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Smoothed Estimating Equations For Instrumental Variables Quantile Regression

  • Kaplan, David M.
  • Sun, Yixiao

The moment conditions or estimating equations for instrumental variables quantile regression involves the discontinuous indicator function. We instead use smoothed estimating equations, with bandwidth h. This is known to allow higher-order expansions that justify bootstrap refinements for inference. Computation of the estimator also becomes simpler and more reliable, especially with (more) endogenous regressors. We show that the mean squared error of the vector of estimating equations is minimized for some h > 0, which also reduces the mean squared error of the parameter estimators. The same h also minimizes higher-order type I error for a χ2 test, leading to improved size-adjusted power. Our plug-in bandwidth consistently reproduces all of these properties in simulations.

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Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number qt888657tp.

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Date of creation: 01 Jan 2012
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Handle: RePEc:cdl:ucsdec:qt888657tp
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  1. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  2. Whitney K. Newey, 2004. "Efficient Semiparametric Estimation via Moment Restrictions," Econometrica, Econometric Society, vol. 72(6), pages 1877-1897, November.
  3. Chen, Xiaohong & Pouzo, Demian, 2009. "Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals," Journal of Econometrics, Elsevier, vol. 152(1), pages 46-60, September.
  4. Phillips, Peter C B & Park, Joon Y, 1988. "On the Formulation of Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 56(5), pages 1065-83, September.
  5. Horowitz, Joel L., 2002. "Bootstrap critical values for tests based on the smoothed maximum score estimator," Journal of Econometrics, Elsevier, vol. 111(2), pages 141-167, December.
  6. 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.
  7. Mathias D. Cattaneo & Richard K. Crump & Michael Jansson, 2007. "Optimal Inference for Instrumental Variables Regression with non-Gaussian Errors," CREATES Research Papers 2007-11, School of Economics and Management, University of Aarhus.
  8. Yoon-Jae Whang, 2003. "Smoothed Empirical Likelihood Methods for Quantile Regression Models," Econometrics 0310005, EconWPA.
  9. Chernozhukov, Victor & Hansen, Christian & Jansson, Michael, 2009. "Finite sample inference for quantile regression models," Journal of Econometrics, Elsevier, vol. 152(2), pages 93-103, October.
  10. Xiaohong Chen & Demian Pouzo, 2009. "Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals," CeMMAP working papers CWP20/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  11. Xiaohong Chen & Demian Pouzo, 2012. "Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals," Econometrica, Econometric Society, vol. 80(1), pages 277-321, 01.
  12. Joel L. Horowitz, 1996. "Bootstrap Methods for Median Regression Models," Econometrics 9608004, EconWPA.
  13. Xiaohong Chen & Demian Pouzo, 2008. "Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals," Cowles Foundation Discussion Papers 1650R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2009.
  14. Otsu, Taisuke, 2008. "Conditional empirical likelihood estimation and inference for quantile regression models," Journal of Econometrics, Elsevier, vol. 142(1), pages 508-538, January.
  15. Xiaohong Chen & Demian Pouzo, 2008. "Efficient Estimation of Semiparametric Conditional Moment Models with Possibly Nonsmooth Residuals," Cowles Foundation Discussion Papers 1640R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2009.
  16. repec:cup:cbooks:9780521496032 is not listed on IDEAS
  17. 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.
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