INTRODUCTION

One of the many topics in the field of time series econometrics to which Peter Phillips has made contributions of great importance and originality is that of the estimation of cointegrated models. This is one of many areas in which his doctoral students from Yale have also made contributions. To enumerate all the contributions that Phillips and his students have made (and are making) in the area of unit roots and cointegration (not to mention fractionally integrated processes) would take a great deal of time and space; thus, in this introduction we restrict ourselves to highlighting some of the more important papers that Phillips has written on the topic of efficient and robust estimation of cointegrating regressions, position these papers within the larger literature on this topic, and then briefly summarize the contents of this chapter.

Phillips and Durlauf (1986) and Stock (1987) have shown that a cointegrating regression can be super consistently estimated by ordinary least squares (OLS). However, OL Sgenerally has a nuisance–parameter-dependent asymptotic distribution and is not asymptotically mixed normally distributed. It is also not efficient in the class of estimators of the “triangular” representation of a cointegrated system on which the variables treated as the regressors are conditioned. In other words, OLS is not asymptotically equivalent to the limited information maximum likelihood estimator (LIMLE) of such a system. The fully modified OLS (FM–OLS) estimator of Phillips and Hansen (1990), however, not only has a nuisance–parameter-free, mixed normal asymptotic distribution, but it will be efficient in the sense of having the same asymptotic distribution as the Gaussian LIMLE.