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Optimal sup-norm rates, adaptivity and inference in nonparametric instrumental variables estimation

Listed author(s):
  • Xiaohong Chen

    ()

    (Institute for Fiscal Studies and Yale University)

  • Timothy M. Christensen

    (Institute for Fiscal Studies)

Registered author(s):

    This paper makes several contributions to the literature on the important yet difficult problem of estimating functions nonparametrically using instrumental variables. First, we derive the minimax optimal sup-norm convergence rates for nonparametric instrumental variables (NPIV) estimation of the structural function h0 and its derivatives. Second, we show that a computationally simple sieve NPIV estimator can attain the optimal sup-norm rates for h0 and its derivatives when h0 is approximated via a spline or wavelet sieve. Our optimal sup-norm rates surprisingly coincide with the optimal L2-norm rates for severely ill-posed problems, and are only up to a [log(n)]? (with ?

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    File URL: http://www.ifs.org.uk/uploads/cemmap/wps/cwp321515.pdf
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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 CWP32/15.

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    Date of creation: 30 Jun 2015
    Handle: RePEc:ifs:cemmap:32/15
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    1. 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.
    2. Richard Blundell & Alan Duncan & Costas Meghir, 1998. "Estimating Labor Supply Responses Using Tax Reforms," Econometrica, Econometric Society, vol. 66(4), pages 827-862, July.
    3. Chen, Xiaohong & Reiss, Markus, 2011. "On Rate Optimality For Ill-Posed Inverse Problems In Econometrics," Econometric Theory, Cambridge University Press, vol. 27(03), pages 497-521, June.
    4. Florens, Jean-Pierre & Simoni, Anna, 2012. "Nonparametric estimation of an instrumental regression: A quasi-Bayesian approach based on regularized posterior," Journal of Econometrics, Elsevier, vol. 170(2), pages 458-475.
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    10. Xiaohong Chen & Timothy M. Christensen, 2014. "Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions," CeMMAP working papers CWP46/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Horowitz, Joel L. & Lee, Sokbae, 2012. "Uniform confidence bands for functions estimated nonparametrically with instrumental variables," Journal of Econometrics, Elsevier, vol. 168(2), pages 175-188.
    12. Xiaohong Chen & Timothy M. Christensen, 2014. "Optimal Uniform Convergence Rates and Asymptotic Normality for Series Estimators under Weak Dependence and Weak Conditions," Cowles Foundation Discussion Papers 1976, Cowles Foundation for Research in Economics, Yale University.
    13. Richard Blundell & Joel L. Horowitz & Matthias Parey, 2013. "Nonparametric estimation of a heterogeneous demand function under the Slutsky inequality restriction," CeMMAP working papers CWP54/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    14. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, vol. 75(6), pages 1613-1669, November.
    15. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics,in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77 Elsevier.
    16. Anne Vanhems, 2010. "Non-parametric estimation of exact consumer surplus with endogeneity in price," Econometrics Journal, Royal Economic Society, vol. 13(3), pages 80-98, October.
    17. Adonis Yatchew & Joungyeo Angela No, 2001. "Household Gasoline Demand in Canada," Econometrica, Econometric Society, vol. 69(6), pages 1697-1709, November.
    18. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
    19. Liao, Yuan & Jiang, Wenxin, 2011. "Posterior consistency of nonparametric conditional moment restricted models," MPRA Paper 38700, University Library of Munich, Germany.
    20. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    21. Xiaohong Chen & Demian Pouzo, 2013. "Sieve Wald and QLR Inferences on Semi/nonparametric Conditional Moment Models," Cowles Foundation Discussion Papers 1897RR, Cowles Foundation for Research in Economics, Yale University, revised Nov 2014.
    22. Gagliardini, Patrick & Scaillet, Olivier, 2012. "Tikhonov regularization for nonparametric instrumental variable estimators," Journal of Econometrics, Elsevier, vol. 167(1), pages 61-75.
    23. Donald W. K. Andrews & Yixiao Sun, 2004. "Adaptive Local Polynomial Whittle Estimation of Long-range Dependence," Econometrica, Econometric Society, vol. 72(2), pages 569-614, March.
    24. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    25. Horowitz, Joel L., 2014. "Adaptive nonparametric instrumental variables estimation: Empirical choice of the regularization parameter," Journal of Econometrics, Elsevier, vol. 180(2), pages 158-173.
    26. 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, January.
    27. Xiaohong Chen & Demian Pouzo, 2014. "Sieve Wald and QLR Inferences on Semi/nonparametric Conditional Moment Models," CeMMAP working papers CWP38/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    28. Hausman, Jerry A, 1981. "Exact Consumer's Surplus and Deadweight Loss," American Economic Review, American Economic Association, vol. 71(4), pages 662-676, September.
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    30. Joel L. Horowitz, 2011. "Applied Nonparametric Instrumental Variables Estimation," Econometrica, Econometric Society, vol. 79(2), pages 347-394, March.
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