the resgressors of ECM

[hk976]

Hello,
I got a question about ECM. Suppose i got two variables (SPREAD and DEBT).
The ECM expressions is below:
D(SPREAD) = A(1,1)*(B(1,1)*SPREAD(-1) + B(1,2)*DEBT(-1) + B(1,3)) + C(1,1)*D(SPREAD(-1)) + C(1,2)*D(SPREAD(-2)) + C(1,3)*D(DEBT(-1)) + C(1,4)*D(DEBT(-2)) + C(1,5)
My question is why not the variable DEBT on the right hand side starts from D(DEBT) rather than D(DEBT(-1))?
Other literatures use D(DEBT). Is that different way of doing ECM? Some authors say it does not matter, but it make some difference in my model.
Always, thankful for your help