A separate Econometrics Toolbox™ function,
jcontest, uses the Johansen framework to test linear constraints on cointegrating relations B and adjustment speeds A, and estimates VEC model parameters under the additional constraints. Constraint testing allows you to assess the validity of relationships suggested by economic theory.
Constraints imposed by
jcontest take one of two forms. Constraints of the form R′A = 0 or R′B = 0 specify particular combinations of the variables to be held fixed during testing and estimation. These constraints are equivalent to parameterizations A = Hφ or B = Hφ, where H is the orthogonal complement of R (in MATLAB®,
null(R')) and φ is a vector of free parameters. The second constraint type specifies particular vectors in the column space of A or B. The number of constraints that
jcontest can impose is restricted by the rank of the matrix being tested, which can be inferred by first running