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SPECIFICATION TESTING FOR ERRORS-IN-VARIABLES MODELS

Published online by Cambridge University Press:  19 June 2020

Taisuke Otsu  and
Luke Taylor
Taisuke Otsu*
Affiliation:
London School of Economics
Luke Taylor
Affiliation:
Aarhus University
*
Address correspondence to Taisuke Otsu, Department of Economics, London School of Economics, Houghton Street, London WC2A 2AE, UK; e-mail: t.otsu@lse.ac.uk.
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Abstract

This paper considers specification testing for regression models with errors-in-variables and proposes a test statistic comparing the distance between the parametric and nonparametric fits based on deconvolution techniques. In contrast to the methods proposed by Hall and Ma (2007, Annals of Statistics, 35, 2620–2638) and Song (2008, Journal of Multivariate Analysis, 99, 2406–2443), our test allows general nonlinear regression models and possesses complementary local power properties. We establish the asymptotic properties of our test statistic for the ordinary and supersmooth measurement error densities. Simulation results endorse our theoretical findings: our test has advantages in detecting high-frequency alternatives and dominates the existing tests under certain specifications.

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Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 4 , August 2021 , pp. 747 - 768
Copyright
© Cambridge University Press 2020

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Footnotes

The authors would like to thank anonymous referees and a co-editor for helpful comments, and acknowledge financial support from the ERC Consolidator Grant (SNP 615882) (T.O.) and the ESRC (L.T.).

References

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