IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i15p3412-d1210952.html
   My bibliography  Save this article

A New Instrumental-Type Estimator for Quantile Regression Models

Author

Listed:
  • Li Tao

    (School of Information, Beijing Wuzi University, Beijing 101149, China)

  • Lingnan Tai

    (School of Economics and Management, The Open University of China, Beijing 100039, China)

  • Manling Qian

    (School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia)

  • Maozai Tian

    (Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing 100872, China
    School of Statistics and Information, Xinjiang University of Finance and Economics, Urumqi 830026, China)

Abstract

This paper proposes a new instrumental-type estimator of quantile regression models for panel data with fixed effects. The estimator is built upon the minimum distance, which is defined as the weighted average of the conventional individual instrumental variable quantile regression slope estimators. The weights assigned to each estimator are determined by the inverses of their corresponding individual variance–covariance matrices. The implementation of the estimation has many advantages in terms of computational efforts and simplifies the asymptotic distribution. Furthermore, the paper shows consistency and asymptotic normality for sequential and simultaneous asymptotics. Additionally, it presents an empirical application that investigates the income elasticity of health expenditures.

Suggested Citation

  • Li Tao & Lingnan Tai & Manling Qian & Maozai Tian, 2023. "A New Instrumental-Type Estimator for Quantile Regression Models," Mathematics, MDPI, vol. 11(15), pages 1-26, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3412-:d:1210952
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/15/3412/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/15/3412/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Markus Brückner & Antonio Ciccone & Andrea Tesei, 2012. "Oil Price Shocks, Income, and Democracy," The Review of Economics and Statistics, MIT Press, vol. 94(2), pages 389-399, May.
    2. Daron Acemoglu & Amy Finkelstein & Matthew J. Notowidigdo, 2013. "Income and Health Spending: Evidence from Oil Price Shocks," The Review of Economics and Statistics, MIT Press, vol. 95(4), pages 1079-1095, October.
    3. Galvao, Antonio F. & Gu, Jiaying & Volgushev, Stanislav, 2020. "On the unbiased asymptotic normality of quantile regression with fixed effects," Journal of Econometrics, Elsevier, vol. 218(1), pages 178-215.
    4. Ivan A. Canay, 2011. "A simple approach to quantile regression for panel data," Econometrics Journal, Royal Economic Society, vol. 14(3), pages 368-386, October.
    5. Paul Contoyannis & Jinhu Li, 2017. "The dynamics of adolescent depression: an instrumental variable quantile regression with fixed effects approach," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(3), pages 907-922, June.
    6. Liang Chen & Yulong Huo, 2021. "A simple estimator for quantile panel data models using smoothed quantile regressions," The Econometrics Journal, Royal Economic Society, vol. 24(2), pages 247-263.
    7. John R. Moran & Kosali Ilayperuma Simon, 2004. "Income and the Use of Prescription Drugs by the Elderly: Evidence from the Notch Cohorts," Center for Policy Research Working Papers 66, Center for Policy Research, Maxwell School, Syracuse University.
    8. Galvao Jr, A. F. & Montes-Rojas, G., 2009. "Instrumental variables quantile regression for panel data with measurement errors," Working Papers 09/06, Department of Economics, City University London.
    9. Antonio F. Galvao & Carlos Lamarche & Luiz Renato Lima, 2013. "Estimation of Censored Quantile Regression for Panel Data With Fixed Effects," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 1075-1089, September.
    10. Chernozhukov, Victor & Hansen, Christian, 2008. "Instrumental variable quantile regression: A robust inference approach," Journal of Econometrics, Elsevier, vol. 142(1), pages 379-398, January.
    11. Kevin M. Murphy & Robert H. Topel, 2006. "The Value of Health and Longevity," Journal of Political Economy, University of Chicago Press, vol. 114(5), pages 871-904, October.
    12. Lamarche, Carlos, 2010. "Robust penalized quantile regression estimation for panel data," Journal of Econometrics, Elsevier, vol. 157(2), pages 396-408, August.
    13. Kengo Kato, 2012. "Asymptotic normality of Powell’s kernel estimator," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(2), pages 255-273, April.
    14. Chernozhukov, Victor & Hansen, Christian, 2006. "Instrumental quantile regression inference for structural and treatment effect models," Journal of Econometrics, Elsevier, vol. 132(2), pages 491-525, June.
    15. Galvao Jr., Antonio F., 2011. "Quantile regression for dynamic panel data with fixed effects," Journal of Econometrics, Elsevier, vol. 164(1), pages 142-157, September.
    16. Harding, Matthew & Lamarche, Carlos, 2009. "A quantile regression approach for estimating panel data models using instrumental variables," Economics Letters, Elsevier, vol. 104(3), pages 133-135, September.
    17. Joseph P. Newhouse, 1977. "Medical-Care Expenditure: A Cross-National Survey," Journal of Human Resources, University of Wisconsin Press, vol. 12(1), pages 115-125.
    18. Harding, Matthew & Lamarche, Carlos, 2014. "A Hausman–Taylor instrumental variable approach to the penalized estimation of quantile panel models," Economics Letters, Elsevier, vol. 124(2), pages 176-179.
    19. Gerdtham, Ulf-G. & Jonsson, Bengt, 2000. "International comparisons of health expenditure: Theory, data and econometric analysis," Handbook of Health Economics, in: A. J. Culyer & J. P. Newhouse (ed.), Handbook of Health Economics, edition 1, volume 1, chapter 1, pages 11-53, Elsevier.
    20. Galvao, Antonio F. & Wang, Liang, 2015. "Efficient minimum distance estimator for quantile regression fixed effects panel data," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 1-26.
    21. Gu, Jiaying & Volgushev, Stanislav, 2019. "Panel data quantile regression with grouped fixed effects," Journal of Econometrics, Elsevier, vol. 213(1), pages 68-91.
    22. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    23. Antonio F. Galvao & Thomas Parker & Zhijie Xiao, 2021. "Bootstrap inference for panel data quantile regression," Papers 2111.03626, arXiv.org.
    24. Besstremyannaya, Galina & Golovan, Sergei, 2021. "Measuring heterogeneity with fixed effect quantile regression: Long panels and short panels," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 64, pages 70-82.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li Tao & Yuanjie Zhang & Maozai Tian, 2019. "Quantile Regression for Dynamic Panel Data Using Hausman–Taylor Instrumental Variables," Computational Economics, Springer;Society for Computational Economics, vol. 53(3), pages 1033-1069, March.
    2. Philip Kostov & Julie Le Gallo, 2018. "What role for human capital in the growth process: new evidence from endogenous latent factor panel quantile regressions," Scottish Journal of Political Economy, Scottish Economic Society, vol. 65(5), pages 501-527, November.
    3. Harding, Matthew & Lamarche, Carlos, 2014. "Estimating and testing a quantile regression model with interactive effects," Journal of Econometrics, Elsevier, vol. 178(P1), pages 101-113.
    4. Panagiotidis, Theodore & Printzis, Panagiotis, 2021. "Investment and uncertainty: Are large firms different from small ones?," Journal of Economic Behavior & Organization, Elsevier, vol. 184(C), pages 302-317.
    5. Denis Chetverikov & Bradley Larsen & Christopher Palmer, 2016. "IV Quantile Regression for Group‐Level Treatments, With an Application to the Distributional Effects of Trade," Econometrica, Econometric Society, vol. 84, pages 809-833, March.
    6. Machado, José A.F. & Santos Silva, J.M.C., 2019. "Quantiles via moments," Journal of Econometrics, Elsevier, vol. 213(1), pages 145-173.
    7. Andini, Corrado & Andini, Monica, 2015. "A Note on Unemployment Persistence and Quantile Parameter Heterogeneity," IZA Discussion Papers 8819, Institute of Labor Economics (IZA).
    8. Sherrilyn Billger & Carlos Lamarche, 2015. "A panel data quantile regression analysis of the immigrant earnings distribution in the United Kingdom and United States," Empirical Economics, Springer, vol. 49(2), pages 705-750, September.
    9. David Powell, 2022. "Quantile regression with nonadditive fixed effects," Empirical Economics, Springer, vol. 63(5), pages 2675-2691, November.
    10. Antonio F. Galvao & Thomas Parker & Zhijie Xiao, 2021. "Bootstrap inference for panel data quantile regression," Papers 2111.03626, arXiv.org.
    11. Frantisek Cech & Jozef Barunik, 2017. "Measurement of Common Risk Factors: A Panel Quantile Regression Model for Returns," Working Papers IES 2017/20, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Sep 2017.
    12. Xiaorong Yang & Jia Chen & Degui Li & Runze Li, 2023. "Functional-Coefficient Quantile Regression for Panel Data with Latent Group Structure," Papers 2303.13218, arXiv.org.
    13. Maria Marino & Alessio Farcomeni, 2015. "Linear quantile regression models for longitudinal experiments: an overview," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 229-247, August.
    14. Zhang, Yingying & Wang, Huixia Judy & Zhu, Zhongyi, 2019. "Quantile-regression-based clustering for panel data," Journal of Econometrics, Elsevier, vol. 213(1), pages 54-67.
    15. Xiao, Zhijie & Xu, Lan, 2019. "What do mean impacts miss? Distributional effects of corporate diversification," Journal of Econometrics, Elsevier, vol. 213(1), pages 92-120.
    16. David Powell & Joachim Wagner, 2021. "The Exporter Productivity Premium Along the Productivity Distribution: Evidence from Quantile Regression with Nonadditive Firm Fixed Effects," World Scientific Book Chapters, in: Joachim Wagner (ed.), MICROECONOMETRIC STUDIES OF FIRMS’ IMPORTS AND EXPORTS Advanced Methods of Analysis and Evidence from German Enterprises, chapter 9, pages 121-149, World Scientific Publishing Co. Pte. Ltd..
    17. Philip Kostov & Julie Le Gallo, 2015. "Convergence: A Story of Quantiles and Spillovers," Kyklos, Wiley Blackwell, vol. 68(4), pages 552-576, November.
    18. Galina Besstremyannaya, 2014. "The efficiency of labor matching and remuneration reforms: a panel data quantile regression approach with endogenous treatment variables," Working Papers w0206, New Economic School (NES).
    19. Galvao, Antonio F. & Gu, Jiaying & Volgushev, Stanislav, 2020. "On the unbiased asymptotic normality of quantile regression with fixed effects," Journal of Econometrics, Elsevier, vol. 218(1), pages 178-215.
    20. Galina Besstremyannaya, 2015. "Heterogeneous effect of residency matching and prospective payment on labor returns and hospital scale economies," Discussion Papers 15-001, Stanford Institute for Economic Policy Research.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3412-:d:1210952. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.