I understand that the state-space representation of the DSGE model is basically about unobserved (state) variables (x) and observed variables (y), and then some shocks and measurement errors.
Why sometimes ‘y’ is labeled as a vector of control variables (see, Graduate Macro Theory II:
Notes on Using Dynare by Eric Sims) or a subset of control variables (see, A Guide to Specifying Observation Equations for the Estimation of DSGE Models by Johannes Pfeifer)?
My understanding is that some control variables are unobserved, so how is that captured in the state-space representation. Via the state equation or the observation equation??
State equation contains only true states (thus, predetermined variables), or does it also include unobserved controls?? Many thanks!
I think you are confusing the notation. Sometimes y is used to denote a generic vector of controls, sometimes it is used to denote output y_t, which is a particular control variable. The basic for of a state space system has a state transition equation that only describes the evolution of the predetermined states and an “observation equation” that indicates how states map into observed and unobserved variables. But you can also find different approaches here, like expanding the vector of states.
Thanks Jpfeifer, for the reply. I appreciate it.
Here, I am referring to generic y, a vector of observable control variables in state-space representation. If my model is quite small, then all my control variables can also be observables (as in Graduate Macro Theory II: Notes on Using Dynare by Eric Sims, 2011). But with a larger model, then I do not have data on all the control variables, right? So some control variables will be unobservables (which are not necessarily state variables). Since the state-space form is silent on unobservable control variables, it appears to be implicit in the state-space representation. Implicit, I mean hidden. And I suspect that these unobservable controls are hidden in the state equations (under state-space representation). Is that correct?
I don’t know where this discussion is going. But anything that is not a state is part of the observation equation, because it tells you have any control y is related to the states x, regardless of whether it is observed or not.
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