Estimation of varying coefficient models with measurement error

Hao Dong, Taisuke Otsu, Luke Taylor

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We propose a semiparametric estimator for varying coefficient models when the regressors in the nonparametric components are measured with error. Varying coefficient models are an extension of other popular semiparametric models, including partially linear and nonparametric additive models, and deliver an attractive solution to the curse-of-dimensionality. We use deconvolution kernel estimation in a two-step procedure and show that the estimator is consistent and asymptotically normally distributed. We do not assume that we know the distribution of the measurement error a priori. Instead, we suppose we have access to a repeated measurement of the noisy regressor and present results using the approach of Delaigle, Hall and Meister (2008) and, for cases when the measurement error may be asymmetric, the approach of Li and Vuong (1998) based on Kotlarski's (1967) identity. We show that the convergence rate of the estimator is significantly reduced when the distribution of the measurement error is assumed unknown and possibly asymmetric. We study the small sample behaviour of our estimator in a simulation study and apply it to a real dataset. In particular, we consider the role of cognitive ability in augmenting the effect of risk preferences on earnings.

Original languageEnglish
Pages (from-to)388-415
Number of pages28
JournalJournal of Econometrics
Issue number2
Publication statusPublished - 2022 Oct
Externally publishedYes

ASJC Scopus subject areas

  • Economics and Econometrics


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