# Policy and transition functions

Just a simple question. How does one interpret the results of the Policy and Transition function matrix.

thank you

solving the rational exectation model

E_t[f(y_{t+1},y_t,y_{t-1},u_t)]=0

means finding an unkown function

y_t = g(y_{t-1},u_t)

that could be plugged into the original model and satisfy the implied restrictions

A first order approximation of this function can be written

y_t = ybar + g_y yhat_{t-1} + g_u u_t

with yhat_t = y_t-ybar and ybar is the steadystate value of y

In Dynare, the table “Policy and Transition function” contains the elements of g_y and g_u

In other words, it is a time recursive (approximated) representation of the model that can generate timeseries that will approximatively satisfy the rational expectation hypothesis contained in the original model.

Kind regards

Michel

Hello,

I’m sorry for asking silly questions, but I’m a newbie to the whole topic.
I am interested in the interpretation of the policy functions.

After running the attached model I got from Dynare(4.3.1) the following policy function for lz:
POLICY AND TRANSITION FUNCTIONS
lc lk lr lz
Constant 1.013173 3.637303 0.010050 0
lk(-1) 0.618247 0.965276 -0.022240 0
lz(-1) 0.289981 0.071603 0.033013 0.950000
e 0.305243 0.075372 0.034750 1.000000

so I suppose that lz = 0.95lz(-1) + 1e;
After I call stoch_simul(), how is the impulse response function for lz calculated(the values in lz_e)?
Aren’t they recursively calculated from lz = 0.95lz(-1) + 1e?
e is 1 only at the beginning and afterwards 0?
I got values in lz_e like: [0.0837, 0.0795, etc] and I was expecting:
lz(1)=0.950(0 is the steady state) + 10.007 = 0.007
lz(2)=0.095*0.007 = 0.00665 - here I suppose that e is 0.
etc.

A little bit of clarification is welcome!
Thanks!
New_Model.mod (945 Bytes)

Hello:

I have a technical question.

Let us suppose that we have n endogenous variables, where n1 are static and n2 are purely forward and n3 are the number of state variables (purely backward + mixed). We have that n1+n2+n3=n.

Let us suppose also that there are m shocks.

Under this notation, then the matrix gy will be of size nxn3 and gnu will be of size nxm.

In the other hand, y and ys will be vectors nx1.

So in size matrix we have,

(nx1) - (nx1) = (nxn3) x (nx1) - (nxm) x (mx1)

That in matrix size will no be posible because n3 < n…

So for this equation be donne we will need that actually matrix gy be in size (nxn). Could you tell me how do you full this matrix please?