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Improved Jive estimators for overidentified linear models with and without heteroskedasticity

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  • Paul J. Devereux
  • Daniel A. Ackerberg

Abstract

We introduce two simple new variants of the Jackknife Instrumental Variables (JIVE) estimator for overidentified linear models and show that they are superior to the existing JIVE estimator, significantly improving on its small sample bias properties. We also compare our new estimators to existing Nagar (1959) type estimators. We show that, in models with heteroskedasticity, our estimators have superior properties to both the Nagar estimator and the related B2SLS estimator suggested in Donald and Newey (2001). These theoretical results are verified in a set of Monte-Carlo experiments and then applied to estimating the returns to schooling using actual data.

Suggested Citation

  • Paul J. Devereux & Daniel A. Ackerberg, 2008. "Improved Jive estimators for overidentified linear models with and without heteroskedasticity," Working Papers 200817, School of Economics, University College Dublin.
  • Handle: RePEc:ucn:wpaper:200817
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    File URL: http://hdl.handle.net/10197/749
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    References listed on IDEAS

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    1. James G. MacKinnon & Russell Davidson, 2006. "The case against JIVE," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(6), pages 827-833.
    2. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    3. Blomquist, Soren & Dahlberg, Matz, 1999. "Small Sample Properties of LIML and Jackknife IV Estimators: Experiments with Weak Instruments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 69-88, Jan.-Feb..
    4. John Chao & Norman Swanson, 2004. "Estimation and Testing Using Jackknife IV in Heteroskedastic Regressions With Many Weak Instruments," Departmental Working Papers 200420, Rutgers University, Department of Economics.
    5. Daniel A. Ackerberg & Paul J. Devereux, 2009. "Improved JIVE Estimators for Overidentified Linear Models with and without Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 91(2), pages 351-362, May.
    6. Angrist, Joshua D & Krueger, Alan B, 1995. "Split-Sample Instrumental Variables Estimates of the Return to Schooling," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(2), pages 225-235, April.
    7. Devereux, Paul J., 2007. "Improved Errors-in-Variables Estimators for Grouped Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 278-287, July.
    8. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-681, May.
    9. Jerry A. Hausman & Whitney K. Newey & Tiemen Woutersen & John C. Chao & Norman R. Swanson, 2012. "Instrumental variable estimation with heteroskedasticity and many instruments," Quantitative Economics, Econometric Society, vol. 3(2), pages 211-255, July.
    10. Paul J. Devereux & Daniel A. Ackerberg, 2006. "Comment on 'The case against JIVE'," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(6), pages 835-838.
    11. Angrist, J D & Imbens, G W & Krueger, A B, 1999. "Jackknife Instrumental Variables Estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 57-67, Jan.-Feb..
    12. John C. Chao & Norman R. Swanson, 2005. "Consistent Estimation with a Large Number of Weak Instruments," Econometrica, Econometric Society, vol. 73(5), pages 1673-1692, September.
    13. Jinyong Hahn & Jerry Hausman & Guido Kuersteiner, 2004. "Estimation with weak instruments: Accuracy of higher-order bias and MSE approximations," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 272-306, June.
    14. Paul J. Devereux, 2007. "Small-sample bias in synthetic cohort models of labor supply," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(4), pages 839-848.
    15. Hahn, Jinyong & Hausman, Jerry, 2002. "Notes on bias in estimators for simultaneous equation models," Economics Letters, Elsevier, vol. 75(2), pages 237-241, April.
    16. Joshua D. Angrist & Alan B. Keueger, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, Oxford University Press, vol. 106(4), pages 979-1014.
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    Cited by:

    1. Jerry A. Hausman & Whitney K. Newey & Tiemen Woutersen & John C. Chao & Norman R. Swanson, 2012. "Instrumental variable estimation with heteroskedasticity and many instruments," Quantitative Economics, Econometric Society, vol. 3(2), pages 211-255, July.
    2. Bekker, Paul A. & Crudu, Federico, 2012. "Symmetric Jackknife Instrumental Variable Estimation," MPRA Paper 37853, University Library of Munich, Germany.
    3. Isaiah Andrews & Timothy B. Armstrong, 2015. "Unbiased Instrumental Variables Estimation under Known First-Stage Sign," Cowles Foundation Discussion Papers 1984R, Cowles Foundation for Research in Economics, Yale University, revised Mar 2015.
    4. Chao, John C. & Hausman, Jerry A. & Newey, Whitney K. & Swanson, Norman R. & Woutersen, Tiemen, 2014. "Testing overidentifying restrictions with many instruments and heteroskedasticity," Journal of Econometrics, Elsevier, vol. 178(P1), pages 15-21.
    5. Isaiah Andrews & Timothy B. Armstrong, 2015. "Unbiased Instrumental Variables Estimation under Known First-Stage Sign," Cowles Foundation Discussion Papers 1984R2, Cowles Foundation for Research in Economics, Yale University, revised Sep 2015.
    6. Chao, John C. & Swanson, Norman R. & Hausman, Jerry A. & Newey, Whitney K. & Woutersen, Tiemen, 2012. "Asymptotic Distribution Of Jive In A Heteroskedastic Iv Regression With Many Instruments," Econometric Theory, Cambridge University Press, vol. 28(01), pages 42-86, February.
    7. Michal Kolesár & Raj Chetty & John Friedman & Edward Glaeser & Guido W. Imbens, 2015. "Identification and Inference With Many Invalid Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 474-484, October.
    8. Jörn-Steffen Pischke & Hannes Schwandt, 2012. "A Cautionary Note on Using Industry Affiliation to Predict Income," NBER Working Papers 18384, National Bureau of Economic Research, Inc.
    9. Devereux, Paul J., 2007. "Improved Errors-in-Variables Estimators for Grouped Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 278-287, July.
    10. Devereux, Paul J. & Fan, Wen, 2011. "Earnings returns to the British education expansion," Economics of Education Review, Elsevier, vol. 30(6), pages 1153-1166.
    11. Phillips, Garry D.A. & Liu-Evans, Gareth, 2016. "Approximating and reducing bias in 2SLS estimation of dynamic simultaneous equation models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 734-762.
    12. John Chao & Jerry Hausman & Whitney Newey & Norman Swanson & Tiemen Woutersen, 2013. "Combining Two Consistent Estimators," Departmental Working Papers 201310, Rutgers University, Department of Economics.
    13. Daniel A. Ackerberg & Paul J. Devereux, 2009. "Improved JIVE Estimators for Overidentified Linear Models with and without Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 91(2), pages 351-362, May.
    14. Pischke, Jörn-Steffen, 2011. "Money and Happiness: Evidence from the Industry Wage Structure," IZA Discussion Papers 5705, Institute for the Study of Labor (IZA).
    15. Isaiah Andrews & Timothy B. Armstrong, 2015. "Unbiased Instrumental Variables Estimation under Known First-Stage Sign," Cowles Foundation Discussion Papers 1984R3, Cowles Foundation for Research in Economics, Yale University, revised Oct 2015.

    More about this item

    Keywords

    Jackknife (Statistics); Linear models (Statistics); Human capital--Mathematical models;

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • J24 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Human Capital; Skills; Occupational Choice; Labor Productivity

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