Spurious rejection by cointegration tests incorporating structural change in the cointegrating relationship

Abstract

In recent research, Leybourne and Newbold have shown commonly employed tests of cointegration to exhibit spurious rejection when applied to independent unit root processes subject to breaks in either level or trend. In the present paper, this research is extended to consider the finite-sample properties of cointegration tests which explicitly incorporate structural change. It is shown that when applied to independent unit root processes subject to regime shifts, cointegration tests permitting structural change in the cointegrating relationship can spuriously reject the null of no cointegration more frequently than the standard tests considered by Leybourne and Newbold.

Notes

 These results can be viewed as a direct extension of the results of Leybourne et al. (1998) for the Dickey–Fuller (1979) unit root test.

 Imposing a break at all possible points in the sample period for both y _t and x _t results in 9801 (99 × 99) experiments, with 70 regressions estimated for each of the models C, C/T and C/S in each experiment. All experiments are conducted using GAUSS, with the required error series generated using pseudo iid N(0,1) random numbers via the RNDNS procedure.

 Note that the calculation for finite-sample critical values is required as Gregory and Hansen (1996) only provide asymptotic critical values for their tests.