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Quantile regression methods for recursive structural equation models

  • Lingjie Ma

    (Institute for Fiscal Studies)

  • Roger Koenker


    (Institute for Fiscal Studies and University of Illinois)

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.

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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP01/04.

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Length: 36 pp.
Date of creation: Feb 2004
Date of revision:
Handle: RePEc:ifs:cemmap:01/04
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  1. Alan B. Krueger, 2000. "Economic Considerations and class size," Working Papers 975, Princeton University, Woodrow Wilson School of Public and International Affairs, Center for Research on Child Wellbeing..
  2. Andrew Chesher, 2001. "Quantile driven identification of structural derivatives," CeMMAP working papers CWP08/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  3. 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.
  4. Hanushek, Eric A., 2006. "School Resources," Handbook of the Economics of Education, Elsevier.
  5. Andrew Chesher, 2001. "Exogenous impact and conditional quantile functions," Econometrics 0108001, EconWPA.
  6. Whitney Newey & Guido Imbens, 2004. "Identification and Estimation of Triangular Simultaneous Equations Models without Additivity," Econometric Society 2004 North American Summer Meetings 594, Econometric Society.
  7. Joshua D. Angrist & Victor Lavy, 1999. "Using Maimonides' Rule To Estimate The Effect Of Class Size On Scholastic Achievement," The Quarterly Journal of Economics, MIT Press, vol. 114(2), pages 533-575, May.
  8. Edward P. Lazear, 2001. "Educational Production," The Quarterly Journal of Economics, MIT Press, vol. 116(3), pages 777-803, August.
  9. 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.
  10. Richard Blundell & James Powell, 2001. "Endogeneity in nonparametric and semiparametric regression models," CeMMAP working papers CWP09/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  11. Card, David, 2001. "Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems," Econometrica, Econometric Society, vol. 69(5), pages 1127-60, September.
  12. 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).
  13. 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.
  14. 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.
  15. Akerhielm, Karen, 1995. "Does class size matter?," Economics of Education Review, Elsevier, vol. 14(3), pages 229-241, September.
  16. Iacovou, Maria, 2001. "Class size in the early years: is smaller really better?," ISER Working Paper Series 2001-10, Institute for Social and Economic Research.
  17. Dobbelsteen, Simone & Levin, Jesse & Oosterbeek, Hessel, 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.
  18. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  19. Summers, Anita A & Wolfe, Barbara L, 1977. "Do Schools Make a Difference?," American Economic Review, American Economic Association, vol. 67(4), pages 639-52, September.
  20. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, 09.
  21. 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(03), pages 295-317, September.
  22. 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 1141-77, September.
  23. Alan B. Krueger, 1999. "Experimental Estimates Of Education Production Functions," The Quarterly Journal of Economics, MIT Press, vol. 114(2), pages 497-532, May.
  24. 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.
  25. Sakata, S., 1998. "Instrumental Variable Estimation Based on Mean Absolute Deviation," Papers 98-08, Michigan - Center for Research on Economic & Social Theory.
  26. Zhao, Quanshui, 2001. "Asymptotically Efficient Median Regression In The Presence Of Heteroskedasticity Of Unknown Form," Econometric Theory, Cambridge University Press, vol. 17(04), pages 765-784, August.
  27. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, 01.
  28. Caroline M. Hoxby, 2000. "The Effects Of Class Size On Student Achievement: New Evidence From Population Variation," The Quarterly Journal of Economics, MIT Press, vol. 115(4), pages 1239-1285, November.
  29. repec:cup:etheor:v:6:y:1990:i:3:p:295-317 is not listed on IDEAS
  30. Amemiya, Takeshi, 1982. "Two Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 50(3), pages 689-711, May.
  31. Powell, James L, 1983. "The Asymptotic Normality of Two-Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 51(5), pages 1569-75, September.
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