It has been known since Elliott (1998) that standard methods of inference on cointegrating relationships break down entirely when autoregressive roots are near but not exactly equal to unity. We consider this problem within the framework of a structural VAR, arguing this it is as much a problem of identification failure as it is of inference. We develop a characterisation of cointegration based on the impulse response function, which allows long-run equilibrium relationships to remain identified even in the absence of exact unit roots. Our approach also provides a framework in which the structural shocks driving the common persistent components continue to be identified via long-run restrictions, just as in an SVAR with exact unit roots. We show that inference on the cointegrating relationships is affected by nuisance parameters, in a manner familiar from predictive regression; indeed the two problems are asymptotically equivalent. By adapting the approach of Elliott, M\"uller and Watson (2015) to our setting, we develop tests that robustly control size while sacrificing little power (relative to tests that are efficient in the presence of exact unit roots).

翻译：自Elliott（1998）以来，人们已知当自回归根接近但不完全等于1时，关于协整关系的标准推断方法会完全失效。我们在结构VAR框架下分析此问题，认为这既是识别失败问题，亦是推断问题。我们基于脉冲响应函数发展了一种协整特征化方法，使得即便在不存在精确单位根的情况下，长期均衡关系仍能保持可识别性。我们的方法还为共同持久成分的结构性冲击提供了识别框架——与存在精确单位根的SVAR类似，这些冲击可通过长期限制条件持续识别。研究表明，协整关系的推断会受到冗余参数的影响，这与预测回归中的情形相似；事实上，这两个问题在渐近意义上是等价的。通过将Elliott、Müller与Watson（2015）的方法适配至我们的场景，我们开发出能稳健控制检验尺度且几乎不损失检验效力的检验方法（相较于在存在精确单位根时具有最优效力的检验）。