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Uniform confidence bands for functions estimated nonparametrically with instrumental variables

Author

Listed:
  • Joel L. Horowitz

    (Institute for Fiscal Studies and Northwestern University)

  • Sokbae (Simon) Lee

    (Institute for Fiscal Studies and Columbia University)

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 an interpolation method 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.

Suggested Citation

  • Joel L. Horowitz & Sokbae (Simon) Lee, 2009. "Uniform confidence bands for functions estimated nonparametrically with instrumental variables," CeMMAP working papers CWP18/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:18/09
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    File URL: http://cemmap.ifs.org.uk/wps/cwp1809.pdf
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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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