IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2304.07331.html
   My bibliography  Save this paper

Generalized Automatic Least Squares: Efficiency Gains from Misspecified Heteroscedasticity Models

Author

Listed:
  • Bulat Gafarov

Abstract

It is well known that in the presence of heteroscedasticity ordinary least squares estimator is not efficient. I propose a generalized automatic least squares estimator (GALS) that makes partial correction of heteroscedasticity based on a (potentially) misspecified model without a pretest. Such an estimator is guaranteed to be at least as efficient as either OLS or WLS but can provide some asymptotic efficiency gains over OLS if the misspecified model is approximately correct. If the heteroscedasticity model is correct, the proposed estimator achieves full asymptotic efficiency. The idea is to frame moment conditions corresponding to OLS and WLS squares based on miss-specified heteroscedasticity as a joint generalized method of moments estimation problem. The resulting optimal GMM estimator is equivalent to a feasible GLS with estimated weight matrix. I also propose an optimal GMM variance-covariance estimator for GALS to account for any remaining heteroscedasticity in the residuals.

Suggested Citation

  • Bulat Gafarov, 2023. "Generalized Automatic Least Squares: Efficiency Gains from Misspecified Heteroscedasticity Models," Papers 2304.07331, arXiv.org.
    • Handle: RePEc:arx:papers:2304.07331
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2304.07331
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Im, Kyung So & Schmidt, Peter, 2008. "More efficient estimation under non-normality when higher moments do not depend on the regressors, using residual augmented least squares," Journal of Econometrics, Elsevier, vol. 144(1), pages 219-233, May.
    2. Hall, Alastair R., 2004. "Generalized Method of Moments," OUP Catalogue, Oxford University Press, number 9780198775201.
    3. Cragg, John G, 1983. "More Efficient Estimation in the Presence of Heteroscedasticity of Unknown Form," Econometrica, Econometric Society, vol. 51(3), pages 751-763, May.
    4. Romano, Joseph P. & Wolf, Michael, 2017. "Resurrecting weighted least squares," Journal of Econometrics, Elsevier, vol. 197(1), pages 1-19.
    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. Pötscher, Benedikt M. & Preinerstorfer, David, 2021. "Valid Heteroskedasticity Robust Testing," MPRA Paper 107420, University Library of Munich, Germany.
    2. Pötscher, Benedikt M. & Preinerstorfer, David, 2023. "How Reliable Are Bootstrap-Based Heteroskedasticity Robust Tests?," Econometric Theory, Cambridge University Press, vol. 39(4), pages 789-847, August.
    3. Michis Antonis A, 2009. "Regression Analysis of Marketing Time Series: A Wavelet Approach with Some Frequency Domain Insights," Review of Marketing Science, De Gruyter, vol. 7(1), pages 1-43, July.
    4. de Mendonça, Helder Ferreira & Tiberto, Bruno Pires, 2014. "Public debt and social security: Level of formality matters," Economic Modelling, Elsevier, vol. 42(C), pages 490-507.
    5. Nadine Chlass & Jens J. Krueger, 2007. "Small Sample Properties of the Wilcoxon Signed Rank Test with Discontinuous and Dependent Observations," Jena Economics Research Papers 2007-032, Friedrich-Schiller-University Jena.
    6. Ioannis Tsamourgelis & Persa Paflioti & Thomas Vitsounis, 2013. "Seaports Activity (A)synchronicity, Trade Intensity and Business Cycle Convergence: A Panel Data Analysis," International Journal of Maritime, Trade & Economic Issues (IJMTEI), International Journal of Maritime, Trade & Economic Issues (IJMTEI), vol. 0(1), pages 67-92.
    7. de Moraes, Claudio Oliveira & Cruz, Guilherme, 2023. "What do we know about the relationship between banks and income inequality? Empirical evidence for emerging and low-income countries," Journal of Economics and Business, Elsevier, vol. 123(C).
    8. Stéphane Albert & Hervé Alexandre, 2018. "Banks’ earnings: Empirical evidence of the influence of economic and financial market factors," Review of Financial Economics, John Wiley & Sons, vol. 36(2), pages 97-116, April.
    9. Katarzyna Jabłońska, 2018. "Dealing With Heteroskedasticity Within The Modeling Of The Quality Of Life Of Older People," Statistics in Transition New Series, Polish Statistical Association, vol. 19(3), pages 423-452, September.
    10. Miller, Steve & Startz, Richard, 2019. "Feasible generalized least squares using support vector regression," Economics Letters, Elsevier, vol. 175(C), pages 28-31.
    11. Frank A. Wolak, 2007. "Quantifying the supply-side benefits from forward contracting in wholesale electricity markets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(7), pages 1179-1209.
    12. A. Craig Burnside, 2007. "Empirical Asset Pricing and Statistical Power in the Presence of Weak Risk Factors," NBER Working Papers 13357, National Bureau of Economic Research, Inc.
    13. Yoici Arai & Taisuke Otsu & Mengshan Xu, 2022. "GLS under monotone heteroskedasticity," STICERD - Econometrics Paper Series 625, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    14. Richard H. Spady & Sami Stouli, 2018. "Simultaneous Mean-Variance Regression," Bristol Economics Discussion Papers 18/697, School of Economics, University of Bristol, UK.
    15. G. C. Montes & L. V. Oliveira & A. Curi & R. T. F. Nicolay, 2016. "Effects of transparency, monetary policy signalling and clarity of central bank communication on disagreement about inflation expectations," Applied Economics, Taylor & Francis Journals, vol. 48(7), pages 590-607, February.
    16. Jeffrey M. Wooldridge, 2001. "Applications of Generalized Method of Moments Estimation," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 87-100, Fall.
    17. Pesaran, M. Hashem & Timmermann, Allan, 2009. "Testing Dependence Among Serially Correlated Multicategory Variables," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 325-337.
    18. Christopher F Baum & Mark E. Schaffer & Steven Stillman, 2003. "Instrumental variables and GMM: Estimation and testing," Stata Journal, StataCorp LP, vol. 3(1), pages 1-31, March.
    19. Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2004. "Estimating nonlinear dynamic equilibrium economies: a likelihood approach," FRB Atlanta Working Paper 2004-1, Federal Reserve Bank of Atlanta.
    20. Gabriel Caldas Montes & Victor Maia, 2023. "The reaction of disagreements in inflation expectations to fiscal sentiment obtained from information in official communiqués," Bulletin of Economic Research, Wiley Blackwell, vol. 75(4), pages 828-859, October.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:2304.07331. 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.