Dynare forums

Dear all,

would it be possible for some of you to generously take a look at my confusion about dynare?


After running dynare mod (for example dynrbc.mod)file, it automatically generates a m_file named dynrbc_dynamic.m.

the function shows up at the top of this file is "function [residual, g1, g2, g3] = dynrbc_dynamic(y, x, params, steady_state, it_)"

Therefore I have some question about variables: y x steady_state it_.
lets say, the original four endogenous variables are c i k a, two exogenous variables are u v. And the M_.lead_lag_incidence=[1 0 0 2;3 4 5 6;0 7 0 8].

Does this mean?
y=[c(+1) a(+1) c i k a i(-1) k(-1)] which contains 8 variables now,
x=[u v];
steady_state=[c_ss a_ss c_ss i_ss k_ss a_ss i_ss k_ss];
it_=1; (this is always true).

if this is the case, what is the format of y and x that preserved in dynare? y and x should be string or cell or some other format? it is column vector or row vector?

And why do we need it_ here? is it necessary?

Best wishes!

Andy

As the manual says

When
computing the Jacobian of the dynamic model, the order of the endogenous variables
in the columns is stored in M_.lead_lag_incidence. The rows of this matrix
represent time periods: the first row denotes a lagged (time t-1) variable, the second
row a contemporaneous (time t) variable, and the third row a leaded (time t+1)
variable. The colums of the matrix represent the endogenous variables in their order
of declaration. A zero in the matrix means that this endogenous does not appear
in the model in this time period. The value in the M_.lead_lag_incidence matrix
corresponds to the column of that variable in the Jacobian of the dynamic model.
Example: Let the second declared variable be c and the (3,2) entry of M_.lead_
lag_incidence be 15. Then the 15th column of the Jacobian is the derivative with
respect to y(+1).

In your example, the first entry (element (1,1)) of M_.lead_lag_incidence corresponds to the lag of the first declared variable. That would be consumption c. M_.lead_lag_incidence says that c(-1) is the first element of y (and not c(+1) as you wrote).

y is a column vector, while x is a [nperiods by M_.exo_nbr] double (note the typo in the header of _dynamic files in 4.4.2 that confused the dimensions) storing the value of the ith declared exogenous variable in period j in element x(j,i). The it_ is needed to select the time period for which the derivatives are computed. It is mostly needed for determinstic simulation where the entries of x are not simply 0.

I hope this helps.

Thanks a lot! jpfeifer, now I see where my problem is, I misunderstood some notions, and thanks again for your help!