From Eric Sim’s tutorial (Graduate Macro Theory II:Notes on Using Dynare, Spring 2011), we have 5 endogenous variables var y i k a c;. I understand that y, c, i and k are endogenous control variables. k(-1) is an endogenous state variable and the variable (a) is an exogenous state variable. Please are these definitions correct?

Also in state-space form, does all the variables (y i k a c) belong to the state equation? And thus we can choose a subset of (y, i, k, c) to be our vector of observables (in the observable equation) assuming we have data on these? Many thanks!!

In this pdf file on this forum question (State space representation in Dynare), it says that the state vector (in the state-space form) contains all the variables in the model (defined under var). So I think it is talking about y i k a c. But this is wrong, right? The state vector (in the state-space form) contains just the true state/pre-determined variables (k(-1) and a). Assuming we have data on just two control variables (y and c). Then the x in the observation equation is vector of y and c. Now variable i is an unobservable control variable, right? And I guess it is implicit in the state-space representation, most likely associated the state equation. Or we cannot actually say which of the two state-space equations implicitly captures variable i. Or we should just ignore unobservable control variables in state-space representation. But actually it is there, right?

I still don’t know where this is going. As mentioned at

it depends on what you want to do. For Kalman smoothing, it may make sense to use a different representation. Unless you have a specific application in mind, it is impossible to give you a satisfying answer. Even Dynare internally uses different representations depending on what is required.