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Smoothed GMM for quantile models

Author

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  • de Castro, Luciano
  • Galvao, Antonio F.
  • Kaplan, David M.
  • Liu, Xin

Abstract

We consider estimation of finite-dimensional parameters identified by general conditional quantile restrictions, including instrumental variables quantile regression. Within a generalized method of moments framework, moment functions are smoothed to aid both computation and precision. Consistency and asymptotic normality are established under weaker assumptions than previously seen in the literature, allowing dependent data and nonlinear structural models. Simulations illustrate the finite-sample properties. An in-depth empirical application estimates the consumption Euler equation derived from quantile utility maximization. Advantages of quantile Euler equations include robustness to fat tails, decoupling risk attitude from the elasticity of intertemporal substitution, and error-free log-linearization.

Suggested Citation

  • de Castro, Luciano & Galvao, Antonio F. & Kaplan, David M. & Liu, Xin, 2019. "Smoothed GMM for quantile models," Journal of Econometrics, Elsevier, vol. 213(1), pages 121-144.
    • Handle: RePEc:eee:econom:v:213:y:2019:i:1:p:121-144
    DOI: 10.1016/j.jeconom.2019.04.008
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    Cited by:

    1. Javier Alejo & Antonio F Galvao & Gabriel Montes-Rojas, 2023. "A first-stage representation for instrumental variables quantile regression," The Econometrics Journal, Royal Economic Society, vol. 26(3), pages 350-377.
    2. Grigory Franguridi & Bulat Gafarov & Kaspar Wuthrich, 2020. "Bias correction for quantile regression estimators," Papers 2011.03073, arXiv.org, revised Nov 2024.
    3. Fusejima, Koki, 2024. "Identification of multi-valued treatment effects with unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 238(1).
    4. Christophe Muller, 2019. "Linear Quantile Regression and Endogeneity Correction," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 9(5), pages 123-128, August.
    5. Xin Liu, 2024. "Averaging Estimation for Instrumental Variables Quantile Regression," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 86(5), pages 1290-1312, October.
    6. de Castro, Luciano I. & Galvao, Antonio F. & Nunes, Daniel da Siva, 0. "Dynamic economics with quantile preferences," Theoretical Economics, Econometric Society.
    7. Javier Alejo & Antonio F. Galvao & Gabriel Montes-Rojas, 2020. "A first-stage test for instrumental variables quantile regression," Asociación Argentina de Economía Política: Working Papers 4304, Asociación Argentina de Economía Política.
    8. David M. Kaplan, 2022. "Smoothed instrumental variables quantile regression," Stata Journal, StataCorp LP, vol. 22(2), pages 379-403, June.
    9. Firpo, Sergio & Galvao, Antonio F. & Pinto, Cristine & Poirier, Alexandre & Sanroman, Graciela, 2022. "GMM quantile regression," Journal of Econometrics, Elsevier, vol. 230(2), pages 432-452.
    10. Di Liu, 2024. "Instrumental-variables quantile regression," French Stata Users' Group Meetings 2024 07, Stata Users Group.
    11. David M. Kaplan & Xin Liu, 2024. "k-Class instrumental variables quantile regression," Empirical Economics, Springer, vol. 67(1), pages 111-141, July.
    12. Hiroaki Kaido & Kaspar Wüthrich, 2021. "Decentralization estimators for instrumental variable quantile regression models," Quantitative Economics, Econometric Society, vol. 12(2), pages 443-475, May.
    13. Di Liu, 2024. "Instrumental variables quantile regression," Chinese Stata Conference 2023 07, Stata Users Group.
    14. Javier Alejo & Gabriel Montes-Rojas, 2021. "Quantile Regression under Limited Dependent Variable," Papers 2112.06822, arXiv.org.
    15. Koki Fusejima, 2020. "Identification of multi-valued treatment effects with unobserved heterogeneity," Papers 2010.04385, arXiv.org, revised Apr 2023.
    16. David Powell, 2022. "Quantile regression with nonadditive fixed effects," Empirical Economics, Springer, vol. 63(5), pages 2675-2691, November.
    17. de Castro, Luciano & Cundy, Lance D. & Galvao, Antonio F. & Westenberger, Rafael, 2023. "A dynamic quantile model for distinguishing intertemporal substitution from risk aversion," European Economic Review, Elsevier, vol. 159(C).
    18. He, Xuming & Pan, Xiaoou & Tan, Kean Ming & Zhou, Wen-Xin, 2023. "Smoothed quantile regression with large-scale inference," Journal of Econometrics, Elsevier, vol. 232(2), pages 367-388.
    19. de Castro, Luciano & Galvao, Antonio F. & Montes-Rojas, Gabriel, 2020. "Quantile selection in non-linear GMM quantile models," Economics Letters, Elsevier, vol. 195(C).

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    More about this item

    Keywords

    Instrumental variables; Nonlinear quantile regression; Quantile utility maximization;
    All these keywords.

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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