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Faculty of Economics

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Duffy, J., Simons, J.

Cointegration without Unit Roots


Abstract: 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, Müller 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).

Keywords: Cointegration, inference, near-integrated processes, least-favourable distributions, nuisance parameters, power

JEL Codes: C01 C32 C40 C80

Author links: Jerome Simons  


Open Access Link:

Keynes Fund Project(s):
Forecasting and Policy in Environmental Econometrics (JHVL)  
Persistence and Forecasting in Climate and Environmental Econometrics (JHUS)