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Smoothed Estimating Equations For Instrumental Variables Quantile Regression

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  • Kaplan, David M.
  • Sun, Yixiao

Abstract

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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Bibliographic Info

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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Keywords: Social and Behavioral Sciences; Physical Sciences and Mathematics; Edgeworth expansion; Instrumental variable; Optimal smoothing parameter choice; Quantile regression; Smoothed estimating equation.;

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  1. Otsu, Taisuke, 2008. "Conditional empirical likelihood estimation and inference for quantile regression models," Journal of Econometrics, Elsevier, vol. 142(1), pages 508-538, January.
  2. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  3. 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.
  4. Joel L. Horowitz, 1996. "Bootstrap Methods for Median Regression Models," Econometrics 9608004, EconWPA.
  5. Peter C.B. Phillips & Joon Y. Park, 1986. "On the Formulation of Wald Tests of Nonlinear Restrictions," Cowles Foundation Discussion Papers 801, Cowles Foundation for Research in Economics, Yale University.
  6. Whitney K. Newey, 2004. "Efficient Semiparametric Estimation via Moment Restrictions," Econometrica, Econometric Society, vol. 72(6), pages 1877-1897, November.
  7. Cattaneo, Matias D. & Crump, Richard K. & Jansson, Michael, 2012. "Optimal inference for instrumental variables regression with non-Gaussian errors," Journal of Econometrics, Elsevier, vol. 167(1), pages 1-15.
  8. Yoon-Jae Whang, 2004. "Smoothed Empirical Likelihood Methods for Quantile Regression Models," Cowles Foundation Discussion Papers 1453, Cowles Foundation for Research in Economics, Yale University.
  9. 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.
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