Recent Developments in Cointegration
It is well known that inference on the cointegrating relations in a vector autoregression
(CVAR) is difficult in the presence of a near unit root. The test for a given cointegration vector can have
rejection probabilities under the null, which vary from the nominal size to more than 90%. This paper
formulates a CVAR model allowing for multiple near unit roots and analyses the asymptotic
properties of the Gaussian maximum likelihood estimator. Then two critical value adjustments
suggested by McCloskey (2017) for the test on the cointegrating relations are implemented for the
model with a single near unit root, and it is found by simulation that they eliminate the serious size
distortions, with a reasonable power for moderate values of the near unit root parameter. The findings
are illustrated with an analysis of a number of different bivariate DGPs.