Bootstrap co-integration rank testing : the effect of bias-correcting parameter estimates

In this paper we investigate bootstrap-based methods for bias-correcting the first-stage parameter estimates used in some recently developed bootstrap implementations of the co-integration rank tests of Johansen (1996). In order to do so we adapt the framework of Kilian (1998) which estimates the bias in the original parameter estimates using the average bias in the corresponding parameter esti- mates taken across a large number of auxiliary bootstrap replications. A number of possible implementations of this procedure are discussed and concrete recommendations made on the basis of finite sample performance evaluated by Monte Carlo simulation methods. Our results show that bootstrap-based bias-correction methods can significantly improve upon the small sample performance of the bootstrap co-integration rank tests. A brief application of the techniques developed in this paper to international dynamic consumption risk sharing within Europe is also considered.