Statistical Tests And Estimators Of The Rank Of A Matrix And Their Applications In Econometric Modelling

Testing and estimating the rank of a matrix of estimated parameters is key in a large variety of econometric modeling scenarios. This paper describes general methods to test for and estimate the rank of a matrix, and provides details on a variety of modeling 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.