IDEAS home Printed from https://ideas.repec.org/a/jns/jbstat/v221y2001i4p418-431.html
   My bibliography  Save this article

Zur korrekten Interpretation der Ergebnisse einer log-linearen Regression bei Heteroskedastie. Eine methodische Untersuchung mit einer Anwendung auf die relativen Löhne von Ausländern / Correctly Interpreting the Results from a Log-linear Regression under Heteroskedasticity. Methods and an Application to the Relative Wages of Immigrants

Author

Listed:
  • Winkelmann Rainer

    (IZA Bonn, Postfach 7240, D-53072 Bonn)

Abstract

The common estimator for relative adjusted wage differentials based on dummy variables in loglinear regressions is inconsistent in the presence of group-specific heteroskedasticity. The direction and magnitude of the bias are derived. At the same time, a heteroskedasticity-consistent estimator is proposed. The formulas are exact for normally distributed errors and approximations otherwise. An example on the wage determination in the German labor market shows that ignoring the problem of heteroskedasticity will lead to an underestimation of the relative wage gap between Germans and Immigrants, since the wages of immigrants are relatively less dispersed. Evidence from the literature as well as an independent analysis using data from the German Socio-Economic Panel for 1996 yield a downward bias of up to 25 percent. The importance of these results extend beyond the case of dummy variables to the general problem of Computing expectations of retransformed variables.

Suggested Citation

  • Winkelmann Rainer, 2001. "Zur korrekten Interpretation der Ergebnisse einer log-linearen Regression bei Heteroskedastie. Eine methodische Untersuchung mit einer Anwendung auf die relativen Löhne von Ausländern / Correctly Inte," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 221(4), pages 418-431, August.
    • Handle: RePEc:jns:jbstat:v:221:y:2001:i:4:p:418-431
    DOI: 10.1515/jbnst-2001-0406
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/jbnst-2001-0406
    Download Restriction: no
    File URL: https://libkey.io/10.1515/jbnst-2001-0406?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
    ---><---

    References listed on IDEAS

    as
    1. George J. Borjas, 2021. "The Economic Benefits from Immigration," World Scientific Book Chapters, in: Foundational Essays in Immigration Economics, chapter 13, pages 411-430, World Scientific Publishing Co. Pte. Ltd..
    2. Schmidt, Christoph M., 1997. "Immigrant performance in Germany: Labor earnings of ethnic German migrants and foreign guest-workers," The Quarterly Review of Economics and Finance, Elsevier, vol. 37(Supplemen), pages 379-397.
    3. Chiswick, Barry R, 1978. "The Effect of Americanization on the Earnings of Foreign-born Men," Journal of Political Economy, University of Chicago Press, vol. 86(5), pages 897-921, October.
    4. Oaxaca, Ronald, 1973. "Male-Female Wage Differentials in Urban Labor Markets," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(3), pages 693-709, October.
    5. Kennedy, Peter E, 1981. "Estimation with Correctly Interpreted Dummy Variables in Semilogarithmic Equations [The Interpretation of Dummy Variables in Semilogarithmic Equations]," American Economic Review, American Economic Association, vol. 71(4), pages 801-801, September.
    6. Dustmann, C, 1993. "Earnings Adjustment of Temporary Migrants," Journal of Population Economics, Springer;European Society for Population Economics, vol. 6(2), pages 153-168, May.
    7. George J. Borjas, 1994. "The Economics of Immigration," Journal of Economic Literature, American Economic Association, vol. 32(4), pages 1667-1717, December.
    8. Manning, Willard G., 1998. "The logged dependent variable, heteroscedasticity, and the retransformation problem," Journal of Health Economics, Elsevier, vol. 17(3), pages 283-295, June.
    9. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    10. Giles, David E. A., 1982. "The interpretation of dummy variables in semilogarithmic equations : Unbiased estimation," Economics Letters, Elsevier, vol. 10(1-2), pages 77-79.
    11. Jacob Mincer, 1958. "Investment in Human Capital and Personal Income Distribution," Journal of Political Economy, University of Chicago Press, vol. 66, pages 281-281.
    12. Halvorsen, Robert & Palmquist, Raymond, 1980. "The Interpretation of Dummy Variables in Semilogarithmic Equations," American Economic Review, American Economic Association, vol. 70(3), pages 474-475, June.
    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. Christian Pfeifer, 2012. "Fixed-term contracts and wages revisited using linked employer-employee data," Journal for Labour Market Research, Springer;Institute for Employment Research/ Institut für Arbeitsmarkt- und Berufsforschung (IAB), vol. 45(2), pages 171-183, July.

    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. Fertig, Michael & Schurer, Stefanie, 2007. "Labour Market Outcomes of Immigrants in Germany: The Importance of Heterogeneity and Attrition Bias," IZA Discussion Papers 2915, Institute of Labor Economics (IZA).
    2. Uebelmesser Silke, 2006. "To Go or Not to Go: Emigration from Germany," German Economic Review, De Gruyter, vol. 7(2), pages 211-231, May.
    3. Smolny, Werner & Rieber, Alexander, 2016. "Labour market integration of immigrants - Evidence for the German guest workers," VfS Annual Conference 2016 (Augsburg): Demographic Change 145629, Verein für Socialpolitik / German Economic Association.
    4. Michael Fertig & Stefanie Schurer, 2007. "Earnings Assimilation of Immigrants in Germany: The Importance of Heterogeneity and Attrition Bias," SOEPpapers on Multidisciplinary Panel Data Research 30, DIW Berlin, The German Socio-Economic Panel (SOEP).
    5. repec:zbw:rwirep:0020 is not listed on IDEAS
    6. Sebastian Gundel & Heiko Peters, "undated". "Assimilation and Cohort Effects for German Immigrants," Working Papers 200123, Institute of Spatial and Housing Economics, Munster Universitary.
    7. Michael Fertig & Stefanie Schurer, 2007. "Labour Market Outcomes of Immigrants in Germany – The Importance of Heterogeneity and Attrition Bias," Ruhr Economic Papers 0020, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    8. repec:zbw:rwirep:0030 is not listed on IDEAS
    9. Gil S. Epstein & Astrid Kunze & Melanie E. Ward, 2009. "High‐Skilled Migration And The Exertion Of Effort By The Local Population," Scottish Journal of Political Economy, Scottish Economic Society, vol. 56(3), pages 332-352, July.
    10. Mathias Sinning, 2007. "Wealth and Asset Holdings of Immigrants in Germany," Ruhr Economic Papers 0030, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    11. Brenzel, Hanna & Reichelt, Malte, 2015. "Job mobility as a new explanation for the immigrant-native wage gap : a longitudinal analysis for the German labor market," IAB-Discussion Paper 201512, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany].
    12. Sinning, Mathias, 2007. "Wealth and Asset Holdings of Immigrants in Germany," IZA Discussion Papers 3089, Institute of Labor Economics (IZA).
    13. Bauer, Thomas K. & Lofstrom, Magnus & Zimmermann, Klaus F., 2000. "Immigration Policy, Assimilation of Immigrants and Natives' Sentiments towards Immigrants: Evidence from 12 OECD-Countries," IZA Discussion Papers 187, Institute of Labor Economics (IZA).
    14. Viola Angelini & Laura Casi & Luca Corazzini, 2015. "Life satisfaction of immigrants: does cultural assimilation matter?," Journal of Population Economics, Springer;European Society for Population Economics, vol. 28(3), pages 817-844, July.
    15. Carl Lin, 2016. "How Do Immigrants From Taiwan Fare In The U.S. Labor Market?," The Singapore Economic Review (SER), World Scientific Publishing Co. Pte. Ltd., vol. 61(05), pages 1-38, December.
    16. Florian Lehmer & Johannes Ludsteck, 2012. "Wage Assimilation of Immigrants: Which Factors Close the Gap? – Evidence from Germany," ERSA conference papers ersa12p262, European Regional Science Association.
    17. Nabil Khattab & Shereen Hussein, 2018. "Can Religious Affiliation Explain the Disadvantage of Muslim Women in the British Labour Market?," Work, Employment & Society, British Sociological Association, vol. 32(6), pages 1011-1028, December.
    18. Florian Lehmer & Johannes Ludsteck, 2015. "Wage Assimilation of Foreigners: Which Factors Close the Gap? Evidence From Germany," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 61(4), pages 677-701, December.
    19. Dustmann, Christian & Schmidt, Christoph M., 2000. "The Wage Performance of Immigrant Women: Full-Time Jobs, Part-Time Jobs, and the Role of Selection," IZA Discussion Papers 233, Institute of Labor Economics (IZA).
    20. José M. Casado-Díaz & Raquel Simón-Albert & Hipólito Simón, 2022. "Reassessing the commuting penalty for immigrants: new evidence from Spain," Transportation, Springer, vol. 49(4), pages 1099-1132, August.
    21. Ekström, Erika, 1998. "Income Distribution and Labour Market Discrimination: A Case Study of Namibia," Working Paper Series 502, Research Institute of Industrial Economics.
    22. Preston, Alison & Wright, Robert E., 2022. "Gender, Financial Literacy and Pension Savings," IZA Discussion Papers 15250, Institute of Labor Economics (IZA).

    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:jns:jbstat:v:221:y:2001:i:4:p:418-431. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.