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Estimating and Testing a Quantile Regression Model with Interactive Effects

  • Harding, Matthew

    ()

    (Stanford University)

  • Lamarche, Carlos

    ()

    (University of Kentucky)

This paper proposes a quantile regression estimator for a panel data model with interactive effects potentially correlated with the independent variables. We provide conditions under which the slope parameter estimator is asymptotically Gaussian. Monte Carlo studies are carried out to investigate the finite sample performance of the proposed method in comparison with other candidate methods. We discuss an approach to testing the model specification against a competing fixed effects specification. The paper presents an empirical application of the method to study the effect of class size and class composition on educational attainment. The findings show that (i) a change in the gender composition of a class impacts differently low- and high-performing students; (ii) while smaller classes are beneficial for low performers, larger classes are beneficial for high performers; (iii) reductions in class size do not seem to impact mean and median student performance; (iv) the fixed effects specification is rejected in favor of the interactive effects specification.

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File URL: http://ftp.iza.org/dp6802.pdf
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Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 6802.

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Length: 32 pages
Date of creation: Aug 2012
Date of revision:
Publication status: published in: Journal of Econometrics, 2014, 178, 101-113
Handle: RePEc:iza:izadps:dp6802
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  1. M. Hashem Pesaran, 2004. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," CESifo Working Paper Series 1331, CESifo Group Munich.
  2. Bandiera, Oriana & Larcinese, Valentino & Rasul, Imran, 2009. "Heterogeneous Class Size Effects: New Evidence from a Panel of University Students," CEPR Discussion Papers 7512, C.E.P.R. Discussion Papers.
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  4. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, Junio.
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  6. Chernozhukov, Victor & Hansen, Christian, 2008. "Instrumental variable quantile regression: A robust inference approach," Journal of Econometrics, Elsevier, vol. 142(1), pages 379-398, January.
  7. Victor Chernozhukov & Iván Fernández‐Val & Jinyong Hahn & Whitney Newey, 2013. "Average and Quantile Effects in Nonseparable Panel Models," Econometrica, Econometric Society, vol. 81(2), pages 535-580, 03.
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  9. Newey, W.K., 1989. "Uniform Convergence In Probability And Stochastic Equicontinuity," Papers 342, Princeton, Department of Economics - Econometric Research Program.
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  11. Giacomo De Giorgi & Michele Pellizzari & William Gui Woolston, 2012. "Class Size And Class Heterogeneity," Journal of the European Economic Association, European Economic Association, vol. 10(4), pages 795-830, 08.
  12. Joshua D. Angrist & Victor Lavy, 1999. "Using Maimonides' Rule to Estimate the Effect of Class Size on Scholastic Achievement," The Quarterly Journal of Economics, Oxford University Press, vol. 114(2), pages 533-575.
  13. Rosen, Adam M., 2012. "Set identification via quantile restrictions in short panels," Journal of Econometrics, Elsevier, vol. 166(1), pages 127-137.
  14. repec:ran:wpaper:710-1 is not listed on IDEAS
  15. Caroline M. Hoxby, 2000. "The Effects of Class Size on Student Achievement: New Evidence from Population Variation," The Quarterly Journal of Economics, Oxford University Press, vol. 115(4), pages 1239-1285.
  16. Chernozhukov, Victor & Hansen, Christian, 2006. "Instrumental quantile regression inference for structural and treatment effect models," Journal of Econometrics, Elsevier, vol. 132(2), pages 491-525, June.
  17. Ma, Lingjie & Koenker, Roger, 2006. "Quantile regression methods for recursive structural equation models," Journal of Econometrics, Elsevier, vol. 134(2), pages 471-506, October.
  18. Chamberlain, Gary, 1982. "Multivariate regression models for panel data," Journal of Econometrics, Elsevier, vol. 18(1), pages 5-46, January.
  19. Lamarche, Carlos, 2010. "Robust penalized quantile regression estimation for panel data," Journal of Econometrics, Elsevier, vol. 157(2), pages 396-408, August.
  20. Tomohiro Ando & Ruey S. Tsay, 2011. "Quantile regression models with factor‐augmented predictors and information criterion," Econometrics Journal, Royal Economic Society, vol. 14(1), pages 1-24, February.
  21. Graham, Bryan S. & Hahn, Jinyong & Powell, James L., 2009. "The incidental parameter problem in a non-differentiable panel data model," Economics Letters, Elsevier, vol. 105(2), pages 181-182, November.
  22. V. Chernozhukov & Ivan Fernandez-Val, . "Quantile and Average Effects in Nonseparable Panel Models," Boston University - Department of Economics - Working Papers Series wp2009-011, Boston University - Department of Economics.
  23. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, 01.
  24. Mundlak, Yair, 1978. "On the Pooling of Time Series and Cross Section Data," Econometrica, Econometric Society, vol. 46(1), pages 69-85, January.
  25. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
  26. Roger Koenker & Zhijie Xiao, 2002. "Inference on the Quantile Regression Process," Econometrica, Econometric Society, vol. 70(4), pages 1583-1612, July.
  27. Jacob M. Markman & Eric A. Hanushek & John F. Kain & Steven G. Rivkin, 2003. "Does peer ability affect student achievement?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(5), pages 527-544.
  28. Harding, Matthew & Lamarche, Carlos, 2009. "A quantile regression approach for estimating panel data models using instrumental variables," Economics Letters, Elsevier, vol. 104(3), pages 133-135, September.
  29. Ivan A. Canay, 2011. "A simple approach to quantile regression for panel data," Econometrics Journal, Royal Economic Society, vol. 14(3), pages 368-386, October.
  30. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, 07.
  31. Galvao Jr., Antonio F., 2011. "Quantile regression for dynamic panel data with fixed effects," Journal of Econometrics, Elsevier, vol. 164(1), pages 142-157, September.
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