A Robust Inference for Predictive Expectile Regression: An IVX-Based Approach

This paper develops a persistence-robust inferential framework for predictive expectile regression with highly persistent regressors. We combine expectile score equations with IVX instruments to construct an IVX-expectile estimator that preserves the distributional interpretation of expectile regression while regularizing the nonstandard effects of near-unit-root regressors, endogeneity, and conditional heteroscedasticity. For fixed expectile levels, we establish consistency and asymptotic normality of the estimator and show that the associated Wald statistic converges to a standard chi-square distribution. Simulation evidence indicates that the proposed procedure delivers accurate size for regressors with differential persistence, with only a modest local-power cost relative to conventional methods. In an application to monthly and quarterly U.S. stock return predictability, the method detects substantially asymmetric predictive ability across expectiles, showing that IVX-expectile regression provides a useful tool for studying heterogeneous predictive effects and downside tail risk when predictors are highly persistent.