Bootstrapping Cointegrating Regressions1

In this paper, we consider bootstrapping cointegrating regressions. It is shown that the method of bootstrap, if properly implemented, generally yields consistent estimators and test statistics for cointegrating regressions. We do not assume any speci ̄c data generating process, and employ the sieve bootstrap based on the approximated ̄nite-order vector autoregressions for the regression errors and the ̄rst di®erences of the regressors. In particular, we establish the bootstrap consistency for OLS method. The bootstrap method can thus be used to correct for the ̄nite sample bias of the OLS estimator and to approximate the asymptotic critical values of the OLS-based test statistics in general cointegrating regressions. The bootstrap OLS procedure, however, is not e±cient. For the e±cient estimation and hypothesis testing, we consider the procedure proposed by Saikkonen (1991) and Stock and Watson (1993) relying on the regression augmented with the leads and lags of di®erenced regressors. The bootstrap versions of their procedures are shown to be consistent, and can be used to do inferences that are asymptotically valid. A Monte Carlo study is conducted to investigate the ̄nite sample performances of the proposed bootstrap methods. This version: February 18, 2002