Fail to obtain True solution.

QuantEcon / ContinuousDPs.jl

Continuous state dynamic programming

BSD 3-Clause "New" or "Revised" License

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Fail to obtain True solution. #24

Open tokuma09 opened 5 years ago

tokuma09 commented 5 years ago

I'm testing this package by computing optimal growth model with productivity shocks.

However, the result by using ContinuousDPs.jl is different from true solution, if I correctly use this package.

Model settings and my implimentation is here. In this example, I use PFI but VFI also fails to obtain true solution.

This package may have some bugs in solve method.

oyamad commented 5 years ago

@tokupooh Thanks. Will you write your Bellman equation in the notebook?

tokuma09 commented 5 years ago

Sure. I add Bellman equation in the notebook. We can access my updated notebook by above link.

In addition, I recognize some difference between this package and algorithm in Judd(1998), however, this may not be related with this problem.

In this package, we check the convergence of polynomial coefficients to stop iteration. On the other hand, Judd proposed we need to check the convergence of approximated value function to stop iteration.

Doesn't this matter ?

oyamad commented 5 years ago

You can check the difference between the computed V and the value of the Bellman operator for V.
I played a bit with your notebook. It seems that the choice of the lower and upper bounds for the state variable, in particular for z, affects the outcome significantly.
I don't know how much we can expect with the collocation method + quadrature method for a choice of the number of grid points, so I can't determine whether the difference between the analytical and the computed solutions is too large.