IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v39y2024i3d10.1007_s00180-023-01379-9.html
   My bibliography  Save this article

A two-stage Bridge estimator for regression models with endogeneity based on control function method

Author

Listed:
  • Fatemeh Bahador

    (Shahid Bahonar University of Kerman)

  • Ayyub Sheikhi

    (Shahid Bahonar University of Kerman)

  • Alireza Arabpour

    (Shahid Bahonar University of Kerman)

Abstract

In this study, we investigate a penalty-based two-stage least square estimator in regression models when the exploratory variables are correlated with the error term. We propose a two-stage Bridge estimator to overcome this endogeneity problem in high-dimensional data. Our proposed estimator enjoys remarkable statistical properties such as consistency and asymptotic normality. As special cases, this method deals some ill-condition situations such as the multicollinearity as well as the sparsity. Performance of the proposed estimators is demonstrated by simulation studies and it is compared to the existing estimators. An application in real data set is presented for illustration.

Suggested Citation

  • Fatemeh Bahador & Ayyub Sheikhi & Alireza Arabpour, 2024. "A two-stage Bridge estimator for regression models with endogeneity based on control function method," Computational Statistics, Springer, vol. 39(3), pages 1351-1370, May.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:3:d:10.1007_s00180-023-01379-9
    DOI: 10.1007/s00180-023-01379-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-023-01379-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-023-01379-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wu, De-Min, 1973. "Alternative Tests of Independence Between Stochastic Regressors and Disturbances," Econometrica, Econometric Society, vol. 41(4), pages 733-750, July.
    2. Anderson, T.W., 2005. "Origins of the limited information maximum likelihood and two-stage least squares estimators," Journal of Econometrics, Elsevier, vol. 127(1), pages 1-16, July.
    3. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    4. Bahadır Yüzbaşı & Mohammad Arashi & S. Ejaz Ahmed, 2020. "Shrinkage Estimation Strategies in Generalised Ridge Regression Models: Low/High‐Dimension Regime," International Statistical Review, International Statistical Institute, vol. 88(1), pages 229-251, April.
    5. Xu-Qing Liu & Feng Gao & Zhen-Feng Yu, 2013. "Improved ridge estimators in a linear regression model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(1), pages 209-220, January.
    6. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    7. Xiaoli Gao & S. E. Ahmed & Yang Feng, 2017. "Post selection shrinkage estimation for high‐dimensional data analysis," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(2), pages 97-120, March.
    8. Wei Lin & Rui Feng & Hongzhe Li, 2015. "Regularization Methods for High-Dimensional Instrumental Variables Regression With an Application to Genetical Genomics," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 270-288, March.
    9. Hastie, Nicholas D. & van der Loos, Matthijs J. H. M. & Vitart, Veronique & Völzke, Henry & Wellmann, Jürgen & Yu, Lei & Zhao, Wei & Allik, Jüri & Attia, John R. & Bandinelli, Stefania & Bastardot,, 2013. "GWAS of 126,559 Individuals Identifies Genetic Variants Associated with Educational Attainment," Scholarly Articles 13383543, Harvard University Department of Economics.
    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. Qinqin Hu & Lu Lin, 2022. "Feature Screening in High Dimensional Regression with Endogenous Covariates," Computational Economics, Springer;Society for Computational Economics, vol. 60(3), pages 949-969, October.
    2. Bahadır Yüzbaşı & S. Ejaz Ahmed, 2020. "Ridge Type Shrinkage Estimation of Seemingly Unrelated Regressions And Analytics of Economic and Financial Data from “Fragile Five” Countries," JRFM, MDPI, vol. 13(6), pages 1-19, June.
    3. Campbell, Randall C. & Nagel, Gregory L., 2016. "Private information and limitations of Heckman's estimator in banking and corporate finance research," Journal of Empirical Finance, Elsevier, vol. 37(C), pages 186-195.
    4. James J. Heckman, 1991. "Randomization and Social Policy Evaluation Revisited," NBER Technical Working Papers 0107, National Bureau of Economic Research, Inc.
    5. Sheikh, Shahbaz, 2018. "The impact of market competition on the relation between CEO power and firm innovation," Journal of Multinational Financial Management, Elsevier, vol. 44(C), pages 36-50.
    6. Doko Tchatoka, Firmin Sabro, 2012. "Specification Tests with Weak and Invalid Instruments," MPRA Paper 40185, University Library of Munich, Germany.
    7. Cawley, John & Markowitz, Sara & Tauras, John, 2004. "Lighting up and slimming down: the effects of body weight and cigarette prices on adolescent smoking initiation," Journal of Health Economics, Elsevier, vol. 23(2), pages 293-311, March.
    8. Edward Ghartey, 2006. "Exchange Pressure, Sterilized Intervention and Monetary Policy in Ghana," EcoMod2006 272100031, EcoMod.
    9. Oded Palmon & Ben J. Sopranzetti, 2017. "On the relationship between the number of a broker’s real estate listings and transaction outcomes," Review of Quantitative Finance and Accounting, Springer, vol. 49(1), pages 65-89, July.
    10. Davidson, Russell & MacKinnon, James G., 1989. "Testing for Consistency using Artificial Regressions," Econometric Theory, Cambridge University Press, vol. 5(3), pages 363-384, December.
    11. O'Brien, Raymond & Patacchini, Eleonora, 2003. "Testing the exogeneity assumption in panel data models with "non classical" disturbances," Discussion Paper Series In Economics And Econometrics 0302, Economics Division, School of Social Sciences, University of Southampton.
    12. James J. Heckman, 1991. "Randomization and Social Policy Evaluation Revisited," NBER Technical Working Papers 0107, National Bureau of Economic Research, Inc.
    13. Mayston, David, 2009. "The determinants of cumulative endogeneity bias in multivariate analysis," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1120-1136, July.
    14. Doko Tchatoka, Firmin & Dufour, Jean-Marie, 2020. "Exogeneity tests, incomplete models, weak identification and non-Gaussian distributions: Invariance and finite-sample distributional theory," Journal of Econometrics, Elsevier, vol. 218(2), pages 390-418.
    15. Sheikh, Shahbaz, 2018. "Corporate social responsibility, product market competition, and firm value," Journal of Economics and Business, Elsevier, vol. 98(C), pages 40-55.
    16. Chi-Young Choi & Ling Hu & Masao Ogaki, 2005. "Structural Spurious Regressions and A Hausman-type Cointegration Test," RCER Working Papers 517, University of Rochester - Center for Economic Research (RCER).
    17. Robert Mulligan, 1996. "Export-import endogeneity in the context of the Thirlwall- Hussain model: an application of the Durbin-Wu-Hausman test incorporating a Monte Carlo experiment," Applied Economics Letters, Taylor & Francis Journals, vol. 3(4), pages 275-279.
    18. Michael O'Connor Keefe & David Gallagher, 2014. "Does the effect of revealed private information on initial public offering (IPO) first trading day return differ by IPO market heat?," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 54(3), pages 921-964, September.
    19. Guilhem Bascle, 2008. "Controlling for endogeneity with instrumental variables in strategic management research," Post-Print hal-00576795, HAL.
    20. Allen, David, 2022. "Asset Pricing Tests, Endogeneity issues and Fama-French factors," MPRA Paper 113610, University Library of Munich, Germany.

    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:spr:compst:v:39:y:2024:i:3:d:10.1007_s00180-023-01379-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.