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Quantile regression methods for recursive structural equation models

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  • Lingjie Ma

    (Institute for Fiscal Studies)

  • Roger Koenker

    (Institute for Fiscal Studies and UCL)

Abstract

Two classes of quantile regression estimation methods for the recursive structural equation models of Chesher (2003) are investigated. A class of weighted average derivative estimators based directly on the identification strategy of Chesher is contrasted with a new control variate estimation method. The latter imposes stronger restrictions achieving an asymptotic efficiency bound with respect to the former class. An application of the methods to the study of the effect of class size on the performance of Dutch primary school students shows that (i.) reductions in class size are beneficial for good students in language and for weaker students in mathematics, (ii) larger classes appear bene cial for weaker language students, and (iii.) the impact of class size on both mean and median performance is negligible.

Suggested Citation

  • Lingjie Ma & Roger Koenker, 2004. "Quantile regression methods for recursive structural equation models," CeMMAP working papers CWP01/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:01/04
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    References listed on IDEAS

    as
    1. Amemiya, Takeshi, 1982. "Two Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 50(3), pages 689-711, May.
    2. Joshua D. Angrist & Alan B. Krueger, 2001. "Instrumental Variables and the Search for Identification: From Supply and Demand to Natural Experiments," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 69-85, Fall.
    3. Alan B. Krueger, 1999. "Experimental Estimates of Education Production Functions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(2), pages 497-532.
    4. Newey, Whitney K. & Powell, James L., 1990. "Efficient Estimation of Linear and Type I Censored Regression Models Under Conditional Quantile Restrictions," Econometric Theory, Cambridge University Press, vol. 6(3), pages 295-317, September.
    5. Eide, Eric & Showalter, Mark H., 1998. "The effect of school quality on student performance: A quantile regression approach," Economics Letters, Elsevier, vol. 58(3), pages 345-350, March.
    6. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, September.
    7. Andrew Chesher, 2001. "Quantile driven identification of structural derivatives," CeMMAP working papers 08/01, Institute for Fiscal Studies.
    8. Alberto Abadie & Joshua Angrist & Guido Imbens, 2002. "Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings," Econometrica, Econometric Society, vol. 70(1), pages 91-117, January.
    9. Zhao, Quanshui, 2001. "Asymptotically Efficient Median Regression In The Presence Of Heteroskedasticity Of Unknown Form," Econometric Theory, Cambridge University Press, vol. 17(4), pages 765-784, August.
    10. repec:fth:prinin:379 is not listed on IDEAS
    11. Eric A. Hanushek, "undated". "The Evidence on Class Size," Wallis Working Papers WP10, University of Rochester - Wallis Institute of Political Economy.
    12. Caroline M. Hoxby, 2000. "The Effects of Class Size on Student Achievement: New Evidence from Population Variation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 115(4), pages 1239-1285.
    13. Sakata, S., 1998. "Instrumental Variable Estimation Based on Mean Absolute Deviation," Papers 98-08, Michigan - Center for Research on Economic & Social Theory.
    14. Jesse Levin, 2001. "For whom the reductions count: A quantile regression analysis of class size and peer effects on scholastic achievement," Empirical Economics, Springer, vol. 26(1), pages 221-246.
    15. Hanushek, Eric A., 2006. "School Resources," Handbook of the Economics of Education, in: Erik Hanushek & F. Welch (ed.), Handbook of the Economics of Education, edition 1, volume 2, chapter 14, pages 865-908, Elsevier.
    16. Edward P. Lazear, 2001. "Educational Production," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 116(3), pages 777-803.
    17. Hanushek, Eric A, 1986. "The Economics of Schooling: Production and Efficiency in Public Schools," Journal of Economic Literature, American Economic Association, vol. 24(3), pages 1141-1177, September.
    18. Alan B. Krueger, 2003. "Economic Considerations and Class Size," Economic Journal, Royal Economic Society, vol. 113(485), pages 34-63, February.
    19. Andrew Chesher, 2001. "Exogenous impact and conditional quantile functions," CeMMAP working papers 01/01, Institute for Fiscal Studies.
    20. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, September.
    21. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    22. Richard Blundell & James L. Powell, 2001. "Endogeneity in nonparametric and semiparametric regression models," CeMMAP working papers 09/01, Institute for Fiscal Studies.
    23. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    24. Powell, James L, 1983. "The Asymptotic Normality of Two-Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 51(5), pages 1569-1575, September.
    25. Maria Iacovou, 2002. "Class Size in the Early Years: Is Smaller Really Better?," Education Economics, Taylor & Francis Journals, vol. 10(3), pages 261-290.
    26. Simone Dobbelsteen & Jesse Levin & Hessel Oosterbeek, 2002. "The causal effect of class size on scholastic achievement: distinguishing the pure class size effect from the effect of changes in class composition," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 64(1), pages 17-38, February.
    27. Joshua Angrist & Alan Krueger, 2001. "Instrumental Variables and the Search for Identification: From Supply and Demand to Natural Experiments," Working Papers 834, Princeton University, Department of Economics, Industrial Relations Section..
    28. Card, David, 2001. "Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems," Econometrica, Econometric Society, vol. 69(5), pages 1127-1160, September.
    29. Summers, Anita A & Wolfe, Barbara L, 1977. "Do Schools Make a Difference?," American Economic Review, American Economic Association, vol. 67(4), pages 639-652, September.
    30. repec:cup:etheor:v:6:y:1990:i:3:p:295-317 is not listed on IDEAS
    31. Koenker, Roger & Park, Beum J., 1996. "An interior point algorithm for nonlinear quantile regression," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 265-283.
    32. Akerhielm, Karen, 1995. "Does class size matter?," Economics of Education Review, Elsevier, vol. 14(3), pages 229-241, September.
    33. Joshua D. Angrist & Victor Lavy, 1999. "Using Maimonides' Rule to Estimate the Effect of Class Size on Scholastic Achievement," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(2), pages 533-575.
    34. Alan Krueger, 1997. "Experimental Estimates of Education Production Functions," Working Papers 758, Princeton University, Department of Economics, Industrial Relations Section..
    35. Hanushek, E.A.omson, W., 1996. "Assessing the Effects of School Resources on Student Performance : An Update," RCER Working Papers 424, University of Rochester - Center for Economic Research (RCER).
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