IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2412.02767.html
   My bibliography  Save this paper

Endogenous Heteroskedasticity in Linear Models

Author

Listed:
  • Javier Alejo
  • Antonio F. Galvao
  • Julian Martinez-Iriarte
  • Gabriel Montes-Rojas

Abstract

Linear regressions with endogeneity are widely used to estimate causal effects. This paper studies a framework that has two common issues, endogeneity of the regressors, and heteroskedasticity that is allowed to depend on endogenous regressors, i.e., endogenous heteroskedasticity. We show that the presence of such conditional heteroskedasticity in the structural regression renders the two-stages least squares estimator inconsistent. To solve this issue, we propose sufficient conditions together with a control function approach to identify and estimate the causal parameters of interest. We establish the limiting properties of the estimator, say consistency and asymptotic normality, and propose inference procedures. Monte Carlo simulations provide evidence of the finite sample performance of the proposed methods, and evaluate different implementation procedures. We revisit an empirical application about job training to illustrate the methods.

Suggested Citation

  • Javier Alejo & Antonio F. Galvao & Julian Martinez-Iriarte & Gabriel Montes-Rojas, 2024. "Endogenous Heteroskedasticity in Linear Models," Papers 2412.02767, arXiv.org, revised Jan 2025.
    • Handle: RePEc:arx:papers:2412.02767
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2412.02767
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jin, Sainan & Su, Liangjun & Xiao, Zhijie, 2015. "Adaptive Nonparametric Regression With Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 31(6), pages 1153-1191, December.
    2. James J. Heckman & Jeffrey Smith & Nancy Clements, 1997. "Making The Most Out Of Programme Evaluations and Social Experiments: Accounting For Heterogeneity in Programme Impacts," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(4), pages 487-535.
    3. Wooldridge, Jeffrey M., 1997. "On two stage least squares estimation of the average treatment effect in a random coefficient model," Economics Letters, Elsevier, vol. 56(2), pages 129-133, October.
    4. Hansen, Christian B., 2007. "Asymptotic properties of a robust variance matrix estimator for panel data when T is large," Journal of Econometrics, Elsevier, vol. 141(2), pages 597-620, December.
    5. A. Colin Cameron & Douglas L. Miller, 2015. "A Practitioner’s Guide to Cluster-Robust Inference," Journal of Human Resources, University of Wisconsin Press, vol. 50(2), pages 317-372.
    6. Alexander Torgovitsky, 2015. "Identification of Nonseparable Models Using Instruments With Small Support," Econometrica, Econometric Society, vol. 83(3), pages 1185-1197, May.
    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. James G. MacKinnon & Matthew D. Webb & Morten Ø. Nielsen, 2017. "Bootstrap And Asymptotic Inference With Multiway Clustering," Working Paper 1386, Economics Department, Queen's University.
    2. Manuel Arellano & Stéphane Bonhomme, 2017. "Quantile Selection Models With an Application to Understanding Changes in Wage Inequality," Econometrica, Econometric Society, vol. 85, pages 1-28, January.
    3. Hagemann, Andreas, 2019. "Placebo inference on treatment effects when the number of clusters is small," Journal of Econometrics, Elsevier, vol. 213(1), pages 190-209.
    4. Laurent Davezies & Xavier D'Haultfoeuille & Yannick Guyonvarch, 2018. "Asymptotic results under multiway clustering," Papers 1807.07925, arXiv.org, revised Aug 2018.
    5. Federico Bugni & Ivan Canay & Azeem Shaikh & Max Tabord-Meehan, 2022. "Inference for Cluster Randomized Experiments with Non-ignorable Cluster Sizes," Papers 2204.08356, arXiv.org, revised Apr 2024.
    6. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    7. Yuya Sasaki & Yulong Wang, 2022. "Non-Robustness of the Cluster-Robust Inference: with a Proposal of a New Robust Method," Papers 2210.16991, arXiv.org, revised Dec 2022.
    8. Pereda-Fernández, Santiago, 2023. "Identification and estimation of triangular models with a binary treatment," Journal of Econometrics, Elsevier, vol. 234(2), pages 585-623.
    9. Nocito, Samuel & Sartarelli, Marcello & Sobbrio, Francesco, 2023. "A beam of light: Media, tourism and economic development," Journal of Urban Economics, Elsevier, vol. 137(C).
    10. Hansen, Bruce E. & Lee, Seojeong, 2019. "Asymptotic theory for clustered samples," Journal of Econometrics, Elsevier, vol. 210(2), pages 268-290.
    11. Steven M. Smith, 2019. "The Relative Economic Merits of Alternative Water Rights," Working Papers 2019-08, Colorado School of Mines, Division of Economics and Business.
    12. Colin F. Camerer & Gideon Nave & Alec Smith, 2019. "Dynamic Unstructured Bargaining with Private Information: Theory, Experiment, and Outcome Prediction via Machine Learning," Management Science, INFORMS, vol. 65(4), pages 1867-1890, April.
    13. Bai, Jushan & Choi, Sung Hoon & Liao, Yuan, 2024. "Standard errors for panel data models with unknown clusters," Journal of Econometrics, Elsevier, vol. 240(2).
    14. Victor Chernozhukov & Christian Hansen & Kaspar Wuthrich, 2020. "Instrumental Variable Quantile Regression," Papers 2009.00436, arXiv.org.
    15. Kasy, Maximilian, "undated". "Instrumental variables with unrestricted heterogeneity and continuous treatment - DON'T CITE! SEE ERRATUM BELOW," Working Paper 33257, Harvard University OpenScholar.
    16. Jungbin Hwang, 2017. "Simple and Trustworthy Cluster-Robust GMM Inference," Working papers 2017-19, University of Connecticut, Department of Economics, revised Aug 2020.
    17. Fraser Summerfield & Ioannis Theodossiou, 2017. "The Effects Of Macroeconomic Conditions At Graduation On Overeducation," Economic Inquiry, Western Economic Association International, vol. 55(3), pages 1370-1387, July.
    18. Richard Blundell & Lorraine Dearden & Barbara Sianesi, 2003. "Evaluating the impact of education on earnings in the UK: Models, methods and results from the NCDS," IFS Working Papers W03/20, Institute for Fiscal Studies.
    19. MacKinnon, James G. & Nielsen, Morten Ørregaard & Webb, Matthew D., 2023. "Cluster-robust inference: A guide to empirical practice," Journal of Econometrics, Elsevier, vol. 232(2), pages 272-299.
    20. Romuald Meango & Esther Mirjam Girsberger, 2023. "Identification of Ex ante Returns Using Elicited Choice Probabilities: an Application to Preferences for Public-sector Jobs," Papers 2303.03009, arXiv.org, revised Jun 2024.

    More about this item

    Statistics

    Access and download statistics

    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:arx:papers:2412.02767. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.