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Small Sample Bias in Synthetic Cohort Models of Labor Supply

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  • Paul J Devereux

    (University College of Dublin)

Abstract

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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Bibliographic Info

Paper provided by School Of Economics, University College Dublin in its series Working Papers with number 200606.

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Length: 31 pages
Date of creation: 26 Apr 2006
Date of revision:
Handle: RePEc:ucn:wpaper:200606

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  1. Joseph Altonji, 1984. "Intertemporal Substitution in Labor Supply: Evidence from Micro Data," Working Papers 562, Princeton University, Department of Economics, Industrial Relations Section..
  2. Deaton, Angus, 1985. "Panel data from time series of cross-sections," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 109-126.
  3. 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, vol. 59(1-2), pages 125-136, September.
  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. Kooreman, P. & Kapteyn, A.J., 1984. "Estimation of rationed and unrationed household labor supply functions using flexible functional forms," Research Memorandum 157, Tilburg University, Faculty of Economics and Business Administration.
  6. Robin, Jean-Marc & Smith, Richard J., 2000. "Tests Of Rank," Econometric Theory, Cambridge University Press, vol. 16(02), pages 151-175, 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. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  9. Nijman, T.E. & Verbeek, M.J.C.M., 1992. "Can cohort data be treated as genuine panal data?," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153281, Tilburg University.
  10. 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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  13. Blundell, Richard & Macurdy, Thomas, 1999. "Labor supply: A review of alternative approaches," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 27, pages 1559-1695 Elsevier.
  14. Paul J. Devereux, 2004. "Changes in Relative Wages and Family Labor Supply," Journal of Human Resources, University of Wisconsin Press, vol. 39(3).
  15. Joshua Angrist, 1988. "Grouped Data Estimation and Testing in Simple Labor Supply Models," Working Papers 614, Princeton University, Department of Economics, Industrial Relations Section..
  16. 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.
  17. 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.
  18. Hausman, Jerry & Ruud, Paul, 1984. "Family Labor Supply with Taxes," American Economic Review, American Economic Association, vol. 74(2), pages 242-48, May.
  19. 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..
  20. 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.
  21. 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.
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  23. 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.
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Cited by:
  1. 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.
  2. 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.
  3. Dang, Hai-Anh & Lanjouw, Peter, 2013. "Measuring poverty dynamics with synthetic panels based on cross-sections," Policy Research Working Paper Series 6504, The World Bank.
  4. Xavier D'Haultfoeuille & Stefan Hoderlein & Yuya Sasaki, 2013. "Nonlinear Difference-in-Differences in Repeated Cross Sections with Continuous Treatments," Boston College Working Papers in Economics 839, Boston College Department of Economics.
  5. Richard Duhautois & Fabrice Gilles, 2013. "Payroll tax reductions and job flows in France," Working Papers hal-01006652, HAL.
  6. Warunsiri, Sasiwimon & McNown, Robert, 2010. "The Returns to Education in Thailand: A Pseudo-Panel Approach," World Development, Elsevier, vol. 38(11), pages 1616-1625, November.
  7. Devereux, Paul J., 2007. "Improved Errors-in-Variables Estimators for Grouped Data," CEPR Discussion Papers 6167, C.E.P.R. Discussion Papers.
  8. 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).
  9. 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.

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