This paper examines whether mixing different orders of integration on the left- and right-hand sides of a balanced time-series equation prevents researchers from identifying a true relationship. Building on prior work about equation balance, the authors focus on consequences for type II error when using general error correction/autoregressive distributed lag (GECM/ADL) models and consider both the asymptotic case and finite-sample behavior. Their analysis combines theoretical results and simulations to show how model selection and standard assumption checks affect practical inference.
General Error Correction/ADL models, asymptotic identification result, finite-sample simulation evidence
Data and methods
The paper uses theoretical asymptotic analysis and simulation experiments. The authors frame their investigation around GECM/ADL specifications when the equation is balanced but the dependent and independent variables have different orders of integration. They then simulate finite samples to examine how well estimation recovers true relationships under realistic data-generating processes and common modeling practices.
Main findings
In the asymptotic ideal, different orders of integration do not prevent identification of a true relationship using the GECM/ADL, provided the equation is balanced. The authors stress, however, that finite samples can be trickier: observed data sometimes fail to reveal the underlying process, making estimation more difficult.
- Asymptotic result: "the different orders of integration do not preclude identification of the true relationship using the GECM/ADL."
- Simulation result: when researchers "select their models based on the observed characteristics of the data and test to be sure that standard model assumptions are met," they typically draw accurate inferences despite finite-sample challenges.
Practical implication for researchers
The paper suggests careful model selection informed by the data and explicit testing of standard assumptions (e.g., balance and other modeling conditions) can mitigate type II error concerns when mixing integration orders in applied time-series work. The authors conclude by discussing implications for applied analysts and for designing simulations with time-series data.
