Testing Cointegrating Vectors and Adjustment Speeds
A separate Econometrics Toolbox™ function,jcontest
, uses the Johansen framework to test linear constraints on cointegrating relationsBand adjustment speedsA, 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 byjcontest
take one of two forms. Constraints of the formR′A= 0 orR′B= 0 specify particular combinations of the variables to be held fixed during testing and estimation. These constraints are equivalent to parameterizationsA=HφorB=Hφ, whereHis the orthogonal complement ofR(in MATLAB®,null(R')
) andφis a vector of free parameters. The second constraint type specifies particular vectors in the column space ofAorB. The number of constraints thatjcontest
can impose is restricted by the rank of the matrix being tested, which can be inferred by first runningjcitest
.