Beyond the Unit Root Question: New Approach Handles Uncertainty in Long-Run Economic Relationships

Applied time-series analysis faces a fundamental challenge when uncertain whether data contain unit roots. This uncertainty causes problems for inferring long-run relationships (LRR). Traditional methods require correct classification, but unit root tests are unreliable and often leave analysts uncertain.

This article builds on the framework developed by Webb, Linn, and Lebo (WLL; 2019) which proposes a bounds approach based on critical values for hypothesis testing about long-run multipliers (LRM). We extend this methodology in three key ways:

• By showing how their procedure can be applied to any fully specified regression model
• By presenting general critical value bounds applicable across different research designs
• By demonstrating its empirical relevance through two economic applications, which show how uncertainty affects real-world inference

These findings have important implications for researchers relying on time-series data. The approach provides robust results even when unit root status is unknown.