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Gel Methods For Nonsmooth Moment Indicators

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  • Parente, Paulo M.D.C.
  • Smith, Richard J.

Abstract

This paper considers the first-order large sample properties of the generalized empirical likelihood (GEL) class of estimators for models specified by nonsmooth indicators. The GEL class includes a number of estimators recently introduced as alternatives to the efficient generalized method of moments (GMM) estimator that may suffer from substantial biases in finite samples. These include empirical likelihood (EL), exponential tilting (ET), and the continuous updating estimator (CUE). This paper also establishes the validity of tests suggested in the smooth moment indicators case for overidentifying restrictions and specification. In particular, a number of these tests avoid the necessity of providing an estimator for the Jacobian matrix that may be problematic for the sample sizes typically encountered in practice.

Suggested Citation

  • Parente, Paulo M.D.C. & Smith, Richard J., 2011. "Gel Methods For Nonsmooth Moment Indicators," Econometric Theory, Cambridge University Press, vol. 27(1), pages 74-113, February.
    • Handle: RePEc:cup:etheor:v:27:y:2011:i:01:p:74-113_00
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    Cited by:

    1. Madeira, João & Palma, Nuno, 2018. "Measuring monetary policy deviations from the Taylor rule," Economics Letters, Elsevier, vol. 168(C), pages 25-27.
    2. Cui, Li-E & Zhao, Puying & Tang, Niansheng, 2022. "Generalized empirical likelihood for nonsmooth estimating equations with missing data," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    3. Hill, Jonathan B. & Prokhorov, Artem, 2016. "GEL estimation for heavy-tailed GARCH models with robust empirical likelihood inference," Journal of Econometrics, Elsevier, vol. 190(1), pages 18-45.
    4. Xu, Ke-Li, 2020. "Inference of local regression in the presence of nuisance parameters," Journal of Econometrics, Elsevier, vol. 218(2), pages 532-560.
    5. Parente, Paulo M.D.C. & Smith, Richard J., 2017. "Tests of additional conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 200(1), pages 1-16.
    6. Chen, Xiaohong & Pouzo, Demian & Powell, James L., 2019. "Penalized sieve GEL for weighted average derivatives of nonparametric quantile IV regressions," Journal of Econometrics, Elsevier, vol. 213(1), pages 30-53.
    7. Fumiya Akashi, 2017. "Self-weighted generalized empirical likelihood methods for hypothesis testing in infinite variance ARMA models," Statistical Inference for Stochastic Processes, Springer, vol. 20(3), pages 291-313, October.
    8. F Bravo, 2008. "Effcient M-estimators with auxiliary information," Discussion Papers 08/26, Department of Economics, University of York.
    9. Otsu, Taisuke, 2008. "Conditional empirical likelihood estimation and inference for quantile regression models," Journal of Econometrics, Elsevier, vol. 142(1), pages 508-538, January.
    10. Hill, Jonathan B., 2015. "Robust Generalized Empirical Likelihood for heavy tailed autoregressions with conditionally heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 131-152.
    11. Nicky L. Grant & Richard J. Smith, 2018. "GEL-based inference with unconditional moment inequality restrictions," CeMMAP working papers CWP23/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    12. Tong Tong Wu & Gang Li & Chengyong Tang, 2015. "Empirical Likelihood for Censored Linear Regression and Variable Selection," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 798-812, September.
    13. Akashi, Fumiya & Taniguchi, Masanobu & Monti, Anna Clara, 2020. "Robust causality test of infinite variance processes," Journal of Econometrics, Elsevier, vol. 216(1), pages 235-245.
    14. Nicky L. Grant & Richard J. Smith, 2018. "GEL-Based Inference from Unconditional Moment Inequality Restrictions," Economics Discussion Paper Series 1802, Economics, The University of Manchester.
    15. Feng, Qiang, 2012. "A GEL-based AIC for model selection," Economics Letters, Elsevier, vol. 116(3), pages 637-639.

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