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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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    Cited by:

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    2. 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.
    3. 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.
    4. Chambers, Marcus J., 2013. "Jackknife estimation of stationary autoregressive models," Journal of Econometrics, Elsevier, vol. 172(1), pages 142-157.
    5. 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.
    6. Crudu, Federico & Sándor, Zsolt, 2011. "On the finite-sample properties of conditional empirical likelihood estimators," MPRA Paper 34116, University Library of Munich, Germany.
    7. Liyuan Cui & Guanhao Feng & Yongmiao Hong, 2024. "Regularized Gmm For Time‐Varying Models With Applications To Asset Pricing," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 65(2), pages 851-883, May.

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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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