Beyond the Unit Root Question: Uncertainty and Inference. Issue 2 (9th February 2020) - Webb, Clayton; Linn, Suzanna; Lebo, Matthew J.
Abstract: A fundamental challenge facing applied time‐series analysts is how to draw inferences about long‐run relationships (LRR) when we are uncertain whether the data contain unit roots. Unit root tests are notoriously unreliable and often leave analysts uncertain, but popular extant methods hinge on correct classification. Webb, Linn, and Lebo (WLL; 2019) develop a framework for inference based on critical value bounds for hypothesis tests on the long‐run multiplier (LRM) that eschews unit root tests and incorporates the uncertainty inherent in identifying the dynamic properties of the data into inferences about LRRs. We show how the WLL bounds procedure can be applied to any fully specified regression model to solve this fundamental challenge, extend the results of WLL by presenting a general set of critical value bounds to be used in applied work, and demonstrate the empirical relevance of the LRM bounds procedure in two applications.