Sowell, Fallaw (2009): The empirical saddlepoint likelihood estimator applied to two-step GMM.
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The empirical saddlepoint likelihood (ESPL) estimator is introduced. The ESPL provides improvement over one-step GMM estimators by including additional terms to automatically reduce higher order bias. The first order sampling properties are shown to be equivalent to efficient two-step GMM. New tests are introduced for hypothesis on the model's parameters. The higher order bias is calculated and situations of practical interest are noted where this bias will be smaller than for currently available estimators.
As an application, the ESPL is used to investigate an overidentified moment model. It is shown how the model's parameters can be estimated with both the ESPL and a conditional ESPL (CESPL), conditional on the overidentifying restrictions being satisfied. This application leads to several new tests for overidentifying restrictions.
Simulations demonstrate that ESPL and CESPL have smaller bias than currently available one-step GMM estimators. The simulations also show new tests for overidentifying restrictions that have performance comparable to or better than currently available tests. The computations needed to calculate the ESPL estimator are comparable to those needed for a one-step GMM estimator.
|Item Type:||MPRA Paper|
|Original Title:||The empirical saddlepoint likelihood estimator applied to two-step GMM|
|Keywords:||Generalized method of moments estimator; test of overidentifying restrictions; sampling distribution; empirical saddlepoint approximation; asymptotic distribution; higher order bias|
|Subjects:||C - Mathematical and Quantitative Methods > C5 - Econometric Modeling
C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General
|Depositing User:||Fallaw Sowell|
|Date Deposited:||10. Jun 2009 05:57|
|Last Modified:||15. Feb 2013 10:25|
Almudevar, Anthony, Chris Field and John Robinson (2000) ``The Density of Multivariate M-Estimates,'' The Annals of Statistics, vol. 28, no. 1, pp. 275-297.
Butler, Ronald W. (2007), Saddlepoint Approximations with Applications, Cambridge University Press.
Daniels, H.E. (1954) ``Saddlepoint approximations in statistics,'' Annals of Mathematical Statistics, vol. 25, pp. 631-650.
Field, C. A.(1982) ``Small Sample Asymptotics for Multivariate M-Estimates,'' Annals of Statistics, vol. 10, pp. 672-689.
Field, C. A. and E. Ronchetti (1990), Small Sample Asymptotics, Hayward, CA. IMS Monograph Series, vol 13.
Goutis, Constantin and George Casella (1999) ``Explaining the Saddlepoint Approximation,'' The American Statistician, vol. 53, no. 3. pp. 216-224.
Gregory, A. W., et al. (2002). ``Information-theoretic estimation of preference parameters: macroeconomic applications and simulation evidence,'' Journal of Econometrics 107(1-2): 213-233.
Hall, A. R. H. (2005). Generalized Method of Moments, Oxford, UK, Oxford University Press.
Hall, Peter and Joel L. Horowitz (1996) ``Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators,'' Econometrica, vol 64, no. 4, pp. 891-916.
Hansen, L.-P., John Heaton, and A. Yaron (1996) ``Finite Sample Properties of Some Alternative GMM Estimators,'' Journal of Business and Economic Statistics, vol. 14 no.3.
Huzurbazar, S. (1999) ``Practical Saddlepoint Approximations,'' The American Statistician, vol. 53, no. 3, pp. 225-232.
Imbens, Guido W. (1997) ``One-Step Estimators for Over-Identified Generalized Method of Moments Models,'' The Review of Economic Studies, vol. 64, no. 3. pp. 359-383.
\item Imbens, Guido W., Richard H. Spady and Phillip Johnson (1998) ``Information Theoretic Approaches to Inference in Moment Condition Models,'' Econometrica, vol. 66, no. 2, pp. 333-357.
Jensen, J. L. (1995), Saddlepoint Approximations, Oxford University Press, Oxford.
Jensen, J. L. and A. T. A. Wood (1998). ``Large Deviation and Other Results for Minimum Contrast Estimators.'' Annals of the Institute of Statistical Mathematics, vol. 50, no. 4, pp. 673-695.
Kitamura, Yuichi and Michael Stutzer (1997) ``An Information-Theoretic Alternative to Generalized Method of Moments Estimation,'' Econometrica, vol. 65, no. 4, pp. 861-874.
Kolassa, J.E. (1997), Series Approximation Methods in Statistics, 2nd edition, new York, Springer-Verlag, Lecture notes in Statistics, 88.
M\'aty\'as, L. (1999). Generalized Method of Moments Estimation, Cambridge, UK, Cambridge University Press.
Monti, A. C. and E. Ronchetti (1993) ``On the Relationship Between Empirical Likelihood and Empirical Saddlepoint Approximation for Multivariate M-Estimators.'' Biometrika, vol. 80 no. 2, pp. 329-338.
Newey, W. K., and D. L. McFadden (1994) ``Large Sample Estimation and Hypothesis Testing.'' in Handbook of Econometrics. Vol. 4. Edited by R. F. Engle and D. McFadden. Amsterdam, The Netherlands: Elsevier Science, 1999, pp. 2113-2245.
Newey, Whitney and Richard J. Smith (2004) ``Higher Order Properties of GMM and Generalized Empirical Likelihood Estimators,'' Econometrica, vol. 72, no. 1, pp. 219-255.
Reid, N. (1988) ``Saddlepoint Methods and Statistical Inference,'' Statistical Science, vol 3, no. 2, pp. 213-227.
Ronchetti, Elvezio and A. H. Welsch (1994) ``Empirical Saddlepoint Approximations for Multivariate M-Estimators,'' Journal of the Royal Statistical Society, Series B, vol. 56, pp. 313-326.
Schennach, S. M. (2007) ``Point Estimation with Exponentially Tilted Empirical Likelihood,'' The Annals of Statistics, vol. 35 no. 2 pp. 634-672.
Skovgaard, I. M. (1990) ``On the Density of minimum contrast estimators,'' Annals of Statistics, vol. 18, pp. 779-789.
Sowell, F. B. (1996) ``Optimal Tests for Parameter Instability in the Generalized Method of Moments Framework,'' Econometrica, vol. 64, no. 5. pp. 1085-1107.
Sowell, F. B. (2007) ``The Empirical Saddlepoint Approximation for GMM Estimators,'' working paper, Tepper School of Business, Carnegie Mellon University.
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