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We consider cointegration tests in the situation where the cointegration rank is deficient. This situation is of interest in finite sample analysis and in relation to recent work on identification robust cointegration inference. We derive asymptotic theory for tests for cointegration rank and for hypotheses on the cointegrating vectors. The limiting distributions are tabulated. An application to US treasury yields series is given.

Asymptotic Theory for Cointegration Analysis When the Cointegration Rank Is Deficient