Abstract
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.
Highlights
Determination of the cointegration rank is an important part of analyzing the cointegrated vector autoregressive model in the framework of Johansen (1988, 1991, 1995), Johansen and Juselius (1990), and Juselius (2006)
We consider the rank deficient case where the cointegration rank of the data generating process is smaller than the rank used in the statistical analysis
The data generating process has more unit roots than the number of unit roots imposed in the statistical analysis and the usual asymptotic theory fails
Summary
Determination of the cointegration rank is an important part of analyzing the cointegrated vector autoregressive model in the framework of Johansen (1988, 1991, 1995), Johansen and Juselius (1990), and Juselius (2006). If an investigator wants to focus on the inference on the cointegrating relations problems can arise if the rank is taken as known when it is deficient These problems mirror those of instrumental variable estimation with weak instruments, see Mavroeidis et al (2014). At the extreme when testing on the cointegrating vector in the case of a deficient rank the model is mis-specified This problem arises in cointegration as well as in instrumental variable estimation. Econometrics 2019, 7, 6 identification problem for cointegration, that is when testing for a known cointegrating vector in the nearly rank deficient situation These authors investigate various methods to adjust the asymptotic distribution in the weak identification case.
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