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Higher order asymptotics and the bootstrap for empirical likelihood J tests

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  • Francesco Bravo

Abstract

In this paper we obtain a second order Edgeworth approximation to the density of a likelihood ratio type J test for overidentifying restrictions by embedding the moment conditions into the empirical likelihood framework. The resulting asymptotic expansion can be used to correct to an order o n^-1 the critical values of the empirical likelihood ratio J test and to justify the second order correctness of an ``hybrid'' bootstrap procedure which we propose to bypass the difficult calculation of the cumulants appearing in the Edgeworth density of the empirical likelihood ratio J test. The resulting bootstrap calibrated empirical likelihood ratio test seems to perform well, as shown in a small Monte Carlo study, and suggest that the combination of the empirical likelihood method together with a suitable bootstrap procedure is an extremely useful method for estimation/inference in moment based econometric models.

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  • Francesco Bravo, "undated". "Higher order asymptotics and the bootstrap for empirical likelihood J tests," Discussion Papers 00/30, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:00/30
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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Sargan, J D, 1980. "Some Approximations to the Distribution of Econometric Criteria Which are Asymptotically Distributed as Chi-Squared," Econometrica, Econometric Society, vol. 48(5), pages 1107-1138, July.
    3. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    4. Back, Kerry & Brown, David P, 1993. "Implied Probabilities in GMM Estimators," Econometrica, Econometric Society, vol. 61(4), pages 971-975, July.
    5. Phillips, Peter C B & Park, Joon Y, 1988. "On the Formulation of Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 56(5), pages 1065-1083, September.
    6. P. Hall & B. Presnell, 1999. "Intentionally biased bootstrap methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 143-158.
    7. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    8. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July.
    9. Bravo, Francesco, 2004. "Empirical Likelihood Based Inference With Applications To Some Econometric Models," Econometric Theory, Cambridge University Press, vol. 20(2), pages 231-264, April.
    10. 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 262-280, July.
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