the returns on stocks and bonds, Journal of Financial Economics 33, 3-56.
Ferson, Wayne, and Stephen R. Foerster, 1994, Finite sample properties of the generalized methods of moments tests of conditional asset pricing models, Journal of Financial Economics 36, 29-56.
Gill, Len, and Arthur Lewbel, 1992, Testing the rank and definiteness of estimated matrices with application to factor, state-space and ARMA models, Journal of the American Statistical Association, 87, 766-776.
Grinblatt, Mark and Sheridan Titman, 1985, Approximate factor structures: Interpretations and implications for empirical tests, Journal of Finance 40, 1367-1373.
Gorman, William M., 1981, Some Engel curves, in Essay in the Theory and Measurement of Consumer Behavior in Honor of Sir Richard Stone, ed. by A. Deaton, New York: Cambridge University Press.
Gregory, Allan W., and Allen C. Head, 1999, Common and country-specific fluctuations in productivity, investment, and the current account, Journal of Monetary Economics 44, 423.
Hannan, Edward J., 1980, The estimation of the order of an ARMA process, Annals of Statistics 8, 1071-1081.
Hannan, Edward. J., 1981, Estimating the dimension of linear system, Journal of Multivariate analysis 11, 459-473. Hannan, Edward J., and B. G. Quinn, 1979, The determinants of the order of an autoregression, Journal of the Royal Statistical Society 41, 190-195.
Hansen, Lars P., 1982, Large sample properties of generalized method of moments estimators, Econometrica 50, 1029-1054.
Hinkley, David V., 1977, Jackknifing in unbalance situations, Technometrics 19, 285-292.
Jones, Christopher S., 2001, Extracting factors from heteroskedastic returns, Journal of Financial Economics 62, 293-325.
Jöreskog, Karl G., 1967, Some contributions to maximum likelihood factor analysis, Psychometrika 34, 183-202.
Kan, Raymond, and Chu Zhang, 1999, Two-pass tests of asset pricing models with useless factors, Journal of Finance 54, 204 235.
Lehmann, Bruce N., and David M. Modest, 1988, The empirical foundations of the arbitrage pricing theory, Journal of Financial Economics 21, 213-254.
Lewbel, Arthur, 1991, The rank of demand system: Theory and nonparametric estimation, Econometrica 59, 711-730.
Newey, Whitney K., and Kenneth D. West, 1987, A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix, Econometrica 55 (3), 703-708
Newey, Whitney K., and Kenneth D. West, 1994. Automatic Lag Selection in Covariance Matrix Estimation The Review of Economic Studies, 61, 631-653
Nishii, Ryuie, 1988, Maximum likelihood principle and model selection when the true model is unspecified, Journal of Multivariate Analysis, 27, 392-403
Roll, Richard W. and Stephan A. Ross, 1980, An empirical investigation of the arbitrage pricing theory, Journal of Finance 35, 1073-1103.
Ross, Stephen A., 1976, The arbitrage theory of capital asset pricing, Journal of Economic Theory 13, 341-360.
Stock, James H., and Mark Watson, 2005, Implication of dynamic factor models for VAR analysis, NBER working paper 11467.
White, Halbert L., 1980, A heteroskedasticity-consistent covariance matrix estimator and direct test for heteroskedasticity, Econometrica 48, 817-838
White, Halbert L., 1999, Asymptotic Theory for Econometricians: Academic Press, San Diego, California.