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When A Factor Is Measured with Error: The Role of Conditional Heteroskedasticity in Identifying and Estimating Linear Factor Models

  • Prono, Todd
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    A new method is proposed for estimating linear triangular models, where identification results from the structural errors following a bivariate and diagonal GARCH(1,1) process. The associated estimator is a GMM estimator shown to have the usual √T-asymptotics. A Monte Carlo study of the estimator is provided as is an empirical application of estimating market betas from the CAPM. These market beta estimates are found to be statistically distinct from their OLS counterparts and to display expanded cross-sectional variation, the latter feature offering promise for their ability to provide improved pricing of cross-sectional expected returns.

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    File URL: http://mpra.ub.uni-muenchen.de/33593/1/MPRA_paper_33593.pdf
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    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 33593.

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    Date of creation: 19 Sep 2011
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    Handle: RePEc:pra:mprapa:33593
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    1. Wooldridge, Jeffrey M., 1990. "A Unified Approach to Robust, Regression-Based Specification Tests," Econometric Theory, Cambridge University Press, vol. 6(01), pages 17-43, March.
    2. Lewellen, Jonathan & Nagel, Stefan, 2003. "The Conditional CAPM Does Not Explain Asset-pricing Anomalies," Working papers 4427-03, Massachusetts Institute of Technology (MIT), Sloan School of Management.
    3. Roberto Rigobon & Brian Sack, 2003. "Measuring The Reaction Of Monetary Policy To The Stock Market," The Quarterly Journal of Economics, MIT Press, vol. 118(2), pages 639-669, May.
    4. Arthur Lewbel, 2003. "Using Heteroskedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models," Boston College Working Papers in Economics 587, Boston College Department of Economics, revised 15 Dec 2010.
    5. Whitney K. Newey & Frank Windmeijer, 2009. "Generalized Method of Moments With Many Weak Moment Conditions," Econometrica, Econometric Society, vol. 77(3), pages 687-719, 05.
    6. J. Ginger Meng & Gang Hu & Jushan Bai, 2011. "Olive: A Simple Method For Estimating Betas When Factors Are Measured With Error," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 34(1), pages 27-60, 03.
    7. Roberto Rigobon, 2003. "Identification Through Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 777-792, November.
    8. He, Changli & Teräsvirta, Timo, 1997. "Properties of Moments of a Family of GARCH Processes," SSE/EFI Working Paper Series in Economics and Finance 198, Stockholm School of Economics.
    9. Fama, Eugene F & MacBeth, James D, 1973. "Risk, Return, and Equilibrium: Empirical Tests," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 607-36, May-June.
    10. Sentana, Enrique & Fiorentini, Gabriele, 2001. "Identification, estimation and testing of conditionally heteroskedastic factor models," Journal of Econometrics, Elsevier, vol. 102(2), pages 143-164, June.
    11. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-31, February.
    12. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
    13. Ravi Jagannathan & Zhenyu Wang, 1996. "The conditional CAPM and the cross-section of expected returns," Staff Report 208, Federal Reserve Bank of Minneapolis.
    14. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, 01.
    15. Rummery, Sarah & Vella, Francis & Verbeek, Marno, 1999. "Estimating the returns to education for Australian youth via rank-order instrumental variables," Labour Economics, Elsevier, vol. 6(4), pages 491-507, November.
    16. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
    17. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-80, July.
    18. Kristensen, Dennis & Linton, Oliver, 2006. "A Closed-Form Estimator For The Garch(1,1) Model," Econometric Theory, Cambridge University Press, vol. 22(02), pages 323-337, April.
    19. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    20. Andrews, Donald W. K., 1987. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Working Papers 645, California Institute of Technology, Division of the Humanities and Social Sciences.
    21. Todd, Prono, 2009. "GARCH-Based Identification and Estimation of Triangular Systems," MPRA Paper 20032, University Library of Munich, Germany.
    22. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
    23. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    24. Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
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