IDEAS home Printed from https://ideas.repec.org/p/bgu/wpaper/0912.html
   My bibliography  Save this paper

Using Ols To Test For Normality

Author

Listed:
  • Haim Shalit

    (Department of Economics, Ben-Gurion University of the Negev)

Abstract

Yitzhaki (1996) showed that the OLS estimator of the slope coefficient in a simple regression is a weighted average of the slopes delineated by adjacent observations. The weights depend only on the distribution of the independent variable. In this paper I demonstrate that equal weights can only be obtained if and only if the independent variable is normally distributed. This characteristic is used to develop a new test for normality which is distribution free and not sensitive to outliers. The test is compared with standard normality tests, in particular, the popular Jarque-Bera test. It is shown that the new test is a better power for testing normality against all classes of alternative distributions. Finally, the test is applied to check normality in time series data from major international financial markets.

Suggested Citation

  • Haim Shalit, 2009. "Using Ols To Test For Normality," Working Papers 0912, Ben-Gurion University of the Negev, Department of Economics.
    • Handle: RePEc:bgu:wpaper:0912
    as

    Download full text from publisher

    File URL: http://in.bgu.ac.il/en/humsos/Econ/Workingpapers/0912.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Bontemps, Christian & Meddahi, Nour, 2005. "Testing normality: a GMM approach," Journal of Econometrics, Elsevier, vol. 124(1), pages 149-186, January.
    2. James J. Heckman & Sergio Urzua & Edward Vytlacil, 2006. "Understanding Instrumental Variables in Models with Essential Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 389-432, August.
    3. Shalit, Haim & Yitzhaki, Shlomo, 2002. "Estimating Beta," Review of Quantitative Finance and Accounting, Springer, vol. 18(2), pages 95-118, March.
    4. Gel, Yulia R. & Gastwirth, Joseph L., 2008. "A robust modification of the Jarque-Bera test of normality," Economics Letters, Elsevier, vol. 99(1), pages 30-32, April.
    5. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
    6. Deb, Partha & Sefton, Martin, 1996. "The distribution of a Lagrange multiplier test of normality," Economics Letters, Elsevier, vol. 51(2), pages 123-130, May.
    7. J. P. Royston, 1982. "The W Test for Normality," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(2), pages 176-180, June.
    8. Poitras, Geoffrey, 2006. "More on the correct use of omnibus tests for normality," Economics Letters, Elsevier, vol. 90(3), pages 304-309, March.
    9. Yitzhaki, Shlomo, 1996. "On Using Linear Regressions in Welfare Economics," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 478-486, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Doron Nisani & Amit Shelef, 2021. "A statistical analysis of investor preferences for portfolio selection," Empirical Economics, Springer, vol. 61(4), pages 1883-1915, October.
    2. Haim Shalit, 2020. "The Shapley value of regression portfolios," Journal of Asset Management, Palgrave Macmillan, vol. 21(6), pages 506-512, October.
    3. Norbert Henze & Stefan Koch, 2020. "On a test of normality based on the empirical moment generating function," Statistical Papers, Springer, vol. 61(1), pages 17-29, February.
    4. Haim Shalit, 2021. "The Shapley value decomposition of optimal portfolios," Annals of Finance, Springer, vol. 17(1), pages 1-25, March.
    5. Haim Shalit, 2014. "Measuring Risk In Israeli Mutual Funds: Conditional Value-At-Risk Vs. Aumann-Serrano Riskiness Index," Working Papers 1409, Ben-Gurion University of the Negev, Department of Economics.
    6. Doron Nisani, 2023. "On the General Deviation Measure and the Gini coefficient," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(3), pages 599-610, September.

    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. Yong Bao, 2013. "On Sample Skewness and Kurtosis," Econometric Reviews, Taylor & Francis Journals, vol. 32(4), pages 415-448, December.
    2. Hui, Wallace & Gel, Yulia R. & Gastwirth, Joseph L., 2008. "lawstat: An R Package for Law, Public Policy and Biostatistics," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 28(i03).
    3. Shoya Ishimaru, 2021. "Empirical Decomposition of the IV-OLS Gap with Heterogeneous and Nonlinear Effects," Papers 2101.04346, arXiv.org, revised Jun 2022.
    4. Yitzhaki, Shlomo & Schechtman, Edna, 2012. "Identifying monotonic and non-monotonic relationships," Economics Letters, Elsevier, vol. 116(1), pages 23-25.
    5. Heckman, James J. & Schmierer, Daniel & Urzua, Sergio, 2010. "Testing the correlated random coefficient model," Journal of Econometrics, Elsevier, vol. 158(2), pages 177-203, October.
    6. Sloczynski, Tymon, 2018. "A General Weighted Average Representation of the Ordinary and Two-Stage Least Squares Estimands," IZA Discussion Papers 11866, Institute of Labor Economics (IZA).
    7. F. Javier Mencía & Enrique Sentana, 2004. "Estimation and Testing of Dynamic Models with Generalised Hyperbolic Innovations," Working Papers wp2004_0411, CEMFI.
    8. Lauren Bin Dong & David E. A. Giles, 2004. "An Empirical Likelihood Ratio Test for Normality," Econometrics Working Papers 0401, Department of Economics, University of Victoria.
    9. Andersen, Torben G. & Bollerslev, Tim & Dobrev, Dobrislav, 2007. "No-arbitrage semi-martingale restrictions for continuous-time volatility models subject to leverage effects, jumps and i.i.d. noise: Theory and testable distributional implications," Journal of Econometrics, Elsevier, vol. 138(1), pages 125-180, May.
    10. Christian Bontemps & Nour Meddahi, 2012. "Testing distributional assumptions: A GMM aproach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 978-1012, September.
    11. Mohamed Boutahar, 2010. "Behaviour of skewness, kurtosis and normality tests in long memory data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(2), pages 193-215, June.
    12. Tomasz Górecki & Lajos Horváth & Piotr Kokoszka, 2020. "Tests of Normality of Functional Data," International Statistical Review, International Statistical Institute, vol. 88(3), pages 677-697, December.
    13. Bontemps, Christian & Meddahi, Nour, 2005. "Testing normality: a GMM approach," Journal of Econometrics, Elsevier, vol. 124(1), pages 149-186, January.
    14. Nazif Durmaz & Hyeongwoo Kim & Hyejin Lee & Yanfei Sun, 2023. "Trend Breaks and the Persistence of Closed-End Fund Discounts," Auburn Economics Working Paper Series auwp2023-08, Department of Economics, Auburn University.
    15. Anirban Basu & James J. Heckman & Salvador Navarro-Lozano & Sergio Urzua, 2007. "Use of instrumental variables in the presence of heterogeneity and self-selection: an application to treatments of breast cancer patients," Health Economics, John Wiley & Sons, Ltd., vol. 16(11), pages 1133-1157.
    16. repec:jss:jstsof:28:i03 is not listed on IDEAS
    17. Nazif Durmaz & Hyeongwoo Kim & Hyejin Lee & Yanfei Sun, 2023. "Trend Breaks and the Persistence of Closed-End Mutual Fund Discounts," Auburn Economics Working Paper Series auwp2023-03, Department of Economics, Auburn University.
    18. Tymon S{l}oczy'nski, 2018. "Interpreting OLS Estimands When Treatment Effects Are Heterogeneous: Smaller Groups Get Larger Weights," Papers 1810.01576, arXiv.org, revised May 2020.
    19. Thorsten Thadewald & Herbert Buning, 2007. "Jarque-Bera Test and its Competitors for Testing Normality - A Power Comparison," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(1), pages 87-105.
    20. Manuel Denzer & Constantin Weiser, 2021. "Beyond F-statistic - A General Approach for Assessing Weak Identification," Working Papers 2107, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    21. Tom Broekel & Thomas Brenner, 2011. "Regional factors and innovativeness: an empirical analysis of four German industries," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 47(1), pages 169-194, August.

    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:bgu:wpaper:0912. 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: Aamer Abu-Qarn (email available below). General contact details of provider: https://edirc.repec.org/data/edbguil.html .

    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.