IDEAS home Printed from https://ideas.repec.org/a/bes/jnlbes/v25y2007p278-287.html
   My bibliography  Save this article

Improved Errors-in-Variables Estimators for Grouped Data

Author

Listed:
  • Devereux, Paul J.

Abstract

In many economic applications, observations are naturally categorized into mutually exclusive and exhaustive groups. For example, individuals can be classified into cohorts and workers are employees of a particular firm. Grouping models are widely used in economics -- for example, cohort models have been used to study labour supply, wage inequality, consumption, and intergenerational transfer of human capital. The simplest grouping estimator involves taking the means of all variables for each group and then carrying out a group-level regression by OLS or weighted least squares. This estimator is biased in finite samples. I show that the standard errors in variables estimator (EVE) designed to correct for small sample bias is exactly equivalent to the Jack-knife Instrumental Variables Estimator (JIVE). Also EVE is closely related to the k-class of instrumental variables estimators. I then use results from the instrumental variables literature to develop an estimator (UEVE) with better finite-sample properties than existing errors in variables estimators. The theoretical results are demonstrated using Monte Carlo experiments. Finally, I use the estimators to implement a model of inter-temporal male labour supply using micro data from the United States Census. There are sizeable differences in the wage elasticity across estimators, showing the practical importance of the theoretical issues discussed in this paper even in circumstances where the sample size is quite large.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • 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.
  • Handle: RePEc:bes:jnlbes:v:25:y:2007:p:278-287
    as

    Download full text from publisher

    File URL: http://www.ingentaconnect.com/content/asa/jbes/2007/00000025/00000003/art00003
    File Function: full text
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Richard Blundell & Alan Duncan & Costas Meghir, 1995. "Estimating labour supply responses using tax reforms," IFS Working Papers W95/07, Institute for Fiscal Studies.
    2. Nathalie Greenan & Jacques Mairesse, 1999. "Using Employee Level Data in a Firm Level Econometric Study," CIRANO Working Papers 99s-12, CIRANO.
    3. Card, David & Lemieux, Thomas, 1996. "Wage dispersion, returns to skill, and black-white wage differentials," Journal of Econometrics, Elsevier, pages 319-361.
    4. Whitney K. Newey, 2009. "Two-step series estimation of sample selection models," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 217-229, January.
    5. Acemoglu, Daron & Pischke, J. -S., 2001. "Changes in the wage structure, family income, and children's education," European Economic Review, Elsevier, pages 890-904.
    6. 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., pages 69-88.
    7. 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, pages 351-362.
    8. Browning, Martin & Deaton, Angus & Irish, Margaret, 1985. "A Profitable Approach to Labor Supply and Commodity Demands over the Life-Cycle," Econometrica, Econometric Society, pages 503-543.
    9. Devereux, Paul J. & Tripathi, Gautam, 2009. "Optimally combining censored and uncensored datasets," Journal of Econometrics, Elsevier, vol. 151(1), pages 17-32, July.
    10. Angrist, Joshua D, 1990. "Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records," American Economic Review, American Economic Association, pages 313-336.
    11. Deaton, Angus, 1985. "Panel data from time series of cross-sections," Journal of Econometrics, Elsevier, pages 109-126.
    12. Joshua D. Angrist & Alan B. Keueger, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, Oxford University Press, pages 979-1014.
    13. Joshua D. Angrist, 1989. "Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records," Working Papers 631, Princeton University, Department of Economics, Industrial Relations Section..
    14. David J. McKenzie, 2001. "Consumption Growth in a Booming Economy: Taiwan 1976-96," Working Papers 823, Economic Growth Center, Yale University.
    15. Phillips, Garry D A & Hale, C, 1977. "The Bias of Instrumental Variable Estimators of Simultaneous Equation Systems," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(1), pages 219-228, February.
    16. Altonji, Joseph G, 1986. "Intertemporal Substitution in Labor Supply: Evidence from Micro Data," Journal of Political Economy, University of Chicago Press, vol. 94(3), pages 176-215, June.
    17. Richard Blundell & Alan Duncan & Costas Meghir, 1998. "Estimating Labor Supply Responses Using Tax Reforms," Econometrica, Econometric Society, pages 827-862.
    18. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, pages 557-586.
    19. Paul J. Devereux, 2004. "Changes in Relative Wages and Family Labor Supply," Journal of Human Resources, University of Wisconsin Press.
    20. Verbeek, Marno & Nijman, Theo, 1993. "Minimum MSE estimation of a regression model with fixed effects from a series of cross-sections," Journal of Econometrics, Elsevier, pages 125-136.
    21. Joshua D. Angrist, 1988. "Grouped Data Estimation and Testing in Simple Labor Supply Models," Working Papers 614, Princeton University, Department of Economics, Industrial Relations Section..
    22. Dolores Collado, M., 1997. "Estimating dynamic models from time series of independent cross-sections," Journal of Econometrics, Elsevier, pages 37-62.
    23. Paul J. Devereux, 2007. "Small-sample bias in synthetic cohort models of labor supply," Journal of Applied Econometrics, John Wiley & Sons, Ltd., pages 839-848.
    24. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
    25. Verbeek, Marno & Nijman, Theo, 1993. "Minimum MSE estimation of a regression model with fixed effects from a series of cross-sections," Journal of Econometrics, Elsevier, pages 125-136.
    26. Donald, Stephen G & Newey, Whitney K, 2001. "Choosing the Number of Instruments," Econometrica, Econometric Society, pages 1161-1191.
    27. Angrist, J D & Imbens, G W & Krueger, A B, 1999. "Jackknife Instrumental Variables Estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., pages 57-67.
    28. Angrist, Joshua D., 1991. "Grouped-data estimation and testing in simple labor-supply models," Journal of Econometrics, Elsevier, pages 243-266.
    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. Kasey S. Buckles & Daniel M. Hungerman, 2013. "Season of Birth and Later Outcomes: Old Questions, New Answers," The Review of Economics and Statistics, MIT Press, pages 711-724.
    2. 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, pages 351-362.
    3. Francisca Antman & David J. McKenzie, 2007. "Earnings Mobility and Measurement Error: A Pseudo-Panel Approach," Economic Development and Cultural Change, University of Chicago Press, vol. 56, pages 125-161.
    4. Paul J. Devereux, 2007. "Small-sample bias in synthetic cohort models of labor supply," Journal of Applied Econometrics, John Wiley & Sons, Ltd., pages 839-848.
    5. Abe, Yukiko & Tamada, Keiko, 2010. "Regional patterns of employment changes of less-educated men in Japan: 1990-2007," Japan and the World Economy, Elsevier, pages 69-79.
    6. Dostie, Benoit & Kromann, Lene, 2012. "Labour Supply and Taxes: New Estimates of the Responses of Wives to Husbands' Wages," IZA Discussion Papers 6392, Institute for the Study of Labor (IZA).
    7. Vitaliy Oryshchenko, 2010. "Does Foreign Ownership Matter for Enterprise Training? Empirical Evidence from Transition Countries," Chapters,in: Global Exchange and Poverty, chapter 10 Edward Elgar Publishing.
    8. 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, pages 351-362.
    9. Devereux, Paul J. & Tripathi, Gautam, 2009. "Optimally combining censored and uncensored datasets," Journal of Econometrics, Elsevier, vol. 151(1), pages 17-32, July.
    10. Robert E.B. Lucas & Lyn Squire & T. N. Srinivasan (ed.), 2010. "Global Exchange and Poverty," Books, Edward Elgar Publishing, number 13102.
    11. Hou, Feng & Lu, Yuqian & Morissette, René, 2009. "Marriage, Cohabitation and Women’s Response to Changes in the Male Wage Structure," CLSSRN working papers clsrn_admin-2009-45, Vancouver School of Economics, revised 30 Aug 2009.

    More about this item

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • J22 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Time Allocation and Labor Supply

    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:bes:jnlbes:v:25:y:2007:p:278-287. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum). General contact details of provider: http://www.amstat.org/publications/jbes/index.cfm?fuseaction=main .

    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 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 profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.