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Local GMM Estimation of Time Series Models with Conditional Moment Restrictions

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Abstract

This paper investigates statistical properties of the local GMM (LGMM) estimator for some time series models defined by conditional moment restrictions. First, we consider Markov processes with possible conditional heteroskedasticity of unknown form and establish the consistency, asymptotic normality, and semi-parametric efficiency of the estimator. Second, inspired by simulation results showing that the LGMM estimator has a significantly smaller bias than the OLS estimator, we undertake a higher-order asymptotic expansion and analyze the bias properties of the LGMM estimator. The structure of the asymptotic expansion of the LGMM estimator reveals an interesting contrast with the OLS estimator that helps to explain the bias reduction in the LGMM estimator. The practical importance of these findings is evaluated in terms of a bond and option pricing exercise based on a diffusion model for spot interest rate.

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  • Nikolay Gospodinov & Taisuke Otsu, 2008. "Local GMM Estimation of Time Series Models with Conditional Moment Restrictions," Working Papers 08010, Concordia University, Department of Economics.
    • Handle: RePEc:crd:wpaper:08010
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    1. Carrasco, Marine & Florens, Jean-Pierre, 2014. "On The Asymptotic Efficiency Of Gmm," Econometric Theory, Cambridge University Press, vol. 30(2), pages 372-406, April.
    2. Manuel A. Domínguez & Ignacio N. Lobato, 2004. "Consistent Estimation of Models Defined by Conditional Moment Restrictions," Econometrica, Econometric Society, vol. 72(5), pages 1601-1615, September.
    3. 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, January.
    4. Kristensen, Dennis, 2009. "Uniform Convergence Rates Of Kernel Estimators With Heterogeneous Dependent Data," Econometric Theory, Cambridge University Press, vol. 25(5), pages 1433-1445, October.
    5. Ball, Clifford A. & Torous, Walter N., 1996. "Unit roots and the estimation of interest rate dynamics," Journal of Empirical Finance, Elsevier, vol. 3(2), pages 215-238, June.
    6. van Giersbergen, Noud P.A., 2005. "On the effect of deterministic terms on the bias in stable AR models," Economics Letters, Elsevier, vol. 89(1), pages 75-82, October.
    7. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    8. David A. Chapman & Neil D. Pearson, 2000. "Is the Short Rate Drift Actually Nonlinear?," Journal of Finance, American Finance Association, vol. 55(1), pages 355-388, February.
    9. Su, Liangjun & White, Halbert, 2014. "Testing conditional independence via empirical likelihood," Journal of Econometrics, Elsevier, vol. 182(1), pages 27-44.
    10. Carrasco, Marine & Florens, Jean-Pierre, 2000. "Generalization Of Gmm To A Continuum Of Moment Conditions," Econometric Theory, Cambridge University Press, vol. 16(6), pages 797-834, December.
    11. Peter C. B. Phillips, 2005. "Jackknifing Bond Option Prices," The Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 707-742.
    12. Yuichi Kitamura & Gautam Tripathi & Hyungtaik Ahn, 2004. "Empirical Likelihood-Based Inference in Conditional Moment Restriction Models," Econometrica, Econometric Society, vol. 72(6), pages 1667-1714, November.
    13. Kuersteiner, Guido M., 2002. "Efficient Iv Estimation For Autoregressive Models With Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 18(3), pages 547-583, June.
    14. Lewbel, Arthur, 2007. "A local generalized method of moments estimator," Economics Letters, Elsevier, vol. 94(1), pages 124-128, January.
    15. Kuersteiner, Guido M., 2001. "Optimal instrumental variables estimation for ARMA models," Journal of Econometrics, Elsevier, vol. 104(2), pages 359-405, September.
    16. Shiqing Ling, 2004. "Estimation and testing stationarity for double‐autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 63-78, February.
    17. Beach, Charles M & MacKinnon, James G, 1978. "A Maximum Likelihood Procedure for Regression with Autocorrelated Errors," Econometrica, Econometric Society, vol. 46(1), pages 51-58, January.
    18. Kenneth West & Ka-fu Wong & Stanislav Anatolyev, 2009. "Instrumental Variables Estimation of Heteroskedastic Linear Models Using All Lags of Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 28(5), pages 441-467.
    19. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(1), pages 17-39, February.
    20. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," The Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
    21. Antoine, Bertille & Bonnal, Helene & Renault, Eric, 2007. "On the efficient use of the informational content of estimating equations: Implied probabilities and Euclidean empirical likelihood," Journal of Econometrics, Elsevier, vol. 138(2), pages 461-487, June.
    22. Song Xi Chen & Wolfgang Härdle & Ming Li, 2003. "An empirical likelihood goodness‐of‐fit test for time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 663-678, August.
    23. Newey, Whitney K, 1990. "Efficient Instrumental Variables Estimation of Nonlinear Models," Econometrica, Econometric Society, vol. 58(4), pages 809-837, July.
    24. Corbae,Dean & Durlauf,Steven N. & Hansen,Bruce E. (ed.), 2006. "Econometric Theory and Practice," Cambridge Books, Cambridge University Press, number 9780521807234.
    25. Carrasco, Marine & Chernov, Mikhail & Florens, Jean-Pierre & Ghysels, Eric, 2007. "Efficient estimation of general dynamic models with a continuum of moment conditions," Journal of Econometrics, Elsevier, vol. 140(2), pages 529-573, October.
    26. Donald, Stephen G. & Newey, Whitney K., 2000. "A jackknife interpretation of the continuous updating estimator," Economics Letters, Elsevier, vol. 67(3), pages 239-243, June.
    27. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2003. "Empirical likelihood estimation and consistent tests with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 117(1), pages 55-93, November.
    28. Stanislav Anatolyev, 2005. "GMM, GEL, Serial Correlation, and Asymptotic Bias," Econometrica, Econometric Society, vol. 73(3), pages 983-1002, May.
    29. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    30. Smith, Richard J., 2007. "Efficient information theoretic inference for conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 138(2), pages 430-460, June.
    31. 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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    Cited by:

    1. Valerio Scalone, 2018. "Estimating Non-Linear DSGEs with the Approximate Bayesian Computation: an application to the Zero Lower Bound," Working papers 688, Banque de France.
    2. Patrick Gagliardini & Diego Ronchetti, 2020. "Comparing Asset Pricing Models by the Conditional Hansen-Jagannathan Distance," Journal of Financial Econometrics, Oxford University Press, vol. 18(2), pages 333-394.
    3. Raymond Kan & Cesare Robotti, 0. "Comment on: Pseudo-True SDFs in Conditional Asset Pricing Models," Journal of Financial Econometrics, Oxford University Press, vol. 18(4), pages 729-735.
    4. Chambers, Marcus J., 2013. "Jackknife estimation of stationary autoregressive models," Journal of Econometrics, Elsevier, vol. 172(1), pages 142-157.
    5. Crudu, Federico & Sándor, Zsolt, 2011. "On the finite-sample properties of conditional empirical likelihood estimators," MPRA Paper 34116, University Library of Munich, Germany.
    6. Zhentao Shi & Huanhuan Zheng, 2018. "Structural estimation of behavioral heterogeneity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(5), pages 690-707, August.

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    More about this item

    Keywords

    Conditional moment restrictions; Local GMM; Higher-order expansion; Conditional heteroskedasticity;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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