Robust econometric inference with mixed integrated and mildly explosive regressors

This paper explores in several prototypical models a convenient inference procedure for nonstationary variable regression that enables robust chi-square testing for a wide class of persistent and endogenous regressors. The approach uses the mechanism of self-generated instruments called IVX instrumentation developed by Magdalinos and Phillips (2009b). We first show that these methods remain valid for regressors with local unit roots in the explosive direction and mildly explosive roots, where the roots are further from unity in the explosive direction than O(n^-1). It is also shown that Wald testing procedures remain robust for multivariate regressors with certain forms of mixed degrees of persistence. These robustifications are useful in econometric inference, for example, when there are periods of mildly explosive trends in some or all of time series employed in the analysis but the exact knowledge on the regressor persistence is unavailable. Some aspects of the choice of the IVX instruments are investigated and practical guidance is provided but the issue of optimal IVX instrument choice remains unresolved. The methods are straightforward to apply in practical work such as predictive regression applications in finance.