A Nonparametric Measure of Heteroskedasticity

41 Pages Posted: 18 Aug 2020

See all articles by Xiaojun Song

Xiaojun Song

Peking University - Guanghua School of Management

Abderrahim Taamouti

University of Liverpool Management School

Date Written: June 17, 2020


We introduce a nonparametric measure to quantify the degree of heteroskedasticity at a fixed quantile of the conditional distribution of a random variable. Our measure of heteroskedasticity is based on nonparametric quantile regressions and is expressed in terms of unrestricted and restricted expectations of quantile loss functions. It can be consistently estimated by replacing the unknown expectations by their nonparametric estimates. We derive a Bahadur-type representation for the nonparametric estimator of the measure. We provide the asymptotic distribution of this estimator, which one can use to build tests for the statistical significance of the measure. Thereafter, we establish the validity of a fixed regressor bootstrap that one can use in finite-sample settings to perform tests. A Monte Carlo simulation study reveals that the bootstrap-based test has a good finite sample size and power for a variety of data generating processes and different sample sizes. Finally, two empirical applications are provided to illustrate the importance of the proposed measure.

Keywords: Bootstrap; Measuring Heteroskedasticity; Nonparametric Quantile Regressions; Income and Years of Education

JEL Classification: C12; C14; C15; C19; G1; G12; E3; E4

Suggested Citation

Song, Xiaojun and Taamouti, Abderrahim, A Nonparametric Measure of Heteroskedasticity (June 17, 2020). Available at SSRN: https://ssrn.com/abstract=3653053 or http://dx.doi.org/10.2139/ssrn.3653053

Xiaojun Song

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871

Abderrahim Taamouti (Contact Author)

University of Liverpool Management School ( email )

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