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Bootstrap Methods for Covariance Structures

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  • Joel L. Horowitz

Abstract

The optimal minimum distance (OMD) estimator for models of covariance structures is asymptotically efficient but has much worse finite-sample properties than does the equally weighted minimum distance (EWMD) estimator. This paper shows how the bootstrap can be used to improve the finite-sample performance of the OMD estimator. The theory underlying the bootstrap's ability to reduce the bias of estimators and errors in the coverage probabilities of confidence intervals is summarized. The results of numerical experiments and an empirical example show that the bootstrap often essentially eliminates the bias of the OMD estimator. The finite-sample estimation efficiency of the bias-corrected OMD estimator often exceeds that of the EWMD estimator. Moreover, the true coverage probabilities of confidence intervals based on the OMD estimator with bootstrap-critical values are very close to the nominal coverage probabilities.

Suggested Citation

  • Joel L. Horowitz, 1998. "Bootstrap Methods for Covariance Structures," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 39-61.
  • Handle: RePEc:uwp:jhriss:v:33:y:1998:i:1:p:39-61
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    Cited by:

    1. Thierry Magnac & Sébastien Roux, 2009. "Dynamique des salaires dans une cohorte," Economie & Prévision, La Documentation Française, vol. 0(1), pages 1-24.
    2. Victor Aguirregabiria & Victor Aguirregabiria & Aviv Nevo & Aviv Nevo, 2010. "Recent Developments in Empirical IO: Dynamic Demand and Dynamic Games," Working Papers tecipa-419, University of Toronto, Department of Economics.
    3. Aretz, Kevin & Bartram, Söhnke M. & Pope, Peter F., 2011. "Asymmetric loss functions and the rationality of expected stock returns," International Journal of Forecasting, Elsevier, vol. 27(2), pages 413-437.
    4. Rasmus Lentz & Dale T. Mortensen, 2008. "An Empirical Model of Growth Through Product Innovation," Econometrica, Econometric Society, vol. 76(6), pages 1317-1373, November.
    5. Laurent Gobillon & Thierry Magnac & Harris Selod, 2011. "The effect of location on finding a job in the Paris region," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(7), pages 1079-1112, November.
    6. Joaquim Ramalho, 2003. "Small Sample Bias of Alternative Estimation Methods for Moment Condition Models: Monte Carlo Evidence for Covariance Structures and Instrumental Variables," Economics Working Papers 9_2003, University of Évora, Department of Economics (Portugal).
    7. Pierre Cahuc & Fabien Postel-Vinay & Jean-Marc Robin, 2006. "Wage Bargaining with On-the-Job Search: Theory and Evidence," Econometrica, Econometric Society, vol. 74(2), pages 323-364, March.
    8. Joon-Woo Nahm, 2008. "Shrinking Middle Class and Changing Income Distribution of Korea: 1995-2005," Korean Economic Review, Korean Economic Association, vol. 24, pages 345-365.
    9. Pang, Lei & Lu, Wenbin & Wang, Huixia Judy, 2012. "Variance estimation in censored quantile regression via induced smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 785-796.
    10. Yuriy Gorodnichenko, 2007. "Using Firm Optimization to Evaluate and Estimate Returns to Scale," NBER Working Papers 13666, National Bureau of Economic Research, Inc.
    11. Ramalho, Joaquim J.S., 2006. "Bootstrap bias-adjusted GMM estimators," Economics Letters, Elsevier, vol. 92(1), pages 149-155, July.
    12. Morin, Louis-Philippe, 2010. "Estimating the BenefiÂ…t of High School for College-Bound Students," CLSSRN working papers clsrn_admin-2010-3, Vancouver School of Economics, revised 30 Jan 2010.
    13. Yuriy Gorodnichenko, 2005. "Reduced-Rank Identification of Structural Shocks in VARs," Macroeconomics 0512011, EconWPA.
    14. Prokhorov, Artem, 2012. "Second order bias of quasi-MLE for covariance structure models," Economics Letters, Elsevier, vol. 114(2), pages 195-197.
    15. Ramalho Joaquim J.S., 2005. "Small Sample Bias of Alternative Estimation Methods for Moment Condition Models: Monte Carlo Evidence for Covariance Structures," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(1), pages 1-20, March.
    16. Gorodnichenko, Yuriy & Ng, Serena, 2010. "Estimation of DSGE models when the data are persistent," Journal of Monetary Economics, Elsevier, vol. 57(3), pages 325-340, April.

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