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Uniform confidence bands for functions estimated nonparametrically with instrumental variables

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  • Horowitz, Joel L.
  • Lee, Sokbae

Abstract

This paper is concerned with developing uniform confidence bands for functions estimated nonparametrically with instrumental variables. We show that a sieve nonparametric instrumental variables estimator is pointwise asymptotically normally distributed. The asymptotic normality result holds in both mildly and severely ill-posed cases. We present methods to obtain a uniform confidence band and show that the bootstrap can be used to obtain the required critical values. Monte Carlo experiments illustrate the finite-sample performance of the uniform confidence band.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 168 (2012)
Issue (Month): 2 ()
Pages: 175-188

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Handle: RePEc:eee:econom:v:168:y:2012:i:2:p:175-188

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Web page: http://www.elsevier.com/locate/jeconom

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Keywords: Bootstrap; Instrumental variables; Sieve estimator; Uniform confidence band;

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References

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  1. Joel L. Horowitz & Sokbae Lee, 2007. "Nonparametric Instrumental Variables Estimation of a Quantile Regression Model," Econometrica, Econometric Society, Econometric Society, vol. 75(4), pages 1191-1208, 07.
  2. V. Chernozhukov & I. Fernández-Val & A. Galichon, 2009. "Improving point and interval estimators of monotone functions by rearrangement," Biometrika, Biometrika Trust, Biometrika Trust, vol. 96(3), pages 559-575.
  3. Xiaohong Chen & Demian Pouzo, 2009. "Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP20/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Whitney Newey & James Powell & Francis Vella, 1998. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Working papers 98-16, Massachusetts Institute of Technology (MIT), Department of Economics.
  5. Xiaohong Chen & Demian Pouzo, 2008. "Estimation of nonparametric conditional moment models with possibly nonsmooth moments," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP12/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  6. Chen, Xiaohong & Pouzo, Demian, 2008. "Estimation of Nonparametric Conditional Moment Models with Possibly Nonsmooth Moments," Working Papers 47, Yale University, Department of Economics.
  7. 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.
  8. 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.
  9. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, Econometric Society, vol. 75(6), pages 1613-1669, November.
  10. Chen, Xiaohong & Pouzo, Demian, 2009. "Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals," Journal of Econometrics, Elsevier, Elsevier, vol. 152(1), pages 46-60, September.
  11. Chernozhukov, Victor & Imbens, Guido W. & Newey, Whitney K., 2007. "Instrumental variable estimation of nonseparable models," Journal of Econometrics, Elsevier, Elsevier, vol. 139(1), pages 4-14, July.
  12. Xiaohong Chen & Demian Pouzo, 2008. "Estimation of Nonparametric Conditional Moment Models with Possibly Nonsmooth Moments," Cowles Foundation Discussion Papers 1650, Cowles Foundation for Research in Economics, Yale University, revised Oct 2008.
  13. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, Econometric Society, vol. 71(5), pages 1565-1578, 09.
  14. Hall, Peter & Titterington, D. M., 1988. "On confidence bands in nonparametric density estimation and regression," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 228-254, October.
  15. Joel L. Horowitz, 2007. "Asymptotic Normality Of A Nonparametric Instrumental Variables Estimator," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1329-1349, November.
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Citations

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Cited by:
  1. Yevgeniy Kovchegov & Nese Yildiz, 2014. "Orthogonal Polynomials for Seminonparametric Instrumental Variables Model," Papers 1409.1620, arXiv.org.
  2. Xiaohong Chen & Demian Pouzo, 2013. "Sieve Wald and QLR Inferences on Semi/nonparametric Conditional Moment Models," Cowles Foundation Discussion Papers 1897R, Cowles Foundation for Research in Economics, Yale University, revised Apr 2014.
  3. Horowitz, Joel L., 2014. "Adaptive nonparametric instrumental variables estimation: Empirical choice of the regularization parameter," Journal of Econometrics, Elsevier, Elsevier, vol. 180(2), pages 158-173.
  4. Joel Horowitz, 2013. "Ill-posed inverse problems in economics," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP37/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Joel Horowitz, 2013. "Adaptive nonparametric instrumental variables estimation: empirical choice of the regularisation parameter," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP30/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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