I was wondering if somebody can explain to me the structure of kstate? I am aware that using this is depreciated, as this is a reminiscence of old dynare versions where we did not create auxiliary variables for leads and lags greater than one, but still I find it is used in several functions dealing with e.g. the perturbation solution or identification toolbox. In any case, I still have problems to get the hang of this. So maybe someone can help me out, given the following simple example:
var Y C K A; varexo eps_A; parameters alph betta rhoA sigA; alph = 0.35; betta = 0.99; rhoA = 0.9; sigA = 0.6; model; C^(-1)=alph*betta*C(+1)^(-1)*A(+1)*K^(alph-1); K=A*K(-1)^alph-C; log(A)=rhoA*log(A(-1))+sigA*eps_A; Y = A*K(-1)^alph; end;
As I understand, my state variables are K and A, i.e.
- the declaration order is Y C K A
- the DR order is Y K A C
- lead_lag_incidence is equal to
where the number corresponds to the corresponding column number in the dynamic files (i.e. derivative wrt the variable)
Now, the kstate variable is given by:
but I do not understand this. As far as I see, there is only one comment in set_state_space.m:
% composition of state vector % col 1: variable; col 2: lead/lag in z(t+1); % col 3: A cols for t+1 (D); col 4: A cols for t (E)
but what is the meaning of z(t+1), A, D and E or to which state space representation do these correspond to?