I am interested in computing transitional dynamics in the context of the neoclassical growth model.
I know I can use Dynare for this, but I am trying to learn computations with dynamic programming, because later I would like to do heterogeneous agents.
So my question is: can I use the toolkit to compute the transition after a foreseen temporary chamge in capital tax rate? For example, I have a 20 percent tax on capital in initial steady state, then at period 10 the capital tax is abolished but at t=20 is restored at the 20 percent level.
In a Ramsey model, yes.
In a Solow-Swan model no.
Difference is that in Solow-Swan the âsavingsâ is not a decision, it is just a rule (save a specific fraction of income). In Ramsey, the savings is a decision (you have an optimization problem to solve).
In some sense, transition in a Ramsey model is just the transition in Aiyagari model, but without idiosyncratic shocks.
PS. The toolkit transition path commands are quite powerful nowadays, especially for OLG models. But there is not so much documentation of them (Iâm working on an âIntro to OLG Transition Pathsâ but it will be a while before it becomes public; happy to send a copy by email request)
PPS. Obviously Solow-Swan is easier to solve than Ramsey, but is just not something the toolkit can do.
Interesting question! While true that Dynare can solve transitions in representative agent models very easily, it will give you an approximation based on perturbation methods (not necessarily loglinearized) so they are always local and accurate only in the vicinity of the steady state.
EDIT
It turns out that Dynare uses nonlinear solutions method when the model is deterministic. See comments below.
@robertdkirkby I will try the transition example in aiyagari and come back here if I need guidance
@aledinola I think Dynare does perturbation around the steady state for stochastic simulations (stoch simul command) but for deterministic transitions its different. It computes the true nonlinear solution using a Newton-type method
My understanding is that @jake88 is correct. Dynare does have specific algorithms for solving âperfect-foresightâ transition paths, and these are not perturbation based. (I donât know if they do Newton-type methods, but this is probably right as it is fairly common and this is what they use for solving steady states.)
Yes, you are right! For deterministic models Dynare solves the non-linear system. I didnât know this since I have used Dynare only a few times, to solve stochastic models.
I have edited my answer above.
