I am trying to solve a stochastic model from an initial point that is not steady state. So I specify the initial value of state variable in the initval block and do not use the steady command. Then I compare the IRs generated using two different initial value of state variable, they are exactly same.
Did I do anything wrong? Can I find the initial value stored somewhere?
Thanks in advance.
What are you trying to achieve? Are you using a nonlinear model (order>1)? For a linear model, the IRFs will always be the same, regardless of where they start. Also, the decision rules will always be approximated around the steady state. If you are trying to compute the IRFs at a given point for a nonlinear model, you should be using the
function. An example is sites.google.com/site/pfeiferecon/RBC_state_dependent_GIRF.mod?attredirects=0
Thanks for you reply.
I solved the Ramsey problem of a given nonlinear model by hand, then I write the ramsey system to dynare. With commitment, the multipliers at t=0 should be zeros but their steady states are not zeros. Can I achieve this using only stoch_simul? I solve the model under both first and second order. Either case, changing the initial value of multipliers give me same IRs.
Could you please explain more about what you said " For a linear model, the IRFs will always be the same, regardless of where they start."?
At first order in a stochastic model, you have certainty equivalence. Due to the linearity of the solution, there is not interaction between shocks and states (like the multiplier) as those would be second order terms.
The response to a shock is therefore always the same, regardless of the point in the state-space. What you seem to have in mind in studying the transition behavior from a point away from the steady state (0 initial multipliers), which will only yield different responses at higher order.