Abstract
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.
Highlights
Elliott (1998) and Cavanagh et al (1995) investigated the test on a coefficient of a cointegrating relation in the presence of a near unit root in a bivariate cointegrating regression
It is assumed that α1 and β1 are known p × ( p − r) matrices of rank p − r, and c is ( p − r) × ( p − r) and an unknown parameter, such that the model allows for a whole matrix, c, of near unit roots
We consider below the likelihood ratio test, Q β, for a given value of β, calculated as if c = 0, that is, as if we have a cointegrating relations in a vector autoregression (CVAR) with rank r
Summary
Elliott (1998) and Cavanagh et al (1995) investigated the test on a coefficient of a cointegrating relation in the presence of a near unit root in a bivariate cointegrating regression. It is assumed that α1 and β1 are known p × ( p − r) matrices of rank p − r, and c is ( p − r) × ( p − r) and an unknown parameter, such that the model allows for a whole matrix, c, of near unit roots. The likelihood ratio test, Q β , for β equal to a given value, is derived assuming that c = 0 and analyzed when near unit roots are present, c 6= 0. For a given nominal size υ (here 10%) These methods are explained and implemented by a simulation study, and it is shown that they offer a solution to the problem of inference on β in the presence of a near unit root
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