Suppose I have 4 variables, A, B, C and D.
I have the following relationship.
A=B
C=B+k*D
A, B, and C are forward looking while D is predetermined. k is a constant. In that case, can C be separately identified from A? If D is predetermined and cannot adjust are A and C just linear combinations of each other every period?.
I am not sure I get the question. If you observe A, you know B for sure. Based on what do you want to do inference on C?
A and C are both a function of B. The only difference between A and C is the additional term kD. However, if D is predetermined isn’t C just perfectly correlated with A since C is a function of A plus some fixed value kD every period (since D is predetermined)?
Well I should specify that yes, K*D is changing every period, but the value of this term is numerically very small, this A and C are not exactly perfectly correlated, but very close to it.
I still don’t get the problem. You know A and therefore B. If you also know k*D then C is observed as well. Where does identification come in here?