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This paper develops an asymptotic distribution theory for a two-stageinstrumentation estimation approach in quantile predictive regressions whenboth generated covariates and persistent predictors are used. The generatedcovariates are obtained from an auxiliary quantile regression model and ourmain interest is the robust estimation and inference of the primary quantilepredictive regression in which this generated covariate is added to the set ofnonstationary regressors. We find that the proposed doubly IVX estimator isrobust to the abstract degree of persistence regardless of the presence ofgenerated regressor obtained from the first stage procedure. The asymptoticproperties of the two-stage IVX estimator such as mixed Gaussianity areestablished while the asymptotic covariance matrix is adjusted to account forthe first-step estimation error.

Estimating Conditional Value-at-Risk with Nonstationary Quantile Predictive Regression Models