Identifying, Estimating and Testing Restricted Cointegrated Systems: An Overview∗

The notion of cointegration has lead to a renewed interest in the identification and estimation of structural relations among economic time series, a field to which Henri Theil has made many pioneering contributions. This paper reviews the different approaches that have been put forward in the literature for identifying cointegrating relationships and imposing (possibly over-identifying) restrictions on them. Next, various algorithms to obtain (approximate) maximum likelihood estimates and likelihood ratio statistics are reviewed, with an emphasis on so-called switching algorithms. The implementation of these algorithms is discussed and illustrated using an empirical example.