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Small sample bias in synthetic cohort models of labor supply

  • Paul J. Devereux

In synthetic cohort models (cross-sectional data grouped at the cohort and year level), researchers often ignore potential biases induced by sampling error because they have 100 or 200 observations per group. I investigate small sample biases in the context of two synthetic cohort labor supply applications - a model of intertemporal labor supply of men (similar to that of Browning, Deaton, and Irish, 1985) and a female labor supply model (similar to that of Blundell, Duncan, and Meghir, 1998). My approach is to use the Current Population Survey to compare the estimates when group sizes are extremely large to those that arise from randomly drawing subsamples of observations from the large groups. This provides a natural framework for examining the extent of small sample biases and the group sizes required so that small sample biases are negligible. I augment this approach with Monte Carlo analysis so as to precisely quantify biases and coverage rates. I find that, in these two applications, thousands of observations per group are required before small sample issues can be ignored in estimation. In these applications, sampling error leads one to underestimate intertemporal labor supply elasticities for men, and conclude that the income response of female labor supply is zero or tiny when in fact it is quite large.

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File URL: http://hdl.handle.net/10197/747
File Function: First version, 2006
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Paper provided by School of Economics, University College Dublin in its series Working Papers with number 200606.

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Date of creation: May 2006
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Handle: RePEc:ucn:wpaper:200606
Contact details of provider: Postal: UCD, Belfield, Dublin 4
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Web page: http://www.ucd.ie/economics

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  1. Richard Blundell & Thomas MaCurdy, 1998. "Labour supply: a review of alternative approaches," IFS Working Papers W98/18, Institute for Fiscal Studies.
  2. Ransom, Michael R, 1987. "An Empirical Model of Discrete and Continuous Choice in Family Labor Supply," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 465-72, August.
  3. Angrist, Joshua D & Krueger, Alan B, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, MIT Press, vol. 106(4), pages 979-1014, November.
  4. Browning, Martin & Deaton, Angus & Irish, Margaret, 1985. "A Profitable Approach to Labor Supply and Commodity Demands over the Life-Cycle," Econometrica, Econometric Society, vol. 53(3), pages 503-43, May.
  5. Nijman, T.E. & Verbeek, M.J.C.M., 1993. "Minimum MSE estimation of a regression model with fixed effects from a series of cross sections," Other publications TiSEM 34c1104a-a64b-4030-be99-b, Tilburg University, School of Economics and Management.
  6. Paul J. Devereux, 2004. "Changes in Relative Wages and Family Labor Supply," Journal of Human Resources, University of Wisconsin Press, vol. 39(3).
  7. 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.
  8. Propper, Carol & Rees, Hedley & Green, Katherine, 2001. "The Demand for Private Medical Insurance in the UK: A Cohort Analysis," Economic Journal, Royal Economic Society, vol. 111(471), pages C180-200, May.
  9. John Pencavel, 1998. "The Market Work Behavior and Wages of Women: 1975-94," Journal of Human Resources, University of Wisconsin Press, vol. 33(4), pages 771-804.
  10. Kooreman, Peter & Kapteyn, Arie, 1986. "Estimation of Rationed and Unrationed Household Labour Supply Functions Using Flexible Functional Forms," Economic Journal, Royal Economic Society, vol. 96(382), pages 398-412, June.
  11. Joshua D. Angrist & Guido W. Imbens & Alan Krueger, 1995. "Jackknife Instrumental Variables Estimation," NBER Technical Working Papers 0172, National Bureau of Economic Research, Inc.
  12. Robin, Jean-Marc & Smith, Richard J., 2000. "Tests Of Rank," Econometric Theory, Cambridge University Press, vol. 16(02), pages 151-175, April.
  13. Verbeek, Marno & Nijman, Theo, 1992. "Can Cohort Data Be Treated as Genuine Panel Data?," Empirical Economics, Springer, vol. 17(1), pages 9-23.
  14. Angrist, Joshua D., 1991. "Grouped-data estimation and testing in simple labor-supply models," Journal of Econometrics, Elsevier, vol. 47(2-3), pages 243-266, February.
  15. Paul J. Devereux, 2006. "Improved errors-in-variables estimators for grouped data," Working Papers 200602, School of Economics, University College Dublin.
  16. Deaton, Angus, 1985. "Panel data from time series of cross-sections," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 109-126.
  17. Moffitt, Robert, 1993. "Identification and estimation of dynamic models with a time series of repeated cross-sections," Journal of Econometrics, Elsevier, vol. 59(1-2), pages 99-123, September.
  18. Richard Blundell & Alan Duncan & Costas Meghir, 1995. "Estimating labour supply responses using tax reforms," IFS Working Papers W95/07, Institute for Fiscal Studies.
  19. 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 S176-S215, June.
  20. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
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  22. Hausman, Jerry & Ruud, Paul, 1984. "Family Labor Supply with Taxes," American Economic Review, American Economic Association, vol. 74(2), pages 242-48, May.
  23. Buchinsky, Moshe, 1995. "Estimating the asymptotic covariance matrix for quantile regression models a Monte Carlo study," Journal of Econometrics, Elsevier, vol. 68(2), pages 303-338, August.
  24. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  25. Dean R. Hyslop, 2001. "Rising U.S. Earnings Inequality and Family Labor Supply: The Covariance Structure of Intrafamily Earnings," American Economic Review, American Economic Association, vol. 91(4), pages 755-777, September.
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