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NONPARAMETRIC SIGNIFICANCE TESTING IN MEASUREMENT ERROR MODELS

Published online by Cambridge University Press:  04 June 2021

Hao Dong  and
Luke Taylor
Hao Dong
Affiliation:
Southern Methodist University
Luke Taylor*
Affiliation:
Aarhus University
*
Address correspondence to Luke Taylor, Department of Economics and Business Economics, Aarhus University, Fuglesangs Allé 4, 8210Aarhus, Denmark; e-mail: lntaylor@econ.au.dk.
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Abstract

We develop the first nonparametric significance test for regression models with classical measurement error in the regressors. In particular, a Cramér-von Mises test and a Kolmogorov–Smirnov test for the null hypothesis $E\left [Y|X^{*},Z^{*}\right ]=E\left [Y|X^{*}\right ]$ are proposed when only noisy measurements of $X^{*}$ and $Z^{*}$ are available. The asymptotic null distributions of the test statistics are derived, and a bootstrap method is implemented to obtain the critical values. Despite the test statistics being constructed using deconvolution estimators, we show that the test can detect a sequence of local alternatives converging to the null at the $\sqrt {n}$ -rate. We also highlight the finite sample performance of the test through a Monte Carlo study.

Type
ARTICLES
Information
Econometric Theory , Volume 38 , Issue 3 , June 2022 , pp. 454 - 496
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

The authors would like to thank the Editor, Associate Editor, three anonymous referees, Karun Adusumilli, Taisuke Otsu, Ricardo Reis, and Peter Robinson for helpful comments. Financial support from the SMU Dedman College Research Fund (12-412268; Dong), and the Aarhus University Research Fund (AUFF-26852; Taylor) is gratefully acknowledged.

References

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