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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: https://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. 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.
    2. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(03), pages 458-467, December.
    3. Meng, Ginger & Hu, Gang & Bai, Jushan, 2007. "Olive: a simple method for estimating betas when factors are measured with error," MPRA Paper 33183, University Library of Munich, Germany.
    4. Jagannathan, Ravi & Wang, Zhenyu, 1996. " The Conditional CAPM and the Cross-Section of Expected Returns," Journal of Finance, American Finance Association, vol. 51(1), pages 3-53, March.
    5. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
    6. Asger Lunde & Peter Reinhard Hansen, 2001. "A Forecast Comparison of Volatility Models: Does Anything Beat a GARCH(1,1)?," Working Papers 2001-04, Brown University, Department of Economics.
    7. Whitney Newey & Richard Smith, 2003. "Higher order properties of GMM and generalised empirical likelihood estimators," CeMMAP working papers CWP04/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. 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.
    9. 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.
    10. Arthur Lewbel, 2010. "Using Heteroscedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 67-80, December.
    11. 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.
    12. Roberto Rigobon & Brian Sack, 2001. "Measuring the reaction of monetary policy to the stock market," Finance and Economics Discussion Series 2001-14, Board of Governors of the Federal Reserve System (U.S.).
    13. He, Changli & Terasvirta, Timo, 1999. "Properties of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 92(1), pages 173-192, September.
    14. 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.
    15. 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.
    16. Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
    17. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
    18. Todd, Prono, 2009. "GARCH-Based Identification and Estimation of Triangular Systems," MPRA Paper 20032, University Library of Munich, Germany.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. Roberto Rigobon, 2003. "Identification Through Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 777-792, November.
    24. 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.
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