Uniform confidence bands for functions estimated nonparametrically with instrumental variables

Joel L. Horowitz; Sokbae Lee

doi:10.1016/j.jeconom.2011.12.001

Uniform confidence bands for functions estimated nonparametrically with instrumental variables

Joel L. Horowitz^*, Sokbae Lee

^*Corresponding author for this work

Economics

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

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.

Original language	English (US)
Pages (from-to)	175-188
Number of pages	14
Journal	Journal of Econometrics
Volume	168
Issue number	2
DOIs	https://doi.org/10.1016/j.jeconom.2011.12.001
State	Published - Jun 2012

Keywords

Bootstrap
Instrumental variables
Sieve estimator
Uniform confidence band

ASJC Scopus subject areas

Economics and Econometrics

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10.1016/j.jeconom.2011.12.001

Cite this

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title = "Uniform confidence bands for functions estimated nonparametrically with instrumental variables",

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.",

keywords = "Bootstrap, Instrumental variables, Sieve estimator, Uniform confidence band",

author = "Horowitz, {Joel L.} and Sokbae Lee",

note = "Funding Information: The work of both authors was supported in part by the Economic and Social Research Council through its funding of the ESRC Centre for Microdata Methods and Practice (RES-589-28-0001). The research of Joel L. Horowitz was supported in part by NSF grant SES-0817552 and the research of Sokbae Lee was supported in part by ESRC research grant RES-000-22-2761, by European Research Council (ERC) research grant ERC-2009-StG-240910-ROMETA, and by the Research Settlement Fund for the new faculty of SNU. We would like to thank Xiaohong Chen and three anonymous referees for helpful comments. ",

year = "2012",

month = jun,

doi = "10.1016/j.jeconom.2011.12.001",

language = "English (US)",

volume = "168",

pages = "175--188",

journal = "Journal of Econometrics",

issn = "0304-4076",

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AU - Lee, Sokbae

N1 - Funding Information: The work of both authors was supported in part by the Economic and Social Research Council through its funding of the ESRC Centre for Microdata Methods and Practice (RES-589-28-0001). The research of Joel L. Horowitz was supported in part by NSF grant SES-0817552 and the research of Sokbae Lee was supported in part by ESRC research grant RES-000-22-2761, by European Research Council (ERC) research grant ERC-2009-StG-240910-ROMETA, and by the Research Settlement Fund for the new faculty of SNU. We would like to thank Xiaohong Chen and three anonymous referees for helpful comments.

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N2 - 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.

AB - 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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KW - Instrumental variables

KW - Sieve estimator

KW - Uniform confidence band

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Uniform confidence bands for functions estimated nonparametrically with instrumental variables

Abstract

Keywords

ASJC Scopus subject areas

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