A review of methods of estimating cointegrating relationships
Six estimators of cointegrating relations are compared -- OLS, Augmented OLS, Fully-Modified, Three-Step, Johansen MLE and Box-Tiao. Monte Carlo simulations were run using a four-dimensional system to assess the effects of a very wide range of problems. The results found that the Johansen estimator was best as long as the sample was reasonable large (about 100) and the model was accurately specified but not otherwise. Given we are rarely sure of our specifications, the results implied using the Johansen method to try and determine the number of cointegrating vectors and if there is one, then to start with OLS, assess the model, move up to FM and assess any changes in the results. If the researcher erroneously underestimated the cointegrating rank, the Johansen estimator faired worse than the single-equation estimators. Accuracy of estimating three-dimensional cointegrating spaces within four space is described separately in Hargreaves ( 1992) where the multidimensional OLS described here and augmented OLS fair very well.
It is now over 12 years since the path-breaking paper by Clive Granger ( 1981) on cointegration. However, it was not really until 1987 that Engleand Granger's paper brought the concept to the attention of most economists let alone specialised econometricians. It seemed then that to estimate a cointegrating relationship all one needed to know was how to carry out a simple regression using ordinary least____________________