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Averaging Of An Increasing Number Of Moment Condition Estimators

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  • Chen, Xiaohong
  • Jacho-Chávez, David T.
  • Linton, Oliver

Abstract

We establish the consistency and asymptotic normality for a class of estimators that are linear combinations of a set of $\sqrt n$ -consistent nonlinear estimators whose cardinality increases with sample size. The method can be compared with the usual approaches of combining the moment conditions (GMM) and combining the instruments (IV), and achieves similar objectives of aggregating the available information. One advantage of aggregating the estimators rather than the moment conditions is that it yields robustness to certain types of parameter heterogeneity in the sense that it delivers consistent estimates of the mean effect in that case. We discuss the question of optimal weighting of the estimators.

Suggested Citation

  • Chen, Xiaohong & Jacho-Chávez, David T. & Linton, Oliver, 2016. "Averaging Of An Increasing Number Of Moment Condition Estimators," Econometric Theory, Cambridge University Press, vol. 32(1), pages 30-70, February.
    • Handle: RePEc:cup:etheor:v:32:y:2016:i:01:p:30-70_00
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    Cited by:

    1. S. Boragan Aruoba & Ronel Elul & Sebnem Kalemli Ozcan, 2022. "Housing Wealth and Consumption: The Role of Heterogeneous Credit Constraints," Working Papers 22-34, Federal Reserve Bank of Philadelphia.
    2. Čížek, Pavel & Lei, Jinghua, 2018. "Identification and estimation of nonseparable single-index models in panel data with correlated random effects," Journal of Econometrics, Elsevier, vol. 203(1), pages 113-128.
    3. Linton, Oliver & Xiao, Zhijie, 2019. "Efficient estimation of nonparametric regression in the presence of dynamic heteroskedasticity," Journal of Econometrics, Elsevier, vol. 213(2), pages 608-631.
    4. Mengli Zhang & Yang Bai, 2021. "On the use of repeated measurement errors in linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 779-803, July.
    5. Boneva, Lena & Linton, Oliver, 2017. "A discrete choice model for large heterogeneous panels with interactive fixed effects with an application to the determinants of corporate bond issuance," Bank of England working papers 640, Bank of England.
    6. Chaudhuri, Saraswata & Renault, Eric, 2023. "Efficient estimation of regression models with user-specified parametric model for heteroskedasticty," The Warwick Economics Research Paper Series (TWERPS) 1473, University of Warwick, Department of Economics.
    7. Frank Windmeijer, 2019. "Two-stage least squares as minimum distance," The Econometrics Journal, Royal Economic Society, vol. 22(1), pages 1-9.
    8. Zhu, Qianqian & Zheng, Yao & Li, Guodong, 2018. "Linear double autoregression," Journal of Econometrics, Elsevier, vol. 207(1), pages 162-174.
    9. Yoonseok Lee & Yu Zhou, 2015. "Averaged Instrumental Variables Estimators," Center for Policy Research Working Papers 180, Center for Policy Research, Maxwell School, Syracuse University.
    10. Matthew Harding & Carlos Lamarche & Chris Muris, 2022. "Estimation of a Factor-Augmented Linear Model with Applications Using Student Achievement Data," Papers 2203.03051, arXiv.org.

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