Testing for Omitted Variables in the Conditional Variance Function in a Heteroscedastic Regression Model

Status: Submitted to the Journal of Multivariate Analysis, manuscript JMVA-D-26-00329.

Authors:

Fuchun Li, Jiajing Sun, and Yuanlin Wang.

This working paper studies omitted-variable testing for the conditional variance function in a heteroscedastic regression model. The central question is whether a subset of conditioning variables can be removed from a nonparametric conditional variance specification without losing relevant information about the error variance.

Summary and Contribution:

The paper proposes a consistent test based on the mean squared distance between the full conditional variance function and a reduced conditional variance function that omits a candidate variable block. The approach is fully nonparametric for the variance function and is designed for settings where the functional form of heteroscedasticity should not be imposed in advance.

The test statistic is shown to have an asymptotic normal distribution under the omitted-variable null, to diverge against fixed alternatives, and to have nontrivial power against a class of local alternatives. The theory is complemented by Monte Carlo experiments assessing finite-sample size and power.

Empirical Illustration:

An online supplement applies the test to daily Canadian interest-rate data. The empirical question is whether the long-term interest rate contains incremental information for the conditional variance of short-rate innovations beyond the current short-rate level.

Availability:

The manuscript and online supplement are not hosted on this website due to copyright and journal submission policy. Presentation slides are available for download: Slides (PDF).