Search

Testing and estimating the rank of a matrix of estimated parameters is key in a large variety of econometric modelling scenarios. This paper describes general methods to test for and estimate the rank of a matrix, and provides details on a variety of modelling scenarios in the econometrics literature where such methods are required. Four different methods to test the true rank of a general matrix are described, as well as one method that can handle the case of a matrix subject to parameter constraints associated with defineteness structures. The technical requirements for the implementation of the tests of rank of a general matrix differ and hence there are merits to all of them that justify their use in applied work. Nonetheless, we review available evidence of their small sample properties in the context of different modelling scenarios where all, or some, are applicable.

This paper reviews the governance framework of the Lisbon Strategy and discusses the specific option of increasing the role of benchmarking as a means of improving the implementation record of structural reforms in the European Union. Against this background, the paper puts forward a possible avenue for developing a strong form of quantitative benchmarking, namely ranking. The ranking methodology relies on the construction of a synthetic indicator using the “benefit of the doubt” approach, which acknowledges differences in emphasis among Member States with regard to structural reform priorities. The methodology is applied by using the structural indicators that have been commonly agreed by the governments of the Member States, but could also be used for ranking exercises on the basis of other indicators.