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

Abstract: This paper develops an asymptotic distribution theory for an endogenous instrumentation approach in quantile predictive regressions when both generated covariates and persistent predictors are used. The generated covariates are obtained from an auxiliary quantile predictive regression model and the statistical problem of interest is the robust estimation and inference of the parameters that correspond to the primary quantile predictive regression in which this generated covariate is added to the set of nonstationary regressors. We find that the proposed doubly IVX corrected estimator is robust to the abstract degree of persistence regardless of the presence of generated regressor obtained from the first stage procedure. The asymptotic properties of the two-stage IVX estimator such as mixed Gaussianity are established while the asymptotic covariance matrix is adjusted to account for the first-step estimation error.