Tests on A answer questions about common driving forces in the system. When constructing constraints, interpret the rows and columns of the n-by- r matrix A as follows:
Row i of A contains the adjustment speeds of variable to disequilibrium in each of the r cointegrating relations.
Column j of A contains the adjustment speeds of each of the n variables to disequilibrium in cointegrating relation j.
For example, an all-zero row in A indicates a variable that is weakly exogenous with respect to the coefficients in B. Such a variable may affect other variables, but does not adjust to disequilibrium in the cointegrating relations. Similarly, a standard unit vector column in A indicates a variable that is exclusively adjusting to disequilibrium in a particular cointegrating relation.
To demonstrate, we test for weak exogeneity of the inflation rate with respect to interest rates:
load Data_Canada Y = Data(:,3:end); % Interest rate data y1 = Data(:,1); % CPI-based inflation rate YI = [y1,Y]; [hA,pValueA] = jcontest(YI,1,'ACon',[1 0 0 0]')
hA = logical 0
pValueA = 0.3206
The test fails to reject the null hypothesis. Again, the test is conducted with default settings. Proper economic inference would require a more careful analysis of model and rank specifications.
Constrained parameter estimates are accessed via a fifth output argument from
jcontest. For example, the constrained, rank 1 estimate of A is obtained by referencing the fifth output with dot (
[~,~,~,~,mles] = jcontest(YI,1,'ACon',[1 0 0 0]'); Acon = mles.paramVals.A
Acon = 4×1 0 0.1423 0.0865 0.2862
The first row of A is 0, as specified by the constraint.